# embeddings_queue

created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1230-c2-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1230, "chunk_number": 2, "type": "text", "chroma:document": "They \ncame on without any precautions. Merry laid his plans quickly. \n     The ruffians  came tramping along  the  East Road, and  without halting \nturned up the Bywater Road,  which ran for  some way sloping up between \nhigh \nbanks with low hedges on top. Round a bend,  about a  furlong from  the main \nroad, they met a stout barrier of old farm-carts upturned. That halted them. \nAt the same  moment they  became aware that  the hedges on  both sides,  just \nabove their  heads, were all lined with hobbits. Behind them  other  hobbits \nnow pushed out  some more waggons  that had  been  hidden in a field, and so \nblocked the way back. A voice spoke to them from above. \n     'Well, you  have walked into a trap, '  said Merry. 'Your  fellows  from \nHobbiton did the same, and one is dead and the  rest are prisoners. Lay down"}


created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1233-c0-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1233, "chunk_number": 0, "type": "text", "chroma:document": "####-big for your purse.' \n     Ted Sandyman spat over the wall: 'Garn!' he said. 'You can't touch  me.  \nI'm  a friend o'  the  Boss's. But he'll touch you all right, if I have  any \nmore of your mouth.' \n     'Don't  waste any more words  on  the  fool, Sam!' said Frodo. 'I  hope \nthere are not many more hobbits that have become like  this.  It  would be a  \nworse trouble than all the damage the Men have done.' \n     'You are dirty and insolent, Sandyman,' said Merry. 'And also very much \nout of your reckoning. We are just going up the Hill to remove your precious \nBoss. We have dealt with his Men.' \n     Ted gaped, for at  that moment he first caught sight of the escort that \nat a sign from Merry now marched over the bridge. Dashing back into the mill \nhe ran out with a horn and blew it loudly. \n     'Save your breath!' laughed Merry. 'I've a better.' Then lifting up his \nsilver horn he winded it, and its clear call rang  over the Hill; and out of"}


created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1234-c0-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1234, "chunk_number": 0, "type": "text", "chroma:document": "####-down Saruman's throat.' \n     'No doubt, no doubt! But you did not, and so I  am  able to welcome you  \nhome.' There standing at the  door was Saruman himself, looking well -fed and \nwell-pleased; his eyes gleamed with malice and amusement. \n     A sudden light broke on Frodo. 'Sharkey!' he cried. \n     Saruman laughed.  'So you have heard the name, have you? All  my people \nused to call me that in Isengard, I believe. A sign of affection, possibly.( \nBut evidently you did not expect to see me here.' \n     'I did not,' said Frodo. 'But I might  have guessed.  A little mischief \nin a mean way: Gandalf warned me that you were still capable of it. \n     'Quite  capable,'  said Saruman, 'and more  than a little. You  made me \nlaugh, you hobbit-lordlings, riding  along with  all  those  great people so \nsecure and so pleased with your little selves. You thought you had done very \nwell out of it a ll, and could now just amble back and have a nice quiet time"}


created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1232-c1-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1232, "chunk_number": 1, "type": "text", "chroma:document": "up  before them;  and as  they drew  near the old  village across the Water, \nthrough rows of new  mean houses along each side of the  road, they saw  the \nnew mill in all its  frowning and  dirty ugliness:  a  great  brick building \nstraddling  the  stream, which  it  fouled  with  a  steaming  and  stinking \noverflow. All along the Bywater Road every tree had been felled. \n     As  they crossed the bridge  and looked up the Hill  they  gasped. Even \nSam's vision in the Mirror  had not prepared  him for what they saw. The Old \nGrange  on the  west side had been knocked down, and its place taken by rows \nof tarred sheds. All the chestnuts were gone. The  banks and  hedgerows were \nbroken. Great  waggons wer e standing in  disorder in  a field beaten bare of \ngrass. Bagshot  Row was a yawning sand and gravel quarry. Bag End up. \nbeyond \ncould not be seen for a clutter of large huts. \n     'They've cut it down!' cried Sam. 'They've cut down the Party Tree!' He"}


created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1217-c2-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1217, "chunk_number": 2, "type": "text", "chroma:document": "was served on a long  bare table that  had not been scrubbed  for weeks. The \nfood  deserved no better  setting. The travellers  were  glad  to  leave the \nplace.  It was about eighteen  miles to  Bywater,  and they  set off at  ten \no'clock  in the morning. They  would have started earlier, only the delay so \nplainly annoyed the Shirriff-leader. The west wind had shifted northward and \nit was turning colder, but the rain was gone. \n     It was rather  a comic  cavalcade that left the village, though the few \nfolk that came out to  stare at the  'get-up' of the travellers did not seem \nquite sure whether laughing was allowed. A dozen Shirriffs had been told off \nas escort to the  'prisoners'; but Merry made  them  march  in front,  while \nFrodo and his friends rode behind. Merry, Pippin, and  Sam sat at their ease \nlaughing and talking  and singing, while the Shirriffs stumped along  trying \nto  look stern and important. Frodo, however, was  silent  and looked rather"}


created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1233-c1-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1233, "chunk_number": 1, "type": "text", "chroma:document": "he ran out with a horn and blew it loudly. \n     'Save your breath!' laughed Merry. 'I've a better.' Then lifting up his \nsilver horn he winded it, and its clear call rang  over the Hill; and out of \nthe  holes and sheds and shabby houses of Hobbiton the hobbits answered, and \ncame pouring out, and  with cheers and loud cries they followed  the company \nup the road to Bag End. \n     At the top of the lane the party halted, and Frodo and his friends went \non; and they came at  last to the once beloved place. The garden wa s full of \nhuts and sheds, some so near the old westward windows that  they cut off all \ntheir  light. There were piles of refuse everywhere. The door  was  scarred; \nthe bell-chain  was dangling  loose, and the bell would not  ring.  Knocking \nbrought no answer. At length they pushed and the door yielded. They went in. \nThe  place stank  and was  full of filth and  disorder: it did not appear to \nhave been used for some time."}


created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1235-c0-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1235, "chunk_number": 0, "type": "text", "chroma:document": "####-     The hobbits recoiled. But Frodo said: 'Do  not believe him! He has lost  \nall power, save his voice that  can still daunt you and deceive you, if  you  \nlet it.  But  I will not  have him slain. It is useless to meet revenge with \nrevenge: it will heal nothing. Go, Saruman, by the speediest way!' \n     'Worm! Worm!' Saruman called; and out of a  nearby hut came \nWormtongue, \ncrawling, almost like a dog. To the road again, Worm!' said Saruman.  'These \nfine fellows and lordlings are turning us adrift again. Come along!' \n     Saruman turned  to go, and Wormtongue shuffled after  him.  But even as \nSaruman passed close to Frodo a knife flashed in his  hand,  and  he stabbed \nswiftly.  The blade turned  on  the hidden  mail-coat  and snapped.  A dozen  \nhobbits, led by Sam, leaped forward with a cry and flung  the villain to the \nground. Sam drew his sword. \n     'No, Sam!' said  Frodo. 'Do not kill him even now.  For he has not hurt"}


created_at: 2025-03-19 11:59:18
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1234-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1234, "chunk_number": 1, "type": "text", "chroma:document": "secure and so pleased with your little selves. You thought you had done very \nwell out of it a ll, and could now just amble back and have a nice quiet time \nin the country. Saruman's home could  be all wrecked, and he could be turned \nout, but no one could touch  yours. Oh  no!  Gandalf would look  after  your  \naffairs.' \n     Saruman laughed  again. 'Not he! When his tools have done their task he \ndrops them. But you must  go dangling  after him,  dawdling and talking, and \nriding round twice as far as you needed. \"Well,\" thought I, \"if they're such  \nfools, I  will  get ahead of them and  teach  them  a  lesson.  One ill turn \ndeserves another.\" It  would  have been  a  sharper lesson, if  only you had \ngiven  me a  little  more time and more Men. Still  I have already done much  \nthat you will  find  it hard to mend or undo in your lives. And  it  will be \nplea sant to think of that and set it against my injuries.'"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1232-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1232, "chunk_number": 2, "type": "text", "chroma:document": "beyond \ncould not be seen for a clutter of large huts. \n     'They've cut it down!' cried Sam. 'They've cut down the Party Tree!' He \npointed to where the tree. had stood under which Bilbo had made his Farewell \nSpeech. It was lying lopped and  dead in the field. As if this was the  last \nstraw Sam burst into tears. \n     A laugh put an end to them. There was a surly hobbit lounging over  the \nlow wall of the  mill-yard. He was grimy -faced and  black -handed.  'Don't  'ee \nlike it, Sam?'  he sneered. 'But  you always  was soft. I thought you'd gone  \noff in  one o' them ships  you used to prattle about, sailing, sailing. What \nd'you want to come back for? We've work to do in the Shire now.' \n     'So I see,' said Sam. 'No time for washing, but time for wall-propping. \nBut  see here,  Master  Sandyman,  I've a score to pay in this village,  and \ndon't you make it any longer with your  jeering, or you'll  foot a bill  too"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1217-c3-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1217, "chunk_number": 3, "type": "text", "chroma:document": "laughing and talking  and singing, while the Shirriffs stumped along  trying \nto  look stern and important. Frodo, however, was  silent  and looked rather  \nsad and thoughtful."}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1228-c2-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1228, "chunk_number": 2, "type": "text", "chroma:document": "grind  more  and faster, or  so he said. He's got other mills  like  it. But \nyou've got to have grist before you can grind; and there was no more for the \nnew mill to do than for the  old. But since Sharkey came they don't grind no \nmore corn at all. They're always a -hammering and a -letting out a smoke and a  \nstench, and there isn't no peace even at night  in  Hobbiton.  And they pour \nout filth a  purpose; they've  fouled all  the lower Water  and it's getting \ndown into Brandywine. If they want to make the Shire into a desert,  they're \ngoing the right way about it. I don't believe that fool of a Pimple's behind \nall this. It's Sharkey, I say.' \n     'That's right!' put in Young Tom. 'Why, they even took Pimple's old ma, \nthat  Lobelia, and he was  fond  of her,  if no one  else was.  Some  of the \nHobbiton folk, they  saw it. She  comes down the lane with her old umbrella. \nSome of the ruffians were going up with a big cart. \n     ' \"Where be you a -going?\" says she."}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1235-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1235, "chunk_number": 1, "type": "text", "chroma:document": "hobbits, led by Sam, leaped forward with a cry and flung  the villain to the \nground. Sam drew his sword. \n     'No, Sam!' said  Frodo. 'Do not kill him even now.  For he has not hurt \nme.  And in any case I do not wish him to be slain in this evil mood. He was \ngreat once, of  a  noble kind that we  should  not  dare to raise  our hands \nagainst. He is fallen, and his cure is beyond us;  but  I would still  spare \nhim, in the hope that he may find it.' \n     Saruman rose to his feet, and stared at Frodo. There was a strange look  \nin his  eyes of mingled wonder and  respect and  hatred.  'You  have  grown, \nHalfling,' he said. 'Yes, you have grown very much. You are wise, and cruel. \nYou  have  robbed  my revenge of  sweetness,  and  now  I must go  hence  in \nbitterness, in debt to your mercy.  I hate it and you! Well, I go and I will \ntrouble you no more. But do  not expect me to wish you health and long life. \nYou will have neither. But that is not my doing. I merely foretell.'"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1233-c2-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1233, "chunk_number": 2, "type": "text", "chroma:document": "brought no answer. At length they pushed and the door yielded. They went in. \nThe  place stank  and was  full of filth and  disorder: it did not appear to \nhave been used for some time. \n     'Where  is that miserable Lotho hiding?' said Merry. They  had searched \nevery room  and found no living thing save rats and  mice. 'Shall we turn on \nthe others to search the sheds?' \n     'This is  worse than Mordor!' said Sam. 'Much worse in  a way. It comes \nhome to you, as  they say; because it is home, and you remember it before it  \nwas all ruined.' \n     'Yes,  this is Mordor,' said Frodo. 'Just one of its works. Saruman was \ndoing  its  work all  the time,  even  when he  thought  he was working  for  \nhimself. And the same with those that Saruman tricked, like Lotho.' \n     Merry looked round in dismay and disgust. 'Let's get out!' he said. 'If \nI had known all the  mischief he had caused, I should  have stuffed my pouch"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1234-c2-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1234, "chunk_number": 2, "type": "text", "chroma:document": "that you will  find  it hard to mend or undo in your lives. And  it  will be \nplea sant to think of that and set it against my injuries.' \n     'Well, if that is what you find  pleasure in,' said Frodo, 'I pity you. \nIt will be a pleasure of memory only, I fear. Go at once and never return!' \n     The hobbits of the villages  had  seen Saruman  come out of one  of the \nhuts, and at once they came crowding up  to  the door of  Bag End. When they \nheard Frodo's command, they murmured angrily: \n     'Don't let him go! Kill him! He's a villain and a murderer. Kill him!' \n     Saruman looked round at their hostile faces and smiled. 'Kill  him!' he \nmocked. 'Kill him, if you think there  are enough of you, my brave hobbits!' \nHe drew himself  up and stared at them darkly  with his black eyes.  'But do \nnot think that when I lost all my goods I lost all my power! Whoever strikes \nme shall  be accursed. And if my blood stains the Shire, it shall wither and \nnever again be healed.'"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1236-c0-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1236, "chunk_number": 0, "type": "text", "chroma:document": "####-fellow, your nice little Boss. Didn't you, Worm? Stabbed him in his sleep, I \nbelieve.  Buried him, I hope;  though Worm has been very hungry lately.  No, \nWorm is not really nice. You had better leave him to me.' \n     A look of wild hatred came into Wormtongue's red eyes. 'You told me to;  \nyou made me do it,' he hissed. \n     Saruman laughed. 'You do what Sharkey says,  always, don't  you,  Worm?  \nWell,  now  he  says:  follow!'  He  kicked  Wormtongue in  the face  as  he \ngrovelled, and  turned and made off. But at that something snapped: suddenly \nWormtongue rose up, drawing a hidden knife, and then with a snarl like a dog \nhe sprang on Saruman's back, jerked his head back, cut his throat, and  with \na yell  ran off  down the lane. Before Frodo could recover or  speak a word, \nthree hobbit-bows twanged and Wormtongue fell dead. \n     To the dismay of those that stood by, about the  body of Saruman a grey"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1231-c2-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1231, "chunk_number": 2, "type": "text", "chroma:document": "afterwards called. The fallen hobbits were  laid together in a grave on  the \nhill-side,  wher e later a great  stone was set up with a garden about it. So \nended the  Battle of Bywater, 1419, the last battle fought in the Shire, and \nthe  only battle since the  Greenfields, 1147, away up in the Northfarthing. \nIn consequence, though it happily cost very few lives, it has a  chapter  to \nitself in the Red Book, and  the names of all those  who took part were made \ninto a Roll, and learned by heart by Shire-historians. The very considerable \nrise in the fame and fortune of the Cottons dates from this time; but at the \ntop of the Roll  in all  accounts  stand the names of  Captains Meriadoc and \nPeregrin. \n     Frodo had been in the battle, but he had not drawn sword, and his chief \npart had  been to prevent the hobbits  in their wrath at  their losses, from \nslaying those  of  their enemies who  threw  down  their  weapons. When  the"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1237-c0-t
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1237, "chunk_number": 0, "type": "text", "chroma:document": "####- \n\nChapter 9. The Grey Havens"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1238-c0-t
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1238, "chunk_number": 0, "type": "text", "chroma:document": "####-borders.  \n     Meanwhile the  labour  of  repair went on apace, and   Sam was kept very \nbusy. Hobbits can work like bees when the mood  and the need comes on  \nthem. \nNow  there were thousands of willing  hands of all ages, from the  small but \nnimble ones of the hobbit lads and lasses to the well-worn and horny ones of \nthe gaffers  and gammers.  Before Yule not a brick was left standing of  the \nnew Shirriff-houses  or of anything that had been built by 'Sharkey's  Men';  \nbut the bricks were used to repair many an old hole, to make it snugger  and  \ndrier. Great stores of goods a nd  food, and beer,  were found that had  been \nhidden away  by  the  ruffians in  sheds and barns and deserted  holes,  and \nespecially in the tunnels  at Michel  Delving  and  in the  old quarries  at \nScary; so that there was a great deal better cheer that Yule than anyone had \nhoped for. \n     One of the first  things done in Hobbiton,  before even  the removal of"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1240-c0-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1240, "chunk_number": 0, "type": "text", "chroma:document": "####-many, were fair to see and strong, and most of them  had a rich golden  hair \nthat had before  been rare  among hobbits.  The fruit was so  plentiful that \nyoung  hobbits very nearly bathed in  strawberries and cream; and later they \nsat on the lawns under the plum-trees  and ate, until they had made piles of \nstones  like  small pyramids or  the  heaped skulls of a conqueror, and then \nthey  moved on. And no  one was ill,  and everyone was pleased. except those \nwho had to mow the grass.  \n     In the  Southfarthing the vines were laden, and the yield of 'leaf' was \nastonishing; and everywhere there was  so much  corn that at  Harvest  every \nbarn was stuffed. 'The  Northfarthing barley  was so fine  that the beer  of \n1420 malt was long remembered and became a byword. Indeed a generation \nlater \none might hear an  old gaffer  in an inn, aft er  a good pint  of well-earned \nale,  put  down his mug with a sigh:  'Ah! that was  proper fourteen-twenty, \nthat was!'"}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1239-c0-t
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1239, "chunk_number": 0, "type": "text", "chroma:document": "####-which was a seed, like a small nut with a  silver shale. 'What can I do with \nthis?' said Sam. \n     'Throw it in the air on  a breezy day  and  let it do  its  work!' said \nPippin. \n     'On what?' said Sam. \n     'Choose one spot  as  a  nursery, and  see what happens  to the  plants \nthere,' said Merry. \n     'But I'm  sure  the Lady  would not like me to keep it all  for my  own \ngarden, now so many folk have suffered,' said Sam. \n     'Use all the wi ts and knowledge you have of your own, Sam,' said Frodo,  \n'and then  use the  gift to  help  your  work  and  better  it. And  use  it \nsparingly. There is not much here, and I expect every grain has a value.' \n     So Sam planted saplings in all the  places where specially beautiful or  \nbeloved trees had been destroyed, and he put a grain of the precious dust in \nthe soil at the root of each. He went up and  down the Shire in this labour; \nbut if he  paid special attention to Hobbiton and Bywater no one blamed h im."}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1236-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1236, "chunk_number": 1, "type": "text", "chroma:document": "three hobbit-bows twanged and Wormtongue fell dead. \n     To the dismay of those that stood by, about the  body of Saruman a grey \nmist gathered, and  rising slowly to a great height like smoke  from a fire, \nas a pale shrouded  figure it loomed over the Hill. For a moment it wavered,  \nlooking to the West; but out of the West came a cold wind, and it bent away,  \nand with a sigh dissolved into nothing. \n     Frodo looked down at the body with pity and horror, for as he looked it \nseemed that long years of death were suddenly revealed in it, and it shrank, \nand the shrivelled face became rags of skin upon a hideous skull. Lifting up \nthe skirt  of the dirty cloak  that sprawled beside  it, he covered it over, \nand turned away. \n     'And  that's  the end of that,'  said Sam. 'A nasty end,  and I  wish I \nneedn't have seen it; but it's a good riddance.' \n     'And the very last end of the War, I hope,' said Merry."}


created_at: 2025-03-19 11:59:19
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1241-c0-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1241, "chunk_number": 0, "type": "text", "chroma:document": "####-abroad at all, poor lass; but as I hadn't spoken, she couldn't say so. And I \ndidn't speak, because I had  a job to  do first. But now I have  spoken, and \nshe says:  \"Well, you've  wasted  a year,  so why wait longer?\"  \"Wasted?\" I  \nsays. \"I wouldn't call it that.\" Still I see what she means. I feel torn  in \ntwo, as you might say.' \n     'I see,' said Frodo: 'you want to get married, and yet you want to live \nwith me in  Bag End too? But my dear  Sam, how easy! Get  married as soon as \nyou  can, and then move in with Rosie. There's room enough in Bag End for as \nbig a family as you could wish for.' \n     And so it was settled. Sam Gamgee married Rose Cotton in the Spring  of \n1420 (which was  also famous  for its weddings), and they came and lived  at \nBag End. And if Sam thought himself lucky, Frodo knew that he was more \nlucky \nhimself; for there was not a hobbit in the  Shire that was looked after with"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1238-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1238, "chunk_number": 1, "type": "text", "chroma:document": "Scary; so that there was a great deal better cheer that Yule than anyone had \nhoped for. \n     One of the first  things done in Hobbiton,  before even  the removal of \nthe new mill, was the clearing of the Hill and Bag End, and the  restoration \nof Bagshot Row. The front of the new sand-pit was all levelled and made into \na large sheltered garden, and new holes were dug in the southward face, back \ninto the Hill, and they  were lined with brick. The Gaffer  was  restored to \nNumber Three; and he said often and did not care who heard it: \n     'It's an  ill wind as  blows nobody no good, as I always say. And All's \nwell as ends Better!' \n     There was some discussion of the name that the new row should be given. \nBattle  Gardens  was thought  of,  or Better  Smials.  But  after a while in \nsensible hobbit-fashion it was just called New Row. It was a purely  Bywater  \njoke to refer to it as Sharkey's End. \n     The trees were the worst loss and damage, for at Sharkey's bidding they"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1240-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1240, "chunk_number": 1, "type": "text", "chroma:document": "later \none might hear an  old gaffer  in an inn, aft er  a good pint  of well-earned \nale,  put  down his mug with a sigh:  'Ah! that was  proper fourteen-twenty, \nthat was!' \n     Sam stayed at first at  the Cottons'  with Frodo; but when  the New Row \nwas ready he went  with the Gaffer. In addition to all his  other  labours he \nwas  busy  directing  the cleaning up and restoring  of Bag End; but he  was \noften away in the Shire on his forestry work. So he was not at home in early \nMarch and did not know that  Frodo had  been ill. On the  thirteenth of that \nmonth  Farmer Cotton found Frodo lying on his bed; he was clutching  a white \ngem that hung on a chain about his neck and he seemed half in a dream. \n     'It is gone for ever,' he said, 'and now all is dark and empty.' \n     But the fit  passed, and  when Sam got back on  the twenty-fifth, Frodo \nhad  recovered, and he said nothing about  himself. In the meanwhile Bag End"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1237-c1-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1237, "chunk_number": 1, "type": "text", "chroma:document": "The clearing up certainly needed a lot of work, but  it took  less time \nthan Sam had feared. The day  after the battle Frodo  rode to Michel Delving \nand released the prisoners from  the Lockholes. One  of the first  that they \nfound was  poor Fredegar Bolger, Fatty no longer. He had been taken when the \nruffians smoked  out a band of rebels that  he  led from their hidings up in \nthe Brockenbores by the hills of Scary. \n     'You  would have  done better  to  come with us  after  all,  poor  old \nFredegar!' said Pippin, as they carried him out too weak to walk. \n     He opened an eye and tried gallantly to  smile. 'Who's this young giant  \nwith the loud voice?' he  whispered. 'Not little Pippin! What's your size in \nhats now?' \n     Then  there  was Lobelia. Poor thing, she looked very old and thin when \nthey rescued her  from a dark and narrow  cell. She insisted on hobbling out \non her own feet; and she had such a welcome, and there was such clapping and"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1239-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1239, "chunk_number": 1, "type": "text", "chroma:document": "the soil at the root of each. He went up and  down the Shire in this labour; \nbut if he  paid special attention to Hobbiton and Bywater no one blamed h im. \nAnd  at  the end he found that he still had a little of the dust left; so he \nwent to the Three-Farthing  Stone, which is as near the centre of the  Shire \nas no matter, and cast it  in  the air with his  blessing. The little silver  \nnut he  planted  in the Party Field where the tree had  once  been;  and  he \nwondered  what would  come  of  it. All through  the winter  he remained  as \npatient  as  he  could,  and tried  to  restrain himself  from  going  round \nconstantly to see if anything was happening. \n     Spring surpassed his wildest hopes. His trees began to sprout and grow, \nas if time was in a hurry and  wished to make one year do for twenty. In the \nParty Field a beautiful young sapling leaped up: it had silver bark and long \nleaves and burst into golden flowers  in April. It was indeed a mallorn, and"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1236-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1236, "chunk_number": 2, "type": "text", "chroma:document": "'And  that's  the end of that,'  said Sam. 'A nasty end,  and I  wish I \nneedn't have seen it; but it's a good riddance.' \n     'And the very last end of the War, I hope,' said Merry. \n     'I hope so,' said Frodo and sighed. 'The very last stroke. But to think  \nthat it  should fall here, at the very  door  of Bag End! Among all my hopes \nand fears at least I never expected that.' \n     'I shan't call it  the end, till we've cleared  up  the mess,' said Sam \ngloomily. 'And that'll take a lot of time and work.'"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1235-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1235, "chunk_number": 2, "type": "text", "chroma:document": "trouble you no more. But do  not expect me to wish you health and long life. \nYou will have neither. But that is not my doing. I merely foretell.' \n     He walked away, and  the hobbits made a lane for him to pass; but their \nknuckles whitened as  they gripped  on their  weapons. Wormtongue hesitated, \nand then followed his master. \n     'Wormtongue!' called Frodo. 'You need not follow him. I know of no evil  \nyou have done to me. You can  have rest and food here for a while, until you  \nare stronger and can go your own ways.' \n     Wormtongue  halted  and  looked  back at  him, half  prepared  to  stay. \nSaruman turned.  'No evil?'  he  cackled. 'Oh no! Even when he sneaks out at \nnight it is only to look at the stars. But did I hear someone ask where poor  \nLotho is hiding? You know, don't you, Worm? Will you tell them?' \n     Wormtongue cowered down and whimpered: 'No, no!' \n     'Then I  will,'  said Saruman.  'Worm killed  your  Chief,  poor little"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1240-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1240, "chunk_number": 2, "type": "text", "chroma:document": "But the fit  passed, and  when Sam got back on  the twenty-fifth, Frodo \nhad  recovered, and he said nothing about  himself. In the meanwhile Bag End \nhad  been  set  in order,  and Merry and Pippin came over  from  Crickhollow \nbringing back  all the old furniture  and gear, so that  the  old hole  soon \nlooked very much as it always had done. \n     When all was at last ready Frodo said: 'When are you  going to  move in \nand join me, Sam?' \n     Sam looked a bit awkward. \n     'There is no need to come yet, if you don't want to,'  said Frodo. 'But \nyou k now the Gaffer  is close at hand, and he will be very well looked after  \nby Widow Rumble.' \n     It s not that, Mr. Frodo, said Sam, and he went ver red. \n     'Well, what is it?' \n     'It's Rosie, Rose Cotton,' said Sam. 'It seems she didn't like my going"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1239-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1239, "chunk_number": 2, "type": "text", "chroma:document": "Party Field a beautiful young sapling leaped up: it had silver bark and long \nleaves and burst into golden flowers  in April. It was indeed a mallorn, and \nit was the wonder of the neighbourhood.  In after years, as it grew in grace \nand beauty, it was known far and wide and people would come long journeys \nto \nsee it: the only mallorn  west of the Mountains and east of the Sea, and one \nof the finest in the world. \n     Altogether 1420 in  the Shire was a marvellous year. Not only was there \nwonderful sunshine and delicious rain, in due times and perfect measure, but \nthere seemed something more: an air of richness and growth, and a gleam of a  \nbeauty  beyond  that  of  mortal summers  that flicker  and  pass  upon this \nMiddle-earth. All the children born or begotten in that year, and there were"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1237-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1237, "chunk_number": 2, "type": "text", "chroma:document": "they rescued her  from a dark and narrow  cell. She insisted on hobbling out \non her own feet; and she had such a welcome, and there was such clapping and \ncheering when she appeared,  leaning on Frodo's arm but still clutching  her  \numbrella, that she was quite touched, and drove away in tears. She had never \nin her life been popular before. But she was crushed  by the news of  Lotho's \nmurder, and she would' not return to Bag End. She gave it back to Frodo, and \nwent to her own people, the Bracegirdles of Hardbottle. \n     When the poor  creature died next Spring-she  was after all more than a  \nhundred years  old  - Frodo was  surprised and much  moved: she had left all  \nthat remained of her money and of Lotho's for him to use in helping  hobbits \nmade homeless by the troubles. So that feud was ended. \n     Old Will Whitfoot had been in the Lockholes longer than any, and though \nhe had  perhaps  been treated  less harshly  than  some,  he needed a lot of"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1242-c0-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1242, "chunk_number": 0, "type": "text", "chroma:document": "####-Sam was  pained to notice how little  honour he  had in his own country. Few \npeople  knew  or  wanted  to  know about  his  deeds and  adventures;  their \nadmiration  and  respect were given mostly  to Mr. Meriadoc and Mr. Peregrin \nand (if Sam had known it) to himself. Also in  the  autumn there appeared  a  \nshadow of old troubles.  \n     One evening Sam came into the  study and  found his master looking very \nstrange. He was very pale and his eyes seemed to see things far away. \n     'What's the matter, Mr. Frodo?' said Sam. \n     'I am wounded,' he answered, 'wounded; it will never really heal.' \n     But then  he  got   up, and the  turn seemed to  pass, and he  was quite \nhimself the next day. It was not until afterwards that Sam recalled that the \ndate  was October the sixth. Two years before on that day it was dark in the \ndell under Weathertop. \n     Time went on, and 1421 came  in. Frodo was ill again in March, but with"}


created_at: 2025-03-19 11:59:20
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1241-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1241, "chunk_number": 1, "type": "text", "chroma:document": "Bag End. And if Sam thought himself lucky, Frodo knew that he was more \nlucky \nhimself; for there was not a hobbit in the  Shire that was looked after with \nsuch care. When the labours of repair  had all been planned and set going he \ntook to a quiet life, writing a great dea l and  going through all his notes. \nHe resigned the office of Deputy Mayor at the Free Fair that mid-summer, and \ndear old Will Whitfoot had another seven years of presiding at Banquets.  \n     Merry and Pippin lived together for some time at Crickhollow, and  there \nwas  much coming  and  going between  Buckland and Bag  End.  The two  \nyoung \nTravellers cut a great  dash in the Shire  with  their songs and their tales \nand their finery,  and  their wonderful  parties. 'Lordly' folk called them, \nmeaning nothing bu t good; for it warmed all hearts to see them go  riding by \nwith their mail-shirts so bright and their shields so splendid, laughing and"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1238-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1238, "chunk_number": 2, "type": "text", "chroma:document": "sensible hobbit-fashion it was just called New Row. It was a purely  Bywater  \njoke to refer to it as Sharkey's End. \n     The trees were the worst loss and damage, for at Sharkey's bidding they \nhad been  cut down recklessly far  and wide over the Shire; and Sam  grieved \nover this more than anything else. For  one thing, this hurt would take long \nto heal, and only  his great-grandchildren, he thought,  would see the Shire \nas it ought to be. \n     Then  suddenly  one day, for he had  been too busy for  weeks to give a  \nthought to  his adventures,   he remembered the gift of Galadriel. He brought  \nthe box  out and showed it to  the  other Travellers (for  so they were  now \ncalled by everyone), and asked their advice. \n     'I wondered when you would think of it,' said Frodo. 'Open it!' \n     Inside it was filled with a grey  dust, soft and fine, in the middle of"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1244-c0-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1244, "chunk_number": 0, "type": "text", "chroma:document": "####-the Shire, supplemented by the accounts of their friends and the learning of \nthe Wise.) \n     Together  with  extracts from  Books of  Lore  translated by  Bilbo  in \nRivendell. \n     'Why, you  have  nearly finished  it, Mr. Frodo!' Sam exclaimed. 'Well, \nyou have kept at it, I must say.' \n     'I have quite finished, Sam,' said Frodo. 'The last pages are for you.' \n     On September the twenty-first  they set out together, Frodo on the pony \nthat  had  borne him  all the  way  from  Minas  Tirith, and was  now called \nStrider; and Sam on his beloved Bill. It  was a fair golden morning, and Sam \ndid not ask where they were going: he thought he could guess. \n     They took the Stock Road over the hills and went towards the Woody End, \nand they let their ponies walk  at their leisure.  They camped  in the Green \nHills,  and  on September the twenty-second  they rode gently down  into the \nbeginning of the trees as afternoon was wearing away."}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1237-c3-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1237, "chunk_number": 3, "type": "text", "chroma:document": "Old Will Whitfoot had been in the Lockholes longer than any, and though \nhe had  perhaps  been treated  less harshly  than  some,  he needed a lot of \nfeeding up before he could look the part of Mayor; so Frodo agreed to act as \nhis Deputy, until Mr. Whitfoot was  in shape again. The  only  thing that he \ndid as  Deputy Mayor was  to reduce the Shirriffs to  their proper functions \nand numbers. The task of  hunting  out the last remnant of  the ruffians was \nleft to Merry and  Pippin,  and  it was soon done. The southern gangs, after  \nhearing the news of the Battle of  Bywater, fled out of the land and offered \nlittle resistance to the Thain. Before the Year's End the few survivors were \nrounded  up in  the  woods,  and those  that  surrendered were shown  to the"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1242-c1-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1242, "chunk_number": 1, "type": "text", "chroma:document": "date  was October the sixth. Two years before on that day it was dark in the \ndell under Weathertop. \n     Time went on, and 1421 came  in. Frodo was ill again in March, but with \na great effort he concealed it, for Sam had other things to think about. The \nfirst of  Sam and Rosie's children was born on the twenty-fifth of  March, a  \ndate that Sam noted. \n     'Well,  Mr. Frodo,' he said. 'I'm in a bit of  a fix.  Rose  and me had \nsettled  to  call him Frodo, with  your leave; but it's  not  him , it's her. \nThough as pretty a maidchild  as any one  could hope for, taking after  Rose \nmore than me, luckily. So we don't know what to do.' \n     'Well,  Sam,' said Frodo,  'what's wrong with the old customs? Choose a  \nflower name like Rose. Half the maidchildren in the Shire are called by such  \nnames, and what could be better?' \n     'I  suppose  you're  right,  Mr.  Frodo,'  said  Sam.  'I've heard some \nbeautiful names on my travels,  but  I  suppose they're  a bit too grand for"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1243-c0-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1243, "chunk_number": 0, "type": "text", "chroma:document": "####-     'It will be Bilbo's Birthday on Thursday, Sam,'  he  said. 'And he will \npass the Old Took. He will be a hundred and thirty-one!' \n     'So he will!' said Sam. 'He's a marvel!' \n     'Well,  Sam,' said Frodo. 'I want you to see Rose  and  find out if she \ncan spare  you, so that you and I can go off together.  You can't go  far or  \nfor a long time now, of course,' he said a little wistfully. \n     'Well, not very well, Mr. Frodo.' \n     'Of course not.  But never mind.  You can see me on my way.  Tell  Rose \nthat you won't be away very long, not more than a fortnight; and you'll come  \nback quite safe.' \n     'I wish I could go all  the way  with  you to Rivendell, Mr. Frodo, and \nsee Mr. Bilbo,' said Sam. 'And yet the only place I really want to  be in is \nhere. I am that torn in two.' \n     'Poor Sam! It will feel like that, I am  afraid,'  said Frodo. 'But you  \nwill be healed. You were meant to be solid and whole, and you will be.'"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1236-c3-t
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1236, "chunk_number": 3, "type": "text", "chroma:document": "####- \n\nChapter 9. The Grey Havens"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1245-c0-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1245, "chunk_number": 0, "type": "text", "chroma:document": "####-     The starlight on the Western Seas. \n     Frodo and Sam halted and sat silent in the soft shadows, until they saw \na shimmer as the travellers came towards them. \n     There was Gildor  and  many fair Elven folk; and there  to Sam's wonder  \nrode Elrond and Galadriel. Elrond wore a  mantle of grey and had a star upon \nhis forehead, and  a silver harp was in his  hand, and upon his finger was a  \nring of gold with a  great blue stone, Vilya, mightiest of  the  Three.  But \nGaladriel sat upon a white palfrey  and  was robed all in glimmering  white,  \nlike  clouds  about the Moon; for  she herself seemed  to shine with a  soft \nlight.  On  her  finger was Nenya, the ring wrought of mithril ,  that bore a  \nsingle white stone  flickering like a frosty star. Riding slowly behind on a  \nsmall grey pony, and seeming to nod in his sleep, was Bilbo himself. \n     Elrond greeted  them gravely and graciously, and Galadriel  smiled upon"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1241-c2-t
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1241, "chunk_number": 2, "type": "text", "chroma:document": "meaning nothing bu t good; for it warmed all hearts to see them go  riding by \nwith their mail-shirts so bright and their shields so splendid, laughing and \nsinging songs of far away; and if they were now large and magnificent,  they  \nwere unchanged otherwise, unless they were  indeed  more fairspoken and \nmore \njovial and full of merriment than ever before. \n     Frodo and Sam, however, went back to ordinary attire,  except that when \nthere was need they both wore long grey cloaks,  finely woven and clasped at \nthe throat with beautiful brooches; and Mr. Frodo wore always a  white jewel \non a chain that he often would finger. \n     All things now went well, with  hope always of becoming  still  better; \nand Sam  was  as busy and as  full of delight as even a hobbit  could  wish. \nNothing  for him marred that whole year, except  for some vague anxiety about \nhis  master. Frodo dropped quietly  out of all the doings of the  Shire, and"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1246-c0-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1246, "chunk_number": 0, "type": "text", "chroma:document": "####-will  come,  and  Rosie-lass,  and Merry, and  Goldilocks,  and Pippin;  and \nperhaps more  that I  cannot see. Your  hands and  your wits will  be needed \neverywhere. You will be the Mayor, of course, as long a s you want to be, and \nthe most famous gardener in history; and you will read things out of the Red \nBook, and keep alive the memory of the age that is gone. so that people will  \nremember the Great Danger and so love their beloved land all the  more.  And \nthat will  keep  you as busy and as  happy as anyone can be, as long as your \npart of the Story goes on. \n     'Come now, ride with me!' \n     Then Elrond and  Galadriel rode on; for the Third Age was over, and the  \nDays of the Rings were passed, and an end was come of the story and  song of \nthose  times. With them  went many  Elves of the High Kindred  who  would \nno \nlonger stay in  Middle-earth; and among them, filled with a sadness that was"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1244-c1-t
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1244, "chunk_number": 1, "type": "text", "chroma:document": "Hills,  and  on September the twenty-second  they rode gently down  into the \nbeginning of the trees as afternoon was wearing away. \n     'If that isn't the very tree you hid  behind when the Black Rider first \nshowed up, Mr. Frodo!' said Sam pointing to the left. 'It seems like a dream \nnow.' \n     It  was  evening, and the stars were glimmering  in the  eastern sky as \nthey passed the ruined oak and turned and went on  down the hill between the \nhazel-thickets. Sam  was  silent,  deep in his memories. Presently he became \naware   that  Frodo  was  singing  softly  to  himself,   singing   the  old \nwalking-song, but the words were not quite the same. \n     Still round the corner there may wait \n     A new road or a secret gate; \n     And though I oft have passed them by, \n     A day will come at last when I \n     Shall take the hidden paths that run \n     West of the Moon, East of the Sun. \n     And  as if in answer,  from down below,  coming up the road out of  the"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1243-c1-t
encoding: FLOAT32
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{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1243, "chunk_number": 1, "type": "text", "chroma:document": "here. I am that torn in two.' \n     'Poor Sam! It will feel like that, I am  afraid,'  said Frodo. 'But you  \nwill be healed. You were meant to be solid and whole, and you will be.' \n     In the next day or  two Frodo went through his papers and  his writings \nwith Sam, and he handed over his keys.  There was  a big book with plain red \nleather  covers; its  tall  pages were  now almost filled.  At the beginning \nthere were many leaves covered with Bilbo's thin wandering hand; but most of \nit was written in Frodo's firm flowing script.  It was divided into chapters \nbut  Chapter 80 was unfinished, and after that  were some  blank leaves. The \ntitle page had many titles on it, crossed out one after another, so: \n \n     My  Diary. My Unexpected  Journey.  There  and  Back  Again.  And  What \nHappened After. \n     Adventures of  Five  Hobbits. The Tale  of the Great  Ring, compiled by \nBilbo  Baggins from his own  observations  and the  accounts of his friends."}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1247-c0-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1247, "chunk_number": 0, "type": "text", "chroma:document": "####-all was being made ready to depart, up rode Merry and Pippin in great haste.  \nAnd amid his tears Pippin laughed. \n     'You tried to give us the slip once before and failed, Frodo.' he said. \n'This time you have nearly  succeeded, but you have failed again. It was not  \nSam, though, that gave you away this time, but Gandalf himself!' \n     'Yes,' said Gandalf; 'for it will be better to ride back three together  \n'than one alone. Well, here at  last, dear friends, on the shores of the Sea  \ncomes the end of our fellowship in Middle-earth.  Go in peace!  I  will  not \nsay: do not weep; for not all tears are an evil.' \n     Then Frodo  kissed Merry  and Pippin,  and last  of all  Sam,  and went \naboard; and the sails were drawn up, and  the wind blew, and slowly the ship \nslipped away  down  the  long  grey firth;  and the  light of  the  glass of \nGaladriel that Frodo bore glimmered and was lost. And the ship went out into"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1246-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1246, "chunk_number": 1, "type": "text", "chroma:document": "those  times. With them  went many  Elves of the High Kindred  who  would \nno \nlonger stay in  Middle-earth; and among them, filled with a sadness that was \nyet  blessed and without bitterness, rode Sam, and Frodo, and Bilbo, and the \nElves delighted to honour them. \n     Though they rode through the midst of the Shire all the evening and all \nthe night, none saw them  pass,  save the wild creatures; or here  and there \nsome wanderer in the dark who saw a swift  shimmer  under  the trees,  or  a  \nlight and shadow flowing  through the grass as the Moon  went westward.  And \nwhen  they had passed from the  Shire,  going about the  south skirts of the \nWhite Downs, they came to the Far Downs,  and to the Towers,  and  looked on \nthe  distant Sea; and  so they  rode down at  last to Mithlond,  to the Grey \nHavens in the long firth of Lune. \n     As  they  came  to the gates Cnrdan the Shipwright came  forth to greet"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1243-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1243, "chunk_number": 2, "type": "text", "chroma:document": "Happened After. \n     Adventures of  Five  Hobbits. The Tale  of the Great  Ring, compiled by \nBilbo  Baggins from his own  observations  and the  accounts of his friends. \nWhat we did in the War of the Ring. \n     Here Bilbo's hand ended and Frodo had written: \n \n     THE DOWNFALL \n     OF THE \n     LORD OF THE RINGS \n     AND THE \n     RETURN OF THE KING \n \n     (as seen by the Little People; being the memoirs  of Bilbo and Frodo of"}


created_at: 2025-03-19 11:59:21
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1245-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1245, "chunk_number": 1, "type": "text", "chroma:document": "small grey pony, and seeming to nod in his sleep, was Bilbo himself. \n     Elrond greeted  them gravely and graciously, and Galadriel  smiled upon  \nthem. 'Well, Master Samwise,'  she said.  'I hear and see that you have used \nmy  gift well. The Shire shall now be  more than ever blessed  and beloved.' \nSam bowed, but found nothing to say. He had forgotten how beautiful the Lady \nwas. \n     Then Bilbo woke up and opened his eyes. 'Hullo, Frodo!' he said. 'Well, \nI have passed the  Old Took today! So that's  settled. And now I think I  am \nquite ready to go on another journey. Are you coming?' \n     'Yes, I am coming,' said Frodo. 'The Ring-bearers should go together.' \n     'Where are you going, Master?' cried Sam, though at last he  understood \nwhat was happening. \n     'To the Havens, Sam,' said Frodo. \n     'And I can't come.' \n     'No, Sam. Not yet anyway, not  further  than the Havens. Though you too \nwere a Ring-bearer, if only  for a little while. Your  time may come. Do not"}


created_at: 2025-03-19 11:59:22
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1246-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1246, "chunk_number": 2, "type": "text", "chroma:document": "the  distant Sea; and  so they  rode down at  last to Mithlond,  to the Grey \nHavens in the long firth of Lune. \n     As  they  came  to the gates Cnrdan the Shipwright came  forth to greet \nthem. Very tall he was,  and his beard  was long, and he  was grey  and old, \nsave that  his eyes were keen as stars; and he looked at them and bowed, and  \nsaid: 'All is now ready.' \n     Then Cnrdan led  them to the Havens, and there  was a white ship lying, \nand upon the  quay  beside a  great  grey horse stood a  figure robed all in \nwhite awaiting them.  As  he turned and came  towards  them  Frodo saw  that \nGandalf now wore openly  upon his  hand the Third Ring, Narya the Great, and \nthe stone upon it was red as fire.  Then those who were to go were glad, for  \nthey knew that Gandalf also would take ship with them. \n     But Sam  was now sorrowful at  heart,  and it seemed to him that if the \nparting would be bitter,  more grievous  still would  be  the long road home"}


created_at: 2025-03-19 11:59:22
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1247-c1-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1247, "chunk_number": 1, "type": "text", "chroma:document": "slipped away  down  the  long  grey firth;  and the  light of  the  glass of \nGaladriel that Frodo bore glimmered and was lost. And the ship went out into \nthe  High Sea and passed on into the West, until at  last on a night of rain \nFrodo smelled  a sweet  fragrance on the air  and heard the sound of singing  \nthat came over the water. And  then it seemed to him that as in his dream in \nthe house of Bombadil, the grey rain-curtain turned all to silver  glass and  \nwas  rolled back, and he beheld white  shores and beyond  them  a far  green \ncountry under a swift sunrise. \n     But to Sam  the evening deepened to darkness as he  stood at the Haven; \nand as he looked at the grey sea he saw only a shadow on the waters that was \nsoon lost in the West. There still he stood  far into the night, hearing only \nthe  sigh and murmur of  the  waves on  the shores  of Middle-earth, and the \nsound of them sank deep into his  heart.  Beside him stood Merry and Pippin, \nand they were silent."}


created_at: 2025-03-19 11:59:22
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1244-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1244, "chunk_number": 2, "type": "text", "chroma:document": "A day will come at last when I \n     Shall take the hidden paths that run \n     West of the Moon, East of the Sun. \n     And  as if in answer,  from down below,  coming up the road out of  the \nvalley, voices sang: \n     A! Elbereth Gilthoniel! \n     silivren penna mnriel \n     o menel aglar elenath, \n     Gilthoniel, A! Elbereth! \n     We still remember, we who dwell \n     In this far land beneath the trees"}


created_at: 2025-03-19 11:59:22
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1245-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1245, "chunk_number": 2, "type": "text", "chroma:document": "'And I can't come.' \n     'No, Sam. Not yet anyway, not  further  than the Havens. Though you too \nwere a Ring-bearer, if only  for a little while. Your  time may come. Do not \nbe too  sad, Sam. You cannot be always torn in two. You will  have to be one \nand whole, for many years. You have so much to enjoy and to be, and to do.' \n     'But,' said  Sam, and tears started  in his eyes, 'I  thought  you were \ngoing  to  enjoy the  Shire, too.  for years and  years, after all you  have \ndone.' \n     'So I thought too, once. But I have been too deeply hurt, Sam. I  tried \nto  save the Shire, and it has been saved, but not  for me. It must often be \nso, Sam, when things are in danger: some one has to give them up, lose them, \nso that others may keep them. But you are my  heir: all that I had and might  \nhave had I leave to you.  And also you  have Rose, and Elanor; and Frodo -lad"}


created_at: 2025-03-19 11:59:22
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1246-c3-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1246, "chunk_number": 3, "type": "text", "chroma:document": "But Sam  was now sorrowful at  heart,  and it seemed to him that if the \nparting would be bitter,  more grievous  still would  be  the long road home \nalone. But  even as they stood there, and the Elves were  going aboard,  and"}


created_at: 2025-03-19 11:59:22
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1247-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1247, "chunk_number": 2, "type": "text", "chroma:document": "the  sigh and murmur of  the  waves on  the shores  of Middle-earth, and the \nsound of them sank deep into his  heart.  Beside him stood Merry and Pippin, \nand they were silent. \n     At last the three companions  turned away, and never again looking back  \nthey rode slowly homewards; and they spoke no word to one another until they \ncame  back to the  Shire. but each had great comfort  in his friends  on the \nlong grey road. \n     At last they rode over the downs and took the East Road, and then Merry \nand Pippin rode on to Buckland; and already they  were singing again as they \nwent. But Sam turned to Bywater,  and so came back up  the Hill,  as day was \nending  once  more. And  he  went on, and there  was  yellow light, and fire \nwithin; and the evening meal was ready, and he  was expected.  And Rose drew \nhim in, and set him in his chair, and put little Elanor upon his lap. \n     He drew a deep breath. 'Well, I'm back,' he said."}


created_at: 2025-03-19 11:59:23
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1247-c3-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1247, "chunk_number": 3, "type": "text", "chroma:document": "####-"}


created_at: 2025-03-19 11:59:24
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1222-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1222, "chunk_number": 2, "type": "text", "chroma:document": "Sam. But  I should a' passed you in the street in that gear. You've been  in \nforeign parts, seemingly. We feared you were dead.' \n     'That I ain't!'  said Sam.  'Nor Mr. Frodo. He's here and  his friends. \nAnd  that's  the to-do. They're raising the Shire. We're going to clear  out \nthese ruffians, and their Chief too. We're starting now.' \n     'Good, good!' cried Farmer Cotton.  'So  it's  begun at last! I've been \nitching for trouble all this year, but folks wouldn't help. And I've had the \nwife  and Rosie to think of. These ruffians don't stick at nothing. But come \non now, lads! Bywater is up! We must be in it!' \n     'What about Mrs.  Cotton and Rosie?' said Sam. 'It  isn't safe  yet for  \nthem to be left all alone.' \n     'My Nibs  is  with them. But you  can  go and help him,  if you  have a  \nmind,' said Farmer Cotton with a grin. Then  he and his sons ran off towards"}


created_at: 2025-03-19 11:59:24
topic: persistent://default/default/00300340-0735-4b39-8bce-93d238b1112e
id: 83285b2c-7e99-48ca-b113-2283b29b4818-p1242-c2-t
encoding: FLOAT32
metadata:
{"document_uuid": "83285b2c-7e99-48ca-b113-2283b29b4818", "page_number": 1242, "chunk_number": 2, "type": "text", "chroma:document": "names, and what could be better?' \n     'I  suppose  you're  right,  Mr.  Frodo,'  said  Sam.  'I've heard some \nbeautiful names on my travels,  but  I  suppose they're  a bit too grand for \ndaily wear and tear, as you  might say. The Gaffer, he says: \"Make it short, \nand  then you won't have to cut it short before you can use it.\" But if it's \nto be a  flower-name, then I don't  trouble about  the length: it  must be a  \nbeautiful  flower, because, you see, I  think  she is very beautiful, and is \ngoing to be beautifuller still.' \n     Frodo  thought  for  a  moment.  'Well,  Sam,  what  about  elanor, the \nsun-star, you remember the little golden flower in the grass of Lothlurien?' \n     'You're  right  again, Mr. Frodo!' said  Sam delighted.  'That's what I \nwanted.' \n     Little  Elanor  was nearly six months  old, and 1421  had passed to its \nautumn, when Frodo called Sam into the study."}


# collections

id: 00300340-0735-4b39-8bce-93d238b1112e
name: AnswerIt
database_id: 00000000-0000-0000-0000-000000000000
config_json_str:
{"hnsw_configuration": {"space": "l2", "ef_construction": 100, "ef_search": 10, "num_threads": 4, "M": 16, "resize_factor": 1.2, "batch_size": 100, "sync_threshold": 1000, "_type": "HNSWConfigurationInternal"}, "_type": "CollectionConfigurationInternal"}


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      <td>1. \ncollect data in one variable through a simple interview. \n2. \npresent data in a pictograph without a scale. \n3. \ninterpret a pictograph without a scale. \n4. \norganize data in a pictograph without a scale into a table.</td>
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      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nrepresent and interpret data in a pictograph without a scale. (DP) \n• \nperform subtraction of numbers where both numbers are less than 100. (NA) \n• \nextend existing repeating patterns and create new repeating patterns. (NA)</td>
      <td></td>
      <td></td>
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The table presents a structured overview of the Grade 1 curriculum for Quarter 4, specifically focusing on two key areas: Data and Probability (DP) and Number and Algebra (NA). Each row of the table is divided into columns which categorize the learning objectives, content areas, and performance standards associated with these topics. The entry for Data and Probability describes the approach to using pictographs without a scale as a method for the representation of data, emphasizing the steps that students should follow, which include collecting data through simple interviews, presenting it visually in pictographs, interpreting these visuals, and organizing the data into tables.

In the section dedicated to Number and Algebra, the table outlines objectives pertaining to subtraction and the concept of repeating patterns. The students are expected to carry out subtraction involving numbers up to 100 and explore the notion of patterns through various activities. Specific learning outcomes include illustrating subtraction problems with concrete and pictorial models, determining missing numbers in equations, and writing equivalent expressions for addition or subtraction sentences. Additionally, it includes tasks such as subtracting two-digit numbers without regrouping and creating repeating patterns using diverse elements like numbers, letters, or objects.

The final row in the table encapsulates performance standards for the quarter, which detail the competencies that learners are expected to achieve by the end of the period. These include the ability to represent and interpret data using pictographs, perform basic subtraction involving small numbers, and extend or create new repeating patterns. This structured approach ensures that students build a foundational understanding of mathematical concepts while integrating practical skills in data handling and numerical operations.


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      <td>communicating, reasoning, and making connections between topic areas.</td>
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      <th>1</th>
      <td>GRADE 6</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber  and  Algebra  (the  four  operations  with  decimals;  the  four  operations  with  different  combinations  of \nfractions,  whole  numbers,  and mixed  numbers;  ratio  and  proportion;  percentages,  and  their  relationships  with \nfractions and decimals; exponential form, including calculation using the GEMDAS rules; common factors, greatest \ncommon  factors, common  multiples,  and  least  common multiples);  Measurement  and  Geometry  (tessellation  of \nshapes;  translation,  reflection,  and  rotation  with  shapes;  units  of  volume  and  capacity;  volume  of  cubes  and \nrectangular prisms; perimeter and area of triangles, parallelograms, trapezoids, and composite figures composed \nof triangles, squares, and rectangles; parts of a circle, including circumference; area of a circle; composite figures \ncomposed  of  any  two  or  more  of:  triangle,  square,  rectangle,  circle,  semi-circle);  and  Data  and  Probability \n(construction and interpretation of pie graphs). This knowledge, skills, and understanding is applied, in association \nwith \nthe  use  of \ntechnology, \nin \nthe  processes  within  Mathematics  of  critical \nthinking,  problem  solving, \ncommunicating, reasoning, and making connections between topic areas.</td>
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      <th>2</th>
      <td>GRADE 7</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber and Algebra (application of percentages; use of rates; rational numbers; square roots of perfect squares, \ncube  roots  of  perfect cubes,  and  irrational  numbers;  sets  and  subsets,  and  the  union  and  intersection  of sets; \nVenn  diagrams;  the  set  of  integers,  and  comparing  and  ordering  integers;  the  four  operations  with  integers; \nsimplification  of  numerical  expressions  involving  integers;  absolute  value  of  an  integer;  the  solution  of  simple \nequations; the evaluation of algebraic expressions following substitution; the rearrangement of a formula to make \na different variable the subject of the formula; operations using scientific notation); Measurement and Geometry \n(regular and irregular polygons and their features/properties; determination of measures of angles and number of \nsides  of  polygons;  conversion  of  units  of  measure;  volume  of  square  and  rectangular  pyramids,  and  cylinders; \nmeasures of length, area, surface area, volume, time, and temperature); and Data and Probability (data collection \nand  sampling  techniques,  and  the  presentation  of  data  in  appropriate  tables  and  graphs;  interpretation  of \nstatistical graphs; outcomes from experiments). This knowledge, skills, and understanding is applied, with the use \nof  technology,  to  the  processes  within  Mathematics  of  critical  thinking,  problem  solving,  communicating, \nreasoning, and making connections between topic areas.</td>
    </tr>
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      <th>3</th>
      <td>GRADE 8</td>
      <td>The  learner  demonstrates  knowledge,  skills  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber and Algebra (algebraic expressions and operations with monomials, binomials, and multinomials; special \nproducts for binomials, and factorization of polynomials; rational algebraic expressions and equations; rules for \nobtaining  terms  in  sequences;  plotting  points,  and  finding  distance  and  the  midpoint  of  line  segments  on  the \nCartesian coordinate plane; earning money, profit and loss, ‘best buys,’ buying on terms; linear equations in one \nvariable; linear inequalities in one variable and their graphs; linear equations in two variables and their graphs; \nsystems  of  linear  equations  in  two  variables;  linear  inequalities  in  two  variables);  Measurement  and  Geometry \n(volume of pyramids, cones, and spheres; the Pythagorean Theorem; triangle inequality theorems); and Data and \nProbability  (measures  of  central  tendency  of  ungrouped  data;  measures  of  variability  for  ungrouped  data; \ninterpretation and analysis of graphs from primary and secondary data; experimental and theoretical probability;</td>
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The information presented outlines the knowledge, skills, and understanding that learners are expected to demonstrate in various curriculum content domains within the mathematics education framework across different grade levels. In Grade 6, students engage with foundational concepts in Number and Algebra, which include performing operations with decimals and fractions, understanding ratios and proportions, calculating percentages and their relationships, using exponential form, and applying GEMDAS rules. They also learn about common factors and multiples. The Measurement and Geometry domain focuses on comprehending shapes, transformations, volume calculations, and the area of various geometric figures including circles and composite shapes. Data and Probability skills involve constructing and interpreting pie charts, highlighting the ability to analyze data.

As learners progress to Grade 7, they deepen their understanding of Number and Algebra through the application of percentages and rates, working with rational numbers, and exploring sets and subsets using Venn diagrams. The measurement skills expand to include unit conversions and volumetric calculations of pyramids and cylinders, while Data and Probability concepts introduce students to data collection methods, sampling techniques, and the effective presentation of data through tables and graphs. The expectation is to interpret statistical graphs and outcomes from experiments.

In Grade 8, learners concentrate on more complex algebraic expressions and operations, including factorization of polynomials and manipulation of rational algebraic expressions. They study linear equations and inequalities, as well as systems of equations in two variables, which are fundamental to understanding higher-dimensional mathematics. The Measurement and Geometry section introduces the Pythagorean Theorem and explores the properties of volumes of various three-dimensional figures. Additionally, students learn about measures of central tendency and variability, essential for analyzing ungrouped data, as well as the principles of experimental and theoretical probability. This robust curriculum aims to foster critical thinking, problem solving, effective communication, and the ability to make connections across different mathematical concepts.


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      <td>Grade 1</td>
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      <th>1</th>
      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners should have knowledge \nThe learners … \nDOMAIN \nand understanding of ...</td>
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      <th>2</th>
      <td>Quarter 1</td>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1.  simple 2-dimensional shapes \nand their features.</td>
      <td>1. \nidentify simple 2-dimensional shapes (triangle, rectangle, square) of different size and \nin different orientation. \n2. \ncompare and distinguish 2-dimensional shapes according to features such as sides and \ncorners. \n3. \ncompose and decompose triangles, squares, and rectangles.</td>
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      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>2.  whole numbers up to 100. \n3.  ordinal numbers up to 10th. \n4.  addition of numbers with sums \nup to 20.</td>
      <td>4. \ncount up to 100 (includes counting up or down from a given number and identifying a \nnumber that is 1 more or 1 less than a given number). \n5. \nread and write numerals up to 100. \n6. \nrecognize and represent numbers up to 100 using a variety of concrete and pictorial \nmodels (e.g., number line, block or bar models, and numerals). \n7. \ncompare two numbers up to 20. \n8. \norder numbers up to 20 from smallest to largest, and vice versa. \n9. \ndescribe the position of objects using ordinal numbers: 1st, 2nd, 3rd, up to 10th. \n10.  compose and decompose numbers up to 10 using concrete materials (e.g., 5 is 5 and 0; \n4 and 1; 3 and 2; 2 and 3; 1 and 4; 0 and 5). \n11. \nillustrate addition of numbers with sums up to 20 using a variety of concrete and \npictorial models and describes addition as “counting up,” and “putting together.” \n12. \nillustrate by applying the following properties of addition, using sums up to 20: \na. the sum of zero and any number is equal to the number, and \nb. changing the order of the addends does not change the sum. \n13.  solve problems (given orally or in pictures) involving addition with sums up to 20.</td>
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      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nidentify and distinguish simple 2-dimensional shapes. (MG) \n• \ncount, recognize and represent whole numbers up to 100. (NA) \n• \nuse ordinal numbers up to 10th to describe position. (NA) \n• \ncompare and order numbers up to 20 and perform addition of numbers with sums up to 20. (NA)</td>
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The table presented outlines the educational content for Grade 1, particularly focusing on Quarter 1 with emphases on Measurement and Geometry (MG) and Number and Algebra (NA). The first column of the table indicates the various aspects of the curriculum, starting with essential standards and competencies that learners are expected to acquire. For the Measurement and Geometry domain, the content standards include recognizing simple 2-dimensional shapes, such as triangles, rectangles, and squares, along with their features. Students are expected to identify shapes in different sizes and orientations, compare shapes by their attributes such as sides and corners, and engage in activities that involve composing and decomposing these shapes.

In the Number and Algebra section, the table outlines key learning components such as an introduction to whole numbers up to 100, ordinal numbers up to the 10th, and the addition of numbers with sums reaching up to 20. Learners are expected to count sequentially to 100, understand and represent numbers through various concrete and pictorial models, and practice comparing and ordering numbers up to 20. Additionally, the curriculum encourages the application of addition properties and the comprehension of basic addition concepts through different models. It also highlights the importance of developing problem-solving skills in mathematics, particularly with addition tasks that have sums up to 20.

At the end of the quarter, the performance standards detail specific competencies that learners should demonstrate. They should be capable of identifying and distinguishing simple 2-dimensional shapes, recognizing and representing whole numbers up to 100, and utilizing ordinal numbers to describe positions. Furthermore, students will be expected to demonstrate their ability to compare and order numbers up to 20, as well as successfully perform addition operations for sums within the same range. This structured approach to learning ensures that Grade 1 students build a solid foundation in fundamental mathematical concepts, preparing them for more complex topics in the future.


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      <td>Measurement \nand \nGeometry  \n(MG)</td>
      <td>1.  measurement of length and \ndistance using non-standard \nunits.</td>
      <td>1. \nmeasure the length of an object and the distance between two objects using non-standard \nunits. \n2. \ncompare lengths and distances using non-standard units. \n3. \nsolve problems involving lengths and distances using non-standard units.</td>
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      <th>3</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>2.  place value in any 2-digit \nnumber. \n3.  addition of numbers, with \nsums up to 100.</td>
      <td>4. \norder numbers up to 100 from smallest to largest, and vice versa. \n5. \ncounts by 2s, 5s and 10s up to 100. \n6. \ndetermine \na.  the place value of a digit in a 2-digit number, \nb.  the value of a digit, and \nc.  the digit of a number, given its place value \n7. \ndecompose any 2-digit number into tens and ones. \n8. \nadd numbers by expressing addends as tens and ones (expanded form). \n9. \nadd numbers with sums up to 100 without regrouping, using a variety of concrete and \npictorial models for: \na. 2-digit and 1-digit numbers, and \nb. 2-digit and 2-digit numbers. \n10.  solve problems (given orally or in pictures) involving addition with sums up to 100 without \nregrouping.</td>
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      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nuse non-standard units to compare and measure length and distance. (MG) \n• \norder and decompose (into tens and ones) numbers up to 100. (NA) \n• \nperform addition of numbers with sums up to 100. (NA)</td>
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The provided table outlines educational content for Grade 1, specifically focusing on performance standards and topics covered in Quarter 2 concerning Measurement and Geometry, as well as Number and Algebra. The table is organized neatly into rows and columns that facilitate easy comprehension. The first column indicates the specific category or standard being addressed, starting with elementary topics in measurement and progressing through more complex concepts in number and algebra.

In the Measurement and Geometry (MG) section, students are engaged in practical activities such as measuring the length of objects and the distances between them using non-standard units. They will also learn to compare lengths and solve problems that involve these concepts. The corresponding performance standards reflect their ability to effectively use non-standard units for measuring and comparing, emphasizing a hands-on approach to understanding basic measurement principles.

Transitioning to Number and Algebra (NA), the content covers vital foundational skills, including understanding place value in 2-digit numbers, addition with sums up to 100, and comparing and ordering numbers. Several methods to illustrate these concepts are introduced, such as decomposing numbers into tens and ones and using visual aids like concrete and pictorial models. By the end of the quarter, learners are expected to demonstrate proficiency in these areas, successfully applying their knowledge of addition and number organization while solving problems without the need for regrouping. The overall goal is to extend basic arithmetic skills while fostering an understanding of measurement through engaging and interactive learning experiences.


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      <td>the  Fundamental  Counting  Principle).  This  knowledge,  skills,  and  understanding  is  applied,  with  the  use  of \ntechnology, to the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, \nand making connections between topic areas.</td>
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      <th>1</th>
      <td>GRADE 9</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber  and  Algebra  (relations  and  functions;  graphs  of  linear  functions,  and  the  identification  of  domain  and \nrange,  slope,  intercepts,  and  zeros;  quadratic  equations  and  graphs  of  quadratic  functions;  the  solution  of \nquadratic equations; direct and  inverse variation); Measurement and Geometry (simple geometric concepts and \nnotations; perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal; quadrilaterals \nand their properties; congruence of triangles; congruence proofs; similarity of polygons; special triangles; triangle \ntheorems  and  triangle \ninequality  theorems;  the  trigonometric  ratios  and  their  application);  and  Data  and \nProbability  (interpretation  and  analysis  of  data  to  assess  whether  the  data  may  be  misleading;  probabilities  of \nsimple and compound events). This knowledge, skills, and understanding is applied, with the use of technology, \nto the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, and making \nconnections between topic areas.</td>
    </tr>
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      <th>2</th>
      <td>GRADE 10</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber and Algebra (quadratic inequalities in one variable and in two variables; absolute value equations and \ninequalities in one variable, and their graphs; radical expressions; the  roots of a quadratic equation; quadratic \nfunctions; equations reducible to quadratic equations;  equation of a circle and the graph of a circle; compound \ninterest and depreciation); Measurement and Geometry (the laws of sines and the laws of cosines;  translations, \nreflections, and rotations, in the Cartesian plane; central angles, inscribed angles, and angles and lengths formed \nby intersecting chords, secants, and tangents of a circle; sectors and segments of a circle, and their areas); and \nData  and  Probability  (box-and-whisker  plots,  and  cumulative  frequency  histograms  and  polygons;  quartiles, \ndeciles, and percentiles; interquartile range, and outliers; evaluation of statistical reports; union and intersection \nof  events,  dependent  and \nindependent  events,  and  complementary  events).  This  knowledge,  skills,  and \nunderstanding is applied, in association with the use of technology, in the processes within Mathematics of critical \nthinking, problem solving, communicating, reasoning, and making connections between topic areas.</td>
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The table presented breaks down the educational frameworks for Grades 9 and 10 in the context of mathematical competencies, specifically in the domains of Number and Algebra, Measurement and Geometry, and Data and Probability. At the top of the table, two primary categories—Grade 9 and Grade 10—are indicated. Each row outlines the competencies expected from learners along with a brief description of the knowledge and skills they should acquire in relation to the curriculum content standards.

For Grade 9, the competencies involve fundamental algebra concepts including relations and functions, linear functions, as well as an introduction to quadratic equations and their graphical representations. Students should be proficient in analyzing these functions, identifying key features such as domain, range, slope, intercepts, and zeros. Furthermore, in the Measurement and Geometry domain, learners are expected to grasp simple geometric concepts, including properties of quadrilaterals, congruence, and basic triangle theorems. Data and Probability competencies focus on interpreting and analyzing data to recognize potentially misleading information and understanding simple and compound probabilities.

In progressing to Grade 10, the mathematical knowledge required becomes more advanced, incorporating topics like quadratic inequalities and absolute value equations, alongside their graphical interpretations. The Measurement and Geometry section expands to include deeper concepts such as the laws of sines and cosines, transformations in the Cartesian plane, and essential characteristics of circles, including their sectors and segments. Additionally, in the Data and Probability domain, concepts such as box-and-whisker plots, cumulative frequency distributions, and evaluation of statistical reports are introduced. The skills obtained in both grades emphasize the application of technology and foster critical thinking, problem solving, reasoning, and communication within mathematical contexts, ensuring a comprehensive understanding that fosters connections across different mathematical topics.


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      <td>GRADE \nLEVEL</td>
      <td>GRADE LEVEL STANDARDS</td>
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      <th>1</th>
      <td>GRADE 1</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber and Algebra (whole numbers up to 100; ordinal numbers up to 10th; addition of numbers with sums up \nto 20; place value in any 2-digit number; addition of numbers, with sums up to 100; subtraction of numbers where \nboth numbers are less than 100; repeating patterns, fractions ½ and ¼; the denominations and values of Philippine \ncoins and bills up to ₱100; addition of money where the sum is up to ₱100 and subtraction of money where both \namounts are less than ₱100); Measurement and Geometry (simple 2-dimensional shapes; measurement of length \nand  distance  using  non-standard  units;  the  movement  of  objects  in  half  turn  or  quarter  turn,  in  clockwise  or \ncounter clockwise direction; time measured in hours, half-hours, quarter hours, days, weeks, months, years); and \nData  and  Probability  (pictographs  without  a  scale  for  the  representation  of  data).  This  knowledge,  skills,  and \nunderstanding  is  applied,  with  the  use  of  technology,  to  the  processes  within  Mathematics  of  critical  thinking, \nproblem solving, communicating, reasoning, and making connections between topic areas.</td>
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      <th>2</th>
      <td>GRADE 2</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber and Algebra (whole numbers up to 1000, ordinal numbers up to 20th,; addition of numbers with sums up \nto 1000; the denominations and values of Philippine coins and bills up to ₱1000, and the addition of amounts of \nmoney  with  sums  up  to  ₱1000;  subtraction  of  numbers  where  both  numbers  are  less  than  1000;  increasing \npatterns  and  decreasing  patterns;  multiplication  and  division  of  whole  numbers  using  the  2,  3,  4,  5,  and  10 \nmultiplication tables; odd and even numbers; unit fractions and similar fractions with denominators 2, 3, 4, 5, 6, \nand 8); Measurement and Geometry (circles, half circles, quarter circles and composite figures made up of squares, \nrectangles, triangles, circles, half-circles, and quarter-circles; one step slides and flips of basic shapes and figures; \nmeasurement, comparison, and estimation of length and distance using appropriate tools and units; duration of \ntime, elapsed time, and telling and writing time in hours and minutes (using a.m. and p.m.); straight and curved \nlines, and flat and curved surfaces; the perimeter of triangles, squares, and rectangles); and Data and Probability \n(pictographs with a scale for the representation of data). This knowledge, skills, and understanding is applied, with</td>
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The table presented outlines the educational standards and learning outcomes for Grade Levels 1 and 2, as part of a mathematics curriculum. Each grade level is matched with specific knowledge, skills, and understanding across various curriculum content domains, including Number and Algebra, Measurement and Geometry, and Data and Probability. For Grade 1, learners are expected to comprehend fundamental mathematical concepts such as whole numbers up to 100, ordinal numbers up to the 10th, simple addition and subtraction, and the recognition of basic fractions such as ½ and ¼. The curriculum also introduces learners to the denominations and values of Philippine currency, focusing on money management concepts where sums do not exceed ₱100. Measurement and Geometry components include an understanding of simple 2-dimensional shapes, the usage of non-standard measurement units, and an introduction to concepts of time.

As students advance to Grade 2, the standards scale up significantly. Learners should demonstrate knowledge of whole numbers up to 1000 and ordinal numbers up to the 20th. They are expected to perform addition and subtraction operations involving sums up to 1000 and to manage monetary values using Philippine coins and bills up to ₱1000. The curriculum builds on the foundations laid in Grade 1 by including more complex operations such as multiplication and division using basic multiplication tables. Additionally, students learn to identify increasing and decreasing patterns and delve into the study of unit fractions. In Measurement and Geometry, the curriculum expands to a more comprehensive understanding of shapes, including circles and composite figures, as well as developing skills for measuring length and time with appropriate tools. The Data and Probability domain incorporates pictographs with a scale for data representation, enhancing learners’ abilities to interpret and present data. Overall, the comprehensive approach in the table emphasizes the integration of critical thinking, problem-solving, and technology in learning processes throughout, preparing students for more advanced mathematical concepts in subsequent grade levels.


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      <td>MATATAG K TO 10 CURRICULUM  \n OF THE K TO 12 PROGRAM \nMATHEMATICS</td>
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The table presented appears to serve as a visual representation of a pivotal aspect of the Philippine educational framework, specifically focusing on the Mathematics curriculum for Grades 1 to 10. It is structured into a grid format, with four columns labeled from 0 to 3, and four rows indicating the same numbering alongside a header row. The majority of the cells remain blank, suggesting that they may be placeholders for future data or commentary.

Notably, within the third row, there is a filled cell that highlights the title "MATATAG K TO 10 CURRICULUM OF THE K TO 12 PROGRAM MATHEMATICS." This phrase carries significant weight, as it encapsulates the essence of the curriculum being discussed. The term "MATATAG" implies a strong and solid foundation in mathematical education, which resonates with the message that the curriculum aims to develop a robust understanding of mathematics as a critical skill necessary for the learners' future engagements both in society and within the evolving landscape of scientific and technological advances.

In the context provided, the importance of cultivating mathematical skills and reasoning in students from an early age is emphasized. The curriculum is designed not only to teach mathematical concepts but also to foster numeracy—defined as the ability to effectively utilize mathematical information in various real-life situations. This aligns with the goal of preparing Filipino students for the 21st century, promoting their ability to analyze, communicate, and apply mathematical knowledge for informed decision-making. The empty cells in the table further suggest an expectation for the ongoing development or refinement of the curriculum, reinforcing the dynamic nature of educational methodologies aimed at nurturing competent and numerate citizens.


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      <td>the use of technology, to the processes within Mathematics of critical thinking, problem solving, communicating, \nreasoning, and making connections between topic areas.</td>
    </tr>
    <tr>
      <th>1</th>
      <td>GRADE 3</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber  and  Algebra  (whole  numbers  up  to  10  000;  ordinal  numbers  up  to  100th;  addition  and  subtraction  of \nnumbers  of  up  to  4  digits,  and  money  up  to ₱10  000;  multiplication  using  6,  7,  8  and  9  multiplication  tables; \nestimation of products of two numbers by first rounding to the nearest multiple of 10; determination of missing \nterms  contained  in  repeating  and  increasing  patterns  and  repeating  and  decreasing  patterns;  generation  of \nrepeating  and  increasing  patterns,  and  repeating  and  decreasing  patterns;  division  using  the  6,  7,  8  and  9 \nmultiplication tables; division of 2- to 4-digit numbers; estimation of quotients by first rounding the divisor and \ndividend to the nearest multiple of 10, addition and subtraction of similar fractions); Measurement and Geometry \n(areas of squares and rectangles; points, lines, line segments, and rays; parallel, perpendicular and intersecting \nlines; measures of mass and capacity; line symmetry; resulting figure after a translation); and Data and Probability \n(data  presented  in  tables  and  single  bar  graphs;  outcomes  from  experiments  and  real-life  situations).  This \nknowledge, skills, and understanding is applied, with the use of technology, to the processes within Mathematics \nof critical thinking, problem solving, communicating, reasoning, and making connections between topic areas.</td>
    </tr>
    <tr>
      <th>2</th>
      <td>GRADE 4</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber  and  Algebra  (whole  numbers  up  to  1  000  000;  addition  of  numbers  with  sums  up  to  1  000  000  and \nsubtraction  of  numbers  where  both  numbers  are  less  than  1  000  000;  multiplication  of  whole  numbers  with \nproducts-up  to  1  000  000;  division  of  up  to  4-digit  numbers  by  up  to  2-digit  numbers,  and  the  MDAS  rules; \naddition and subtraction of similar fractions, including mixed numbers; dissimilar and equivalent fractions; factors \nand multiples of numbers up to 100; addition and subtraction of dissimilar fractions; simple patterns; number \nsentences; decimal numbers and their relationship to fractions); Measurement and Geometry (right, acute, and \nobtuse  angles;  properties  of  triangles  and  quadrilaterals;  perimeter  of  quadrilaterals,  and  composite  figures \ncomposed  of  triangles  and  quadrilaterals;  conversion  of  units  of  length,  mass,  capacity,  and  time;  symmetric \nfigures and designs; reflection with shapes); and Data and Probability (presentation and interpretation of data in \ntabular form and in a simple line graph). This knowledge, skills, and understanding is applied, with the use of \ntechnology, to the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, \nand making connections between topic areas.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>GRADE 5</td>
      <td>The  learner  demonstrates  knowledge,  skills,  and  understanding  in  relation  to  the  curriculum  content  domains \nNumber  and  Algebra  (the  GMDAS  rules  for  operations  with  numbers;  multiplication  and  division  of  fractions; \ndecimal  numbers  with  decimal  parts  up  to  ten  thousandths;  addition  and  subtraction  of  decimal  numbers; \ndivisibility rules; prime and composite numbers; multiplication and division of decimal numbers; GMDAS rules \nwhen performing three or more operations with fractions and decimals); Measurement and Geometry (12- and 24-\nhour time, and world time zones; area of a parallelogram, triangle, and trapezoid; prisms and pyramids; surface \narea of solid figures; cubes and rectangular prisms; rotation about a point given an angle); and Data and Probability \n(double bar graphs and double line graphs; theoretical probability). This knowledge, skills, and understanding is \napplied,  with  the  use  of  technology,  to  the  processes  within  Mathematics  of  critical  thinking,  problem  solving,</td>
    </tr>
  </tbody>
</table>


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The table presents a structured overview of the curriculum content for Grade 3, Grade 4, and Grade 5 in mathematics. Each grade level includes detailed descriptions of the knowledge, skills, and understanding that learners are expected to acquire across various domains of mathematics. 

In Grade 3, learners engage with numbers up to 10,000, including understanding ordinal numbers and performing operations such as addition and subtraction of four-digit numbers and money up to ₱10,000. They are introduced to multiplication involving 6, 7, 8, and 9 tables, as well as estimation techniques for multiplication and division. Additionally, Grade 3 covers basic patterns and properties of fractions, alongside concepts in measurement and geometry such as calculating areas of simple shapes and understanding symmetry. Data and probability aspects are introduced through the presentation of data using tables and single bar graphs.

Moving on to Grade 4, the curriculum expands to encompass whole numbers up to 1,000,000 and includes more complex operations. In this grade, students learn to add and subtract numbers with sums that can go up to 1,000,000, engage with multi-digit multiplication and division, and explore the relationships between decimal numbers and fractions. Measurement and geometry concepts cover angles and properties of shapes, while data presentation and interpretation become more sophisticated, incorporating data in tabular form and simple line graphs.

In Grade 5, the curriculum further builds on previous knowledge by introducing the GMDAS rules for operations with numbers, encompassing multiplication and division of both fractions and decimals. Students also explore the measurement of time and understand the area of more complex shapes like parallelograms and trapezoids. The study of data and probability progresses with students working with double bar graphs and theoretical probability, highlighting an increased complexity in mathematical reasoning and application. Overall, this structured approach emphasizes not only numerical proficiency but also critical thinking and the effective use of technology in mathematics.


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      <th></th>
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      <th>1</th>
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    </tr>
  </thead>
  <tbody>
    <tr>
      <th>0</th>
      <td>Grade 2</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>1</th>
      <td>Quarter 4</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1.  unit fractions and similar \nfractions with denominators 2, \n3, 4, 5, 6, and 8.</td>
      <td>1. \nrepresent and identify unit fractions with denominators 2, 3, 4, 5, 6, and 8. \n2. \nread and write unit fractions in fraction notation. \n3. \norder unit fractions from smallest to largest, and vice versa. \n4. \nrepresent and identify similar fractions with denominators 2, 3, 4, 5, 6, and 8 using groups \nof objects, fraction charts, fraction tiles, and the number line. \n5. \nread and write similar fractions in fraction notation. \n6. \norder similar fractions from smallest to largest, and vice versa.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>2.  duration of time, elapsed time, \nand telling and writing time in \nhours and minutes (using \na.m. and p.m.). \n3.  straight and curved lines, and \nflat and curved surfaces. \n4.  the perimeter of triangles, \nsquares, and rectangles.</td>
      <td>7. \ndescribe the duration of an event in terms of number of days and/or weeks using a \ncalendar. \n8. \nread and write time in hours and minutes, with a.m. and p.m., using an analog clock. \n9. \nsolve problems involving elapsed time (minutes in an hour, hours in a day, days in a week), \nincluding timetables. \n10. \nidentify and explain the difference between straight and curved lines, and flat and curved \nsurfaces of 3-dimensional objects. \n11. \nidentify and measure the perimeter of a plane figure using appropriate tools.  \n12. \nfind the perimeter of triangles, squares, and rectangles. \n13.  solve problems involving perimeter of triangles, squares, and rectangles.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nrepresent, identify, and order unit fractions and similar fractions with denominators 2, 3, 4, 5, 6, and 8. (NA) \n• \nidentify and work with time measured in hours, half-hours, quarter hours, days, weeks, months, years. (MG) \n• \ndescribe duration of time and elapsed time, and read and write time in hours and minutes. (MG) \n• \ndistinguish between straight and curved lines, and between flat and curved surfaces. (MG) \n• \nfind the perimeter of triangles, squares, and rectangles. (MG)</td>
      <td></td>
      <td></td>
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The table presents educational content standards and learning competencies for Grade 2, specifically tailored for Quarter 4, organized under two main domains: Number and Algebra (NA) and Measurement and Geometry (MG). In the Number and Algebra domain, the focus is on unit fractions and similar fractions with denominators ranging from 2 to 8. Learners are expected to develop skills such as representing and identifying unit fractions, reading and writing these fractions in proper notation, ordering them, as well as representing and identifying similar fractions through various visual aids like fraction charts and number lines. The learning competencies also emphasize the importance of understanding how to compare these fractions, ensuring students can demonstrate their comprehension effectively.

In the Measurement and Geometry domain, the competencies are quite diverse, addressing various mathematical concepts. Students will learn to describe duration of time in terms of days and weeks, as well as read and write time using hours and minutes, incorporating both a.m. and p.m. The curriculum includes distinguishing between straight and curved lines, as well as flat and curved surfaces, enhancing spatial awareness. Furthermore, learners are tasked with measuring and calculating the perimeters of geometric shapes such as triangles, squares, and rectangles, which involves solving practical problems associated with these concepts. The performance standards at the quarter's end indicate that students should be equipped not only with the ability to represent, identify, and order fractions but also with a foundational understanding of time measurement and geometric principles, rounding out their essential skills for progression in mathematics.


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      <th></th>
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      <th>1</th>
      <th>2</th>
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  <tbody>
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      <th>0</th>
      <td>Grade 2</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>1</th>
      <td>Quarter 3</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Data \nand \nProbability  \n(DP)</td>
      <td>1.  a pictograph with a scale for \nthe representation of data.</td>
      <td>1. \npresent raw data, or data in tabular form, in a pictograph with a scale, or vice versa.  \n2. \ninterpret data in tabular form and in a pictograph with or without scale.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Number \nand \nAlgebra</td>
      <td>2.  multiplication and division of \nwhole numbers using the 2, \n3, 4, 5, and 10 multiplication \ntables. \n3.  odd and even numbers.</td>
      <td>3. \ncount the number of concrete objects in a group by repeated addition and create equal \ngroups, using language such as “5 groups of 3” and “5 threes”. \n4. \nillustrate and write multiplication as repeated addition, using a variety of concrete and \npictorial models and numerals, and using  \na. groups of equal quantities, \nb. arrays, \nc. counting by multiples, and \nd. equal jumps on a number line. \n5. \nmultiply numbers using the 2, 3, 4, 5, and 10 multiplication tables. \n6. \nsolve multiplication problems using the 2, 3, 4, 5, and 10 multiplication tables, including \nproblems involving money. \n7. \nillustrate division through equal distribution of a number of objects into several groups. \n8. \nillustrate and write division expressions using a variety of concrete and pictorial models \nand numerals, in modelling division as:  \na. equal sharing or formation of equal groups of objects, and \nb. repeated subtraction. \n9. \ndivide numbers using the 2, 3 4, 5, and 10 multiplication tables.   \n10. \nfind the missing number in a number sentence involving multiplication or division by 2, 3, \n4, 5, and 10.  \n11.  distinguish even and odd numbers using division by 2. \n12.  solve division problems using the 2, 3, 4, 5, and 10 multiplication tables, including \nproblems involving money.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to… \n• \nrepresent and interpret data in a pictograph with a scale. (DP) \n• \nperform multiplication and division of whole numbers using the 2, 3, 4, 5, and 10 multiplication tables. (NA) \n• \ndistinguish even and odd numbers. (NA)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
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The table presented outlines educational content for Grade 2 students within the context of their learning progression for Quarter 3. It is structured with four notable columns, which highlight specific mathematical concepts and related performance standards in a clear and organized manner. The columns are labeled numerically from 0 to 2, with the first row indicating the levels of data grouped accordingly, whereas the first column is utilized for numbering the different sections of the learning material.

In the second row, the subject focus shifts to Data and Probability (DP). Here, the table delineates key learning goals such as a student’s ability to present raw data in pictorial form—a pictograph with a scale—and interpret data in various formats, including tabular form with or without a scale. This lays the groundwork for foundational skills in data representation and analysis that students are expected to develop throughout this quarter.

The table seamlessly transitions into Number and Algebra (NA) within the third section, elucidating objectives related to multiplication and division using whole numbers based on the 2, 3, 4, 5, and 10 multiplication tables. The comprehensiveness of the content reflects a systematic approach where students learn to count objects through repeated addition, illustrate multiplication using diverse models, and solve problems involving both multiplication and division—emphasizing real-life applications, including financial literacy through money-related problems. Additionally, it identifies performance standards for students to achieve by the end of the quarter, such as the ability to represent data in a pictograph, perform basic multiplication and division, and distinguish even and odd numbers. Overall, the table effectively organizes critical learning outcomes that are essential for the mathematical development of Grade 2 learners in a cohesive and structured manner.


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      <td>Grade 2</td>
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      <td>Quarter 2</td>
      <td></td>
      <td></td>
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    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1. \nthe denominations and values \nof Philippine coins and bills \nup to ₱1000, and the addition \nof amounts of money with \nsums up to ₱1000.</td>
      <td>1. \ndetermine and write the value of a number of bills, or a number of coins, or a combination \nof bills and coins up to ₱1000 (centavo coins only, peso coins only, peso bills only, \ncombined peso coins and peso bills). \n2. \ncompare the values of different denominations of peso coins and bills up to ₱1000.  \n3. \nsolve problems involving addition with sums up to 1000, including problems involving \nmoney, with and without regrouping.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>2.  measurement, comparison, \nand estimation of length and \ndistance using appropriate \ntools and units.</td>
      <td>4. \nmeasure and compare lengths of objects, in meters (m) or centimeters (cm), and distance in \nmeters, using appropriate measuring tools. \n5. \nidentify and use the appropriate unit (m or cm) to measure the length of an object and the \ndistance between two locations.  \n6. \nestimate length using meters or centimeters, and distance using meters. \n7. \nsolve problems involving length and distance.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3.  subtraction of numbers where \nboth numbers are less than \n1000. \n4. \nincreasing patterns and \ndecreasing patterns.</td>
      <td>8. \nillustrate subtraction of 2-digit by 1-digit on the number line and as an inverse of addition. \n9. \nsubtract numbers where both numbers are less than 100 with regrouping: \na. 2-digit minus 1-digit numbers, and \nb. 2-digit minus 2-digit numbers. \n10.  solve problems (given orally or in pictures) involving subtraction where both numbers are \nless than 100, with and without regrouping.  \n11.  subtract numbers, where both numbers are less than 1000, with and without regrouping. \n12.  solve 1- and 2-step problems involving subtraction where both numbers are less than 1000 \n(including problems involving money), with and without regrouping. \n13.  determine the next term/s in increasing or decreasing patterns, e.g., numbers, letters and \nrhythmic properties, visual elements in arts, and repetitions. \n14.  create increasing or decreasing patterns.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ndetermine, and compare the value of, combinations of Philippine coins and bills up to ₱1000. (MG) \n• \nperform addition of amounts of money with sums up to ₱1000. (NA) \n• \nmeasure, compare, and estimate, length and distance using appropriate units. (MG) \n• \nperform subtraction of numbers where both numbers are less than 1000. (NA) \n• \nextend existing increasing patterns and decreasing patterns and create new increasing patterns and decreasing patterns. (NA)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The provided table outlines the curriculum for Grade 2 students during Quarter 2, organized into several key subject areas including Number and Algebra (NA), Measurement and Geometry (MG), and a section dedicated to performance standards. Each subject area is subdivided into specific competencies and learning objectives designed to facilitate the development of essential mathematical skills.

In the Number and Algebra (NA) section, students are introduced to the denominations and values of Philippine coins and bills up to ₱1000. They learn to determine and write the value of various combinations of these coins and bills, as well as compare their values. The curriculum also focuses on enhancing their addition skills involving amounts of money with sums up to ₱1000, including problems that necessitate regrouping. Another area covered includes the subtraction of numbers where both numbers are less than 1000, alongside an introduction to patterns, where students can create and identify both increasing and decreasing sequences.

The Measurement and Geometry (MG) section emphasizes measurement, comparison, and estimation of length and distance. This includes specific learning objectives such as measuring and contrasting lengths in meters and centimeters using appropriate tools and units. Students are expected to identify the correct unit of measure for different objects and distances, as well as estimate lengths and distances accurately. Through hands-on activities and problem-solving tasks, the goal is for learners to solidify their understanding of using measurement tools effectively. Additionally, the performance standards set clear expectations for what learners should achieve by the end of the quarter, which encompasses accurate handling of currency, effective measurements, and proficiency in addition and subtraction, ultimately preparing them for more complex mathematical concepts in future lessons.


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      <td>Grade 1</td>
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      <th>1</th>
      <td>Quarter 4</td>
      <td></td>
      <td></td>
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    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1. \nfractions 1\n and 1\n. \n2\n4\n2.  the denominations and \nvalues of Philippine coins \nand bills up to ₱100. \n3.  addition of money where the \nsum is up to ₱100 and \nsubtraction of money where \nboth amounts are less than \n₱100.</td>
      <td>1. \nillustrate 1\n  and 1\n  as parts of a whole.  \n2\n4\n2. \ncompare 1\n  and 1\n  using models. \n2\n4\n3. \ncount halves and quarters \n4. \nrecognize coins (excluding centavo coins) and bills up to ₱100 and their notations. \n5. \ndetermine the value of a number of bills and/or a number of coins (excluding centavo \ncoins) up to ₱100. \n6. \ncompare different denominations of peso coins (excluding centavo coins) and bills up to \n₱100. \n7. \nsolve 1-step problems (given orally or in pictures) involving addition of money where the \nsum is up to ₱100, or subtraction of money where both amounts are less than ₱100.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry  \n(MG)</td>
      <td>4.  the movement of objects in \nhalf turn or quarter turn, in \nclockwise or counter \nclockwise direction. \n5.  time measured in hours, half \nhours, quarter hours, days, \nweeks, months, and years.</td>
      <td>8. \nidentify the position of objects moved in half turn or in quarter turn, in clockwise or in \ncounter-clockwise direction, given an initial facing direction. \n9. \nread and write time by the hour, half hour, and quarter hour using an analog clock. \n10.  give the days of the week and months of the year in the correct order. \n11.  determine the day and month of the year using a calendar. \n12.  solve problems involving time (hour, half hour, quarter hour, days in a week, and months \nin a year).</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nillustrate and compare the fractions 1\n and 1\n. (NA) \n2\n4\n• \nrecognize, and determine the value of, Philippine coins and bills up to ₱100. (NA) \n• \nadd money where the sum is up to ₱100 and subtract money where both amounts are less than ₱100. (NA) \n• \nidentify the position of an object following a half turn or quarter turn, in clockwise or counter-clockwise direction. (MG) \n• \nidentify and work with time measured in hours, half hours, quarter hours, days, weeks, months, and years. (MG)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The table presents a clear and organized overview of the curriculum standards for Grade 1, particularly focusing on the subjects of Number and Algebra (NA) as well as Measurement and Geometry (MG) for Quarter 4. Each row details specific content standards and corresponding learning competencies that aim to equip learners with fundamental mathematical knowledge and skills.

Under the domain of Number and Algebra, the standards include the introduction of fractions, specifically representing 1/2 and 1/4, as well as recognizing and understanding the denominations and values of Philippine coins and bills that total up to ₱100. Learners are expected to engage in practical applications, such as adding and subtracting money, provided that the sums do not exceed ₱100. The competencies designed for the learners encourage them to illustrate fractions as parts of a whole, understand comparative values through models, and to solve one-step monetary problems based on given scenarios, enhancing both their mathematical and real-life problem-solving abilities.

Similarly, the Measurement and Geometry section outlines key learning areas associated with understanding object movement, particularly the concepts of half turns and quarter turns in both clockwise and counter-clockwise directions. Additionally, students are tasked with recognizing and recording time in various formats, including hours, half hours, and quarter hours, alongside an understanding of days, weeks, months, and years. The articulated performance standards at the table's end mandate that by the quarter's conclusion, students should demonstrate proficiency in fractions, money recognition, spatial understanding, and time measurement, resulting in a well-rounded mathematical foundation.


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      <td>Grade 2</td>
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      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners should have \nThe learners … \nDOMAIN \nknowledge and understanding of ...</td>
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      <th>2</th>
      <td>Quarter 1</td>
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      <th>3</th>
      <td></td>
      <td>Measurement \nand \nGeometry  \n(MG)</td>
      <td>1.  circles, half circles, quarter \ncircles and composite figures \nmade up of squares, rectangles, \ntriangles, circles, half circles, \nand quarter circles. \n2.  one step slides and flips of \nbasic shapes and figures.</td>
      <td>1. \nrepresent and describe circles, half circles and quarter circles. \n2. \ncompose and decompose composite figures made up of squares, rectangles, triangles, \ncircles, half circles, and quarter circles, using cut-outs and square grids. \n3. \ndescribe and draw the effect of one-direction multi-step slide (or translation) in basic \nshapes and figures.</td>
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      <th>4</th>
      <td></td>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3.  whole numbers up to 1000. \n4.  ordinal numbers up to 20th. \n5.  addition of numbers with sums \nup to 1000.</td>
      <td>4. \ncount up to 1000. \n5. \nread and write numerals up to 1000. \n6. \nrecognize and represent numbers up to 1000 using a variety of concrete and pictorial \nmodels, and numerals. \n7. \ncount by 2s, 5s, 10s, 20s, 50s, and 100s (not beyond 1000). \n8. \norder numbers up to 1000 from smallest to largest, and vice versa. \n9. \ndescribe the position of objects using ordinal numbers up to 20th. \n10.  determine \na.  the place value of a digit in a 3-digit number, \nb.  the value of a digit, and \nc.  the digit of a number, given its place value. \n11. \nillustrate addition of 2-digit and by 1-digit numbers as “counting up” on the number \nline. \n12.  add numbers with sums up to 1000 in expanded form. \n13.  add numbers with sums up to 1000, with or without regrouping. \n14. \nillustrate and apply the following properties of addition using sums up to 1000: \na. the sum of zero and any number is equal to the number, \nb. changing the order of the addends does not change the sum, and \nc. changing the grouping of the addends does not change the sum.</td>
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The table presents an educational structure outlining the performance standards for Grade 2 students by the end of the first quarter, specifically focusing on their achievements in Mathematics. There are key subject domains highlighted, categorized as Measurement and Geometry (MG) and Number and Algebra (NA), signifying the diverse mathematical skills expected of learners. For Measurement and Geometry (MG), students are required to become proficient in representing and describing circles, half circles, and quarter circles, along with their ability to compose and decompose composite figures that consist of various geometric shapes such as squares, rectangles, triangles, and circles. Additionally, learners should understand the effects of single-step transformations like slides or flips applied to basic shapes and figures.

Within the context of Number and Algebra (NA), the standards specify that students should count, recognize, and represent whole numbers extending up to 1000, as well as utilize ordinal numbers up to the 20th position to articulate arrangements. The skills further extend to performing additions of numbers, ensuring that students can handle sums up to 1000. To achieve these learning milestones, the expectations include the ability to read, write, and represent numerals using a variety of tangible and illustrative models. The educators also emphasize foundational mathematical concepts, such as the place value of digits in three-digit numbers and the principles of addition including the properties of operations that allow flexibility in computation.

Overall, the table is effectively organized to delineate the distinct formats in which students will learn and apply mathematical concepts and operations. This structured approach not only ensures consistency in learning outcomes but also provides a clear roadmap for educators to assess student progress in critical areas of mathematics, aligning with educational goals and performance standards for Grade 2 learners.


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      <td>Grade 3</td>
      <td></td>
      <td></td>
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    <tr>
      <th>1</th>
      <td>Quarter 2</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1.  measures of mass and \ncapacity.</td>
      <td>1. \nmeasure mass in grams (g), kilograms (kg) and/or milligrams (mg), using appropriate \nmeasuring tools. \n2. \nestimate mass of an object using grams, kilograms, and/or milligrams. \n3. \ncompare masses of objects including the use of a balance scale. \n4. \nmeasure capacity in liters (L) and/or milliliters (mL), using appropriate measuring tools. \n5. \nestimate capacity using liters and/or milliliters. \n6. \ncompare capacities of two containers.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Number and \nAlgebra (NA)</td>
      <td>2. \naddition and subtraction of \nnumbers of up to 4 digits and \nmoney up to ₱10 000.</td>
      <td>6. \nread and write money in words and using: \na. Philippine currency symbols (₱ and PhP) up to ₱10 000, and \nb. the centavo sign. \n7. \nadd numbers with sums up to 10 000, with and without regrouping. \n8. \nestimate the sum of addends with up to 4 digits. \n9. \nsolve problems involving addition of numbers with sums up to 10 000, including problems \ninvolving money. \n10.  subtract numbers, where both numbers are less than 10 000, with and without \nregrouping. \n11.  estimate the difference of two numbers of up to 4 digits. \n12.  perform addition and subtraction of 3 to 4 numbers of up to 2 digits, observing correct \norder of operations. \n13.  solve problems involving addition and subtraction with 3 to 4 numbers of up to 2 digits, \nincluding problems involving money.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n•  measure, estimate, and compare mass of objects. (MG) \n•  measure and estimate capacity. (MG) \n• \nadd and subtract whole numbers (including amounts of money) of up to 4 digits. (NA)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
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The content of the table is structured to provide an overview of the Grade 3 curriculum for Quarter 2, detailing the specific areas of focus in Mathematics, particularly in Data and Probability (DP), Measurement and Geometry (MG), and Number and Algebra (NA). It outlines the key concepts and skills that students are expected to learn, and assesses their performance standards by the end of the quarter.

In the Data and Probability section, students are introduced to the collection and presentation of data through tables and single bar graphs, both horizontal and vertical. They will learn to interpret data from these visual aids, solve problems using the represented data, and describe real-life outcomes using specific terminology such as “equally likely” and “impossible.” 

The Number and Algebra segment emphasizes the mastery of multiplication through the 6, 7, 8, and 9 multiplication tables, and also covers important properties of multiplication that students should apply. It includes instructions on multiplying numbers with and without regrouping and techniques for estimating products by rounding numbers to the nearest multiple of ten. Furthermore, students are guided to identify and generate patterns, both repeating and increasing or decreasing, enabling them to solve problems and find missing terms within those patterns. The outlined performance standards ensure that by the end of this quarter, learners will be able to demonstrate proficiency in measuring, estimating, and comparing mass and capacity, as well as performing arithmetic operations involving up to four-digit numbers, including currency.


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      <td>Grade 3</td>
      <td></td>
      <td></td>
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    <tr>
      <th>1</th>
      <td>Quarter 3</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>1. \ndata presented in tables and \nsingle bar graphs. \n2. \noutcomes from experiments \nand real-life situations.</td>
      <td>1. \ncollect data from experiments with a small number of possible outcomes (e.g., rolling a die \nor tossing a coin). \n2. \npresent data in tables and single bar graphs (horizontal and vertical). \n3. \ninterpret data in tables and single bar graphs (horizontal and vertical). \n4. \nsolve problems using data presented in a single bar graph (horizontal and vertical). \n5. \ndescribe and compare outcomes in real-life situations using the following terms: equally \nlikely, less/least likely, more/most likely, certain, and impossible.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3.  multiplication using 6, 7, 8, \nand 9 multiplication tables. \n4. \nproperties of multiplication \n5.   multiplication of numbers \nwith and without regrouping \n6.   estimation of products of two \nnumbers by first rounding to \nthe nearest multiple of 10. \n7. \ndetermination of missing \nterms contained in repeating \nand increasing patterns, and \nrepeating and decreasing \npatterns. \n8. \ngeneration of repeating and \nincreasing patterns, and \nrepeating and decreasing \npatterns.</td>
      <td>6.  multiply numbers using the 6, 7, 8, and 9 multiplication tables. \n7. \nillustrate and apply properties of multiplication for the 6, 7, 8, and 9 multiplication tables: \na. one multiplied by any number is equal to the number;  \nb. zero multiplied by any number is zero; \nc. changing the order of the numbers being multiplied does not change the   product; \nd. changing the grouping of the numbers being multiplied does not change the \n \nproduct; and \ne. multiplying the sum of two addends by a number is the same as the sum of the \nproducts of a number by each addend. \n8.  multiply numbers with and without regrouping: \na.  2- to 3-digit numbers by a 1-digit number, and \nb. 2- to 4-digit numbers by a number whose leading digit is the only non-zero digit, with \nproducts up to 10 000. \n9. \nestimate the product of 2- to 3-digit numbers by 1- to 2-digit numbers by estimating the \nfactors using multiples of 10. \n10.  solve 1-to 2-step multiplication problems, including problems involving money. \n11.  determine the missing term/s in a pattern with repeating and increasing components or \nrepeating and decreasing components (e.g., 1a, 1b, 1c, 2a, 2b, 2c, …). \n12.  explain how to generate a given pattern with repeating and increasing components or \nrepeating and decreasing components.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \npresent and interpret data in tables and single bar graphs. (DP) \n• \ndescribe and compare outcomes of events. (DP) \n•  multiply using 6, 7, 8, and 9 multiplication tables. (NA) \n• \nillustrate and applies properties of multiplication. (NA) \n•  multiply numbers with and without regrouping. (NA) \n• \nestimate products of two numbers by first rounding to the nearest multiple of 10. (NA) \n• \nfind a missing term and generate repeating and increasing patterns, and repeating and decreasing patterns. (NA)</td>
      <td></td>
      <td></td>
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The table presents an overview of the curriculum objectives for Grade 3 students during Quarter 4, specifically focusing on the areas of Number and Algebra (N/A) and Measurement and Geometry (M/G). Under the "Number and Algebra" section, the curriculum outlines several key topics. These include division concepts based on multiplication tables of 6, 7, 8, and 9, as well as the division of 2- to 4-digit numbers. Furthermore, students are expected to estimate quotients by rounding both the divisor and dividend to the nearest multiple of ten. Additional skills involve the addition and subtraction of similar fractions, thereby enhancing their understanding of numerical relationships and operations.

Further elaborating on the division aspect, the curriculum emphasizes the importance of illustrating division through equal jumps on number lines and as an inverse operation to multiplication. Activities are structured to help students find missing numbers in number sentences related to multiplication and division, ensuring they build proficiency with problems that include remainders as well. Specifically, learners are tasked to divide 2- and 3-digit numbers by 1-digit numbers, as well as perform division by powers of ten like 10, 100, and 1000. To consolidate their skills, students are encouraged to apply estimating techniques for quotients and solve division problems, including those set in contexts like financial transactions. Furthermore, students are required to represent and manipulate fractions that are equal to or greater than one using models, and they must be capable of adding and subtracting these fractions.

Transitioning to the "Measurement and Geometry" segment, the curriculum highlights significant geometric concepts such as line symmetry and the effects of translations on figures. Students will explore symmetrical shapes by learning to identify and draw lines of symmetry and manipulating shapes through translations. In terms of performance standards, the curriculum outlines broad expectations for learners by the end of the quarter. They should be able to confidently use multiplication tables for division, estimate quotients, add and subtract similar fractions, and recognize and depict symmetrical figures. This comprehensive approach ensures that students not only grasp mathematical concepts theoretically but also apply them practically, equipping them with essential skills as they progress in their education.


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      <td>Grade 4</td>
      <td></td>
      <td></td>
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    <tr>
      <th>1</th>
      <td>Quarter 3</td>
      <td></td>
      <td></td>
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    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1.  dissimilar and equivalent \nfractions. \n2.  factors and multiples of \nnumbers up to 100. \n3.  addition and subtraction of \ndissimilar fractions.</td>
      <td>1. \nrepresent dissimilar fractions, with denominators up to 10, using models. \n2. \ncompare dissimilar fractions using the symbols =, &gt;, and &lt;. \n3. \norder dissimilar fractions from smallest to largest, and vice versa. \n4. \ngenerate equivalent fractions using models. \n5. \ndetermine equivalent fractions. \n6. \nidentify the multiples of given numbers up to 100. \n7. \nfind all the factors of a given number up to 100. \n8. \nreduce fractions to simplest form. \n9. \nadd and subtract dissimilar fractions using models. \n10.  add and subtract dissimilar fractions:  \na. two proper fractions, \nb. two mixed numbers, \nc. a mixed number and a proper fraction, \nd. a whole number and a proper fraction, and \ne. a whole number and a mixed number. \n11.  solve multi-step problems involving addition and/or subtraction of fractions.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>4.  symmetric figures with respect \nto a line \n5.  resulting images after \napplying reflection with \nrespect to a line.</td>
      <td>12. \nidentify symmetry with respect to a line. \n13.  complete a figure that is symmetric with respect to a line. \n14.  draws the image of an object after applying reflection with respect to a line, including glide \nreflection.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nrepresent, compare, and order dissimilar fractions. (NA) \n• \nfind factors and multiples of numbers up to 100. (NA) \n• \nidentify symmetry with respect to a line, and create figures that have line symmetry. (MG) \n• \nperform reflection with respect to a line, including glide reflection, to obtain images of shapes. (MG)</td>
      <td></td>
      <td></td>
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The table presents a structured overview of the curriculum objectives for Grade 4, specifically detailing the content covered in Quarter 3 with a focus on two major areas: Number and Algebra (NA) and Measurement and Geometry (MG). The table is segmented into five rows, with each row providing distinct information about these subjects. The first two rows indicate both the grade level and the quarter, while the subsequent rows break down the topics and skills associated with each area of mathematics.

In the Number and Algebra (NA) section, the table outlines various competencies for students, such as understanding dissimilar and equivalent fractions, factors and multiples of numbers up to 100, and the addition and subtraction of dissimilar fractions. It further elaborates on the learning objectives, which include representing dissimilar fractions using models, comparing them with relational symbols, ordering them, generating equivalent fractions, and mastering the arithmetic operations involving fractions, including multi-step problem-solving tasks.

The Measurement and Geometry (MG) section highlights concepts related to symmetry and reflection. It specifies objectives like identifying symmetry relative to a line, completing symmetrical figures, and drawing the image of objects after reflection, including glide reflection techniques. Conclusively, the final row encapsulates the expected performance standards for students by the end of the quarter, emphasizing their ability to represent and compare fractions, understand factors and multiples, and perform symmetrical operations. This structured approach ensures a comprehensive framework for assessing and guiding students in their mathematical journey throughout the quarter.


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      <td>Grade 4</td>
      <td></td>
      <td></td>
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      <th>1</th>
      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners should have \nThe learners … \nDOMAIN \nknowledge and understanding of ...</td>
      <td></td>
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    <tr>
      <th>2</th>
      <td>Quarter 1</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1.  measures of angles  \n2.  properties of triangles and \nquadrilaterals. \n3.  perimeter of quadrilaterals, and \ncomposite figures composed of \ntriangles and quadrilaterals.</td>
      <td>1. \nillustrate different angles (right, acute, and obtuse) using models. \n2. \nmeasure and draw angles using a protractor. \n3. \ndraw and state the properties of triangles and quadrilaterals.  \n4. \nclassify triangles and quadrilaterals according to sides and angles. \n5. \ndifferentiate different quadrilaterals. \n6. \nfind the perimeter of quadrilaterals that are not squares or rectangles. \n7. \nfind the perimeter of composite figures composed of triangles and quadrilaterals.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>4.  whole numbers up to  \n1 000 000. \n5.  addition of numbers with sums \nup to 1 000 000 and \nsubtraction of numbers where \nboth numbers are less than  \n1 000 000.</td>
      <td>8. \nread and write numbers up to 1 000 000 in numerals and in words. \n9. \ndetermine \na.  the place value of a digit in a 6-digit number, \nb.  the value of a digit, and \nc.  the digit of number, given its place value. \n10.  compare numbers up to 1 000 000 using =, &lt; and &gt;. \n11. \nround numbers to the nearest hundred thousand. \n12.  estimate the sum and difference of two 5- to 6-digit numbers by rounding the addends to \nthe nearest large place value of the numbers. \n13.  add numbers with sums up to 1 000 000 and subtracts numbers where both numbers \nare less than 1 000 000, with and without regrouping.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nillustrate and measure different angles (MG) \n• \nclassify triangles and quadrilateral, and differentiate quadrilaterals, by applying their properties. (MG) \n• \nfind the perimeter of quadrilaterals and composite figures composed of triangles and quadrilaterals. (MG) \n• \nread, write, and compare whole numbers up to 1 000 000. (NA) \n• \nperforms addition of numbers with sums up to 1 000 000 and subtraction of numbers where both numbers are less than 1 000 000. (NA)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The provided table outlines the curriculum expectations for Grade 4, specifically focusing on the Quarter 2 content within the domains of Number and Algebra (NA) and Measurement and Geometry (MG). The curriculum emphasizes specific content standards and learning competencies that learners should achieve. For the Number and Algebra domain, the key topics revolve around the multiplication of whole numbers (with products up to 1,000,000), division of up to 4-digit numbers by 2-digit numbers, and the application of the MDAS (Multiplication, Division, Addition, Subtraction) rules. It includes objectives for learners to multiply and divide various numbers, estimate products and quotients, solve multi-step problems related to calculations involving money, and represent mathematical situations using number sentences.

In the Measurement and Geometry section, the curriculum encompasses various aspects such as the conversion of units across length, mass, capacity, and time. The specific learning competencies ensure that learners will be able to convert common units of measurement—such as meters to centimeters and kilograms to grams, as well as vice versa—while also addressing time conversions from seconds to hours and minutes to days. Additionally, students are encouraged to solve problems that involve the conversion of these units and the calculation of elapsed time, further reinforcing their understanding of the subject matter.

Lastly, the table also highlights the performance standards that learners should meet by the end of the quarter. It includes competencies in illustrating and measuring angles, classifying and differentiating various geometric shapes, as well as reading, writing, comparing, and performing operations on whole numbers up to 1,000,000. These standards collectively aim to ensure that students not only grasp fundamental mathematical concepts but also apply them practically and in varied contexts.


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      <th>0</th>
      <td>Grade 3</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>1</th>
      <td>Quarter 4</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(N/A)</td>
      <td>1. \ndivision using the 6, 7, 8, \nand 9 multiplication tables. \n2. \ndivision of 2- to 4-digit \nnumbers. \n3. \nestimation of quotients by \nfirst rounding the divisor \nand dividend to the nearest \nmultiple of 10. \n4. \naddition and subtraction of \nsimilar fractions.</td>
      <td>1. \nillustrate division through equal jumps on the number line and as inverse of \nmultiplication. \n2. \ndivide numbers using the 6, 7, 8, and 9 multiplication tables. \n3. \nfind the missing number in a number sentence involving multiplication or division by 6, \n7, 8, and 9 (e.g., __ x 7 = 56; 56 ÷ __ = 7). \n4. \ndivide numbers with and without remainder: \na.  2- to 3-digit numbers by 1-digit number without remainder, \nb. 2-digit numbers by 1-digit number with remainder, and \nc. 2- to 4-digit numbers by 10,100, and 1000. \n5. \nestimate the quotient of 2- to 3-digit numbers divided by 1- to 2-digit numbers, using \nmultiples of 10 or 100 as appropriate \n6. \nsolve division problems involving 2- to 3 -digit numbers by a 1-digit number, including \nproblems involving money. \n7. \nrepresent fractions that are equal to one and greater than one using models. \n8. \nadd and subtract similar fractions using models.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(M/G)</td>
      <td>5. \nline symmetry. \n6. \nresulting figure after a \ntranslation.</td>
      <td>9. \ndescribe and draw the effect of a two-direction multi-step slide (or translation) in basic \nshapes and figures. \n10. \nidentify shapes or figures that show line symmetry by drawing the line of symmetry. \n11.  complete a figure that is symmetric with respect to a line.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nuse the 6, 7, 8, and 9 multiplication tables to divide numbers. (N/A) \n• \ndivide 2- to 4-digit numbers. (N/A) \n• \nestimate quotients by first rounding the divisor and dividend to the nearest multiple of 10. (N/A) \n• \nadd and subtract similar fractions. (N/A) \n• \nidentify a symmetrical shape and draw the line of symmetry. (M/G)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The presented table outlines the curriculum standards and learning competencies for Grade 3, detailing specific content domains and objectives for Quarter 4. It is structured to provide clear distinctions between various subjects, namely Number and Algebra (N/A) and Measurement and Geometry (M/G), along with performance standards that learners are expected to achieve by the end of the quarter.

The first content domain is dedicated to Number and Algebra, where learners are expected to grasp key concepts surrounding division, specifically using the 6, 7, 8, and 9 multiplication tables. The learning competencies in this domain include performing division on 2- to 4-digit numbers, estimating quotients by rounding both the divisor and dividend to the nearest multiples of ten, and engaging in addition and subtraction of similar fractions. The competencies emphasize practical skills such as illustrating division as equal jumps on a number line and solving division problems that may involve remainders, which are crucial for building foundational arithmetic skills.

In the Measurement and Geometry section, key topics include an exploration of line symmetry and the transformation of figures through translation. Learners are encouraged to describe and demonstrate these concepts, including drawing shapes that exhibit line symmetry and understanding multi-step slides of figures. The performance standards encapsulate the expected outcomes for the learners, reflecting their ability to employ multiplication tables for division, round numbers sensibly, and engage with geometric concepts like symmetry. Overall, this table serves a vital role in guiding the educational framework for Grade 3 students, ensuring a comprehensive understanding of essential mathematical principles.


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      <th>1</th>
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      <th>0</th>
      <td>Grade 3</td>
      <td></td>
      <td></td>
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      <th>1</th>
      <td>CONTENT \nDOMAIN</td>
      <td>CONTENT STANDARDS \nThe learners should have knowledge \nand understanding of ...</td>
      <td>LEARNING COMPETENCIES \nThe learners …</td>
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      <th>2</th>
      <td>Quarter 1</td>
      <td></td>
      <td></td>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1. \nareas of squares and \nrectangles. \n2. \npoints, lines, line segments, \nand rays. \n3. \nparallel, perpendicular, and \nintersecting lines.</td>
      <td>1. \nillustrate and estimate the area of a square or rectangle using square tile units. \n2. \nexplore inductively the derivation of the formulas for the areas of a square and a \nrectangle using square tile units.  \n3. \nfind the areas of squares and rectangles in sq. cm and sq. m. \n4. \nsolve problems involving areas of squares and rectangles. \n5. \nrecognize, using models, and draws a point, line, line segment, and ray. \n6. \nrecognize and draw parallel, intersecting, and perpendicular lines. \n7. \nidentify and draw line segments of equal length using a ruler.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>4.  whole numbers up to 10 000. \n5. \nordinal numbers up to 100th.</td>
      <td>8. \nrepresent numbers up to 10 000 using pictorial models and numerals. \n9. \nread and write numbers up to 10 000 in numerals and in words. \n10.  describe the position of objects using ordinal numbers up to 100th. \n11.  determine \na.  the place value of a digit in a 4-digit number, \nb.  the value of a digit, and \nc.  the digit of number, given its place value. \n12. \nround numbers to the nearest ten, hundred, or thousand. \n13.  compare numbers up to 10 000 using the symbols =, &gt;, and &lt;. \n14.  order numbers up to 10 000 from smallest to largest, and vice versa.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ndetermine the area of squares and rectangles. (MG) \n• \nrecognize and draw points, lines, lines segments, rays, and parallel and perpendicular lines. (MG) \n• \nrepresent, round, compare, and order numbers up to 10 000. (NA)</td>
      <td></td>
      <td></td>
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The table outlines the educational framework for Grade 3, particularly focusing on the second quarter’s content in Mathematics, which is divided into two main domains: Measurement and Geometry (MG) and Number and Algebra (NA). Under Measurement and Geometry, the content standards emphasize the importance of understanding measures of mass and capacity. Specific competencies include measuring mass in grams, kilograms, and milligrams with proper tools, estimating the mass of objects, and comparing masses using a balance scale. Students are also expected to measure capacity in liters and milliliters, estimate these values, and compare the capacities of various containers. 

In the Number and Algebra domain, the focus shifts to the addition and subtraction of whole numbers, up to four digits, as well as handling monetary values up to ₱10,000. Competencies include reading and writing monetary amounts in both words and numerical symbols, performing addition and subtraction operations with numbers and monetary amounts, and solving related problems. The learning goals further require learners to estimate sums and differences, perform operations on smaller sets of two-digit numbers, and solve problems involving addition and subtraction that includes 3 to 4 numbers. 

By the end of the quarter, performance standards indicate that learners should be proficient in measuring, estimating, and comparing masses and capacities, as well as adding and subtracting whole numbers and monetary values of up to four digits. This structured approach in the curriculum aims to build essential mathematical skills that are foundational for students' development in mathematics. The table effectively summarizes the alignment between content standards and learning competencies, establishing a comprehensive guide for educators in assessing educational milestones for Grade 3 students.


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      <td>Quarter 2</td>
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      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1.  multiplication of whole \nnumbers with products-up to \n1 000 000, division of up to  \n4-digit numbers by up to  \n2-digit numbers, and the \nMDAS rules.</td>
      <td>1. \nmultiply two numbers with and without regrouping:  \na. 3- to 4-digit numbers by a 1-digit number, and \nb. 2- to 3-digit numbers by 2-digit numbers, with products up to 1 000 000. \n2. \nestimate the result of multiplying two numbers where the product is less than \n1 000 000. \n3. \nsolve multi-step problems involving one or more of the four operations with results of \ncalculations up to 1 000 000, including problems involving money. \n4. \ndivide two numbers with and without regrouping \na.  3- to 4-digit numbers by 1-digit numbers \nb.  2- to 3-digit numbers by 2-digit numbers \n5. \nestimate the quotient when dividing 3- to 4-digit dividends by 1- to 2-digit divisors, by first \nestimating the dividends and divisors using multiples of 10. \n6. \nrepresent situations involving one or more of the four operations using a number sentence. \n7. \nperform two or more different operations by applying the MDAS rules.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>2.  conversion of units of length, \nmass, capacity, and time.</td>
      <td>8. \nconvert common units of measure from larger to smaller units, and vice versa: \na. meter and centimeter, \nb. kilometer and meter, \nc. kilogram and gram, \nd. gram and milligram, and \ne. liter and milliliter. \n9. \nconvert time measures from smaller to larger units, and vice versa: \na. seconds to minutes, \nb. minutes to hours, \nc. hours to days, \nd. days to weeks  \ne. weeks to months, and \nf. months to years. \n10.  solve problems involving conversion of units of length, mass, capacity, and time, including \nproblems involving elapsed time in hours and minutes.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number and \nAlgebra (NA)</td>
      <td>3.  addition and subtraction of \nsimilar fractions, including \nmixed numbers.</td>
      <td>11. \nidentify proper fractions, improper fractions, and mixed numbers. \n12. \nrewrite improper fractions into mixed numbers, and vice versa. \n13. \nplot fraction (proper fractions, improper fractions, and mixed numbers) with denominators \n2, 4, 5, and 10 on the number line. \n14. \nadd and subtract similar fractions: \na. two proper fractions, \nb. two mixed numbers, \nc. a mixed number and a proper fraction, \nd. a whole number and a proper fraction, and \ne. a whole number and a mixed number.</td>
    </tr>
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The table presents a structured overview of the performance standards for Grade 4 learners during Quarter 2, specifically categorized into two main subjects: Number and Algebra (NA) and Measurement and Geometry (MG). Each subject features specific competencies that students are expected to master by the end of the quarter. 

Under the Number and Algebra category, learners will engage with multiplication involving whole numbers with products reaching up to 1,000,000, and will also practice division of up to 4-digit numbers by 2-digit numbers, adhering to the MDAS (Multiplication, Division, Addition, Subtraction) rules. The expectations within this category include multiplication of multi-digit numbers, where students will be required to multiply 3- to 4-digit numbers by 1-digit numbers, and 2- to 3-digit numbers by 2-digit numbers, estimating results effectively. In addition, learners are tasked with multi-step problem-solving that can include financial calculations and division tasks which require regrouping, alongside estimating quotients using multiples of 10. Finally, representing these numerical operations through number sentences and applying the MDAS rules to solve problems are key learning outcomes.

The Measurement and Geometry section emphasizes the conversion of units pertaining to length, mass, capacity, and time. Students are expected to convert common units of measure, for instance, from meters to centimeters and vice versa, and understand conversions of time units from seconds to minutes or minutes to hours. Problems involving these conversions also present a practical dimension where learners will calculate elapsed time in hours and minutes. In the second part of the number and algebra focus, students will explore addition and subtraction of similar fractions and mixed numbers, encompassing an identification of proper, improper fractions, and mixed numbers, as well as transforming between these forms and plotting them on a number line. Key competencies include adding and subtracting similar fractions in various combinations, thereby solidifying the foundational skills of fraction operations during this grade level.


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      <td>Quarter 4</td>
      <td></td>
      <td></td>
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      <th>2</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>1.  presentation and \ninterpretation of data in \ntabular form and in a \nsingle line graph.</td>
      <td>1. \ncollect data with time element using appropriate sources. \n2. \npresent data in a tabular form, or in a single line graph. \n3. \ninterpret data presented in a tabular form, or in a single line graph. \n4. \nsolve problems using data for at most two variables in a tabular form, or in a single line \ngraph.</td>
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    <tr>
      <th>3</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>2.  simple patterns. \n3.  number sentences. \n4.  decimal numbers and \ntheir relationship to \nfractions.</td>
      <td>5. \ndescribe the rule used to generate a given simple pattern. \n6. \ncomplete a number sentence:  \na. to represent a property of operations (e.g., 4 + 3 = 3 + __) (commutative property of addition) \nb. to represent equivalent number facts (e.g., 4 + __ = 6 + 3) \n7. \nrepresent decimal numbers using models and manipulatives to show the relationship to \nfractions. \n8. \nread and write decimal numbers with decimal parts to hundredths. \n9. \ndetermine \na.  the place value to hundredths of a digit in a given decimal number, \nb.  the value of a digit, and \nc.  the digit of number, given its place value. \n10.  convert decimal numbers to fractions, and fractions with denominators 10 or 100 to decimals. \n11.  plot decimal numbers with tenth decimal part on the number line. \n12.  compare and order decimal numbers with decimal parts to hundredths. \n13. \nround decimal numbers to the nearest whole number and to the nearest tenth.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \npresent and interpret data in tabular form and in a single line graph. (DP) \n• \ngenerate a simple pattern and describe the rule used. (NA) \n• \ncomplete number sentences to represent number properties and number facts. (NA) \n• \nrepresent, compare, order, and round decimal numbers. (NA) \n• \nconvert decimal numbers to fractions and fractions (with denominators 10 or 100) to decimals. (NA)</td>
      <td></td>
      <td></td>
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The content presented in the table reflects a structured approach to the learning standards for Grade 4 across various mathematical domains during Quarter 4. The table is organized into four main rows, each focusing on different content areas, demonstrating a clear delineation of learning objectives and competencies for students. The first row is unoccupied in the second and third columns, detailing only the grade level as "Grade 4." This establishes the frame of reference for the educational standards outlined in the subsequent rows.

In the second row, the subject of Data and Probability (DP) is introduced, emphasizing key competencies that students are expected to achieve. These include the ability to collect data over time using appropriate sources, the presentation of data in tabular form or single line graphs, and the interpretation of such data. Additionally, the students are tasked with solving problems using data pertaining to at most two variables. This competency ensures that learners can effectively engage with data representation and understand its implications.

The next row shifts focus to Number and Algebra (NA), outlining additional core concepts that students should master. These concepts encompass simple patterns, number sentences, and the relationship between decimal numbers and fractions. Students are expected to describe rules used to generate simple patterns, complete numerical sentences demonstrating properties of operations, and accurately read, write, and compare decimal numbers. Furthermore, they will learn to convert decimal numbers to fractions and vice versa, round them, and assess their ordering on a number line. The table concludes with a summary of the performance standards for the quarter, encapsulating the objectives of presenting and interpreting data, generating patterns, completing number sentences, and manipulating decimal numbers, thereby setting a comprehensive pathway for students' mathematical proficiency.


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      <td>Quarter 3</td>
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      <td></td>
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      <th>2</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>1. \ndouble bar graphs and double \nline graphs. \n2. \ntheoretical probability.</td>
      <td>1. \ncollects bivariate data from interview, questionnaire, and other appropriate sources. \n2. \nidentify the appropriate graph (bar graph or line graph) to represent a given set of data. \n3. \nconstruct double bar graphs and double line graphs. \n4. \ninterpret data presented in a double bar graph or a double line graph. \n5. \ndraw conclusions or make inferences based on data presented in a double bar graph or a \ndouble line graph. \n6. \nsolve problems using data presented in a double bar graph or a double line graph. \n7. \ndescribe probability as a measure of the chance of an event occurring. \n8. \ncalculate the theoretical probability of a simple event by listing all possible outcomes.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3.  multiplication and division of \ndecimal numbers.</td>
      <td>9. \nestimate each of two decimal numbers to the nearest whole number to estimate their \nproduct. \n10.  multiply decimal numbers with decimal parts of up to 2 decimal places. \n11.  solve multi-step problems involving multiplication of decimals that may or may not also \ninvolve addition or subtraction of decimals, including problems involving money. \n12.  estimate the quotient when dividing two decimal numbers by estimating the dividend and \ndivisor to the nearest whole number. \n13.  divide: \na.  1- to 2-digit whole numbers resulting in a terminating decimal quotient \n \n(e.g., 4 ÷ 5 = 0.8), and \nb.  a decimal of up to 2 decimal places by a 1- to 2-digit whole number, resulting in a \nterminating decimal quotient of up to 3 decimal places.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nidentify, construct, and interpret double bar graphs and double line graphs. (DP) \n• \ndraw conclusions and make inferences from data represented in double bar graphs and double line graphs. (DP) \n• \ncalculate theoretical probability. (DP) \n•  multiply and divide decimal numbers. (NA)</td>
      <td></td>
      <td></td>
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The content presented outlines the curriculum for Grade 5 mathematics, specifically focusing on Quarter 3. The curriculum encompasses two main areas: Data and Probability (DP) and Number and Algebra (NA). Each area includes specific topics and performance standards designed to guide the learning process. 

In the Data and Probability section, students are introduced to key concepts such as double bar graphs and double line graphs, as well as theoretical probability. They are expected to collect bivariate data through various means like interviews and questionnaires, and to identify and construct the appropriate graphs for data representation. Additionally, students will engage in interpreting the data from these graphs, drawing conclusions, and making inferences based on their findings. This understanding of probability is framed as a measure of the likelihood of an event occurring, with tasks including calculating the theoretical probability of simple events by listing all possible outcomes.

The Number and Algebra component focuses on operations involving decimal numbers, specifically multiplication and division. Students will estimate decimal numbers to the nearest whole number in order to simplify calculations, perform multiplication of decimals with up to two decimal places, and tackle multi-step problems that may involve both multiplication and addition or subtraction of decimal values, especially in the context of money. Performance standards for this section also emphasize the skills of dividing whole numbers resulting in decimal outcomes, as well as dividing decimal numbers by whole numbers to produce terminating decimal quotients. Collectively, these topics and performance metrics are designed to equip learners with essential mathematical skills, preparing them for more advanced concepts in future grades.


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      <td>Grade 5</td>
      <td></td>
      <td></td>
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      <th>1</th>
      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners should have knowledge \nThe learners … \nDOMAIN \nand understanding of ...</td>
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      <td></td>
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      <th>2</th>
      <td>Quarter 1</td>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1. \n12- and 24-hour time, and \nworld time zones.</td>
      <td>1. \ndescribe a 12- and 24-hour clock system. \n2. \nconvert 12-hour time to 24-hour time, and vice-versa. \n3. \nsolve problems involving 12- and 24-hour time. \n4. \ncompare the time in different world time zones to the time in the Philippines using a \nworld time zone map. \n5. \nsolve problems on comparing the time in different world time zones to the time in the \nPhilippines.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>2. \nthe GMDAS rules for operations \nwith numbers. \n3.  multiplication of fractions.</td>
      <td>6. \nperform three or more different operations by applying the GMDAS rules. \n7. \nmultiply fractions using models. \n8. \nmultiply a fraction by a fraction. \n9. \nsolve multi-step problems involving multiplication of fractions that may or may not also \ninvolve addition or subtraction of fractions.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>4. \narea of a parallelogram, \ntriangle, and trapezoid.</td>
      <td>10. \nidentify the height of a parallelogram, triangle, and trapezoid, in different orientations. \n11. \nfind the area of a parallelogram, triangle, and trapezoid, in sq. cm or sq. m, using \nformulas. \n12.  estimate the areas of triangles and quadrilaterals (parallelogram, rhombus, trapezoid) \nusing grids.</td>
    </tr>
    <tr>
      <th>6</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nuse 12- and 24- hour time. (MG) \n• \ncompare the time in world time zones with the time in the Philippines. (MG) \n• \nuse the GMDAS rules for 3 or more different operations. (NA) \n•  multiply fractions. (NA) \n• \ndetermine the area of a parallelogram, triangle, and trapezoid. (MG)</td>
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The document presents an overview of Grade 5 mathematics curriculum for Quarter 2, focusing on the domains of Number and Algebra (NA), and Measurement and Geometry (MG). In this quarter, students are expected to deepen their understanding of various mathematical concepts, particularly the division of fractions, handling decimal numbers, and discerning the properties of numbers, including prime and composite classifications. The curriculum outlines specific learning competencies that learners should achieve, which include various operations with fractions and decimals such as division, addition, and subtraction, while also incorporating real-life applications such as financial problems involving decimals.

Within the table, the curriculum is organized into distinct sections representing different quarters, beginning with Quarter 1. Each section details the content standards and elaborate learning competencies, demonstrating a progression of mathematical skills among topics like time conversions, operations involving fractions, and geometric calculations such as the area of shapes. For instance, in Quarter 1's focus on Measurement and Geometry, students explore concepts of time, learning to convert between 12-hour and 24-hour formats, while in the NA section, they are introduced to rules governing operations with numbers, such as the GMDAS rules, and experience the multiplication of fractions. The learning outcomes are clearly stated, emphasizing the essential skills students will acquire by the end of the quarter, which include the ability to utilize time systems effectively, execute various operations involving fractions, and calculate areas of diverse geometric shapes.

Lastly, performance standards are listed, serving as a benchmark for both educators and students to assess mastery of the subject matter by the conclusion of the quarter. Students will be evaluated on their proficiency in using time formats, employing mathematical operations systematically, and determining areas of basic geometrical shapes, thereby ensuring a comprehensive understanding essential for their mathematical development in Grade 5.


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      <td>Quarter 2</td>
      <td></td>
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      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1. \ndivision of fractions. \n2. \ndecimal numbers with decimal \nparts up to ten thousandths. \n3. \naddition and subtraction of \ndecimal numbers. \n4. \ndivisibility rules. \n5. \nprime and composite numbers.</td>
      <td>1. \ndivide fractions using models. \n2. \ndivide a fraction by a fraction. \n3. \nsolve multi-step problems involving division of fractions that may or may not involve the \nother operations with fractions. \n4. \ndetermine \na. \nthe place value to thousandths of a digit in a given decimal number, \nb.  the value of a digit, and \nc. \nthe digit of a number, given its place value. \n5. \nread and write decimal numbers with decimal parts to thousandths. \n6. \nconvert terminating decimals to fractions, and vice versa. \n7. \ncompare and order decimal numbers with decimal parts to thousandths. \n8. \nround decimal numbers to the nearest thousandths. \n9. \nadd and subtract decimal numbers with decimal parts of up to 3 decimal places. \n10.  solve multi-step problems involving addition and/or subtraction of decimals, including \nproblems involving money. \n11.  use divisibility rules to find common factors of numbers: \na. divisibility rules for 2, 5, and 10, \nb. divisibility rules for 3, 6, and 9, and \nc. divisibility rules for 4, 8, 11, and 12. \n12.  distinguish prime numbers from composite numbers using the Sieve of Eratosthenes.</td>
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      <th>3</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ndivide fractions. (NA) \n• \ncompare, order, and round decimals to the nearest one thousandth. (NA) \n• \nadd and subtract decimal numbers. (NA) \n•  use divisibility rules. (NA) \n•  distinguish prime numbers from composite numbers. (NA)</td>
      <td></td>
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The provided table outlines the educational objectives for Grade 5 students during Quarter 2, particularly focusing on the areas of Number and Algebra (NA). The table is structured in a grid format with a header row indicating columns labeled 0, 1, and 2. The first column lists different categories and objectives, with the accompanying cells detailing the specific content to be covered. 

In the second row, the content begins with the topic of Number and Algebra (NA), which encompasses a variety of mathematical concepts including the division of fractions, operations with decimal numbers, addition and subtraction of decimals, divisibility rules, and the differentiation between prime and composite numbers. The objectives are elaborately divided across three main areas where students will learn to perform operations like dividing fractions using models, solving multi-step problems involving these operations, and determining place values up to thousandths in decimal numbers. Furthermore, students will be expected to read and write decimal numbers with precision, convert between fractions and decimals, and apply divisibility rules to find common factors.

The performance standards, positioned in the last row, summarize the learning outcomes expected by the end of the quarter. Students should be proficient in dividing fractions, comparing and ordering decimal numbers, rounding decimals to the nearest thousandth, and utilizing divisibility rules effectively. Additionally, they should have the capability to distinguish prime numbers from composite numbers. This organized information in the table presents a comprehensive overview of the skills students are expected to acquire, ensuring that they develop a strong foundation in mathematical concepts and operations crucial for their academic progression.


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      <td>Grade 6</td>
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      <th>1</th>
      <td>Quarter 2</td>
      <td></td>
      <td></td>
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    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1. \nratio and proportion. \n2. \npercentages, and their \nrelationships with \nfractions and \ndecimals. \n3. \nexponential form, \nincluding calculation \nusing the GEMDAS \nrules.</td>
      <td>1. \ndescribe the relationship between quantities using ratio for: \na. part-whole relationships, and \nb. part-part relationships. \n2. \nexpress one number as a fraction of another given their ratio, and vice versa. \n3. \nidentify and write equivalent ratios. \n4. \nsolve problems involving ratio. \n5. \nillustrate ratio and proportion in given situations using tables and/or the double number line \nmodel. \n6. \nfind how many times one value is larger than another given their ratio, and vice versa. \n7. \nsolve problems involving ratio and proportion. \n8. \nillustrate and explain the relationships between percentages, fractions, and decimals. \n9. \nidentify and explain the uses of percentages. \n10.  write numbers in exponential form e. g., 2 × 2 × 2 = 23, and vice versa \ne.g., 23 = 2 × 2 × 2. \n11. \ngive the value of numbers expressed in exponential form. \n12. \nperform calculations involving numbers in exponential form by applying the GEMDAS rules.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ndescribe and apply the concepts of ratio and proportion. (NA) \n• \nrelate percentages to fractions and decimals. (NA) \n• \nevaluate, and perform calculations with, numbers expressed in exponential form. (NA)</td>
      <td></td>
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</table>


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The table captures essential information regarding the Grade 6 curriculum for Quarter 2, specifically focusing on the Number and Algebra (NA) segment. The first row of the table highlights the grade level as "Grade 6" and notes the quarter as "Quarter 2," establishing the educational timeframe for the content that follows. Subsequent rows delve into the key topics and performance standards associated with the Number and Algebra curriculum. 

The second row outlines the content areas covered in this quarter, which include ratios and proportions, percentages in relation to fractions and decimals, and exponential form. Each topic is mapped to specific learning objectives; for example, learners are expected to describe relationships between quantities using ratios, express one number in terms of another within set ratios, identify equivalent ratios, and solve problems related to these concepts. Furthermore, students are encouraged to illustrate these relationships using visual aids like tables and double number line models. The curriculum also emphasizes understanding percentages and converting between percentages, fractions, and decimals, as well as writing numbers in exponential form and performing calculations that follow the GEMDAS rules.

Finally, the third row outlines the performance standards for the learners by the end of the quarter. It details that students should be able to describe and apply the concepts of ratio and proportion, relate percentages to fractions and decimals effectively, and evaluate and perform various calculations with numbers expressed in exponential form. This structured approach underscores the comprehensive scope of knowledge that learners are expected to acquire, linking foundational mathematical principles to real-world applications.


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      <td>1. \nsolve multi-step problems involving division of decimals that may or may not also involve \nthe other operations with decimals, including problems involving money. \n2. \nperform three or more different operations with fractions and decimals by applying the \nGMDAS rules.</td>
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      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>2. \nprisms and pyramids. \n3. \nsurface area of solid figures. \n4. \ncubes and rectangular prisms. \n5.    resulting image after rotation</td>
      <td>3. \nillustrate different solid figures using concrete and pictorial models. \n4. \nrelate plane figures to solid figures using concrete and pictorial models. \n5. \ndescribe and differentiate prisms and pyramids using their vertices, faces, and/or edges. \n6. \nillustrate and describe solid figures and their nets. \n7. \nmake models of solid figures. \n8. \nillustrate and find the surface area of solid figures. \n9. \nsolve problems involving the surface area of solid figures. \n10.  describe and distinguish cubes and rectangular prisms. \n11.  estimate the volume of a cube and of a rectangular prism using non-standard units of \nmeasurement. \n12.  draw the image of an object after applying rotation about a point given an angle of \nrotation, clockwise or counterclockwise.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \napply the GMDAS rules with operations with fractions and decimals. (NA) \n• \nillustrate and describe solid figures and their nets. (MG) \n• \ndetermine the surface area of solid figures. (MG) \n•  distinguish between cubes and rectangular prisms, and estimate their volumes. (MG) \n• \ndraw the image of an object after applying rotation about a point (MG)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
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The table displays educational content standards and learning competencies for Grade 5, specifically focusing on the subjects of Number and Algebra (NA) and Measurement and Geometry (MG). The content is categorized into two main domains, with clear objectives and outcomes intended for students by the end of the quarter. 

For the Number and Algebra section, it details essential knowledge for students, including the application of the GMDAS rules when performing three or more operations involving fractions and decimals. Learning competencies in this domain emphasize the ability to solve multi-step problems that require division of decimals, as well as the execution of multiple operations with fractions and decimals while adhering to the GMDAS rules. These competencies aim to prepare students for more complex mathematical challenges by fostering problem-solving skills and operational proficiency.

On the other hand, the Measurement and Geometry section outlines key learning components such as understanding prisms and pyramids, calculating surface areas of solid figures, and comprehending the relationship between plane and solid figures. Competencies highlight the importance of using concrete and pictorial models to illustrate solid figures, constructing models, and applying geometric principles like rotation to manipulate and understand shapes. Performance standards underscore the expectations that by the quarter's end, students will not only grasp these concepts but will also able to effectively apply them in various mathematical contexts, signifying a holistic approach to their education in these domains.


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      <td>Grade 6</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>1</th>
      <td>Quarter 3</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1.  units of volume and \ncapacity. \n2.  volume of cubes and \nrectangular prisms. \n3.  perimeter and area of \ntriangles, parallelograms, \ntrapezoids, and composite \nfigures composed of \ntriangles, squares, and \nrectangles. \n4.  parts of a circle, including \ncircumference.</td>
      <td>1. \ndetermine appropriate units for measuring volume and capacity. \n2. \nconvert cu. cm to L, and vice versa. \n3. \nfind the volume of a cube and of a rectangular prism using standard units of measurement. \n4. \nsolve problems involving volumes of cubes and rectangular prisms. \n5. \nsolve problems involving capacity. \n6. \nconvert sq. cm to sq. m, and vice versa. \n7. \nfind the area, in sq. m or sq. cm, of composite figures composed of triangles, squares, and \nrectangles. \n8. \nsolve problems involving the perimeter and area of triangles, parallelograms, trapezoids, and \ncomposite figures composed of triangles, squares, and rectangles. \n9. \ndraw circles with different radii using a pair of compasses. \n10. \nidentify and describes the parts of a circle. \n11.  measure the circumference of circles using appropriate tools. \n12.  approximate the value of pi (𝜋) (the ratio of circumference to diameter). \n13. \nfind the circumference of a circle using 𝐶 = 𝜋𝑑 or 𝐶 = 2𝜋𝑟.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nconvert between units of volume and capacity. (MG) \n• \nfind the volume of cubes and rectangular prisms. (MG) \n• \nfind the perimeter and area of triangles, parallelograms, trapezoids, and composite figures composed of triangles, squares, and rectangles. (MG) \n• \ndescribe the parts of a circle. (MG) \n• \nuse pi (𝜋) to calculate the circumference of a circle. (MG)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The content provided reveals educational standards and competencies for Grade 6 students, focusing on various mathematical concepts and skills to be developed by the end of Quarter 4. The key areas of study include Measurement and Geometry (MG), Data and Probability (DP), and Number and Algebra (NA). For Measurement and Geometry, students are introduced to the area of a circle, as well as composite figures that incorporate triangles, squares, rectangles, circles, and semicircles. The foundational goals for students encompass exploring how the area of a circle can be derived and expressed with the formula \(A = \pi r^2\), finding the area of different composite shapes, and solving problems related to the circumference and area of these figures.

Within the domain of Data and Probability, students are expected to learn about pie graphs. The curriculum emphasizes skills such as determining angle measures and percentages from given data, constructing pie graphs with the appropriate tools, and interpreting both graphically and tabular data. Furthermore, students are encouraged to draw conclusions based on the information derived from pie graphs and to tackle problems using data presented in this particular format. 

The Number and Algebra section focuses on common factors and multiples, including methods for determining the greatest common factor (GCF) and least common multiple (LCM) of two numbers. Students will engage in problem-solving activities that require the application of these concepts utilizing various methods, including listing, prime factorization, and continuous division. By the end of the quarter, the goal is for learners to confidently find areas of circles and composite figures, construct and analyze pie graphs, and identify both common factors and multiples within the framework laid out in the curriculum. This comprehensive approach ensures students have a solid grounding in crucial mathematical concepts that will serve as a foundation for future learning.


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      <td>Grade 7</td>
      <td></td>
      <td></td>
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    <tr>
      <th>1</th>
      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners should have \nThe learners … \nDOMAIN \nknowledge and understanding of ...</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Quarter 1</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand Geometry \n(MG)</td>
      <td>1. \nregular and irregular \npolygons and their \nfeatures/properties. \n2. \ndetermination of measures of \nangles and number of sides of \npolygons.</td>
      <td>1. \ndraw and describe regular and irregular polygons with 5, 6, 8, or 10 sides, based on \nmeasurements of sides and angles, using a ruler and protractor. \n2. \ndraw triangles, quadrilaterals, and regular polygons (5, 6, 8, or 10 sides) with given \nangle measures. \n3. \ndescribe and explain the relationships between angle pairs based on their measures. \n4. \nclassify polygons according to the number of sides, whether they are regular or irregular, \nand whether they are convex or non-convex.  \n5. \ndeduce the relationship between the exterior angle and adjacent interior angle of a \npolygon. \n6. \ndetermine the measures of angles and the number of sides of polygons.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3. \napplication of percentages. \n4. \nuse of rates. \n5. \nrational numbers.</td>
      <td>7. \nsolve problems involving: \na. percentage increase, and \nb. percentage decrease. \n8. \nsolve money problems involving percentages (e. g., discount, commission, sales tax, \nsimple interest). \n9. \ncreate a financial plan. \n10. \nidentify and explain the uses of rates. \n11.  solve problems involving rates (e.g., speed). \n12.  describe given rational numbers as fractions, decimals, or percentages. \n13.  order rational numbers on a number line. \n14.  perform operations on rational numbers.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ndraw, and describe the features/properties of, regular and irregular polygons. (MG) \n• \nuse percentages in different contexts. (NA) \n• \nidentify and use rates. (NA) \n• \ncreate a financial plan. (NA) \n• \ndescribe, order, and perform operations on, rational numbers. (NA)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
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The content outlined in the table pertains to the Grade 7 curriculum for Quarter 2, specifically focusing on Number and Algebra (NA) and Measurement and Geometry (MG). The table is structured with headers indicating different categories including the subject areas, content standards, and learning competencies that students are expected to achieve by the end of the quarter. The first row of the table presents the grade level, which is Grade 7, while each subsequent row delineates the content, performance standards, and essential learning competencies within the specified domains of Number and Algebra and Measurement and Geometry.

For Measurement and Geometry (MG), the curriculum includes concepts such as the conversion of units of measure and the calculation of volumes of geometric shapes, namely square and rectangular pyramids and cylinders. More specifically, students are expected to convert units of measure within the International System of Units (SI) and between different measurement systems, as well as to explain the volume of a cylinder through inductive reasoning, ultimately leading to the identification of its formula. Students will also find the volume of cylinders and solve related problems, similarly exploring the volumes of pyramids, estimating their dimensions, and addressing practical problems involving these shapes.

In the realm of Number and Algebra (NA), the curriculum encompasses the understanding of square roots of perfect squares and cube roots of perfect cubes, along with the identification and placement of irrational numbers on a number line. Students will delve into sets and subsets, exploring the union and intersection of sets through Venn diagrams. The performance standards indicate that students should be able to perform tasks such as determining square roots and cube roots, converting units of measure, calculating volumes of geometric shapes, and illustrating mathematical concepts using sets, thereby enabling a comprehensive understanding of these mathematical principles by the conclusion of Quarter 2.


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      <td>Grade 7</td>
      <td></td>
      <td></td>
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      <th>1</th>
      <td>Quarter 4</td>
      <td></td>
      <td></td>
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    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>the solution of simple \n1. \nequations. \nthe evaluation of algebraic \n2. \nexpressions following \nsubstitution. \n3. \nthe rearrangement of a \nformula to make a different \nvariable the subject of the \nformula.</td>
      <td>1. \nsolve simple equations represented by bar models to find unknowns. \n2. \ndistinguish a variable from a constant in an algebraic expression. \n3. \nevaluate algebraic expressions given the value/s of the variable/s. \n4. \ntranslate verbal phrases into algebraic expressions. \n5. \nillustrate the properties of equality. \n6. \nsolve one variable in terms of the other variables in a formula. \n7. \nwrite equations in algebraic form. \n8. \nfind the value of an unknown in an equation where the unknown is non-negative. \n9. \nsolve problems involving algebraic expressions and formulas</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>4. \noutcomes from experiments.</td>
      <td>10.  collect data from experiments (e.g., number of heads obtained when tossing a coin, a \nnumber of times, number of prime numbers obtained when rolling a die a number of \ntimes). \n11.  express outcomes in words and/or symbols, and represents outcomes in tables and/or \ngraphs. \n12.  solve problems using the outcomes of experiments.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>5. \noperations using scientific \nnotation.</td>
      <td>11.  write numbers in scientific notation to represent very large or very small numbers, and \nvice versa. \n12.  perform operations on numbers expressed in scientific notation.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nsolve simple equations. (NA) \n• \nsubstitute into an algebraic expression to evaluate the expression. (NA) \n• \nrearrange a formula to make a different variable the subject of the formula. (NA) \n• \ngather data from experiments and represent the data in different forms. (DP) \n•  write numbers in scientific notation and perform operations on numbers written in scientific notation. (NA)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The table presented is a structured overview of the content standards and learning competencies for Grade 7 students, specifically focusing on the domains of Number and Algebra (NA) and Data and Probability (DP) for Quarter 4. In the first column, the relevant grades and quarters are identified, establishing a clear context for the educational standards being addressed. For instance, the content specifically addresses students' understanding of simple equations, algebraic expressions, and the rearrangement of formulas in the NA domain, while highlights in DP include the outcomes of experiments and the skills necessary for data collection and representation.

Under the Number and Algebra section, learners are expected to grasp several key concepts, which include solving simple equations, evaluating algebraic expressions following substitutions, and distinguishing between variables and constants within these expressions. The competencies further extend to translating verbal phrases into algebraic forms, demonstrating the properties of equality, and solving for unknown variables within mathematical formulas. This comprehensive framework sets forth clear expectations for learners, ensuring they develop essential algebraic skills crucial for their academic journey.

In the Data and Probability domain, students are taught to analyze outcomes from various experiments, such as tossing a coin or rolling a die. They are required to collect and express data from these activities both verbally and symbolically. Additionally, the importance of representing outcomes in tables or graphs is emphasized, concluded with an expectation for students to solve problems drawn from experimental outcomes. The performance standards at the end of the table summarize the intended competencies by the end of the quarter, showcasing a blend of algebraic skills and practical data handling, crucial for the holistic educational development of students in this grade level.


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      <th>0</th>
      <td>Grade 6</td>
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      <td></td>
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      <th>1</th>
      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners should have knowledge \nThe learners … \nDOMAIN \nand understanding of...</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>2</th>
      <td>Quarter 1</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1.  tessellation of shapes. \n2. translation, reflection and \nrotation with shapes</td>
      <td>1. \nexplore whether or not a shape tessellates. \n2. \ntessellate a surface using different shapes, including triangles, squares, and rectangles. \n3. \ndraw resulting images of shapes that undergo translation, reflection, rotation</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>2.  the four operations with \ndecimals. \n3.  the four operations with different \ncombinations of fractions, whole \nnumbers, and mixed numbers.</td>
      <td>4. \nadd and subtract decimals with decimal parts of up to 4 decimal places. \n5. \nsolve multi-step problems involving addition and/or subtraction of decimals, including \nproblems involving money. \n6.  mentally multiply decimals of up to 2 decimal places by 0.1, 0.01, 0.001, 10, 100, and \n1000. \n7. \nsolve multi-step problems involving multiplication of decimals that may or may not also \ninvolve addition or subtraction of decimals, including problems involving money. \n8. \ndivide: \na. 1- to 2-digit whole numbers resulting in a repeating (non-terminating) decimal \n \nquotient. (e. g., 1\n= 0.3333 … ), and \n3\nb. a whole number by a decimal of 1 decimal place. \n9.  mentally divide:  \na. decimals of up to 4 decimal places by 0.1, 0.01, and 0.001, and \nb. decimals of up to 2 decimal places by 10, 100, and 1000. \n10.  solve problems involving division of decimals that may or may not involve the other \noperations with decimals and/or whole numbers. \n11.  obtain products that result from multiplying different combinations of fractions, whole \nnumbers, and mixed numbers. \n12.  solve multi-step problems involving multiplication that may or may not involve addition or \nsubtraction of different combinations of fractions, whole numbers, and mixed numbers. \n13.  divide different combinations of fractions, whole numbers, and mixed numbers.  \n14.  solve multi-step problems involving division of different combinations of fractions, whole \nnumbers, and mixed numbers that may or may not involve any of the other operations of \nfractions.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ntessellate a surface using different shapes. (MG) \n• \nperform the four operations with decimals. (NA) \n• \nperform the four operations with different combinations of fractions, whole numbers, and mixed numbers. (NA)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The table details the curriculum structure for Grade 6 as it pertains to Mathematics, specifically focusing on content standards and learning competencies associated with Quarter 2. The subjects are organized under the domains of Number and Algebra (NA), with an emphasis on key topics such as ratios, proportions, and their interrelationships with percentages, fractions, and decimals. The first column identifies the content and learning objectives, listing essential skills that learners are expected to develop. This includes the ability to describe relationships using ratios, solve problems involving these concepts, and understand the equivalence and manipulation of ratios. 

In conjunction with ratios and proportions, the curriculum also covers the topic of percentages, examining how they are related to fractions and decimals. Students are expected to explain these relationships and recognize their applications in real-world contexts. The table further outlines the expectation for learners to grasp the concept of exponential form, including the ability to write numbers in this format and perform calculations following the GEMDAS rules. 

The performance standards highlight the competencies learners should achieve by the end of the quarter. This includes not only a demonstration of mathematical understanding concerning ratios and their application, but also proficiency in evaluating and calculating with numbers in exponential form. The comprehensive nature of the table indicates that the curriculum is designed to reinforce foundational mathematical concepts through practical application and problem-solving, ensuring that students build a strong mathematical foundation as they progress through their studies.


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      <th>0</th>
      <td>Grade 8</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>1</th>
      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners demonstrate knowledge \nThe learners… \nDOMAIN \nand understanding of...</td>
      <td></td>
      <td></td>
    </tr>
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      <th>2</th>
      <td>Quarter 1</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>3</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>1.  measures of central tendency of \nungrouped data.</td>
      <td>1. \ndetermine measures of central tendency of ungrouped data. \n2. \ndraw conclusions from statistical data using the measures of central tendency.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>2.  algebraic expressions and \noperations with monomials, \nbinomials, and multinomials. \n3,  special products for binomials, \nand factorization of polynomials. \n4.  rational algebraic expressions and \nequations. \n5.  rules for obtaining terms in \nsequences.</td>
      <td>3. \nmodel real-life situations using algebraic expressions. \n4. \nadd and subtract simple monomials. \n5. \nmultiply and divide simple monomials, leading to the derivation of the laws of exponents. \n6. \nmultiply simple monomials and binomials with simple binomials and multinomials, using \nthe distributive property with various techniques and models. \n7. \nuse special product patterns to multiply binomials. \n8. \ncompletely factor different types of polynomials (polynomials with common monomial \nfactor; difference of two squares; quadratic trinomials, including perfect square trinomials). \n9. \nsolve problems involving special products and factors of polynomials. \n10.  simplify rational algebraic expressions. \n11.  perform operations on rational algebraic expressions. \n12.  solve problems involving simple rational algebraic equations (using cross-multiplication). \n13. \nformulate the rule for finding the next term in a sequence by looking for patterns.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ndetermine measures of central tendency of ungrouped data and use the measures to draw conclusions. (DP) \n• \nadd and subtract monomials, and multiply combinations of monomials, binomials, and multinomials. (NA) \n• \nobtain special binomial products. (NA) \n• \nfactorize different types of polynomials. (NA) \n• \nsimplify, and operate with, rational algebraic expressions and solve simple rational algebraic equations. (NA) \n• \nobtain the rule for finding the next term in a sequence. (NA)</td>
      <td></td>
      <td></td>
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The provided material outlines the curriculum framework for Grade 8, focusing on Quarter 1 subjects, which include Data and Probability (DP) and Number and Algebra (NA). The first section of the table elaborates on the primary content areas and the associated content standards. Under Data and Probability, students engage with measures of central tendency concerning ungrouped data, aiming to determine these measures and draw conclusions from statistical data. This foundational understanding of data analysis is crucial for interpreting and presenting data effectively.

Moving to the domain of Number and Algebra, the table delineates numerous learning competencies that the learners are expected to master. Students will explore algebraic expressions and operations, starting with monomials and advancing to binomials and multinomials. Significant emphasis is placed on grasping special products for binomials and the factorization of polynomials, alongside rational algebraic expressions and equations. Additionally, it includes rules for identifying terms in sequences, which reinforces pattern recognition and analytical skills. The learning outcomes also specify that by the end of the quarter, students should be proficient in multiple algebraic operations, including addition, subtraction, multiplication of different algebraic forms, simplification of rational expressions, and problem-solving involving rational equations.

The final entry in the table discusses performance standards, categorically summarizing the learning objectives for the quarter. By culmination, students should be capable of determining measures of central tendency, conducting various arithmetic operations with monomials, and factorizing polynomials effectively. Such competencies not only fulfill the educational standards but also provide learners with essential skills that extend beyond classroom learning, preparing them for practical applications in real-life situations involving mathematical reasoning and problem-solving.


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      <td>Grade 7</td>
      <td></td>
      <td></td>
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      <th>1</th>
      <td>Quarter 2</td>
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      <td></td>
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      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1. \nsquare roots of perfect \nsquares, cube roots of perfect \ncubes, and irrational \nnumbers.</td>
      <td>1. \ndetermine the square roots of perfect squares and the cube roots of perfect cubes. \n2. \nidentify irrational numbers involving square roots and cube roots, and their locations on \nthe number line.</td>
    </tr>
    <tr>
      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>2. \nconversion of units of \nmeasure. \n3. \nvolume of square and \nrectangular pyramids, and \ncylinders.</td>
      <td>3. \nconvert units of measure within the International System of Units (SI) and across \ndifferent systems of measure. \n4. \nexplain inductively the volume of a cylinder using the area of a circle, leading to the \nidentification of the formula. \n5. \nfind the volume of a cylinder. \n6. \nsolve problems involving the volumes of cylinders. \n7. \nexplore inductively the volume of square and rectangular pyramids using rectangular \nprisms, leading to the identification of the formula. \n8. \nestimate volumes of square and rectangular pyramids.  \n9. \nsolve problems involving volumes of square or rectangular pyramids.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>4. \nsets and subsets, and the \nunion and intersection of sets \nusing Venn diagrams \n5. \nsubset of real numbers.</td>
      <td>10.  describe sets and their subsets, the union of sets, and the intersection of sets  \n11. \nillustrate sets and their subsets, the union of sets, and the intersection of sets, through \nthe use of Venn diagrams. \n12. \nillustrate the different subsets of real numbers.</td>
    </tr>
    <tr>
      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n•  determine square roots of perfect squares and cube roots of perfect cubes, and identify irrational numbers. (NA) \n• \nconvert units of measure from different systems of measure. (MG) \n• \nfind the volume of square and rectangular pyramids, and the volume of cylinders. (MG) \n•  describe sets and their subsets, and the union and intersection of sets. (NA) \n• \nillustrates sets and subsets, and union and intersection of sets, using Venn diagrams. (NA)</td>
      <td></td>
      <td></td>
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  </tbody>
</table>


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The provided table outlines the educational objectives and performance standards for Grade 7 students, particularly focusing on various domains such as Number and Algebra (NA), Measurement and Geometry (MG), as well as Data and Probability (DP) for Quarter 2. It spans five rows, each categorized by different mathematical themes, specifically detailing concepts the learners are expected to grasp by the end of the quarter.

The first row introduces the section header for the table, indicating it pertains to Grade 7, Quarter 2. Following this, the second row specifies the focus on Number and Algebra (NA), detailing key topics such as square roots of perfect squares, cube roots of perfect cubes, and the identification of irrational numbers. In addition, the expected competencies include determining square roots and cube roots, and understanding the placement of irrational numbers on the number line.

Continuing, the third row shifts to Measurement and Geometry (MG), highlighting aspects such as the conversion of measurement units and calculating the volume of square and rectangular pyramids, along with cylinders. Learners will be required to convert units of measure from the International System of Units (SI) and solve problems involving volumes, developing both theoretical understanding and practical application of these concepts. Furthermore, the fourth row revisits Number and Algebra (NA), delving into sets and subsets, with a focus on the union and intersection of sets as visualized through Venn diagrams. Lastly, the performance standards presented in the fifth row summarize the anticipated outcomes, including competencies in determining square and cube roots, unit conversion, and proficiency in illustrating set concepts through Venn diagrams, thereby encompassing a well-rounded mathematical curriculum for the learners.


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      <td>Grade 6</td>
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      <th>1</th>
      <td>Quarter 4 \nMeasurement \n1. \narea of a circle \n1. \nexplore inductively the area of a circle leading to the formula 𝐴 = 𝜋𝑟2. \nand \n2. \nfind the area of a circle using the formula. \n2. \ncomposite figures \nGeometry \n3. \nfind the area of composite figures composed of any two or more of the following: triangle, square, \ncomposed of any two or \n(MG) \nrectangle, circle, and semicircle. \nmore of: triangle, square, \n4. \nsolve problems involving circumference and area of circles, and composite figures. \nrectangle, circle, semi-\ncircle.</td>
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      <th>2</th>
      <td>Data \n5. \nfind the angle measures and/or percentages based on the given data for a pie graph. \n3. \npie graphs. \nand \n6. \nconstruct a pie graph using appropriate tools. \nProbability \n7. \ninterpret data presented in a pie graph. \n(DP) \n8. \ninterpret data from digital media that are presented in tabular or graphical form. \n9. \ndraw conclusions or make inferences based on data presented in a pie graph. \n10.  solve problems using data presented in a pie graph.</td>
      <td></td>
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      <th>3</th>
      <td>Number \n4. \ncommon factors, \n11.  determine the common factors and the greatest common factor (GCF) of two numbers using the \nand \ngreatest common \nfollowing methods: listing, prime factorization, and continuous division. \nAlgebra \nfactors, common \n12.  find the common multiples and least common multiple (LCM) of two numbers using the following \n(NA) \nmultiples, and least \nmethods: listing, prime factorization, and continuous division. \ncommon multiples. \n13.  solve problems involving GCF and LCM.</td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nfind the area of a circle. (MG) \n• \nfind the area of composite figures composed of any two or more of: triangle, square, rectangle, circle, semi-circle. (MG) \n• \nconstruct and interpret pie graphs. (DP) \n• \nfind common factors, greatest common factors, common multiples, and least common multiples. (NA)</td>
      <td></td>
      <td></td>
    </tr>
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The table outlines the curricular content and performance standards for Grade 6 across various mathematical domains. The first row serves as the header, distinguishing between the different categories but lacks specific entries in the columns labeled 0, 1, and 2, which appear to be placeholders. Each subsequent row corresponds to a different learning area marked by the first column.

The first substantive row focuses on the Measurement domain for Quarter 4, particularly the exploration of the area of a circle. It highlights the need for students to engage inductively with the formula \( A = \pi r^2 \) and to apply this understanding in calculations involving circles and composite figures, which may include various shapes like triangles, squares, rectangles, and semicircles. Additionally, learners are tasked with solving problems associated with both the circumference and the area of these figures, showcasing a comprehensive approach to geometry.

Moving to the second row, the focus shifts to Data and Probability. Here, the standards emphasize the interpretation and analysis of data through the construction and use of pie graphs. Students must find angle measures and percentages from provided data, create pie graphs, and interpret data presented in both graphical and tabular forms. They are also expected to draw conclusions and make inferences based on their findings, emphasizing critical thinking skills in data representation.

The third row addresses Number and Algebra, concentrating on the understanding of common factors and multiples. It details the methods through which students should determine the greatest common factor (GCF) and least common multiple (LCM) of two numbers via listing, prime factorization, and continuous division. These skills are not only fundamental to algebraic concepts but also integral for solving related mathematical problems.

Finally, the Performance Standards summarize the key competencies learners should achieve by the end of the quarter. These include calculating the area of a circle and composite figures, constructing and interpreting pie graphs, and identifying common factors and multiples, ensuring a well-rounded mathematical foundation for the students.


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      <td>Grade 7</td>
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      <td>Quarter 3</td>
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      <td>Data \nand \nProbability \n(DP)</td>
      <td>1.  data collection and sampling \ntechniques, and the \npresentation of data in \nappropriate tables and graphs. \n2. \ninterpretation of statistical \ngraphs.</td>
      <td>1. \ninvestigate different data collection and sampling techniques. \n2. \norganize statistical data in a frequency distribution table. \n3. \nuse appropriate graphs to represent organized data: pie graph, bar graph, line graph, \nand stem-and-leaf plot. \n4. \ninterpret statistical graphs.</td>
    </tr>
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      <th>3</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3. \nthe set of integers, and \ncomparing and ordering \nintegers. \n4. \nthe four operations with \nintegers. \n5. \nsimplification of numerical \nexpressions involving integers. \n6.  absolute value of an integer.</td>
      <td>5. \ndescribe the set of integers. \n6. \nuse positive and negative numbers to describe directions or opposites in real-life \nsituations. \n7. \nlocate integers on the number line. \n8. \ncompare and order integers. \n9. \nadd and subtract integers; using concrete models (e.g., counters, integer chips), pictorial \nmodels (e.g., bar models, number lines), and with integers written as numerals. \n10.  multiply and divide integers. \n11.  simplify numerical expressions involving integers using number properties and the order \nof operations (GEMDAS). \n12. \nidentify the absolute value of an integer, and its meaning on the number line.</td>
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      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ncollect data, and organize data in a frequency distribution table. (DP) \n• \nrepresent and interpret data in different types of graphs. (DP) \n• \ncompare and order integers, including through the use of the number line. (NA) \n• \nperform the four operations with integers. (NA) \n• \nsimplify numerical expressions involving integers. (NA) \n• \nidentify the absolute value of an integer. (NA)</td>
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The table outlines the curriculum for Grade 7, specifically focusing on content for Quarter 3, categorized into two main subjects: Data and Probability (DP) and Number and Algebra (NA). It is organized in a grid format, where the first column labels the row with sequential identifiers, while the subsequent columns detail the subject areas and the specific topics covered within them. For instance, under the section for Data and Probability, students are introduced to data collection and sampling techniques, and the importance of presenting data using appropriate tables and graphs. Further emphasis is placed on the interpretation of statistical graphs, which lays a foundation for skills such as organizing data into frequency distribution tables and representing that data through various types of graphs, such as pie graphs, bar graphs, line graphs, and stem-and-leaf plots.

In the section dedicated to Number and Algebra, several core topics are outlined, including the understanding of the set of integers, the operations involving integers, simplification of numerical expressions, and the concept of absolute value. Students are expected to gain proficiency in comparing and ordering integers, applying both concrete and pictorial models to facilitate comprehension of addition, subtraction, multiplication, and division of integers. The curriculum also emphasizes the importance of simplifying numerical expressions using properties and established order of operations, referred to as GEMDAS. 

As a culmination of the instructional content, the performance standards at the end of the table encapsulate the expected learning outcomes for students by the end of the quarter. These standards affirm that learners should be capable of collecting data and organizing it into frequency distribution tables as part of the Data and Probability section. They should also proficiently represent and interpret data using different types of graphs. In the context of Number and Algebra, skills required include comparing and ordering integers, executing the four fundamental operations with them, as well as simplifying numerical expressions and identifying the absolute value. This organized approach ensures that students not only acquire essential mathematical skills but also understand their practical applications in real-world situations.


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      <td>Grade 8</td>
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      <th>1</th>
      <td>Quarter 2</td>
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      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1. \nplotting points, and finding \ndistance and the midpoint of \nline segments on the Cartesian \ncoordinate plane.</td>
      <td>1. \nillustrate and describe the Cartesian coordinate plane. \n2. \nplot points on the Cartesian coordinate plane and determine the coordinates of a point \non the plane. \n3. \nsolve problems involving distance between two points and midpoint of a line segment on \nthe Cartesian coordinate plane.</td>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>2. \nvolume of pyramids (other than \nsquare and rectangular \npyramids), cones, and spheres. \n3. \nthe Pythagorean Theorem. \n4. \ntriangle inequality theorems.</td>
      <td>4. \nexplore inductively the volume of pyramids other than square and rectangular pyramids. \n5. \nfind the volume of pyramids other than square and rectangular pyramids. \n6. \nsolve problems involving volume of pyramids. \n7. \nexplore inductively the volumes of cones and spheres, leading to their formulas. \n8. \nfind the volumes of cones and spheres. \n9. \nsolve problems involving the volume of cones and spheres. \n10. \napply the Pythagorean Theorem in finding the missing side of a right triangle, and its \nconverse in classifying triangles. \n11. \napply the triangle inequality theorems to establish results for angles and sides in \ntriangles.</td>
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      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>5. \nearning money, profit and loss, \n‘best buys’, buying on terms.</td>
      <td>12. \nsolve financial problems involving: \na. \nearning money, \nb.  profit and loss, \nc. \nbuying amounts of products that represent the best value (‘best buys’), and \nd.  buying on terms (‘instalment plan’).</td>
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      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nplot points, find the distance between two points, and find the midpoint of line segments, on the Cartesian coordinate plane. (NA) \n• \nfinds the volume of pyramids other than square and rectangular pyramids, and the volumes of cones and spheres. (MG) \n• \nuse the Pythagorean theorem to find sides in right triangles and its converse to classify triangles. (MG) \n• \nuse the triangle inequality theorems to establish results for angles and sides in triangles. (MG) \n• \nsolve financial problems involving earning money, profit and loss, “best buys,” and buying on terms. (NA)</td>
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The table presents an extensive overview of the learning objectives and performance standards for Grade 8 students during Quarter 2, focusing on key areas of study within Number and Algebra (NA) and Measurement and Geometry (MG). The first row establishes the context, denoting the grade and the quarter being examined. In the succeeding rows, the curriculum is divided into different subject areas. For instance, in the Number and Algebra section, students are introduced to concepts such as plotting points and determining distances and midpoints in the Cartesian coordinate plane, which establishes foundational skills in geometry. They are also tasked with solving problems that involve these concepts, thereby emphasizing practical applications of theoretical understanding.

Moreover, the Measurement and Geometry section details various mathematical concepts, including the volume of non-standard pyramids, cones, and spheres, as well as significant theorems like the Pythagorean Theorem and triangle inequality theorems. These topics not only enrich students’ understanding of geometric principles but also challenge them to apply these principles in problem-solving contexts. Alongside these specific learning objectives, the table outlines the performance standards expected by the end of the quarter. It signifies that learners should be proficient in tasks such as plotting points, calculating distances, and solving complex geometric inquiries while also being capable of applying financial mathematics concepts, including profit and loss as well as best buying strategies.

The final row consolidates the performance standards, succinctly summarizing what students are expected to achieve across both subjects. It reinforces significant mathematical competencies, ensuring learners are equipped not only with knowledge but also with practical skills necessary for future academic endeavors. The carefully structured format of the table allows for a clear understanding of the educational aims set forth for Grade 8 students, reflecting a comprehensive curriculum design that balances concept mastery with practical problem-solving.


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      <td>Grade 8</td>
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      <td>Quarter 3</td>
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      <td>Number \nand \nAlgebra  \n(NA)</td>
      <td>1.  linear equations in one \nvariable. \n2.  linear inequalities in one \nvariable and their \ngraphs. \n3.  linear equations in two \nvariables and their \ngraphs. \n4.  systems of linear \nequations in two \nvariables. \n5.  linear inequalities in two \nvariables.</td>
      <td>1. \nsolve linear equations in one variable. \n2. \nsolve problems (e.g., number problems, geometry problems, and money problems) involving linear \nequations in one variable. \n3. \nsolve linear inequalities in one variable. \n4. \ngraph on a number line the solution of linear inequalities in one variable. \n5. \nsolve problems involving linear inequalities in one variable. \n6. \ndescribe a linear equation in two variables and express its solution using ordered pairs. \n7. \ndefine and determine the slope and intercepts of a line. \n8. \nfind the equation of a line given:  \na. two points, \nb. the slope and a point, \nc. the slope and y-intercept, and \nd. the x– and y– intercepts. \n9. \nsketch the graph (straight line) of a linear equation given:  \na. any two points on the line, \nb. the x– and y– intercepts, and \nc. the slope and a point on the line. \n10.  define and illustrate a system of linear equations in two variables. \n11.  solve a system of linear equations (with integer solutions) by graphing. \n12.  classify the types of systems of linear equations based on the number of solutions. \n13.  solve algebraically a system of linear equations in two variables. \n14.  solve problems involving systems of linear equations in two variables. \n15.  recognize and solve problems involving linear inequalities in two variables.</td>
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      <th>3</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nsolve linear equations and linear inequalities in one variable. (NA) \n• \ngraph linear inequalities in one variable. (NA) \n• \ngraph linear equations in two variables. (NA) \n• \nsolve a system of linear equations graphically and algebraically. (NA) \n• \nuse linear inequalities in two variables in the solution of problems. (NA)</td>
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The table presented on Page 56 of the Mathematics CG 2023 document outlines the curriculum for Grade 8 in Quarter 3, specifically focusing on the topic of Number and Algebra (NA). The first row identifies the grade level, indicating that it is meant for students in Grade 8, although there is a lack of additional data in the subsequent columns for this initial row. The second row pertains to the subjects covered under Quarter 3, detailing the core areas of study which include linear equations and inequalities in both one and two variables, their graphs, and systems of linear equations. It highlights a total of five key concepts, starting from the basics of linear equations in one variable, extending to more complex topics such as systems of linear equations in two variables.

Accompanying the list of subjects is a detailed enumeration of the expected competencies for learners by the end of the quarter. The skills detailed in the third row include being able to solve linear equations and inequalities in one variable, graph these equations and inequalities, and manage systems of linear equations both graphically and algebraically. It emphasizes the various methods students are expected to master, such as defining and determining the slope and intercepts of lines, finding equations based on given parameters, and classifying systems based on their solutions. In total, the performance standards outline an engaging and comprehensive range of tasks and knowledge that learners are expected to acquire, reinforcing both theoretical understanding and practical application in algebra.

This comprehensive curriculum structure is designed to offer students a robust foundation in their mathematical education, preparing them to tackle more advanced concepts in future grades. The skills and knowledge expected of learners not only encourage proficiency in solving algebraic problems but also foster analytical thinking through graphing and interpreting linear relationships. Thus, students will be equipped to engage with mathematical concepts in a meaningful context, ultimately enhancing their overall mathematical literacy.


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      <td>Grade 9</td>
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      <td>Quarter 3</td>
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      <td>Number \nand \nAlgebra \n(N/A)</td>
      <td>1. \nquadratic equations and graphs \nof quadratic functions. \n2. \nthe solution of quadratic \nequations.</td>
      <td>1. \nrepresent real-life situations that can be modelled using quadratic relationships. \n2. \ngraph equations in two variables to represent quadratic relationships, such as \n𝑦 = 𝑎𝑥2, 𝑦 = 𝑎𝑥2 + 𝑏, 𝑦 = 𝑎(𝑥 − 𝑏)2. \n3. \ninterpret features of a parabola such as vertex, axis of symmetry, x–intercepts, opening \ndirection, minimum or maximum value, zeros, and increasing and decreasing intervals. \n4. \ntransform the quadratic functions 𝑦 = 𝑎𝑥2, 𝑦 = 𝑎𝑥2 + 𝑏, 𝑦 = 𝑎(𝑥 − 𝑏)2 \nand 𝑦 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 into the form 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘, and vice versa. \n5. \nsketch the graph of quadratic functions expressed in equation form. \n6. \nanalyze the effect of changing the values of the parameters on the behavior of its graph \nand on the properties of the quadratic function 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘. \n7. \nfind the zeros of quadratic functions in factored and standard form, graphically and \nalgebraically. \n8. \nsolve quadratic equations by:  \na. extracting square roots, \nb. factoring, and \nc. using the quadratic formula. \n9. \nsolve problems involving quadratic functions and equations</td>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>3. \nsimilarity of polygons. \n4. \nspecial triangles.</td>
      <td>10. \nillustrate similarity of polygons. \n11. \nillustrate and apply triangle similarity theorems in different situations. \n12. \nsolve problems involving triangle similarity. \n13. \nsolve problems involving measures of sides and angles of special triangles (30-60-90, \n45-45-90).</td>
    </tr>
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      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>5. \ndirect and inverse variation.</td>
      <td>13. \nillustrate real-life situations that involve direct variation and real-life situations that \ninvolve inverse variation. \n14. \ntranslate a relationship between two quantities into a variation statement and/or a \nmathematical equation, given a table of values or a graph. \n15.  solve problems involving variation.</td>
    </tr>
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      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nrepresent quadratic relationships. (NA) \n• \ninterpret features of a parabola. (NA) \n• \nexpress quadratic functions in different forms. (NA) \n• \nsketch the graph of a quadratic function. (NA) \n• \nsolve quadratic equations. (NA) \n• \nillustrate and apply similarity of polygons, including triangles. (MG) \n• \napply direct and inverse variation. (NA)</td>
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The table presents an outline for Grade 9 Mathematics, specifically for the curriculum segments of Quarter 3 and Quarter 4, which include key areas of study such as Number and Algebra, Measurement and Geometry, and Performance Standards. Each of these areas is detailed in a structured format showing both the topics to be covered and the expected learning outcomes for students.

In Quarter 3, the focus is on Number and Algebra (N/A), where the curriculum emphasizes quadratic equations and the graphs of quadratic functions. Students are expected to engage in various activities such as representing real-life situations through quadratic relationships and graphing equations to reflect these relationships. Additionally, they will learn to analyze the features of a parabola, including its vertex, intercepts, and the effects of different parameters on the graph. Important skills such as transforming quadratic functions into standard forms and solving quadratic equations through various methods are also outlined. 

Quarter 4 shifts towards Measurement and Geometry (MG), where learners will explore topics including triangle theorems, triangle inequality, and trigonometric ratios. The curriculum aims for students to solve problems involving the properties and theorems related to triangles, as well as apply these to real-life situations through the lens of trigonometry. Furthermore, the Data and Probability (DP) section addresses the interpretation and analysis of data, teaching students to assess the validity of data presentations and calculate probabilities associated with simple and compound events. The performance standards at the conclusion of this quarter summarize the skills expected to be acquired, including the application of mathematical concepts related to quadratic functions, geometry, and probability in various contexts.


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      <td>Grade 9</td>
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      <td>Quarter 2</td>
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      <th>2</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1. \nparallelism and \nperpendicularity of lines. \n2. \ndifferent quadrilaterals and \ntheir properties. \n3. \ncongruence of triangles. \n4. \ncongruence proofs.</td>
      <td>1. \ndetermine conditions that guarantee parallelism and perpendicularity of lines. \n2. \nclassify quadrilaterals based on formal definitions. \n3. \nuse properties of parallelograms to find measures of angles, sides, perpendicular height, \nand diagonals.  \n4. \nsolve problems involving parallelograms, rectangles, squares, or rhombuses by applying \ntheir different properties. \n5. \nprove properties of parallelograms by applying the relevant theorems. \n6. \nderive the properties of trapezoids and kites by exploring the relationship between their \nparts and secondary parts. \n7. \nsolve problems on trapezoids and kites by applying their properties. \n8. \ndistinguish inductive and deductive reasoning for establishing proofs. \n9. \nstate postulates and theorems about defined and undefined terms in geometry, and \nformulates proofs involving them. \n10.  use the triangle congruence postulates and theorems to illustrate congruence of \ntriangles, including CPCTC (definition of congruent triangles). \n11. \nsolve problems involving right triangle congruence theorems, isosceles triangle theorem, \nperpendicular bisector theorem, and midline theorem \n12. \nconstruct and justify the construction of segments, angles and triangles, including, but \nnot limited to, the triangle’s secondary parts and centers, using the triangle congruence \npostulates and theorems. \n13. \nconstruct congruence proofs involving triangles or corresponding parts of triangles \nusing a two-column proof.</td>
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      <th>3</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ndetermine the conditions for lines to be parallel or perpendicular. (MG) \n• \nuse geometric properties to find unknown sides and angles of quadrilaterals. (MG) \n• \napply the triangle congruence postulates and theorems. (MG) \n• \nconstruct and justify the construction of segments, angles, and triangles. (MG) \n• \nconstruct proofs of the congruence of triangles. (MG)</td>
      <td></td>
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    </tr>
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The content presented outlines the educational framework for Grade 9 students, specifically focusing on Quarter 2's curriculum which covers Measurement and Geometry (MG). One of the key objectives includes understanding the parallelism and perpendicularity of lines. The curriculum details knowledge students are expected to acquire, such as identifying conditions that guarantee parallel lines and perpendicular lines. Furthermore, it emphasizes the classification of quadrilaterals based on their formal definitions and encourages students to use properties of parallelograms to calculate measures related to angles, sides, perpendicular heights, and diagonals. 

Additionally, students are expected to engage in complex problem-solving involving various quadrilaterals, such as parallelograms, rectangles, squares, and rhombuses, while applying relevant geometric properties. The students will also learn to derive properties of trapezoids and kites through exploring the relationships between the shapes' parts. An important focus is on building critical reasoning skills; students will learn to distinguish between inductive and deductive reasoning in the context of proofs. This includes understanding and formulating geometric proofs regarding postulates and theorems associated with defined and undefined terms.

Moving into triangle congruence, the curriculum challenges students to apply triangle congruence postulates and theorems, including the often-utilized CPCTC (corresponding parts of congruent triangles are congruent). Students will be tasked with solving problems rooted in right triangle congruence theorems, isosceles triangle theorem, perpendicular bisector theorem, and midline theorem. As they progress, students will construct and justify segments, angles, triangles, and their respective secondary parts using these triangle properties. Lastly, the achievement of constructing proofs that establish the congruence of triangles, either through two-column proofs or other methods, is highlighted as a performance standard expected by the end of the quarter.


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      <td>Grade 8</td>
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      <th>1</th>
      <td>Quarter 4</td>
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      <td>Data \nand \nProbability \n(D/P)</td>
      <td>1.  measures of variability for \nungrouped data. \n2. \ninterpretation and \nanalysis of graphs from \nprimary and secondary \ndata. \n3. \nexperimental and \ntheoretical probability. \n4. \nthe Fundamental \nCounting Principle.</td>
      <td>1. \ncalculate the measures of variability (range, mean deviation, and standard deviation) for \nungrouped data. \n2. \ndraw conclusions from statistical data using the measures of variability. \n3. \ninvestigate, interpret, and analyze graphs from primary data (e.g., examination scores). \n4. \ninvestigate, interpret, and analyze graphs from secondary data. \n5. \ndifferentiate theoretical from experimental probability by conducting an experiment or an \ninvestigation. \n6. \ndescribe the sample space of an experiment. \n7. \nuse the Fundamental Counting Principle to determine the number of possible outcomes of an \nexperiment. \n8. \ncalculate the theoretical probability of a single event by listing all possible outcomes. \n9. \ndescribe probability as a measure of the chance of an event occurring. \n10.  calculate the probability of simple combined events by listing, or by possibility diagrams or \ntree diagrams. \n11.  solve problems involving experimental probability and/or theoretical probability using the \nFundamental Counting Principle.</td>
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      <th>3</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ncalculate measures of variability for ungrouped data. (DP) \n• \ninterpret and analyze graphs from primary and secondary data. (DP) \n• \ndetermine the number of possible outcomes of an experiment using the Fundamental Counting Principle. (DP) \n• \ncalculate the probability of a single event and the probability of simple combined events. (DP)</td>
      <td></td>
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    </tr>
  </tbody>
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The table presented offers a systematic overview of the educational content and standards for Grade 8 in the area of Data and Probability (D/P) during Quarter 4. It elaborates on the learning competencies and performance standards that students are expected to achieve by the end of the quarter. In the first column of the table, various content standards are specified, which include measures of variability for ungrouped data, interpretation and analysis of graphs derived from both primary and secondary data, experimental and theoretical probability, and an introduction to the Fundamental Counting Principle.

Accompanying each content standard is a detailed list of learning competencies targeted at the students. For instance, learners are expected to calculate various measures of variability including the range, mean deviation, and standard deviation for ungrouped data. They are also required to draw conclusions based on statistical data using these measures. The curriculum emphasizes the importance of graph interpretation, urging students to investigate, interpret, and analyze graphs from both primary and secondary data, with specific references to practical examples such as examination scores. Furthermore, the table outlines competencies associated with experimental probability, encouraging students to conduct experiments to differentiate between theoretical and experimental probability.

In addition to the content standards and learning competencies, the table encapsulates performance standards that summarize the overarching goals for students by the end of the quarter. These expectations include the ability to calculate measures of variability for ungrouped data, proficiently interpret and analyze relevant graphs, determine the possible outcomes of various experiments using the Fundamental Counting Principle, and calculate both theoretical and experimental probabilities for single events as well as simple combined events. This structured approach not only sets clear expectations for learners but also provides educators with a framework to assess student understanding and application of data and probability concepts effectively.


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      <td>Grade 9</td>
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      <td>CONTENT \nCONTENT STANDARDS \nLEARNING COMPETENCIES \nThe learners demonstrate knowledge \nThe learners … \n \nDOMAIN \nand understanding of ...</td>
      <td></td>
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      <td>Quarter 1</td>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1. \nsimple geometric concepts and \nnotations. \n2. \nperpendicular and parallel \nlines, and angles formed by \nparallel lines cut by a \ntransversal.</td>
      <td>1. \nillustrate and describe point, line, ray, line segment, angle, and plane using models and \ngeometric notations. \n2. \nconstruct perpendicular and parallel lines. \n3. \nidentify the relationships between angles formed by parallel lines cut by a transversal. \n4. \ndetermine angle measures involving angle pairs, parallel and perpendicular lines, and \nparallel lines cut by a transversal.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>relations and functions. \n3. \n4. \ngraphs of linear functions, and \nthe identification of domain and \nrange, slope, intercepts, and \nzeros.</td>
      <td>5. \nidentify relations that are functions based on the definitions of relations and functions. \n6. \ndetermine the domain and the range of a function expressed in different \nrepresentations. \n7. \nexpress the relationship between two variables as a function. \n8. \ndetermine the slopes (as rate of change) and the zeros of linear functions represented in:  \na. graphs,  \nb. equations, and  \nc. tables of values.  \n9. \ngraph a linear function and determine its: \na. domain, \nb. range, \nc. intercepts, and \nd. slope. \n10. \nrepresent linear relationships found in real-life situations using different \nrepresentations. \n11.  solve problems involving linear functions.</td>
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      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nillustrate and describe points, lines, rays, line segments, angles, and planes. (MG) \n• \nconstruct perpendicular and parallel lines. (MG) \n• \ndetermine the measure of the angles formed by parallel lines cut by a transversal. (MG) \n• \nidentify relations and functions. (NA) \n• \ngraph a linear function and identify the domain and range, intercepts, slope, and zeros. (NA)</td>
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The content outlined in the provided table pertains to the Grade 9 curriculum for Quarter 2, specifically focusing on Measurement and Geometry (MG). The first row identifies the grade level as Grade 9, while the second row elaborates on the content standards and learning competencies associated with this subject area. Under Measurement and Geometry, key learning topics include the understanding of parallelism and perpendicularity of lines, various quadrilaterals and their properties, and proofs of triangle congruence. 

Each key learning area delineates important competencies that students are expected to achieve by the end of the quarter. For instance, students will learn how to determine the conditions for lines to be parallel or perpendicular, classify quadrilaterals based on formal definitions, and apply the properties of parallelograms, rectangles, squares, or rhombuses to solve problems. Alongside these concepts, learners are encouraged to engage in proving the properties of parallelograms using relevant theorems, understanding trapezoids and kites through the exploration of their structural relationships, and developing reasoning skills in both inductive and deductive contexts.

Furthermore, the performance standards at the end of the quarter encapsulate the expected outcomes for students, including achieving proficiency in identifying geometric properties to find unknown measurements and constructing geometric figures, such as segments and triangles. This comprehensive approach aims to ensure that learners have a solid grasp of geometric principles, enabling them to construct logical proofs of triangle congruence using two-column methods and applying various triangle congruence postulates and theorems effectively throughout the learning period.


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      <td>rade 9</td>
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      <td>Quarter 4</td>
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      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1. \ntriangle theorems and triangle \ninequality theorems. \n2. \nthe trigonometric ratios and their \napplication.</td>
      <td>1. \nsolve problems involving the perpendicular bisector theorem, isosceles triangle theorem, \ntheorems on equilateral triangles, and the midline theorem. \n2. \nexplain theorems on triangle inequalities and apply these theorems in comparing \nmeasures in a triangle. \n3. \ndetermine the values of the sine, cosine, and tangent trigonometric ratios corresponding \nto the angles of the special triangles. \n4. \nfind the values of the sine, cosine, and tangent ratios of any acute angle. \n5. \nuse the trigonometric ratios in solving right triangles. \n6. \nillustrate angles of elevation and angles of depression. \n7. \nsolve real-life problems involving right triangles through the application of the \ntrigonometric ratios.</td>
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      <th>3</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>3. \ninterpretation and analysis of \ndata to assess whether the data \nmay be misleading. \n4. \nprobabilities of simple and \ncompound events.</td>
      <td>8. \ninterpret and analyze data from the digital media that are in tabular or graphical form to \nassess whether the data may be misleading. \n9. \nillustrate simple and compound events. \n10.  determine the probabilities of simple and compound events. \n11.  solve problems involving probabilities of simple and compound events.</td>
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      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \napply triangle theorems and triangle inequality theorems. (MG) \n• \napply trigonometric ratios to solve right triangles. (MG) \n• \ninterpret and analyze data to assess whether the data may be misleading. (DP) \n• \ndetermine the probabilities of simple and compound events. (DP)</td>
      <td></td>
      <td></td>
    </tr>
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</table>


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The table outlines the curriculum standards for Grade 9, specifically focusing on Quarter 4, and is divided into two main content domains: Measurement and Geometry (MG) and Data and Probability (DP). In the Measurement and Geometry domain, the content standards include triangle theorems and triangle inequality theorems, along with the application of trigonometric ratios. The learning competencies associated with this domain involve solving problems related to various triangle theorems, including the perpendicular bisector theorem and the isosceles triangle theorem, as well as explaining theorems on triangle inequalities. Furthermore, it covers determining the values of sine, cosine, and tangent trigonometric ratios for special angles and using these ratios to solve right triangles. Real-life applications, such as illustrating angles of elevation and depression, are also emphasized, allowing learners to connect mathematical concepts with practical scenarios.

In the Data and Probability domain, the content standards focus on the interpretation and analysis of data to assess potential misleading elements, along with understanding the probabilities of both simple and compound events. The learning competencies include interpreting and analyzing data presented in both tabular and graphical forms, highlighting the necessity for critical thinking when evaluating data. Learners are taught to illustrate these events and to determine the associated probabilities, thus equipping them with the necessary skills to tackle problems involving these statistical concepts. 

The performance standards set out clear expectations for learner outcomes by the end of the quarter. These standards specify that learners will be able to apply triangle and triangle inequality theorems, utilize trigonometric ratios in solving right triangles, and critically analyze data while determining probabilities of various events. This structured approach ensures that students not only grasp theoretical knowledge but are also able to apply it effectively in diverse mathematical contexts and real-world situations.


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      <td>CONTENT \nDOMAIN</td>
      <td>CONTENT STANDARDS \nThe learners demonstrate knowledge \nand understanding of ...</td>
      <td>LEARNING COMPETENCIES \nThe learners …</td>
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      <th>2</th>
      <td>Quarter 1</td>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>1.  the laws of sines and the laws of \ncosines. \n2.  translations, reflections, and \nrotations, in the Cartesian plane.</td>
      <td>1. \napply laws of sines in solving oblique triangles, including ambiguous cases. \n2. \napply laws of cosines in solving oblique triangles. \n3. \ndescribe the position of points in the Cartesian plane. \n4. \ndescribe translations, reflections, and rotations, in the Cartesian plane using \ncoordinates. \n5. \nsolve problems involving laws of sines and cosines, including bearings.</td>
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      <th>4</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3.  quadratic inequalities in one \nvariable and in two variables. \n4.  absolute value equations and \ninequalities in one variable and \ntheir graphs.</td>
      <td>6. \nillustrate on the number line quadratic inequalities in one variable. \n7. \nsolve quadratic inequalities in one variable and expresses solutions in various notations. \n8. \nsolve problems involving quadratic inequalities in one variable. \n9. \nsolve quadratic inequalities in two variables. \n10.  determine the region of solutions of a linear or quadratic inequality in two variables. \n11.  solve absolute value equations in one variable and express solutions in various \nnotations) \n12.  solve absolute value inequalities in one variable and express solutions in various \nnotations</td>
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      <th>5</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nfind sides and angles in oblique triangles using the laws of sines and the laws of cosines. (MG) \n• \ndescribe translations, reflections, and rotations in the Cartesian plane. (MG) \n• \nsolve and graph the solutions of quadratic inequalities in one variable and in two variables. (NA) \n• \nsolve absolute value equations in one variable and absolute value inequalities in one variable, and graph the solutions. (NA)</td>
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The provided table outlines the curriculum for Grade 10 mathematics during Quarter 2, particularly focusing on two main content domains: Data and Probability (DP) and Number and Algebra (NA). Under the Data and Probability section, students are expected to grasp various statistical concepts, including box-and-whisker plots, cumulative frequency histograms, and the understanding of quartiles, deciles, and percentiles. They will learn how to illustrate these measures of position, construct and interpret relevant plots, and calculate specific statistical elements such as the interquartile range and outliers from ungrouped data. Additionally, students will be trained to calculate the percentile rank of a score and draw conclusions based on the statistical data analyzed.

In the Number and Algebra domain, the curriculum addresses several essential mathematical concepts such as radical expressions, quadratic equations, and the nature of their roots. Students will learn to simplify radical expressions, perform operations involving them, and explore quadratic functions and equations, including those reducible to quadratics. The learning competencies indicate that learners will be able to determine the nature of the roots using the discriminant, solve quadratic equations given in various formats (like a table of values or a graph), and tackle real-world problems involving quadratic functions. The performance standards at the end of the quarter show that students should also be proficient in solving and graphing solutions for quadratic inequalities and absolute value equations and inequalities. This structured outline emphasizes the importance of both theoretical understanding and practical application in the learning process for Grade 10 students.


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      <td>Grade 10</td>
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      <td>Quarter 2</td>
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      <th>2</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>1.  box-and-whisker plots, and \ncumulative frequency \nhistograms and polygons. \n2.  quartiles, deciles, and \npercentiles; interquartile range, \nand outliers.</td>
      <td>1. \nillustrate measures of position (quartiles, deciles, and percentiles). \n2. \nconstruct and interpret box-and-whisker plots and cumulative frequency histograms and \npolygons. \n3. \ncalculate a specified measure of position, interquartile range, and outliers, from ungrouped \ndata. \n4. \ncalculate the percentile rank of a given score from ungrouped data. \n5. \ndraw conclusions from statistical data using the measures of position.</td>
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      <th>3</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>3. \nradical expressions. \n4. \nthe roots of a quadratic \nequation. \n5.  quadratic functions. \n6.  equations reducible to \nquadratic equations.</td>
      <td>6. \nillustrate the laws of rational non-integral exponents. \n7. \nsimplify radical expressions. \n8. \nperform operations involving radical expressions, including rationalizing the denominator. \n9. \ndetermine the nature of roots of a quadratic equation using the discriminant. \n10.  determine the equation of a quadratic function given: \na. a table of values \nb. its graph, and \nc. its zeros. \n11.  solve equations reducible to quadratic equations, e.g., 𝑥 4 − 5𝑥2 + 4 = 0 \n12.  solve problems involving quadratic functions. \n13.  solve radical equations, including equations reducible to linear or quadratic equations.</td>
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      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \nconstruct and interpret box-and-whisker plots, and cumulative frequency histograms and polygons. (DP) \n• \ncalculate quartiles, deciles, and percentiles; interquartile range, and outliers. (DP) \n• \nsimplify, and perform operations, involving radical expressions. (NA) \n• \ndetermine the nature of roots of a quadratic equation. (NA) \n• \ndetermine the equation of a quadratic function. (NA) \n• \nsolve equations reducible to quadratic equations and radical equations. (NA)</td>
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      <td></td>
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The document outlines the Grade 10 curriculum for Quarter 2, focusing specifically on two major areas: Data and Probability (DP) and Number and Algebra (NA). It presents a structured overview of what students are expected to learn and accomplish by the end of the quarter. Within the Data and Probability section, the curriculum emphasizes the importance of various statistical concepts, including box-and-whisker plots, cumulative frequency histograms, quartiles, deciles, percentiles, interquartile range, and outliers. Students are expected not only to illustrate these measures of position but also to construct and interpret visual data representations. Additionally, they will learn to calculate specific measures of position, assess the interquartile range, identify outliers, and draw conclusions from statistical data.

The Number and Algebra segment delves into topics such as radical expressions, the roots of quadratic equations, quadratic functions, and equations reducible to quadratic equations. Students will gain proficiency in illustrating the laws of rational non-integral exponents and will learn to simplify radical expressions while performing related operations. Critical skills include determining the nature of the roots of a quadratic equation using the discriminant, deducing the equation of a quadratic function from various forms such as tables of values, graphs, and zeros, as well as solving quadratic-related equations. 

Finally, performance standards are presented, summarizing the competencies that learners should demonstrate by the quarter's end. These include constructing and interpreting statistical diagrams (DP) and mastering several aspects of algebra, from simplification of expressions to solving quadratic equations (NA). The integration of these knowledge areas ensures a comprehensive mathematical foundation for the learners, preparing them for further academic challenges in mathematics.


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      <th>1</th>
      <td>Quarter 4</td>
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      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1. \nsimple interest, compound \ninterest, and depreciation.</td>
      <td>1. \nexplore inductively the relationship between simple interest and compound interest. \n2. \ncalculate compound interest by repeated applications of simple interest. \n3. \nsolve problems involving compound interest by repeated applications of simple interest. \n4. \nexplain inductively the formulas for compound interest and depreciation. \n5. \nexplore inductively the differences in the amount of compound interest obtained on \namounts of money invested: \na. \nannually, \nb. \nquarterly, and \nc.  monthly. \n6. \nsolve real-life problems involving: \na. \ncompound interest, and \nb.  depreciation.</td>
    </tr>
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      <th>3</th>
      <td>Measurement \nand \nGeometry \n(MG)</td>
      <td>2. \ncentral angles; inscribed \nangles; and angles and \nlengths formed by \nintersecting chords, secants, \nand tangents of a circle. \n3. \nsectors and segments of a \ncircle, and their areas.</td>
      <td>7. \nestablish properties and relationships for central angles, inscribed angles, secants, and \ntangents, of a circle. \n8. \nsolve problems involving: \na. central angles, \nb. inscribed angles, \nc. angles formed by two intersecting chords, \nd. angles formed by two secants intersecting outside the circle, \ne. angles formed by two intersecting tangents, and \nf. angles formed by intersecting secant and tangent. \n9. \nestablish properties and relationships for chords, secants, and tangents. \n10.  solve problems involving lengths of: \na. intersecting chords, \nb. two secant segments intersecting outside a circle, and \nc. two intersecting tangent segments. \n11.  define sectors and segments of a circle and finds their areas. \n12.  solve problems involving area of a sector of a circle, segment of a circle, and shaded regions \nin other figures that involve sectors or segments.</td>
    </tr>
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      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ncalculate compound interest and depreciation. (NA) \n• \napply properties and relationships of central angles, inscribed angles, chords, secants, and tangents of circles. (MG) \n• \ndefine sectors and segments of a circle, and find their areas. (MG)</td>
      <td></td>
      <td></td>
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The provided table outlines the curriculum standards for Grade 10 Mathematics, specifically focusing on Quarter 4 of the academic year. It divides the content into two main sections: Number and Algebra (NA) and Measurement and Geometry (MG), with each section detailing specific topics, competencies, and performance standards. For the Number and Algebra domain, students are expected to explore several key concepts, such as simple interest, compound interest, and depreciation. This includes an inductive exploration of the relationship between simple and compound interest, the calculation of compound interest through repeated applications of simple interest, and problem-solving involving both concepts. Additionally, learners are required to understand the formulas for compound interest and depreciation as well as differentiate between the amounts of compound interest accrued when amounts are invested annually, quarterly, and monthly.

In the Measurement and Geometry section, the table highlights topics such as central angles, inscribed angles, and the relationships and properties concerning intersecting chords, secants, and tangents of circles. Students are expected to establish properties for these angles and solve various practical problems related to them, including understanding lengths and addressing relationships between different lines interacting with a circle. The content also includes defining sectors and segments of a circle and determining their areas. Performance standards for the quarter ensure that by the end, learners will not only be adept at calculating compound interest and depreciation but also proficient in applying geometric properties and solving problems with sectors and segments of circles. This comprehensive layout illustrates a structured approach to mathematical education, aligning with the curriculum goals outlined in the Grades 1 to 10 Mathematics Curriculum Guide.


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      <td>Quarter 3</td>
      <td></td>
      <td></td>
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    <tr>
      <th>2</th>
      <td>Number \nand \nAlgebra \n(NA)</td>
      <td>1.  equation of a circle and the \ngraph of a circle.</td>
      <td>1. \ntransform the equation of a circle from center-radius form to general form, and vice versa. \n2. \ndetermine the center and the radius of a circle from a given equation. \n3. \nsketch the graph of a circle given its equation. \n4. \nfind the equation of a circle from given conditions, e.g., given two points as the endpoints of \na diameter. \n5. \nsolve problems involving geometric figures on the Cartesian plane.</td>
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      <th>3</th>
      <td>Data \nand \nProbability \n(DP)</td>
      <td>2.  evaluation of statistical reports. \n3.  union and intersection of \nevents, dependent and \nindependent events, and \ncomplementary events.</td>
      <td>6. \nevaluate statistical reports by linking claims to displays, statistics, and representative data. \n7. \nillustrate mutually exclusive events and non-mutually exclusive events. \n8. \nidentify complementary events. \n9. \nsolve probability problems involving: \na.  union and intersection of events, including mutually and non-mutually exclusive events; \nb.  dependent and independent events, including conditional probability where the solution \nis limited to the use of contingency tables or Venn diagrams; and \nc. \ncomplementary events.</td>
    </tr>
    <tr>
      <th>4</th>
      <td>Performance Standards \nBy the end of the quarter, the learners are able to … \n• \ntransform the equation of a circle from center-radius form to general form, and vice versa, and determine the center and radius from a given \nequation. (NA) \n• \ngraph a circle from a given equation of the circle. (NA) \n• \nevaluate statistical reports. (DP) \n• \ncalculate probabilities in relation to union and intersection of events; dependent and independent events; and complementary events. (DP)</td>
      <td></td>
      <td></td>
    </tr>
  </tbody>
</table>


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The table presented summarizes the educational content and performance standards for Grade 10 students in the subjects of Number and Algebra (NA) and Data and Probability (DP), specifically for Quarter 3. The first section delineates the key topics under the Number and Algebra category, which includes the equation of a circle and its graph. Students are expected to transform between the center-radius form and general form of the circle's equation, alongside determining the center and radius from a given equation. Additionally, students will learn how to sketch the graph of a circle based on its equation and solve problems that involve geometric figures on the Cartesian plane.

In the Data and Probability section, the focus shifts to key concepts such as the evaluation of statistical reports, as well as union and intersection of events including dependent and independent events, and complementary events. Students will engage in various activities to evaluate statistical reports by connecting claims to displays and representative data. They will also illustrate examples of mutually and non-mutually exclusive events and identify complementary events. Furthermore, the curriculum requires students to solve probability problems involving these events, applying concepts of union and intersection, as well as conditional probabilities assessed through contingency tables or Venn diagrams.

By the end of Quarter 3, students are expected to have achieved specific performance standards. These include competencies in transforming circular equations, graphing circles, evaluating statistical reports, and calculating probabilities related to different types of events. The structured approach to learning ensures that students not only grasp theoretical concepts but can also apply them practically, preparing them for more advanced topics in mathematics.


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Curriculum Framework 
The framework designed for the revised Mathematics curriculum for Grades 1 to 10 guides teachers in their preparation of 
mathematically rich lessons and helps them in working towards the main curriculum goal. 
To achieve the main goal, three facilitating facets have been developed: content, skills, and disposition.  
The three facilitating facets are further reinforced by three supporting components: pedagogy, assessment, and resources, with 
each of these being relevant to the learning context, the curriculum content, and the learning phases of the learners. 
Figure 1 shows the diagrammatic representation of the framework designed for the revised curriculum. 
 
 
Figure 1. The Revised Grades 1 – 10 Mathematics Curriculum Framework 
 
Through the teaching and learning of the revised curriculum, it is also intended that learners exhibit the qualities emanating


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These strands are: 
• Conceptual Understanding – comprehension of mathematical concepts, operations, and relations; 
 
• Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately; 
• Strategic Competence – ability to formulate, represent, and solve mathematical problems; 
• Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification; and 
• Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in 
diligence and one’s own efficacy (p. 116).  
 
These intertwining strands of mathematical proficiency are also covered in the SEAMEO Basic Education Stand ards (SEA-
BES): Common Core Regional Learning Standards (CCRLS) in Mathematics and Science (2017). The SEA -BES CCRLS refers to: (1) 
cultivating basic human characters through mathematical values, attitudes and habits of mind; (2) developing creative human capital


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The revised mathematics curriculum will have three content domains: (1) Number and Algebra; (2) Measurement and Geometry; 
and (3) Data and Probability. 
Skills 
As proficient problem solvers, learners need to possess a range of mathematical skills. Such skills enhance the ability to analyze 
and evaluate mathematical situations and obtain solutions to real-world problems.  
In today ’s highly technological world, the teaching and learning of mathematics needs to include, and also  go beyond , 
calculations and algorithmic procedures.  This is because such calculations and procedures can be carried out by calculation devices 
and software applications.  
Disposition 
Disposition is closely related to “attitude” and “value.”  Values are the “guiding principles that underpin what people believe to 
be important when making decisions in private and public life … [while] attitudes are underpinned by values and beliefs and have an


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With the curriculum goal centered on developing mathematical proficiency, critical thinking,  and problem solving,  the 
assessment process should not only record learners’ level of achievement in understanding concepts, reasoning, and the solution of 
mathematics problems, but should also result in the development of appropriate feedback for improving instruction.  
Assessments, whether for formative or summative purposes, should be administered in various forms.   
Resources  
The learning of mathematics needs to be supported with a variety of teaching and learning resources.  Electronic and print 
resources need to be carefully selected and judici ously used. T eachers and other instructional leaders are acknowledged as key 
resources in the implementation of the curriculum. 
 
Structure of the Learning Area 
 
Big Ideas 
 
Charles (2005) define s a big idea as “a statement of an idea that is central to the learning of mathematics, one that links


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Piaget’s theory of cognitive development (1977) states that all knowledge is constructed , and the i nstrument of instruction 
includes cognitive structures that themselves are products of continued construction. In the preoperational stage , Piaget suggests 
that elementary school children need concrete objects, pictures, actions, and symbol s to develop a deep understanding of 
mathematical concepts. In addition, Bruner concurs that conceptual learning begins from active engagement or experiences with 
concrete tasks (‘enactive’), moves towards perceptual images (‘iconic’), and then to abstract (‘symbolic’) representations (Bruner, 1966). 
For instance, when teaching addition with regrouping for obtaining, for example, 8 + 6, Grade 1 learners should move blocks in two 
groups to act out the idea of using part of one addend so that the other addend will become a complete “ten.” This hands-on approach


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Development of the Curriculum 
 
Curriculum Goals 
 
The main goal of the curriculum is for Filipino learners to become mathematically proficient and critical problem solvers.  
The development of mathematical proficiency among learners involves the development of confidence and competence in 
different aspects of mathematics and includes becoming increasingly aware of the value and usefulness of mathematics. 
According to Polya (1981), problem solving is “finding a way out of a difficulty, a way around an obstacle, attaining an aim 
which was not immediately attainable” (p. ix). Further, the National Council of Teachers of Mathematics (NCTM), (2000) asserts that 
“solving problems is not only a goal of learning mathematics but also a major means of doing so” (p. 52). 
In mathematics education, problem solving has been consi dered as a goal, as a process, and as a basic skill. The processes


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cultivating basic human characters through mathematical values, attitudes and habits of mind; (2) developing creative human capital 
and process skills; and (3) the importance of knowledge of mathematics in cultivating well-qualified citizens. 
Facione and Gittens (2016) define critical thinking as “the process of purposeful, reflective judgmen t” (p. 386). They further 
asserted that “the critical thinking process applies cognitive skills of interpretation, analysis, inference, evaluation, explanation, and 
self-regulation in an effort to judge what to believe or what to do” (p. 36). 
The revised Mathematics curriculum will aim  to de velop among learners ’ proficiency in solving mathematical problems 
critically, grounded in strong conceptual knowledge, strategic use of math ematical skills and processes, and desirable values and 
disposition in mathematics, thus assisting them to become productive and successful 21st-century citizens. 
 
The Facilitating Facets


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be important when making decisions in private and public life … [while] attitudes are underpinned by values and beliefs and have an 
influence on behaviour” (Organization for Economic Co -operation and Development [OECD], 2019, p. 4). Mathematical dispositio n 
also incorporates appreciation of values intrinsic to mathematics such as its coherence and consistency, precision and clarit y, and 
generality and extendibility. 
A sound mathematical disposition facilitates genuine learning and the development of the mathematical proficiency needed for 
efficient and successful problem solving. 
 
The Supporting Components 
 
The three components designed to support the facilitating facets for achieving the curriculum goal of the Grades 1 to 10 
Mathematics curriculum are pedagogy, assessment, and resources. 
Pedagogy  
Pedagogy is concerned with the methods used to deliver a curriculum. The quality of mathematics learn ing depends on the


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Figure 1. The Revised Grades 1 – 10 Mathematics Curriculum Framework 
 
Through the teaching and learning of the revised curriculum, it is also intended that learners exhibit the qualities emanating 
from the five intertwining strands of mathematical proficiency as defined by the National Research Council (NRC, 2001).


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groups to act out the idea of using part of one addend so that the other addend will become a complete “ten.” This hands-on approach 
views numbers as quantities and not mere numerals, and progresses to pictorial representation of the same problem type. Learners’ 
advancement leads to mental visualization and application of manipulation s to abstract prob lems. Thus, the ultimate object ive of 
mathematics education , as outlined in the Concrete -Representational-Abstract (CRA) Model, is to guide learners towards 
representations and operations that involve abstract symbols (Hui et al., 2017). 
Vygotsky (1978), on the other hand, states that an individual cannot develop without interacting with the environment as 
emphasized in his zone of proximal development. By incorporating this theory into their teaching practices, teachers can tail or 
strategic instructional plans for groups or individual learners at various developmental stages. By effectively connecting co mplex


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In mathematics education, problem solving has been consi dered as a goal, as a process, and as a basic skill. The processes 
involved in solving mathematical problems, from recognizing and understanding a problem, to modelling the problem through different 
representations, to planning a solution, to executing the  solution, and to finally checking whether the problem has been solved, 
demonstrate that problem solving is a very important life skill for 21st-century citizens to possess. 
 
Theoretical and Philosophical Bases 
 
Mathematics is a diverse discipline. With it s universal applicability, it finds widespread use in various fields of endeavor, 
especially in solving real-world problems. It is essential that learners be mathematically proficient and critical thinkers to effectively 
tackle such problems.  
 
Effective m athematics teaching requires understanding  what students know and need to learn , and then challenging and


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Republic of the Philippines  
Department of Education 
DepEd Complex, Meralco Avenue, Pasig City 
 
 
 
 
 
MATATAG K TO 10 CURRICULUM  
 OF THE K TO 12 PROGRAM 
 
 
 
MATHEMATICS


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Structure of the Learning Area 
 
Big Ideas 
 
Charles (2005) define s a big idea as “a statement of an idea that is central to the learning of mathematics, one that links 
numerous mathematical understandings into a coherent whole” (p. 10). 
The notion of Big Ideas lays the foundation for defining the context of the curriculum in terms of its mathematics content. The 
formulation of thes e Big Ideas illustrates the connections across the various mathematical concepts in the different stages of the 
learning process. 
These Big Ideas are present in curriculum content domains and across the curriculum stages. They are interconnected and 
support and reinforce the integration of key concepts , while supporting and reinforcing each other.  With the notion of Big Ideas, 
“mathematics is no longer seen as a set of disconnected concepts, skills, and facts. Rather, mathematics becomes a coherent se t of 
ideas” (p. 10). 
The revised curriculum identifies twelve Big Ideas:


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disposition in mathematics, thus assisting them to become productive and successful 21st-century citizens. 
 
The Facilitating Facets  
 
The three facilitating facets for achieving the curriculum goal of the Grades 1 to 10 Mathematics curriculum are content, skills, 
and disposition. 
Content 
To become mathematically proficient and critical problem solver s, learners need to be equipped with strong mathematical 
knowledge and understanding. Lessons that are logically sequenced and interconnected enable students to learn deeply and flexibly.


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Mathematics curriculum are pedagogy, assessment, and resources. 
Pedagogy  
Pedagogy is concerned with the methods used to deliver a curriculum. The quality of mathematics learn ing depends on the 
quality of the various learning experiences employed to engage and instruct learners. 
Assessment 
Assessment complements pedagogical approaches and is a vital aspect of curriculum implementation in mathematics.


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THE SHAPE OF THE 
GRADES 1 TO 10 MATHEMATICS CURRICULUM 
 
 Mathematics is a powerful means of identification, description , and application of patterns and relationships; generalization; 
and communication. It provides opportunities for challenge, creativity, and users’ recognition and appreciation of the nature, beauty 
and power of mathematical processes, strategies, and reasoning. 
 
 The successful study of mathematics in Grades 1 to 10 is a key component of Filipino learners’ preparation for life in the 21st 
century. For full participation in society, learners need to develop sound mathematical knowledge, skills, and understanding for 
making informed decisions and for solving problems in a variety of contexts relevant to their daily lives.  
 Historically, mathematics arose from necessity of the human society, with real -world problems giving birth to its existence,


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3. Shapes, Space, and Graphs – Mathematical objects such as geometric figures, solids, equations, inequalities, relations, and 
data can be visualized using shapes and graphs and in space. 
4. Patterns, Relations, and Functions – Mathematical rule, graph, or table can be used to assign object(s) from one set to object(s) 
from another set to show specific relations between the two sets. 
5. Data – Data can be collected and processed to obtain meaningful information. 
6. Chance – The number 0 and 1 (inclusive) can be used to quantify and describe the chances for an event to occur. 
7. Representations and Communications – Mathematical objects, properties, ope rations, and quantities (known or unknown) 
can be translated, represented, and communicated concretely or visually in a precise manner by using numbers, symbols, 
notations, variables, expressions, equations, geometric figures, flowcharts, tables, and graphs.


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tackle such problems.  
 
Effective m athematics teaching requires understanding  what students know and need to learn , and then challenging and 
supporting them to learn it well.   It also requires knowing and understanding mathematics, students as learners, and pedagogical 
strategies (NCTM, 2000). 
The teaching practices recommended by NCTM are grounded in views of knowledge, learning , and teaching informed by a 
constructivist perspective (e.g., Ball & Bass; Confrey, 1991; Gelman, 1994; Smith, diSessa & Roschelle, 1993).  Teaching mathematics 
through constructivist methods allows students to deepen their knowledge beyond rote memorization, to develop meaningful contexts, 
and to take charge of the learning process as active participants rather than mere observers (WGU, 2020). These constructivist 
theories point to active learning, cognitive development in the context of social interaction, and conceptual understanding as critical 
in the teaching of mathematics.


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finding solutions.  Mensuration and calculation a re core competencies in E dukasyon Pantahanan at Pangkabuhayan 
(EPP)/Technology Livelihood Education (TLE). 
It is also clear that skills in data management and analysis are required by learners , especially for dealing with big data. 
Knowledge and skills in Number and in the use of money are fundamentally important in daily-life activities, including in budgeting, 
spending, saving, and earning, which are key to the development of strong financial literacy. Proficiency in Mathematics arguably 
facilitates better understanding in other learning areas, where it is used as a tool for learning the concepts and skills in those learning 
areas. 
Development of 21st Century Skills 
 
The knowledge, skills, attitudes, and competencies that learners need to develop so that they can prepare for and succeed  in


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ideas” (p. 10). 
The revised curriculum identifies twelve Big Ideas: 
1. Numbers – Real numbers can be paired one -to-one with the points on the number line, and so can quantify and describe a 
mathematical or real-world object and its attributes. 
2. Measures – Some attributes of a mathematical or real-world object can be quantified by using measures, so that they can be 
studied further.


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Historically, mathematics arose from necessity of the human society, with real -world problems giving birth to its existence, 
emphasizing problem solving at its core.  In schools, mathematics serves as an ideal training ground, fostering the problem -solving 
ability learners. 
 Additionally, in this age of scientific and technological innovations, being “numerate” is crucial for engaging in various 
endeavors. The Organisation for Economic Co -operation and Development (OECD) defines numeracy as “the ability to access, use, 
interpret, and communicate mathematical information and ideas, in order to engage in and manage the mathematics demands of a 
range of situations in adult life.”  
“Numeracy, a significant ancillary to problem solving, relates to a high proportion of the mathematics content of the Grades 1  
to 10 Mathematics curriculum. Learners become increasingly ‘numerate’ as they develop the confidence and ability to:


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notations, variables, expressions, equations, geometric figures, flowcharts, tables, and graphs. 
8. Relationships – The relationships that exists between mathematical concepts (e.g. objects, statements) can be used to generate 
more properties about them and to connect them to other concept in mathematics. 
9. Operations and Transformations – Meaningful operations or transformations can be performed on a collection of mathematical 
objects or statements to obtain another mathematical object or statement that models a situation. 
10. Properties and Applications – A mathematical object has properties that define the object or describe its attributes, and these 
properties and their logical consequences can be applied to mathematical and real-world problems. 
11. Equivalence – Mathematical objects or statements can be represented or stated in different ways that have the s ame value, 
form, or logical meaning.


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Utilizing the EDP in the instruction allows learners to repeat steps as many times as needed to make improvements, learn from 
unsuccessful attempts, and discover different or novel design possibilities to arrive at optimal solutions. In the curriculum , EDP is 
exhibited through problem solving and investigative approaches where learners apply their mathematical, scientific, and technological 
understanding to formulate, conjecture, reason, create and evaluate a solution to a real-world problem. 
 
Financial Literacy 
Financial literacy is “the ability to use knowledge and skills to manage one’s financial resources effectively for lifetime financial 
security” (Mandell, 2009). 
The Financial Education Policy (DO 22, s. 2021) targets the financial literacy and capability of learners. The policy reitera tes 
the need to integrate financial concepts across learning areas at different levels. In Mathematics, learners focus on concepts relating


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Life and career skills are evidenced in the curriculum through tasks that require skills  for informed decision-making and 
collaboration that foster adaptive leade rship. Self -discipline, resilience, and adversity management may be manifested through 
learners’ perseverance in solving mathematical problems by using different approaches or strategies.  
Social Issues and Government Priorities 
 
The learning competencies and performance standards of the curriculum are relevant in the address of some societal issues.  
The curriculum equips learners with the mathematical concepts and skills that may be relevant to social justice, cultural 
diversity, sustainable development, and disaster risk reduction and management. Mathematical model ling, for example, could be 
utilized to address simple problems related to sustainable development and disaster risk reduction and management. 
STEM


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The curriculum views the attainment of its goals with all learners in mind. Through its standards and competencies,  the 
curriculum acknowledges the different needs of learners, fosters their engagement with learning, and promotes the use of appropriate 
language and technologies to make learning accessible. 
The curriculum is informed by reviews that have identified the different levels of performance of Filipino learners. At the same 
time, diversity, equity, and inclusion need to be continually considered throughout the teaching and learning of Mathematics. 
Assessment  
 As a vital aspect of curriculum implementation in Mathematics, assessment plays a key role in shaping learners ’ thinking 
about their mathematical potential, moving away from performance and towards an emphasis on growth and learning (Boaler, Dance 
& Woodbury, 2018).  
 Regardless of whether assessment is formal or informal, assessment tools should be varied in order to understand the different


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to 10 Mathematics curriculum. Learners become increasingly ‘numerate’ as they develop the confidence and ability to: 
• choose and use mathematics effectively in its application to situations that arise in their life at home, at work, and in the 
community; and 
• apply, evaluate, and communicate their mathematical thinking.


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11. Equivalence – Mathematical objects or statements can be represented or stated in different ways that have the s ame value, 
form, or logical meaning. 
12. Reasoning and Proof – Mathematical reasoning and proofs establish and communicate the truth and falsity of a mathematical 
statement, computational and/or verbal procedure, and problem-solving process. 
 
Through these Big Ideas, concepts and their competencies that are essential in the succeeding levels of the curriculum and 
that prepare the learners for higher-level mathematics are selected. A concept or a skill is “essential” if it is indispensable in building 
concepts and skills to equip learners for subsequent grade levels and, at the same time, for lifelong learning.  
 
Spiral Progression 
 
Spiral progression was fostered by J.S. Bruner (1977) based on the hypothesis that “any subject can be taught in some


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strategic instructional plans for groups or individual learners at various developmental stages. By effectively connecting co mplex 
material to familiar concepts, teachers can offer appropriate scaffolding such as strategic social interactions, tailored lea rning 
experiences, and instructions aligned with a learner’s prior performance, intuition, and current thought processes. This improves the 
learner’s ability to make sense of new situations, build on prior knowledge, and transfer learning. In teaching mathematics, these 
strategic instructional plans include the use of manipulatives, games, models, partial solutions, or making use of contextual problems 
based on the learner’s interest.  
Meanwhile, Glasersfeld (1987) claims that knowledge is not passively received but actively built up by the cognizing individual 
and thus, knowledge is the result of a self -organized cognitive process.  This suggests that all knowledge is constructed rather than


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& Woodbury, 2018).  
 Regardless of whether assessment is formal or informal, assessment tools should be varied in order to understand the different 
dimensions of students’ learning (SEI-DOST, 2011). While examinations and quizzes have a place in measuring skills  learned, and 
knowledge development and acquisition, many aspects of mathematical learning could be effectively measured by other means such 
as interview tasks, analysis of student work samples, presentations by learners, and questioning by teachers.  
Formative and summative assessment tasks that are appropriate to the grade level and relevant conceptual understanding 
and skills, should be develope d in conjunction with other learning areas. For example, developing a healthy menu plan for a week 
may be primarily in Health or Science, may include Mathematics on the computation of a budget for the daily meal, English for the 
written presentation of the menu, and Arts for the visual presentation of the menu.


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utilized to address simple problems related to sustainable development and disaster risk reduction and management. 
STEM  
Science, Technology, Engineering, and Mathematics (STEM) is a government priority and is significant in the development of 
problem solvers and innovative thinkers. As depicted in the STEM Framework, this is achieved through three learning areas in the K 
to 12 curriculum – Science, Mathematics , and T echnology and Livelihood Education (TLE) , which may collectively employ the 
Engineering Design Process (EDP) to attain curriculum goals. Though distinct and taught separately, these three learning area s are 
interrelated, and each contributes knowledge and skills for the solution of real-world problems. Figure 2 shows a  diagrammatic 
representation of the STEM Framework. 
Figure 2. The diagrammatic representation of the STEM Framework


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the need to integrate financial concepts across learning areas at different levels. In Mathematics, learners focus on concepts relating 
to the identification and value of money and use these concepts to solve specific problems on investment, saving, budgeting, and 
spending. 
 
Pedagogy, Assessment and Resources 
 
The achievement of the Mathematics curriculum goals requires explicit guidance on instruction, on the role of assessment, on 
the use of resources for teaching and learning, and on the use of student context.  
Pedagogy 
In broader terms, there are two types of knowledge at play in a mathematics classroom: the mathematical knowledge that the 
learners have gained from their everyday experiences and the mathematic al knowledge articulated in  the curriculum. Relating 
learners’ informal knowledge of mathematical concepts and facilitating learners’ internalization of school mathematics are major tasks


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Teaching and learning have been assisted and made more inclusive through the use of technology. From calculating devices, 
instructional manipulatives and software applications , to assistive and adaptive devices, the curriculum strongly recommends the 
use of these available technologies to facilitate the teaching and learning of concepts and skills, and to enhance problem solving.  
In particular, the curriculum presupposes the use of instructional manipulatives and software applications in Key Stages 1, 2 
and 3, calculating devices as additional technological support in Key Stage 3, and assistive and adaptive devices for learner s with 
special needs. 
The TIMSS 2019 results show that “there is a modest positive association between home educational resources and average 
mathematics achievement at the country level ” (Mullis et al., 2020, p. 285). Relevant to the level of these home resourc es are the


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areas. 
Development of 21st Century Skills 
 
The knowledge, skills, attitudes, and competencies that learners need to develop so that they can prepare for and succeed  in 
work and life in the 21st century are referred to as “21st century skills.” Through the facilitating facets and supporting components, 
the mathematics curriculum promotes and develops information , media and technology skills ; learning and innovation sk ills; 
communication skills; and life and career skills (DepEd Order 21 S. 2019, p. 6). 
To support learners in meeting the challenges of the 21st century, it is important to nurture their abilities to create innovative 
solutions to real-world problems. This gives further emphasis to the main curriculum goal. 
Through the various mathematical tasks that they undertake, learners are engaged in cognitive processes to understand and 
solve problems using a variety o f approaches, such as modelling, data analysis, and logical reasoning. Such approaches to solving


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and thus, knowledge is the result of a self -organized cognitive process.  This suggests that all knowledge is constructed rather than 
perceived through the senses. For instance, learning multiplication is not just about memorizing the multiplication facts, but it is 
also important for learners to understand the concepts und erlying multiplication. Learners who lack understanding of fundamental 
concepts are more likely to struggle with higher-order thinking. 
The use of representations in mathematics helps to demonstrate a learner ’s thinking.  Whether these representations are 
concrete or abstract, the y help them analyze the problem at hand, formulate an idea, and extend their reasoning.  The NCTM 
Standards (2000) include that c urriculum should emphasize that learners create and use representations to organize, record, and 
communicate mathematical ideas; select, apply, and translate mathematical representations to solve problems; and use


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Spiral Progression 
 
Spiral progression was fostered by J.S. Bruner (1977) based on the hypothesis that “any subject can be taught in some 
intellectually honest form to any child at any stage of development ” (p. 33). It asserts that even the most complex mathematical 
concept can be learned at a young age if it is properly structured, suitably scaffolded, and progressively revisited over a span of time, 
gaining mastery and rigor along the way.


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Key Stage Curriculum and Standards 
Key Stage 1 Curriculum 
Key Stage 1 (KS 1) of the Mathematics curriculum focuses on Grades 1 to 3 learners. At this stage, the curriculum addresses 
the development of early numeracy by focusing on the learners’ understanding of 1-to-4-digit numbers, measures, basic shapes, and 
simple data. It also develops their fluency in carrying out procedures or operations involving these mathematical objects in their 
various representations (concrete, contextual, verbal, visual, and symbolic). Mastery of early numeracy concepts lays the groundwork 
for understanding more complex mathematical concepts and solving more complex problems. 
Learning experiences include basic mathematical explorations of these objects and operations that will engage learners in a v ariety 
of thinking processes in real, in situated, and in purely mathematical contexts. The goal of learning experiences is to suppo rt and


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solve problems using a variety o f approaches, such as modelling, data analysis, and logical reasoning. Such approaches to solving 
problems encourage learners to pursue other Learning and Innovation Skills such as creativity, critical thinking, and reflective 
thinking. Presented with non -routine problems, learners can identify new connections between concepts and ideas, examine the m 
from various perspectives, consider alternative ideas or solutions, and demonstrate willingness to try other methods or strategies in 
spite of previous unsuccessful attempts.  
In developing skills in Informat ion, Media and Technology, learners closely examine, interpret, and communicate 
understanding of various objects, shapes, symbols, and text types to stimulate and nurture visual literacy. By considering di fferent 
objects, shapes and symbols, learners are a ble to bring their understanding of number, geometry, or data management to the


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mathematics achievement at the country level ” (Mullis et al., 2020, p. 285). Relevant to the level of these home resourc es are the 
availability of Internet connection, books, and one’s own room, as well as parents’ level of education. The learners’ home environment, 
together with the availability of technological resources, plays a significant role in supporting the implementation of the curriculum. 
 
The Role of Language 
Mathematics has its own specialized terminology to name objects such as numbers, polygons and functions; its own specialized 
symbolic and representational system; and its own rules for working with these objects. 
Foundational understanding of mathematics is contingent on the learner ’s ability to communicate in the language of 
mathematics. The use of particular mathematical terms and representations demonstrates how a learner’s thinking processes evolve.


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real-life situations). This knowledge, skills and understanding i s applied, with the use of technology, to the processes within 
Mathematics of critical thinking, problem solving, communicating, reasoning, and making connections between topic areas. 
 
Key Stage 2 Curriculum 
Key Stage 2 (KS 2) of the Mathematics curriculum  focuses on Grades 4 to 6 learners. At this stage, the curriculum extends 
numbers, algebra, measures, geometry, data and probability. The coverage includes more complex properties, operations, and 
problems in different contexts that demand efficient written and mental methods of calculation. 
The learning standards of the KS 2 Mathematics curriculum aim to ensure that learners: 
● use efficient mental and written mathematical concepts, operations, procedures, relationships, and tools to solve routine and  
non-routine real-world problems.


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communicate mathematical ideas; select, apply, and translate mathematical representations to solve problems; and use 
representations to model and interpret physical, social, and mathematical phenomena (cited in Fennell & Rowan, 2001).


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objects, shapes and symbols, learners are a ble to bring their understanding of number, geometry, or data management to the 
interpretation of data sets presented in tables and graphs, and to the creation of engaging presentations and infographics. 
The development of communication skills is critical for learners to be able to express their ideas, explain their solutions, and 
justify their reasoning in oral and/or written form. Learning tasks that involve activities that require teamwork and collaboration are 
also avenues for the  development of interpersonal skills, intrapersonal skills, interactive communication, and non -verbal 
communication.


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mathematics. The use of particular mathematical terms and representations demonstrates how a learner’s thinking processes evolve. 
For example, at an early stage of learning, a learner may describe a square as “a shape with four equal sides,” then at a middle stage, 
“a rectangle with four equal sides,” and, at a later stage, “a quadrilateral with four equal angles and four equal sides.” 
For mathematical terms in a multi-lingual classrooms, it is recommended that the English terms be adopted. Furthermore, the 
learner’s language can be used as a tool in learning and understanding mathematics across all levels.


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Harden and Stamper (1999) present the following features of a curriculum that incorporates a spiral progression: 
• topics are revisited; 
• there are increasing levels of difficulty; 
• new learning is related to previous learning; 
• the competence of students increases as learning progresses (p. 141). 
 
Spiral progression is proposed in the structuring of the curriculum. Through this approach, mathematical knowledge and skills 
increase in depth and breadth as the grade level incr eases. Mathematical concepts are revisited in higher grade levels leading to 
increased complexity, increased conceptual understanding, and enhanced problem-solving skills.  
 
Vertical and Horizontal Articulation 
Vertical and horizontal articulation are used with the aim of ensuring that standards and competencies are logically sequenced 
within the mathematics curriculum and across learning areas.  
 
 Vertical Articulation


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learners’ informal knowledge of mathematical concepts and facilitating learners’ internalization of school mathematics are major tasks 
of teaching. It necessitates teaching strategies that bring into the fore what learners already know, such as using in tasks situations 
that are familiar to the learners to draw out the mathematics that they already know in this context.   
For achieving the Mathematics curriculum goal, a variety of pedagogical approaches can be used. Strategies that can be adopted 
include: guided discovery learnin g, inquiry -based learning, reflective learning, experiential learning, and the concrete -
representational-abstract (CRA) instructional approach, among others. In addition, pedagogical approaches that include guided or 
direct instruction coupled with opportunities for learners’ inquiry in generating their own solutions, collaborative learning with peers,


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Key Stage 3 Curriculum 
Key Stage 3 (KS 3) of the Mathematics curriculum focuses on Grades 7 to 1 0 learners. At this stage, the curriculum covers 
algebra, measurement, geometry, and data and probability with greater emphasis on cognitive development towards self-directed 
learning. 
Dealing with more complex and abstract forms, Key Stage 3 concentrates on sets and real numbers, functions, equations, 
inequalities, sequences, axiomatic structure of geometry, triangle congruence and similarity, basic trigonometry, basic statistical 
measures, and probability. 
The learning standards of the KS 3 Mathematics curriculum aim to ensure that learners: 
● apply mathematical concepts, operations, procedures, facts, relationships, and tools to describe, explain, investigate, model, 
and predict phenomena. 
● reason mathematically, construct plausible arguments, evaluate the reasoning of others, and ask useful questions to clarify 
or improve arguments.


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written presentation of the menu, and Arts for the visual presentation of the menu. 
Together with data from international assessments, results from classroom assessments need to be analyzed and used to 
improve planning for further instruction and learning. 
Formative and summative assessments provide opportunities for learners to demonstrate higher-order mathematical thinking, 
justify their solutions , communicate their understandin g, and express their ideas well in written and/or oral form . For instance, 
portfolios of learner’s mathematical work on meaningful tasks (e.g., drawing interconnections of mathematical concepts across various 
disciplines), as well as reports, including mathematical investigations, may be employed. 
 As envisioned for the revised curriculum, the continuous inte raction of teaching and learning may be realized through 
assessment tasks that are information driven and are seamlessly designed to communicate the goals of successful learning. 
Resources


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of thinking processes in real, in situated, and in purely mathematical contexts. The goal of learning experiences is to suppo rt and 
strengthen the young learners’ interest and appreciation of mathematics as a tool for solving problems and for communicating ideas 
in everyday situations. 
The learning standards of the Key Stage 1 Mathematics curriculum aim to ensure that learners: 
● accurately understand and apply concepts, operations, procedures, and relationships in solving routine and non -routine 
problems related to their day-to-day lives. 
● acquire high-level skills and fluency in the procedures and processes of mathematics through varied frequent practice and 
meaningful learning experiences. 
● communicate and represent mathematical concepts and understanding using developmentally appropriate language. 
● acquire problem-solving and critical thinking skills through real, situated or purely mathematical problems.


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direct instruction coupled with opportunities for learners’ inquiry in generating their own solutions, collaborative learning with peers, 
and independent learning, may also be employed. Mastery learning is also emphasized to ensure that learners reach a certain level 
of proficiency to be able to engage in a new learning task successfully.


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the use of technology, to the processes within Mathematics of critical thinking, problem solving, communicating, 
reasoning, and making connections between topic areas. 
GRADE 3 The learner demonstrates knowledge, skills, an d understanding in relation to the curriculum content domains 
Number and Algebra ( whole numbers up to 10 000; ordinal numbers up to 100 th; addition and subtraction of 
numbers of up to 4 digits, and money up to ₱10 000; multiplication using 6, 7, 8 and 9 mu ltiplication tables; 
estimation of products of two numbers by first rounding to the nearest multiple of 10; determination of missing 
terms contained in repeating and increasing patterns and repeating and decreasing patterns; generation of 
repeating and inc reasing patterns, and repeating and decreasing patterns; division using the 6, 7, 8 and 9 
multiplication tables; division of 2 - to 4-digit numbers; estimation of quotients by first rounding the divisor and


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Cartesian plane; central angles, inscribed angles, and angles and lengths formed by intersecting chords, secants, and tangents of a 
circle; sectors and segments of a circle, and their areas); Data and Probability (Fundamental Counting Principle; probabilities of simple 
and compound events; box-and-whisker plots, and cumulative frequency histograms and polygons; quartiles, deciles, and percentiles; 
interquartile range, and outliers; evaluation of statistical reports; union and intersection of events, dependent and independent events, 
and complementary events). This knowledge, skills and understanding is applied, with the use of technology, to the processes within 
Mathematics of critical thinking, problem solving, communicating, reasoning, and making connections between topic areas. 
 
GRADE LEVEL STANDARDS 
GRADE 
LEVEL 
GRADE LEVEL STANDARDS 
GRADE 1 The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains


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within the mathematics curriculum and across learning areas.  
 
 Vertical Articulation 
Vertical articulation is concerned with the development of mathematical knowledge, skill s, and understanding across the 
grades in the curriculum.  Key Stage 1 centers on foundational competencies in the three content domains.  These competencies 
gradually progress to Key Stages 2 and 3, with an emphasis on analysis, reasoning, and communicating mathematically to confidently 
solve mathematical problems. 
Emphasizing the key concepts identified, the Big Ideas reinforce the learning to achieve mathematical proficiency. Learners are 
equipped with skills and processes to carry out mathematical procedures and to solve problems. They are then able to communicate 
their reasoning and successfully complete tasks of higher cognitive demand. 
 
Horizontal Articulation 
Horizontal articulation is concerned with the role of mathematics across the curriculum. For instance, the concepts and skills


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assessment tasks that are information driven and are seamlessly designed to communicate the goals of successful learning. 
Resources 
Appropriate resources are fundamental to supporting the delivery  of a quality curriculum. Such resources are developed and 
disseminated to schools for the various learning areas and grades.


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communicating, reasoning, and making connections between topic areas. 
GRADE 6 The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains 
Number and Algebra ( the four operations with decimals; the four operations with different combinations of 
fractions, whole numbers,  and mixed numbers; ratio and proportion; percentages, and their relationships with 
fractions and decimals; exponential form, including calculation using the GEMDAS rules; common factors, greatest 
common factors, common multiples, and least common multiple s); Measurement and Geometry ( tessellation of 
shapes; translation, reflection, and rotation with shapes; units of volume and capacity; volume of cubes and 
rectangular prisms; perimeter and area of triangles, parallelograms, trapezoids, and composite figures composed 
of triangles, squares, and rectangles; parts of a circle, including circumference; area of a circle; composite figures


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GRADE LEVEL STANDARDS 
GRADE 
LEVEL 
GRADE LEVEL STANDARDS 
GRADE 1 The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains 
Number and Algebra (whole numbers up to 100 ; ordinal numbers up to 10 th; addition of numbers with su ms up 
to 20; place value in any 2-digit number; addition of numbers, with sums up to 100; subtraction of numbers where 
both numbers are less than 100; repeating patterns, fractions ½ and ¼; the denominations and values of Philippine 
coins and bills up to ₱100; addition of money where the sum is up to ₱100 and subtraction of money where both 
amounts are less than ₱100); Measurement and Geometry (simple 2-dimensional shapes; measurement of length 
and distance using non -standard units; the movement of objects  in half turn or quarter turn, in clockwise or 
counter clockwise direction; time measured in hours, half-hours, quarter hours, days, weeks, months, years); and


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and predict phenomena. 
● reason mathematically, construct plausible arguments, evaluate the reasoning of others, and ask useful questions to clarify 
or improve arguments. 
● access, use, interpret and communicate mathematical information and ideas to engage in and manage the mathematical 
demands in various 21st-century contexts. 
● utilize mathematical thinking in decision making and acquire problem -solving and critical thinking skills through real, 
situated, or purely mathematical problems; and 
● strengthen appreciation, curiosity, interest, creativity, and other desirable values, attitudes , and dispositi ons in 
mathematics. 
 
Key Stage 3 Standards 
At the end of Grade 10, the learner demonstrates knowledge, skills, and understanding in relation to the curriculum content 
domain Number and Algebra (use of rates; sets and subsets, and the union and intersection of sets; Venn diagrams; operations using


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the Fundamental Counting Principle ). This knowledge, skills, and understanding is applied, with the use of 
technology, to the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, 
and making connections between topic areas. 
GRADE 9 The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains 
Number and Algebra ( relations and functions; graphs of linear functions, and the identification of dom ain and 
range, slope, intercepts, and zeros; quadratic equations and graphs of quadratic functions; the solution of 
quadratic equations; direct and inverse variation ); Measurement and Geometry ( simple geometric concepts and 
notations; perpendicular and parallel lines, and angles formed by parallel lines cut by a transversal; quadrilaterals 
and their properties; congruence of triangles; congruence proofs; similarity of polygons; special triangles; triangle


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multiplication tables; division of 2 - to 4-digit numbers; estimation of quotients by first rounding the divisor and 
dividend to the nearest multiple of 10, addition and subtraction of similar fractions); Measurement and Geometry 
(areas of squares and rectangles; points, lines, line segments, and rays; parallel, perpendicular and intersecting 
lines; measures of mass and capacity; line symmetry; resulting figure after a translation); and Data and Probability 
(data presented in tables and single bar graphs; outcomes from experiments and real -life situations ). This 
knowledge, skills, and understanding is applied, with the use of technology, to the processes within Mathematics 
of critical thinking, problem solving, communicating, reasoning, and making connections between topic areas. 
GRADE 4 The learner demonstrates knowledge, skills, and understanding in relat ion to the curriculum content domains


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● acquire problem-solving and critical thinking skills through real, situated or purely mathematical problems. 
● develop appreciation, curiosity, interest, creativity, and other desirable values, attitudes and dispositions in mathematics. 
 
Key Stage 1 Standards 
At the end of Grade 3, the learner demonstrates knowledge, skills , and understanding in relation to the curriculum content 
domain Number and Algebra (whole numbers up to 10 000; ordinal numbers up to 100th; addition and subtraction of numbers of up 
to 4 digits, and money up to ₱10 000; multiplication and division using 6, 7, 8 and 9 multiplication tables; estimation of products of 
two numbers; determination of missing terms contained in patterns; generation of patterns; division of 2 - to 4 -digit numbers; 
estimation of quotients; addition and subtraction of similar fractions); Measurement and Geometry (areas of squares and rectangles;


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Horizontal Articulation 
Horizontal articulation is concerned with the role of mathematics across the curriculum. For instance, the concepts and skills 
in Key Stage 1 are indispensable in the development of foundational skills in other learning areas.  Predominantly falling under 
languages learning areas, foundational skills in reading and writing are requisite to a fuller understanding of mathematical concepts 
and skills, including in reading and writing numbers expressed using numerals and in words, determining place value, and counting.  
Meanwhile, concepts and skills in Mathematics are articulated vis-à-vis those in other learning areas. For example, describing 
the motion of an object in terms of distance, velocity , and acceleration in Science requires knowledge o f formulating equations and


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domain Number and Algebra (use of rates; sets and subsets, and the union and intersection of sets; Venn diagrams; operations using 
scientific notation; rules for obtaining terms in sequences; earning money, profit and loss, ‘best buys’, buying on terms; relations and 
functions; graphs of linear functions, and the identification of domain and r ange, slope, intercepts, and zeros; direct and inverse 
variation; quadratic inequalities in one variable and in two variables; absolute value equations and inequalities in one vari able, and 
their graphs; radical expressions; the roots of a quadratic equation; quadratic functions; equations reducible to quadratic equations; 
equation of a circle and the graph of a circle; compound interest and depreciation); Measurement and Geometry (volume of squa re 
and rectangular pyramids, and cylinders; measures of length, area, surface area, volume, time, and temperature; volume of pyramids,


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of triangles, squares, and rectangles; parts of a circle, including circumference; area of a circle; composite figures 
composed of any two or more of: triangle, square, rectangle, circle, semi -circle); and Data and Probability 
(construction and interpretation of pie graphs). This knowledge, skills, and understanding is applied, in association 
with the use of technology, in the processes within Mathematics of critical thinking, problem solving, 
communicating, reasoning, and making connections between topic areas. 
GRADE 7 The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains 
Number and Algebra (application of percentages; use of rates; rational numbers; square roots of perfect squares, 
cube roots of perfect cubes , and irrational numbers; sets an d subsets, and the union and intersection of sets; 
Venn diagrams; the set of integers, and comparing and ordering integers; the four operations with integers;


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and their properties; congruence of triangles; congruence proofs; similarity of polygons; special triangles; triangle 
theorems and triangle inequality theorems; the trigo nometric ratios and their application ); and Data and 
Probability (interpretation and analysis of data to assess whether the data may be misleading; probabilities of 
simple and compound events). This knowledge, skills, and understanding is applied, with the  use of technology, 
to the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, and making 
connections between topic areas. 
GRADE 10 The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains 
Number and Algebra ( quadratic inequalities in one variable and in two variables; absolute value equations and 
inequalities in one variable, and their graphs; radical expressions; the roots of a quadratic equation; quadratic


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counter clockwise direction; time measured in hours, half-hours, quarter hours, days, weeks, months, years); and 
Data and Probability ( pictographs without a scale for the representation of data ). This knowledg e, skills, and 
understanding is applied, with the use of technology, to the processes within Mathematics of critical thinking, 
problem solving, communicating, reasoning, and making connections between topic areas. 
GRADE 2 The learner demonstrates knowledg e, skills, and understanding in relation to the curriculum content domains 
Number and Algebra (whole numbers up to 1000, ordinal numbers up to 20th,; addition of numbers with sums up 
to 1000; the denominations and values of Philippine coins and bills up to  ₱1000, and the addition of amounts of 
money with sums up to ₱1000; subtraction of numbers where both numbers are less than 1000; increasing 
patterns and decreasing patterns; multiplication and division of whole numbers using  the 2, 3, 4, 5, and 10


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GRADE 4 The learner demonstrates knowledge, skills, and understanding in relat ion to the curriculum content domains 
Number and Algebra ( whole numbers up to 1 000 000; addition of numbers with sums up to 1 000 000  and 
subtraction of numbers where both numbers are less than 1 000 000; multiplication of whole numbers with 
products-up to 1 000 000; division of up to 4 -digit numbers by up to 2 -digit numbers, and the MDAS rules; 
addition and subtraction of similar fractions, including mixed numbers; dissimilar and equivalent fractions; factors 
and multiples of numbers up to 100; addition a nd subtraction of dissimilar fractions; simple patterns; number 
sentences; decimal numbers and their relationship to fractions ); Measurement and Geometry ( right, acute, and 
obtuse angles; properties of triangles and quadrilaterals; perimeter of quadrilaterals, and composite figures 
composed of triangles and quadrilaterals; conversion of units of length, mass, capacity, and time; symmetric


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estimation of quotients; addition and subtraction of similar fractions); Measurement and Geometry (areas of squares and rectangles; 
points, lines, line segments, and rays; parallel, perpendicular, and intersecting lines; measures of mass and capacity; line symmetry; 
resulting figure translation; duration of time, elapsed time, and telling and writing time in hours and minutes (using a.m. and p.m.); 
composite figures made up of squares, rectangles, triangles, circles, half-circles, and quarter-circles; perimeter of triangles, squares, 
and rectangles); Data and Probability (data presented in tables, pictographs, and single bar graphs; outcomes from experiments and


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and rectangular pyramids, and cylinders; measures of length, area, surface area, volume, time, and temperature; volume of pyramids, 
cones, and spheres; the Pythagorean Theorem; triangle inequality theorems; perpendicular and parallel lines, and angles formed by  
parallel lines cut by a transversal; congruence of tr iangles; congruence proofs; similarity of polygons; special triangles; triangle 
theorems and triangle inequality theorems; the laws of sines and the laws of cosines; translations, reflections, and rotations in the


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Grade 1 
CONTENT 
DOMAIN 
CONTENT STANDARDS 
The learners should have knowledge 
and understanding of ... 
LEARNING COMPETENCIES 
The learners … 
Quarter 1 
Measurement 
and 
Geometry 
(MG) 
1. simple 2-dimensional shapes 
and their features. 
1. identify simple 2-dimensional shapes (triangle, rectangle, square) of different size and 
in different orientation. 
2. compare and distinguish 2-dimensional shapes according to features such as sides and 
corners. 
3. compose and decompose triangles, squares, and rectangles. 
Number 
and 
Algebra 
(NA) 
2. whole numbers up to 100. 
3. ordinal numbers up to 10th. 
4. addition of numbers with sums 
up to 20. 
4. count up to 100 (includes counting up or down from a given number and identifying a 
number that is 1 more or 1 less than a given number). 
5. read and write numerals up to 100. 
6. recognize and represent numbers up to 100 using a variety of concrete and pictorial


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inequalities in one variable, and their graphs; radical expressions; the roots of a quadratic equation; quadratic 
functions; equations reducible to quadratic equations; equation of a circle and the graph of a circle; compound 
interest and depreciation); Measurement and Geometry ( the laws of sines and the laws of cosines; translations, 
reflections, and rotations, in the Cartesian plane; central angles, inscribed angles, and angles and lengths formed 
by intersecting chords, secants, and tangents of a circle; sectors and segments of a circle, and their areas ); and 
Data and Probability ( box-and-whisker plots, and cumulative fre quency histograms and polygons; quartiles, 
deciles, and percentiles; interquartile range, and outliers; evaluation of statistical reports; union and intersection 
of events, dependent and independent events, and complementary events ). This knowledge, skills , and


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Venn diagrams; the set of integers, and comparing and ordering integers; the four operations with integers; 
simplification of numerical expressions involving integers; absolute value of an integer; the sol ution of simple 
equations; the evaluation of algebraic expressions following substitution; the rearrangement of a formula to make 
a different variable the subject of the formula; operations using scientific notation ); Measurement and Geometry 
(regular and irregular polygons and their features/properties; determination of measures of angles and number of 
sides of polygons; conversion of units of measure; volume of square and rectangular pyramids, and cylinders; 
measures of length, area, surface area, volume, time, and temperature); and Data and Probability (data collection 
and sampling techniques, and the presentation of data in appropriate tables and graphs; interpretation of


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patterns and decreasing patterns; multiplication and division of whole numbers using  the 2, 3, 4, 5, and 10 
multiplication tables; odd and even numbers; unit fractions and similar fractions with denominators 2, 3, 4, 5, 6, 
and 8); Measurement and Geometry (circles, half circles, quarter circles and composite figures made up of squares, 
rectangles, triangles, circles, half-circles, and quarter-circles; one step slides and flips of basic shapes and figures; 
measurement, comparison, and estimation of length and distance using appropriate tools and units ; duration of 
time, elapsed time, and telling and writing time in hours and minutes (using a.m. and p.m.); straight and curved 
lines, and flat and curved surfaces; the perimeter of triangles, squares, and rectangles); and Data and Probability 
(pictographs with a scale for the representation of data). This knowledge, skills, and understanding is applied, with


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Grade 1 
Quarter 2 
Measurement 
and 
Geometry  
(MG) 
1. measurement of length and 
distance using non-standard 
units. 
1. measure the length of an object and the distance between two objects using non-standard 
units. 
2. compare lengths and distances using non-standard units. 
3. solve problems involving lengths and distances using non-standard units. 
Number 
and 
Algebra 
(NA) 
2. place value in any 2-digit 
number. 
3. addition of numbers, with 
sums up to 100. 
4. order numbers up to 100 from smallest to largest, and vice versa. 
5. counts by 2s, 5s and 10s up to 100. 
6. determine 
a. the place value of a digit in a 2-digit number, 
b. the value of a digit, and 
c. the digit of a number, given its place value 
7. decompose any 2-digit number into tens and ones. 
8. add numbers by expressing addends as tens and ones (expanded form). 
9. add numbers with sums up to 100 without regrouping, using a variety of concrete and 
pictorial models for:


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Data 
and 
Probability  
(DP) 
1. a pictograph without a scale 
for the representation of data. 
1. collect data in one variable through a simple interview. 
2. present data in a pictograph without a scale. 
3. interpret a pictograph without a scale. 
4. organize data in a pictograph without a scale into a table. 
Number 
and 
Algebra 
(NA) 
2. subtraction of numbers where 
both numbers are less than 
100. 
3. repeating patterns. 
5. illustrate subtraction involving numbers up to 20 using a variety of concrete and 
pictorial models, and describes subtraction as “taking away.”  
6. find the missing number in addition or subtraction sentences involving numbers up to 
20. 
7. write an equivalent expression to a given addition or subtraction expression (e.g., 2+3 = 
1+4; 10-5 = 6-1). 
8. solve subtraction problems (given orally or in pictures) where both numbers are less 
than 20. 
9. subtract numbers where both numbers are less than 100 using concrete and pictorial


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and sampling techniques, and the presentation of data in appropriate tables and graphs; interpretation of 
statistical graphs; outcomes from experiments). This knowledge, skills, and understanding is applied, with the use 
of technology, to the processes within Mathematics of critical thinking, problem solving, communicating, 
reasoning, and making connections between topic areas. 
GRADE 8 The learner demonstrates knowledge, skills and understa nding in relation to the curriculum content domains 
Number and Algebra (algebraic expressions and operations with monomials, binomials, and multinomials; special 
products for binomials, and factorization of polynomials; rational algebraic expressions and e quations; rules for 
obtaining terms in sequences; plotting points, and finding distance and the midpoint of line segments on the 
Cartesian coordinate plane; earning money, profit and loss, ‘best buys,’ buying on terms; linear equations in one


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number that is 1 more or 1 less than a given number). 
5. read and write numerals up to 100. 
6. recognize and represent numbers up to 100 using a variety of concrete and pictorial 
models (e.g., number line, block or bar models, and numerals). 
7. compare two numbers up to 20. 
8. order numbers up to 20 from smallest to largest, and vice versa. 
9. describe the position of objects using ordinal numbers: 1st, 2nd, 3rd, up to 10th. 
10. compose and decompose numbers up to 10 using concrete materials (e.g., 5 is 5 and 0; 
4 and 1; 3 and 2; 2 and 3; 1 and 4; 0 and 5). 
11. illustrate addition of numbers with sums up to 20 using a variety of concrete and 
pictorial models and describes addition as “counting up,” and “putting together.” 
12. illustrate by applying the following properties of addition, using sums up to 20: 
a. the sum of zero and any number is equal to the number, and 
b. changing the order of the addends does not change the sum.


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composed of triangles and quadrilaterals; conversion of units of length, mass, capacity, and time; symmetric 
figures and designs; reflection with shapes); and Data and Probability ( presentation and interpretation of data in 
tabular form and in a simple line graph ). This knowledge, skills, and understanding is applied, with the use of 
technology, to the processes within Mathematics of critical thinking, problem solving, communicating, reasoning, 
and making connections between topic areas. 
GRADE 5 The learner demonstrates knowledge, skills, and understanding in relation to the curriculum content domains 
Number and Algebra ( the GMDAS rules for operations with numbers; multiplication and division of fractions; 
decimal numbers with decimal pa rts up to ten thousandths; addition and subtraction of decimal numbers; 
divisibility rules; prime and composite numbers; multiplication and division of decimal numbers; GMDAS rules


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Number 
and 
Algebra 
(NA) 
1. fractions 
1
2 and 
1
4. 
2. the denominations and 
values of Philippine coins 
and bills up to ₱100. 
3. addition of money where the 
sum is up to ₱100 and 
subtraction of money where 
both amounts are less than 
₱100. 
1. illustrate 
1
2  and 
1
4  as parts of a whole.  
2. compare 
1
2  and 
1
4  using models. 
3. count halves and quarters 
4. recognize coins (excluding centavo coins) and bills up to ₱100 and their notations. 
5. determine the value of a number of bills and/or a number of coins (excluding centavo 
coins) up to ₱100. 
6. compare different denominations of peso coins (excluding centavo coins) and bills up to 
₱100. 
7. solve 1-step problems (given orally or in pictures) involving addition of money where the 
sum is up to ₱100, or subtraction of money where both amounts are less than ₱100. 
Measurement 
and 
Geometry  
(MG) 
4. the movement of objects in 
half turn or quarter turn, in 
clockwise or counter


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of events, dependent and independent events, and complementary events ). This knowledge, skills , and 
understanding is applied, in association with the use of technology, in the processes within Mathematics of critical 
thinking, problem solving, communicating, reasoning, and making connections between topic areas.


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8. solve subtraction problems (given orally or in pictures) where both numbers are less 
than 20. 
9. subtract numbers where both numbers are less than 100 using concrete and pictorial 
models, without regrouping: 
a. 2-digit minus 1-digit numbers, and  
b. 2-digit minus 2-digit numbers. 
10. subtract numbers by expressing minuends and subtrahends as tens and ones 
(expanded form), without regrouping. 
11. determine the next term/s in a repeating pattern (patterns could use rhythmic 
properties, visual elements in the arts, …) 
(e.g., numbers: 2, 4, 2, 4__, __; letters: a, b, c, a, b, c, a, __, __,). 
12. create repeating patterns using objects, images, or numbers. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• represent and interpret data in a pictograph without a scale. (DP) 
• perform subtraction of numbers where both numbers are less than 100. (NA) 
• extend existing repeating patterns and create new repeating patterns. (NA) 
 
  
Grade 1


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Cartesian coordinate plane; earning money, profit and loss, ‘best buys,’ buying on terms; linear equations in one 
variable; linear inequalities in one variable and their graphs; linear equations in two variables and their graphs; 
systems of linear equations in two variables; linear inequalities in two variables ); Measurement and Geometry 
(volume of pyramids, cones, and spheres; the Pythagorean Theorem; triangle inequality theorems); and Data and 
Probability ( measures of central tendency of ungrouped data; measures of variability for ungrouped data; 
interpretation and analysis of graphs from primary and secondary data; experimental and theoretical probability;


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a. the sum of zero and any number is equal to the number, and 
b. changing the order of the addends does not change the sum. 
13. solve problems (given orally or in pictures) involving addition with sums up to 20.  
Performance Standards 
By the end of the quarter, the learners are able to … 
• identify and distinguish simple 2-dimensional shapes. (MG) 
• count, recognize and represent whole numbers up to 100. (NA) 
• use ordinal numbers up to 10th to describe position. (NA) 
• compare and order numbers up to 20 and perform addition of numbers with sums up to 20. (NA)


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Grade 2 
CONTENT 
DOMAIN 
CONTENT STANDARDS 
The learners should have 
knowledge and understanding of ... 
LEARNING COMPETENCIES 
The learners … 
 
Quarter 1 
Measurement 
and 
Geometry  
(MG) 
1. circles, half circles, quarter 
circles and composite figures 
made up of squares, rectangles, 
triangles, circles, half circles, 
and quarter circles. 
2. one step slides and flips of 
basic shapes and figures.  
1. represent and describe circles, half circles and quarter circles. 
2. compose and decompose composite figures made up of squares, rectangles, triangles, 
circles, half circles, and quarter circles, using cut-outs and square grids. 
3. describe and draw the effect of one-direction multi-step slide (or translation) in basic 
shapes and figures. 
Number 
and 
Algebra 
(NA) 
3. whole numbers up to 1000. 
4. ordinal numbers up to 20th. 
5. addition of numbers with sums 
up to 1000. 
4. count up to 1000. 
5. read and write numerals up to 1000.


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divisibility rules; prime and composite numbers; multiplication and division of decimal numbers; GMDAS rules 
when performing three or more operations with fractions and decimals); Measurement and Geometry (12- and 24-
hour time, and world time zones; area of a parallelogram, triangle, and trapezoid; prisms and pyramids; surface 
area of solid figures; cubes and rectangular prisms; rotation about a point given an angle); and Data and Probability 
(double bar graphs and double li ne graphs; theoretical probability). This knowledge, skills, and understanding is 
applied, with the use of technology, to the processes within Mathematics of critical thinking, problem solving,


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8. add numbers by expressing addends as tens and ones (expanded form). 
9. add numbers with sums up to 100 without regrouping, using a variety of concrete and 
pictorial models for: 
a. 2-digit and 1-digit numbers, and 
b. 2-digit and 2-digit numbers. 
10. solve problems (given orally or in pictures) involving addition with sums up to 100 without 
regrouping. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• use non-standard units to compare and measure length and distance. (MG) 
• order and decompose (into tens and ones) numbers up to 100. (NA) 
• perform addition of numbers with sums up to 100. (NA)


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Measurement 
and 
Geometry  
(MG) 
4. the movement of objects in 
half turn or quarter turn, in 
clockwise or counter 
clockwise direction. 
5. time measured in hours, half 
hours, quarter hours, days, 
weeks, months, and years. 
8. identify the position of objects moved in half turn or in quarter turn, in clockwise or in 
counter-clockwise direction, given an initial facing direction. 
9. read and write time by the hour, half hour, and quarter hour using an analog clock. 
10. give the days of the week and months of the year in the correct order. 
11. determine the day and month of the year using a calendar. 
12. solve problems involving time (hour, half hour, quarter hour, days in a week, and months 
in a year). 
Performance Standards 
By the end of the quarter, the learners are able to … 
• illustrate and compare the fractions 
1
2 and 
1
4. (NA) 
• recognize, and determine the value of, Philippine coins and bills up to ₱100. (NA)


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Performance Standards 
By the end of the quarter, the learners are able to … 
• represent and describe circles, half circles and quarter circles. (MG) 
• compose and decompose composite figures made up of squares, rectangles, triangles, circles, half circles, and quarter circles. (MG) 
• describe and draw the effect of one-step slides or flips in basic shapes and figures. (MG) 
• count, recognize, and represent, whole numbers up to 1000. (NA) 
• use ordinal numbers up to 20th to describe position. (NA) 
• perform addition of numbers with sums up to 1000. (NA)


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Number 
and 
Algebra 
(NA) 
3. whole numbers up to 1000. 
4. ordinal numbers up to 20th. 
5. addition of numbers with sums 
up to 1000. 
4. count up to 1000. 
5. read and write numerals up to 1000. 
6. recognize and represent numbers up to 1000 using a variety of concrete and pictorial 
models, and numerals. 
7. count by 2s, 5s, 10s, 20s, 50s, and 100s (not beyond 1000). 
8. order numbers up to 1000 from smallest to largest, and vice versa. 
9. describe the position of objects using ordinal numbers up to 20th. 
10. determine 
a. the place value of a digit in a 3-digit number, 
b. the value of a digit, and 
c. the digit of a number, given its place value. 
11. illustrate addition of 2-digit and by 1-digit numbers as “counting up” on the number 
line. 
12. add numbers with sums up to 1000 in expanded form. 
13. add numbers with sums up to 1000, with or without regrouping. 
14. illustrate and apply the following properties of addition using sums up to 1000:


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Grade 2 
Quarter 3 
Data 
and 
Probability  
(DP) 
1. a pictograph with a scale for 
the representation of data. 
1. present raw data, or data in tabular form, in a pictograph with a scale, or vice versa.  
2. interpret data in tabular form and in a pictograph with or without scale. 
Number 
and 
Algebra 
 
2. multiplication and division of 
whole numbers using the 2, 
3, 4, 5, and 10 multiplication 
tables. 
3. odd and even numbers. 
3. count the number of concrete objects in a group by repeated addition and create equal 
groups, using language such as “5 groups of 3” and “5 threes”. 
4. illustrate and write multiplication as repeated addition, using a variety of concrete and 
pictorial models and numerals, and using  
a. groups of equal quantities, 
b. arrays, 
c. counting by multiples, and 
d. equal jumps on a number line. 
5. multiply numbers using the 2, 3, 4, 5, and 10 multiplication tables.


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Grade 2 
Quarter 2 
Number 
and 
Algebra 
(NA) 
1. the denominations and values 
of Philippine coins and bills 
up to ₱1000, and the addition 
of amounts of money with 
sums up to ₱1000. 
1. determine and write the value of a number of bills, or a number of coins, or a combination 
of bills and coins up to ₱1000 (centavo coins only, peso coins only, peso bills only, 
combined peso coins and peso bills). 
2. compare the values of different denominations of peso coins and bills up to ₱1000.  
3. solve problems involving addition with sums up to 1000, including problems involving 
money, with and without regrouping. 
Measurement 
and 
Geometry 
(MG) 
2. measurement, comparison, 
and estimation of length and 
distance using appropriate 
tools and units. 
4. measure and compare lengths of objects, in meters (m) or centimeters (cm), and distance in 
meters, using appropriate measuring tools.


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Grade 2 
Quarter 4 
Number 
and 
Algebra 
(NA) 
1. unit fractions and similar 
fractions with denominators 2, 
3, 4, 5, 6, and 8. 
1. represent and identify unit fractions with denominators 2, 3, 4, 5, 6, and 8. 
2. read and write unit fractions in fraction notation. 
3. order unit fractions from smallest to largest, and vice versa. 
4. represent and identify similar fractions with denominators 2, 3, 4, 5, 6, and 8 using groups 
of objects, fraction charts, fraction tiles, and the number line. 
5. read and write similar fractions in fraction notation. 
6. order similar fractions from smallest to largest, and vice versa. 
Measurement 
and 
Geometry 
(MG) 
2. duration of time, elapsed time, 
and telling and writing time in 
hours and minutes (using 
a.m. and p.m.). 
3. straight and curved lines, and 
flat and curved surfaces. 
4. the perimeter of triangles, 
squares, and rectangles. 
7. describe the duration of an event in terms of number of days and/or weeks using a


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• illustrate and compare the fractions 
1
2 and 
1
4. (NA) 
• recognize, and determine the value of, Philippine coins and bills up to ₱100. (NA) 
• add money where the sum is up to ₱100 and subtract money where both amounts are less than ₱100. (NA) 
• identify the position of an object following a half turn or quarter turn, in clockwise or counter-clockwise direction. (MG) 
• identify and work with time measured in hours, half hours, quarter hours, days, weeks, months, and years. (MG) 
 
  
Grade 1 
Quarter 4


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Grade 3 
CONTENT 
DOMAIN 
CONTENT STANDARDS 
The learners should have knowledge 
and understanding of ... 
LEARNING COMPETENCIES 
The learners … 
 
Quarter 1 
Measurement 
and 
Geometry 
(MG) 
1. areas of squares and 
rectangles. 
2. points, lines, line segments, 
and rays. 
3. parallel, perpendicular, and 
intersecting lines. 
1. illustrate and estimate the area of a square or rectangle using square tile units. 
2. explore inductively the derivation of the formulas for the areas of a square and a 
rectangle using square tile units.  
3. find the areas of squares and rectangles in sq. cm and sq. m. 
4. solve problems involving areas of squares and rectangles. 
5. recognize, using models, and draws a point, line, line segment, and ray. 
6. recognize and draw parallel, intersecting, and perpendicular lines. 
7. identify and draw line segments of equal length using a ruler. 
Number 
and 
Algebra 
(NA) 
4. whole numbers up to 10 000. 
5. ordinal numbers up to 100th.


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• perform subtraction of numbers where both numbers are less than 100. (NA) 
• extend existing repeating patterns and create new repeating patterns. (NA) 
 
  
Grade 1 
Quarter 3


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13. add numbers with sums up to 1000, with or without regrouping. 
14. illustrate and apply the following properties of addition using sums up to 1000: 
a. the sum of zero and any number is equal to the number, 
b. changing the order of the addends does not change the sum, and 
c. changing the grouping of the addends does not change the sum.


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a. groups of equal quantities, 
b. arrays, 
c. counting by multiples, and 
d. equal jumps on a number line. 
5. multiply numbers using the 2, 3, 4, 5, and 10 multiplication tables. 
6. solve multiplication problems using the 2, 3, 4, 5, and 10 multiplication tables, including 
problems involving money. 
7. illustrate division through equal distribution of a number of objects into several groups. 
8. illustrate and write division expressions using a variety of concrete and pictorial models 
and numerals, in modelling division as:  
a. equal sharing or formation of equal groups of objects, and 
b. repeated subtraction. 
9. divide numbers using the 2, 3 4, 5, and 10 multiplication tables.   
10. find the missing number in a number sentence involving multiplication or division by 2, 3, 
4, 5, and 10.  
11. distinguish even and odd numbers using division by 2. 
12. solve division problems using the 2, 3, 4, 5, and 10 multiplication tables, including 
problems involving money.


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flat and curved surfaces. 
4. the perimeter of triangles, 
squares, and rectangles. 
7. describe the duration of an event in terms of number of days and/or weeks using a 
calendar. 
8. read and write time in hours and minutes, with a.m. and p.m., using an analog clock. 
9. solve problems involving elapsed time (minutes in an hour, hours in a day, days in a week), 
including timetables. 
10. identify and explain the difference between straight and curved lines, and flat and curved 
surfaces of 3-dimensional objects. 
11. identify and measure the perimeter of a plane figure using appropriate tools.  
12. find the perimeter of triangles, squares, and rectangles. 
13. solve problems involving perimeter of triangles, squares, and rectangles. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• represent, identify, and order unit fractions and similar fractions with denominators 2, 3, 4, 5, 6, and 8. (NA)


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Grade 3 
Quarter 2 
Measurement 
and 
Geometry 
(MG) 
1. measures of mass and 
capacity. 
1. measure mass in grams (g), kilograms (kg) and/or milligrams (mg), using appropriate 
measuring tools. 
2. estimate mass of an object using grams, kilograms, and/or milligrams. 
3. compare masses of objects including the use of a balance scale. 
4. measure capacity in liters (L) and/or milliliters (mL), using appropriate measuring tools. 
5. estimate capacity using liters and/or milliliters. 
6. compare capacities of two containers. 
Number and 
Algebra (NA) 
2. addition and subtraction of 
numbers of up to 4 digits and 
money up to ₱10 000. 
6. read and write money in words and using: 
a. Philippine currency symbols (₱ and PhP) up to ₱10 000, and 
b. the centavo sign. 
7. add numbers with sums up to 10 000, with and without regrouping. 
8. estimate the sum of addends with up to 4 digits.


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● use efficient mental and written mathematical concepts, operations, procedures, relationships, and tools to solve routine and  
non-routine real-world problems. 
● reason and communicate using precise mathematical language to discuss ideas, investigate problems, and justify solutions. 
● exhibit willingness and confidence to explore alternative solutions, and to take risks necessary to solve real-world problems. 
● acquire problem-solving and critical thinking skills through real, situated, or purely mathematical problems; and 
● enhance appreciation, curiosity, interest, creativity, and other desirable values, attitudes and dispositions in mathematics. 
 
Key Stage 2 Standards 
At the end of Grade 6, the learner demonstrates knowledge, skills , and understanding in relation to the curriculum content 
domain Number and Algebra (the four operations with decimals; the four operations with different combinati ons of fractions, whole


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7. identify and draw line segments of equal length using a ruler. 
Number 
and 
Algebra 
(NA) 
4. whole numbers up to 10 000. 
5. ordinal numbers up to 100th. 
8. represent numbers up to 10 000 using pictorial models and numerals. 
9. read and write numbers up to 10 000 in numerals and in words. 
10. describe the position of objects using ordinal numbers up to 100th. 
11. determine 
a. the place value of a digit in a 4-digit number, 
b. the value of a digit, and 
c. the digit of number, given its place value. 
12. round numbers to the nearest ten, hundred, or thousand. 
13. compare numbers up to 10 000 using the symbols =, >, and <. 
14. order numbers up to 10 000 from smallest to largest, and vice versa. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• determine the area of squares and rectangles. (MG) 
• recognize and draw points, lines, lines segments, rays, and parallel and perpendicular lines. (MG)


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Performance Standards 
By the end of the quarter, the learners are able to … 
• represent, identify, and order unit fractions and similar fractions with denominators 2, 3, 4, 5, 6, and 8. (NA) 
• identify and work with time measured in hours, half-hours, quarter hours, days, weeks, months, years. (MG) 
• describe duration of time and elapsed time, and read and write time in hours and minutes. (MG) 
• distinguish between straight and curved lines, and between flat and curved surfaces. (MG) 
• find the perimeter of triangles, squares, and rectangles. (MG)


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Grade 3 
Quarter 4 
Number 
and 
Algebra 
(N/A) 
1. division using the 6, 7, 8, 
and 9 multiplication tables. 
2. division of 2- to 4-digit 
numbers. 
3. estimation of quotients by 
first rounding the divisor 
and dividend to the nearest 
multiple of 10. 
4. addition and subtraction of 
similar fractions. 
 
1. illustrate division through equal jumps on the number line and as inverse of 
multiplication. 
2. divide numbers using the 6, 7, 8, and 9 multiplication tables. 
3. find the missing number in a number sentence involving multiplication or division by 6, 
7, 8, and 9 (e.g., __ x 7 = 56; 56 ÷ __ = 7). 
4. divide numbers with and without remainder: 
a.  2- to 3-digit numbers by 1-digit number without remainder, 
b. 2-digit numbers by 1-digit number with remainder, and 
c. 2- to 4-digit numbers by 10,100, and 1000. 
5. estimate the quotient of 2- to 3-digit numbers divided by 1- to 2-digit numbers, using 
multiples of 10 or 100 as appropriate


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distance using appropriate 
tools and units. 
4. measure and compare lengths of objects, in meters (m) or centimeters (cm), and distance in 
meters, using appropriate measuring tools. 
5. identify and use the appropriate unit (m or cm) to measure the length of an object and the 
distance between two locations.  
6. estimate length using meters or centimeters, and distance using meters. 
7. solve problems involving length and distance. 
Number 
and 
Algebra 
(NA) 
3. subtraction of numbers where 
both numbers are less than 
1000. 
4. increasing patterns and 
decreasing patterns. 
8. illustrate subtraction of 2-digit by 1-digit on the number line and as an inverse of addition. 
9. subtract numbers where both numbers are less than 100 with regrouping: 
a. 2-digit minus 1-digit numbers, and 
b. 2-digit minus 2-digit numbers. 
10. solve problems (given orally or in pictures) involving subtraction where both numbers are 
less than 100, with and without regrouping.


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Grade 3 
Quarter 3 
Data 
and 
Probability 
(DP) 
1. data presented in tables and 
single bar graphs. 
2. outcomes from experiments 
and real-life situations. 
1. collect data from experiments with a small number of possible outcomes (e.g., rolling a die 
or tossing a coin). 
2. present data in tables and single bar graphs (horizontal and vertical). 
3. interpret data in tables and single bar graphs (horizontal and vertical). 
4. solve problems using data presented in a single bar graph (horizontal and vertical). 
5. describe and compare outcomes in real-life situations using the following terms: equally 
likely, less/least likely, more/most likely, certain, and impossible. 
Number 
and 
Algebra 
(NA) 
3. multiplication using 6, 7, 8, 
and 9 multiplication tables. 
4. properties of multiplication 
5.   multiplication of numbers 
with and without regrouping 
6.   estimation of products of two 
numbers by first rounding to 
the nearest multiple of 10.


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4, 5, and 10.  
11. distinguish even and odd numbers using division by 2. 
12. solve division problems using the 2, 3, 4, 5, and 10 multiplication tables, including 
problems involving money. 
Performance Standards 
By the end of the quarter, the learners are able to… 
• represent and interpret data in a pictograph with a scale. (DP) 
• perform multiplication and division of whole numbers using the 2, 3, 4, 5, and 10 multiplication tables. (NA) 
• distinguish even and odd numbers. (NA)


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b. the centavo sign. 
7. add numbers with sums up to 10 000, with and without regrouping. 
8. estimate the sum of addends with up to 4 digits. 
9. solve problems involving addition of numbers with sums up to 10 000, including problems 
involving money. 
10. subtract numbers, where both numbers are less than 10 000, with and without 
regrouping. 
11. estimate the difference of two numbers of up to 4 digits. 
12. perform addition and subtraction of 3 to 4 numbers of up to 2 digits, observing correct 
order of operations. 
13. solve problems involving addition and subtraction with 3 to 4 numbers of up to 2 digits, 
including problems involving money. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• measure, estimate, and compare mass of objects. (MG) 
• measure and estimate capacity. (MG) 
• add and subtract whole numbers (including amounts of money) of up to 4 digits. (NA)


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• determine the area of squares and rectangles. (MG) 
• recognize and draw points, lines, lines segments, rays, and parallel and perpendicular lines. (MG) 
• represent, round, compare, and order numbers up to 10 000. (NA)


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c. 2- to 4-digit numbers by 10,100, and 1000. 
5. estimate the quotient of 2- to 3-digit numbers divided by 1- to 2-digit numbers, using 
multiples of 10 or 100 as appropriate 
6. solve division problems involving 2- to 3 -digit numbers by a 1-digit number, including 
problems involving money. 
7. represent fractions that are equal to one and greater than one using models. 
8. add and subtract similar fractions using models. 
Measurement 
and 
Geometry 
(M/G) 
5. line symmetry. 
6. resulting figure after a 
translation. 
9. describe and draw the effect of a two-direction multi-step slide (or translation) in basic 
shapes and figures. 
10. identify shapes or figures that show line symmetry by drawing the line of symmetry. 
11. complete a figure that is symmetric with respect to a line. 
 
Performance Standards 
By the end of the quarter, the learners are able to … 
• use the 6, 7, 8, and 9 multiplication tables to divide numbers. (N/A) 
• divide 2- to 4-digit numbers. (N/A)


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b. 2-digit minus 2-digit numbers. 
10. solve problems (given orally or in pictures) involving subtraction where both numbers are 
less than 100, with and without regrouping.  
11. subtract numbers, where both numbers are less than 1000, with and without regrouping. 
12. solve 1- and 2-step problems involving subtraction where both numbers are less than 1000 
(including problems involving money), with and without regrouping. 
13. determine the next term/s in increasing or decreasing patterns, e.g., numbers, letters and 
rhythmic properties, visual elements in arts, and repetitions. 
14. create increasing or decreasing patterns. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• determine, and compare the value of, combinations of Philippine coins and bills up to ₱1000. (MG) 
• perform addition of amounts of money with sums up to ₱1000. (NA) 
• measure, compare, and estimate, length and distance using appropriate units. (MG)


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Grade 4 
CONTENT 
DOMAIN 
CONTENT STANDARDS 
The learners should have 
knowledge and understanding of ... 
LEARNING COMPETENCIES 
The learners … 
 
Quarter 1 
Measurement 
and 
Geometry 
(MG) 
1. measures of angles  
2.  properties of triangles and 
quadrilaterals. 
3. perimeter of quadrilaterals, and 
composite figures composed of 
triangles and quadrilaterals. 
1. illustrate different angles (right, acute, and obtuse) using models. 
2. measure and draw angles using a protractor. 
3. draw and state the properties of triangles and quadrilaterals.  
4. classify triangles and quadrilaterals according to sides and angles. 
5. differentiate different quadrilaterals. 
6. find the perimeter of quadrilaterals that are not squares or rectangles. 
7. find the perimeter of composite figures composed of triangles and quadrilaterals. 
Number 
and 
Algebra 
(NA) 
4. whole numbers up to  
1 000 000. 
5. addition of numbers with sums 
up to 1 000 000 and


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domain Number and Algebra (the four operations with decimals; the four operations with different combinati ons of fractions, whole 
numbers, and mixed numbers; ratio and proportion; percentages, and their relationships with fractions and decimals; exponential 
form, including calculation using the GEMDAS rules; greatest common factors, least common multiples); Measurement and Geometry 
(right, acute, and obtuse; tessellation of shapes; resulting figure after translation, reflection and rotation; units of volume and capacity; 
volume of cubes and rectangular prisms; properties of triangles and quadrilaterals; perimeter and area of triangles, parallelograms, 
trapezoids; parts of a circle, including circ umference; area of a circle; composite figures composed of any two or more of: triangle, 
square, rectangle, circle, semi-circle; prisms and pyramids; surface area of solid figures; symmetric figures and designs; 12- and 24-


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4. properties of multiplication 
5.   multiplication of numbers 
with and without regrouping 
6.   estimation of products of two 
numbers by first rounding to 
the nearest multiple of 10. 
7. determination of missing 
terms contained in repeating 
and increasing patterns, and 
repeating and decreasing 
patterns. 
8. generation of repeating and 
increasing patterns, and 
repeating and decreasing 
patterns. 
6. multiply numbers using the 6, 7, 8, and 9 multiplication tables. 
7. illustrate and apply properties of multiplication for the 6, 7, 8, and 9 multiplication tables: 
a. one multiplied by any number is equal to the number;  
b. zero multiplied by any number is zero; 
c. changing the order of the numbers being multiplied does not change the  product; 
d. changing the grouping of the numbers being multiplied does not change the 
 product; and 
e. multiplying the sum of two addends by a number is the same as the sum of the 
products of a number by each addend.


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Grade 4 
Quarter 2 
Number 
and 
Algebra 
(NA) 
1. multiplication of whole 
numbers with products-up to 
1 000 000, division of up to  
4-digit numbers by up to  
2-digit numbers, and the 
MDAS rules. 
1. multiply two numbers with and without regrouping:  
a. 3- to 4-digit numbers by a 1-digit number, and 
b. 2- to 3-digit numbers by 2-digit numbers, with products up to 1 000 000. 
2. estimate the result of multiplying two numbers where the product is less than 
1 000 000. 
3. solve multi-step problems involving one or more of the four operations with results of 
calculations up to 1 000 000, including problems involving money. 
4. divide two numbers with and without regrouping 
a. 3- to 4-digit numbers by 1-digit numbers 
b. 2- to 3-digit numbers by 2-digit numbers 
5. estimate the quotient when dividing 3- to 4-digit dividends by 1- to 2-digit divisors, by first 
estimating the dividends and divisors using multiples of 10.


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Performance Standards 
By the end of the quarter, the learners are able to … 
• use the 6, 7, 8, and 9 multiplication tables to divide numbers. (N/A) 
• divide 2- to 4-digit numbers. (N/A) 
• estimate quotients by first rounding the divisor and dividend to the nearest multiple of 10. (N/A) 
• add and subtract similar fractions. (N/A) 
• identify a symmetrical shape and draw the line of symmetry. (M/G)


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Performance Standards 
By the end of the quarter, the learners are able to … 
• perform multiplication of whole numbers with products up to 1 000 000. (NA) 
• perform division of up to 4-digit numbers by up to 2-digit numbers. (NA) 
• perform different operations by applying the MDAS rules. (NA) 
• convert units of length, mass, capacity, and time. (MG) 
• perform addition and subtraction of similar fractions, including mixed numbers. (NA)


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Grade 4 
Quarter 3 
Number 
and 
Algebra 
(NA) 
1. dissimilar and equivalent 
fractions. 
2. factors and multiples of 
numbers up to 100. 
3. addition and subtraction of 
dissimilar fractions. 
1. represent dissimilar fractions, with denominators up to 10, using models. 
2. compare dissimilar fractions using the symbols =, >, and <. 
3. order dissimilar fractions from smallest to largest, and vice versa. 
4. generate equivalent fractions using models. 
5. determine equivalent fractions. 
6. identify the multiples of given numbers up to 100. 
7. find all the factors of a given number up to 100. 
8. reduce fractions to simplest form. 
9. add and subtract dissimilar fractions using models. 
10. add and subtract dissimilar fractions:  
a. two proper fractions, 
b. two mixed numbers, 
c. a mixed number and a proper fraction, 
d. a whole number and a proper fraction, and 
e. a whole number and a mixed number.


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square, rectangle, circle, semi-circle; prisms and pyramids; surface area of solid figures; symmetric figures and designs; 12- and 24-
hour time, and world time zones);  Data and Probability (presentation and interpretation of data in tabular form and in a single line 
graph; double bar graphs and double line graphs; theoretical probability; pie graphs ). This knowledge, skills and understanding is 
applied, with the use of technology, to the processes within Mathematics of critical thinking, problem solving, communicating, 
reasoning, and making connections between topic areas.


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• perform addition of amounts of money with sums up to ₱1000. (NA) 
• measure, compare, and estimate, length and distance using appropriate units. (MG) 
• perform subtraction of numbers where both numbers are less than 1000. (NA) 
• extend existing increasing patterns and decreasing patterns and create new increasing patterns and decreasing patterns. (NA)


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Number 
and 
Algebra 
(NA) 
4. whole numbers up to  
1 000 000. 
5. addition of numbers with sums 
up to 1 000 000 and 
subtraction of numbers where 
both numbers are less than  
1 000 000. 
8. read and write numbers up to 1 000 000 in numerals and in words. 
9. determine 
a. the place value of a digit in a 6-digit number, 
b. the value of a digit, and 
c. the digit of number, given its place value. 
10. compare numbers up to 1 000 000 using =, < and >. 
11. round numbers to the nearest hundred thousand. 
12. estimate the sum and difference of two 5- to 6-digit numbers by rounding the addends to 
the nearest large place value of the numbers. 
13. add numbers with sums up to 1 000 000 and subtracts numbers where both numbers 
are less than 1 000 000, with and without regrouping. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• illustrate and measure different angles (MG)


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Grade 4 
Quarter 4 
Data 
and 
Probability 
(DP) 
1. presentation and 
interpretation of data in 
tabular form and in a 
single line graph. 
1. collect data with time element using appropriate sources. 
2. present data in a tabular form, or in a single line graph. 
3. interpret data presented in a tabular form, or in a single line graph. 
4. solve problems using data for at most two variables in a tabular form, or in a single line 
graph. 
Number 
and 
Algebra 
(NA) 
2. simple patterns. 
3. number sentences. 
4. decimal numbers and 
their relationship to 
fractions. 
5. describe the rule used to generate a given simple pattern. 
6. complete a number sentence:  
a. to represent a property of operations (e.g., 4 + 3 = 3 + __) (commutative property of addition) 
b. to represent equivalent number facts (e.g., 4 + __ = 6 + 3) 
7. represent decimal numbers using models and manipulatives to show the relationship to 
fractions.


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Grade 5 
Quarter 2 
Number 
and 
Algebra 
(NA) 
1. division of fractions. 
2. decimal numbers with decimal 
parts up to ten thousandths. 
3. addition and subtraction of 
decimal numbers. 
4. divisibility rules. 
5. prime and composite numbers. 
1. divide fractions using models. 
2. divide a fraction by a fraction. 
3. solve multi-step problems involving division of fractions that may or may not involve the 
other operations with fractions. 
4. determine 
a. the place value to thousandths of a digit in a given decimal number, 
b. the value of a digit, and 
c. the digit of a number, given its place value. 
5. read and write decimal numbers with decimal parts to thousandths. 
6. convert terminating decimals to fractions, and vice versa. 
7. compare and order decimal numbers with decimal parts to thousandths. 
8. round decimal numbers to the nearest thousandths. 
9. add and subtract decimal numbers with decimal parts of up to 3 decimal places.


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5. estimate the quotient when dividing 3- to 4-digit dividends by 1- to 2-digit divisors, by first 
estimating the dividends and divisors using multiples of 10. 
6. represent situations involving one or more of the four operations using a number sentence. 
7. perform two or more different operations by applying the MDAS rules. 
Measurement 
and 
Geometry 
(MG) 
2. conversion of units of length, 
mass, capacity, and time. 
8. convert common units of measure from larger to smaller units, and vice versa: 
a. meter and centimeter, 
b. kilometer and meter, 
c. kilogram and gram, 
d. gram and milligram, and 
e. liter and milliliter. 
9. convert time measures from smaller to larger units, and vice versa: 
a. seconds to minutes, 
b. minutes to hours, 
c. hours to days, 
d. days to weeks  
e. weeks to months, and 
f. months to years. 
10. solve problems involving conversion of units of length, mass, capacity, and time, including 
problems involving elapsed time in hours and minutes.


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product; and 
e. multiplying the sum of two addends by a number is the same as the sum of the 
products of a number by each addend. 
8. multiply numbers with and without regrouping: 
a.  2- to 3-digit numbers by a 1-digit number, and 
b. 2- to 4-digit numbers by a number whose leading digit is the only non-zero digit, with 
products up to 10 000. 
9. estimate the product of 2- to 3-digit numbers by 1- to 2-digit numbers by estimating the 
factors using multiples of 10. 
10. solve 1-to 2-step multiplication problems, including problems involving money. 
11. determine the missing term/s in a pattern with repeating and increasing components or 
repeating and decreasing components (e.g., 1a, 1b, 1c, 2a, 2b, 2c, …). 
12. explain how to generate a given pattern with repeating and increasing components or 
repeating and decreasing components. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• present and interpret data in tables and single bar graphs. (DP)


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are less than 1 000 000, with and without regrouping. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• illustrate and measure different angles (MG) 
• classify triangles and quadrilateral, and differentiate quadrilaterals, by applying their properties. (MG) 
• find the perimeter of quadrilaterals and composite figures composed of triangles and quadrilaterals. (MG) 
• read, write, and compare whole numbers up to 1 000 000. (NA) 
• performs addition of numbers with sums up to 1 000 000 and subtraction of numbers where both numbers are less than 1 000 000. (NA)


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b. to represent equivalent number facts (e.g., 4 + __ = 6 + 3) 
7. represent decimal numbers using models and manipulatives to show the relationship to 
fractions. 
8. read and write decimal numbers with decimal parts to hundredths. 
9. determine 
a. the place value to hundredths of a digit in a given decimal number, 
b. the value of a digit, and 
c. the digit of number, given its place value. 
10. convert decimal numbers to fractions, and fractions with denominators 10 or 100 to decimals. 
11. plot decimal numbers with tenth decimal part on the number line. 
12. compare and order decimal numbers with decimal parts to hundredths. 
13. round decimal numbers to the nearest whole number and to the nearest tenth. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• present and interpret data in tabular form and in a single line graph. (DP) 
• generate a simple pattern and describe the rule used. (NA)


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Grade 5 
Quarter 3 
Data 
and 
Probability 
(DP) 
1. double bar graphs and double 
line graphs. 
2. theoretical probability. 
1. collects bivariate data from interview, questionnaire, and other appropriate sources. 
2. identify the appropriate graph (bar graph or line graph) to represent a given set of data. 
3. construct double bar graphs and double line graphs. 
4. interpret data presented in a double bar graph or a double line graph. 
5. draw conclusions or make inferences based on data presented in a double bar graph or a 
double line graph. 
6. solve problems using data presented in a double bar graph or a double line graph. 
7. describe probability as a measure of the chance of an event occurring. 
8. calculate the theoretical probability of a simple event by listing all possible outcomes. 
Number 
and 
Algebra 
(NA) 
3. multiplication and division of 
decimal numbers. 
9. estimate each of two decimal numbers to the nearest whole number to estimate their


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Grade 5 
CONTENT 
DOMAIN 
CONTENT STANDARDS 
The learners should have knowledge 
and understanding of ... 
LEARNING COMPETENCIES 
The learners … 
Quarter 1 
Measurement 
and 
Geometry 
(MG) 
1. 12- and 24-hour time, and 
world time zones. 
1. describe a 12- and 24-hour clock system. 
2. convert 12-hour time to 24-hour time, and vice-versa. 
3. solve problems involving 12- and 24-hour time. 
4. compare the time in different world time zones to the time in the Philippines using a 
world time zone map. 
5. solve problems on comparing the time in different world time zones to the time in the 
Philippines. 
Number 
and 
Algebra 
(NA) 
2. the GMDAS rules for operations 
with numbers. 
3. multiplication of fractions. 
6. perform three or more different operations by applying the GMDAS rules. 
7. multiply fractions using models. 
8. multiply a fraction by a fraction. 
9. solve multi-step problems involving multiplication of fractions that may or may not also


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8. round decimal numbers to the nearest thousandths. 
9. add and subtract decimal numbers with decimal parts of up to 3 decimal places. 
10. solve multi-step problems involving addition and/or subtraction of decimals, including 
problems involving money. 
11. use divisibility rules to find common factors of numbers: 
a. divisibility rules for 2, 5, and 10, 
b. divisibility rules for 3, 6, and 9, and 
c. divisibility rules for 4, 8, 11, and 12. 
12. distinguish prime numbers from composite numbers using the Sieve of Eratosthenes. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• divide fractions. (NA) 
• compare, order, and round decimals to the nearest one thousandth. (NA) 
• add and subtract decimal numbers. (NA) 
• use divisibility rules. (NA) 
• distinguish prime numbers from composite numbers. (NA)


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Grade 5 
Quarter 4 
Number 
and 
Algebra 
(NA) 
1. GMDAS rules when performing 
three or more operations with 
fractions and decimals. 
1. solve multi-step problems involving division of decimals that may or may not also involve 
the other operations with decimals, including problems involving money. 
2. perform three or more different operations with fractions and decimals by applying the 
GMDAS rules. 
Measurement 
and 
Geometry 
(MG) 
2. prisms and pyramids. 
3. surface area of solid figures. 
4. cubes and rectangular prisms. 
5.    resulting image after rotation 
3. illustrate different solid figures using concrete and pictorial models. 
4. relate plane figures to solid figures using concrete and pictorial models. 
5. describe and differentiate prisms and pyramids using their vertices, faces, and/or edges. 
6. illustrate and describe solid figures and their nets. 
7. make models of solid figures. 
8. illustrate and find the surface area of solid figures.


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a. two proper fractions, 
b. two mixed numbers, 
c. a mixed number and a proper fraction, 
d. a whole number and a proper fraction, and 
e. a whole number and a mixed number. 
11. solve multi-step problems involving addition and/or subtraction of fractions. 
Measurement 
and 
Geometry 
(MG) 
4. symmetric figures with respect 
to a line 
5. resulting images after 
applying reflection with 
respect to a line. 
12. identify symmetry with respect to a line. 
13. complete a figure that is symmetric with respect to a line. 
14. draws the image of an object after applying reflection with respect to a line, including glide 
reflection. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• represent, compare, and order dissimilar fractions. (NA) 
• find factors and multiples of numbers up to 100. (NA) 
• identify symmetry with respect to a line, and create figures that have line symmetry. (MG)


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e. weeks to months, and 
f. months to years. 
10. solve problems involving conversion of units of length, mass, capacity, and time, including 
problems involving elapsed time in hours and minutes. 
Number and 
Algebra (NA) 
3. addition and subtraction of 
similar fractions, including 
mixed numbers. 
11. identify proper fractions, improper fractions, and mixed numbers. 
12. rewrite improper fractions into mixed numbers, and vice versa. 
13. plot fraction (proper fractions, improper fractions, and mixed numbers) with denominators 
2, 4, 5, and 10 on the number line. 
14. add and subtract similar fractions: 
a. two proper fractions, 
b. two mixed numbers, 
c. a mixed number and a proper fraction, 
d. a whole number and a proper fraction, and 
e. a whole number and a mixed number.


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repeating and decreasing components. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• present and interpret data in tables and single bar graphs. (DP) 
• describe and compare outcomes of events. (DP) 
• multiply using 6, 7, 8, and 9 multiplication tables. (NA) 
• illustrate and applies properties of multiplication. (NA) 
• multiply numbers with and without regrouping. (NA) 
• estimate products of two numbers by first rounding to the nearest multiple of 10. (NA) 
• find a missing term and generate repeating and increasing patterns, and repeating and decreasing patterns. (NA)


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Number 
and 
Algebra 
(NA) 
3. multiplication and division of 
decimal numbers. 
9. estimate each of two decimal numbers to the nearest whole number to estimate their 
product. 
10. multiply decimal numbers with decimal parts of up to 2 decimal places. 
11. solve multi-step problems involving multiplication of decimals that may or may not also 
involve addition or subtraction of decimals, including problems involving money. 
12. estimate the quotient when dividing two decimal numbers by estimating the dividend and 
divisor to the nearest whole number. 
13. divide: 
a. 1- to 2-digit whole numbers resulting in a terminating decimal quotient 
 (e.g., 4 ÷ 5 = 0.8), and 
b. a decimal of up to 2 decimal places by a 1- to 2-digit whole number, resulting in a 
terminating decimal quotient of up to 3 decimal places. 
Performance Standards 
By the end of the quarter, the learners are able to … 
• identify, construct, and interpret double bar graphs and double line graphs. (DP)


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7. multiply fractions using models. 
8. multiply a fraction by a fraction. 
9. solve multi-step problems involving multiplication of fractions that may or may not also 
involve addition or subtraction of fractions. 
Measurement 
and 
Geometry 
(MG) 
4. area of a parallelogram, 
triangle, and trapezoid. 
10. identify the height of a parallelogram, triangle, and trapezoid, in different orientations. 
11. find the area of a parallelogram, triangle, and trapezoid, in sq. cm or sq. m, using 
formulas. 
12. estimate the areas of triangles and quadrilaterals (parallelogram, rhombus, trapezoid) 
using grids. 
 
Performance Standards 
By the end of the quarter, the learners are able to … 
• use 12- and 24- hour time. (MG) 
• compare the time in world time zones with the time in the Philippines. (MG) 
• use the GMDAS rules for 3 or more different operations. (NA) 
• multiply fractions. (NA) 
• determine the area of a parallelogram, triangle, and trapezoid. (MG)


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By the end of the quarter, the learners are able to … 
• present and interpret data in tabular form and in a single line graph. (DP) 
• generate a simple pattern and describe the rule used. (NA) 
• complete number sentences to represent number properties and number facts. (NA) 
• represent, compare, order, and round decimal numbers. (NA) 
• convert decimal numbers to fractions and fractions (with denominators 10 or 100) to decimals. (NA)


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Grade 6 
CONTENT 
DOMAIN 
CONTENT STANDARDS 
The learners should have knowledge 
and understanding of... 
LEARNING COMPETENCIES 
The learners … 
Quarter 1 
Measurement 
and 
Geometry 
(MG) 
1. tessellation of shapes. 
2. translation, reflection and 
rotation with shapes 
1. explore whether or not a shape tessellates. 
2. tessellate a surface using different shapes, including triangles, squares, and rectangles. 
3. draw resulting images of shapes that undergo translation, reflection, rotation 
Number 
and 
Algebra 
(NA) 
2. the four operations with 
decimals. 
3. the four operations with different 
combinations of fractions, whole 
numbers, and mixed numbers. 
4. add and subtract decimals with decimal parts of up to 4 decimal places. 
5. solve multi-step problems involving addition and/or subtraction of decimals, including 
problems involving money. 
6. mentally multiply decimals of up to 2 decimal places by 0.1, 0.01, 0.001, 10, 100, and 
1000.


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Grade 6 
Quarter 2 
Number 
and 
Algebra 
(NA) 
1. ratio and proportion. 
2. percentages, and their 
relationships with 
fractions and 
decimals. 
3. exponential form, 
including calculation 
using the GEMDAS 
rules. 
1. describe the relationship between quantities using ratio for: 
a. part-whole relationships, and 
b. part-part relationships. 
2. express one number as a fraction of another given their ratio, and vice versa. 
3. identify and write equivalent ratios. 
4. solve problems involving ratio. 
5. illustrate ratio and proportion in given situations using tables and/or the double number line 
model. 
6. find how many times one value is larger than another given their ratio, and vice versa. 
7. solve problems involving ratio and proportion. 
8. illustrate and explain the relationships between percentages, fractions, and decimals. 
9. identify and explain the uses of percentages. 
10. write numbers in exponential form e. g., 2 × 2 × 2 = 23, and vice versa


