Caribbean Primary Mathematics Level 6 - Hodder Education

© Hodder & Stoughton Limited 2019 1

Caribbean Primary Mathematics Level 6

Answers Topic 1 Getting ready Page 2 Revising knowledge from previous years is an important starting point for the new year. This gives students confidence and an interest to learn more and gives the teacher a better understanding of where each child is in their progress. Number concepts Page 2 1 a Forty-one thousand five hundred and thirty-nine b 1 c Ten thousand / 40 000 d 9 e 93 541 f 55 000 + 41 539 = 96 539 g 90 000 + 6000 + 500 + 30 + 9 (9 10 000) + (6 1000) + (5 100) + (3 10) + (9 1) 2 29 $100 = $2900 3 a 20 b 9 4 Student’s drawing

5 a 1 b

c d =

Page 3 6 , 0.75, 75%,

7 18:12

8 , , , ,

9 a 2, 3, 5, 7, 11 b II, III, V, VII, XI 10 a 20 156 + 9046 + 198 = 29 400 b 1000 – 346 = 654 c 34 7 = 238 d 714 ÷ 3 = 238 11 a Pen, sharpener, stapler b $15.40 c $6.50 + $0.65 = $7.15 d Eraser: $1.25 – $0.25 = $1.00 Sharpener: $2.50 – $0.50 = $2.00 12 a 25 12 = 300 cookies b 300 ÷ 3 = 100 packs

13 a +

= +

=

b –



= –

=

c 2 + 1

= 3 +

= 3

d 1 1

= 2

e 0.2 3.5 = 0.7 f 3.6 ÷ 4 = 0.9

14 –

= of the cake is left.

15 8 packets 16 (6 5) $5 = 30 5 =$150 $150 2 = $300 Geometry, measurement and data Page 4 1 a Square b Cube c Scalene triangle d Trapezium e Pentagon f Cube, cone, cylinder Page 5 2 Metres – trundle wheel Litres – jug Grams – scale Seconds – stop watch Degrees Celsius – thermometer 3 a Metres b Kilometres c Centimetres 4 3:37 p.m. 15:37 5 15:40 + 0:35 = 16:15 6 a Angle a: acute Angle b: obtuse Angle c: right angle b Shape d: trapezium Shape e: rectangle Shape f: square c Shape g: cuboid



Shape h: cylinder Shape i: cylinder Page 6 7 a 34°C b 34°C – 31°C = 3°C cooler 8 a (15 2) + (8 2) = 30 + 16 = 46 metres b 15 8 = 120 m2 c 50 50 = 2 500 cm2 per tile 2 500 cm2 = 0.25 m2

120 ÷ 0.25 = 480 You would need 480 tiles. Page 7 9 a Friday b It was hot. c Friday d 24 – 8 = 16 e $2.50 16 = $40.00 f $25 ÷ $2.50 = 10

The tuck shop did not sell exactly 10 ice-creams on any day; the closest total to $25 is $30 sold on Tuesday.

10 a Student’s drawing of a bar graph; make sure there is a title and labels for the x- and y-axes.

b 32 c 3 d 9

e

11 a 6 b 6 c 3 and 9 d 7 e 6 12 a Survey or questionnaire b Tally, frequency table or bar graph

Topic 2 Number sense (1) Page 8 The students will continue to count in higher numbers, rounding them off, writing them in expanded notation and identifying large numbers in real life. Make sure the students do not get anxious when working with large numbers. Allow them to discuss the work in pairs to assist them in their understanding of the work. A Counting and place value Page 10 1 a 14 723 b 25 474 c 163 412 d 307 289 2 a 25 338 b 58 943 c 383 893 d 294 725 3 a 500 b 50 000 c 5000 d 500 000



e 5 f 50 Page 11 4 a 40 000 b 4 000 000 c 80 d 200 000 e 8000 f 900 000 g 900 h 9 Problem-solving 5 a A: 3 552 000 B: 1 465 250 C: 3 552 000 D: 1 499 300 b 1 876 125 What did you learn? 1 1 500 000 2 3 200 000 3 2 466 000 4 2 100 000 B Rounding and estimating Page 12 1 a 24 000, 24 000 b 13 900, 14 000 c 232 000, 232 000 d 19 200, 19 000 e 897 300, 897 000 f 276 600, 277 000 g 99 100, 99 000 h 129 000, 129 000 Problem-solving 2 a St Lucia: 171 500, 172 499 Barbados: 282 500, 283 499 Trinidad and Tobago: 1 356 500, 1 357 499 Jamaica: 2 728 500, 2 729 499 Puerto Rico: 3 507 500, 3 508 499 b Jamaica Page 13 Challenge 3 a Trinidad: 1 000 000 Jamaica: 3 000 000 Puerto Rico: 4 000 000 b Barbados 4 a 39 + 42 80 b 499 – 67 430 c 32 876 – 12 909 20 000 d 29 + 187 230 e 148 – 9 + 24 160 f 58 22 1 200



g 32 12 300 h 32 876 + 13 087 40 000 Problem-solving 5 a 14 000 + 26 000 + 19 000 + 19 000 + 22 000 = 100 000 b i 22 000 – 19 000 = 3000 ii 26 000 + 22 000 = 48 000 iii 26 000 – 14 000 = 12 000 6 4000 + 6000 + 7000 = 17 000 7 20 000 ÷ 200 = 100 sets What did you learn? $9000 + $3000 + $9000 + $13 000 + $11 000 = $ 45 000 C Large numbers in real life Page 14 1 a 9 631 261, 8 526 429, 8 157 896, 7 167 998, 5 640 184, 5 443 497, 5 091 924,

2 108 434 b Macedonia, Finland, Norway, Denmark c Sweden, Austria, Switzerland d Finland, Norway, Denmark 2 a 5 940 000 < 6 151 000 b 4 million c 3 828 415 2 = 7 656 830 Yes, more than 7 million. 3 a 3 b After 9 it clicks onto the dial to the left. c 8 037 369 d 8 047 369 What did you learn? They are only estimates. Topic 2 Review Page 15 Key ideas and concepts 1 millions 2 place 3 expanded notion 4 decrease 5 hundreds 6 estimated 7 Population Think, talk, write … 1 a three million eight hundred and seventy-six thousand and sixteen b Look at the digits and their place values. c Count the digits (should have 7 digits). 2 Crowds, population, finances Quick check 1 a 14 999 b 1 324 000 2 a 23 456 = 20 000 + 3000 + 400 + 50 + 6 b 4 000 000 = 4 million



c 876 000 = 800 000 + 70 000 + 6000 d 2 345 009 = 2 000 000 + 300 000 + 40 000 + 5000 + 9 3 a 20 000 b 700 000 c 9 000 000 d 9000 4 a 9 876 542 b 2 456 789 c 8 769 542 d 5 246 789 5 a Brazil b Venezuela c Argentina d 916 445, 1 098 580, 1 138 910, 1 285 220, 2 766 890, 8 514 877 e 916 000, 1 099 000, 1 139 000, 1 285 000, 2 767 000, 8 515 000 f 15 721 000

Topic 3 Computation (1) Page 16 The students will continue to strengthen their abilities to compute mentally to increase speed in solving problems. Assist the students with their pen-and-paper calculations to ensure they add the correct values together. A Mental strategies Page 19 1 a 63 b 84 c 103 d 89 e 64 f 105 g 90 h 77 i 51 j 73 k 72 l 101 2 a 33 b 35 c 67 d 19 e 28 f 44 g 50 h 55 i 58 j 28 k 26 l 16 3 a 230 b 1900 c 450 d 12 300 e 160 f 216 g 200 h 160 i 350 j 460 k 210 l 4200 4 a $42 b 12 c $45 d 105 Investigate If you halve 100 you get 50, and if you then halve 50 you get 25. This will then be your answer when multiplying by 25. 12 25: 12 100 = 1200 1 200 ÷ 2 = 600 600 ÷ 2 = 300 12 25 = 300 What did you learn? 1 a 1900 b 850



c 640 d 1400 e 1900 f 800 2 a 26 b 37 c 21 d 75 e 67 f 92 B Addition and subtraction Page 20 1 a Estimate: 100 + 100 + 100 = 300 142 + 117 + 131 = 390 b Estimate: 300 + 2000 + 1 000 = 3300 289 + 2114 + 1309 = 3712 c Estimate: 12 000 + 5000 + 100 = 17 100 12 345 + 4568 + 99 = 17 012 d Estimate: 1000 + 8000 + 8000 = 17 000 1456 + 7654 + 8123 = 17 233 e Estimate: 800 + 1000 + 700 + 100 = 2600 765 + 1234 + 678 + 99 = 2776 f Estimate: 44 000 + 13 000 = 57 000 43 568 + 12 897 = 56 465 Page 21 2 a Estimate: 9000 – 1000 = 8000 8798 – 1307 = 7491 b Estimate: 8000 – 4000 = 4000 8032 – 4156 = 3876 c Estimate: 12 000 – 9000 = 3000 12 345 – 8765 = 3580 d Estimate: 300 000 – 200 000 = 100 000 321 098 – 158 987 = 162 111 e Estimate: 90 000 – 40 000 = 50 000 88 950 – 43 999 = 44 951 f Estimate: 120 000 – 110 000 = 10 000 121 625 – 112 887 = 8738 3 a 27 560 + 48 320 = 75 880 square kilometres b 48 320 – 27 560 = 20 760 square kilometres 4 a 6992 – 5464 = 1528 km b 6418 + 5464 = 11 882 km c 6853 2 = 13 706 km d 6992 + 6853 + 6418 + 6275 + 5464 = 32 002 km Think and talk 5

– + Minus CombineDeduct Total Find the difference Sum How many less How many moreTake away Altogether How many in all How much



Page 22 6 329 + 89 = 418 700 – 418 = $282 Her profit is $282. 7 a Jonelle: 230 Keshawn: 235 Kezia: 237 Leroy: 228 b 237 – 228 = 9 8 a Madagascar: 2 175 959 Greenland: 623 200 United Kingdom: 2 537 223 Baffin: 2 246 549 New Guinea: 1 953 689 Cuba: 2 643 140 b Madagascar; 578 041 – 507 451 = 70 590 square kilometres c New Guinea (800 000 km2) + United Kingdom (200 000 km2) What did you learn? 1 a Estimate: 200 000 + 10 000 + 10 000 = 220 000 190 991 + 12 234 + 14 568 = 217 793 b Estimate: 3 000 000 + 2 000 000 = 5 000 000 3 132 819 + 2 343 214 = 5 476 033 c Estimate: 2 000 000 + 6 000 000 = 8 000 000 2 112 345 + 6 123 145 = 8 235 490 d Estimate: 100 000 – 30 000 = 70 000 113 285 – 29 873 = 83 412 e Estimate: 3 000 000 – 1 000 000 = 2 000 000 3 229 876 – 1 314 388 = 1 915 488 f Estimate: 8 000 000 – 2 000 000 = 6 000 000 8 234 000 – 1 939 453 = 6 294 547 C Multiplication and division Page 24 1 a Estimate: 3000 8 = 24 000 3006 8 = 24 048 b Estimate: 2000 10 = 20 000 2406 9 = 21 654 c Estimate: 3000 7 = 21 000 3008 7 = 21 056 d Estimate: 90 100 = 9000 87 98 = 8526 e Estimate: 300 50 = 15 000 312 45 = 14 040 f Estimate: 400 90 = 36 000 423 87 = 36 801 g Estimate: 100 200 = 20 000 145 208 = 30 160 h Estimate: 900 40 = 36 000 876 39 = 34 164



i Estimate: 400 600 = 240 000 412 602 = 248 024 j Estimate: 300 500 = 150 000 342 456 = 155 952 k Estimate: 300 300 = 90 000 298 342 = 101 916 l Estimate: 600 40 = 24 000 612 43 = 26 316 m Estimate: 4 000 50 = 200 000 4 123 45 = 185 535 n Estimate: 1 000 200 = 200 000 1 467 234 = 343 278 o Estimate: 12 000 300 = 3 600 000 12 098 312 = 3 774 576 2 a Estimate: 800 ÷ 10 = 80 800 ÷ 7 = 114 r 2 b Estimate: 300 ÷ 10 = 30 345 ÷ 6 = 57 r 3 c Estimate: 900 ÷ 10 = 90 872 ÷ 8 = 109 d Estimate: 800 ÷ 20 = 40 786 ÷ 24 = 32 r 18 e Estimate: 800 ÷ 30 = 26 r 20 832 ÷ 25 = 33 r 7 f Estimate: 300 ÷ 20 = 15 347 ÷ 23 = 15 r 2 g Estimate: 1000 ÷ 20 = 50 1 345 ÷ 21 = 64 r 1 h Estimate: 3000 ÷ 10 = 300 3 214 ÷ 13 = 247 r 3 i Estimate: 5000 ÷ 70 = 71 r 30 5330 ÷ 65 = 82 j Estimate: 13 000 ÷ 30 = 433 r 10 12 765 ÷ 27 = 472 r 21 k Estimate: 14 000 ÷ 70 = 200 14 235 ÷ 70 = 203 r 25 l Estimate: 11 000 ÷ 50 = 220 10 819 ÷ 51 = 212 r 7 3 a $1245.80 ÷ 4 = $311.45 per person b $1241.75 ÷ 5 = $248.35 per person c $218.97 ÷ 3 = $72.99 per person d $2036.40 ÷ 6 = $339.40 per person e $254.60 ÷ 4 = $63.65 per person Problem-solving 4 3600 cm ÷ 15 = 240 cm per present. 5 381 cm ÷ 23 = 16 r 13 Each piece is 16 cm long. 6 128 502 = 64 256 pages 7 624 (52 – 2) = 624 50



= 31 200 cakes per year 8 1276 ÷ 58 = 22 Each crate should have 22 pineapples. Page 25 9 460 ÷ 24 = 19 r 4 The 4 remaining students could be used as the leaders of the parade. 10 $10.00 – $8.25 = $1.75 She saves $1.75 per week. $25.00 ÷ $1.75 = 14 r 50 It will take Jasmine 15 weeks to save $25. 11 $257.00 23 = $5911.00 for all the motors. 12 850 ÷ 12 = 70 r 10 Hyacinth will use about 71 litres of petrol. 13 a 36 80¢ = $28.80 per box b 1100 ÷ 36 = 30 r 20 The tuck shop will need 31 boxes. c (31 36) 80¢ = 1116 80¢ = $892.80 per week d $1.00 – $0.80 = $0.20 1100 20¢ = $220.00 profit per week 14 48 52 = 2496 seats 15 8760 ÷ 24 = 365 L per single journey 16 a (9 $23.00) + (25 $12.00) + (32 $16.00) = $207.00 + $300.00 + $512.00 = $1 019.00 b 896 ÷ 16 = 56 students What did you learn? 1 a 325 6 = 1950 b 754 38 = 28 652 c 107 39 = 4173 d 98 ÷ 17 = 5 r 13 e 130 718 ÷ 6 = 21 786 r 2 f 34 213 ÷ 34 = 1006 r 9 2 2462 ÷ 32 = 76 r 30 He can fill 76 crates; 30 mangoes are left over. Challenge 3 23 14 = 322 cm Perimeter: (2 322) + (2 23) = 644 + 46 = 690 cm Area: 322 23 = 7406 cm2 D Problem-solving strategies Page 27 Problem-solving 1 a 10 9 8 = 720



b 579 2 $25.00 – $16.00 = $9.00 $9.00 ÷ 2 = $4.50 $4.50 + $16.00 = $20.50 The card cost $4.50. 3 B = 14 squares C = 26 squares Page 28 4 a 7 + 1, 6 + 2, 5 + 3 b 7 + 2 + 1, 6 + 3 + 1, 5 + 3 + 2, 4 + 5 + 1 5 (15 5) 48 = 75 48 = 3600 dinghies a year 6 a 1 b 10 c 45

d

7 a 15 + x = 20 x = 5 b a – 10 = 30 a = 40 c 15 – b = 10 b = 5 d x ÷ 2 = 22 x = 44 e 2 y = 30 y = 15 f x x = 16 x = 4 8 (60 – 34) + 3 = 26 + 3 = 29 years old 9 $ 66.60 Challenge 10 Charles White What did you learn? 1 a 1.904 m is longer. 1.904 – 1.895 = 0.009 m b 4.5 – (1.904 + 1.895) = 4.5 – 3.799 = 0.701 m is still needed. 2 a 10 10¢ 5 20¢ 4 25¢ 2 50¢ 50¢ + 25¢ + 25¢ 50¢ + 20¢ + 20¢ + 10¢ 20¢ + 20¢ + 20¢ + 20¢ + 10¢ + 10¢ (etc.)



Topic 3 Review Page 29 Key ideas and concepts A Mental strategies: revise strategies for +, –, x, ÷. Develop strategies for percentages and fractions of amounts. B Addition and subtraction: use written methods to + and –. Regroup numbers in any place. Estimate. C Multiplication and division; use pen-and-paper methods to and ÷ using larger numbers. Solve and ÷ problems. D Problem-solving strategies; revise strategies. Use appropriate strategies to solve different problems. Quick check 1 a $349 b $670 c $1800 d $1250 e $467.10 2 a 12 345 + 9987 = 22 332 b 12 098 – 3945 = 8153 c 23 412 9 = 210 708 d 4123 45 = 185 535 e 2314 ÷ 11 = 210 r 4 f 43 126 ÷ 21 = 2053 r 13 3 857 ÷ 55 = 15 r 32 They will need 16 buses. 5 good – better – best good – best – better better – good – best better – best – good best – better – good best – good – better 6 12 4 = 48 11 3 = 33 48 + 33 = 81 7 x – 9 = 5 8 x = 49

Topic 4 Shape and space (1) Page 30 The students will continue to revise their understanding of lines, angles and 2-D shapes. They will now move further on and start measuring the angles. Make sure they use the protractor correctly and that they label their angles accurately. Have a few quizzes in class to check their understanding of quadrilaterals and triangles. Repeat the information numerous times so it becomes easy knowledge for the students to recall. A Angles and lines Page 33 1 a–b MNO: obtuse angle MNP: right angle PNO: acute angle 2 a Obtuse b Straight angle



c Obtuse d Right angle e Acute f Acute 3 a Angle ABC = 90° b Angle MNO = 20° c Angle PQR = 60° d Angle DEF = 125° e Angle GHI = 150° f Angle JKL = 175° 4 a 50° b 95° c 70° d 160° e 140° f 90° 5 a 45° b 100° c 70° d 160° e 120° f 90° Investigate 7 0° on the vertices, and the one line on the line of the protractor showing 0°. 8 Draw a line to start. Place the 0° on the one point of the line you have drawn. Plot the point where 115° is shown on the protractor. Remove the protractor and draw a line from the point where you placed the protractor to the marking on your page for 115°. Make sure the students label their angle drawing XYZ. Page 35 9 a 14 acute angles b Greatest = 120°; smallest = 2° c 115°, 155°, 98°, 130°, 140° d 10 pairs of parallel lines e 26 90° angles / 12 perpendicular lines What did you learn? Student’s drawings B Shapes and their properties Page 37 1 a Triangle b Pentagon c Quadrilateral d Circle e Quadrilateral f Quadrilateral g Quadrilateral h Quadrilateral i Triangle j Quadrilateral k Pentagon l Quadrilateral 2 a Circumference b Radius c Diameter d Centre 3 2.5 cm 2 = 5 cm 4 11 cm 5 2.5 km ÷ 5 = 0.5 = 500 m 6 Right angle, acute angle, obtuse angle, right angle Page 38 Problem-solving

7 25 ÷ 2 = 12 cm



Page 39 8 a Opposite sides are equal in length and parallel to each other. The opposite angles

are equal in size = parallelogram. b Four right angles, opposite sides are equal in length and parallel to each other = rectangle.

c Only one pair of parallel sides, which are not equal in length = trapezium. d Two pairs of equal sides that lie next to each other = kite. e Four sides of equal length and four right angles. Opposite sides are parallel to each

other = square. 9 a A pair of parallel sides. b Opposite sides parallel and opposite angles equal. c Four right angles, opposite sides parallel. 10 a, c, d, f 11 a True – opposite sides equal in length and parallel, opposite angles equal in size. b False – all four sides are not right angles, all four sides are not equal in length. c True – opposite sides equal in length and parallel, opposite angles equal in size. d False – all four angles are not right angles. What did you learn? 1 Student’s drawing 2 a Square, rectangle, parallelogram, rhombus b Square, rhombus c Square, rectangle, parallelogram, rhombus d Square, rectangle C Classifying triangles Page 41 3 a Acute-angled triangle b Obtuse-angled triangle c Isosceles triangle d Equilateral triangle e Right-angled triangle 4 a 5 cm b 180° – (90° + 60°) = 180° – 150° = 30°

c The longest side is opposite the biggest angle. The shortest side is opposite the smallest angle.

d 6 cm e 60° + 50° + 70° 70° + 30° + 80° 60° + 40° + 80° Challenge 5 a 130°; scalene triangle b 90°; right-angled triangle c 30°; isosceles triangle d 99°; scalene triangle What did you learn? 1 Equilateral 2 90°



3 Yes 4 No, the three angles inside a triangle must add up to 180°. D Shapes around us Page 42 1 The triangular shape on each frame helps to distribute the weight more evenly, putting less pressure on one specific side. Topic 4 Review Page 43 Think, talk, write … 1 It is easy to explain shapes to people. Quick check 1 Obtuse angle 2 Rectangle, square 3 No, a parallelogram has to have two pairs of sides parallel and a trapezium on has one. 4 Yes 5 Divide the diameter by two to get the radius. 6 ABCD = square ABFE, CDEF = rectangles ABC, ADC, ABD, BCD = isosceles triangles EHMJ, GHMI, MIFL, LMJK = kites IDF, HEC, EJB, ALF = scalene triangles FIM, FLM, MHE, MJE = right-angled triangles AGBM, MDKC = quadrilaterals

Topic 5 Number sense (2) Page 44 It is important for the students to master working out different types of fractions. Work carefully through this topic to prevent any misconceptions with fractions, decimals, percentages, ratio and proportion. A Revisit fractions Page 47

1 a 3 b 6

c 12 d 13

2 a b

c d

3 a Yes b No c No

4 a b

c d

e

5 a b



c d

e

6 a b

c d

e f

g h

i j

7 a b

c d

e f

g h

i j

8 𝟏

𝟓 = = =

𝟐

𝟕 =

𝟓

𝟖 = =

𝟑

𝟒 = = =

9 a , , , , , ,

b , ,

c , ,

Problem-solving

10

Ordering and comparing fractions Page 48

1 a b

c d

e f

2 =

=

=

=



=

=

=

=

, , , , , , ,

Page 49

3 a , = , =

Descending: , ,

b = , = ,

Descending: , ,

c = , = , = , =

Descending: , , ,

d = , = , =

Descending: , ,

e = , = , = , = , =

Descending: , , , ,

f = , = , = , , =

Descending: , , , ,

Problem-solving

4 a and b 0 and

c and d and

e and f and 1

5 a kg, kg, kg, kg, kg, kg

b kg, kg, kg

6 a , , , ,

b All of the students What did you learn?

1 Set A: =

Set B: =

2 <

Alex has completed more homework.



3 a

b

c

4 LCD = 60

, , , , ,

B Revisit decimals Page 51 1 a 115.8 km/h b $45.95 c 39.9 kg d 97.2% e 49.55 cm 2 a 23.07 < 23.4 b 67.91 < 67.92 c 7.74 > 7.47 d 1.99 > 1.9 e 300.99 > 300.09 f 3.6 < 3.65 3 a 806 b 6 095 c 4 d 20 e 674 f 20 4 a 42.8 b 69.2 c 65.2 d 81.9 e 10.0 f 12.1 5 Colin, Denae, Benni, Andre 6 3.9 m, 3.5 m, 3.35 m, 3.09 m, 3.05 m Problem-solving 7 a 82.67 m, 84.38 m, 84.39 m, 84.58 m, 85.28 m, 85.38 m b 84.58 m, 85.28 m, 85.38 m c 90.57 m – 85.38 m = 5.19 m further to reach to reach the Olympic record, 5.2 m to

beat the record. d 85.38 m + 0.3 m = 85.68 m What did you learn? 1 a 12.78, 12.92, 13.29, 13.51, 13.58 b 0.03, 0.20, 0.2, 0.23, 0.3 2 a 13, 12.9 14, 13.6 13, 13.3 14, 13.5 13, 12.8 C Fractions, decimals and percentages Page 53

1 a =

b =

c =

d =

e =



2 a 20% b 90% c 24% d 14% e 60% f 45% g 63% h 38% 3 a 0.12 b 0.98 c 0.02 d 0.8 e 0.07 f 1.8 4 a 13% b 9% c 65% d 99% e 60% f 150% g 250% h 42% i 1% j 100% 5 0.5 > 0.05 (True)

1 > 0.75 (True)

4.3 < 4.03 (False)

= 63% (True)

< 0.8 (True)

= 0.20 (True)

2.05 < 2.50 (True)

0.67 > (True)

The End What did you learn?

1 =

2 =

3 =

4 =

5 =

D Ratio and proportion Page 54 1 a Dean got $20 b Jay got $32 c $30:$15

2 a b

c d

3 a 2:3 b 3:4 c 1 cm:4 cm d 1:10 4 a 2:5 = 4:10, 6:15, 8:20, 10:25, 12:30 b 1:2 = 2:4, 3:6, 4:8, 5:10, 6:12 c 4:7 = 8:14, 12:21, 16:28, 20:35, 24:42 d 7:8 = 14:16, 21:24, 28:32, 35:40, 42:48 e 4:5 = 8:10, 12:15, 16:20, 20:25, 24:30



Page 55 5 a 1:3 b 2:3 c 1:4 d 3:4 e 2:3 6 a 6 kg:3 kg b 65:35 c 20:80 d 15:60 7 a

Girls BoysX X X X XX X X X X X X X X XX X X X X X X X X X X X X X X

b 30 girls c 16 boys 8 a 4 eggs b 1 egg c 5 eggs Problem-solving 9 a 50:100/1:2 b 20:100/1:5 c 80:100/4:5 10 a

Small collection Big collectionX X X X X XX X X X X X X X X X X XX X X X X X X X X X X X X X X X X X

b 40:80 Page 56 11 Janine picked 33 mangoes, Shay picked 21 mangoes. 12 a

Kershaw JayX X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X

X X X X X X X X X X X X X X X X X

b 34 mangoes c 17 mangoes What did you learn? 1 a 9:10 b 11:8 c 10:9 d 1:1 2 150 ml red paint and 250 ml blue paint 3 $32 and $48 respectively Topic 5 Review Page 57 Quick check

1 a

b



2 a 0.7; 70% b 1.3; 130% c 0.5; 50% d 0.8; 80% 3 a 1.43 b 0.83 c 45.93 d 0.13 e 4.03 f 0.03 4 0.9 kilometres

5

6 50%, 60%, 80%, 70% Descending: 80%, 70%, 60%, 50%

7 1:1, , 50%

Topic 6 Computation (2) Page 58 Computation of fractions – addition, subtraction, multiplication and division – all require important rules to adhere to. Revise the rules already taught and repeat all the rules as often as possible to avoid any misconceptions in class. A Calculating with fractions Page 60

1 a b = 2

c = d = 1

e 1 f =

g 2

h 7 – 3

= 4

= 4

i –

=

j 1

k –

=

= 2

l –

=

= 2

m 1 –

= 1

= 1



n 2 – 1

= 1

o 3 – 2

= 1

p 2 – 1

= 1

q 1 = 2 r 1 = 2

s 5 = 6 t 9 = 10

Page 61

2 a +

= +

=

= 1

b +

= +

=

= 1

c +

= +

=

= 1

d +

= +

=

= 1

e +



= +

=

= 1

f +

= +

=

= 1

g –

= –

=

h –

= –

=

i –

= –

=

j –

= –

=

k –

= –

=

=

l –

= –

=



3 a 3 = 4

b 1 + 1

= 1 + 1

= 2

c 2 + 3

= 2 + 3

= 5

d 1 + 4

= 1 + 4

= 5

e 3 +

= 3

= 4

f 4 + 2

= 4 + 2

= 6

= 7

g 2 + 3

= 2 + 3

= 5

h 3 + 1

= 3 + 1

= 4

= 5

i 2 + 1

= 2 + 1



= 3

j 3 + 2

= 3 + 2

= 5

= 5

k 3 + 2

= 3 + 2

= 5

= 6

l 1 + 3

= 1 + 3

= 4

= 5

4 a 4 – 1

= 4 – 1

= 3

b 3 – 1

= 3 – 1

= 2

c 4 – 2

= 4 – 2

= 2

d 3 – 1

= 3 – 1

= 2

e 5 – 3



= 5 – 3

= 4 – 3

= 1

f 4 – 1

= 4 – 1

= 3 – 1

= 2

g 5 – 2

= 5 – 2

= 4 – 2

= 2

= 2

h 4 – 2

= 4 – 2

= 3 – 2

= 1

i 4 – 2

= 4 – 2

= 3 – 2

= 1

j 4 – 1

= 4 – 1

= 3 – 1

= 2

k 1 –

= –



=

l 7 – 4

= 7 – 4

= 6 – 4

= 2

= 2

5 a + +

= + +

=

b + +

= + +

=

= 2

c – –

= – –

=

=

d + –

= + –

=

e + –

= + –

=

= 1

f – +

= – +



=

g 2 + 2 – 2

= 2 + 2 – 2

= 2

= 3

h 4 – 1 + 3

= 4 – 1 + 3

= 6

i 2 + 3 – 3

= 2 + 3 – 3

= 2

j 3 + 2 – 2

= 3 + 2 – 2

= 5 – 2

= 4 – 2

= 2

k 2 – 1 + 3

= 2 – 1 + 3

= 4

= 5

l 2 – 1 + 3

= 2 – 1 + 3

= 1 – 1 + 3

= 3

= 4



Problem-solving

6 a x – 4 = 1

x = 5

b 3 + x = 5

x = 2

c x – 2 = 3

x = 5

7 3 + 1 + +

= 3 + 1 + +

= 5 cups

8 14 – 12

= 14 – 12

= 2 lengths more

9 12 + 12 + 4 + 4

= 12 + 12 + 4 + 4

= 34 m

10 + +

= + +

=

– = of the garden is left for flowers

Multiplying fractions Page 63

1 a b

c d

e f

g 10 h

2 a b

c d

e = f



g h

i = 2 j = 3

k l

3 a b =

c = d

e f

g 1 h 1

4 a –

= –

= –

=

=

b ( + )

=

=

c +

= +

= +

=

d +

= +

= +

=

e –

= –

= –



=

f + –

= + –

= + –

=

= 1

g +

= +

= +

=

= 1

h ( + )

=

=

=

i –

= –

= –

=

Problem-solving

5 a

= 64 red T-shirts

b

= 80 green T-shirts

c

= 120 blue T-shirts

d 320 – 264 = 56

= T-shirts are white



6 = km still to go

7

= 725 mangoes have been sold

8 of 320 = 64 students do not walk to school

9

= m2

Dividing fractions Page 65

1 a b

c d

e f

g h

i j

2 a

b

c

d

e

3 a = b =

c = d =

e = = 1

4 a =

n = 3

b =

n = 3

c =

n = 6

d =

n = 8

5 a =

= 1

b =



c =

d =

=

e =

= 2

f =

g =

h =

i =

j = 10

Problem-solving 6 25 times around the block 7 15 children in the class 8 34 lengths What did you learn?

1 4 – 2 = 2

2 3 – 2

= 3 – 2

= 1

3 5 + 2

= 7 +

= 7

= 8

4 = 14

5 =

6 =

=

7 +

= +

= +

=



= 1

8 ( – )

=

=

9 + 1

= + 1

= + 1

= 1

= 1

10 =

11 =

= 1

12 =

= 1

B Calculating with decimals Page 66 1 a 0.6 b 0.9 c 0.9 d 0.2 e 1.1 f 0.43 g 0.33 h 1.2 i 0.5 j 0.3 k 0.7 l 0.1 m 1.5 n 1.2 o 12.0 p 1.7 Page 67 2 a 0.23 + 0.93 = 1.16 b 0.37 + 0.65 = 1.02 c 0.42 + 0.55 = 0.97 d 0.28 + 0.67 = 0.95 e 1.49 + 0.99 = 2.48 f 2.34 + 0.07 = 2.41 g 4.09 + 2.80 = 6.89 h 5.32 + 5.48 = 10.8 i 0.87 – 0.43 = 0.44 j 0.90 – 0.65 = 0.25 k 0.86 – 0.40 = 0.46 l 0.40 – 0.23 = 0.17 m 14.30 – 3.09 = 11.21 n 12.09 – 4.50 = 7.59 o 5.45 – 0.99 = 4.46 p 3.67 – 2.80 = 0.87 q 16.000 – 5.234 = 10.766 r 9.000 – 1.008 = 7.992 s 25.000 – 14.809 = 10.191 t 342.00 – 45.09 = 296.91 3 a 5.99 + 15.32 + 231.09 = 252.4 b 214.6 + 87.99 + 234.9 = 537.49 c 612.5 + 132.09 + 99.5 = 844.09 d 231.9 + 54.3 + 9.085 = 295.285 e 325.300 – 124.865 = 200.435 f 243.00 – 124.55 = 118.45



g 412.890 – 128.805 = 284.085 h 100.000 – 45.087 = 54.913 4 a $5.87 + $500.00 + $235.50 + $100.99 = $842.36 b 6.876 km + 500.000 km + 1.2000 km = 508.076 km c 56.004 seconds + 12.500 seconds = 68.504 seconds d 78.13 kg – 32.95 kg = 45.18 kg e 300.000 L – 234.565 L = 65.435 L f 12 cm + 12.3 cm + 3.4 cm + 0.9 cm = 28.6 cm Problem-solving 5 50 m – (13.5 m + 8.25 m) = 50.00 m – 21.75 m = 28.25 m 6 0.75 + 1.08 = 1.83 kg 7 $40.00 – $28.75 = $11.25 8 123.65 + 132.08 + 109.00 = 364.73 km 9 1.800 + 1.090 + 2.400 + 1.875 + 2.000 + 2.050 = 11.215 km 10 1.2 + 2.45 + 1.5 + 0.459 + 0.2 + 0.25 = 6.059 kg Yes, he can take his bag as hang luggage. Multiplying and dividing decimals Page 68 1 a 36 b 65 c 4 d 12 e 0.02 f 120 g 4.56 h 8 i 0.04 j 2.35 k 1.62 l 0.25 2 a 4.5 4 = 18 b 2.4 8 = 19.2 c 3.7 5 = 18.5 d 3.23 3 = 9.69 e 1.25 6 = 7.5 f 3.42 9 = 30.78 g 3.45 12 = 41.4 h 4.56 20 = 91.2 i 25.4 31 = 787.4 j 2.8 25 = 70 k 9.13 25 = 228.25 l 0.89 13 = 11.57 m 8.7 30 = 261 n 0.76 23 = 17.48 o 24 8.25 = 198 p 21 4.55 = 95.55 Page 69 Problem-solving 3 25 12.68 = $317.00 for 25 m 4 12 345 ÷ 100 = $ 123.45 per guest 5 a 10 000 1.99 = $19 900 was raised b 19 900 ÷ 100 = $199.00 was given to each charity 6 a 0.9 ÷ 3 = 0.3 b 0.8 ÷ 4 = 0.2 c 1.2 ÷ 4 = 0.3 d 4.9 ÷ 7 = 0.7 e 6.4 ÷ 8 = 0.8 f 0.36 ÷ 2 = 0.18 g 3.6 ÷ 12 = 0.3 h 0.24 ÷ 4 = 0.06 7 a 114 ÷ 5 = 22.8 b 11.4 ÷ 5 = 2.28 c 907.92 ÷ 12 = 75.66 d 9 079.2 ÷ 12 = 756.6 e 77.76 ÷ 32 = 2.43 f 777.6 ÷ 32 = 24.3 g 838.35 ÷ 15 = 55.89 h 8 383.5 ÷ 15 = 558.9



8 a 116.8 b 15.99 c 1.15 d 1.47 What did you learn? 1 a $32.65 + $23.08 – $12.00 = $43.73 b 6.51 kg + 14 kg + 12.8 kg = 33.31 kg c 32.85 ÷ 15 = 2.19 d 23 12.86 = 295.78 2 a 12 0.9 = 10.8 b 1.9 2 = 3.8 c 0.8 80 = 64 3 12.8°C + 4.8°C = 17.6°C at noon 17.6°C + 2°C = 19.6°C in the afternoon 19.6°C – 2.9°C = 16.7°C in the early evening 16.7°C – 8.4°C = 8.3°C at midnight C Mixed problems Page 70

1 2 kg + 3 kg + 2 kg

= 2 + 3 + 2

= 7

= 8 kg

2 2 L – 1 L

= 2 – 1

= 1 – 1

= litres

3 a 364.25 5 = 1 821.25 days b 225.835 days 4 a 13.36 ÷ 4 = 3.34 m / 334 cm b 24.99 ÷ 3 = 8.33 m / 833 cm c 17.75 ÷ 5 = 3.55 m / 355 cm 5 a i 21.96 m ÷ 12 = 1.83 m ii 49.20 m ÷ 15 = 3.28 m iii 35.88 m ÷ 13 = 2.76 m b $23.65 15 = $354.75 Topic 6 Review Page 71 Key ideas and concepts 1 find the lowest common denominator 2 simplify the fractions first 3 are adding 4 when you invert a fraction during division of fractions 5 you multiply the numbers instead once you have found the reciprocal of the last number 6 line the digits up according to where the decimal point is found



7 to place the decimal point in the product so that there are the same number of decimal places after the decimal point as there were altogether in the factors 8 you place the decimal point in the quotient above the decimal point in the dividend Quick check

1 a +

= +

=

= 1

b 2 +

= 2 +

= 2

c –

= –

=

d 2 – 1

= 1 – 1

=

e 60 = 40

f $24 = $18

g $10 = $7.50

h =

i =

j – +

= – +

=

= 1 / 1

k – + )

= – + )

= –

=

=



l +

= +

= +

=

=

m

=

n

=

o

=

= 7

2 a 4.700 + 12.650 + 0.812 + 12.000 = 30.162 b 18.80 – 9.25 = 9.55 c 2.000 – 0.875 = 1.125 d 1.5 6 = 9 e 0.12 7 = 0.84 f 0.2 12 = 2.4 g 2.46 ÷ 3 = 0.82 h 0.27 ÷ 3 = 0.09 i 1.75 ÷ 13 = 0.135 Problem-solving 3 13 $5.50 = $71.50 4 88.5 m 25 = 2212.5 m

Test yourself (1) Page 72 1 a 3 025 203 b 99 463 2 a Two million three hundred and twelve thousand and sixty-five b Four million one hundred thousand eight hundred and seventy-six c Nine million ninety-eight thousand and eighty-nine 3 a 140°: obtuse angle b 60°: acute angle c 90°: right angle 4 a 2304 b 2688 c 12 499 r 1 d 12 648 5 a 11

b 5



c

d

6 a 1 + 2

= 3 +

= 3

= 4

b 6 – 4

= 1

c

=

d

=

7 a

b =

c 4 = 4

d 5 = 5

8 a 4.33 b 15.25 c 0.004 d 18.4 e 2 345 f 1.81 g 2.45 h 19 i 315 9 a 0.8 b 194.12 c 19.16 d 1.00 Page 73 10 a Parallelogram b 4 c 4 d 2 pairs

11 a =

b

c 1 = 1

d 2 = 2

12 a 50% b 80% c 125% d 24% 13 a 0.85



b 0.05 c 0.255 d 2.00 14 a A: $15 B: $75 C: $25 D: $28 b A: $85 B: $25 C: $75 D: $72 c A: $20.87; $79.13 change B: $75.80; $24.20 change C: $22.49; $77.51 change D: $30.03; $69.97 change 15 A: right-angled triangle; one of the angles is 90° B: scalene triangle; no angle is the same size C: acute-angled triangle; all the angles are smaller than 90° 16 a 1 429 r 9 b 616 664 c 170 554 d 329 111

17 of 115 = 69 km/h

18 16.68 kg ÷ 8 = 2.085 kg each 19 300 m $40.78 = $12 234 20 $156 ÷ 400 = $0.39 21 $20.67 38 = $785.46

Topic 7 Measurement (1) Page 74 Understanding the different systems used for measuring, being able to measure length, mass and capacity, and understanding scale drawings are practical life skills. Allow the students to learn from each other, but be on hand to assist where it is needed. A Measuring systems and units Page 76 3 a ml b L c kl d kl 4 a A laptop computer, a bag of sweet potatoes, a small car

b The distance from the halfway line on a football field to the goalposts, the distance a person can walk in 10 minutes, the distance a car can drive in 5 minutes

Problem-solving 6 $2.20 + (8 $0.80) = $2.20 + $6.40 = $8.60 Page 78 12 a Conversion from kilometres to miles



b 25 miles c 40 kilometres d 40 miles is further Page 79 13 a 2.5 L b 3000 g c 5.5 centilitres d 2.5 grams 15 a 35 000 g b 0.56 kg c 450 g d 0.025 kg e 25 000 ml f 3.2 L g 375 ml h 1500 ml i 1 500 m j 2.5 km k 3.5 cm l 320 cm Page 80 Problem-solving 16 150 g of salt is more than 1 500 milligrams of salt 17 0.5 m, 1.15 m, 2 500 mm, 350 cm, 1.20 m 18 a To convert pints to quarts, divide by 2. b To convert inches to feet, divide by 12. c To convert quarts to gallons, divide by 4. 19 a 63 inches b 0.75 gallons c 16 pints d 2 feet e 72 inches What did you learn? 1 a pound, kilogram, gram, stone, ounce, milligram b Metric: kilogram, gram, milligram Customary: pound, gallon, stone, ounce c kilogram, pound 2 a 4 L b 230 m c 987 g d 24 500 m e 19 400 L f 23 500 g 3 2 litres is more. 2 gallons = 9.09 litres B Length and scale diagrams Page 81 1 a mm b m c mm d km e m f km g mm h cm i m 2 a 6 cm, 60 mm b 5.2 cm, 52 mm c 2.1 cm, 21 mm d 1.3 cm, 13 mm Page 82 Problem-solving 4 3.84 m + 6.76 m = 10.6 m 5 a Henry walked further.



b 3125 m – 2670 m = 455 m further Page 83 7 a It is an accurate drawing that shows something at a smaller size than it really is. b Chichen Itza: 130 m Eiffel Tower: 310 m Petronas Towers: 460 m c 1:100 (100 times larger) 8 a 2 cm = 5 km b 1 cm = 25 000 km c 1 cm = 10 m 9 a 2.1 cm b 3.6 cm c 6.1 cm d 7.7 cm 10 a 1050 m b 1800 m c 3050 m d 3850 m 11

As the crow flies Along the road a 350 m 660 mb 520 m 700 mc 320 m 320 md 470 m 530 me 340 m 480 mf 350 m 350 mg 290 m 390 mh 760 m 1 010 m

12 a Long Street to High Street then Main Street. b 920 metres Page 84 13 a 4080 m b 1460 m c 3840 m d 3480 m e 2280 m f 1100 m g 1620 m 14 a 1100m b 800 m c 1420 – 1100 = 320 m further for Sue 2520 – 800 = 1720 m further for Carol 15 8 cm 16 16 cm apart on the map 17 5.5 cm 18 75 mm What did you learn? 2 a 1 cm line b 6 cm line c 2.5 cm line 3 1 625 m / 1.63 km C Mass Page 85 1 a 10 tonnes b 7 kg c 1 gram d 300 g



e 3.5 kg f 1 tonne g 1 kg h 200 g 2 a 0.550 kg + 1.200 kg + 0.233 kg = 1.983 kg b 0.420 kg + 1.500 kg + 0.908 kg = 2.828 kg c 0.960 kg + 0.850 kg + 0.500 kg = 2.31 kg 3 a 0.420 kg b 1.518 g c 1 220 kg d 0.037 t e 400 mg f 80 g 4 2 400 g ÷ 5 = 480 g each Page 86 5 4.72 t – 3.18 t = 1.54 t 6 (400 g 42) + 900 g = 16 800 + 900 = 17 700 g = 17.7 kg 7 56 000 ÷ 500 = 112 packets can be filled 8 a 85 kg – 70 kg = 15 kg is what she needs to lose b 15 ÷ 12 = 1.25 kg per week over 12 weeks 9 2 000 000 ÷ 625 = 3 200 bricks 10 a 75 g b 4.75 kg c 290 g d 925 g What did you learn?

1 4000 mg, 800 g, 2 500 g, 2.6 kg, 2 kg

2 3600 ÷ 30 = 120 g each 3 1000 ÷160 = 6.25 7 cricket balls 1000 ÷ 58 = 17.24 18 tennis balls D Capacity Page 87 2 a millilitres b litres c litres d millilitres e millilitres 3 a 0.125 L b 0.015 L c 0.0025 L d 0.306 L e 2.498 L f 0.05139 L g 31 L h 0.2168 L 4 a 1960 ml b 3006 ml c 16 000 ml d 2400 ml e 670 ml f 81 000 ml g 57 ml h 300 ml 5 A: 75 ml B: 150 ml C: 200 ml D: 50 ml



Page 88 Problem-solving 6 3300 ml ÷ 200 = 16.5 You can pour 16 cups of water. 7 140 ÷ (4 5) = 140 ÷ 20 = 7 days 8 a 5.370 + 3.5 + 1.75 + 3.708 = 14.328 L b 15.000 – 14.328 = 0.672 L 9 a 200 7 = 1400 L of water is lost per week b 900 000 – 600 = 899 400 L is left. 10 a 16.7 L b 43.3 L What did you learn? 2 5000 ml 3 18 330 = 5940 ml Sally bought 5.94 L of juice. Topic 7 Review Page 89 Key ideas and concepts 1 Millimetres, centimetres 2 They are units that measure length. 3 Salt (anything light) 4 2.75 g = 2750 mg 5 The container can hold a kilolitre of liquid. 6 1 cm on a diagram is the same as 200 cm/m/km in real life. Quick check 1 a Kilometres/metres b Millilitres 2

Kilo- Hecto- Deca- Metre Deci- Centi- Milli- 1 000 m 100 m 10 m 1 m 0.1 m 0.01 m 0.001 m

3 a 0.025 cm, 1.8 cm, 0.3 m, 32 cm, 330 mm b 37.8 cm, 0.99 m, 1 300 mm, 150 cm, 2.2 m 4 a 100 1.35 m = 135 m b 1 000 1.35 m = 1 350 m 5 3400 ÷ 100 = 34 beakers 6 10 cm 7 6.5 20 = 130 miles apart 8 45 ÷ 15 = 3 cm apart

Topic 8 Data handling (1) Page 90 Revise data handling completed in previous levels before introducing new skills for the students to develop. Work through the different methods of collecting data, how to organise data and working out averages. Assist any students who may require extra assistance.



A Collecting and organising data Page 92 1 a ‘Do you buy food from the school canteen?’ They are not trying to work out who does or does not buy food from the canteen. b ‘Do you like pink or blue best?’ This question is asking for a preference between two colours only. 2

Data Possible source Some methods The sports games that will be on television during the next week

The Internet, the radio, television, magazines

Reading, browsing the Internet

The land area of my country and the five nearest Caribbean countries

Reference books, the Internet, television, magazines, experts in specific subjects

Reading, asking questions, browsing the Internet, interview people

Favourite sports teams of the children at my school

People around us (family, friends, community members, leaders, strangers)

Observation, asking questions, telephone survey, interview people, survey, questionnaire

Interest rates local banks pay on savings accounts

The Internet, the radio, television, magazines, People around us (family, friends, community members, leaders, strangers), shops and businesses, experts in specific subjects

Reading, asking questions, browsing the Internet, telephone survey, interview people

How children in my school get to school (for example, by walking, by bus or by taxi)

People around us (family, friends, community members, leaders, strangers)

Observation, asking questions, telephone survey, interview people, survey, questionnaire

Page 93 4 a 17 boys b 19 girls c 1 more girl than boy d 35 boys in total e 33 students in total 5 a Through sales

b It helps the business to know what is selling well so they make sure they have enough in stock to supply customers and helps them to not bring in unnecessary large amounts of unwanted goods.

c 35 + 214 = 249 d 113 – 43 = 70 6

Item Tally Frequency Sandwich IIII 5Cookies IIII II 7Cold drink IIII 4Fruit IIII 4Chocolate II 2



Page 94 What did you learn? 1 Data is a set of values that become information when viewed in context. Latin word meaning large quantity of information. B Averages Page 95 1 a 13 b 19 c 3 d 33 2 a 14. It is the number that appears the most. b 14 3 a 15 b 15 Page 96 Problem-solving 4 a $18.81 b $20.46 5 a Ryan. Mean: add the goals together and divide by 5. b Benoni as there is less chance of him scoring. c Ryan and Jo as they have the highest strike rate. Investigate 6 a 19. It is the value of the middle number of the set of numbers. What did you learn? 1 a mean b the number that appears the most 2 a $55.00 b $34.00 Topic 8 Review Page 97 Quick check 1 a Prices of mobile phones b Internet c $35.37 d No, this is the average cost of a mobile phone from a range of different phones. e $39.99 f $49.99

Topic 9 Number sense (3) Page 98 Classifying numbers as odd or even, composite or prime helps the students to understand numbers better. Continue to work through this with the students, as well as factors, multiples, prime factorisation and Roman numerals. A Classifying numbers Page 100 1 a 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149 b 42, 44, 46, 48, 50, 52, 54, 56, 58 c 2, 3, 5, 7, 11, 13 d 21, 22, 24, 25, 26, 27, 28 2 a False



b False c False 3 a 8 714 b 1 487 c 1 487 Investigate 4 b 6 629 pieces of paper What did you learn? 23: odd, prime 45: odd, composite 64: even, composite, square 91: odd, composite 100: even, composite, square B Factors and multiples Page 102 1 a 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 b 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 c 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 d 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 e 11, 22, 33, 44, 55, 66, 77, 88, 99, 110 2 a 12 b 24 c 24 d 10 3 a 1, 2, 4, 8, 16, 32 b 1, 2, 4, 8, 16 c 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 d 1, 2, 4, 5, 10, 20, 25, 50, 100 e 1, 2, 3, 4, 6, 9, 12, 18, 36 4 a F12: 1, 2, 3, 4, 6, 12 F16: 1, 2, 4, 8, 16 HCF: 4 b F18: 1, 2, 3, 6, 9, 18 F40: 1, 2, 4, 5, 8, 10, 20, 40 HCF: 2 c F40: 1, 2, 4, 5, 8, 10, 20, 40 F60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 HCF: 20 d F38: 1, 2, 19, 38 F39: 1, 3, 13, 39 HCF: 1 5 a 14 = 2 7 b 32 = 2 2 2 2 2 c 40 = 5 2 2 2 2 d 36 = 2 2 3 3 e 100 = 2 2 5 5 f 156 = 2 2 3 13 g 225 = 5 5 3 3 h 80 = 2 40 = 2 2 2 2 5



i 24 = 3 2 2 2 j 1 000 = 2 2 2 5 5 5 Problem Solving 6 a 12 minutes b 84 minutes 7 30 bangles 8 1 cm / 4 cm Page 103 9 a 5 b 4 c 4 d 6 e 5 f 10 g 6 h 9 10 a 15 b 8 c 12 11 a 15 = 3 5 18 = 2 3 3 HCF = 3 LCM = 2 3 3 5 = 90 b 24 = 2 2 2 3 28 = 2 2 7 HCF = 2 2 = 4 LCM = 2 2 2 3 7 = 168 c 22 = 2 11 25 = 5 5 HCF = 1 LCM = 2 5 5 11 = 550 d 18 = 2 3 3 24 = 2 2 2 3 HCF = 2 3 = 6 LCM = 2 2 2 3 3 = 72 e 25 = 5 5 30 = 2 3 5 HCF = 5 LCM = 2 3 5 5 = 150 f 72 = 2 2 2 3 3 108 = 2 2 3 3 3 HCF = 2 2 3 3 = 36 LCM = 2 2 2 3 3 = 216 g 95 = 5 19 120 = 2 2 2 3 5 HCF = 5 LCM = 2 x 2 x 2 x 3 x 5 x 19 = 2280 h 22 = 2 11 33 = 3 11 HCF = 11 LCM = 2 3 11 = 66 12 a 36 = 2 2 3 3 60 = 2 2 3 5 HCF = 2 2 3 = 12



LCM = 2 2 3 3 5 = 180 b 36 = 2 2 3 3 48 = 2 2 2 2 3 HCF = 2 2 3 = 12 LCM = 2 2 2 2 3 3 = 144 c 60 = 2 2 3 5 80 = 2 2 2 2 5 HCF = 2 2 5 = 20 LCM = 2 2 2 2 3 5 = 240 d 52 = 2 2 13 78 = 2 3 13 HCF = 2 13 = 26 LCM = 2 2 3 13 = 156 What did you learn? 1 a Factors of 24: 16 Factors of 23: 3, 7

b It helps you to work through the factors systematically, omitting potential factors as you go along.

2 a LCM = 12 b 2 3 LCM = 240 HCF = 2 C Roman numerals Page 104 1 a XII b X c IX d XIX e XX f XVII Problem-solving 2 a 30 b 700 c MCC = 1200 d 950 e 95 f 1009 g 663 h 14 i 2 009 3 For example: 2019 = MMIXX 4 CD = 400; DC = 600 What did you learn? 0: Not found 5: V 10: X 15: XV 20: XX 25: XXV 30: XXX 35: XXXV 40: XL 45: XLV 50: L



55: LV 60: LX 65: LXV 70: LXX 75: LXXV 80: LXXX 85: LXXXV 90: XC 95: XCV 100: C Topic 9 Review Page 105 Key ideas and concepts 1 Prime numbers 2 Odd numbers 3 Multiple 4 Highest common factor (HCF) 5 Even numbers 6 Lowest common multiple (LCM) 7 Composite number 8 Multiplication 9 Prime factorisation Think, talk, write … 1 Should be the HCF of two numbers. 2 To find the HCF of two numbers you need to work out the product of the prime factors and

then work out factor pairs. 3 LCM of 4 and 6 is 12. 4 The HCF of two prime numbers is 1. Quick check 1 a False b True c True d False e False f False g True 2 a F36: 1, 2, 3, 4, 6, 9, 12, 18, 36 b 36 = 2 2 3 3 c 36, 72, 108, 144 d 4, 9, 36 3 (11 + 13 + 17 + 19) – (2 + 3 + 5 + 7) = 60 – 17 = 43 4 HCF = 3 LCM = 180

Topic 10 Algebraic thinking Page 106 Students are to use their knowledge of numbers and number sequences to solve problems using equations. Take care when working through this topic as it can cause confusion. Encourage the students to work together and discuss their workings.



A Sequences Page 109 1 8th: 64 10th: 100 20th: 400 2 a 36, 100, 25 b 3, 15 c No, as rectangular numbers can only be composite numbers and 7 is a prime

number. d 5 dots on the length and 6 dots on the width gives 30 dots in total. This is both rectangular and oblong.

e 3, 5, 7, 17, 11, 19 Problem-solving 3 10 or 12 as the length and breadth have a difference of 1 between them. 4 No, she is not correct. 3 7 = 21, which would make it a rectangular number. Page 110 Investigate 5 a 3 7 = 21, 3 9 = 27 Yes, it would work. b Yes, it works. (1 + 6) + (2 + 5) + (3 + 4) = 7 + 7 + 7 = 7 3 = 21 c Adding consecutive square numbers. Yes, it will work. What did you learn? 1 Triangular: 1 + 2 + 3 = 6 Rectangular: 2 3 = 6 Oblong: 3 2 = 6 2 Move the top 3 and the right 3 at the bottom. Add them to the arrangement so that there are 6 6 dots. B Using equations to solve problems Page 112 1 a n + 6 = 23 n + 6 – 6 = 23 – 6 n = 17 b n – 9 = 42 n – 9 + 9 = 42 + 9 n = 51 c n – 7 = 51 n – 7 + 7 = 51 + 7 n = 58 d n 8 = 72 n 8 ÷ 8 = 72 ÷ 8 n = 9 e n ÷ 5 = 8



n ÷ 5 5 = 8 5 n = 40 f (n ÷ 2) + 8 = 23 (n ÷ 2) + 8 – 8 = 23 – 8 n ÷ 2 2= 15 2 n = 30 2 a 2 x + 10 = 25 2 x + 10 – 10 = 25 – 10 2 x = 15 2 ÷ 2 x = 15 ÷ 2

x = 7

b x 10 – 12 = 18 x 10 – 12 + 12 = 18 + 12 x 10 ÷ 10 = 30 ÷ 10 x = 3 c (x + 10) 5 = 75 (x + 10) 5 ÷ 5 = 75 ÷ 5 x + 10 – 10 = 15 – 10 x = 5 d 3 x – 15 = 12 3 x – 15 + 15 = 12 + 15 3 x = 27 3 ÷ 3 x = 27 ÷ 3 x = 9 e 5 x – 100 = 400 5 x – 100 + 100 = 400 + 100 5 ÷ 5 x = 500 ÷ 5 x = 100 f x 5 + 14 = 44 x 5 + 14 – 14 = 44 – 14 x 5 ÷ 5 = 30 ÷ 5 x = 6 Problem-solving 3 x + $1.50 = $ 2.25 x + $1.50 – $1.50 = $2.25 – $1.50 x = $0.75 The sharpener cost 75 cents. 4 23 minutes + x = 45 minutes 23 – 23 + x = 45 – 23 x = 22 minutes The mathematics took 22 minutes. 5 x $5.00 = $105.00 x $5.00 ÷ $5.00 = $105.00 ÷ $5.00 x = 21 She bought 21 tickets. 6 (2 x) + 14 = 27 (2 x) + 14 – 14 = 27 – 14 2 x = 13 2 ÷ 2 x = 13 ÷ 2



x = 6

Nadia and Ann are both 6 years old.

7 x 12 = 156 x 12 ÷ 12 = 156 ÷ 12 x = 13 He could make 13 groups. 8 a x 4 = 220 cm x 4 ÷ 4 = 220 ÷ 4 x = 55 cm b y 3 = 57 cm y 3 ÷ 3 = 57 ÷ 3 y = 19 c (z 2) + 12 cm = 46 cm (z 2) + 12 – 12 = 46 – 12 z 2 = 34 z 2 ÷ 2 = 34 ÷ 2 z = 17 cm 9 x 7 = $1.00 – $0.15 x 7 = $0.85 x 7 ÷ 7 = 85 ÷ 7 x = $0.12 Each plum cost about 12 cents. 10 x + x + 10 = 98¢ 2 x + 10 = 98¢ 2 x = 88¢ x = 44¢ An orange costs 44 cents and a mango costs 54 cents. 11 x + x – 6 kg = 88 kg 2x = 94 kg x = 47 kg Keshawn weighs 47 kg. Bruce weighs 41 kg. What did you learn? 1 4 2 Length = 6 cm Width = 2 cm Topic 10 Review Page 113 Key ideas and concepts Pattern: specific sequence of numbers or shapes Sequence: set of numbers that obeys a particular rule Rectangular number: the product of the dots of its length and width Square number: number of dots on one side of the square is multiplied by itself Triangular number: sum of consecutive numbers Equation: mathematical statement that makes two quantities equal Think, talk, write … 1 Square numbers 2 Insert the number (answer) into the place of the letter that represented it.



Quick check 1 a 2, 12, 20 b 1, 25, 100 c 2, 3, 11 d 3, 15, 21 e 12, 20 2 a True: number of dots multiplied by itself to find the total number of dots. b True: oblong numbers are a specific type of rectangular number. c True: a square number is the product of a number multiplied by itself; when the

answer is 16, a rectangular number could be 16 when you say 2 8. d False: you cannot have an array of one row for rectangular numbers. e False: square numbers are the product of the same number; oblong numbers are

the product of two consecutive numbers. 3 a n + 5 = 23 n + 5 – 5 = 23 – 5 n = 18 b n + 9 = 17 n + 9 – 9 = 17 – 9 n = 8 c n – 12 = 34 n – 12 + 12 = 34 + 12 n = 46 d n 12 = 96 n 12 ÷ 12 = 96 ÷ 12 n = 8 e (n ÷ 2) + 13 = 63 (n ÷ 2) + 13 – 13 = 63 – 13 n ÷ 2 2 = 50 2 n = 100 4 5 8 = n – 9 40 = n – 9 40 + 9 = n – 9 + 9 49 = n 5 (n 10) + 6 = 96 (n 10) + 6 – 6 = 96 – 6 n 10 ÷ 10 = 90 ÷ 10 n = 9

Topic 11 Measurement (2) Page 114 The students will continue to develop their skills of solving perimeter and area. The students will now be introduced to volume. Work through it carefully and repeat the formulae as often as possible. A Perimeter Page 116 1 a 2.3 cm + 2.7 cm + 1.5 cm = 6.5 cm 23 mm + 27 mm + 15 mm = 65 mm b 2.3 cm + 1.5 cm + 3.0 cm + 1.5 cm = 8.3 cm 23 mm + 15 mm + 30 mm + 15 mm = 83 mm c 2.3 cm 4 = 9.2 cm



23 mm 4 = 92 mm d 3.7 cm 4 = 14.8 cm 37 mm 4 = 148 mm e 3.8 cm + 0.9 cm + 0.9 cm + 3.7 cm + 0.9 cm + 0.9 cm = 11.1 cm 38 mm + 9 mm + 9 mm + 37 mm + 9 mm + 9 mm = 111 mm f 1.5 cm 4 = 6 cm 15 mm 4 = 60 mm 3 a 13 cm 4 = 52 cm b (11 mm 2) + (7 mm 2) = 22 mm + 14 mm = 36 mm c 4 cm + 2 cm + 9 cm + 2 cm + 10 cm = 27 cm Page 117 3 d 6 m + 7 m + 1 m + 5 mm + 2 m + 5 m = 26 m e 6 cm 3 = 18 cm f 10 cm + 7 cm + 5 cm = 22 cm g 6 cm + 6 cm + 6 cm + 4 cm + 4 cm + 5 cm + 5 cm = 36 cm h 1.5 m + 1.5 m + 5 m + 5 m + 8 m + 5 m + 3 m = 29 m i (6 mm 4) + (8 mm 2) + 4 mm + 16 mm = 24 mm + 16 mm + 4 mm + 16 mm = 60 mm 4 a Two triangles, for example: 3 cm + 5 cm + 4 cm = 12 cm 2 cm + 6 cm + 4 cm = 12 cm b Two rectangles, for example: (5 cm 2) + (7 cm 2) = 24 cm (8 cm 2) + (4 cm 2) = 24 cm Problem-solving 5 a 5 m ÷ 4 = 1.25 cm b 20 – 16 = 4 4 ÷ 2 = 2 The other side is 2 cm. c 68 cm d 30 cm e 10 4 = 40 m f (8 m 2) + (16 m 2) = 16 m + 32 m = 48 m What did you learn? 1 P = 2 (l + w) 2 P = 4 l 3 a 7.5 cm 3 = 22.5 cm b 3.1 cm 4 = 12.4 cm c 2 (2.5 m + 3 m) = 11 m d 12 mm + 11 mm + 15 mm + 15 mm + 14 mm = 67 mm



B Area Page 118 1 a 5 cm 3 cm = 15 cm2 b 7 cm 2 cm = 14 cm2 c 4 cm 4 cm = 16 cm2 d 5.5 cm 5.5 cm = 30.25 cm2 2 a 2.2 m 3.6 m = 7.92 m2 b 70 – (15 2) = 70 – 30 = 40 40 ÷ 2 = 20 cm 15 20 = 300 cm2 c 24 – (4 m 2) = 24 – 8 = 16 ÷ 2 = 8 m 4 m 8 m = 32 m2 d 6.5 cm (6.5 cm 2) = 6.5 cm 13 cm = 84.5 cm2 Page 119 3 a Estimate: 6 squares

A = (4 3)

= 12

= 6 squares

b Estimate: 5 squares

A = (3 2 )

= 8.75

= 4.375 squares c Estimate: 13 squares

A = (3 9)

= 27

= 13 squares

4 a (40 mm 20 mm)

= 800 mm

= 400 mm2

b (4 cm 2.5 cm)

= 10 cm

= 5 cm2 5 2 = 10 cm2

c (3 cm 4 cm)

= 12 cm

= 6 cm2



d (7 cm 12 cm)

= 84 cm

= 42 cm2

e (8.2 cm 3.4 cm)

= 27.88 cm

= 13.94 cm2

f (9 9) + (9 6.6 cm)

= 81 cm2 + 59.4 cm2

= 81 cm2 + 29.7 cm2 = 110.7 cm2 Page 120 5 a (3 9) + (3 6) = 27 cm2 + 18 cm2 = 45 cm2 b (8 cm 2 cm) + (2 cm 6 cm) = 16 cm2 + 12 cm2 = 28 cm2 c (12 cm 3 cm) + (3 cm 6 cm) + (6 cm 3 cm) = 36 cm2 + 18 cm2 + 18 cm2 = 72 cm2 d (10 cm 4 cm) + (10 cm 4 cm) + (3 cm 16 cm) = 40 cm2 + 40 cm2 + 48 cm2 = 128 cm2 Challenge 6 Length = 20 cm Width = 5 cm What did you learn? 1 a l l b l w

c (l w)

C Volume Page 121 1 a 1 cm 1 cm 2 cm = 2 cm3 b 5 cm 2 cm 4 cm = 40 cm3 c 5 cm 5 cm 4 cm = 100 cm3 d 4 cm 6 cm 5 cm = 120 cm3 e 6 cm 3 cm 3 cm = 54 cm3 2 a 3 cm 3 cm 3 cm = 27 cm3 b 5 cm 5 cm 5 cm = 125 cm3 Page 122 Problem-solving 3 8 cm 6 cm 3 cm = 144 cm3



4 162 ÷ (9 6) = 162 ÷ 54 = 3 cm 5 8 5 4 = 160 cm3 160 cm3 ÷ 2 cm3 = 80 cubes 6 2 160 ÷ 15 = 144 12 12 = 144 The width and the height are each 12 cm. Investigate 7 a 6 cm 10 cm 4 cm = 240 cm3 240 cm3 ÷ 8 cm3 = 30 boxes 8 a 2 000 cm3 ÷ 25 = 80 25 40 2 = 2000 cm3 25 16 5 = 2000 cm3 25 20 4 = 2000 cm3 25 8 10 = 2000 cm3 b 25 40 2 The boxes will be long and thin. c 25 8 10 The boxes are squarer and are therefore wider. What did you learn? 1 Measure length, breadth and height, then multiply them together. 2 Brick: 12 cm 8 cm 23 cm = 2208 cm3 Sponge: 13 cm 10 cm 15 cm = 1950 cm3 The brick has the greater volume. Topic 11 Review Page 123 Key ideas and concepts

Perimeter of a rectangle: 2 (l b)

Area of a triangle: (l w)

Area of a square: l l Volume of a rectangular prism: l b h

Quick check 1 a P: 2 (2 cm + 6 cm) = 2 12 cm = 24 cm A: 2 cm 6 cm = 12 cm2 b P: 3 cm 4 = 12 cm A: 3 cm 3 cm = 9 cm2 c P = 7 cm + 7.28 cm + 2 cm = 16.28 cm

A: (7 cm 2 cm)



= 14 cm2

= 7 cm2 2 a Area of a square is the same number multiplied by itself. Rectangle will be two different numbers for the length and breadth.

b Right-angled triangle is the area of a rectangle.

3 a 3.6 cm + 6.1 cm b 3.6 cm 200 = 720 m 6.1 200 = 1220 m c 2 (720 m + 1220 m) = 2 1940 m = 3880 m d 720 m 1220 m = 878 400 m2

e 2 m 3 m 1 m = 9 m3

Topic 12 Shape and space (2) Page 124 Students work with 3-D shapes, looking at their properties and identifying them. Work carefully through this section and repeat the names and properties as often as possible for the students to identify the shapes easily. The students will also look at the nets of 3-D shapes. Allow the students to work together to work out the coordinates, and in so doing they will learn from each other. A 3-D objects and their properties Page 127 1 a Triangular prism: 5 faces, 6 vertices, 9 edges b Cuboid: 6 faces, 8 vertices, 12 edges c Cube: 6 faces, 8 vertices, 12 edges d Sphere: no faces, edges or vertices e Square-based pyramid: 5 faces, 5 vertices, 8 edges f Cylinder: 2 faces, 1 curved surface, no edges/vertices g Triangular pyramid: 4 faces, 4 vertices, 6 edges h Cone: 1 face, 1 curved surface, 1 apex 2 a Cuboid: laptop, box of fruit, desk Cube: bin, post box Cylinder: poles, lamp posts, in fencing, canned food Sphere: ball b a, e, g, h c They are stronger structures. 3 a Cylinders: ball container, pens, cans of beans Sphere: balls Cubes: boxes Cones: rose holder, party hats, ice-cream cones Page 128 4 a C: it is a cylinder whereas the others are cuboids. b F: the other shapes all have a circular face. c L: all the other shapes have a cylindrical hole in them. d P: the other shapes are all cuboids. e Q: it is the only square-based pyramid. The other shapes are triangular-based pyramids.



What did you learn? 1 Cone 2 Pentagon-based pyramid 3 Pentagonal prism 4 Pentagonal prism 5 Sphere 6 Hexagonal pyramid B Construct and draw 3-D objects Page 129 1 d, e, h, i 2 Open cuboid 3 One square and a hexagon are needed to make a hexagonal prism. Page 130 4 Student’s drawings 5 Student’s drawings: check both 3-D shapes are included. 6 a Hexagonal prism b Rectangle c Because of the angle at which you are looking at the shape. d It is a plant pot that is open on one side. What did you learn? 1 Student’s drawing of four squares with a fifth square on one side 2 Student’s drawing: make sure the vertices are connected with parallel lines. C Coordinate systems Page 131 1 a i (1,6) ii (3, 0) iii (7, 6) b i Harbour ii Marine beacon iii Town centre c (7,2); (5,2) Page 132 2 a (2,2); (2,3); (2,4); (3,4); (4,4); (5,3); (6,2); (8,1); (8,2); (8,4); (9,5); (10,5); (10,4); (9,3); (9,1); (11,1) b The number remains the same for the x-axis markings. c The number remains the same for the y-axis markings. 3 a i C ii M iii H iv F b i (0,2) ii (5,1) iii (0,0) iv (0,4) v (6,2) Page 133 4 a STUDY HARDER!



What did you learn? 1 (8,6) 2 Marlin City 3 (1,6) 4 Grouper Grotto; (1,2) D Shape and space at work Page 134 1 a Cube: tissues Cuboid: GPS, chocolates, pills, drill bits Cylinder: dog food, pens Pyramid: pencils b Cube: 6 faces, 12 edges, 8 vertices Cuboid: 6 faces, 12 edges, 8 vertices Cylinder: 2 faces, 1 curved surface Pyramid: 5 faces, 6 vertices, 9 edges Page 135 What did you learn? For example:

To store foodstuffs/packaging. Shapes are used as road signs. Furniture is made up of different geometric shapes.

Topic 12 Review Page 136 Quick check 1 a Cylinder, sphere b Cone, cylinder c Cone, cylinder, sphere d Cube e Pentagonal prism 2 A, B, D C will not work as one square face is in the wrong position. Page 137 3 A: Triangular prism B: Square-based pyramid 4 a Origin b (1,0); (2,0); (3,1); (2,1); (1,3); (2,4); (3,4) c (7,6) d Vertex

Test yourself (2) Page 138 1 a 24 b 4, 49 c 2, 17, 41 d 4, 2 e 12 f 10

2 24 cm2

3 a 18, 21, 24



b 10, 1, 0.1 c 15, 21, 28 4

5.7 mm 5.7 mm = 32.49 mm2 4.2 mm 6.4 mm = 26.88 mm2

(20 mm 20 mm) + (14 mm 20 mm)

= 400 mm2 + 140 mm2 = 540 mm2 5 a The ant on the page is 5 times bigger than the real-life ant. b Bigger c 4 cm d 0.8 cm/8 mm Page 139 6 a 6.8 cm b 10.8 cm c 300 cm d 300 000 cm 7 a 5000 g b 0.13 g c 5500 g d 8.7 g 8 a 4234 ml b 734 cl c 0.145 L 9 a Questionnaire as the students may not bring all their brothers or sisters to school so

the teacher could not use observation. b

Sibling numbers Frequency 0 1 1 102 8 3 3 4 1 5 1 6 1

c 1 10 a Mode: 2 Mean: 3.3 b Mode: there is no mode Mean: 35 11 a 18 = 2 3 3 b 48 = 2 2 2 2 3 c 100 = 2 2 5 5 12 a 14 b 4 13 a Cuboid b Cylinder c Cube d Student’s drawings e Student’s drawing of a cuboid 14 (6 cm 2 cm 3 cm) + (4 cm 3 cm 2 cm) = 36 cm3 + 24 cm3 = 60 cm3 15 a 48 ÷ (4 2) = 48 ÷ 8



= 6 6 boxes fit along the length. b 36 ÷ (3 4) = 36 ÷ 12 = 3 3 boxes fit along the width of the box.

Topic 13 Computation (3) Page 140 The students will continue to build on their knowledge of working with percentages, profit and loss, and ratio. Work through the knowledge they have gained from the previous levels and make sure there are no gaps in their understanding of the work before building on their knowledge. A Calculating with percentages Page 142 1 a 4 b 60 c 100 d 16 e 37.5 f 2 g 72 h 9 2 a 8.5 b 8.55 c 13.5 d 3.2 e 45 f 112.32 g 550 h 375 i 216.3 Page 143 3 a 30% of 400 students = 120 students are boys b 400 – 120 = 280 280 students are girls 4 25% of 6.4 kg = 1.6 kg The fish lost 1.6 kg through drying. 5 a 50% b 50% c 34% d 20% e 45% f 50% 6 a 40% b 60% 7 100 km

8 a 100 = 50

b 100 = 100

c 100 = 60

John’s salary is $60. Problem-solving 9 45 out of 75

10 100 = $160

Page 144 11 Ladies’ shoes: 20% of $80.00 = $16.00



$80.00 – $16.00 = $64.00 Gents’ shoes: 20% of $100 = $20.00 $100.00 – $20.00 = $80.00 Boys’ shoes: 20% of $50.00 = $10.00 $50.00 – $10.00 = $40.00 12 a 15% of $800 = $120 $800 + $120 = $920 b 15% of $650 = $97.50 $650 + $97.50 = $747.50 c 15% of $350 = $52.50 $350 + $52.50 = $402.50 Page 145 13 a 25% of $300 = $75 $300 + $75 = $375 b 10% of $520 = $52 $520 – $52 = $468 c 25% of $12 000 = $3 000 $12 000 – $3 000 = $9 000 14 10% of $480 = $48 $480 + $48 = $528 15 $5 000 – $4 200 = $800

100 = 16% loss

16 a 100 $8 = $800 She made a profit.

b 100 = 50% profit was made

What did you learn? 1 a 150 b 294 c 6 2 20% of $749 = $149.80 $749.00 – $149.80 = $599.20 for the table 20% of $550 = $110 $550 – $110 = $440 for the bookshelf

3 a 100 = 10% loss

b

100 = 20% profit

B Calculating with ratio Page 147 1 a 3:6:12 b John: 8; Troy: 16 c Martin: 3; Troy: 12 They eat 21 mangoes altogether.

2 a 2 300 = $690

b 2 300 = $276

c 2 300 = $1 081 is left over



Page 148 Problem-solving

3 4 paper clips

4 a Maria: 6:18 Robert: 12:12 Glenroy: 16:8 b 48 ÷ 24 = 2 cm2 per block 18 2 = 36 cm2 c 9 cm 4 cm = 36 cm2 36 cm2 ÷ 24 = 1.5 cm2 per block Purple: 1.5 cm2 4 = 6 cm2

Green: 1.5 cm2 8 = 12 cm2 Yellow: 1.5 cm2 12 = 18 cm2 d 12 ÷ 24 = 0.5 cm2 per block Red: 0.5 8 = 4 cm2 Yellow: 0.5 16 = 8 cm2 What did you learn? 1 a $10:$30 b $16:$24 c $24:$16 d $32:$8 2 $22:$33 Topic 13 Review Page 149 Key ideas and concepts 1 Write the percentage as a fraction with a denominator of 100 and find the fraction of the

amount. You can cancel to make it easier to work with the numbers. 2 The whole amount is 100%, so multiply 5 (which is 1%) by 100 to work this out.

100

3 If you sell something for more than it cost you, you make a profit. If you have to sell something for less than it cost you, you make a loss.

4 multiplied by the normal cost. You then subtract the answer from the initial cost to work

out the discount.

5

100

100 = 6.25% profit

6 Out of a total amount of 10, one gets 3 parts and the other one will get 7 parts. 7 Subtract the number of females from the total number of people at the concert. Then write it as a ratio female:male. 300 – 120 = 180 120:180 Think, talk, write …

1 a 25 = $5 increase.

$7 per hour extra is a better option as it is $2 more.

b 40 = $8



The 20% increase is better as it is $1 more for her. 2 1:1 1:3 Quick check 1 a $45 b 32 people c 45 oranges d $24

e 52 mangoes

f $60 2 a 100% – (46% + 35%) = 100% – 81% = 19%

b 900 = 414 students walk to school

900 = 315 students travel by bus to school

900 = 171 students travel by other means

3 $500 000 = $675 000

The council spent $675 000 on refuse removal.

4 $3 000 = $600

$3 000 – $600 = $2 400 The cost price of the computer was $2 400. 5 a 5 out of 7 sweets are green; 2 out of 7 sweets are yellow b 12 are yellow c 60 will be green

Topic 14 Measurement (3) Page 150 The students will continue to build on their knowledge and skills when working with time, distance, speed, money and temperature. Remind the students to always add the units of measurement. A Working with time Page 152 1 a 12:20 p.m. b 11:30 a.m. c 1:00 a.m. d 1:00 p.m. e 7:05 p.m. f 12:00 p.m. 2 a New York: 18:05; 18:20 Barbados: 19:00; 19:00 Trinidad: 22:05; 21:45 b 15 minutes late c Early, by 20 minutes d 17:10 e 16:05 Page 153 3 a 10:30 a.m. b 1:45 p.m. c 7:05 p.m. d 11:49 p.m. 4 a CPM-4 b CPM-3 c 8 hours and 20 minutes d 17:30 5 a 15:05



b 22:50 c 13:15/1:15 p.m. 6 a 17:15 b 20:40 7 a 13:45 – 13:07 = 38 minutes b 14:05 – 13:38 = 27 minutes c 19:07 – 18:27 = 40 minutes What did you learn? 1 15:30 – 13:50 = 1 hour 40 minutes 2 3:45 p.m. 15:45 Quarter to four in the afternoon B Time, distance and speed Page 155 1 a 6 km b 180 ÷ 2 = 90 km c 1 hour 30 minutes

2 = 4

4 hours 45 minutes 3 a 80 4 = 320 km

b 80 5 = 440 km

c 80 2 = 180 km

4 400 ÷ 80 = 5 hours

5 hour 9 = 4.5 km

Problem-solving

6 .

. = 9

. = 15

Jerome ran faster. 7 243 ÷ 2.25 = 108 km/h 8 900 2 = 1 800 km 760 2 = 1 520 km 1 800 km + 1 520 km = 3 320 km What did you learn? 1 You will travel 80 km in one hour. 2 Speed = distance ÷ time Distance = speed time Time = distance ÷ speed C Money Page 156 1 $215 600.00: Two hundred and fifteen thousand six hundred dollars $8 061 918.00: Eight million sixty-one thousand nine hundred and eighteen dollars $1 000 754.00: One million seven hundred and fifty-four dollars 2 a $8.93 b $28.86 c $61.20 d $263.04



e $2.03 f $1.35 g $12.84 h $23.08 Page 157 4 a US$50.50 b US$92.00 c US$174.69 5 a EC$6.75 b EC$35.10 c EC$60.75 6 a US$7.00 = EC$18.55 b US$120.00 = EC$318.00 7 Exchange rates change regularly. Look on the Internet to see the current exchange rate. What did you learn? 1 $50.00 – $34.65 = $15.35 2 a EC$300.00 b EC$152.40 c EC$37.00 D Temperature Page 158 1 a 42°C b 22°C c 36°C d –15°C 2 160°C 3 a 28°C; 72°C more to reach boiling point b 60°C; 40°C more to reach boiling point c 40°C; 60°C more to reach boiling point What did you learn? 1 Body temperature: 37°C, 98.6°F Boiling point of water: 100°C, 212°F Freezing point of water: 0°C, 32°F 2 0°F Topic 14 Review Page 159 Think, talk, write … 1 The exchange rate determines the value of money at a given time. 2 Fahrenheit and Celsius scales are different values for specific temperatures and could cause problems if misinterpreted. Quick check 2 1 hour 15 minutes 3 3 hours 53 minutes 4 4 80 = 320 km 5 35 ÷ 7 = 5 hours 6 a 450 ÷ 5 = 90 km/h

b 80 7 = 600 km

c 1 080 ÷ 80 = 13 hours

7 EC$400 250 = TT$1 000



8 a 37°C, 98.6°F b 100°C, 212°F c 0°C, 32°F

Topic 15 Data handling (2) Page 160 The students will continue to develop their skills and knowledge in reading and interpreting graphs, drawing graphs and working with probability. Allow the students to work together to solve the problems. A Reading and interpreting graphs Page 162 1 a Number of people swimming at Redoubt Beach at noon for a week b 3 swimmers c Saturday. No, as you can see it is the longest line. d Wednesday, Thursday and Friday e Tuesday and Sunday Page 163 2 a 150 3 = 450 people b 300 3 = 900 bananas c i 1 800 oranges

ii 5 oranges

d i 300 sweets ii 150 sweets 3 a $15 b $15 c $30 + $20 = $50 d ($15 4) + ($30 4) = $60 + $120 = $180 4 a Followers of well-known sport stars on a social networking service b LeBron James c 2 million followers d LeBron James is the most popular, followed by Serena Williams, Usain Bolt and

then Chris Froome. 5 a Monthly and average rainfall on an island in the Caribbean b February, April, May, June c January d For example: temperature; hours of sunshine Page 164 6 a Day 8 b Day 4 c 42°C; 20°C d Summer e Days 8 and 9 = 9ºC f Days 5 and 6 = 8°C Days 7 and 8 = 8°C g When it goes up = rising, when it goes down = dropping



7 a Pleased b They know how their clothes are selling so they will know what to stock their shelves/rails with and when stock is needed.

c Compare sales from different years. Add lines in different colours. 8 a There is a key on the side of the graph. b 40 students c Helps to know how one part of the data is related to another part and also how it is

related to the whole set of data. d Bar graph What did you learn? 1 Football, volleyball, hockey 2 Basketball 3 Hockey 4 23 + 11 = 34 students play basketball 5 Double bar graph: it helps to identify how many boys and girls participate in a sport as well as how many students play each sport. B Drawing graphs Page 165 1 a Line graph: shows progression b Bar graph: useful for comparing different data c Line graph: shows progression d Pie chart: total is divided into sectors for easy comparison in the different areas Page 166 2 Student’s drawing of a bar graph a June b None c 340 mm d May and June e 825 mm f 137.5 mm 3 Student’s drawing of a bar graph: must include a title, headings and markings on the x- and

y-axes. 4 a Student’s drawing of a bar graph: must include a title, headings and markings on the

x- and y-axes. b 12:30: 27°C 14:30: 29°C

c As the sun shines on the sea, it warms the temperature of the water. The sea water retains the heat for a long time after the sun has set.

What did you learn?

Decide which tytpe of graphy would be best to represent the information. Make sure the graph has a title. Make sure the axes are clearly labelled. Include a key if appropriate.

C Probability Page 167 1 a or



b or

c

2 a 3 possible outcomes

b Red: or

Blue:

Yellow:

3 a

b or

c or

d

Problem-solving 4 Red: 5 counters Blue: 4 counters Yellow: 2 counters Purple: 9 counters What did you learn? One out of ten chance it will not rain = 10% Topic 15 Review Page 168 Key ideas and concepts 1 Double bar graph 2 Pictograph 3 Bar graph 4 Line graph Think, talk, write … 1 Organising data in a meaningful way so it can be understood and interpreted. 2 Easier to skip count for large amounts and there is less chance of errors when tallying up

the amounts. 3 4 oranges = 15 oranges A third of an orange will represent the 1 remaining orange. Quick check 1 a 10 days b June, July, August, September c 24 – 10 = 14 days d Observes days of rain each month, records data for each month and plots it on the

graph. 2 Student’s drawing of a bar graph: must include a title and headings for the axes. 3 a 1 in 3 b Equally likely c Impossible



Test yourself (3) Page 169 1 a 35 b 47, 95, 191 c The pattern is doubling the difference between the previous two numbers (5 – 2 = 3;

11 – 5 = 6; 23 – 11 = 12), so you add 24 to the fourth number, 48 to the fifth number, 96 to the sixth number, etc.

2 a Thousand b 8 c For example: 342 165 3rd digit: 100 4th digit: 2 000 d $8 085.00 3 a 51 and 63 b 9 c iii 4 a 2 2 2 5 b 24 c 4 5 a 36 oranges b 30 sweets c 242 plums 6 x + 9 = 24 7 a x + 1 567 = 3 458 x = 1 891 b 47 + (2 47) + (47 – 13) = 47 + 94 + 34 = 175 marbles altogether c 270 ÷ 6 = 45 There are 45 chairs in each row. d

Hours Money 4 $120 8 $240 12 $360 16 $480

It will take 16 hours to make $480. Page 170

8 a

b 0.29

c , ,

9 a 1 ( – )

= ( – )

=

=

b –

= –



=

10 a of $420 = $140 of her money still remains.

b of 24 = 20 students like football.

c 600 L d 1 200 mm – 350 mm = 850 mm 850 mm will be left over e 2 (100 + 70) = 2 170 = 340 m 11 Tenth 12 a 31.3 – 25.0 kg = 6.3 kg needs to be removed from the bag. b $20 – ($8.95 + $3.75) = $20.00 – $12.70 = $7.30 change c 7.5 + 43.2 + 135.8 = 186.5 d x + 3.85 = 9.27 x = 5.42 e 4.95 2.1 = 10.395 13 a 0.7 kg = 700 g b 3 600 g = 3.6 kg c (5 3 ounces) + 25 ounces = 15 + 25 = 40 ounces 14 a litres b 3 000 – (750 + 500) = 3 000 – 1 250 = 1 750 ml of juice is still in the bottle 15 a $24 b 20% c 18 girls d 32 out of 40 e 75 f $90 g 40 students Page 171 16 a $75 b 60 sheep 17 a 3:30 b 15:30 c 4:20 p.m. d 8:15 p.m. e 85 minutes f 315 km 18 175 km 19 9 4 = 36 cm2

20 (6 12)

= 36 cm2 21 a Yes b YZ parallel to WX 22 a 50° b Obtuse angle 23 a A b 60°: the angles inside a triangle must add up to 180° c Acute-angled triangle, scalene triangle d Straight line e When added up, the angles would then be more than 180°.



Page 172 24 a Questionnaire, survey b 11 c 12 d 12 – the mean remains the same. 25 One 26 a Right angle b Obtuse angle c Acute angle 27 EC$390 28 b 29 a Pets owned by students in class b 2s c Bird d 5 students e 31 students

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Caribbean Primary Mathematics Level 6 - Hodder Education