Y5 – Spring – Block 3 – Step 1 – Decimals up to 2 d.p. Answers

Question Answer

1There are 0 ones, 2 tenths and 3 hundredths.The number is 0.23

2

a) There are 0 ones, 5 tenths and 6 hundredths.b) There are 0 ones, 0 tenths and 8 hundredths.c) There is 1 one, 4 tenths and 8 hundredths.d) There are 2 ones, 0 tenths and 7 hundredths.

3

a) 4 onesb) 4 hundredthsc) 4 hundredthsd) 4 tense) 4 tenthsf) 4 tenths

4

a)

b) multiple possible answers, e.g. 0.03, 52.63, 2.93

5

a) 0.04b) 0.03c) 0.35d) 0.86

6

0.1 + 0.630.2 + 0.530.4 + 0.330.5 + 0.230.6 + 0.13

7

a) any number between 1.30 and 1.39b) 1.30, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 1.39c) The number has 4 hundredths.

8

Y5 – Spring – Block 3 – Step 1 – Decimals up to 2 d.p. Answers (continued)

Question Answer

9

a) falseThe greatest number is 5.20

b) trueThe smallest digit needs to start the number and the largest digit needs to end it.

c) true0.25, 0.52, 2.05, 2.50, 5.02, 5.20

Y5 – Spring – Block 3 – Step 2 – Understand thousandths Answers

Question Answer

1

a) 5.321b) 1.734c) 0.357

2

a)

b) 0.512 = 0.5 + 0.01 + 0.0021.352 = 1 + 0.3 + 0.05 + 0.0022.003 = 2 + 0.003

3

a) It is split into 1,000 parts.

b) 1131000

c) 0.113

4

a) fraction = 3711000

decimal = 0.371

b) fraction = 5021000

decimal = 0.502

5

a)

b)

Y5 – Spring – Block 3 – Step 2 – Understand thousandths Answers (continued)

Question Answer

6

a)

b)

c)

7

8a) 4.276b) 0.504

Y6 – Spring – Block 1 – Step 1 – Three decimal places Answers

Question Answer

1

a)

b)

c)

d)

2

There are 3 ones.There are 2 tenths.There are 4 hundredths.There are 5 thousandths.The number in digits is 3.245

3

a) 3 onesb) 3 thousandthsc) 3 tenthsd) 3 hundredthse) 3 tensf) 3 hundredths

Y6 – Spring – Block 1 – Step 1 – Three decimal places Answers (continued)

Question Answer

4

a)

b)

5

a) 17.134 = 10 + 7 + 0.1 + 0.03 + 0.004b) 94.077 = 90 + 4 + 0.07 + 0.007c) 34.079 = 30 + 4 + 0.07 + 0.009

6

1.456 = 1 + 0.4 + 0.05 + 0.0061.456 = 1 + 0.3 + 0.15 + 0.0061.456 = 1 + 0.2 + 0.25 + 0.0061.456 = 1 + 0.45 + 0.006

7

AnnieAnnie has 12 counters in the hundredths columns, which is equivalent to 1 tenth and 2 hundredths.

0.004

0.07

0.1

7

0.01

Y6 – Spring – Block 1 – Step 2 – Multiply by 10, 100 and 1,000 Answers

Question Answer

1

a) 2.3 × 10 = 23When the number is multiplied by 10 the counters move 1 place to the left.

b) 2.3 × 100 = 230When the number is multiplied by 100 the counters move 2 places to the left.

c) 2.3 × 1,000 = 2,300When the number is multiplied by 1,000 the counters move 3 places to the left.

2

3

a)

b) 4.4 × 1 = 4.44.4 × 10 = 444.4 × 100 = 4404.4 × 1,000 = 4,400The digits stay the same and move one more place to the left with each multiplication.

4

a) 13.44 × 10 = 134.4b) 41.4 × 100 = 4,140c) 0.415 × 1,000 = 415d) 4.4 × 1,000 = 4,400e) 103 = 1.03 × 100f) 30.44 = 3.044 × 10

30.6 306

Y6 – Spring – Block 1 – Step 2 – Multiply by 10, 100 and 1,000 Answers (continued)

Question Answer

5

The final answers are all the same.× 10 × 10 × 10 is the same as × 100 × 10 is the same as × 1,000 10 × 10 × 10 = 100 × 10 = 1,000

6

==<<

7

Kim has multiplied by 2 and then added 2 zeros, instead of moving 28.6 two places to the left.The correct answer is 2,860

8

possible answers:0.002 × 1 × 1,000 × 1,000 = 2,0000.002 × 10 × 100 × 1,000 = 2,0000.002 × 100 × 100 × 100 = 2,000The numbers on the cards must multiply together to give 1,000,000So there are three possible answers, as listed above, but the cards can be in any order.

70.39 703.9 7,039

703.9 7,039

7,039

Question Answer

1

a) 140 ÷ 10 = 14When the number is divided by 10 the counters move 1 place to the right.

b) 140 ÷ 100 = 1.4When the number is divided by 100 the counters move 2 places to the right.

c) 140 ÷ 1,000 = 0.14When the number is divided by 1,000 the counters move 3 places to the right.

2

3

a)

b) 123 ÷ 1 = 123123 ÷ 10 = 12.3123 ÷ 100 = 1.23123 ÷ 1,000 = 0.123The digits stay the same and move one more place to the right with each multiplication.

4

a) 16 ÷ 10 = 1.6b) 43.4 ÷ 100 = 0.434c) 614 ÷ 1,000 = 0.614d) 332 ÷ 1,000 = 0.332e) 2.4 ÷ 200 = 0.012f) 5.09 = 101.8 ÷ 20

Y6 – Spring – Block 1 – Step 3 – Divide by 10, 100 and 1,000 Answers

4.3 0.43

Y6 – Spring – Block 1 – Step 3 – Divide by 10, 100 and 1,000 Answers (continued)

Question Answer

5

The final answers are all the same.÷ 10 ÷ 10 ÷ 10 is the same as ÷ 100 ÷ 10 is the same as ÷ 1,000 10 × 10 × 10 = 100 × 10 = 1,000

6

=<=>

7Yes.Dexter has moved the digits two places to the right. 54.00 is the same as 54

8

No.Rosie has divided by 100 twice. She should have divided by 2 to get 1,800 and then moved the digits two places to the right.The correct answer is 18

31.4 3.14 0.314

3.14 0.314

0.314

Question Answer

1a) 9.6b) 9.2

2

36.6

3

a)

b)

4

a) 20.8b) 42.9c) 54.6d) 7.02e) 46.02f) 57.612

5 1 kg

6

a) 14.428.857.657.6

b) 10.35103.51,035

7

No.He should have divided 136 by 10, because 3.4 = 34 ÷ 10The correct answer is 13.6

Y6 – Spring – Block 1 – Step 4 – Multiply decimals by integers Answers

0 2 43 2 06 0 019 4 41

0 5 40 0 02 0 012 5 41

Question Answer

8

a) multiple possible answers, e.g.:1.23 × 4 = 4.924.13 × 2 = 8.16There are 12 possible answers.

b) 3.21 × 4 = 12.84c) 2.34 × 1 = 2.34d) 4.12 × 3 = 12.36Children can compare answers to see if they have all 12 possible calculations between them.

Y6 – Spring – Block 1 – Step 4 – Multiply decimals by integers Answers (continued)

Question Answer

1a) 2.1b) 4.1

2

4.1

3

a)

b)

4

a) 3.2b) 3.7c) 3.08d) 3.89e) 67.45f) 11.68

Y6 – Spring – Block 1 – Step 5 – Divide decimals by integers Answers

3 22 1

1 2

2 3 1

0

0

Question Answer

5

a)

9.2 ÷ 4 = 2.3b)

16.5 ÷ 3 = 5.5Children may have partitioned their numbers differently. Both numbers must be divisible by the integer.

6

a) 2.4124.10.2411.205

b) 2.162.172.18

73.6 ÷ 4 = 36 ÷ 403.6 ÷ 4 = 7.2 ÷ 8

8

possible answers with single-digit divisors:8.4 ÷ 8 = 4.2 ÷ 48.4 ÷ 6 = 4.2 ÷ 38.4 ÷ 4 = 4.2 ÷ 28.4 ÷ 2 = 4.2 ÷ 1The first number is twice the second number.

Y6 – Spring – Block 1 – Step 5 – Divide decimals by integers Answers (continued)

÷ 4 ÷ 4

8 1.2

2 0.3

÷ 3 ÷ 3

15 1.5

5 0.5

Question Answer

1 340

2 £3.33

3 4 km

4a) 0.55 mb) 1.65 m

5 80 days

6a) 25b) 86

7

Shop BShop A: A tin of paint costs £4.68Shop B: A tin of paint costs £4.67

8

No.The remainders are not worth the same amount.146 ÷ 5 = 29.2117 ÷ 4 = 29.25

9possible answers:158, 168, 178, 188, 198

Y6 – Spring – Block 1 – Step 6 – Division to solve problems Answers

Question Answer

1

a) The whole has been divided into 10 equal parts.Each part is worth 0.1

This is equivalent to 110

b) The whole has been divided into 100 equal parts.Each part is worth 0.0110 parts out of 100 are shaded.

This is equivalent to 10100 (or 1

10)

2

a)

17 parts out of 100 are shaded.

0.17 = 17100

b)

20 parts out of 100 are shaded.

0.2 = 15

3

0.2 = 210 =

15

0.4 = 410 =

25

0.8 = 810 =

45

4

a) 0.54 = 54100 =

2750

b) 0.6 = 610 =

35

c) 0.3 = 310 =

30100

d) 0.09 = 9100

e) 0.9 = 910

f) 2150 =

42100 = 0.42

Y6 – Spring – Block 1 – Step 7 – Decimals as fractions Answers

Question Answer

5a) 1

2 =510 = 0.5

b) 0.1 = 110 =

220

6

0.37 = 37100

Y6 – Spring – Block 1 – Step 7 – Decimals as fractions Answers (continued)

0.3 0.37

Question Answer

1

a) Each square represents 1100

1100 of the whole square is shaded.This is equivalent to 0.01 as a decimal.

b) 50100 of the whole square is shaded.

This can be simplified to 12This is equivalent to 0.5 as a decimal.

2

a)

b)

Both number lines go up in tenths.The number line is part a) is labelled with decimals and the number line in part b) is labelled with fractions in their simplest form.

3

a) 2850 =

56100 = 0.56

b) 620 =

30100 = 0.30

c) 925 =

36100 = 0.36

d) 24200 =

12100 = 0.12

4

a) 27500 =

541000 = 0.054

b) 62250 =

2481000 = 0.248

c) 51200 =

2551000 = 0.255

d) 1282000 =

641000 = 0.064

5

a) 0.20.10.050.025

b) 0.050.10.150.3

Y6 – Spring – Block 1 – Step 8 – Fractions to decimals (1) Answers

0.2 0.3 0.4 0.5 0.90.6 0.7 0.8

15

310

25

35

710

910

45

Question Answer

6

Eva

Tommy’s method: 60200 =

30100 = 0.30 = 0.3

Alex’s method: 60200 =

3001000 = 0.300 = 0.3

They get the same answer.

7multiple possible answers, e.g.: 24, 1020In all the fractions that the children find, the denominator must be twice the numerator.

Y6 – Spring – Block 1 – Step 8 – Fractions to decimals (1) Answers (continued)

Question Answer

1

a) 13 = 1 ÷ 3

b) 23 = 2 ÷ 3

c) 47 = 4 ÷ 7

d) 35 = 3 ÷ 5

e) 37 = 3 ÷ 7

f) 110 = 1 ÷ 10

2 0.4

3

a) 0.25b) 0.8c) 0.375

4

a) 0.875b) 1.4c) 0.0625d) 0.5625

5 0.98

6Jack worked out 2 ÷ 1 instead of 1 ÷ 2The correct answer is 0.5

7

multiple possible answers, e.g.:9

2041

1002150

There is an infinite number of possible answers.

80.333333…Some children may not have realised that the sequence goes on forever.

Y6 – Spring – Block 1 – Step 9 – Fractions to decimals (2) Answers