Y5 – Autumn – Block 2 – Add whole numbers with more than 4 digits (column method) Answers

Question Answer

1

a)

b)

2

Each addition involves at least one exchange.The last digit stays the same. The number of exchanges is different.

3

a) 37,568b) 37,573c) 38,091d) 12,245

4

a) c)

b) d)

5 match 3

3 7 75

9 1 861

0 0 111

0 0 101

8 9 191

9 0 191

1 1 1

1 1

1

8 45 6 16 4 5

+ 11

1

314

6 0 09 4 25 4 2

+315

000

0 7 26 8 77 5 9

+4

41

022

£££

ggg

cmcmcm

7 3 26 0 0+

1 09

££

8 2 051

0£4 8 73 1£

111

1

Y5 – Autumn – Block 2 – Add whole numbers with more than 4 digits (column method) Answers (continued)

Question Answer

6

a)

b)

7

a) 265b) 8,974c) 9,128

8Dexter has not added the 1 digit that has been exchanged from the previous column.Eva has not lined up the digits correctly.

65112

65032

Y5 – Autumn – Block 2 – Subtract whole numbers with more than 4 digits (column method) Answers

Question Answer

1

a)

b)

c)

2

a)

b)

c)

d)

3 £19,058

4 624 miles

2 1 15

0 7 44

8 9 51

2 1

12 16

3 3 06

8 2 1£ 00

7 8 02 8

2 13 1

3 8 43 1

11 1143

Y5 – Autumn – Block 2 – Subtract whole numbers with more than 4 digits (column method) Answers (continued)

Question Answer

5

a)

b)

6

Rosie has written the numbers the wrong way round and then found the difference between the digits in each column.Whitney has found the difference between the digits in each column, instead of taking the second digit from the first digit, exchanging where necessary.

7

a) 9b) 3,273c) 5,925

Work out 15,923 – 10,000 and add 2Work out 15,925 – 10,000Count up from 9,998 to 15,923

8a) 19,415b) 75,305

9

multiple possible answers, e.g.:5,189 and 8,1595,198 and 8,1958,159 and 9,5188,591 and 9,815

51,294

6,618

Y5 – Autumn – Block 2 – Inverse operations (addition and subtraction) Answers

Question Answer

1

2

3

a)

or

b)

or

4

Tommy should check his calculation using a subtraction.91,380 – 12,350 or 91,380 – 7,90320,253

5

6

a) 4,835b) 7,658c) 17,057

7 2,910

8

possible methods include:Add 3,729 and 8,451, then subtract this total from 20,000Subtract 3,729 from 20,000, then subtract 8,451 from the answer.7,820

1 2 21 4 22 6 4

+538

3 3 33 6 09 7 3

–412

3 3 3

3 6 09 7 3–

4

12

1 4 21 1 22 6 4

+358

12 13 12 13

Y5 – Autumn – Block 2 – Multi-step addition and subtraction problems Answers

Question Answer

1

a) 44b) 82c) 41

2 1,300

3No.349 + 199 + 479 = 1,027 and 1,027 < 1,000

4the Websters£60

5 2,500

6

Jack has 500 stickers.Amir has 150 stickers.Whitney has 250 stickers.

7 2,642 and 3,842

8

The total of the two numbers must be 7,440e.g. The two numbers could be 2,000 and 5,440One of the numbers cannot be greater than 6,440

Y6 – Autumn – Block 2 – Add and subtract integers Answers

Question Answer

1

a)

b)

c)

d)

2

a)

b)

c) 1,057,001d) 555,555

3

For each calculation, we need to decide what to round to.

6 0 141

71

1 9 64 1 4

5 22 4 83 0 0

+4

1

358

606

4

1

0 5 95 4 25 1 7

–3

1

431

12 1

4 11 1

1,825

4,604

Y6 – Autumn – Block 2 – Add and subtract integers Answers (continued)

Question Answer

4

a)

b)

c)

d)

5

a) 87,600b) 262,650c) 713,500

6 The difference between A and B is 275,000

7

multiple possible answers, e.g.:975 – 130 = 845closest answer to 500:597 – 103 = 494

8 any number between 2,050,045 and 2,050,054

4

4381

0900

00

0392 9

4

919

57

Y5 – Spring – Block 1 – Multiply 4-digits by 1-digit Answers

Question Answer

1

There are 9 ones altogether.There are 3 tens altogether.There are 6 hundreds altogether.There are 6 thousands altogether.2,213 × 3 = 6,639

2

3

The attendance for all 4 matches was 8,856

4

Nijah has ignored the 0 as a placeholder in the ones column and hasn’t used the correct place value for each digit.7,290

5

a) 9,378b) 9,624c) 24,792d) 7,510

6 No. Multiplying by 0 gives an answer of 0

7

5,69211,38422,768

Each answer is double the previous answer.

8

248 × 9 = 248 × (10 − 1) = 248 × 10 − 248 × 1 = 2,480 − 248 = 2,232

Children may have different opinions on which method is easier.

9Various answers available.The closest product to 8,000 is 8,270

8048

65881

Y5 – Spring – Block 1 – Multiply 2-digits (area model) Answers

Question Answer

1

There are 2 ones altogether.There are 8 tens altogether.There are 6 hundreds altogether.31 × 22 = 682

2a) 168b) 299

3

a)

There are 4 ones altogether.There are 14 tens altogether.There are 6 hundreds altogether.

b) Exchange 10 tens for 1 hundred.c) 744

4a) 375b) 432

5

26 × 32 = 832

600 180

40 12

Y5 – Spring – Block 1 – Multiply 2-digits (area model) Answers (continued)

Question Answer

6

a) 28 × 14 = 392

b) 27 × 16 = 432

c) 35 × 22 = 770d) 45 × 36 = 1,620

7

504468775

8

24 × 32 = 768

9e.g. 23 × 45 = 1,035There are various answers for this question.

200 80

80 32

200 70

120 42

20 710

6

Y5 – Spring – Block 1 – Multiply 2-digits by 2-digits Answers

Question Answer

1

a) 36360

b) 96960

c) 96960

d) 63630

e) 84840

f) 1441,440

In the second calculation in each part, one of the numbers is 10 times one of the numbers in the first. This means that the second answer in each part is 10 times the first.

2

a)

b)

c)

3Mo has correctly multiplied 24 by 3, but has then multiplied by 2 rather than 20The correct answer is 782

5 5 9

3 3 6

5 2 5

2 52 1

21

21

6

10

Y5 – Spring – Block 1 – Multiply 2-digits by 2-digits Answers (continued)

Question Answer

4

a) 1,768b) 1,232c) 2,944d) 2,961

5 4,140

6

a) 2,022 m2

b) 822 m2

When calculating the area of the compound shapes the area of the grey rectangle and two white rectangles are added together. When calculating the area of the shaded part in b), the area of the white rectangle is subtracted from the area of the grey rectangle.

Y5 – Spring – Block 1 – Multiply 3-digits by 2-digits Answers

Question Answer

1

a) 39390

b) 2602,600

c) 1001,000

d) 8168,160

2

a)

b)

3

Brett has multiplied 216 by 3 tens and then by 2 ones when he should have multiplied by 3 ones and then by 2 tens. He has worked out 216 × 32 not 216 × 23The correct answer is 4,968

4

a) 4,402b) 15,502c) 11,342d) 4,392

5

a)

6,200b) Any valid explanation such as 308 is only 2 away from 310 and 19 is only one away

from 20c) Filipd) 5,852

3

512

512

4

20

003

8822

11

1

Y5 – Spring – Block 1 – Multiply 3-digits by 2-digits Answers (continued)

Question Answer

6a) 6,656 m2

b) 3

7a) >>

8697£111.52

Y6 – Autumn – Block 2 – Multiply up to a 4-digit number by a 2-digit number Answers

Question Answer

1Eva is correct.7 × 4 = 28, so the answer must end with 8

2

a)

b)

c)

3

4 2,660

5 £112.50

6 621 × 53 = 32,913

7Rosie does more sit-ups.She does 2,035 more sit-ups.

8Before playing the game, children need to work out the letter intervals. Each interval is 10,000, so A is 0–10,000, B is 10,000–20,000, etc.

1 7 56 03 7 0 5

5 4 56 5

0 7 28 06 1 4 4

6 8 69 4

8 4 68 01 8 6 8

0 3 23 8

1

445

2 32 4 1 3

5 4 95 9

3 71 2 4 7

6 1 34 9

2 92 0 3 1

8 8 95 9

Y5 – Spring – Block 1 – Divide 4-digits by 1-digit Answers

Question Answer

1

a)

There is 1 group of 3 thousands.There are 3 groups of 3 hundreds.There is 1 group of 3 tens.There are 2 groups of 3 ones.3,936 ÷ 3 = 1,312.

b) 2,101

2

a) 4,266b) 1,324c) 1,013

3

a) 712b) 304c) 1,631d) 1,631e) 1,561f) 2,079

4

𝑎 = 1,345𝑏 = 666𝑐 = 80

5

a)

b)

6 Deal B is the best value.

3 1 2

44

41

22 2

21

Y5 – Spring – Block 1 – Divide with remainders Answers

Question Answer

1

a)

There is 1 group of 3 thousands.There are 3 groups of 3 hundreds.There is 1 group of 3 tens.There are 2 groups of 3 ones. There are 2 ones left over.3,936 ÷ 3 = 1,312 remainder 2

b) 2,101 remainder 3

2

a) 2,531 remainder 21,312 remainder 22,141 remainder 31,311 remainder 2

b) >>

3

The fourth column is empty because you can’t have a remainder of 4 when dividing by 4

4

Yes7,816 = 7,815 + 1 and 7,815 is divisible by 57,861 = 7,860 + 1 and 7,860 is divisible by 56,781 = 6,780 + 1 and 6,780 is divisible by 51,786 = 1,785 + 1 and 1,785 is divisible by 5

5No, 459 ÷ 7 = 65 remainder 4If there was only 65 tables then 4 children wouldn’t have a seat. They need 66 tables.

6 135

7 a) E.g. 325 ÷ 4 = 81 remainder 1

8 Various answers e.g. 564 (564 ÷ 7 = 80 remainder 4)

3 1 2 r2

9,513 ÷ 4 5,066 ÷ 4 6,563 ÷ 4

6,562 ÷ 4 9,515 ÷ 4

1,234 ÷ 4

Y6 – Autumn – Block 2 – Short division Answers

Question Answer

1

a)

b)

2

72, 84, 96, 108

3

4

a) 127 r2b) 129 r4c) one hundred and eighty-one remainder nined) 99

5

a) a = 198b) b = 371c) c = 90d) d = 288

650pPossible mistakes include dividing 12 by 6, not converting between pounds and pence.

7 841

2 32 4 1 3

3 71 2 4 7

2 92 0 3 1

1 1 31

1 3 311

9 3 04 1

3 2 1 3 2 41

6 9 32 2

5 2 16 2 1

1 6 72 8 8

9 91 11 10

0

0 0

0

Y6 – Autumn – Block 2 – Short division Answers (continued)

Question Answer

8

a)

b)

c)

82 8

9

58

Y6 – Autumn – Block 2 – Division using factors Answers

Question Answer

1

a)

260 ÷ 20 = 13b)

360 ÷ 30 = 12c)

240 ÷ 60 = 4d)

480 ÷ 24 = 20

2

a) Jack: 816 ÷ 8 = 102, 102 ÷ 6 = 17Rosie: 816 ÷ 12 = 68, 68 ÷ 4 = 17

b) 8 × 6 = 48 and 12 × 4 = 48c) Different children may find different divisions easier.

3 Dora is correct.

4

a)

b) 3,024 ÷ 12 ÷ 33,024 ÷ 18 ÷ 2

5

a) 9b) 25c) 85d) 400

637

7a) c = 306b) divide 9,180 by 5 to find a, divide a by 3 to find b, divide b by 2 to find c

8 200

26 13

36 12

24 4

120 20

✔ ✔

4 24 2

Y6 – Autumn – Block 2 – Long division (1) Answers

Question Answer

1

2

a)

b) 41c) 15d) 27

3 17

4

5 29

5

a) 168 × 5 = 24 × 35b) Work out 168 × 5, then divide by 35: 168 × 5 = 840 840 ÷ 35 = 24

Divide 35 by 5 to get 7, then divide 168 by 7: 35 ÷ 5 = 7 168 ÷ 7 = 24

6

a) 21b) 23c) 28,577

2 61 31 3

0

2 1

7 81 31 3

0

6 1

3 95 25 2

0

3 4

7 89 19 1

0

6 7

92 115 138 161 184 207

✔ ✔

Y6 – Autumn – Block 2 – Long division (2) Answers

Question Answer

1

a) 4,080 ÷ 10 mental division4,080 ÷ 4 mental or short division4,080 ÷ 24 long division or short division by factors 4 then 64,080 ÷ 34 long division

b) 4,080 ÷ 10 = 4084,080 ÷ 4 = 1,0204,080 ÷ 24 = 1704,080 ÷ 34 = 120

2

3 250 m

4

a) 187b) 299c) 166

5 125 g

6

28,072A good way of finding a long division that works is to multiply two numbers together, e.g. 74 × 19 = 1,406, so 74 = 1,406 ÷ 19

3 73 73 7

0

1 1 0

3 72 52 5

0

1 0 7

99

3 73 33 3

0

1 0 9

33

7 41 41 4

0

2 0 4

88

Y6 – Autumn – Block 2 – Long division (3) Answers

Question Answer

1

2 136 is not exactly divisible by 15

3a) 54 r8b) 102 r4

4

a) 35b) Add together 380, 24 and 9. Divide the total by 12 and round up to the next whole

number of tables.

5

6Party Supplies: £52.80Fun Stores: £56.00

7 B

8

a) 532 ÷ 14 or 215 ÷ 43 remainder 0b) 213 ÷ 54 or 321 ÷ 54 remainder 51Children could discuss strategies for finding the smallest/greatest remainders.

30 45 60 75 90 105 120 135 150

7 51 0

5 0 r10

9 04 64 5

1

6 3

6 04 03 5

5

4 9

1 51 0

1 0

r1

r10

r5

11

✔ ✔

B

C

D

E

FG

H

Y6 – Autumn – Block 2 – Long division (4) Answers

Question Answer

1

a) 138 r16b) 277 r14c) 416 r12d) 208 r12

2

a) 1,000 ÷ 13 = 76 r12Allow any prediction with justification.

b) 1,000 ÷ 11 = 90 r101,000 ÷ 12 = 83 r41,000 ÷ 13 = 76 r121,001 ÷ 11 = 911,001 ÷ 12 = 83 r51,001 ÷ 13 = 77

3

a) 7b) 15c) 31d) 78

4 It will take 104 journeys to transport all 8,200 lorries.

5 99

Y5 – Autumn – Block 4 – Factors Answers

Question Answer

1a) 2 and 8 are both factors of 16b) The bottom row is incomplete.

2

a) Children should make a 2 by 10 array.b) Children should make a 4 by 5 array.c) Children should show that when there are 6 counters in a row, the fourth row will be

incomplete.

3

a)

1, 2, 3, 4, 6, 12b) 1, 2, 3, 4, 6, 8, 12, 24

4

a) 1, 2, 4, 8, 16, 32b) Children can pair the factors up and check that other numbers e.g. 3 and 5 are not

factors.

5

a)

b) E.g. 45

6a) No, 1 and 11 are factors of 11b) 23

7 48

8a) These are multiples not factors.b) Factors have to be integers.

a) 195 has a 5 in the ones place so is divisible by 5. 196 is 1 more than 195 so 5 is not a factor.

b) 177 has a digit sum of 15 which is divisible by 3, so 177 is divisible by 3. 178 is 1 more than 177 so 3 is not a factor.

c) 20 multiplied by 9 is 180 so 20 is a factor of 180. The next multiple of 20 after 180 is 200 so 20 is not a factor of 190

Sometimes. Children should give reasons to support this e.g. 1 only has one factor and one is odd.

4 6

Y6 – Autumn – Block 2 – Common factors Answers

Question Answer

1

a) 1, 2, 3, 6, 9, 18b) 1, 2, 3, 4, 6, 8, 12, 24c) 1, 2, 3, 6

2

3

a) 1, 2, 4b) 1c) 1, 2, 5, 10d) 1, 2, 4, 5, 10, 20

4

a)

b) 1, 5, 25

5 60, 90, 180

6

No.If she puts 5 sweets and 5 balloons in each bag, she will make 5 bogs, but she will have 10 sweets left over.She can make 5 bags, with 7 sweets and 5 balloons in each bag.

7 70

8

Identify a common factor and divide both the top and bottom by this factor, e.g.18: 1, 2, 3, 6, 9, 1846: 1, 2, 23, 46

1846 = 9

23

12

3

45

6 8

1215

24

753 × 255 × 15

1 × 1002 × 504 × 255 × 20

10 × 10

÷ 2

÷ 2

Y6 – Autumn – Block 2 – Common multiples Answers

Question Answer

1

28, 36, 54, 72, 90

2

a)

b) 20, 40, 60c) They are all multiples of 4 × 5 = 20

Any multiple of 20 is a common multiple of 4 and 5No, we will never run out of common multiples.

3

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98

4

Jack’s method will find common multiple, but Rosie is also correct that he will miss some.12, 36, 60, … are also multiples of 4 and 6All multiples of 12 are multiples of 4 and 6

5

a) 6, 12, 18, 24, 30b) 12, 24, 36, 48, 60c) 30, 60, 90, 120, 150

6any two ages from:5, 6, 9, 10, 15, 18

7 72 cm or 96 cm

40

16

60

25

24

75

3020

Y6 – Autumn – Block 2 – Primes to 100 Answers

Question Answer

1

a) The factors of 6 are 1, 2, 3, 6The factors of 8 are 1, 2, 4, 8The factors of 9 are 1, 3, 9

b) The factors of 3 are 1, 3The factors of 5 are 1, 5The factors of 7 are 1, 7

c) All the numbers in both part a) and part b) have 1 and the number as factors. In part a) there are also other factors, but in part b) these are the only factors.

All the numbers in part b) are prime numbers.

218 = 1 × 18 18 = 2 × 9 18 = 3 × 618 has 6 factors so it is not prime.

3

a)

b)

c)

4

a) An integer has exactly two factors, 1 and the number. 1 only has one factor (1) so is not prime.

b) Many people think that no even numbers can be prime, since they are all a multiple of 2. But the only factors of 2 are 1 and zero, so 2 is prime.

5

6

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

7No.87 = 3 × 29, so is not prime.

multiple possible answers, e.g.

3, 11, 19

multiple possible answers, e.g.

9, 21, 25

multiple possible answers, e.g.

6, 10, 12

2

Y6 – Autumn – Block 2 – Primes to 100 Answers (continued)

Question Answer

8

a)

b)

c) multiple possible prime factor trees, depending on how 36 is factorisedPrime factors are:2, 2, 3, 3

d) multiple possible prime factor trees, depending on how 66 is factorised Prime factors are:2, 3, 11

9

3 and 9711 and 8917 and 8329 and 7141 and 5947 and 53

6

2 3

9

3 3

Y6 – Autumn – Block 2 – Square and cube numbers Answers

Question Answer

1

2 × 2 = 4 3 × 3 = 9 4 × 4 = 16

2

3 27

4

5

2 squared < 2 cubed2 squared = 2 × 22 squared = 42 squared > 1 cubed

6

7 121, 144, 169, 196

8 7,600

9 a) multiple possible answers, e.g. 1 and 4, 4 and 9b) multiple possible answers, e.g. 1 and 3, 1 and 16

8

9

27

125

3 × 3

3 × 3 × 3

5 × 55

33

Y6 – Autumn – Block 2 – Order of operations Answers

Question Answer

1

multiple possible answers, e.g.:a)

b)

c)

d)

2

a) (3 + 2) × 2b) 5 + 2 × 4c) (5 – 2) × 3d) 15 – (2 × 5)

3

4

5 multiple possible answers, depending on operations and brackets

6100 + 25 – 7 × (5 + 2) = 76Dora has £76 left.

748 ÷ 3 – 15 = 1She kept one county.

8 children’s story problems

( )

( ) ( )

( )

( )

Y6 – Autumn – Block 2 – Mental calculations Answers

Question Answer

1

a) 92b) added 5c) 25 + 48 = 73 250 + 480 = 730

62 + 55 = 117 620 + 550 = 1,170260 + 250 + 240 = 750

2

Whitney add 20 + 30 + 40 and then subtracts 3. 19 = 20 – 1, 29 = 30 – 1 and 39 = 40 – 1, so 19 + 29 + 39 = 20 + 30 + 40 – 1 – 1 – 1Amir does a column addition, exchanging 20 ones for 2 tens.Children need to justify the method they think is more efficient, e.g.:Whitney’s method involves simple additions.Amir’s method does not involve changing any of the numbers.

3

a) 128pb) 495 cmc) £4.01d) 1,402 ml

4

a) multiple possible answers, e.g.:750 – 200 = 550550 – 30 = 520so 750 – 230 = 520

b) multiple possible answers, e.g.:750 – 300 = 450450 + 20 = 470so 750 – 280 = 470

c) 89 – 35 = 54 890 – 350 = 54080 – 25 = 55 800 – 250 = 55082 – 45 = 37 820 – 450 = 370

5a) £92,249b) £42,250

6

a) 10 × 8 = 80 c) 18 × 5 = 9020 × 8 = 160 34 × 5 = 17040 × 8 = 320 5 × 430 = 2,150

b) 18 × 10 = 180 d) 21 × 6 = 12618 × 20 = 360 7 × 32 = 22418 × 200 = 3,600 336 = 84 × 4

Children may have used different methods. They need to be able to explain why their method works.

7

a) 190b) 460c) 2,700d) 34,000

Y6 – Autumn – Block 2 – Reason from known facts Answers

Question Answer

1

a) 4 × 5 = 204 × 50 = 2004 × 500 = 2,000

b) 4 × 5 of an amount = 20 × amountc)

4 × 0.5 = 2

2

a) 5 × 7 = 35 c) 8 × 9 = 7250 × 7 = 350 72 ÷ 9 = 8500 × 7 = 3,500 720 ÷ 9 = 80

720 ÷ 8 = 90b) 6 × 3 = 18 d) 12 × 5 = 60

6 × 300 = 1,800 600 ÷ 12 = 5030 × 6 = 180 6,000 ÷ 500 = 12

300 ÷ 12 = 25

3

85 × 50 = 4,250 425 ÷ 85 = 585 × 500 = 42,500 425 ÷ 5 = 8585 × 5,000 = 425,000 4,250 ÷ 5 = 850

4,250 ÷ 850 = 5

485 × 6 = 85 × 5 + 85 = 51086 × 5 = 85 × 5 + 5 = 430

5

When adding two numbers, we can add 1 to one number and subtract 1 from the other number to give the same total.When subtracting two numbers, we can add or subtract 1 from both numbers to give the same difference.

6 280 cm

0.1 0.1

0.1 0.1

0.1 0.1 0.1

0.1 0.1

0.1 0.1 0.1

0.1 0.1

0.1 0.1 0.1

0.1 0.1

0.1

Y6 – Autumn – Block 2 – Reason from known facts Answers (continued)

Question Answer

7

890p98 – 8 × (99 – 98)

1,190

136

11,900

17

0.07

819

17