Y4 – Spring – Block 3 – Step 1 – What is a fraction? Answers

Question Answer

1

a) 15

b) 35

c) 34

d) 47

2

a) any single triangle shadedb) any five triangles shadedc) any five rectangles shadedd) any five ovals shaded

3 The numerator is 1

4

a)

b) There are 3 equal parts altogether.1 out of the 3 equal parts is shaded.13 of the shape is shaded.

5

a)

b)

c)

d)

!

!

!

Y4 – Spring – Block 3 – Step 1 – What is a fraction? Answers

Question Answer

655 is the same as 1

7 four representations of 34, with 4 equal parts and 3 parts shaded

8

a) 17b) 47

c) 67d) multiple possible answers, e.g.:

Out of 5 shapes, there should always be 1 square and 2 triangles. The final 2 shapes can be any shape with 4 or more sides, but neither of them can be a square.

Y4 – Spring – Block 3 – Step 2 – Equivalent fractions (1) Answers

Question Answer

1

a)

b)

c)

d)

2

a) 12 =24

b) 12 =48

c) 24 =48

d) 28 =14

e) 68 =34

f) 22 =44 =

88

3

a)

b) 13 =26 =

39

23 =

46 =

69

33 =

66 =

99

4

a) trueb) falsec) trued) falsee) truef) falsechild’s equivalent fraction statements

13

13

13

16

16

16

16

16

16

19

19

19

19

19

19

19

19

19

Y4 – Spring – Block 3 – Step 2 – Equivalent fractions (1) Answers (continued)

Question Answer

5

a)

multiple possible answers, e.g.:

diagrams showing 45 >25 but

12 >

25

b)

multiple possible answers, e.g.:

diagrams showing 24 and 36 both equivalent to

12

c)

multiple possible answers, e.g.:

bar model showing 12 together with the statementNo matter how many parts the bar is split into, the shaded number will be half the total parts.

Y5 – Spring – Block 2 – Step 1 – Equivalent fractions Answers

Question Answer

1

a)

b)

c)

d)

2

3

a) equivalent to 14 : 312

624

520

28

equivalent to 13 : 515

26

824

412

b) multiple possible answers, e.g.:

equivalent to 14 : 416

equivalent to 13 : 39

4

a) 214

b) 1014

c) 1416

d) 68

e) 1216

f) 912

g) 23

h) 25

i) 1035j) The numerator and denominator are both multiplied by 5

3

9

212

1012

Y5 – Spring – Block 2 – Step 1 – Equivalent fractions Answers (continued)

Question Answer

5

multiple possible answers, e.g.:

a) 12 =714

18 =

756

1100 =

7700

b) 78 =1416

710 =

1420

77 =

1414

c) 17 =214

27 =

414

67 =

1214

6

No.

Any correct diagrams showing that 14 =28 =

312 and therefore

14,

58 and

912 are not equivalent.

Alternatively diagrams could be drawn for 14, 58 and

912 and then children could indentify that

there is a different amount shaded in each.

7 A = 1, B = 27, C = 10

8 C = 28

9 = 14

Y4 – Spring – Block 3 – Step 4 – Fractions greater than 1 Answers

Question Answer

1

a) 7 fifths = 1 whole + 2 fifthsb) There are 13 fifths altogether.

13 fifths = 2 wholes + 3 fifthsc) There are 13 quarters altogether.

13 quarters = 3 wholes + 1 quarter

2

a)

53 = 1 whole + 2 thirds = 1

23

b)

83 = 2 wholes + 2 thirds = 2

23

c)

85 = 1 whole + 3 fifths = 1

35

3

a) 6 wholesb) 3 wholesc) 2 wholesd) 4 wholese) 5 wholesf) 3 wholesg) 3 wholes + 3 quartersh) 7 wholes + 1 half

4

a) Whitney can fill 6 boxes.b) Whitney needs 2 muffins to fill another box.

She will fill 6 boxes, with 2 muffins left over, so she needs 2 more muffins to make another 4

264 = 6 wholes and 2 quarters, meaning 6 full boxes with 2 muffins left over.

5

a) >b) <c) =d) >e) >f) =

Y4 – Spring – Block 3 – Step 4 – Fractions greater than 1 Answers (continued)

Question Answer

6

a)

b) \

c)

35

1 35

2

Y5 – Spring – Block 2 – Step 2 – Improper to mixed numbers Answers

Question Answer

1

a) 85 = 135

b) 125 = 225

c) 94 = 214

d) 53 = 123

2

a)

b)

c)

d)

3

a) 5

b) 313

c) 224 or 212

d) 2

e) 225

f) 216

g) 167

h) 378

213

223

214

234

Y5 – Spring – Block 2 – Step 2 – Improper to mixed numbers Answers (continued)

Question Answer

4 312 litres

5

Dexter has just moved the firsts number of the denominator to be the whole number. He needs to divide 32 by 3 to find the whole number and the remainder.323 = 10

23

6 = 5

7

possible answers:= 7 = 4= 14 = 2= 28 = 1

Y5 – Spring – Block 2 – Step 3 – Mixed numbers to improper fractions Answers

Question Answer

1

a) 114

b) 198

c) 278

2

a)

c)

d)

e)

94

73

103

175

Y5 – Spring – Block 2 – Step 3 – Mixed numbers to improper fractions Answers (continued)

Question Answer

3

a) 217 =157

227 =167

237 =177

247 =187

b) 315 =165

415 =215

515 =265

615 =315

c) 512 =112

514 =214

518 =418

5 116 =8116

In part a), the denominator stays the same and the numerator goes up by 1 each time.In part b), the denominator stays the same and the numerator goes up by 5 each time.In part c), all the numerators end in 1

4 23

5

No.Whitney has converted the wholes by multiplying 7 by 4 but forgotten to add the 1

417 =297

6

8

13

23

43

83

17

100

Y5 – Spring – Block 2 – Step 4 – Number sequences Answers

Question Answer

1

a)

b)

2

a)

b)

c)

3

a) 3 58 378 4

18

b) 4 47 417 3

57

c) 4 811 4511 4

211

They are both descending sequences.The difference between terms is different.

4

1 3511 45

1 45 215 2

35

1 2767

87

97

237

267

297

2 67 327 4

17

218

188

3 2 58 228 1

78 1

48 1

18

Y5 – Spring – Block 2 – Step 4 – Number sequences Answers (continued)

Question Answer

5

a) No.There are eight differences, so the missing fractions are eighths.

b) 3 18 328 3

38 3

48 3

58 3

68 3

78

c) Yes.48 is equivalent to

12, so 3

48 is equivalent to 3

12

d) 3 28 = 314

3 68 = 334

6 add one third or subtract one third

Y5 – Spring – Block 2 – Step 5 – Compare and order fractions less than 1 Answers

Question Answer

1

78 >

34

912 =

34

712 <

23

2

a) <b) >c) =d) >e) >f) =g) <h) >i) =j) =k) <l) <

3

4

a) 15

b) 16 or 26

c) any numerator between 1 and 9

d) 13 or 23

e) any denominator less than 9f) any denominator less than 6g) any denominator less than 8h) any denominator less than 6i) any denominator less than 6Where children have different answers, they can discuss how they found their answer.

5Both methods will work, and children may prefer different methods.Children need to justify why they prefer one method.

23

16

12

26

29

512

412

415

515

Y5 – Spring – Block 2 – Step 5 – Compare and order fractions less than 1 Answers (continued)

Question Answer

6

a) 21027

25

24

23

b) 1929

59

23

56

c) 15310

12

35

710

d) 2713

617

38

1230

71015

1115

1215

1315

Y5 – Spring – Block 2 – Step 6 – Compare and order fractions greater than 1 Answers

Question Answer

1

a) >b) =c) <

2

a) >b) <c) >d) =e) <f) >g) >h) =i) <

3Scott has more juice.

4

Rosie has only looked at the numerator.The number of parts is the same but the size of their parts is different.74 =

148 so

74 >

78

Rosie’s ribbon is longer.

5

a) 8283

168

45

815

b) 15673

159

129

79

c) 31145

2710

4220

1710

6

a) three possible answers:24

34

44

b) four possible answers:415

515

615

715

c) five possible answers:85

86

87

88

89

7Dora has more cake left.

8

multiple possible answers, e.g.:29 <

13

310 <

12

317 <

12

Y5 – Spring – Block 2 – Step 7 – Add and subtract fractions Answers

Question Answer

1

a) 75 = 125

b) 95 = 145

c) 25

d) 65 = 115

2

a) 67

b) 77 = 1

c) 87 = 117

d) 57

e) 159 = 169 or 1

23

f) 99 = 1

g) 89

h) 179 = 189

i) 1715 = 1215

j) 1315

3

twelve possible answers:18+

128 =

138

28+

118 =

138

38+

108 =

138

48+

98 =

138

58+

88 =

138

68 +

78 =

138

78+

68 =

138

88+

58 =

138

98 +

48 =

138

108 +

38 =

138

118 +

28 =

138

128 +

18 =

138

Y5 – Spring – Block 2 – Step 7 – Add and subtract fractions Answers (continued)

Question Answer

4 Dora has 128 litres left.

5

a) 38+108 =

138

b) 138 −68 =

78

c) 138 −58 = 1

d) 119 +119 =

229 = 2

49

e) 119 +99 =

209 = 2

29

f) 229 −29 =

209 = 2

29

g) 47 +67 +

47 = 2

h) 57 +47 +

57 = 2

i) 67 +27 +

67 = 2

j) 147 +37 +

47 = 3

k) 157 +17+

57 = 3

l) 167 +67 +

67 = 4

As the given fractions increase but the answer stays the same, the answer decreases.If both numerators go up by 1, then the numerator of the answer decreases by 2

6

98 +

78

138 +

38

18+ 1

78

7Annie’s rope is 1 14 m long.Dexter’s rope is 2 m long.

Y5 – Spring – Block 2 – Step 8 – Add fractions within 1 Answers

Question Answer

1

a) 46 =23

b) 36 =12

c) 56

2

3 There are 1318 litres of water altogether.

4

a)

b) In the first set of additions, the first number goes up in fifths and the answer goes up by 210 each time.In the second set of calculations, the first fraction is doubled each time and the numerator in the answer goes up by twice as much each time.

c) 55+1

10 =1110 1 +

532 =

3732

310

910

510

710

732

2132

932

1332

Y5 – Spring – Block 2 – Step 8 – Add fractions within 1 Answers (continued)

Question Answer

5

a)

b)

c)

d)

6

18+

1216 =

78

28+

1016 =

78

38+

816 =

78

48+

616 =

78

58+

416 =

78

68 +

216 =

78

812 or

23

912 or

34

1112

712

Y5 – Spring – Block 2 – Step 8 – Add fractions within 1 Answers (continued)

Question Answer

7

a)

b)

c) 34

2128

514

1128

2432

832

816

Y5 – Spring – Block 2 – Step 9 – Add 3 or more fractions Answers

Question Answer

1

a) 1012 =56

b) 1112

c) 1112

d) 912 =34

2

a) 1720

b) 1932

c) 2124 =78

d) 1516

e) 1618 =89

f) 2535 =57

All the fractions can be converted to the same denominator, which is a common multiple of all the denominators.

31518 (or

56) of the patch contains carrots, potatoes or onions.

4

a)

b)

c)

d) multiple possible answers, e.g.:

part a), because parts b) and c) both have 18 as one of their fractions.

1516

1516

1516

Y5 – Spring – Block 2 – Step 9 – Add 3 or more fractions Answers (continued)

Question Answer

5

a) 216

b) 616

c) 216

d) 616

e) 916

f) 716

6

child’s magic square

110

320

1120

320

310

Y5 – Spring – Block 2 – Step 10 – Add fractions Answers

Question Answer

1

a) 1210 = 1210 or 1

15

b) 1010 = 1

c) 1912 = 1712

2

a) 2320 = 13

20

b) 3220 = 11220 or 1

35

c) 1412 = 1212 or 1

16

d) 2112 = 1912 or 1

34

e) 2015 = 1515 or 1

13

f) 3615 = 2615 or 2

25

3

4a) 1 412 = 1

13 kg

b) 812 =23 kg

Y5 – Spring – Block 2 – Step 10 – Add fractions Answers (continued)

Question Answer

5

a)

b)

c)

6

14+

212+

23 =

1312

14+

612+

13 =

1312

24+

312+

13 =

1312

56

36 or

12

2

210 or

15

410 or

25

910

56

16

1 23

Y5 – Spring – Block 2 – Step 11 – Add mixed numbers Answers

Question Answer

1 Children need to justify the method that they prefer.

2

a) 3 710

b) 4 710

c) 4 910

d) 5 1516

e) 6 1516

f) 4 1415

3 Ron can convert 1310 to the mixed number 1

310 and add this to 3 to give 4

310

4

a) 6 16

b) 6 14

c) 9 112

d) 10 115

5a) 6 19 m

b) 4 1718 m

6 18914 cm

7

multiple possible answers, e.g.:

1 15+ 5815 = 6+

1115 = 6

1115

225+ 4515 = 6+

1115 = 6

1115

335 + 3215 = 6+

1115 = 6

1115

Children may have the whole number parts the other way round, but these are the fractions

they are likely to have used. If they used 45 , then the sum of the fractions would be greater

than 1115

8a) 8 512

b) 5 34

Y5 – Spring – Block 2 – Step 12 – Subtract fractions Answers

Question Answer

1

a) 26 =13

b) 36 =12

c) 18

d) 18

2

3 Jack walks 19 km further than Aisha.

4

a) 13169165161

16

b) 162111216211

21In part a), the numerator in the first fraction decreases by 2 each time and the numerator in the answer decreases by 4 each time.In part b), the numerator in the first fraction decreases by 1 each time, the numerator in the second fraction increases by 2 each time and the numerator in the answer decreases by 5 each time.

5a) 312 or

14 of an hour

b) 15 minutes

Y5 – Spring – Block 2 – Step 12 – Subtract fractions Answers (continued)

Question Answer

6

a) 34−12

b) 56−13

c) 1112−56

56−

34

7215 m

Y5 – Spring – Block 2 – Step 13 – Subtract mixed numbers Answers

Question Answer

1

a) 1 38

b) 1 18

c) 1 18

2

Both methods involve counting up from 13 to 156

Dexter converts to a common denominator at the start. He then adds 1 and then wotks out

how much more to reach 1 56

Whitney works out how much to 1 and then adds another 56. She converts to a common

denominator when adding the jumps.

1 716

3

a) 3 124

b) 3 116

c) 2 16

d) 7 724

e) 4 827

f) 6 16

4 There are 113 litres of orange juice left in the jug.

5

four possible answers:

3 15−3

20 = 31

20

3 25−7

20 = 31

20

335 −1120 = 3

120

345 −1520 = 3

120

Children may find it helps to work systematically in order to be sure they have found all the possible ways.

Y5 – Spring – Block 2 – Step 13 – Subtract mixed numbers Answers (continued)

Question Answer

612 38 m

8 14 m

14 13 m

Y5 – Spring – Block 2 – Step 14 – Subtract fractions – breaking the whole Answers

Question Answer

1

a) 1 1112

b) 1 912 = 134

c) 1 812 = 123

2

a) 3 183

2 78

2 68 = 234

b) 3 14−38

The fraction in the second number is greater than the fraction in the first number.c)

3

a) 2 1115

b) 2 716

c) 3 712

d) 1 912 = 134

e) 2 918 = 212

f) 2 2627

4

a) The carrots weigh 710 kg more than the cheese.

b) Jack has 1120 kg of carrots left.

c) The leftover potatoes weigh 1 810 (or 145) kg.

5 Eva jumps 259 m on her 2nd attempt.

! !

Y5 – Spring – Block 2 – Step 14 – Subtract fractions – breaking the whole Answers (continued)

Question Answer

6

a) seven possible answers:

1 116 and 316

1 316 and 516

1 516 and 716

1 716 and 916

1 916 and 1116

1 1116 and 1316

1 1316 and 1516

b) The fraction must be 216 more than the fraction part of the mixed number.

The numerator of the fraction cannot be greater than 15

Y5 – Spring – Block 2 – Step 15 – Subtract 2 mixed numbers Answers

Question Answer

1 Children need to justify why they prefer one method.

2

a) 2 510 = 212

b) 2 38

c) 11 14

d) 5 512The answer to part d) is the same as the number that was subtracted.

3 Car B travels 6212 (or 6

16) miles further than Car A.

4

a) Yes.For Amir’s method to work, the second fraction needs to be less than the first fraction.

b) The first fraction is now larger than the second fraction, so the second fraction can be subtracted.

c) 2 45

5

a) 1 910

b) 1 78

c) 2 714 = 212

d) 1 1018 =79

6

He has found the difference between the wholes and the difference between the fractions, but he has subtracted the first fraction from the second fraction.

correct answer: 1 56

7

a) 4 56− 412 =

26 =

13

b) 4 56− 31

12 = 1912 = 1

34

8

2 14

1 2511120 2

25

2 310

Y5 – Spring – Block 2 – Step 15 – Subtract 2 mixed numbers Answers (continued)

Question Answer

9

a) 1 510 = 112 miles

b) 6 35 miles

Y5 – Spring – Block 2 – Step 16 – Multiply unit fractions by an integer Answers

Question Answer

1

a) 15+15+

15 =

35 3 ×

15 =

35

b) 17+17+

17+

17 =

47 4 ×

17 =

47

c) 18+18+

18+

18+

18 =

58 5 ×

18 =

58

d) 110 +1

10 +1

10 +1

10 +1

10 +1

10 +1

10 =7

10 7 ×1

10 =7

10

2

a) 38

b) 310

c) 58

d) 910

e) 45

f) 89

g) 811

h) 1011

3

4 5 ×16 =

56

5

a) 65 = 115

b) 95 = 145

Y5 – Spring – Block 2 – Step 16 – Multiply unit fractions by an integer Answers (continued)

Question Answer

6

a) 1110 = 11

10

b) 119 = 129

c) 118 = 138

d) 117 = 147

e) 116 = 156

In the mixed numbers, the numerator goes up by 1 each time, and the denominator goes down by 1The pattern does not continue, as the next calculation is:

11 × 15 =115 = 2

15

7

a) 2b) 3c) 7d) 10e) 11f) 7g) 10h) 13

Y5 – Spring – Block 2 – Step 17 – Multiply non-unit fractions by an integer Answers

Question Answer

1

a) 27 +27 +

27 =

67 3 ×

27 =

67

b) 310 +310 +

310 =

910 3 ×

310 =

910

c) 29+29+

29+

29 =

89 4 ×

29 =

89

d) 49+49 =

89 2 ×

49 =

89

The answers are the same.In part d), the whole number is half the value and the fraction is twice the value compared with part c).

2

a) 67

b) 911

c) 811

d) 1011

e) 1415

f) 1415

3

Alex has multiplied both the numerator and denominator of the fraction by the whole number. She should only multiply the numerator by the whole number.

correct answer: 811

4 The cat eats 815 of the bag in 4 days.

5

a) 94 = 214

b) 125 = 225

c) 125 = 225

Y5 – Spring – Block 2 – Step 17 – Multiply non-unit fractions by an integer Answers (continued)

Question Answer

6

a) 103 = 313

b) 165 = 315

c) 227 = 317

d) 289 = 319

e) 3411 = 3111

f) The whole number part in the mixed number answers is always 3The numerator in the fraction part of the mixed number answers is always 1The denominator goes up by 2 each time.

g) five possible answers:

5 × 813 =4013 = 3

113

8 × 513 =4013 = 3

113

4 × 1013 =4013 = 3

113

10 × 413 =4013 = 3

113

20 × 213 =4013 = 3

113

7 3 ×58 =

158 = 1

78 or 5 ×

38 =

158 = 1

78

Y5 – Spring – Block 2 – Step 18 – Multiply mixed numbers by integers Answers

Question Answer

1

a) 4 × 1 = 4

4 × 15 =45

4 + 45 = 445

b) 4 × 2 = 8

4 × 15 =45

8 + 45 = 845

c) 4 × 2 = 8

4 × 25 =85 = 1

35

8 + 1 35 = 935

d) 4 × 2 = 8

4 × 23 =83 = 2

23

8 + 2 23 = 1023

2

a) 24 67

b) 24 411

c) 24 811

d) 24 1219

e) 24 2425

f) 24 815The whole number part is 24 in all the answers.The fraction part is different.

3 834 kg

4

a) 5 × 2 23 = 10 +103 = 13

13

b) 4 37× 5 = 20 +157 = 22

17

c) 8 × 2 512 = 16 +4012 = 19

412 or 19

13

d) 7 × 3 15 = 21 +75 = 22

25

e) 4 29× 8= 32 +169 = 33

79

f) 11 × 4 310 = 44 +3310 = 47

310

Y5 – Spring – Block 2 – Step 18 – Multiply mixed numbers by integers Answers (continued)

Question Answer

5

No.

5 × 3 211 = 15 +1011 = 15

1011

3 × 5 211 = 15 +611 = 15

611

6 2313 litres

7a) 6 34 kg

b) 416 =14 kg

Y4 – Spring – Block 3 – Step 9 – Fractions of a quantity Answers

Question Answer

1

a) 5b) 4c) 2d) 10e) 5f) 10g) 12h) 6

2a) The mass of one piece is 12 g.b) Filip eats 36 g of chocolate.

3

a) 618

b) 51525

c) 420

d) 405680

4

5

a)

b) child’s calculations in each circle

12 of 16

14 of 24

23 of 9

32 of 4

16 of 48

Y4 – Spring – Block 3 – Step 9 – Fractions of a quantity Answers (continued)

Question Answer

6

a) <b) =c) =d) =

Y5 – Spring – Block 2 – Step 19 – Fractions of an amount Answers

Question Answer

1

a) The total bar is 45 and it has been divided into 5 equal parts, so one small bar is15 of 459

b) The total bar is 45 and it has been divided into 5 equal parts, so three small bars are35 of 4527

c) Both questions involve finding 15 of 45, but Mo then needs to multiply this value by 3

2

a) 91827

b) 24126

c) 303030

In part a), the answers go up in 9s.In part b), each answer is half the previous answer.

In part c), the fractions are all equivalent to 13 so all the answers are the same.

3

4

a) >b) <c) >d) <

5

a) 55b) 66c) 33

Y5 – Spring – Block 2 – Step 19 – Fractions of an amount Answers (continued)

Question Answer

6All the other calculations have the answer 60

7a) 112b) 32

!

Y5 – Spring – Block 2 – Step 20 – Fractions as operators Answers

Question Answer

1

a) 13× 6 =63 = 2

b) 13 of 6 = 6 ÷ 3 = 2c) They both find the same amount.

d) 23 of 6 = 6 ÷ 3 × 2 = 4

e) 23× 6 =123 = 4

2

a) 44

b) 33

c) 88

d) 99

The answers to the two calculations are the same in each part.

3

a)

b)

c)

d)

Children may find different calculations easier to work out.

4

a) 56× 12 =56 of 12 = 10

b) 34× 24 =34 of 24 = 18

c) 27× 28 =27 of 28 = 8

d) 45× 45 =45 of 45 = 36

5

a) 35× 12035 of 120

b) Three pieces of chocolate weigh 72 g.

!

!

!

!

Y5 – Spring – Block 2 – Step 20 – Fractions as operators Answers (continued)

Question Answer

6

a) 18b) 18c) Children need to justify why they prefer one method.d) It is easier to find a fraction of an amount when the number is divisible by the

denominator of the fraction.

Y5 – Spring – Block 2 – Problem solving with fractions Answers

Question Answer

1

2 = 15

3154

4 3

5a) 28b) 8

6 12

7a) 8b) 64

8

a) 910

b) 57

c) 5 14

91364

102960

!