Page 1

Student Book 5

Nelson International Maths Whole numbers in figures and words (p5) 1 a) four thousand, nine hundred and eightytwo b) two thousand and eighty-five c) three thousand, one hundred and twenty-six d) six thousand, five hundred and thirty-four e) eight thousand and eighty f) four thousand and eleven g) five thousand and nine h) two thousand, nine hundred and four

Answers

More ordering and comparing numbers (p8) 1 a) < b) < c) < d) < e) < f) < g) < h) < i) > j) < k) < l) >

2 a) 700 b) 50 c) 8000 d) 0

2 a) 11 927, 12 635, 13 168 b) 26 671, 26 716, 26 761 c) 213 450, 214 530, 215 430 d) 126 301, 127 849, 129 642 e) 342 765, 342 767, 342 776 f) 489 879, 489 978, 489 987 g) 876 055, 876 500, 876 505 h) 800 900, 809 009, 890 009

3 a) 1 053 b) 10 000 c) 516 d) 4 404

Rounding to the nearest 10 or 100 (p9)

4 Students’ own work.

1 a) 10 b) 40 c) 60 d) 90 e) 130 f) 340 g) 990 h) 1000 i) 1230 j) 9880 k) 9050 l) 4040

Numbers beyond 9999 (p6) 1 a) 10 001 b) 10 009 c) 10 124 d) 10 490 e) 11 319 f) 12 356 g) 15 214 h) 18 338 2 a) 12 386 b) 35 850 c) 70 599 d) 110 645 e) 257 338 f) 650 219 3 a) (5 × 10 000) + (9 × 1000) + (8 × 100) + (2 × 1) b) (4 × 10 000) + (5 × 1000) + )1 × 100) + (9 × 10) + 5 × 1) c) (1 × 100 000) + (2 × 10 000) + (6 × 100) + 5 × 10) d) (9 × 100 000) + (9 × 10 000) + (9 × 1000) + (9 × 100) + (9 × 10) + (9 × 1) e) (1 × 10 000) + 2 × 1000) + (5 × 1) f) (1 × 100 000) + (7 × 10 000) + (2 × 1000) + (4 × 100) g) (7 × 100 000) + (3 × 10 000) + 5 × 1000) h) (1 × 100 000) + (9 × 10 000) + (2 × 1000) + (9 × 10) Comparing numbers (p7) 1 a) 9 000 b) 6 825 c) 9 050 d) 3 780 e) 4 050 f) 7388 2 a) 4 012 < 9 000 b) 5 149 < 6 825 c) 8 400 < 9 050 d) 3 699 < 3 780 e) 4 018 < 4 050 f) 7 387 < 7388 3 1 983 km, 4 025 km, 6 500 km, 7 052 km, 12 105 km

2 a) 400 b) 300 c) 600 d) 1000 e) 3400 f) 8800 g) 1100 h) 1000 i) 7300 j) 8600 k) 1200 l) 4000 3 a) false; 500 to the nearest 100 is 500 b) true c) true d) true e) false; 1399 is 1400 to the nearest 10 f) false; 5416 is 5400 to the nearest 100 Rounding to the nearest 1000 (p10) 1 a) 4000 b) 5000 c) 5000 d) 4000 e) 5000 f) 4000 g) 5000 h) 4000 i) 5000 j) 5000 k) 4000 l) 5000 2 a) 2000 b) 7000 c) 9000 d) 3000 e) 6000 f) 8000 g) 4000 h) 9000 i) 3000 j) 1000 k) 4000 l) 9000 3 a) 1500, 2499 b) 4500, 5499 c) 2500, 3499 d) 6500, 7499 4 The numbers differ by 999. Adding and subtracting lots of numbers (p11) 1 a) 297 b) 41, 82 c) 20, 21, 44 d) 348 e) yellow 2 a) One example: 12 + 3 + 4 + 56 + 7 + 8 = 90 b) Students’ own work.

1


Student Book 5

Nelson International Maths

Answers

Inverse operations (p7)

Revising polygons (p16)

1 a–d) Students’ own work.

1 Triangle, square, pentagon, hexagon, heptagon, octagon, nonagon. Students to discuss their reasons.

2 Students’ own work. 3 a) 898 b) 228 c) 49 d) 102 e) 1566 f) 882 g) 143 h) 348 i) 4629 Order of operations (p13) 1 Chandra and Mohinder both added 6 and 24 before dividing 6 by 2. Jay took 1 from three before multiplying by 4. 2 a) Incorrect b) Incorrect c) Correct d) Correct e) Correct f) Correct Working in order (p14) 1 a) 34 b) 52 c)18 d) 44 e) 9 f) 4 g) 42 h) 14 2 a) 11 b) 15 c) 9 d) 623 e) 25 f) 20 g) 106 h) 23 i) 51 j) –17 k) 74 l) 15 m) 320 3 a) 6 b) 8 c) 8 d) 28 e) 27 f) 30 g) 24 h) 6 i) 22 4 a) 2 + 21 ÷ 3 = 9 b) 5 × 3 – 8 = 7 c) 15 – 6 ÷ 2 = 12 d) 14 – 8 – 6 = 0 e) 9 – 6 + 10 = 13 f) 12 × 4 ÷ 6 = 8 g) 18 – 8 – 2 = 8 h) 36 ÷ 6 + 2 = 8 i) 15 ÷ (3 × 5) + (3 × 5) = 16 j) 6 + 12 ÷ (3 – 1) = 9

2 Students’ own work. Line symmetry (p17) 1 2 2 1 3 2 4 1 5 1 6 1 7 5 8 1 9 1 Symmetry patterns (p18) 1 Canada, Maldives, Argentina, Vietnam 2 Jamaica, UK, Switzerland 3 Portugal

Rotational symmetry (p19) Three-digit target numbers (p15) 1 a) e.g. 25 × (8 + 5) – 3 b) e.g. 75 × (7 + 4) + 8 c) e.g. (50 × 2 – 3) × 5 d) e.g. (100 – 6) × (4 + 3) + 5 e) e.g. 26 × 7 + 10 + 5 + 2 f) e.g. (50 + 4) × (7 + 3) + 1 – 8 2 Students’ own work.

1 a) 3, 5, 6, 4, 8, 10 b) yes, 3; yes, 5; yes, 6, yes 4; yes, 8, yes 10 Rotating squares (p20) 1 Students’ own work. 2 Students’ own work. 3 Students’ own work. 4 Students’ own work.

2


Student Book 5

Nelson International Maths

2 a) 12:39 b) 37 minutes c) 4 minutes after d) 2 hours later e) Yes

Different triangles (p21) 1 a) right-angled b) acute-angled c) right-angled d) obtuse-angled

How long did it take? (p25)

2 a) isosceles b) scalene c) scalene d) equilateral

1 Runner

Starting time

Elapsed time

Finishing time

A

08:20

5h 10min

13:30

B

10:05

6h 2min

16:07

C

09:13

7h 7min

16:20

D

08:27

7h 23min

15:50

Classifying triangles (p22)

B

ü ü

D

Acuteangled

ü

Obtuseangled

Rightangled

ü ü

C E

Scalene

Isosceles

equilateral

Triangle

1

A

ü

ü

ü

ü

ü

F

ü

G

ü

Answers

ü ü

2 18:45 Races and records (p26) 1 a) 48.7, 48.1, 47.8, 47.7, 47.6, 47.1 b) Gold: Trevor Williamson, Silver: Michael Lewis, Bronze: Ralph Bell c) Keith Young d) John Masamba and Ralph Bell e) Boris Burghardt 2 Students’ own work. Athletics records (p27) 1 0.91 seconds

2 A – right-angled scalene; B – acute-angled isosceles; C – acute-angled scalene; D – acute-angled isosceles E – Equilateral triangle; F – Right-angled isosceles; G – obtuse-angled isosceles

4 Yes

The 24-hour clock (p23)

5 Students’ own estimates.

1 a) half past one b) quarter to midnight c) midnight d) quarter past four e) twentyfive past five f) five to eight g) ten past one h) eight o’clock 2 a) 09:20 b) 19:15 c) 11:35 d) 03:55 e) 16:40 f) 05:25 g) 19:45 h) 00:00 i) 21:15 j) 12:30 k) 22:25 l) 19:50 Reading timetables (p24)

2 More than twice as long. 3 2 minutes

Days, weeks, months and years (p28) 1 a) 2 weeks and 2 days b) 5 weeks and 1 day c) 16 weeks and 6 days d) 6 weeks and 0 days 2 8 months, 2 weeks and 1 day 3 22 June 4 4 years and 7 months

1 a) 09:46 b) C19 and D23 c) 16:31 d) C19

3


Student Book 5

Nelson International Maths 5 a) 2 years and 10 months b) 13 years c) 4 years and 9 months d) 12 years and 1 month e) Students’ own answers Place value to tenths and hundredths (p29) 1 a) 0.06; 0.94 b) 0.57; 0.43 c) 0.22; 0.78 d) 0.02; 0.98 e) 0.13; 0.87 f) 0.78; 0.22 Reading and writing decimal fractions (p30) 1 a) 9.4 b) 3.19 c) 12.03 d) 0.45 e) 0.9 f) 0.09 2 a) a – 0.2; b – 0.9; c – 1.5; d – 2.3; e – 2.9 b) f – 12.1; g – 13.3 ; h – 14.5; i – 15.3; j – 15.9 c) k – 0.05; l – 0.25; m – 0.33; n – 0.49; o – 0.61 d) p – 8.19; q – 8.25; r – 8.38; s – 8.47; t – 8.51 Comparing decimals (p31) 1 a) > b) < c) > d) < 2 a) < b) = c) > d) < Rounding decimals to the nearest whole number (p32) 1 a) 1 b) 1 c) 10 d) 5 e) 13 f) 20 2 a) 164 b) 235 c) 765 d) 543 e) 516 f) 600 3 a & b) 25 kg – 25.2 kg; 24.5 kg; 25.33 kg; 24.98 kg 26 kg – 26.09 kg; 25.6 kg; 25.9 kg; 26.34 kg: 25.8 kg 24 kg – 24.49 kg 20 kg – 19.99 kg; 20.35 kg; 20.3 kg 29 kg – 28.5 kg; 29.45 kg 30 kg – 29.8 kg; 30.09 kg; 29.55 kg

Answers

More decimals (p33) 1 Value of digits: a) 2/10; 7/100; 0 b) 1; 9/10; 8/100 c) 2/10; 4/100; 6 d) 8; 4/100; 3/100 0 Next three numbers: a) 0.29, 0.30, 0.31 b) 1.99, 2.00, 2.01 c) 6.22, 6.21, 6.20 d) 8.01, 8.00, 7.99 2 Value of digits: a) 2/10; 8/10; 9/10; 3/10 b) 4/100; 4/10; 1/100; 1 c) 2; 2/100; 1/10; 1 d) 2/10; 3/100; 1/100; 1 Arranged in order: a) 1.35, 1.85, 2.26, 2.9 b) 0.40, 1.01, 1.04, 1.4 c) 1.38, 2.17, 2.79, 5.12 d) 1.25, 1.48, 2.71, 3.03 3 a) Orange and passion fruit, Blackberries, Apple juice, Satsuma juice, Mayonnaise, Mineral water, Granary loaf, Apricot halves, Fromage frais, Half-fat milk b) Toilet-brush holder, Gold-plated mirror, Shelf, Towel rail, Soap dish, Toilet-roll holder, Towel ring, Tumbler and holder 4 a) $1 + $1 + $1 + $0 + $2 + $1 + $1 + $2 + $0 + $1 = $10 b) $10.29, 29c difference Length (p34) 1 a) 15 mm b) 24 mm c) 19 mm d) 9 mm e) 5 mm 2 a) mm or cm b) mm or cm c) cm d) cm or m e) m f) m or km 3 a) 1.1 cm b) 4.5 cm c) 128 cm d) 328.4 cm e) 2600 cm f) 26 700 cm Mass (p35) 1 a) grams b) kilograms c) tonne d) kilograms e) tonne f) grams 2 a) 5000 g b) 3500 g c) 1143 g d) 7200 g e) 45 000 g f) 11 700 g 3 5200 kg; 5 tonnes; 92 500 g; 12 876 g; 5298 g; 4.5 kg; 1 kg; 980 g; 250 g; 20 g

4 a) 40 km;, 123 km;, 60 km b) 223 km 4


Student Book 5

Nelson International Maths Capacity (p36)

4 Students’ own work.

1 250 ml; 15 ml; 1 l; 750 ml; 1.5 l; 500 ml; 25 l

Counting on to add (p42)

2 a) 1000 ml b) 5000 ml c) 10 000 ml d) 12 400 ml e) 4500 ml f) 15 800 ml 3 4 ml; 90 ml; 0.9 l; 976 ml; 1200 ml; 1.6 l; 2500 ml; 3 l; 3 l and 250 ml; 4.5 l; 8000 ml Measuring scales (p37) kg, 500grams; ml, 20ml; cm, 2mm Reading measuring scales (p38) a) 5 °C b) 25 °C c) 37 °C d) 2.6 l e) 3.4 l f) 4.2 l g) 4.5 cm h) 5.75 cm i) 1.5 kg j) 2.05 kg k) 9.5 kg l) 9.75 kg m) 1.25 m n) 44 °C o) 18 °C p) −2 °C q) 400 g or 0.4 kg r) 2.2 kg s) 2.5 kg Measuring and drawing lines (p39) 1 4 cm; 9 cm; 3 cm; 1 cm; 5 cm; 7 cm 2 Students’ own drawings. 3 Students own estimates and measures. More measuring and drawing (p40) 1 55 mm, 83 mm, 32 mm, 40 mm, 25 mm, 12 mm, 90 mm, 65 mm

Answers

1 a) 158 b) 105 c) 183 d) 146 e) 261 f) 960 2 a) 618 b) 868 c) 700 d) 1641 e) 1221 f) 1273 3 a) 2376 b) 3711 c) 4405 d) 5243 e) 3315 f) 7551 Counting on and back to subtract (p43) 1 a) 72 b) 26 c) 71 2 a) 142 b) 165 c) 156 d) 230 e) 2233 f) 1611 3 a) 472 b) 3128 c) 4124 d) 4590 e) 612 f) 988 Rounding numbers to add and subtract (p44) 1 a) 1140 b) 2133 c) 4198 d) 2767 e) 1989 f) 7011 2 a) 461 b) 126 c) 201 d) 1406 e) 3602 f) 1797 3 a) 741 b) 243 c) 171 d) 2955 e) 104 f) 2326 4 2450 km

2 Students’ own drawings.

Find the pairs (p45)

3 a) 22.5 cm; 225 mm b) 226 mm

1 262 + 738 = 1000, 462 + 538 = 1000, 181 + 819 = 1000, 658 + 1342 = 2000, 929 + 1071 = 2000, 856 + 1144 = 2000, 959 + 4041 = 5000, 1254 + 3746 = 5000, 2354 + 2646 = 5000, 1164 + 3836 = 5000

4 Students’ own work. Counting in steps (p41) 1 Oral activity 2 Oral activity 3 a) 12; 25; 38; 51; 64; 77 b) 135; 124; 113; 102; 91; 80 c) 12; 5; –2; –9; –16; –23 d) 19; 13; 7; 1; –5; –11 e) –4; –2; 0; 2; 4; 6 f) –25; –15; –5; 5; 15; 25

2 Students’ own work. 3 a) 1215 + 3785 b) 1099 + 4901 c) 4276 + 5724 = 10 000 d) 2000 + 4000 e) 1100 + 1900 4 Students’ own work.

5


Student Book 5

Nelson International Maths Addition and subtraction problems (p46) 1 a) 1 905 b) 3 448 c) 6 946 d) 7 014

Answers

2 a) 9 b) 12 c) 5 d) 9 e) 12 f) 5 g) 12 h) 7 i) 7 j) 12 k) 8 l) 7 m) 9 n) 6 o) 9 p) 9 q) 6 r) 9 Multiples (p51)

e) 5 654 f) 9 446 g) 5 516 h) 9 200 i) 10 998 2 a) 117 b) 656 c) 855 d) 2 406 e) 9 949 f) 6 021 3 a) 2 383 b) 4 724 c) 15 831 d) 917 e) 127 f) 2 200 Position on a grid (p47) 1 a) L b) A c) J d) M e) D f) H 2 a) (1, 1) b) (3, 3) c) (4, 9) d) (6, 9) e) 7, 6) f) (0, 0) Position on maps (p48) 1 a) Dungeons of despair b) Short dead end c) Underground sea 2 Various answers possible. Allow students to check each other’s work. 3 a) (3, 6) b) (3, 4) c) the crossroads d) 2 down and then three right Multiplication and division facts (p49) 1 a) 16 b) 27 c) 8 d) 25 e) 32 f) 45 g) 20 h) 28 i) 27 j) 24 k) 45 l) 18 m) 20 n) 30 o) 16 p) 18

1 a) 24; 48; 72; 54; 36; 60 b) 28; 56; 70; 49; c) 24; 48; 56; 72; 32 d) 72; 45; 54; 36 e) 24; 48; 72 f) none g) 72 h) 28; 45; 70; 49; 54; 36; 60 2 It ends with 0. 3 a) 12; 18; 24; 30; 36; 42; 48 b) 21; 28; 35; 42; 49; 56; 63 c) 81; 72; 63; 54; 45; 36; 27 d) 72; 64; 56; 48; 40; 32; 24 4 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 a) All of them b) All of them c) The answer is the same Multiple problems (p52) 1 Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40; Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 a) 12, 24, 36 b) 12 2 a) 24 b) 42 c) 45 d) 20 e) 35 f) 9 3 a) 6, 12, 18, 24… b) 12, 24, 36, 48… Square numbers (p53) 1 a)

b)

c)

d)

2 a) 3, 6, 9, 12, 15, 18 b) 5, 10, 15, 20, 25, 30 c) 4, 8, 12, 16, 20, 24 3 a) 8 b) 9 c) 4 d) 8 e) 2 f) 7 g) 9 h) 8 i) 9 j) 9 k) 5 l) 3 More multiplication and division facts (p50) 1 a) 30 b) 27 c) 36 d) 36 e) 63 f) 72 g) 24 h) 40 i) 49 j) 48 k) 42 l) 72 m) 24 n) 21 o) 63 p) 54 q) 60 r) 81 s) 100 t) 80 6


Student Book 5

Nelson International Maths e)

f)

Answers

More factors (p55) 1 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6, 9 × 4, 12 × 3, 18 × 2, and 36 × 1 2 1 × 40, 2 × 20, 4 × 10, 5 × 8, 8 × 5, 10 × 4, 20 × 2 and 40 × 1

g)

h)

3 a) 180 cm2 b) 1 × 180, 2 × 90, 3 × 60, 4 × 45, 5 × 36, 6 × 30, 9 × 20, 10 × 18, 12 × 15, 15 × 12, 18 × 10, 20 × 9, 30 × 6, 36 × 5, 45 × 4, 60 × 3, 90 × 2 and 180 × 1 c) Students’ own work.

2 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144

Fun with factors (p56)

3 a) 3 b) 1 c) 2 d) 9 e) 8 f) 7 g) 12 h) 10 i) 4 j) 5 k) 11 l) 6

2 12, 18, 20

4 42 is 4×4 not 4×2

1 a) 28 = 1 + 2 + 4 + 7 + 14 b) 496

3 91, 92, 93, 94, 95, 97, 98, 99 Divisibility rules (p57)

5 The packs with 16 and 36 tiles.

1 2

Factors (p54)

2 2, 5, 10

1 a) 1 × 24 = 24; 2 × 12 = 24 ; 3 × 8 = 24; 4 × 6 = 24 b) 1, 2, 3, 4, 6, 8 12 and 24

3 2,

2 Possible answers are: a) 1 × 16; 2 × 8; 4 × 4 b) 1 × 20; 2 × 10; 4 × 5 c) 1 × 18, 2 × 9; 3 × 6 d) 1 × 32, 2 × 16, 4 × 8 3 Possible answers are: a) 1 × 30; 2 × 15; 3 × 10; 5 × 6 b) 1 × 40; 2 × 20; 4 × 10; 5 × 8 c) 1 × 50; 2 × 25; 5 × 10 d) 1 × 60; 2 × 30; 3 × 20; 4 × 15; 5 × 12; 6 × 10 e) 1 × 100; 2 × 50; 4 × 25; 5 × 20; 10 × 10 f) 1 × 56; 2 × 28; 4 × 14; 7 × 8 g) 1 × 68; 2 × 34; 4 × 17 h) 1 × 81; 3 × 27; 9 × 9 4 Students’ own work.

4 5 5 2, 5, 10 6 No 7 2 8 No 9 2 10 2 11 No 12 No 13 2 14 No 15 No 16 2, 5, 10 17 2, 5, 10 18 2, 5,10 and 100 7


Student Book 5

Nelson International Maths Seedling sale (p58)

What do you watch? (p63)

1 a) tomato b) onion c) lettuce, pansy, spinach d) 5

1 a) 55 b) Crime c) Nature, Sport and Keep- fit

Answers

2 Students’ own work.

2 Students’ own work.

3 Students’ own work.

3 a) Type of seedling b) Number sold

Positive and negative numbers (p64)

4 Students’ own explanation.

1 −7

How many words per day? (p59)

2 +6

1

3 −50

Student

Emma

Claire

Sean

Tony

4 −25

Total

263

265

287

160

5 +6

2 a) Sean b) Tony c) 975 3 a) Yes b) The scale is compacted so it’s hard to see the difference in the data c) Students’ own graphs. Show choices on a pictogram (p60-61) 1 See Workbook Answers 2 Pony-trekking, water-skiing and Dinghy sailing or canoeing (they have the largest number of symbols on the graph). 3 Climbing and abseiling or parachuting (they have the fewest symbols or tallies) 4 Students’ own table. 5 Students’ own graph. 6 Discussion The mode (p62) 1 a) Pony-trekking b) Students’ own results c) Knowing which activity is most popular will allow the organisers to make sure they have enough instructors and equipment. 2 a) 75 b) 6 c) 5 (on the top side of the dice) d) red and blue e) jeans f) track and field

6 −4 7 +300 8 −8 Comparing positive and negative numbers (p65) 1 a) −3 b) −1 c) 5 d) 0 e) 1 f) −2 g) 2 h) −1 2 a) < b) > c) > d) < e) < f) < Temperature changes (p66) 1 a) 28 °C; 10 °C; 22 °; 15 °C; 8 °C b) 6 °C; −12 °C; 0°C; −7 °C; −14 °C 2 a) −8 °C b) 7 °C c) 0 °C d) 3 degrees Number sequences (p67) 1 a) Add 2; 12, 14, 16 b) Add 2; 19, 21, 23 c) minus 3; 28, 25, 22 d) add 2; 4, 6, 8; e) minus 5; −15, −20, −25 f) add 25; 225, 250, 275 g) minus 50; 300, 250, 200 h) minus 7; −16, −23, −30 2 a) 8, 16, 24, 32, 40, 48 (add 8) b) 27, 38, 49, 60, 71, 82 (add 11) c) 88, 79, 70, 61,52, 43 (minus 9) d) 80, 72, 64, 56, 48, 40 (minus 8) e) −18, −27, −36, −45, −54, −63 (multiples of minus −9) f) 1, 4, 9, 16, 25, 36, 49 (square numbers) 3 Students’ to work on grid. 8


Student Book 5

Nelson International Maths

Answers

More number sequences (p68)

Measuring angles accurately (p72)

1 a) 145, 150, 155, 160, 165. These are all multiples of 5. b) 380, 390, 400, 410, 420. These are all multiples of 2, 5 and 10. c) 525, 550, 575, 600, 625. These are all multiples of 5 and 25. d) 750, 800, 850, 900, 950. These are all multiples of 2, 5, 10 and 50. e) 600, 700, 800, 900, 1000. These are all multiples of 2, 5, 10, 50 and 100

1 a) 30° b) 45° c) 35° d) 70° e) 10°

2 a) 825, 850, 875 b) 450, 500, 550, 600, 650, 700, 750 c) 100, 200 … 900, 1000 d) 150, 200 3 a) Add 4 b) Square numbers descending from 10 c) minus 30 d) Multiply by 10 e) halve f) Add 4 4 Students’ own investigations. Odd and even numbers (p69) 1 a) It ends in an odd digit (1, 3, 5, 7, or 9) b) It ends in an even digit (0, 2, 4, 6, 8)

Drawing angles (p73) 1 a) 19° angle and 6 cm lines b) 65° angle and 5.6 cm lines c) 30° angle and 7.1 cm lines d) 72° angle and 6 cm lines 2 a) Drawing of 7° angle b) Drawing of 51° angle c) Drawing of 90° angle Classifying angles (p74) 1 a) 1 acute angle, 2 right angles, 1 obtuse angle b) 2 acute angles, 2 obtuse angles c) 3 right angles, 2 obtuse angles d) 4 right angles e) 2 acute angles, 1 right angle f) 6 obtuse angles 2 a) less than 90° b) 90° c) less than 90° d) more than 90° e) less than 90° f) 90° Angles in a straight line (p75)

2 18 766; 254 988; 9000; 4804; 12 762; 125 318; 980; 3330

1 a) Students’ own drawings. b) 90° c) 90° + 90° = 180° d) Angles in a straight line add up to 180°.

3 Students’ diagrams.

2 Students’ own work.

4 a) even b) odd c) odd d) even e) even f) even g) odd

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

5 No 6 Yes, 7 × 2 = 14 (an odd number multiplied an even number of times will give you an even number as a product.) Parallel lines (p70) 1 a) yes b) yes c) no d) no e) yes f) no 2 Students’ own work. Perpendicular lines (p71) 1 (a–f) Students’ own work. 2 Students’ own work. 3 Students’ own work.

Review of fractions (p76) 3 4

1 a)

shaded;

unshaded c) 1 3

d)

1

2 a)

1 2

unshaded b)

3 4

shaded;

shaded; 1 3

b)

3 Five:

1 6

;

2 6

c) ;

1 12

2 3

4 5

d)

;

4 6

3 6

d= ;e=

1 6

1 9

2 5

e)

and 1 4

9 36

1 4

3 8

shaded;

5 8

unshaded

unshaded

=

4 a) 36 b) a = c=

1 4

9 10

f) 2

4 5

5 6

;b=

1 8

;

c) greater

9


Student Book 5

Nelson International Maths Find the fraction (p80)

Equivalent fractions (p77) 1 Oral discussion 2 a) h)

2 12

1 2

b)

3 4

i)

2 10

3 5

j)

1 $1.25

4 6

c)

2 3

d) 1 2

k)

4 5

e)

1 4

f)

4 10

g)

2 25 cm

6 10

l)

3 600 ml 4 12 kg

3 a) < b) = c) < d) = e) > f) > 4 a)

1 4

;

3 4

5 a)

4 8

,

5 10

c) 6 a)

4 20 1 4

2 4

;

6 12

,

4 5

b)

,

5 25

,

b)

1 8

c)

3 5

;

4 12

b)

5 15

,

5 $3.60

1 5

;

6 875 m

6 18

,

7 36 c

6 30

8 $26

1 6

1 10

d)

9 400 g 10 62.5 m

Improper fractions and mixed numbers (p78) 5 3

=1

d)

13 10

=1

h)

18 5

=3

1 a)

2 a) 1

1 2

2 3

15 12

b)

3 10

=1

6 3

e)

1 4

7 4

c)

= 2 f)

5 2

1 4

1 4

=1

=2

1 2

Perimeter (p81)

3 4

g)

13 4

=3

1 4

3 5 3 4

b) 2

c) 3

d) 4

e) 5

1 2

2

1 3

2 5

k) 1

2 a) 5 g) i)

1 2

20 2 40 3

1 4

d) 1

3 4

1 3

l) 4

b) 2

e) 2 and one

i) four and three quartes j)

1 6

3 4

9 5

c)

d) 3

2 7

e) 1

2 3

f) 3

h) Neither, they are equal j)

2 a) 8 cm b) 120 cm c) 40 cm

1 (a & b) 33.2 cm = 332 mm; 5.7 cm = 57 mm; 156 cm = 1560 mm; 31.4 cm = 314 mm; 61 cm = 610 mm; 15 cm = 150 mm 2 26 cm ; 2.9 cm; 24 cm ; 15 mm; 28 mm; 2.2 cm Finding the areas of rectangles (p83)

h) 4 5 6

c) 1

1 7

quarter f) 2 g) 2

1 3

b) 1

1 a) 8 cm b) 6.8 cm c) 8.8 cm d) 8.8 cm e) 10.7 cm f) 11 cm

More perimeter (p82)

3 4

Changing improper fractions to mixed numbers (p79) 1 a) 1

Answers

19 5

k) 7

9 5

1 4

3 a) 1

1 2

,

b)

3 4

,

12 5

,

19 6

c)

3 2

,

12 8

,

9 4

2 7 7 3

,2 ,

,

l)

7 6 8

,

15 6

Use the formula (p84) 1 4 cm × 12 cm = 48 cm2; 10 cm × 50 cm = 500 cm2; 4 cm × 2.5 cm = 10 cm2; 6 cm × 10.5 cm = 63 cm2

21 9 , 5 2

, 7 3

,

12 5

(note

3 4

1 a) 4 cm × 6 cm = 24 cm2 b) 7 cm × 5 cm = 35 cm2 c) 8 cm × 5 cm = 40 cm2 d) 3 cm × 9 cm = 27 cm 2 e) 7 cm × 2 cm = 14 cm2

3 2

=

12 8

) 10


Student Book 5

Nelson International Maths

2 a) 800 b) 1600 c) 1800 d) 1500 e) 1800 f) 3600 g) 3500 h) 4800 i) 6300 j) 7200 k) 1800 l) 5600

2 Length

Breadth

Area

5 cm

3 cm

15 cm2

6 cm

2 cm

12 cm

2

9 cm

4 cm

36 cm2

10 cm

8 cm

80 cm2

7 cm

5 cm

35 cm

2

15 cm

6 cm

90 cm2

12 cm

6 cm

72 cm2

4 cm

2

8 cm

32 cm

Answers

3 Students’ own work. Multiplying by 10 and 100 (p85)

3 a) 540 seagulls b) 1200 fish c) 6400 ants d) 480 elephants e) 3600 antelope f) 5600 locusts g) 200 caterpillars h) 1600 birds Doubling and halving (p88) 1 a) 24 b) 38 c) 122 d) 198 e) 240 f) 660 g) 2400 h) 4800 2 a) 23 b) 34 c) 92 d) 98 e) 190 f) 230 g) 2350 h) 4150 3 a) 90 b) 2 c) 2 d) 650 e) 840 f) 550 g) 2100 h) 3200 i) 1450

1 a) 40 b) 190 c) 880 d) 1320 e) 4000 f) 9870 g) 10 980 h) 85 000 i) 99 990

Using factors to multiply (p89)

2 a) 900 b) 2800 c) 9000 d) 42 500 e) 80 000 f) 76 200 g) 120 800 h) 180 000 i) 805 000

2 a) 138 b) 152 c) 156 d) 135 e) 186 f) 264

3 120 apples 4 $2300 5 1200 months 6 a) 24 860 pieces b) 248 600 pieces What happens when you divide by 10 or 100? (p86) 1 a) 67 b) 80 c) 42 d) 990 e) 876 f) 200 g) 50 h) 32 i) 99 2 a) 34 b) 59 c) 80 d) 340 3 a) 5 b) 44 c) 90 d) 89 Multiplying tens and hundreds (p87) 1 a) 60 b) 180 c) 400 d) 280 e) 480 f) 140 g) 540 h) 250 i) 240 j) 640 k) 810 l) 360

1 a) 98 b) 96 c) 102 d) 207 e) 90 f) 76

Multiplying by 19 or 21 (p90) 1 a) 171 b) 168 c) 209 d) 273 e) 672 f) 361 g) 882 h) 1218 i) 1197 2 735 trees 3 285 paving stones 4 Students’ discussion Multiplying by 25 (p91) 1 a) 600 b) 800 c) 475 d) 400 e) 1200 f) 675 g) 1550 h) 2025 i) 1800 2 No, he’ll only have 875 3 1050 people 4 a) Yes b) Discussion Reflections (p92) 1 a) B b) B c) B d) A 2 Students’ discussion.

11


Student Book 5

Nelson International Maths Translations (p93) 1 a) forward 7 b) up 7 c) down 5 d) backward 6

Answers

2 3.15 + 6.85; 4.81 + 5.19; 6.13 + 3.87; 8.27 + 1.73; 9.04 + 0.96; 7.39 + 2.61 Doubling and halving decimals (p98)

2 a) (2, 6), (5, 6), (5, 1), (2, 1); (9, 6), (12, 6), (12, 1), (9, 1) b) (3, 5), (6, 5), (6, 3), (8, 3), (8, 1), (3, 1); (3, 12), (6, 12), (6, 10), (8, 10), (8, 8), (3, 8) c) (3, 10), (7, 10), (7, 6); (3, 5), (7, 5), (7, 1) d) (8, 6), (11, 6), (13, 1), (10, 1); (2, 6), (5, 6), (7, 1), (4, 1)

1 a) 16.2 b) 18.8 c) 15.6 d) 19.8 e) 18.4 f) 90.6 g) 37 h) 123

More translations (p94)

1 a) 5.27b) 4.79 c) 6.3 d) 46.49 e) 51.57 f) 22.07

1 a) (4, 9), (4, 5), (7, 5) b) (2, 5), (2, 1), (5, 1) c) (5, 4), (8, 4), (8, 7), (5, 7) 2 a) Shape drawn with the following vertexes: E(4,10), F(9,10), G(9,6), H(4,6) b) rectangle c) (2, 7), (7,7), (7, 3), (2, 3) Pairs of decimals that make 1 (p95) 1 a) 0.9 b) 0.3 c) 0.5 d) 0.2 e) 0.4 f) 0.8 g) 0.7 h) 0.2 i) 0.4 j) 1 k) 0.9 l) 0.5 2 She is two blocks short. More pairs of decimals that make 1 (p96) 1 a) 27 + 73; 0.27 + 0.73 b) 55 + 45; 0.55 + 0.45 c) 83 + 17; 0.83 + 0.17 d) 39 + 61; 0.39 + 0.61 e) 68 + 32; 0.68 + 0.32 f) 92 + 8; 0.92 + 0.08 2 0.64 + 0.36; 0.47 + 0.53; 0.39 + 0.61; 0.81 + 0.19; 0.2 + 0.8; 0.4 + 0.6; 0.22 + 0.78; 0.93 + 0.07

2 6.4 cm; 9.3 cm; 21.05 cm; 10.1 cm; 13.2 cm; 28.4 cm Adding and subtracting decimals (p99)

2 a) 3.51 b) 6.52 c) 4.31 d) 3.04 e) 3.36 f) 1.63 3 a) $13.44 b) $3.46 C) $1.56 Frequency tables (p100) 1 a) 11 letters b) 1 letter 2 4 letters 3 Own tables based on text in book. 4 Students to read data from their own tables. 5 Students’ own data. 6 Students’ own answers. Frequency tables with groups (p101) 1 Time(mins)

Number of students

0 – 20

0

21 – 40

5

41 – 60

7

61 – 80

1

Making 10s (p97) 1 2.7 + 7.3; 8.1 + 1.9; 6.9 + 3.1; 3.4 + 6.6; 7.5 + 2.5; 0.2 + 0.8

12


Student Book 5

Nelson International Maths 2 Note students will need to add another row to this table (> 250) Height (cm)

Frequency

50 – 100

3

101 – 150

12

151 – 200

22

201 – 250

10

> 250

3

Bar line graphs (p102) See Workbook answers for graphs More bar line graphs (p103) 1 a) Student’s own graph b) Student’s own graph 2 a) 400 b) 300 c) Student’s own graph Line graphs (p104)

Answers

b) The hall filled up slowly from 3 to 6 pm. By 7 pm there were 100 people in the hall. This number remained the same from 7 to 8 pm. The hall emptied completely between 8 and 9 pm. c) At 4 pm, this is when people started to come in. d) Sometime between 8 and 9, but you cannot tell when from this graph. Making sense of line graphs (p106 and 107) 1 a) The line on the graph slopes downwards b) i) 1.4 m ii) 1.1 m c) Just after 11.00 d) The line would slope upwards 2 a) About 50 students were absent on Monday, the number then decreased for Tuesday and Wednesday before increasing again on Thursday. Most students were absent on Friday. b) The data is not continuous c) A bar graph or a bar line graph

1 a) The growth of a bean plant over a period of time b) Time, days c) Height (mm) d) 5 mm e) 10 mm f) On Thursday g) Sometime between Wednesday and Thursday

Revise division facts (p108)

More line graphs (p104)

1 a) 17 b) 16 c) 19 d) 23 e) 14 f) 12 g) 12 h) 19 i) 13

1 See Workbook answers for graph 2 a) 26 °C b) It remained the same c) Because the temperature decreased over this period d) Sometime between 9 and 10 am. 3 a) See Workbook answers for graph

1 a) 4 b) 2 c) 8 d) 8 e) 6 f) 24 g) 8 h) 16 i) 32 j) 9 k) 5 l) 15 m) 9 n) 18 o) 45 p) 10 q) 1 r) 2 2 6 children 3 9 sweets More division (p109)

2 a) 26 b) 94 c) 141 d) 24 e) 31 f) 22 g) 49 h) 26 i) 39 3 22 boxes Dividing with a remainder (p110) 1 a) 135 r 2 b) 143 c) 144 r 1 d) 81 r 1 e) 50 r 6 f) 72 r 1 g) 84 r 1 h) 44 r 4 i) 42 r 4 j) 71 r 3 k) 46 r 6 l) 81 r 1

13


Student Book 5

Nelson International Maths

Answers

2 a) 19 teams b) 3

4 27 boxes (round up)

3 a) 49 b) 300 cm

5 57 weeks (round up)

4 79

6 12 (round down)

Can you divide the remainder? (p111)

7 125

1 2 r.2

Shapes and nets (p115)

2 1.5 lettuces

1 a, e and f

3 3 r.3

6 62.5 g

2 Discussion. Note that the first net is an open cube with one face fewer than the net of a cube. The second net is a cuboid and has the same number of faces as the cube. The main difference is in the shape of the faces.

7 16 r.2

Matching shapes to their nets (p116)

8 2 r.3

1 Discussion.

What will you do with the remainder? (p112)

2 a) cuboid b) square-based pyramid c) cube d) cylinder e) triangular prism

4 1.25 metres 5 3 r.1

1 36 boxes

Making cubes and cuboids (p117)

2 31.25 g

1 Students’ own work.

3 31 km/h

2 Students’ own work.

4 7 rides

3 Students’ own work.

5 44c

4

More division (p113) 1 a) 201 b) 103 c) 100 d) 111 e) 213 f) 301 g) 110 h) 141 i) 312 j) 120 k) 330 l) 100 2 a) $302 b) 210 people c) 314 stickers 3 a) 29 sheets with 2 left over b) 32.44 ml c) 81.33 grams; none left over Division problems (p114) 1 83 2 25.2 cm 3 56

5

4 6 3

2

1

5 6

4

1

4

2 6 5

3

3

5 6 2

2

1 3

4 1

5 Students’ own work. Comparing amounts (p118) Writing ratios (p60) 1 a) 2 to 1 b) 1 to 2 c) 1 to 4 d) 4 to 3 e) 2 to 5 f) 1 to 7

14


Student Book 5

Nelson International Maths 2 a) 1 to 2 b) 2 to 1 c) 4 to 1 d) 3 to 4 e) 5 to 2 f) 7 to 1

Answers

Mixing paint (p123) 2 5

1 a) Comparing parts to the whole set (p119)

b) 9 c) 4 d) 1

1 2

e) 12 blue, 18 yellow

2 Studentsâ&#x20AC;&#x2122; own work.

1 a) 14 b) 4/14 = 2/7 c) 6/14 = 3/7 d) 6/14 = 3/7

Percentages (p124)

2

1 a) 55% b) 84% c) 10% d) 95% Salma

Marie

2 a) 45% b) 16% c) 90% d) 5%

a)

5 8

3 4

3 86%

b)

7 16

1 4

4 a) 30% b) 20%

c)

3 16

3 8

5 37%

d)

3 16

1 8

Percentages, decimals and fractions (p125) 1

More about ratios (p120) 1 a) 1 to 2 b) 1 to 5 c) 250 to 15 2 a) 1 to 100 b) 1 to 2 c) 1 to 200 3 Studentsâ&#x20AC;&#x2122; own work.

1%

10%

60%

75%

83%

90%

98%

0.01

0.1

0.6

0.75

0.83

0.9

0.98

1 100

1 10

83 100

9 10

Fractions and ratios (p121) 1 a)

1 14 7 4 1 6 or b) or c) or 4 24 12 24 6 24

2 a) 6 to 14 = 3 to 7 b) 4 to 14 = 2 to 7 c) 6 to 4 = 3 to 2 3 a) 15 b) 3 c) 5 School ratios (p122) 1 a) 32 to 16 = 2 to 1 b) 32 to 32 = 1 to 1 c) 120 to 32 = 15 to 4 d) 40 to 32 = 5 to 4 e) 48 to 32 = 3 to 2 f) 32 to 12 = 8 to 3 g) 50 to 32 = 25 to 16 h) 32 to 10 = 16 to 5 2 Studentsâ&#x20AC;&#x2122; own work. 3 a) 5 to 10 = 1 to 2 b) 2 to 4 = 1 to 2 c) 4 to 8 = 1 to 2

2 a)

27 100

b) 4%, c) 0.03,

3 5

, 50%, 0.6 1 4

, 0.4

3 10

5 100

49 50

3 4

1 2

, 33% 0.9 ,

1 2

, 15%, 0.5,

3 4

d) 0.02, 0.2, e)

3 4

22 100

Finding percentages of an amount (p126) 1 a) 3 b) 9 c) 6 2 a) 15 b) 6 c) 3 d) 6 3 a) 90 tickets b) 110 c) $1730

15


Student Book 5

Nelson International Maths

Answers

Express fractions as percentages (p127)

Revising multiplication (p132)

1 a) 50%; 90%; 5%; 30%

1 a) 405 b) 168 c) 266 d) 469 e) 792 f) 675 g) 472 h) 294 i) 279

1 2

b) ;

9 10

;

5 100

;

3 10

c) 50%; 10%; 95%; 70% d)

1 2

;

1 10

;

19 20

;

7 10

2 50%; 63%; 97%; 5%; 55%; 90% More equivalent fractions (p128) 1 a) 25% b) 40% c) 50% d) 50% 2 a) 2/10 b) 3/20 c) 9/10 d) 2/5

2 581 3 240 bottles + 195 oranges = 435 items Multiplying bigger numbers (p133) 1 a) 144 b) 711 c) 710 d) 1074 e) 891 f) 861 g) 264 h) 2315 2 a) 1295 eggs b) $1386 c) 432 seats Multiplying by two-digit numbers (p134)

3 a) 0.5 b) 0.6

1 a) 195 b) 900 c) 925 d) 1188 e) 741 f) 1978 g) 792 h) 1242 i) 1729

4 60% of 60 = 36 children

2 a) 1485 b) 2116 c) 3050 d) 3969

How likely? (p129)

Other methods of multiplication (p135)

1 a) certain OR likely to happen (dependent on child) b) unlikely to happen c) impossible d) certain OR likely to happen or unlikely to happen (dependent on child) e) impossible

1 a) 1081 b) 2146 c) 1976 d) 800

2 Students’ own work.

1 a) 2990 b) 475 c) 665 d) 500 e) 1248 f) 1143 g) 2392 h) 2100 i) 252

3 Students’ own work. Likely and unlikely events (p130) 1 Some answers will vary. The following should be accurate though: c) impossible e) even chance f) certain g) certain j) certain

2 $4628 Practise multiplying (p136)

2 a) 1708 stickers b) 654 cows c) 756 plants d) $2095 e) 2690 stickers f) $992 g) 780 blocks h) 2730 seats 3 a) 3024 cars b) 4536 cars 4 a) 762 m b) 3810 m or 3.81 km

2 Students’ own work.

5 $4565

Good chance, poor chance (p131)

6 No; It is 1578

1 a) good chance b) poor chance c) no chance

7 a) No, too few b) Order 14 more 8 a) 890 litres b) 1246 litres

2 a) poor chance b) no chance c) good chance

Multiplying decimals (p137)

3 a) no chance b) good chance c) poor chance

1 a) 5.4 b) 25.5 c) 9.2 d) 13.8 e) 59.4 f) 13.5 g) 30.8 h) 17.6

4 (a–b) Students’ own work.

2 a) $20 b) 9 m

16


Student Book 5

Nelson International Maths More multiplying decimals (p138)

More mixed operations (p141)

1 a) 12.6 b) 30.5 c) 27.9 d) 20.8 e) 48.3 f) 8.8 g) 21.6 h) 65.1 i) 42

1 a) $2540 b) $1500 c) 1349

2 a) 10.8 cm b) 12 cm c) 15.6 cm d) 24.6 cm 3 (a–c) 2 bowls Watermelon 2.4 kg

5 bowls

8 bowls

6 kg

9.6 kg

Apple

3.4 kg

8.5 kg

13.6 kg

Pineapple

2.2 kg

5.5 kg

8.8 kg

Grapes

1 kg

2.5 kg

4 kg

Mango

3.6 kg

9 kg

14.4 kg

Answers

2 a) 7866 b) 126 360 c) 165 370 d) 65 130 e) 22 029 f) 13 725 g) 172 r.6 h) 486 i) 7201 3 a) Students’ own work. b) Students’ own work. c) Students’ own work. 5 a) 15 beads b) 30 plums c) $30 d) 49 pencils Brain power (p142) 1 a) 76 + 224 b) 5 × 18 c) 79 + 21 d) 15 × 6 2 a) 7100 b) 0 c) 105 d) 4848 e) 2 f) 792

Decimal problems (p139) 1 a) 9.1 m b) $81.90 2 a) 8.7 kg b) 21.5 kg c) 1.4 kg d) 78.3 kg 3 9.6 l; 15.2 l; 20 l; 30.4 l; 36.8 l 4 a) 17.5 cups b) 1.75 cups 5 a) 15.2 m b) 1.9 × 4 = 7.6 m c) 7.6 × 4 = 30.4 m Mixed operations (p140) 1 a) 37 b) 15 c) 36 d) 200 2 a) true b) false c) true d) false 3 a) 350 – 150 = 200 b) 9 x 5 = 45 c) 100 /25 = 4d) 10x9 = 90 e) 8 x 2 = 16 f) 100/2 = 50 g) square root of 144 = 12 4 a) 10 999 b) 10 004 c) 10 014 d) 10 119 5 a) 786 b) 442 c) 2463 d) 3957 e) 5272 f) 12149

17

Nelson international maths pupil book 5 answers  
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