Nelson international maths pupil book 6 answers by hany mufeid

Student Book 6

Nelson International Maths Revising place value (p5) 1 a) 39 b) 357 c) 9 421 d) 8 812 e) 643 994 2 a) 59 b) 704 c) 23 022 d) 943 502 3 a) 5 units b) 5 hundreds c) 5 tens d) 5 hundreds e) 5 thousands f) 5 tens g) 5 hundred thousands h) 5 tens of thousands i) 5 tens of thousands j) 5 thousands k) 5 units l) 5 hundred thousands. 4 654 210 5 112 478 Comparing and ordering numbers (p6) 1 a) 124, 143, 148, 412, 416 b) 8164, 8414, 8416, 8461, 8641 c) 15 115, 15 151, 15 515, 15 551 d) 900 000, 919 900, 990 000, 999 000 e) 234 444, 243 444, 324 444, 432 444

Answers

4 a) no $9000 b) yes c) yes d) no $13 000 e) no $11 000 Revising place value to hundredths (p8) 1 a) 0.95 b) 1.1 c) 1.4 d) 1.48 2 a) 9 tenths b) 9 hundredths c) 4 units d) 3 hundredths e) 5 tenths f) four tens g) 7 tens h) 1 hundredth 3 a) 0.4 b) 0.12 c) 0.07 d) 0.15 e) 2.5 f) 10.05 g) 213. 3 h) 128.33 4 a) $4.25 b) $10.99 c) $200.50 d) $29.03 Numbers below zero (p9) 1 a) –28 b) –20 c) –12 d) –10 e) –4 f) 8 g) 16 h) 26 2 a) 18 oC b) 12 oC c) 5 oC d) 0 oC e) 30 oC f) –1 oC g) –5 oC h) –3 oC

2 a) 1321, 1231, 312, 231, 123 b) 12 999, 12 700, 12 345, 12 098, c) 145 321, 145 231, 145 213, 145 123 d) 423 320, 342 340, 324 430, 239 430 e) 432 000, 342 000, 324 000, 234 000

3 a) –2 oC<2 oC b) 0oC>–5 oC c) –3oC<3oC d) –5 oC<–3 oC e) –10 oC>–12 oC f) 8 oC>–8 oC

3 a) 200 b) 500 c) 800

1 a) 20 °C b) 29 °C c) 14 °C d) 14 °C e) 27 °C f) 10 °C g) 14 °C h) 30 °C i) 23 °C j) 14°C k) 20 °C l) 20 °C

4 a) 50 b) 200 c) 400, d) 600 e) 725 f) 900

2 30 °C warmer

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

3 53 °C colder

Rounding Numbers (p7)

4 a) It puts a minus sign before the amount b) It puts a plus sign before the amount c) 777.00

1 a) 60 b) 460 c) 213 460 d) 4000 e) 211 110 f) 8050 g) 34 760 h) 980 650

Temperature differences (p10)

2 a) 400 b) 100 c) 600 d) 12 800 e) 7300 f) 12 100 g) 15 800 h) 524 600 3 a) 2000 b) 6000 c) 53 000 d) 1000 e) 91 000 f) 6000 g) 567 000 h) 347 000

Student Book 6

Nelson International Maths

Answers

Days, weeks, months and years (p11)

5 a) Friday b) Sunday c) Sunday

Revising time (p13)

Number of weeks

Number of days

Number of months

420

1 a) 15:00 b) 09:30 c) 17:30 d) 03:05 e) 22:15 f) 00:45 2 a) 15:20 b) 09:50 c) 17:50 d) 03:25 e) 22:35 f) 01:05 3 a) 14:50 b) 09:20 c) 17:20 d) 02:55 e) 22:05 f) 00:35

Number 1 of years

120

180

1200

4 a) Students’ own work. b) Times cannot be confused between a.m. and p.m.

100

More about 24-hour time (p14)

2 a) 35 b) 56 c) 23 d) 76 3 a) 5 b) 6 c) 10 d) 101 4 a) 60 b) 120 c) 150 d) 1200 5 a) 3 b) 5 c) 20 d) 10 1 2

6 There are 15 weeks and 4 days. Students to show their own methods of working. Allow calculator methods as well.

1 a) 8.45 a.m. b) 12.30 p.m. c) 2.20 p.m. d) 2.45 a.m. e) 11.20 p.m. f) 4.35 p.m. g) 7.10 p.m. h) 9.15 p.m. 2 a) 06:32 b) 15:45 c) 10.10 d) 08:15 e) 20.15 f) 11:40 g) 23:40 h) 00:00 i) 12:00 3 a) 04:30 b) 16:45 c) 18:10 d) 06:40 4 a) 09:30 to 10:00 b) 15:30 to 16:30 c) 18:00 to 19:00 d) 19:45 to 21:00 5 a)

1 hour, 2

3 4

1 4

1 hour, 1 hour, 1 hours

Working with calendars (p12)

b) 3

1 a) Sunday b) 10 November c) 6 October

c) 225 minutes d) It is 13 500 seconds, so it less than 15 000 seconds

2 a) 38 b) 35 c) 42 d) 123 3 10 months later 4 a) 8 months b) Answers will depend on how students calculate. If you count the actual weeks there are 34.5 weeks in this time and that will give 68 + 1 = 69 lessons. If students take 8 months × 4 weeks, they will only get 32 weeks or 64 lessons. Allow for comparison and discussion of methods.

hours

Different times in different places (p15) 1 a) 12.15 p.m. b) 10.45 p.m. c) 7.15 p.m. d) 12.15 p.m. e) 11.15 a.m. f) 2.15 a.m. (the next day) g) 3.15 a.m (the next day) h) 8.15 pm i) 9.15 a.m. the same day j) 11.15 p.m. 2 Students’ own work.

Student Book 6

Nelson International Maths Revising 3-D shapes (p16) 1 Students’ own work.

Answers

Revising addition and subtraction facts (p20)

Properties of 3-D shapes (p17)

1 a) 20 b) 20 c) 20 d) 20 e) 20 f) 20 g) 30 h) 40, i) 30

1 a) C b) F c) B d) D

2 a) 50 b) 40 c) 40 d) 70 e) 100 f) 90

2 A, C F G, H, I

3 0.2 + 0.8; 0.1 + 0.9; 0.4 + 0.6; 0.7 + 0.3; 0.5 + 0.5

3 B, D, E 4 C

4 a) 0.6 b) 0.3 c) 0.5 d) 0.2 e) 0.9 f) 0.4

5 B

6 B, D, E

100

5.8

3.9

0.61

7.3

0.73

8 G, H

4.6

0.46

9 B, D, E

8.1

0.19

7 A, C, F, I

3-D Shapes and their nets (p18) 1 a) cube b) triangular prism c) Pentagonal based pyramid d) Hexagonal prism e) cylinder f) square based pyramid 2 a) C b) D c) B d) A e) E f) F Investigate different nets (p19) 1 Student’s own work. 2 a) A, E, F, H, I, L, N, O, R, S, T b) Students to discuss and demonstrate if necessary. Mostly the others won’t work because a side will overlap when you try to fold it up; Diagram M won’t work as it has 7 faces. Any net with four blocks arranged in a square (as in J) won’t work as it cannot be folded.

Adding whole numbers (p21) 1 a) 769 b) 571 c) 505 d) 1580 e) 1120 f) 3585 More addition (p22) 1 a) 195 b) 385 c) 885 d) 1066 e) 994 f) 186 g) 4095 h) 3821 i) 10 288 2 a) 2435 b) 2474 c) 5108 d) 4375 e) 5257 f) 11 953 3 a) 4490 b) 2359 c) 4221 km d) 7732 4 25 644 5 3013 6 a) 384+ 123 = 507 b) 324 + 462 = 786 c) 257+ 282 = 539

Student Book 6

Nelson International Maths

Answers

2 a) 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 b) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48 c) 6, 12, 18, 24, 30, 36 d) 9, 18, 27, 36, 45, 54, 63, 72

Subtracting whole numbers (p23) 1 a) 671 b) 431 c) 221 d) 186 e) 365 f) 6627 g) 8153 h) 206 i) 222 2 8531

3 1655 4 469 5 a) 384 –143 = 241 b) 835 – 424 = 411 c) 987 – 388 = 299 More subtraction (p24) 1 a) 375 b) 484 c) 124 d) 1050 e) 7 f) 3677 g) 14 225 h) 5334 i) 3354 2 565 3 a) 20 000 b) 1st box: 4801 2nd box: 4643 3rd box: 2891 4th box: 783 c) 13 118 parts in total.

14 (15)

9 (20)

35 (30)

40 (50)

77 (70)

4 Heart is 4, flower is 2, star is 12 and wheel is 6 Further multiplication facts (p26)

5 Many possible answers an example is 200 and 116.

1 a) 39, 52, 65, 78 b) 56, 70, 84, 98 c) 90, 105, 120, 135 d) 48, 80, 112, 144 e) 68, 102, 136, 170

Multiplication facts (p25)

2 Student’s own work.

Multiplying by 10, 100 and 1000 (p27)

4 a) 1597 b) 219

10 12 14 16 18 20

12 15 18 21 24 27 30

12 16 20 24 28 32 36 40

10 15 20 25 30 35 40 45 50

12 18 24 30 36 42 48 54 60

14 21 28 35 42 49 56 63 70

16 24 32 40 48 56 64 72 80

18 27 36 45 54 63 72 81 90

1 a) 90 b) 120 c) 1.8 d) 230 e) 390 f) 4.8 g) 1230 h) 4560 i) 98.7 j) 12 340 k) 34 560 l) 67.7 2 a) 900 b) 1200 c) 0.18 d) 2300 e) 3900 f) 0.48 g) 12 300 h) 45 600 i) 9.87 j) 123 400 k) 345 600 l) 67.7 3 a) 9000 b) 12 000 c) 18 000 d) 23 000 e) 39 000 f) 48 000 g) 123 000 h) 456 000 i) 987 000 j) 1.234 k) 3.456 l) 6.77

10 20 30 40 50 60 70 80 90 100

Student Book 6

Nelson International Maths

Answers

Multiplication (p28)

Rules of divisibility (p32)

1 a) 474 b) 112 c) 252 d) 485 e) 504 f) 344 g) 522 h) 490

Number

125

More multiplication (p29)

1 a) 1035 b) 3002 c) 2080 d) 1406 e) 3588 f) 1494 g) 1682 h) 1768

300

208

2 6048 pages

225

3 810 newspapers

250

4 a) 1274 stickers b) 1372 stickers

510

2 a) 992 b) 3888 c) 1592 d) 2922 e) 798 f) 2631 g) 3944 h) 3272 i) 7404 j) 27 351 k) 43 810 l) 18 090

Dividing whole numbers (p30) 1 a) 144 b) 131 c) 244 d) 127 e) 55 f) 120 g) 121 h) 88 2 a) 121 r2 b) 63 r7 c) 179 r1 d) 69 r6 3 245ml Multiplication and division problems (p31) 1 16 boxes 2 $276.00 3 a) 196 marbles b) 147 marbles 4 15 rows 5 1150 counters 6 $84.00 7 a) $52.00 b) $130.00 c) 52 × 13 = $676.00 8 a) 9 pieces b) 4 cm 9 $102.00

Using the divisibility rules (p33) 1 a) 46, 64, 88, 90, 124, 136, 128, 456, 1234, 1546, 4654, 9800, 8754 b) 64, 88, 124, 136, 128, 456, 9800 2 a) 8514, 3640, 2468, 3740, 54 000, 63 000 b) 3640, 2468, 3740, 54 000, 63 000 c) 8514 and 2468 d) 3640, 3740, 54 000 and 63 000 3 a) 8400, 9360, 8000, 6612 b) 8400 and 8000 c) 8400, 9360, 5730, 8000 d) 8400 and 8000 e) All of them except for 8400 and 8000. 4 a) Any number ending in 5 or 0 b) any number ending in 0 c) any number where the last two digits can be divided by 4 d) any number that ends in 0, 4 or 8 e) any number that ends in 50 or 100 Units of measurement (p34) 1 a) Metres, b) kilometres c) litres d) kilograms e) kilometres f) metres g) kilograms h) millilitres i) millimetres j) metres

Student Book 6

Nelson International Maths

Answers

Choosing units (p35)

5 6 hours

1 a) mm b) cm c) m d) m

More converting units (p39)

2 a) 8m b) 3kg c) 4m d) 300g e) 250ml

3 a) g b) kg c) kg d) kg e) g f) g

Nick’s measurement

Metres and centimetres

Centimetres only

Millimetres only

15 m

1500

15 000

12.6 m

12 m and 60 cm

1260

12 600 mm

23.8 m

23 m and 80 cm

2380

23 800

1 a) 1cm b) 3.7cm c) 14.5cm d) 324.5cm

13.45 m

13 m and 45 cm

1345

13 450

2 a) 1000g b) 29 000g c) 480 000g d) 138 500 g

20.89 m

20 m and 89 cm

2089

20 890

3 a) 1l b) 5l c) 12.5l d) 0.5l

17.09 m

17 m and 9 cm

1709

17 090

4 2l

12.245 m

12 m and 24.5 cm

1224.5

12 245

5 450g

30.075 m

30 m and 7.5 cm

3007.5

30 075

4 a) e & f weighing scales; b bathroom scales; c & d hydraulic scales b) they are too big to fit on a normal set of scales. Changing from one unit to another (p36)

6 7.2km Working with units of length (p37) 1 a) 108.5 cm; 1085 mm; 1.085 m b) 110 cm; 1100 mm, 1.1 m c) 113.9 cm; 1139mm; 1.139 m d) 119.6 cm; 1196 mm; 1.196 m e) 120.2 cm; 1202 mm; 1.202 m 2 Students’ own work. Working with kilometres (p38) 1 a) 2km b) 5km c) 6.5km d) 12km 2 a) 463km b) 316km c) 216km d) 881km e) 1225 km f) 348km g) 667km h) 811km

2 a) 1900 g b) 3500 g c) 12 750 g d) 9050 g 3 a) 12 250 ml b) 5500 ml c) 12 250 ml d) 100 065 ml 4 Student’s own solutions. Allow some time for discussion and c omparison of methods. Other measuring systems (p40) 1 a) 16 km b) 160 km c) 65.5 km 2 a) 1.6 m b) 2 metres

1 c) 4

2ft

d) 4 feet e) 20 litres f) 450 litres g) 4 litres h) 90 pints 3 a) 2 b) 3 c) 17 d) 5 e) 4 f) 2 g) 4 h) 6

3 463 000m

4 Just over 5 gallons (You would have 24 litres and 24 ÷ 4.5 = 5.33)

4 a) 470km b) 425km c) 405km d) 490km

5 Student discussion in groups or as a class.

Student Book 6

Nelson International Maths Revising fractions (p41)

Answers

2 b)

2 4

4 8

1 2

1 a) A

3 4

2 3

1 2

7 8

1 2

5 6

3 8

11 12

3 a)

1 4

1 3

1 2

1 8

1 2

1 6

5 8

1 12

b) A

1 2

5 10

1 2

2 4

3 4

9 12

6 8

3 4

5 6

9 15

4 6

2 3

8 12

2 5

4 10

2 a) A

9 10

b) A

1 10

4 12

8 12

1 6

3 11

8 11

6 15

9 15 6 15

7 4

4 3

8 5

11 8

13 5

17 6

2 Unifix models or drawings of the following fractions a)

6 5

7 3

12 5

b) f)

c) 3

4 3 5

2 5

d) 2

11 4

1 5 8 3

Changing fractions from one type to another (p43) 1 a)

5 3

29 7

39 7

3 2

23 5

22 9

47 12

46 5

2 a)

g) 1 3 a) 1

2 1 5

i) 1

9 5

8 5

2 5

e) 2

h) 1

4 5

7 5

4 5

5 4

1 2 4

6 11

4 5

12 5

2 9

j) 2 2 5

>1 1 5

1 1 8

2 5

c) 2

> 2 f)

14 5

7 1 8

k) 1 3 5

5 12

1 1 6

l) 2

5 6

11 5 3 5

Equivalent fractions (p44) 1 a) 3 12

1 2

3 6

7 8

14 16

8 10

1 2 3 4 5 6 2 4 6 8 10 12

1 2 5 10

1 2 6 12

1 2 3 4 3 6 9 12

1 2 4 8

2 3

3 12

3 6

1 4

3 4

20 35

7 12

9 12

28 48

3 5

6 10

60 100

6 10

15 24

4 6

9 12

10 24

2 a)

6 12

3 12

4 12

2 12

8 12

10 12

2 12

4 12

8 12

1 6

1 4

3 4

1 2

5 6

1 2

y) 1

1 5 1 2

2 3

m) 2 1 3

6 9

1 a)

3 a)

2 6

1 2

Making equivalent fractions (p45)

Mixed numbers and improper fractions (p42) 1 a)

1 3

4 8

n) t)

1 3

1 4

1 3

3 4

4 5

3 10

7 20

o) 5 p) 4 7

19 20

1 2 2 3

1 3

x) 7

1 7

Comparing and ordering fractions (p46) 1 a)

3 2 5 5

6 8 12 12

10 12 40 40

5 6 8 8

8 9 12 12

24 25 40 40

15 16 20 20

8 7 12 12

2 a)

3 4 2 3 5 15 5 5

5 1 5 5 18 2 9 6

2 5 2 7 18 9 3 9

3 Jan

Student Book 6

Nelson International Maths Comparing and ordering mixed numbers (p47) 1

7 7 4 , , 7 4 2

12 10

5 5 5 5 , , , 24 12 4 3

Student discussion

10 8

Answers

Rounding decimals (p50) 1 a) 2 b) 18 c) 5 d) 0 e) 1 2 a) 0.4 b) 3.8 c) 6.6 d) 9.1 e) 0.5

1 3

b) 1 , 1

2 5

1 2

3 4

1 4

b) 2 , 2 , 3 , 3

1 2

Place value to thousandths (p48) 1 a) 79.366 b) 74.948 c) 39.559 d) 34.948 e) 46.748 f) 55.999 g) 48.247 h) 54.808 i) 56.007 2 a) 5 tenths b) 4 hundredths c) 9 tenths d) 7 thousandths e) 2 hundredths f) 1 tenth g) 4 hundredths h) 2 tenths Comparing and ordering decimals (p49) 1 a) 0.48 < 0.71 b) 0.06<0.31 c) 0.8>0.36 d) 0.4 > 0.04 e) 0.1 < 0.99 f) 1.2 > 0.9 2 a) 0.07 b) 0.27 c) 0.4 d) 0.39 e) 0.01 f) 0.2 3 a) 2.4, 0.42, 0.24 b) 3.3, 0.3, 0.03 c) 0.55, 0.5, 0.05 d) 9.0, 0.99, 0.9 e) 6.70, 0.76, 0.67 f) 8.08, 8.0, 0.8

3 a) 48.12 b) 59.97 c) 48.12, 49.27, 49.36, 50.01, 50.55, 51.17, 51.72, 53.08, 56.76, 59.97 d) 53.1, 60.0, 49.3, 48.1, 50.0 51.2, 56.8, 51.7, 50.6, 49.4 More rounding 1 a) $3.50 b) $12.40 c) $4.50 d) $9.20 e) $20.00 f) $50.10 2 Students own work. Discuss their answers as a class. 3 a) yes b) no c) no d) no e) no 4 Student discussion, but Maria did not put a decimal point before the 54 (i.e. she added 54 to 5.67 rather than adding $0.54) Sorting data (p52) 1 Shape

Frequency

Cube

Cylinder

Sphere

Pyramid

Total

Grouped data (p53) 1 a) 35 b) 5 c) 9 d) 22 to 24 e) 16, 17 or 18 marks

Student Book 6

Nelson International Maths More grouped data (p54)

Answers

1 Number Range

Frequency

1–99

100–199

200–299

300–399

400–499

500–599

600–699

700–799

800–899

900–999

2 1–199 3 400–499 and 800–899 4 Students’ own work. Graphs from tables (p55) 1

Line graphs (p56) 1 a) 50 b) 350 c) 500 d) 0 2 50 3 150 4 7:15 5 The children went out of the yard and into the school building. More line graphs (p57) 1 Every hour 2 a) 28°C b) 26°C c) 16°C d) 13.5°C 3 31°C at 1p.m. 4 13.5°C at 11p.m. 5 a) 12p.m. and 2p.m. b) 4p.m. c) 7p.m. d) 6p.m. 6 a) 27°C b) 18°C c) 15°C d) 13.75°C 7 Students’ own work.

Student Book 6

Nelson International Maths Unusual graphs (p58) Students’ own work. More unusual graphs (p59) 1 Burj Khalifa,,Taipei 101, Shanghai World Financial Centre, Petronas Towers, Sears Tower Chicago. 2 828m 3 319m

Answers

Comparing common fractions and decimals (p63) 1 a)

9 10

2 5

1 5

1 2

3 20

7 25

1 4

1 100

17 50

7 10

1 8

1 125

2 a) 0.5 b) 0.25 c) 0.75 d) 0.2 e) 0.4 f) 0.6 g) 0.8 h) 0.2 i) 0.125 j) 0.375 k) 0.625 l) 0.6

4 452m

3 a) 2.5 b) 3.25 c) 10.75 d) 12.4 e) 1.2 f) 3.25 g) 4.3 h) 2.8 i) 4.375 j) 1.2 k) 1.16 l) 5.05

5 509m

Repeating decimals (p64)

6 Students’ own ideas.

1 3, 6 and 9

Multiplying and dividing decimals by 10 and 100 (p60)

2 Students’ own work.

Student investigation and discussion. More operations with 10 and 100 (p61) 1 a) 3.45 b) 34.5 c) 1234.5 d) 12 345 e) 123.4 f) 1234 g) 15.6 h) 156 2 a) 14.5 b) 342.34 c) 23.45 d) 3412.4 e) 34 270 f) 199 g) 340 h) 144.5 i) 1290 j) 2.4 k) 24 l) 1910 3 a) 2.34 b) 23.45 c) 0.12 d) 0.48 e) 4.88 f) 12.78 g) 0.36 h) 36.75 i) 42.73 4 a) $455.00 b) $500.50 5 $466 6 $125.00 7 $1.99 each with 9c left over 8 $135 9 Student’s own work. Extending multiplication and division facts to decimals (p62) Students to do the answers mentally and then to use a calculator to check their answers.

3 a) 0.3 with a dot over the 3 b) 0.7 with a dot over the 7 c) 0.9 with a dot over the 9 d) 0.31 with a dot over the 3 and over the 1 e) 0.2 with a dot over the 2 f) 0.451 with dots over the 4, and the 1. g) 1.245 with dots over the 2, and the 5 h) 3.27 with dots over the 2 and the 7 i) 9.74 with dots over the 7 and the 4. 4 a) 0.16 with a dot over the 6 b) 0.83 with a dot over the 3 c) 0.142857 with dots over the 1, and 7 d) 0.285714 with dots over the 2, and 4 e) 0.428571 with dots over the 4, 2, 8, 5, 7 and 1 f) 0.571428with dots over the 5, and 8g) 0.714285 with dots over the 7, and 5 h) 0.857142 with dots over the 8, and 2 i) 0.1 with a dot over the 1 j) 0.4 with a dot over the 4 k) 0.09 with dots over the 0 and the 9 l) 0.27 with dots over the 2 and the 7 m) 0.583 with a dot over the 3 n) 0.26 with a dot over the 6 o) 0.6 with a dot over the 6.

Student Book 6

Nelson International Maths Adding and subtracting decimals (p65) 1

a) 0.7; 0.3 b) 0.8; 0.2 c) 55; 10; 5.5 d) 100; 0.66; 0.66 e) 27; 2.7; 0.27

0.4 + 0.6; 0.55 + 0.45; 0.01 + 0.99; 0.65 + 0.35; 0.75 + 0.25; 0.5 + 0.5; 0.83 + 0.17

a) 0.55 b) 1 c) 0.72 d) 1 – 0.81 = 0.19 e) 0.95 f) 0.01

Answers

Remind the students to round answers up the nearest whole cent. Sponge $1.05; Towel $0.83; Soap $0.90 (for 3); Toothpaste $4.47 (for 6); washbag $2.93; Brush $1.18; Shampoo $1.00 each or $1.75 for 2; Toothbrush $0.75 each or $2.15 for 3

Mixed decimal problems (p69) 1

a) 37.10, 38.06, 38.24, 38.58, 38.66 b) 1.56 seconds c) Russia, they ran it in the shortest time d) 4.7 seconds faster e) Canada 19.33; Trinidad and Tobago 19.03; Japan 19.12; Jamaica 18.55; Germany 19.29 f) Students can do this task by dividing the times by 4, however, they are more likely to discuss which runners in a relay are likely to run fastest. Allow them to use a calculator to do this task.

Calculating with decimals (p67)

All of them except for the rolls of tape.

1 $7.65

Students own work but answer is 5.43 × 6

2 3.7m

Revising 2-D shapes (p70)

3 422.56g

1 a) Pentagon b) Hexagon c) Octagon d) Triangle e) Pentagon f) Hexagon g) Decagon h) Quadrilateral

4 2.1 + 7.9 OR 2.9 + 7.1 More addition and subtraction of decimals (p66) 1

a) 5.6 b) 3.4 c) 4.3 d) 5.7 e) 7.2 f) 3.9

a) 35.77 b) 134.15 c) 502.01 d) 316.65 e) 3.54 f) 5.03

a) $4.12 b) $9.18 c) $25.28 d) $12.64 e) $92.99 f) $71.51

4 26.9°C 5 334.098 6 15.544l 7 0.14 seconds 8 $45.10, $25.35 9 a) $10.15 b) $20.15

Triangles and their properties (p71) 1 a) Isosceles b) Equilateral c) Scalene 2 Students’ own work. Properties of quadrilaterals (p72)

10 a) 5.432kg b) 25.176kg c) 20.616kg

1 Rectangle, Parallelogram, Square, Rhombus.

Doubling and halving decimal amounts (p68)

2 Rectangle, Parallelogram, Trapezium, Rhombus, Square

a) Crayons $5.98; pencils $0.90; Books $2.54; erasers $1.30; Pens $2.70 b) $254.00 c) $13.00 + $9.00 = $22.00

3 Square, Rhombus 4 Square, Rectangle 11

Student Book 6

Nelson International Maths 5 There are two acute angles and two obtuse angles. An obtuse and an acute angle add to make 180° and all four angles add to make 360°. 6 The two longer sides are the same length and the two shorter sides are the same length. Naming quadrilaterals (p73) 1 a) Parallelogram, b) Trapezium c) Rectangle d) Rhombus e) Quadrilateral f) Trapezium g) Parallelogram h) Trapezium i) Rhombus j) Parallelogram k) Square l) Quadrilateral m) Parallelogram n) Kite o) Kite p) Quadrilateral q) Parallelogram r) Rectangle s) Square. 2 Students’ measurements may vary slightly depending on how accurately they can measure. Allow them to check each other’s work. 3 Students can work together to complete this task based on their own measurements. Special parallelograms (p74) 1 Students’ own diagrams. 2 Students’ own diagrams. 3 Students to use their own diagram to complete the task. More about quadrilaterals (p75) Students’ own work. Identifying and drawing shapes (p76) 1 a) Square b) Trapezium c) Rhombus d) Quadrilateral

Answers

3 a) and b) square – all four sides equal in length, all interior angles are right angles, opposite sides are parallel; rectangle – opposite sides are equal in length, all interior angles are right angles; opposite sides are parallel; trapezium – one pair of opposite sides are parallel and (in this example) two angles are right-angled; kite – two pairs of adjacent sides are equal in length, diagonals intersect at right angles, long diagonal bisects the shorter diagonal (cuts it in half) Perimeter (p77) 1 a) 24cm b) 12cm c) 24cm d) 52m e) 41cm f) 44cm g) 16cm h) 37.4m i) 11.8m More perimeter (p78) 1 a) 61m b) 80mm c) 100mm d) 61cm e) 32m f) 24m g) 49m 2 a) 26cm b) 62.4cm c) 74.5mm d) 26 m e) 520mm 3 Side lengths are 10.75 cm, 10.75 cm, 6.75cm and 6.75cm 4 4.7 m More about multiples (p79) 1 a) 4, 6, 8, 10, 12, 14 b) 6, 9, 12, 15, 18, 21 c) 18, 27, 36, 45, 54, 63 d) 20, 30, 40, 50, 60, 70 e) 12, 18, 24, 30, 36, 42 f) 8, 12, 16, 20, 24, 28 g) 24, 36, 48, 50, 60, 72 h) 10, 15, 20, 25, 30, 35 i) 14, 21, 28, 35, 42, 49 j) 16, 24, 32, 40, 48, 56 2 a) 20, 24, 28, 32, 36, 40 and 44 b) 42, 48, 54, 60 and 66 c) 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000 3 a) 6, 12, 18 b) 10, 20, 30 c) 24, 48, 72

2 Students’ own work.

Student Book 6

Nelson International Maths 4 a) 20 b) 24 c) 21 d) 30 e) 18 f) 60 g) 90 h) 24 i) 60

Answers

Prime factors (p82)

6 28 adds to 10 and 56 adds to 11.

1 a) 10=2×5 b) 30= 2×5×3 c) 16=2×2×2×2 d) 24=2×2×2×3 e) 48=2×2×2×2×3 f) 60=2×2×3×5 g) 64=2×2×2×2×2×2 h) 33=3×11

Factors (p80)

Multiplication by multiples of 10 (p83)

1 a) 1, 2, 4, 8, 16 b) 1, 2, 3, 5, 6, 10, 15, 30 c) 1, 2, 4, 7, 14, 28 d) 1, 2, 3, 4, 6, 9, 12, 18, 36 e) 1, 2, 4, 5, 8, 10, 20, 40

1 a) 360 b) 7400 c) 1000 d) 9000 e)19 000 f) 10 000 g) 3000 h) 60 000 i) 50 000

5 36

2 a) 1 and 8, 2 and 4 b) 1 and 15, 3 and 5 c) 1 and 22, 2 and 11 d) 1 and 44, 2 and 22 4 and 11 e) 1 and 30, 2 and 15, 3 and 10, 5 and 6 f) 1 and 90, 2 and 45, 3 and 30, 5 and 18, 6 and 15, 9 and 10 g) 1 and 56, 2 and 28, 4 and 14, 7 and 8 h) 1 and 27, 3 and 9 i) 1 and 110, 2 and 55, 5 and 22, 10 and 11 j) 1 and 200, 2 and 100, 4 and 50, 5 and 40, 8 and 25, 10 and 20 3 a) 2 b) 4 c) 6 d) 11 e) 8 f) 8 g) 10 h) 3 i) 12 4 1 5 2 6 The number itself Prime numbers (p81) 1 a) 9, 3×3 b) 1 only has one factor, so is not a prime number c) 30, 3×10, 6×5 or 2 × 15 d) 48, 4×12 or 6×8 or 2×24 e) 21, 3×7 f) 75, 3×25, 5×15 g) 95, 19×5 h) 18, 2×9, 3×6 i) 99, 11×9 , 3 × 33 2 2nd, 3rd, 5th, 7th, 11th, 13th, 17th, 19th, 23rd plus 29th and 31st if appropriate. 3 Solutions from: 10=3+7, 16=3+11, 24=19+5, 24=7+17, 24=11+13, 30=23+7, 30=19+11, 30=17+13, 36 = 3 + 33, 36 = 5 + 31, 36 = 7 + 29, 36 = 13 + 23, 36 = 17 + 19

2 a) 1000 b) 32 c) 1000 d) 96 e) 100 f) 100 3 13

123

150

459

550

990

×10

130

260

490

1230

1500

4590

5500

9900

×100

1300

2600

4900

12300

15 000

45 900

55 000

99 000

×1000

13000

26000

49000

123000

150 000

459 000

550 000

990 000

4 a) 60 b) 80 c) 100 d) 160 e) 240 f) 320 g) 240 h) 360 i) 480 j) 400 k) 600 l) 800 Multiplying pairs of multiples of 10 and 100 (p84) 5 × 8 = 40

50 × 80 = 4000

50 × 800 = 40 000

6 × 7 = 42

60 × 70 = 4200

60 × 700 = 42 000

7 × 5 = 35

70 × 50 = 3500

700 × 50 = 35 000

8 × 9 = 72

80 × 90 = 7200

800 × 90 = 72 000

9 × 5 = 45

90 × 50 = 4500

900 × 50 = 45 000

6 × 3 = 18

60 × 30 = 1800

60 × 300 = 18 000

9 × 7 = 63

90 × 70 = 6300

900 × 70 = 63 000

9 × 10 = 90

90 × 10 = 9000

90 × 100 = 90 000

Student Book 6

Nelson International Maths 2 a) 1500 b) 2400 c) 2700 d) 800 e) 2000 f) 3200 g) 1800 h) 5400 i) 8100 3 a) 8 b) 600 c) 700 d) 6 e) 60 f) 70 g) 4 h) 30 i) 100 4 1200 km

Answers

4 ¸

100

150

200

500

100

1.5 150

200

500

100

2500

5 $2400 Multiplying by near multiples of 10 (p85) 1 a) 1230 b) 990 c) 2560 d) 4410 e) 4150 f) 4350 g) 91 200 h) 79 200 i) 702 000 2 a) 2380 b) 30 320 c) 40 800 d) 6020 e) 12 800 f) 399 200 3 a) 780 b) 4880 c) 4160 d) 7800 e) 37 800 f) 63 200 g) 80 800 h) 185 400 i) 180 900 j) 64 320 k) 66 220 l) 180 450 Division by multiples of 10 (p86) 1 a) 9 b) 9 c) 9 d) 2500 e) 6600 f) 9.6 2 a) 100 b) 100 c) 320 000 d) 10 3 a) 400 b) 6 c) 110 d) 50 e) 11 f) 21

250 10

1.5

15 50

4 100

1.5

0.5

2 5 a) 20 b) 50 c) 90 d) 800 e) 21f 34 g) 45 r6 h) 98 r 7 i) 1240 j) 1324 r 5 k) 907 r 6 l 45 r 0.69 6 a) 120 b) 95 c) 123.45 d) 0.09 Measuring and drawing angles (p88) 1 Students’ own discussion work. 2 Students’ own work.

4 a) 41r2 b) 310 r4 c) 45 r32 d) 70r7 e) 18 r32 f) 26r4

3 a) 40° b) 100° c) 32° d) 64° e) 102° f) 90°

Mixed calculations (p87)

Calculating the size of angles (p89)

a) × 10 b) ÷ 10 c) × 10 d) × 1000 e) ÷ 100 f) ÷ 100 g) × 1000 h) × 100 i) ÷ 10

a) 63 × 8 b) 1 × 33 c) × 100; 85 × 1 d) 2 e) 80 × 60 f) 3

a > b) > c) < d) >

1 a) 65o b) 108o c) 135o Missing angles (p90) 1 57o 2 29o 3 65o 4 35o 5 x = 94, y = 86 6 x = 90, y = 90 7 x = 30, y = 150 14

Student Book 6

Nelson International Maths

Answers

8 x = 60, y = 120

Percentages, fractions and decimals (p95)

9 x = 50

1 a)

Angles in a triangle (p91) 1, 2 & 3

1 10

7 20

13 20

1 5

23 25

2 5

1 2

3 4

4 5

1 4

9 50

3 20

3 50

11 50

1 20

Triangle

Size of angle a

Size of angle b

Size of angle c

a+b+ c

More conversions (p96)

27°

78°

75°

180°

55°

53°

72°

180°

1 a) 30% b) 90% c) 40% d) 25% e) 35% f) 50% g) 75% h) 64% i) 35% j) 90%

40°

50°

90°

180°

37°

33°

110°

180°

60°

180°

44°

34°

102°

180°

4 The sum of the angles in a triangle is always 180°. Calculating angles in triangles (p192) 1 a) × = 55o b) × = 55o c) × = 80o d) 137o 2 a) 50o b) 45o c) 74o 3 a) a=30o b=35o c=105o b) Students’ own work. Angles of rotation (p93) 1 a) 90o clockwise b) 90o anti-clockwise c) 90o anti-clockwise d) 90o clockwise Percentages (p94) 1 a) 50% b) 36% c) 27% d) 58% e) 20% f) 18% g) 37% h) 3% i) 96% j) 75% k) 0% l) 75% 2 a) 50% b) 64% c) 73% d) 42% e) 80% f) 82% g) 63% h) 97% i) 4% k) 25% k) 100% l) 25%

2 a) 0.27 b) 0.74 c) 0.09 d) 0.96 e) 0.17 f) 0.06 g) 0.12 h) 0.45 i) 0.04 j) 1 3 a) 75% b) 83% c) 8% d) 49% e) 50% f) 25% g) 80% h) 60% i) 15% j) 1% 4 Fraction

Decimal

Percentage

1 4

0.25

25%

1 2

0.5

50%

3 4

0.75

75%

1 5

0.2

20%

3 5

0.6

60%

4 5

0.8

80%

3 8

0.375

37.5%

7 20

0.35

35%

5 a) 73%, 74/100, 0.75 b) c) 9%,

4 , 5

1 , 3

0.4, 50/100

90/100 d) 25%, 0.3,

3 4

e) 0.099,

99/100, 100% 6 a) 65% b) 47.5% c) 52.5% d) 80% e) 95% .

f) 76. 6 % 15

Student Book 6

Nelson International Maths

Answers

Finding percentages of amounts (p97)

Working with money (p100)

1 a) 5 b) 12 c) 36 d) 13.5 e) 50 f) 300 g) 15 h) 108 i) 7

1 a) $34.00 b) $8.00 c) $35 d) $1.00 e) $200.00 f) $3000.00

2 a) 10 girls b) 12 cows c) 20 children d) 12 bottles e) 10 cars f) 14 sweets

2 a) $5.98 b) $17.98 c) $3.75 d) $20.70 e) $7.56

3 a) $1.25 b) 1kg c) 0.75l or 75 cl or 750ml d) 9 e) $0.08 f) 405g g) 18 hours h) 9cm i) 90m j) 18ml

4 a) $12 000 b) $13 680

4 Save the Children – $501.20, Working for clean water – $801.92, Earthquake relief – $400.96, Disability aid $300.72. More percentage amounts (p98) 1 a) 100mm b) 120mm c) 50mm d) 150mm e) 150mm 2 a) i) 50% ii) 20% iii) 30% b) i) 25% ii) 25 % iii) 50% c) i) 10% ii) 60% iii) 30% d) i) 96.6% (with a dot over the 6) ii) 3.3% (with a dot over the 3) iii) 0% e) i) 40% ii) 40% iii) 20% 3 a) Age in years

Girls

Boys

3 a) $55.97b) $44.03 5 $0.39 6 $43.60 7 $70 Checking calculator addition (p101) 1 a) 56.94 b) 650.84 c) 210.04 d) 194.94 e) 50.94 f) 75.89 g) 303.97 h) 1154.20 2 Students’ own work. More money calculations (p102) 1 a) Table 1 – 6.37, Table 2 – 15.18, Table 3 – 21.23, Table 4 – 19.72 b) Table 1 – 0.64 service 7.01 total, Table 2 – 1.52 service, 16.70 total, Table 3 – 2.12 service, 23.35 total , Table 4 – 1.97 service, 21.69 total. 2 Students’ own work. 3 a) Fish and chips

2.09

Sandwich and fries

2.52

Fried chicken

2.09

Noodles and Vegetables

1.35

Just Fries

0.53

Dealing with discounts (p99)

Salad

1.05

1 a) $53.10 b) $30.00 c) $191.25 d) $116.10 e) $24.40 f) $170.05 g) $50.00

Ice Cream

2.09

Fruit Salad

1.58

2 a) $50.15 b) $28.00 c) $180.00 d) $109.65 e) $22.88 f) $161.10 g) $45.00

Fresh Juice

1.35

Cola

1.46

Milkshake

2.89

b) 219 girls c) 224 boys

Student Book 6

Nelson International Maths b) c) and d) Students’ own work.

2 a) likely

7 8

Answers

b) likely

4 Students’ own work.

d) unlikely

Paying by mass (p104)

most yellow

1 4

5 8

c) unlikely

3 8

e) spinner (a) because it has

1 a) $7.00 b) $4.00 c) $19.00 d) $10.00 e) $7.00 f) $31.00 g) $28.00 h) $38.00

3 a) even b) unlikely c) likely d) even e) even f) certain

2 a) $3.50 b) $1.75 c) $10.50 d) $5.25 e) $3.50 f) $21.00g) $21.00

Revising co-ordinates (p109) 1 a) N b) P c) A d) O e) F g) J h) H i) G j) E k) L l) K m) I n) M o) D p) C

How much does it weigh? (p105) 1 a) 24.9kg b) 20.6kg c) 21.8kg d) 17.1kg e) 22.2kg f) 21.5kg g) 33.6kg h) 25.4kg i) 27.5kg j) 21.4kg k) 27.9kg l) 22.3kg

Extending the grid (p110) 1 A(0,4) B(1,2) C(3,3) D(2,1) E(4,0) F(2,–1) G(3,–3) H(1,–2) I(0,–4) J(–1,–2) K(–3,–3) L(–2,–1) M(–4,0) N(–2,1) P(–3,3) Q(–1,2)

2 a) Sets b, c, d, e, f, j, l b) Sets a, g, h, i, k, c) d, b, j

Coordinates and quadrants (p111) Describing probability (p106) 1 a) Students’ own work. b) Students’ own work. c) Impossible d) Students’ own work. e) Even chance f) Certain g) Certain h) Students’ own work. i) Students’ own work. j) Certain. 2 Students’ own work.

1 (–3,4) and (–4,1) 2 Negative 3 Positive 4 The x-co-ordinates are always negative and the y-co-ordinates are always positive. Reflections (p112)

What is the chance? (p107)

1 a) even b) unlikely c) unlikely 2 a) even b) even c) impossible

D & J, D & E, D & I, E & J, E & I, E & D, C & K, F & H, A & B, L & M, A & M, B & L

Translations (p113)

3 a) likely b) unlikely c) unlikely

1 a) D to E b) D to F c) A to C d) A to B

4 a) even b) impossible c) certain 5 Students’ own work.

2 a) (3, –4); (5, –4); (3, –5); (5, –5) b) (1, –7); (3, –7); (1, –8); (3, –8)

More probability (p108)

Find the matching shapes (p114)

1 a) Even chance

1 2

b) likely

2 3

c) unlikely

d) certain 1 e) Spinner c as there is less red on that one

1 4

a) F b) T c) T d) F e) T f) T g) F

Students’ own work

Student Book 6

Nelson International Maths Revising mental strategies for division (p 115) 1 a) 45, 5, 9, 5.625, 4.5 b) 8, 8, 8, 0.8, 7.2 c) 42, 42, 6, 0.6, 4.2 d) 8, 8, 8, 0.8, 6.4 e) 54, 54, 6, 0.9, 5.4 2 a) < b) < c) > d) < e) < f) >g) > h) < i) = 3 a) ÷ 10, ÷ 100 , ÷ 100 b) ÷ 100, ÷10, ÷ 100 c) ÷ 10, ÷ 10, ÷ 10 d) ÷ 100 , ÷ 100, ÷ 100 4 a) 0.6 b) 0.6 c) 0.8 d) 0.6 e) 0.6 f) 0.8 g) 0.7 h) 0.5 5 a) $17.40 b) $12.06 c) $9.18 d) $50.25 e) $17.95 f) $11.74 g) $9.93 h) $49.95 Division – remainders with fractions (p116)

Answers

5 93 6 66 7 a) 42 b) 48 Rounding to estimate answers (p119) 1 a) estimate 900, actual 1012 b) estimate 2100 actual 2088 c) Estimate 750 actual 810 d) estimate 2400 actual 2592 e) Estimate 4800 Actual 5250 f) Estimate 8000 Actual 7296 g) Estimate 56 000 Actual 54 108 h) Estimate 18 000 Actual 19 712 2 Estimated answers a) 160 b) 90 c) 220 d) 60 e) 475 f) 215 g) 85 3 Estimate 120 Actual 118 4 Estimate 18 Actual 19

1 a) 21 b) 21

3 4

c) 16

1 6

2 a) 10.6 b) 20.25 c) 6.3 3

1 1 , 4

1 1 , 2

1 2 , 3

2 14 5

Division by repeated subtraction (p117) 1 a) 49 b) 204 c) 85 d) 48 e) 59 f) 17 g) 243 h) 47 i) 57 2 a) 51 r 5 b) 101 r 4 c) 52 r 3 d) 46 r 7 e) 164 r 3 f) 99 r 5 3 a) 35 b) 61 c) 7 Division – rounding the remainder (p118) 1 a) 7 b) 9 c) 29 d) 101 e) 188 f) 61 2 39 3 43 4 58

5 Estimate 20 000 Actual 20 176 Multiplying larger numbers (p121) 1 a) 9872 b) 16 040 c) 8196 d) 36 891 e) 20 516 f) 64 800 g) 18 870 h) 31 215 i) 72 008 2 a) 33 072 b) 23 090 c) 56 196 d) 46 971 e) 32 516 f) 24 800 g) 20 790 h) 36 215 i) 35 368 3 Estimated answers a) 4000 b) 10 000 c) 6000 d) 12 000 e) 12 000 f) 16 000 g) 27 000 h) 18 000 i) 28 000 j) 15 000 k) 24 000 l) 36 000 m) 12 000 n) 48 000 o) 40 000 p) 24 000 q) 42 000 r) 54 000 s) 24 000 t) 56 000 u) 54 000 Actual answers a) 5824 b) 7835 c) 5961 d) 14 736 e) 10 360 f) 16 776 g) 28 503 h) 18 588 i) 24 892 j) 14 628 k) 25 128 l) 36 684 m) 11 086 n) 45 432 o) 40 032 p) 24 344 q) 41 988 r) 55 791 s) 24 294 t) 56 861 u) 54 522

Student Book 6

Nelson International Maths

Answers

Multiplication by two-digit numbers (p121)

Working with ratios (p124)

1 a) 5564 b) 3553 c) 4140 d) 8 664 e) 12 972 f) 16 443 g) 16 200 h) 19 548 i) 18 810

2 a) 5382 b) 29 445 c) 13 464 d) 36 720 e) 39 044 f) 24 852 g) 18 468 h) 74 382 i) 22 834 j) 33 354 k) 31 913 l) 24 721 m) 30 597 n) 29 502 o) 75 255 Multiplication and division problems (p122) 1 $4500 2 a) $5220 b) $9324 c) $4104 3 14 850m 4 a) 9810g b) $408.75 5 134 ml 6 71 pages per hour

Actual length

Magnified length

Ladybird

1.2 cm

6 cm

Caterpillar

1.4 cm

7 cm

3 cm

15 cm

Ant

0.3 cm

1.5 cm

Snail

1.1 cm

5.5 cm

5 cm

25 cm

Spider

Beetle 2 0.6 cm 3 $2.61 (261 cents) 4 270 grams 5 8 cm

7 $7.64

6 15 peaches

8 32 tables (round up)

Proportion (p125) 1 a)

9 9 buses (round up) Ratio (p123)

1 6 to 3 2 4 to 4 3 8 to 2 4 3 to 2 5 1 to 1

0.80

1.60

2.40

3.20

4.00

6 2 to 5

4.00

7 6 to 3

8.00

12.00

16.00

20.00

Student Book 6

Nelson International Maths

Using the properties of multiplication (p 129)

c) kg

5.88

11.76

17.64

23.52

29.40

1 a) 0 b) 432 c) 1 d) anything e) 24 f) 25 g) 0.5 h) 3 i) 8 2 Various answers are possible. Examples include: a) 100 × 27 b) 14 × 160 c) 105 × 95 d) 3000 × 28 e) 3 × 3.6 f) 189 × 312 3 Students to check using calculator.

2 a) $1.50 b) $2.50 c) $2.25

4 a) 30 b) 97 c) 0.6 d) 50

3 a) $12.75 b) $25.50 c) $6.38

5 a) 0 b) 108 c) 300 d) 9600 e) 12 900 f) 6300 g) 0 h) 17 000

Ratio and proportion problems (p126) 1 a) 2

2 3

Answers

1 4

6 Students to discuss. The statements are all true except for the second one (top right).

3 4

Combining multiplication and addition (p 130)

7 20

3 $18.00

1 a) 594 b) 1188 c) 2450 d) 1032 e) 2232 f) 7474 g) 4794 h) 748 i) 3150 j) 187 k) 145 l) 2060

4 a) 1 to 20 b) 0.5 litres c) 125ml 5 27

2 a) 1100 b) 220 c) 28 d) 380 e) 371 f) 320

6 a) 140km b) 280km c) 420km d) 46.7km 7 Miles

Kilometres

1.6

3.2

4.8

6.4

9.6

11.2

Making sense of bar graphs (p131) 1 a) 10 b) 6 c) 3 d) 1 e) 68 f) there is no 0 on a dice

This is a student investigation. Allow some time in class for them to share their ideas.

2 a) 57 b) between 171cm and 180cm c) No, we are not told the exact height of the trees only the ranges d) Because there are at least 8 in each class interval.

Properties of multiplication (p128)

Making sense of line graphs (p132)

Investigating multiplication (p127)

Students’ own diagrams.

a) T b) F c) T d) T e) T f) T g) T h) F i) F j) T

Students to discuss. Share their tables with the class if possible.

1 a) Temperature figures for Town A and Town B b) Months c) 1 square is 5oC d) December Town A and June Town B e) November to March in Town A – May, June and July in Town B f) June, July and August Town A – January and February

Student Book 6

Nelson International Maths Town B g) Town B h) Town A

Number machines (p138) 1 a) 21, 103, 111, 215 b) 25, 18, 7, 4.3 c) 689, 104, 70, 81 d) 0.9, 2.7, 10.7, 342.1 ea) 0.12, 0.64, 1.26, 1.94 fb) 0.012, 0.9, 0.1, 0.045

2 a) 22°C b) 11°C c) 16°C d) 11°C e) 5°C Working with data (p133)

More number machines (p139)

1 a) 133cm b) 4 c) 7 d) 2 e) 19 f) 46

1 i) (a) 8 (b) 10 (c) 60 (d) 15 ii) (a) 186 (b) 90 (c) 32 (d) 36 iii) (a) 16 (b) 26 (c) 70 (d) 77 iv) (a) 33 (b) 20 (c) 102 (d) 106 v) (a) 10 (b) 15 (c) 24 (d) 1000 vi) (a) 2 (b) 46 (c) 124 (d) 1262

2 Students’ own work. The median (p134) 1 a) 132 b) 46 c) 11 2 a) Median scores: Alice 2, Katie 2, Sam 3, Jonas 3, Beauty 3, Petros 4 b) 10

The mean (p135) 1 a) 130.86 cm b) 11.1 years 1 3

b) 12.1667 c) 22 d) 143.6

e) 130.5 f) 36.4 3 There is no middle number. So a median could be the average of the middle two numbers 4 and 5 which is 4.5 4 The mean number can be a decimal because it doesn’t have to represent an actual whole number of brothers and sisters that anyone has. It is only the total number of brothers and sisters of the people Joe asked divided by the number of people Joe asked. Shape patterns (p136)

D 4, 8, 12 C 3, 6, 9 E 3, 5, 7 F 3, 5, 7

1 a) 12 8 34 40 42 48 26 b) Even numbers always end with an even digit c) If you add two even numbers your answer will be even. If you add two odd numbers your answer will be even. If you add three odd numbers your answer will be odd. If you multiply only even numbers your answer will be even. If you multiply two odd numbers, your answer will be odd. 2 Nick, Aisha, Nomi 3 a) 9,11 b) 121, 120 c) 208, 210 d) 19, 23 e) 75, 85 f) 750, g) 160, 320 h) 100, 50 Patterns of odd and even numbers (p141) 1 EE 2 E

1 Drawings 2 A 3, 6, 9 5, 9, 13

2 i) (a) 7 (b) 12 (c) 18 (d) 28 ii) (a) 25 (b) 53 (c) 195 (d) 201 Number patterns (p140)

3 a) 60cm b) 25oC c) 13m d) 10 l e) 41kg

2 a) 6

Answers

3 OE 4 EO

3 Students’ own work.

5 OE

Finding the rules for patterns (p137)

6 EO

See workbook answers. 21

Student Book 6

Nelson International Maths

Answers

7 Student to discuss and formulate their own explanation.

8 a) 240 secs b) 390 secs c) 269 secs d) 184 secs

Number sequences (p142)

Timetables (p145)

1 a) 41, 43, 45 b) 2, 0, –2 c)

7 9 11 , , 8 8 8

d) 11.5, 11.25, 11 e) 5.5, 6.5, 7.5 f) 3,9, 4,2, 4.5 g) 32, 64, 128 1 2

1 4

h) 12 , 6 , 3 2 a) 48, 24 … 1

1 8 1 2

1 a) 16:19 b) 16:33 2 a) 14 mins b) 14 mins 3 17:07 4 14:55

b) 4.5, 45, 450

c) 1.2 … 4.8, 6 d) 2 … 5, 9, 17 e) 1250 … 2

5 a) 1 hr 45 mins b) 10:28 c) 09:49 Revising area (p146) 1 a) 12 cm2 b) 44 cm2 c) 4 m2 d) 80 m2 e) 1200 m2 f) 1008 m2 g) 6050 mm2 h) 100 000 m2

3 a) This is the pattern of square numbers (1 × 1; 2 × 2 etc) b) This pattern is the squares of multiples of 10 (10 × 10; 20 × 20; 30 × 30, etc

2 a) 10 cm b) 100 mm c) 25 m d) 20 cm

Calculating periods of time (p143)

Area of combined shapes (p147)

1 a) 2 hours and 5 minutes b) 2 hours and 20 minutes c) 2 hours and 15 minutes d) 5 hours and 15 minutes

1 a) 8 cm2 b) 13.5 cm2 c) 15 cm2

2 a) 11.37 a.m. b) 3.29 p.m. c) 23:12 More calculations involving time (p144) 1 a) 3 hrs 15 mins b) 3 hrs 40 mins c) 3 hrs 25 mins d) 19 hrs 5 mins 2 a) 19 hrs b) 14 ¼ hrs 3 a) 5 p.m., 17:00 b) 12.10 p.m., 12:10 c) 9 p.m., 21:00 d) 9.35 p.m., 21:35 4 2.05 p.m. 5 5 hrs and 19 minutes 6 a) 149 mins b) 225 mins c) 555 mins d) 365 mins 7 a) 1 hr 30 mins b) 1 hr 25 mins c) 4 hrs 52 mins d) 6 hrs 15 mins

Estimating areas using a grid (p148) a) Approximately 18 cm2 b) Approximately 13 cm2 c) Approximately 19 cm2 d) Approximately 17 cm2 e) Approximately 9 cm2 f) Approximately 18 cm2 More estimating area (p149) 1 Students own estimates. These will vary, but allow some time for class discussion for students to say how they estimated the area of these irregular shapes. 2 a) 10 b) Pakistan c) 5 3 a) About 66 squares b) About 74 squares 4 Afghanistan is about 3 blocks on the map; 650 000 km2 ÷ 3 = 216 667 km2, so one block on the map is an area of about that. 22

Student Book 6

Nelson International Maths

Answers

Area problems (p150)

4 a) 27 b) 90 c) 97 d) 58 e) 55 f) 64

1 Discussion work.

5 a) 7 b) 9 c) 10 d) 5 e) 4 f) 6

2 a) 500 cm2 b) Area of the floor 20 m2 or 200 000 cm2, 80 tiles are needed c) Area of garden 600 m2, area covered by lawn 489 m2. d) Yes he can.

6 a) yes b) no c) no d) yes e) yes f) no

Revise division with remainders (P151) 1 a) 37 r 1 b) 28 r 1 c) 54 r 1 d) 64 r 1 e) 174 r 1 f) 216 r 1 g) 472 r 1 h) 490 r 1 2 a) 12 f) 7

1 2

l) 18

1 2

b) 15

g) 6

1 2

1 3

c) 4

h) 6

1 4

3 7

d) 7

i) 13

4 7

1 2

e) 4

j) 10

1 9

4 9

k) 16

7 a) 41.75 b) 31.4 c) 57.1 d) 51.5 e) 140.8 f) 28.57 8 Studentsâ&#x20AC;&#x2122; own work. Long division (p152) 1 a) 65 b) 42 c) 39 d) 25 e) 16 f) 12 2 24 kg

1 2

3 21 trees

3 4

3 a) 23.4 b) 43.2 c) 98.1 d) 1.29 e) 3.12 f) 2.98

Student Book 6

Nelson International Maths

Answers

More division (p153) 1 Note that this is one possible way of estimating, the students may use different numbers. Divide

Round numbers to nearest 10 and/or 100

Estimated answer

Calculated answer

Difference between estimated and calculated answer

266 ¸ 19

270 ÷ 20

13.5

0.5

792 ¸ 22

800 ÷ 20

510 ¸ 15

510 ÷ 20

522 ¸ 18

520 ÷ 20

868 ¸ 28

870 ÷ 30

960 ¸ 32

1000 ÷ 30

33.3

3.3

2 $19.00

Division problems (p155)

3 32 desks

1 a) 3.23 b) 0.49 c) 17.4 d) 84.6

4 5040

2 a) 2.47 b) 8 c) 8

5 16 928

3 From left to right: 42, 2.75, 0.45(recurring), 1.42

6 32 7 17 8 a) 15 b) 23 c) 31 Dividing decimals (p154)

4 Students’ own problems. 5 a) 8.33 m b) 0.833 m c) 1.19 m d) 1.47 m 6 $6.60

1 a) 0.41 b) 1.25 c) 3.03 d) 1.63 e) 1.3 f) 3.45

7 a) $9.55 b) That is the largest whole amount you can give; $9.56 per person would require more money than you have.

2 $2.70

8 a) Yes b) Student discussion.

3 $50.14 with 4 c left over 4 15 cents 5 0.45 m

Student Book 6

Nelson International Maths Mixed calculations (p156)

6 2.24 cm

1 a) 19 b) 4.1 c) 820 d) 3116

Mixed problems (p 157)

2 a) 254 + 49 = 303 b) 49 â&#x20AC;&#x201C; 12.45 = 36.55 c) 49 is exactly divisible, but all are divisible by 7 with a remainder d) 12.45 Ă&#x2014; 100 = 1245 e) 254/100 = 2.54

1 a) 71.4

3 a) 17 b) 35 c c) $1.00 4 a) Bananas $5, Apples $5, Berries $8.75 b) $18.75 c) $1.25 5 a) The number is too large b) Made a decimal point error c) 3.435

Answers

2 5.8, 11.6 3 a) $8.05 b) $8.30 4 4.3 m 5 21 m 6 12.5, 75, 15, 27.6, 0.92. 1.84, 1.8, 180, 200, 16