Year 6 Practice Book 6A Unit 1: Place Value Within 10,000,000
Year 6 Practice Book 6AUnit 1: Place value within 10,000,000Unit 1: Place valuewithin 10,000,000Lesson 2: Numbers to10,000,000 (1) pages 9–11Lesson 1: Numbers to 1,000,0001. a) 500,000b) 1,000,000c) 1,600,000 pages 6–81. a) 329,412b) 72,3042. a) 2,903,471; two million, nine hundred and threethousand, four hundred and seventy-oneb) 3,005,765; three million, five thousand, sevenhundred and sixty-five2. a) 123,000b) 439,286c) 97,103d) 305,2463. Counters drawn in columns:a)3. a) 40 or 4 tensb) 4,000 or 4 thousandsc) 3 or 3 onesd) 500,000 or 5 hundred thousandse) 4 or 4 onesf) 100 or 1 hundredb)6. a) 74,400b) . Yes, Danny is correct. You can tell if a number is odd oreven using just the ones digit – if the ones digit is 0, 2,4, 6 or 8, then the number is even; if it is 1, 3, 5, 7 or 9,then the number is odd.ReflectThe value of each digit in 8,027,361: 8,000,000or 8 million; 20,000 or 2 ten thousands; 7,000 or7 thousands; 300 or 3 hundreds; 60 or 6 tens; 1 or 1 one.40,00073,500660,167TTh15. 643,506 or 6,*43,506 where * is any digit5. a) Missing numbers from le to right along thenumber line: 310,000; 320,000; 340,000;350,000; 360,000; 380,000; 390,00030,000HTh64. a) 1,084,300b) 2,202,002c) 92,0924. a) Answers will vary – any number using all six digitswith a 4 or 8 in the ones column.b) Answers will vary – any number using all six digitswith a 3, 5, 7 or 9 in the ones column.c) Answers will vary – any number using all six digitswith a 5 in the ones column.d) Answers will vary – any number using all six digitswith a 5 in the hundred thousands column.b)M73,390651,167Lesson 3: Numbers to10,000,000 (2)7. Answers will vary – ensure that number is greaterthan 500,000, is odd, has the same digit in the onesand the thousands column and the digits total 26.Example answers: 853,163; 507,707. pages 12–141. a) 2,000,000 300,000 20,000 6,000 400 50 7 2,326,457Luis has 2,326,457.b) 300,000 50,000 30 7 350,037Bella has 350,037.c) Jamilla has 2,100,320.ReflectAnswers will vary. Encourage children to write down factsthey know about the number. Include information aboutodd and even, place value and comparing and orderingnumbers or digits.2. a) 7,000; 10b) 60,3203. a) 7b) 400 20 9c) 200,000 60,000 300 90 2d) 8,512e) 723,572f) 3,056,825g) 412,000 Pearson Education 20181
Year 6 Practice Book 6AUnit 1: Place value within 10,000,000Lesson 5: Comparingand ordering numbers to10,000,0004. a) 3,098,828b) 3,099,728c) 3,108,728d) 2,098,728e) 2,998,728 pages 18–205. a) 7 million or 7,000,000b) 7 hundred thousands or 700,000c) 7 thousands or 7,000d) 7 tens or 701. Number A is greater. Explanations may vary, forexample: Number A is greater because the twonumbers have the same millions, hundred thousandsand ten thousands, but A has the greater number ofthousands than B.6. Answers will vary. One possible answer is 1,523,324.Reflect2. a) 9,580 9,5709,580 9,6809,580 9,681b) 540,000 54,000540,000 450,000540,000 540Answers will vary. Ensure that children have partitionedthe number correctly. Parts should total 4,508,375 whenrecombined, for example:4,000,000 500,000 8,000 300 70 53,000,375 1,508,0009,580 9,5899,580 10,00010,000 9,580540,000 half a million540,000 600,000540,000 3,000,0003. D ( 357,905); A ( 370,500); C ( 375,000); B ( 429,700)4. Benny is fed third.Lesson 4: Number line to10,000,0005. 73,000; 725,906; 725,960; 728,0006. a) 0, 1 or 2b) 6, 7, 8 or 9c) 4, 5, 6, 7, 8 or 9d) 0, 1, 2, 3, 4, 5, 6, 7 or 8e) 0 pages 15–171. a) 100,000sb) 1,000s7. Answers may vary. Ensure that each number in therow is bigger than the previous number.First number: Missing digit can be any digit.Second number: First missing digit is 6; secondmissing digit is 8 or 9.Third number: First missing digit is 1, 2 or 3; secondmissing digit can be any digit.2. a) 5,700; 5,800; 5,900; 6,000; 6,100; 6,200b) 66,340; 66,350; 66,3603. a) 130,520; 131,520; 132,520b) 720,700; 820,700; 920,700c) 7,100; 7,000; 6,900d) 3,230,000; 3,240,000; 3,250,0004. a) 20,000; 70,000; 95,000b) 2,300,000; 2,550,000c) 620; 730; 785 approximatelyReflectFalse – Ensure children know that to order numbers, wefirst need to look at the place value of each digit startingfrom the largest value place. In this case, the digit 1 in120,000 is 1 hundred thousand compared to the digit1 in 15,600, which is only 1 ten thousand. Thereforethe numbers are not in descending order as 120,000 isbigger than 15,600.5. Arrows drawn to number line:815,000a)800,000900,0008,400b)851,000 870,0008,9508,0009,5009,999Lesson 6: Rounding numbers10,0006. a) Answer may vary 5,450,000b) Answer may vary 7,100,000c) Answer may vary 8,300,000 pages 21–231. a) Olivia is incorrect. She needs to look at thehundreds column and then decide if she will needto round the thousands column up to 4 thousandsor down to 3 thousands.b) 14,00013,700ReflectEncourage children to use reasoning to explain theirchosen number. The number is less than half-waybetween 200,000 and 300,000 so will be less than250,000. Estimate 2,400,000. Pearson Education 20182. The number rounds to 7,000,000 because it is closerto 7,000,000 than 6,000,000.2
Year 6 Practice Book 6AUnit 1: Place value within 10,000,0003. a) 100,000100,000200,000200,000b) 60,00060,00060,00060,000Lesson 7: Negative numbers4.3. 14 metresRounded to the nearest pages 24–261. a) 1 Cb) 10 C2. 8 places128,3811,565,9004. a) –10 C; –5 C; 5 C; 10 C; 25 Cb) –16; –12; –8; –4; 4; 8; 12; 16c) –20; 0; 20; 40; 60; 80; 100; ,4001,565,90072,30010128,3801,565,90072,3105. a) 7 section H17·5 section K11 section I– 13 2 section D–5 section D–11·1 section Bb) Three numbers between –12 and –95. Circled: 17,450; 16,790; 17,399; 16,500; 16,999; 17,0986. a) 15,692b) Answers will vary but must have 56, 59, 61 or 62thousands.c) 59,612 or 59,6216. A –16B 87. a) 175b) –2257. a) 10b) Any digitc) 25,497 rounded to the nearest 10 and 100 is25,500.d) 25,997 rounded to the nearest 10, 100 and 1,000 is26,000.ReflectA –50; B 20. Explanations will vary. Encourage childrento explain that between 0 and 40, there are 4 intervals,which means that each interval is worth 10. Now weknow that B is 20 and if we count backwards in tens fromzero, then A –50.ReflectThe answer is true. Explanations will vary. Encouragechildren to give two explanations to prove it, perhapsusing a number line and using a ‘rule’ that they may havecome up with.End of unit check pages 27–28My journalAnswers may vary. Ensure that each number satisfies thestatement.Power puzzle5,293,187 Pearson Education 20183
Year 6 Practice Book 6AUnit 2: Four operations (1)Unit 2: Fouroperations (1)Lesson 2: Problem solving– using written methods ofaddition and subtraction (2)Lesson 1: Problem solving– using written methods ofaddition and subtraction (1) pages 32–341. a) 14,321 – 1,234 13,087b) Methods may vary, for example:14,321 – (1,234 9,876) 3,211 or13,087 – 9,876 3,211c) 1,234 – 909 325; 9,876 – 909 8,967;14,321 – 909 13,412 pages 29–311.ThH3 3TO2145647782. 6 years. Methods may vary – encourage children touse mental strategies of counting on or back, whichthey can show on a number line.3. C 18,186Total 7,614 12,900 18,186 38,700Alternatively, since B is mid-way, it is the average ofthe three numbers so the total is 3 12,900, which is38,700.2. Numbers from le to right along number line: 21,310;21,312; 21,32225,322 – 4,012 21,3103. a) 1,141HTh TTh Th–HTO101573100432001141HTO4. a) 3,087b) 6,419,7545. 15,200 21,500 – 29,750 6,95015,200 21,500 6,950 43,650b) 274,579HTh TTh Th2 2345014007874579AmeliaBellaExplanations may vary – encourage children to explainthat both numbers have decreased by 1, meaningthat the difference remains the same. However, thecalculation has become simpler as there is no longer anyexchange needed in the calculation.5,000 – 1,728 4,999 – 1,727 3,27250,000 – 26,304 49,999 – 26,303 23,6966.–HTOHT9325TTh Th110111830124014210246102496049 OLesson 3: Multiplying numbersup to 4 digits by a 1-digitnumber7. a) 9,090,909b) 969,499 pages 35–37Reflect1. a) 3 2,324 6,9722,324 2,324 2,324 6,9726,000 900 60 12 6,972b) 2,153 5 10,765The missing number is 53,305. Problems will vary.Encourage children to write a story where the unknownis the part that was taken away from the whole of 74,505to leave 21,200 behind.52,00010050310,00050025015c) 5,203 6 31,218d) 7 1,593 11,151 Pearson Education 2018?21,500Reflect5. Max has added in the hundreds column instead ofsubtracting. In the ten thousands column, Max thinksthat 2 take away 0 is 0. The correct answer is 23,048.315,200They scored 43,650 points altogether.4. a) 2,438 – 1,330 1,108She flew 1,108 km further on Monday than onTuesday.b) 2,438 – 227 2,2112,438 1,330 2,211 5,979She flew 5,979 km in total.TTh Th29,7506,9501
Year 6 Practice Book 6AUnit 2: Four operations (1)2. 3,050 6 18,30051 3. a) 251 7 1,7572313b) 1,251 7 8,757153693 5,1235123010 5,123c) 1,251 8 10,00866599c) 1,972 24 47,3284. a) 2 5,500 11,000; 11,000 1,350 12,350The total mass of the boxes is 12,350 g.b) 1,350 5 6,750The total mass of the boxes is 6,750 g.c) 5,500 3 16,500; 1,350 3 4,050;16,500 4,050 20,550Alternative method: 5,500 1,350 6,850;6,850 3 20,550The total mass of the boxes is 20,550 g.2. a) 365 24 8,760There will be 8,760 hours in 2021.b) 3,600 24 86,400There are 86,400 seconds in a day.3. Column multiplication showing:5,056 7 35,392; 35,392 2 70,784;5,056 14 70,784An explanation that 2 7 14 so you can firstmultiply 5,056 by 7 and then the answer by 2 and thiswill give the same answers as 5,056 14.5. a) Answers will vary. Ensure that children have takenthe smaller product from the larger product to findthe difference.b) Biggest number 8,765 9 78,885Smallest number 6,789 5 33,9454. 17 379 6,443The pool has 6,443 litres of water in it, so it is not full.5. 3,629 55 199,595ReflectReflectExplanations may vary. Encourage children to noticethe link between multiplying out each column in theshort multiplication and where the answer is found onthe grid method, for example: The 12,000 in the gridmethod can be seen as 1 ten thousand and 2 thousandsin the column method. The 150 and 21 in the gridmethod combine in the column method to show 171 as1 hundred, 7 tens and 1 one.Reasoning may vary, for example:1,254 21 26,334; 2,508 11 27,588 so 2,508 11 islarger.2,508 11 1,254 2 11 1,254 22, which is largerthan 1,254 21 so 2,508 11 is larger.Lesson 5: Dividing numbersup to 4 digits by a 2-digitnumber (1)Lesson 4: Multiplying numbersup to 4 digits by a 2-digitnumber pages 41–431. pages 38–4061. a) 3,125 15 46,87531 1525152565361,536 6 255 51005 205005 1000005 3,0005010 520010 20100010 1003000010 3,0004687516 216 1050,0001,00020030315,000300609225600660 75,00060163,600 16 b) 5,123 13 20200 7,200 602. a) 759 33 23b) 2,954 14 21121016016256256 16 3,000 Pearson Education 20181162002053,20032080
Year 6 Practice Book 6AUnit 2: Four operations (1)3. 3,500 25 140. Max can use 140 g of guinea pig foodper day.using an example or a diagram, for example:160 4 40 and 320 8 40. This means that if Idouble both the dividend and divisor, the quotientremains the same.4. a) 468 9 52b) 4,689 9 521c) 378 18 21d) 3,798 18 2115.22031368866,886 22 313Reflect21031465946,594 21 6,440 20 322Methods may vary, for example:6,440 2 3,220; 3,220 10 3226,440 5 1,288; 1,288 4 322314ReflectLesson 7: Dividing numbersup to 4 digits by a 2-digitnumber (3)1,887 17 111Methods may vary. Children could use short division orthe inverse grid method. Some children may alreadyhave an idea of the ‘chunking’ or ‘partitioning’ methodand could show these too. pages 47–491. a) 399 19 21Lesson 6: Dividing numbersup to 4 digits by a 2-digitnumber (2)101019190190192119399 pages 44–461. a) 3,500 7 500500 2 2503,500 14 250There is 250 ml of juice in each glass.b) 360 6 6060 4 15Aki can make 15 clay shells.90091901919101010b) 385 11 35c) 888 37 242. 992 31 32There are 32 classes.2. 1,260 10 126; 126 2 63; 1,260 20 63180 3 60; 60 5 12; 180 15 12960 2 480; 480 8 60; 960 16 601,100 11 100; 100 2 50; 1,100 22 50 or1,100 2 550; 550 11 50; 1,100 22 503. a) 182 13 14b) 364 13 28c) 528 11 48d) 528 22 244. Answers may vary.Mo could have done:33. a) Factors may vary. 2,700 18 150b) Factors may vary. 7,200 12 600c) Factors may vary. 5,400 36 150d) Dividing by factors 7 and 2 (in either order)5,600 14 400374. a) i) 480 8 6060 2 30So, 480 16 30ii) 960 480 2 and 32 2 16Therefore, 960 32 480 multiplied by 2,divided by 2 and divided by 16.Multiplying by 2 and dividing by 2 are inverseoperations so will cancel each other out.So 960 32 480 16 30b) Ambika is correct – encourage children to provethis using an example or by drawing a diagram, forexample:160 4 40 and 160 8 20. This means that if Idouble the divisor, the quotient is halved.Bella is incorrect – encourage children to disprove Pearson Education 20181201112132174048137011111201013033Olivia could have 713705. 702 26 271033
Year 6 Practice Book 6AUnit 2: Four operations (1)3. Lines drawn to match calculations to remainders:450 20 10301 10 1955 50 5685 25 10335 33 5ReflectAnswers may vary – encourage children to check theanswer using the inverse calculation of 23 24.Lesson 8: Dividing numbersup to 4 digits by a 2-digitnumber (4)4. a) 300 11 27 remainder 3b) 300 31 9 remainder 21c) 750 17 44 remainder 2d) 850 17 505. 475 35 13 remainder 20The ranger needs to buy 14 bags of seeds. pages 50–521. a) 735 15 49b) 1,890 15 126c) 5,610 15 3746. Answers will vary. Encourage children to use theirknowledge of multiples to solve this. The missingnumber can be 1 less than any multiple of 41.This will always leave a remainder of 40. For example:41 10 410, so 409 41 9 remainder 402. 1,331 11 121There will be 121 teams.3. 2,444 26 94, Jen cycles 94 km per day.2,325 25 93, Toshi cycles 93 km per day.Jen cycles more kilometres per day than Toshi.ReflectExplanations may vary. Encourage children to useReena’s method and then check if 300 21 has aremainder of 2. Reena is incorrect although hercalculation is correct i.e. 300 3 100; then100 7 14 remainder 2. However, this remainder as afraction is 27 and if you use equivalence and link it back to6the original divisor, 27 21. There the remainder is 6 andnot 2.4. a) I know that 10 61 610, not 620. Ebo has made amistake at 7 61, as it should be 427, not 437.Number line corrections: 427, 488, 549, 610b) 8,845 61 1455. 2,790 31 905,580 31 9302,790 62 180 31 302,790 31 558 31 45279 901883731 9Lesson 10: Dividing numbersup to 4 digits by a 2-digitnumber (6) 31 27Reflect pages 56–582,553 23 circled. Explanations may vary – encouragechildren to notice that 23 is a prime number so there areno useful factors to divide by to make the calculationeasier.1. a) 2,000 75 26 remainder 50Amelia can make 26 ice lollies. She will have 50 mlof juice le .b) 2,500 95 26 remainder 30Bella has 30 ml of juice le , which is less thanAmelia.c) Amelia can make 50or 23 of an ice lolly with her75remaining juice.6Bella can make 30or 19of an ice lolly with her95remaining juice.1,440 30 482,553 23 111Lesson 9: Dividing numbersup to 4 digits by a 2-digitnumber (5)2. a) 1,000 11 90 remainder 10b) 2,000 11 181 remainder 9c) 4,000 22 181 remainder 18d) 8,000 22 363 remainder 14Answers will vary, for example:2,000 11 (2 1,000) 11. The answer will thereforebe 2 90 with a remainder of 2 10. However, itdoes not make sense to have a remainder of 20when dividing by 11. Instead this gives 1 more groupof 11 with a remainder of 9. So, 2,000 11 181remainder 9. pages 53–551. Aki is correct.100 13 7 remainder 9Emma: 100 14 7 remainder 2Aki: 101 13 7 remainder 102. 200 15 13 remainder 5Andy can fill up 13 pages and will have 5 stickers leover. Pearson Education 20184
Year 6 Practice Book 6AUnit 2: Four operations (1)3. 2,515 20 125 remainder 15So, working out the division exactly gives125 15or 125 34 . 34 of 1 is 75p or 0·7520Each class gets 125·75.4. Answers may vary. Encourage a systematic approach –make the divisor the largest possible number so thatyou can make larger remainders.1,137 95 11 remainder 92ReflectAnswers will vary. Encourage children to work out adivision equation that leaves a remainder of 10 first.They can then use this equation to create the storyproblem.Encourage children to use multiplication to find adivision calculation which will have a remainder of 10,for example: 35 20 700. Therefore 700 35 20 so710 35 20 remainder 10.End of unit check pages 59–60My journalAnswers will vary. Encourage children to use theirnumber sense (in this case, knowing the patterns inmultiples of 25) to help them find an equation thatleaves a remainder of 10 when divided by 25.Power puzzleChildren should find that, whatever numbers they beginwith, they eventually find themselves ‘stuck’, constantlyusing and reusing the digits 6, 1, 4, 7. Pearson Education 20185
Year 6 Practice Book 6AUnit 3: Four operations (2)Unit 3: Fouroperations (2)Lesson 2: Common multiplesLesson 1: Common factors1. pages 64–66 pages 61–631. a) 1 14 142 7 141 18 182 9 183 6 18The factors of 14 are 1, 2, 7 and 14.The factors of 18 are 1, 2, 3, 6, 9 and 18.b) The common factors of 14 and 18 are 1 and 2.c) Children can draw diagrams to show that 14 doesnot form into an array with rows of 6. So 6 is not afactor of 14 and it therefore cannot be a commonfactor of 14 and 18.12345678910131415161718192011122122 23 24 25 26 27 28 29 303132 33 34 35 36 37 38 39 404142 43 44 45 46 47 48 49 505152 53 54 55 56 57 58 59 606162 63 64 65 66 67 68 69 707172 73 74 75 76 77 78 79 808182 83 84 85 86 87 88 89 909192 93 94 95 96 97 98 99 100The common multiples of 6 and 8 up to 100 are 24, 48,72 and 96.2. a)2. Factors of 40: 1 40; 2 20; 4 10; 5 8Factors of 100: 1 100; 2 50; 4 25; 5 20; 10 1012345678910111213141516171819202122 23 24 25 26 27 28 29 303132 33 34 35 36 37 38 39 404142 43 44 45 46 47 48 49 50The common factors of 40 and 100 are: 1, 2, 4, 5, 10,205152 53 54 55 56 57 58 59 606162 63 64 65 66 67 68 69 703. 8 is in the wrong place because it is a factor of both80 and 200. 8 10 80; 8 25 2007172 73 74 75 76 77 78 79 808182 83 84 85 86 87 88 89 909192 93 94 95 96 97 98 99 1005 is in the wrong place because it is a factor of both80 and 200. 5 16 80; 5 40 200b)1234567891011121314151617181920Factors of 702122 23 24 25 26 27 28 29 3013132 33 34 35 36 37 38 39 404142 43 44 45 46 47 48 49 504 a)Factors of 351Factors of 501522755351077172 73 74 75 76 77 78 79 8025108182 83 84 85 86 87 88 89 9050149192 93 94 95 96 97 98 99 100355152 53 54 55 56 57 58 59 606162 63 64 65 66 67 68 69 703.Multiple of 570b) Answers may vary but must be a multiple of 60.The lowest common factor of 1, 2, 3, 4 and 5 is 60,so any multiple of 60 will be a common factor.15166045201006Common factors of 15 and 60: 1, 3, 5, 15Description may vary, for example: I notice that all thecommon multiples of 4 and 5 are multiples of 20.No, you would not need to check all the numbers up to60. All the common factors mus
Year 6 Practice Book 6A Unit 2: Four operations (1) Pearson Education 2018 5 1 2 3 1 3 6 6 5 9 9 2. There
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