Y7 – Autumn – Block 4 – Step 1 – Recognise the place value of any number in any integer up to one billion Answers

Question Answer

1

a) 35,612b) 510,900c) 8,302

2

a)

b)

c)

d)

3

a)

seven hundred thousandb)

seventy million

4a) 107,213,042b) 47,401,510

Y7 – Autumn – Block 4 – Step 1 – Recognise the place value of any number in any integer up to one billion Answers (continued)

Question Answer

5

6

a) sixtyb) six thousandc) sixty thousandd) sixty millione) six millionf) six hundred million

7

multiple possible answers, e.g.:a) 50,050 and 12,354,657b) 50,500,000 and 51,511,111

8

a) 300b) 700,000 + 10,000 + 5,000c) 20,957d) 20,957e) 817,000

9The basic partition is:10,000,000 + 3,000,000 + 400,000 + 6,000 + 900 + 20 + 8

5

3006,00020,000

5,000,000

20,000,000

Y7 – Autumn – Block 4 – Step 2 – Understand and write integers up to one billion in words and figures Answers

Question Answer

1

a) 7,561b) 130,800c) 9,000,070d) 9,000,007

2132,033one hundred and thirty-two thousand and thirty-three

328,302,320twenty-eight million, three hundred and two thousand, three hundred and twenty

4

a) nine thousand, five hundred and seventyb) eighty-nine thousand, nine hundred and fourc) eight million, three hundred and twenty thousand and fiftyd) one billion

5

a) 16,250,508b) 15,350,508c) 15,280,508

6 a) One million is 1,000,000, so half a million is 500,000, which is five hundred thousand.

7a) Tommy has missed out the 0 in the hundreds place.b) 42,510,089

8

a) three hundred and twenty-nine million, two thousand, three hundred and twenty-sevenb) sixty-six million, eight hundred and fifty thousand

66,850,000c) 250,000,000

Y7 – Autumn – Block 4 – Step 3 – Work out intervals on a number line Answers

Question Answer

1No.There are 5 intervals, so the number line is going up in 20s.

2

There are 10 intervals. 1,000 ÷ 10 = 100, not 10100s

3

4

a)

b)

5

a)

b)

c)

d)

The number of intervals would stay the same.The values would be divided by 2

100 200 300 400 500 600 700 800 900

10,0000 2,000 4,000 8,0006,000

200 400 600 800

250 500 750

60 180 240 300

30 90 15060

40 160 20080

24 72 9648

Y7 – Autumn – Block 4 – Step 3 – Work out intervals on a number line Answers (continued)

Question Answer

6

a)

b)

7 The difference between A and B is 35

8

40sThere are 5 intervals between 0 and 200200 ÷ 5 = 40

9

a) X = 400b) Y = 47,000c) Z = 248,500

200 600

5226

Y7 – Autumn – Block 4 – Step 4 – Position integers on a number line Answers

Question Answer

1

a)

b)

c)

Work out the interval for the number line, then identify which marker corresponds to 600

2

a)

b)

c)

d)

3

a) 40sb)

4

a) 1,300 is closer to 1,500 than 1,000 but the arrow is closer to 1,000b) estimated answer near 1,100c) Answers may vary, as students are estimating how far along the interval the arrow is

600

600

600

600

30016020 390

Y7 – Autumn – Block 4 – Step 4 – Position integers on a number line Answers (continued)

Question Answer

5

a), b)

6

a) estimated answer near 650b) estimated answer near 260c) Yes, two people may get different answers because they are estimating the values.

7

estimated answers near: a) 18 °Cb) −10 °Cc) 73 °C

2,000 4,263

Y7 – Autumn – Block 4 – Step 5 – Round integers to the nearest power of 10 Answers

Question Answer

1

a) 57 rounded to the nearest 10 is 60257 rounded to the nearest 10 is 260657 rounded to the nearest 10 is 6601,157 rounded to the nearest 10 is 1,160230,457 rounded to the nearest 10 is 230,460

b) 1,183 rounded to the nearest 10 is 1,1801,184 rounded to the nearest 10 is 1,1801,185 rounded to the nearest 10 is 1,1901,186 rounded to the nearest 10 is 1,190

2

Mo has looked at the wrong position to decide which way to round. He should have looked at the tens place.1,288 rounded to the nearest 100 is 1,300

3

a) 700b) 1,700c) 7,700d) 11,900e) 10,000f) 0

4

a)

b) 15,649This is the largest integer that will round to 15,600 to the nearest 100

5

MoSome numbers, e.g. 7,001, rounded to the nearest 10, 100 or 1,000 all give the answer 7,000

6

a)

b) any numbers between 17,250 and 17,349

7

• possible answers: 42,509 42,590 42,905 42,950• 95,204• multiple possible answers, e.g.: 45,029 45,092 54,902 54,920There are four possible answers for the first number, one possible answer for the second number and many possible answers for the third number.

40,000

130,000

80,000

10,000

36,900

126,400

81,100

7,900

37,000

126,000

81,000

8,000

Y7 – Autumn – Block 4 – Step 5 – Round integers to the nearest power of 10 Answers (continued)

Question Answer

8

a) No.The number is likely to have been rounded to the nearest 10,000

b) 34,999c) 25,000d) Answers will differ, depending on what power of 10 students decided the number had

been rounded to.

9

No.40 + 50 + 30 + 40 + 50 = 210 kgEach box could weigh up to 5 kg more than it is labelled.5 × 5 kg = 25 kg210 kg + 25 kg = 235 kg, which is greater than 225 kg.

Y7 – Autumn – Block 4 – Step 6 – Compare numbers using symbols Answers

Question Answer

1

a) 502 is greater than 5252 is less than 502

b) 30,099 is less than 90,00390,003 is greater than 30,099

c) 76,590 is not equal to 75,60975,609 is not equal to 76,590

2

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

3

a)

b)

4

a) ≠b) =c) ≠d) ≠

✔

✔

Y7 – Autumn – Block 4 – Step 6 – Compare numbers using symbols Answers (continued)

Question Answer

5

a)

b)

6

multiple possible answers, e.g.:a) 7,135 < 7,420 7,335 < 7,429b) 979 > 978 970 > 968c) 3,879 < 3,976 3,819 < 3,876

7multiple possible answers, e.g.:50,181 50,185 50,190, 50,198 50,199

8

a) trueA is less than B and B is less than C, so A must be less than C.

b) falseA is less than B so cannot be equal to it.

c) trueB is greater than A and less than C, so it must lie between them.

9

Multiple possible answers, e.g.:48,019 < 56,273The first digit of the second number must be 5, but the other digits can go in any position.

2,370

500,001,500 50,001,500

2,280

>

>

Y7 – Autumn – Block 4 – Step 7 – Order a list of integers Answers

Question Answer

1

a) 37,900b) It has the highest value in the ten thousands column.c) 37,900 27,903 20,709 20,307

2a) 8,700 kg 12,995 kg 13,000 kg 15,700 kgb) 89,000 two hundred thousand 950,000 3 million

3

a)

b) It is the only number with a value in the hundred millions column.c) 102,212,032d) 102,212,032 47,500,000 47,401,410

4

No.Whitney has not considered the place value of the digits. 100,001 has a 1 in the hundred thousands column, but the other numbers start in the ten thousands column.

5a) Db) B

6

multiple possible answers, e.g.:5107 < 5,110 < 6,011 < 9,561There are many solutions. The missing digit in the second number must be greater than 0. If the first digits in the third and fourth numbers are greater than 5 and increasing, then the other digits can have any value.

7

a) Sao Paulob) multiple possible answers, e.g.:

21,000,000 21,040,000If the populations are all rounded to the nearest 10 thousand, the possible values are:21,000,000 21,010,000 21,020,000 21,030,000 21,040,000

✔

Y7 – Autumn – Block 4 – Step 7 – Order a list of integers Answers (continued)

Question Answer

8

multiple possible answers, e.g.:

The digits shown in red can only take the values shown.The missing digit in the last number must be greater than 4The first missing digit in the first number cannot be greater than 7

7

0

0

2

2

3

0

4

0

2

9

7 2

0

5

Y7 – Autumn – Block 4 – Step 8 – Find the range of a set of numbers Answers

Question Answer

1

a) She has used the first and last values, instead of the highest and lowest values. She needs to put the values in order first.

b) 400 g

2

a) 7b) £13c) 144 md) 65

3 98 litres

4 2,475,054

5

a) 11b) multiple possible answers, e.g.: 11, 16 24, 20c) multiple possible answers, e.g.: 115, 124, 120 129, 125, 125Parts b) and c) have more than one possible answer.

6a) 325b) 211

7 5

8 145 seconds

9a) Annie has not converted 200 ml and 500 ml to litres.b) 3.8 litres or 3,800 ml

Y7 – Autumn – Block 4 – Step 9 – Find the median of a set of numbers Answers

Question Answer

1

a)

It is the middle value when the towers are in height order.b)

It will be the middle value when the towers are put in height order.

2

a) 4b) 26 cmc) £17d) 345 ge) 61%

3

a) multiple possible answers, e.g.: 1, 2, 8, 15, 20b) When the cards are in order, the middle number is the same, but the other numbers can

be any values.

4a) 14b) 42 kg

5

multiple possible answers, e.g.:8, 10, 10, 129, 9, 11, 136, 10, 10, 10

6 275 ml

7 The median could increase or stay the same.

8 41

Y7 – Autumn – Block 4 – Step 10 – Understand place value for decimals Answers

Question Answer

1

a) 0.53 is equal to 5 tenths and 3 hundredths.0.53 = 0.5 + 0.03

b) 5.27 is equal to 5 ones, 2 tenths and 7 hundredths.5.27 = 5 + 0.2 + 0.07

2 2.304

3

0.7

0.75

1.75

1.85

1.853

Y7 – Autumn – Block 4 – Step 10 – Understand place value for decimals Answers (continued)

Question Answer

4

a)

5 tenths and 2 hundredthsb)

5 ones and 2 tenthsc)

5 tens and 2 hundredths

5

a)

b)

c)

d)

0.08

1 0.5

0.75

0.635

Y7 – Autumn – Block 4 – Step 10 – Understand place value for decimals Answers (continued)

Question Answer

6

7

8

a) 5 tens + 3 ones + 6 tenths + 2 hundredths = 53.62b) 9 hundreds + 2 ones + 4 tenths = 902.4c) 7 tens + 3 ones + 9 hundredths = 73.09d) 2 tenths + 8 hundredths = 0.28

9

Jack0.45 = 4 tenths + 5 hundredths and 4 tenths = 40 hundredthsSo 0.45 = 40 hundredths + 5 hundredths = 45 hundredths

Y7 – Autumn – Block 4 – Step 11 – Position decimals on a number line Answers

Question Answer

1

a)

b)

c)

d)

2

3

a)

b)

c)

4No.The intervals are 0.2, not 0.1, so the arrow is pointing to 4.4

5 Each interval on the number line represents 0.2

6

7

0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.8 0.90.7

0.6 0.7 0.8 0.9

0.5 0.75

3 3.5 4.5

5 8.5

7.2 7.7 7.85

2.51 2.555 2.585

5 6.4 1.5 4.9

11.9 11.95 12.05 12.1 12.15

Y7 – Autumn – Block 4 – Step 11 – Position decimals on a number line Answers (continued)

Question Answer

8

a)

b)

c)

d)

9

multiple possible answers, e.g.: 5 and 5.44.2 and 6.2The two numbers must be the same distance either side of 5.2

2

2

2

2

Y7 – Autumn – Block 4 – Step 12 – Compare and order any number up to one billion Answers

Question Answer

1RosieShe has more counters in the ones column.

2

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

3No.5.3 has 3 tenths and 5.18 has 1 tenth and 8 hundredths, so 5.3 is greater than 5.18

4

a)

b) 0.12, 0.21, 2.01, 10.02, 10.1, 20.2

5

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

6

a) 20.73 kg, 20.7 kg, 20.37 kgb) possible answers: 20.71 kg, 20.72 kg

There are two possible answers.

7a) 0.45, 0.504, 4.5, 45b) 130.9 km, 132.5 km, 135 km, 1,039.5 km

8

1

2

1

0

0

0

0

2

0

0

2

2

1

0

1

2

1

1

2

Y7 – Autumn – Block 4 – Step 12 – Compare and order any number up to one billion Answers (continued)

Question Answer

9

multiple possible answers, e.g.:a) possible answers: 5.8 > 5.08 upto 5.8 > 5.78

possible answers: 5.8 < 5.88 or 5.8 < 5.98b) possible answers: 30.0 < 32.64 upto 32.6 < 32.64

possible answers: 32.7 > 32.64 upto 39.9 > 32.64For part a), there are eight possible answers for > and two possible answers for .

10

multiple possible answers, e.g.:0.91 0.98 1.1 1.12 1.32The numbers in red can only have the values shown.

Y7 – Autumn – Block 4 – Step 13 – Round a number to 1 significant figure Answers

Question Answer

1

2

a) 300b) 2,000c) 1,000d) 80e) 90f) 80g) 10h) 100

3

a) Yes.The first significant figure is in the hundreds column. 459 rounded to the nearest 100 is 500

b) No.Ron is only correct when the first significant figure is in the hundreds column.

4

They all have one digit, 8

5

Dora should have looked at the thousandths column to round, as the first significant digit is in the hundredths column. 0.09

6

a) 0.050.50.0005

b) 0.000070.00032

7 Remove the zeros after the significant figure: 0.004

hundreds 700hundreds 800thousands 7,000thousands 8,000

hundred thousands 700,000ones 8

tenths 0.7

✔✔

✔✔

✔✔✔

Y7 – Autumn – Block 4 – Step 13 – Round a number to 1 significant figure Answers (continued)

Question Answer

8

a) 99 is 2 significant figures.100

b) 0.93750.9

9

a) 30,000b) 64,999c) 55,000

10 When the first significant figure is in the tens column.

Y7 – Autumn – Block 4 – Step 14 – Write 10, 100, 1,000 etc. as powers of ten Answers

Question Answer

1

a) 23 = 2 × 2 × 2b) 56 = 5 × 5 × 5 × 5 × 5 × 5c) 35 = 3 × 3 × 3 × 3 × 3d) 6 × 6 = 62e) 9 × 9 × 9 × 9 × 9 × 9 × 9 = 97

2

a) 102b) 10 × 10 × 10 = 103c) 10 × 10 × 10 × 10 × 10 = 105d) 101e) 108

3No.Eva needs to write 1 followed by 5 zeros.

4

a) 100b) 10,000c) 1,000,000,000d) 1,000,000,000,000When working out powers of 10, the power indicates the number of zeros.

5

6

a) ten millionb) one thousandc) one billion

7

one hundred, 103, 104, one hundred thousand, 1,0002, ten million, one billionEither convert each number to an ordinary number, express each number in words or convert each number to a power of 10

8 1015

9 1,000,000,000,000

10a) one trillion or 1012b) one thousand or 103

Y7 – Autumn – Block 4 – Step 14 – Write 10, 100, 1,000 etc. as powers of ten Answers (continued)

Question Answer

11

a) 105b) Write out 103 and 102 as ordinary numbers, multiply them together and convert the

answer to a power of 10Some children may realise that they just need to add the powers.

c)

d) multiple possible answers, e.g.:103 × 105104 × 104104 × 102 × 102

✔

✔ ✔

Y7 – Autumn – Block 4 – Step 15 – Write positive integers in the form A × 10n Answers

Question Answer

1

a) 30 = 3 × 10b) 300 = 3 × 10 × 10 = 3 × 102c) 3,000 = 3 × 10 × 10 × 10 = 3 × 103d) 30,000 = 3 × 10 × 10 × 10 × 10 = 3 × 104e) 300,000 = 3 × 10 × 10 × 10 × 10 × 10 = 3 × 105f) 3,000,000 = 3 × 10 × 10 × 10 × 10 × 10 × 10 = 3 × 106

2

3

a) 8b) 7c) 2d) 5

4

a) 3b) 5c) 9d) 9

5

a) 8,000,000b) 100,000,000c) 900,000

6

a) 9 × 102b) 3 × 107c) 6 × 10d) 5 × 104e) 4 × 105f) 7 × 106g) 6 × 104

7

Dexter4 × 107 = 40,000,0006 × 105 = 600,000So 4 × 107 > 6 × 105

5 × 8108 × 1036 × 10 50,000

15 × 1087 × 106

student’s number of the form A × 10n

student’s number in any form other than A × 10n

Y7 – Autumn – Block 4 – Step 15 – Write positive integers in the form A × 10n Answers (continued)

Question Answer

8 4 × 106 has the greater power so is the greater number.4,000,000 > 70,000

9 699,200

10

a)

b) Jupiterc) Neptune, Mercury, Mars, Venus, Earth, Uranus, Saturn, Jupiterd) 55,000,000 m

3 × 106

60,000,000

3 × 107

6 × 106

20,000,000

2,000,000

7,000,000

70,000,000

Y7 – Autumn – Block 4 – Step 16 – Investigate negative powers of ten Answers

Question Answer

1

When the power increases by 1, the answer is ten times greater.When the power decreases by 1, the answer is ten times smaller.

2

a) 10−4b) 10−1c) 10−5

d) 10−6e) 10−11

f) 10−6

3

a) 0.01b) 0.00001c) 0.00000001

4

No.The power of 10 are negative and −4 < −210−4 = 0.0001 and 10−2 = 0.01 So 10−4 < 10−2

5

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

6 103 = 1,000

7a) 10−6b) 10−18

8 E, B, F, D, A, C

10 × 10 × 10 × 1010 × 10 × 10

10 × 1010

1 ÷ 10 ÷ 10 ÷ 101 ÷ 10 ÷ 10 ÷ 10 ÷ 10

1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10

10,0001,00010010

100,000

0.0010.0001

0.00001

0.01

Y7 – Autumn – Block 4 – Step 16 – Investigate negative powers of ten Answers (continued)

Question Answer

9a) 10−1b) 102

10 𝑥 = 105

Y7 – Autumn – Block 4 – Step 17 – Write decimals in the form A × 10n Answers

Question Answer

1

a) 4 × 10−4b) 7 × 10−1c) 2 × 10−6d) 3 × 10−11

2

a) 0.00008b) 0.00000005c) 0.006d) 0.5

3

a) 9 × 10−4b) 3 × 10−6c) 5 × 10−1d) 2 × 10−2e) 6 × 10−5f) 4 × 10−4g) 8 × 10−6h) 9 × 10−9

4

a) The powers of 10 are the same. The integers are different.b) The integers are the same. The powers of 10 are different.c) The integers are the same. The powers of 10 have the same number but the opposite

sign.

5

a) 𝑔 = 9 × 10−2b) 𝑏 = 4 × 10−4c) 𝑝 = 3 × 10−3

6

7 5 × 10−4, 6 × 10−5, 7 × 10−6

8 3 × 10−1

9 625

10

multiple possible answers, e.g.:5 × 10−2, 5 × 10−2, 9 × 10−2, 1 × 10−1, 4 × 10−15 × 10−2, 8 × 10−2, 9 × 10−2, 1 × 10−1, 4 × 10−1Keeping all the other terms the same as above, the second term can take any value between 5 × 10−2 and 8 × 10−2