a complete numeracy programme for primary schools...

A COMPLETE NUMERACY PROGRAMME FOR PRIMARY SCHOOLS6th Class Satellite Book Answers

229Planet Maths Teacher Resources • 6th Class

Topic 1: Place Value Page 5

A 1. 4,703,612 2. 3,960,723 3. 493,206 4. 7,364,518B 1. Highest Number Lowest Number (a) 9,544,320 0,234,459 (b) 9,863,221 1,223,689 (c) 9,764,310 0,134,679 (d) 8,543,210 0,123,458 2. (a) 1,000,000 + 200,000 + 50,000

+ 4,000 + 600 + 90 + 2 (b) 4,000,000 + 300,000 + 20,000

+ 1,000 + 600 +50 +3 (c) 2,000 + 100 + 40 + 3 (d) 400,000 + 20,000 + 3,000 +

100 + 6 3. (a) 400,000 (b) 4,000,000 (c) 40 (d) 4,000 4. (a) 732,160, 732,200, 732,000 (b) 914,310, 914,300, 914,000 (c) 536,920, 536,900, 537,000 (d) 345,190, 345,200, 345,000C 1. False 2. True 3. False 4. False 5. True

Topic 1: Place Value Page 6

D Numeral – a symbol used to

represent a number Expanded notation/extended form

– a way of writing numbers to show place value.

To Round – to change a number to a more convenient value.

Place Value – the value of a digit depending on its place in a number.

E

Blue Phone Alpha Phones

Highest 2019 2019

Lowest 2015 2015

1.

Race Phones Sports Phones Power Phones

2014 2015 2015

2011 2010 2011

2. 200,000, 70, 90,000, 8,000, 200.F 1. (a) 1,539,050 (b) 1,539,000 (c) 1,539,000 2. 6,174,017 3. 626,168, 574,162, 562,681,

530,610, 519,825 4. 1,724, 767

Test Yourself! Page 7

1. 4,100 2. 234,568

3. 6,000,000 + 700,000 + 40,000 + 6,000 + 900 + 20 + 3

4. 60,000 5. 816,052 6. 261,082 7. 325,648 8. 55,000 9. Six hundred and twenty-four

thousand and eighty-five. 10. 465,988, 456,987, 456,943,

456,832, 451,930

Topic 2: Addition and Subtraction Page 8

A 1. 46 2. 15 3. 53 4. 34 5. 24 6. 13 7. 10 8. 75 9. 35 10. 18 11. 5,318 12. 361 13. 12 14. 15 15. 27B 1. (a) 15,000 + 300 = 15,300 (b) 437,000 – 34,100 = 402,900 (c) 934,000 + 35,000 = 969,000 (d) 654,000 + 493,000 = 1,147,000 2. (a) 619,385 (b) 405,308 (c) 810,173 (d) 433,389 (e) 521,307 3. (a) 839,482 (b) 96,699 (c) 845,599 (d) 865,739 (e) 722,502 4. (a) 1,343,353 (b) 213,729 (c) 343,989 (d) 655,978C 1. Add 2. Subtract 3. Divide 4. Add

Topic 2: Addition and Subtraction Page 9

D Difference between two numbers –

subtract Find the sum of – add Decrease – to make smaller Increase – to make biggerE 1. 1,389,847km2

2. 37,585km2

3. 2,176,000km2, 786,000km2, 748,000km2

4. 3,709,521km2

5. See AtlasF 1. €1,631,008 2. €179,395 3. 825,286 4. €35,531 5. 5,451,091

Test Yourself! 0

1. 521,432 2. 630,063 3. 443,747 4. 2 large + 1 small 5. 384,003 6. 444,865

7. 7 8. 2 hours 32min 16sec 9. 102,019 10. 634

Topic 3: Data Page 11

A 1. 4,800 2. 65,300 3. 240 4. 79,320 5. 50 6. 480 7. 46 8. 1,800 9. 66 10. 9 11. 9 12. 26 13. €16 14. €27 15. €25B 1. It shows a pattern of activity over time. 2. (a) Years 8 and 9 (b) Year 7 (c) €16,250 (d) Years 8 and 9C 1. €8.72 2. 16 3. 126

Topic 3: Data Page 12

D Graph – drawing or diagram used to

record information. Average – add up all the amounts

and divide the total by how many amounts there are.

Data – collection of information. Table – mathematical information

organised in columns and rows.E 1. (a) 2015 (b) 2011 2. 90 3. (a) 2 (b) 3 4. Birth rate rose in preceding years,

more houses built in the area.F 1. Draw graph in copy 2. Tuesday, Saturday 3. Tuesday 4. Saturday 5. 65 6. Sunday


1. 12 2. €2.20 3. x-axis 4. y-axis 5. 2,000 6. December and April

Nov Dec Jan

1,000 4,000 3,000

Feb Mar Apr

1,000 1,000 2,000

7.

8. 4,000 9. 18 10. €24

Topic 4: Multiplication 1 Page 14

A 1. 27 2. 800 3. 70 4. 66 5. 6,000 6. 36 7. 50 8. 76,800 9. 61

230 Planet Maths Teacher Resources • 6th Class

10. 48 11. 20,000 12. 39 13. 72 14. 3,450 15. 51B 1. (a) 67 (b) 25.9 (c) 19.97 2. (a) 44 (b) 29.0 (c) 39.69 3. (a) 35 (b) 28.4 (c) 69.37C 1. (a) 3,415 (b) 2,568 (c) 44,448 (d) 63,558 (e) 609,201 (f) 236,530 2. (a) 136.30 (b) 999.40 (c) 3,240 (d) 2,157.10 (e) 2,995.20 (f) 4,113.00 3. (a) 2,389.46 (b) 438.702 (c) 6,295.10 (d) 507.87 (e) 311.664 4. (a) 23,049.63 (b) 35,955.68 (c) 34,426.28 (d) 797.657 (e) 769.6136 5. (a) 2,559.90 (b) 150.24 (c) 528.41


D 1. (a) €132 (b) €184 (c) €160 (d) €192 2. €187.50 3. €60E 1. €413 2. 62 3. €22.10 4. €54.75 5. €8,096.24F 13, 25, 43, 55, 67, 85


1. 856 2. 224.66 3. 64,770 4. 984.798km 5. 68,300 6. 16 7. €255 8. 148.92 9. 9,326 10. 37.60

Topic 5: Lines and Angles Page 17

A 1. (a) straight (b) right (c) acute (d) acute (e) acute (f) reflex (g) obtuse (h) acute 2. (a) 180° (b) 360° (c) 120° (d) 270°B 1. (a) 60°, 60° (b) 40°, 40° (c) 130°, 135° (d) 80°, 81° 2. (a) 45° (b) 62° (c) 30° (d) 102° (e) 108° 3. (a) 180° (b) 270° (c) 360° (d) 72°C 1. True 2. False 3. True 4. True 5. False 6. False

Topic 5: Lines and Angles Page 18

D Rotation – to turn an object. Protractor – instrument used to

measure angles. Quadrilateral – polygon with four

sides. Polygon – a plane shape having three

or more straight sides.E 1. (a) right angle (b) right angle (c) right angle 2. Diameter 3. 86m 4. (a) Semi-circle (b) 10 F 1. Draw in your copy

2. (a) 12 (b) 1

4 (c) 16 (d) 1

5 3. (a) 180° (b) 90° (c) 90° (d) 135° (e) 45°


1. 100° 2. 270° 3. Perpendicular 4. 125° 5. 60° 6. Draw in your copybook 7. Obtuse angle 8. 135° 9. 45° 10. 180°

Topic 6: Division 1 0

A 1. 10 2. 8 3. 1 4. 19 5. 2 6. 200 7. 25 8. 54 9. 2.86 10. 8 11. 7 12. 3.487 13. 10 14. 80 15. 7.23B 1. 10 2. 30 3. 5 4. 10 5. 80 6. 60C 1. (a) 48.6 (b) 0.5640 (c) 30.44 (d) 73.6 (e) 0.7198 (f) 0.943 (g) 3.609 (h) 0.06946 (i) 0.03694 2. (a) 183 (b) 1285 (c) 877 (d) 14 (e) 34 (f) 23 (g) 134 (h) 121 (i) 142 3. (a) 0.85 (b) €0.41 (c) 3.22 (d) 0.49km (e) €0.46 (f) €18.53 (g) 0.111 (h) 4.22 (i) €4.75 4. (a) €1.45 (b) €2.48 (c) €1.67 (d) €2.03 (e) €3.4 (f) €2.04

Topic 6: Division 1 Page 21

D Divisor – the number that will do the

dividing. Product – the result when two

numbers are multiplied.

Sum – the result of adding. Horizontal – parallel to the horizon.E 1. €5.52 2. €132.32 3. €8.27F 1. €50 2. €9.50 3. €4.60 4. 145 litres 5. (a) 118 (b) 24G

2 5 6 4 1 3

3 4 1 2 5 6

5 1 3 6 4 2

4 6 2 1 3 5

6 3 4 5 2 1

1 2 5 3 6 4


1. 554 2. €76.40 3. 29 4. 0.059 5. 54 6. 18kg 7. 0.5 cent 8. 600m¬ 9. 4.90 10. 0.256

Topic 7: Fractions 1 Page 23

A

1. 23 2. 6

8 3. 3 4. 46

5. 312 6. 9

15 7. 57 8. 36 9. 61 10. 21 11. 5,070 12. 210 13. 8 14. 10 15. 15B

1. (a) 18, 38, 78 (b) 6

48, 16, 38

(c) 16, 3

12, 23 (d) 13, 12, 7

12

(e) 1120, 34, 45 (f) 3

36, 29, 49 2.

Whole Numbers Proper Fractions

6 38, 23

Improper fractions Mixed Numbers65 61

3, 112

3. (a) 124 (b) 61

8 (c) 158 (d) 1 6

20

(e) 216

4. (a) 52 (b) 43

4 (c) 485 (d) 25

8C

1. (a) 26 (b) 16

20 (c) 1824 (d) 21

24

(e) 921

2. (a) 12 (b) 5

6 (c) 910 (d) 1

5

(e) 16


D Numerator – the number above the

line in a fraction. Improper fraction – the numerator is

larger than the denominator.


Denominator – bottom number in a fraction.

Common denominator – a number into which the denominators will divide evenly.

E

1. 4 112 litres 2. 15 litres

3. 10 litres 4. 9 litres

5. 114 litres 6. 21

6 litresF

1. 58 2. 7

18

3. (a) 18 (b) 7

8

4. 24 5. 1115

G 1. (2 x 2 x 2 x 2) + (2 x 2 x 2) 2. 33 + 3 3. (5 x 5) + (5 x 5)


1. 1116 2. 3 squares 3. 1

5

4. 15 5. 11

6 6. 625 7. 54

8. 3 320 9. 15

18 10. 34

Topic 8: 2D Shapes Page 26

A 1. 51 2. 32 3. 42 4. 14 5. 63 6. 24 7. 21 8. 4 9. 12 10. 45 11. 16 12. 12B 1. (a) Pentagon (b) Hexagon (c) Square (d) Heptagon (e) Scalene Triangle (f) Equilateral Triangle (g) Octagon (h) Nonagon (i) Decagon (j) Isosceles Triangle 2. (a) Pentagon (b) Kite (c) Trapezium (d) Parallelogram (e) Decagon 3. (a) 4 (b) 3 (c) 1 (d) 2 (e) 9C 1. True 2. True 3. False 4. True


D 1. 5 sides 2. 0 equal sides 3. heptagon 4. 2 equal sidesE 1. Octagon 2. 8 sides and 8 angles 3. Obtuse 4. 135° 5. 1080° (each angle is 135°) 6. 8 7. Copy work 8. RegularF 1. 110° 2. Teacher Check

3. Teacher Check 4.

Name of shape

Number of sides

Number of equal sides

Rectangle 4 2

Rhombus 4 4

Kite 4 2

Trapezium 4 0

Name of shape

Number of pairs of parallel lines

Numbers of lines of symmetry

Rectangle 2 2

Rhombus 2 2

Kite 0 2

Trapezium 2 2


1. 2. Trapezium 3. Scalene 4. No 5. Octagon 6. Polygons 7. 49 8. Teacher Check 9. Equilateral 10. A protractor


A

1. (a) 1420 (b) 9

12 (c) 1821 (d) 25

30

(e) 1015

2. (a) 216 (b) 21

5 (c) 423 (d) 32

3

(e) 214

3. (a) 114 (b) 31

6 (c) 195 (d) 19

4

(e) 8310

B

1. (a) 910 (b) 4

5 (c) 98 (d) 11

12

2. (a) 38 (b) 9

48 (c) 699 (d) 3

20

3. (a) 3554 (b) 18

32 (c) 6108 (d) 30

135 4. (a) 49 (b) 45 (c) 45 (d) 108 5. (a) 24 (b) 56 (c) 22 (d) 24

6. (a) 23 (b) 1

2 7. (a) 27 (b) 40 (c) 32 (d) 14C 1. Multiply, 12 2. Divide and multiply, 189 3. Subtract, €5.50 4. Divide and multiply, 84

Topic 9: Fractions 2 0

D Mixed number – number written as a

whole number with a fraction. Whole number – a counting number

from zero to infinity. Quarter – one of four equal parts. Simplify a fraction – to reduce the

numerator and denominator in a fraction to the smallest they can be.

E

1. 3 730kg (Hint: bring each fraction to a

common factor.)

2. 32 23 3. 5 babygros for €30 4. 12 blue, 9 pink and 15 were cream.F

1. 1820 2. 16 3. €6.65

4. €15, 310 5. 72


1. 160 2. 45 3. 72 4. 72

5. 429 6. 48 7. €15 8. 3

10 9. 72 cent 10. 63

Topic 10: Decimal Numbers Page 32

A 1. 0.17 2. 0.004 3. 0.3 4. 0.09 5. 0.6 6. 0.043 7. 0.0167 8. 0.264 9. 0.003539 10. 0.1 11. 0.62 12. 0.46 13. 0.701 14. 0.023 15. 0.729B 1. €4 2. €13 3. €57 4. €5C 1. (a) 0.304, 0.346, 3 (b) 5.59, 5.6, 5.61 (c) 8.6m, 8.63m, 8.632m 2. (a) 65.4 (b) 394.6 (c) 6.5 (d) 499.3 (e) 935.5 (f) 10.5 (g) 182.2 3. (a) 4.69 (b) 3.53 (c) 8.72 4. (a) 0.3 (b) 0.004 (c) 0.17 (d) 0.75 (e) 0.4

Topic 10: Decimal Numbers Page 33

D Decimal point – a point between a

whole number and a decimal fraction. Thousandth – one of a thousand

equal parts. Order – arrangement according to

size, amount or value. Tenth – one of ten equal parts.E 1. False 2. True 3. True 4. False F 1. 1.459 seconds 2. 139.617 seconds (2 minutes +

19.617 seconds) 3. 46.539 seconds


G 1. (a) €18 (b) €54 2. 608 3. 2,550 4. €304.52 5. (a) €36 (b) €60


1. 856.77 2. 38.4

3. 59.652 4. 410

5. 0.126 6. 110

7. 53.208km 8. 38

9. 0.083 10. 14.95

Topic 11: Numbers Page 35

A 1. 4 2. 4 3. 36 4. 1,000 5. 5 6. 41 7. 7 8. 27 9. 12 10. 10 11. 189 12. 100,000 13. 17 14. 256 15. 8B 1. (a) 1, 2, 3, 4, 6, 9, 12, 18, 36 (b) 1, 2, 3, 6, 7, 14, 21, 42 (c) 1, 2, 3, 6 2. (a) 3 (b) 3 (c) 5 (d) 1 3. (a) 25, 16, 9, 36 (b) 11, 19, 13, 17 (c) 10, 15, 21, 25 4. (a) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 (b) 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 (c) 12, 24 5. (a) 100 (b) 30 (c) 12 (d) 28 (e) 36 (f) 168C 1. True 2. True 3. True 4. False 5. False – 2 is an even number but it is

a prime number. It is the only even prime number!

Topic 11: Numbers Page 36

D 1. 1, 4, 9, 16, 25, 36, 49, 81, 100, 121 2. 25 3. 49 4. 23 5. (a) 20 (b) 81 (c) 7 (d) 64 (e) 5E 1. 11 metres 2. (a) 6 metres (b) 24 metres 3. 32 metres 4. 16 5. (a) 53 (b) 11F Gráinne 44, Pierre 11, Orlaith 22,

James 55, Maria 33 and Tobias 66


1. 5 2. 250 3. 1,000 4. 30 5. 4 6. 16 7. 1, 2, 3, 4, 6, 8, 12, 24 8. 7 9. 12 10. 6


A 1. 46 2. 528 3. 3,928 4. 560 5. 5,600 6. 78 7. 12 8. 41 9. 255 10. 32 11. 825 12. 69 13. 820 14. 7,320 15. 6,800B 1. 40 2. 49 3. 49 4. 102 5. 141 6. 289 7. 107 8. 299C 1. (a) 4.0 (b) 2.1 (c) 3.6 (d) 0.42 (e) 0.4 (f) 33.95 (g) 35.46 2. (a) 0.9 (b) 18.72 (c) 40.74 (d) 1.263 (e) 2.673 (f) 3.5 (g) 0.736 3. (a) 54.81 (b) 24.7 (c) 77.28 (d) 151.68 4. (a) 734.40 (b) 355.16 (c) 5,866.73 (d) 3,330.86D 1. False 2. False 3. True 4. False 5. True 6. True


E 1. (a) Egan (b) Quinn 2. 0.446 minutes 3. (a) 21.825 minutes (b) 12.879 minutes (c) 18.81 minutes (d) 47.76 minutes (e) 3.3195 minutesF 1. €21.75 2. 50.56km 3. (a) €114.21 (b) €139.59 4. 381.444cm (3.81444m) 5. 31.15kgG First digit(s) gives you the month you

were born. Second digit(s) give you the day of the

month you were born. Last digit(s) give you the year of your

birth.

Test Yourself! 0

1. 24,472 2. 30.66 3. 329.4 4. 234.03 5. 58.142 6. 22.178 7. 2443.02 8. 418.795 9. 1.8 10. 206.34m

Topic 13: Length Page 41

A 1. 65cm 2. 16m 3. 48m 4. 400m 5. 3,500m 6. 8m 7. 4km 698m 8. 3,490m 9. 6cm 10. 0.369km 11. 700cm 12. 316cm 13. 2,456cm 14. 40km 15. 60mB 1. 23.2m 2. 64cm² 3. (a) 36m 13cm (b) 57m 51cm (c) 51km 591m (d) 7cm 3mm (e) 11m 96cm (f) 21km 821m 4. (a) 42.56m (b) 161.433km (c) 342.37 (d) 141.71km (e) 254.32m (f) 361.545km 5. (a) 1.24m (b) 1.486km (c) 0.493km (d) 0.88m (e) 0.849km 6. (a) 78m 48cm (b) 4.7615kmC 1. True 2. False 3. False 4. False 5. False

Topic 13: Length Page 42

D Perimeter – distance around the

outside of a shape. A plan – a diagram showing the view

from directly above. Millimetre – a standard metric unit

for measuring length. Distance – the length between two

points or objects.E 1. 247.50km 2. (a) 3,960,000m (3.96 million metres) (b) 396,000,000 (396 million centimetres) 3. 2475km 4. 990km 5. See atlasF 1. 42.75m 2. 36m 3. 3.15m 4. 3,010km 5. 127.5km


1. 281.60cm 2. 4.616km 3. 0.026km 4. 60.7km 5. 420m 6. 26,136m 7. 5.63m 8. 10km 9. 6.25 10. 6km 849m


A 1. 9 2. 6 3. 36 4. 3.60 5. 68.50 6. 4.28 7. 0.853 8. 23 9. 9 10. 7 11. 2.3 12. 17.10 13. 0.50 14. 0.08 15. 7


B 1. (a) 0.2, 3.87, 37.8 (b) 0.3, 13.9, 16.87 (c) 4.3, 20.8, 42.7 (d) 0.66, 6.66, 66 (e) 0.44, 4.44, 44 (f) 0.22, 2.22, 22 2. (a) 65 (b) 98 (c) 38 3. (a) 0.73 (b) 2.34 (c) 5.6 4. (a) 8.6 (b) 3.14 (c) 0.74 5. (a) 1.11 (b) 24 (c) 13.8 6. (a) 53.8 (b) 20.26 (c) 82.88 7. (a) 120.10 (b) 7.94 (c) 264.40C 1. False 2. False 3. True 4. True 5. False 6. False


D Remainder – amount left over after

dividing one number by another. Dividend – the number which is

being divided by another number. Sharing – dividing into equal parts. Skip counting – counting forwards or

backwards in multiples or intervals of a given number, e.g. 2, 4, 6, 8...

E 1. Michael 175, Louise 225 and Maria 190 2. 0.6 cent 3. 9.1 cent 4. €17.99F 1. 75 2. 3.5 3. 4 4. 12 5. 72G

(Hint: move two matches from bottom left square and one from bottom right square.)


1. 11.61 2. 240 3. 21 4. 5kg 5. 17 6. 21.9 7. 0.05863 8. 190m¬ 9. 13.5kg 10. 23.564kg

Topic 15: Percentages 1 Page 47

A 1. Any 60 2. Any 93

3. Any 35 4. Any 312 squares

B 1. 79.2 2. 61.5 3. 4.5 4. 22.5C 1. (a) 17% (b) 31% (c) 47% (d) 63%

(e) 1% (f) 87%

2. (a) 21100 (b) 7

100

(c) 91100 (d) 17

100

(e) 37100 (f) 53

100 3. (a) 70% (b) 30% (c) 40% (d) 25%

(e) 1212% (f) 5%

4. (a) 910 (b) 1

10 (c) 34 (d) 17

20

(e) 1725 (f) 3

25 5. (a) 75% (b) 50% (c) 37.5% (d) 30%


D 1. (a) 77% (b) 17%

(c) 3712% (d) 662

3%

(e) 8889% (f) 855

7% 2. (a) 50% (b) 80% (c) 70% (d) 69% (e) 45% (f) 8%

3. (a) none of these (b) 6623%

(c) 20% (d) none of these

(e) 8712% (f) 111

9% 4. (a) 68 (b) 42 (c) 47 (d) 59 (e) 98 (f) 62 (g) 16 (h) 112 5. (a) 693 (b) 702 (c) 511 (d) 1,410 6. (a) 393 (b) 546 (c) 620 (d) 237.6D Teacher Check


1. 2.5% 2. none of these

3. 38 4. 44%

5. 476 6. 32 questions 7. 195g 8. 3 hours 9. 21 people

Topic 16: Time 0

A 1. (a) 74kph, 85kph, 99kph (b) 103kph, 174kph, 180kph (c) 209kph, 211kph, 219kph

2. (a) 12 (b) 1

4 (c) 15 (d) 1

6

(e) 160 (f) 5

12B Teacher CheckC 1. (a) 84km (b) 168km (c) 252km (d) 336km (e) 21km (f) 42km (g) 63km (h) 14km (i) 28km (j) 56km (k) 126km (l) 231km 2. 270km 540km 810km

1,080km 135km 67.5km 45km 4.5km

Topic 16: Time Page 51

D 1. (a) 1:15pm (b) before 1:15 to allow for

unexpected delay (c) 3:20pm (d) 10:50am 2. (a) 20kph (b) 200kph (c) 120kph (d) 30kph (e) 45kph (f) 80kph (g) 160kph (h) 60kph (i) 90kph 3. (d) 120kphE 1. (a) 1,106km (b) 1,431km (c) 1,882km 2. (a) 773km (b) 1,469km (c) 777km 3. (a) 1,062km (b) 1,757km (c) 2,230km 4. (a) Dublin and Paris (b) Istanbul and Copenhagen (c) Paris and London 5. (a) Dublin and Istanbul (b) Paris and Brussels


1. none of these 2. 65kph 3. 80kph 4. 22:20 5. 8hr 41min 6. 15km 7. 2 hr 20min 8. 1:40pm 9. 05:30


B 1. (a) 6 (b) 3 (c) 26 (d) 18 2. (a) 15 (b) 32 (c) 63 (d) 13 3. (a) 11 (b) 16 (c) 54 (d) 36C 1. (a) 0.4 (b) 0.04 (c) 63% 2. (a) 0.41 (b) 0.32 (c) 0.9 (d) 0.09 (e) 0.11 (f) 0.99 3. (a) 63% (b) 83% (c) 60% (d) 6% (e) 1% (f) 10% 4. (a) 0.33 and 33% (b) 0.7 and 70% (c) 0.05 and 5% (d) 0.31 and 31% (e) 0.4 and 40%

(f) 0.005 and 12%


D 1. (a) 88.06 (b) 455.52 (c) 73.52 (d) 326.89 (e) 337.61 (f) 104.37 (g) 4.77 (h) 144.54 2. (a) 225.75 (b) 389.13 (c) 835.83 3. (a) 173.88 (b) 616.4 (c) 795.96


4. (a) 2,520 (b) 4,000 (c) 480 5. 24 out of 25E 1. 12% 2. Wednesday 3. Saturday 2% 4. Tuesday

5. 712% 6. Tuesday

7. Saturday 8. 8112%

9. 2 euroF 2 such men


1. 30% 2. none of these 3. 0.09 and 9% 4. 51.52 5. 900 6. Clara 7. 14.64m 8. 19.68kg

9. 116,235.71 10. 212%

Topic 18: Area Page 56

A 1. (a) 63m2 and 32m (b) 44m2 and 30m (c) 160m2 and 52m (d) 100m2 and 50m 2. (a) 49m2 and 28m (b) 81m2 and 36m (c) 121m2 and 44m (d) 225m2 and 60mC 1. (a) 34m2 (b) 52m2

(c) 56m2 (d) 40m2

2. (a) 50m2 (b) 40m2

(c) 30m2 (d) 56m2

Topic 18: Area Page 57

D

1. False 2. False 3. True 4. True

5. False 6. False

E

Your answers may differ a little

1. 10cm2 approx. 2. 16cm2 approx.




F

1. 1,360m2

2. bowling 112m2

horse riding 216m2

archery 160m2

badminton 160m2

swimming 192m2

3. 520m2

4. horse-riding


1. 264cm2 2. none of these 3. 196cm2 4. 40m2

5. 420m2 6. 360m2

7. 486cm2 8. 600m2

Topic 19: Problem Solving 1 Page 59

A 1. 3:2 2. 3:4 3. 2:3 4. 6:5 5. 1:20 6. 2:1 7. 7:3 8. 1:2 9. 3:4 10. 6:7 11. 10:7 12. 7:10 13. 2:1 14. 4:1 15. 7:12B Teacher CheckC 1. (a) 12cm:20cm (b) 36km:60km (c) €27:€45 2. (a) 15:30 (b) 30:40 (c) 5:4 (d) 16:28 (e) 32:64 (f) 7:3 3. €780:€260:€520 4. (a) €117 (b) 2.2556

(c) 64263 (d) 69

(e) €13.77 (f) 250km 5. (a) 312.5m (b) 60°

Topic 19: Problem Solving 1 0

D Ratio – the comparative value of two

or more amounts. Problem solving – working out the

answer to a problem. Odd number – a number that is not

divisible by 2. Deduct – to subtract.E 1. €1.50 2. €7.50 3. €8.00 4. €8.00 5. €24.00 6. €32.00 7. No administration work for staffF 1. €21 2. €1,408

3. 780 (Hint: 712 – 5

12 = 212 so 2

12 = 130

so 112 = 65 so 12

12 = 65 x 12 = 780 4. €42 5. €77.60G

LIFT


1. 36:27:18 2. 1:2.50:1.5 3. €36 4. John €30, Michael €25, Alice €45 5. €8.40 6. €32:€20:€12 7. €332 8. 12 9. 210km 10. 1.2, 0.6, 0.3

Topic 20: Chance Page 62

A n/aB Teacher CheckC 1. red 2. pink 3. >3 4. >5

Topic 20: Chance Page 63

D 1. false 2. false 3. true (so long as there are more than 2

tickets) 4. false 5. false 6. falseE green 9 red 4

blue 1 yellow 6 1. green 2. blue

3. 15 4. 3

10 5. 920

6. green 45% yellow 30% blue 5% red 20%

F 1. 1 in 6 2. 1 in 2 (50-50) 3. 1 in 100 4. 1 in 5 (20 in 100) 5. 3 in 8 6. 1 in 2 (50-50) 7. 1 in 4


1. Teacher Check 2. Teacher Check 3. 7 in 10 4. number is >20 5. the number has an 8 and a 9 6. the number is 10 7. one head and one tail 8. 1 in 8 9. n/a 10. n/a

Topic 21: Money Page 65A 1. €46.50 2. €46.40 3. €13.60 4. €17.85 5. €7.85 6. €31.85 7. €42 8. €12 9. €27 10. €15 11. €21 12. €7 13. €24 14. €9 15. €12B1. (a) 10c, 5c, 1c (b) 20c, 5c, 2c, 2c (c) 50c, 20c, 20c, 2c, 2c (d) €2, €1, 50c, 10c, 5c, 2c, 1c 2. (a) €20, €20, €5 (b) €50, €20, €20, €5 (c) €100, €20, €10, €5 (d) €200, €100, €20, €10C 1. 9 apples @ €3.06 2. (a) €858 (b) €270.25 3.

Amount €100 €50 €20 €10

€75.34 1 1

€82.46 1 1 1

€118.22 1 1

€94.26 1 2

€186.46 1 1 1 1

€556.74 2 4 5 3


Amount €5 €2 €1 50c

€75.34 1

€82.46 1

€118.22 1 1 1

€94.26 2

€186.46 1 1

€556.74 3 4 2

Amount 20c 10c 5c 2c 1c

€75.34 1 1 2

€82.46 2 1 1

€118.22 1 1

€94.26 1 1 1

€186.46 2 1 1

€556.74 7 1 3 3 3

Topic 21: Money Page 66

D 1. €60 2. €54 3. €46E 1. €96 2. €133.50 3. €164 4. €393.50F 1. €71.50 2. $181.25 3. €35 4. €80 5. camera in Dublin €156


1. €128 2. Goods Total €345, VAT €72.45,

Total €417.25 3. €20 4. €660 5. €44 6. €5,121.62 7. US$390 8. €7,490 9. 6 for €2.40 10. €248.40

Topic 22: Directed Numbers Page 68

A 1. A +300m B –200m C +600m D 0 E –700m 2. 500m 3. 1,300m 4. 200mB 1. (a) 6 (b) 8 (c) 6 (d) 9 (e) 8 (f) 10 (g) 14 (h) 14 (i) 8 (j) 22 (k) 25 (l) 91 2. (a) > (b) < (c) > (d) < (e) > (f) > (g) < (h) < (i) > (j) > (k) > (l) < 3. (a) +10 ▼+5▼ 0▲ +5▲ +10 (b) +20▼ +12 ▼+4 ▼–4▼ –12 (c) +10▼ +2▼ –8 ▲–1▼ –9 (d) –7 ▲+1▲ +10▼ +3▼ –6 (e) +5▼ –6▲ 0▼ –8▲ +2 (f) +3▼ –6 ▲–2▼ –8▲ 5

Topic 22: Directed Numbers Page 69

C 1. 31°C in June 2. –11°C in January 3. (a) 5°C (b) 11°C 4. (a) 3°C (b) 2°C (c) 6°C 5. (a) 25°C (b) 24°C (c) 42°C

Test Yourself! 0

1. –13 –4 +7 +11 2. 7 3. –15 –9 –3 0 +2 +8

4. 712m

5. –12 6. none of these 7. +3 8. –€40 9. –€60

Topic 23: The Circle Page 71

A 1. yes 2. infinite number 3. 14 4. one 5. half of a circle 6. electrical circuit / racingC 1. (a) 2.5m and 15.7m (b) 4m and 25.12m (c) 5.5m and 34.54m (d) 3.9m and 24.492m (e) 2.8m and 17.584m (f) 1.55m and 9.734m (g) 2.1m and 13.188m 2. (a) 314cm (b) 1,256cm (c) 1,570cm (d) 1,884cm

Topic 23: The Circle Page 72

E 1. (a) 10.5m (b) 21m (c) 210m (d) 2,100m 2. (a) twice (b) 4 times (c) 12 times (d) 50 times 3. (a) 6,280km (b) 12,560km


1. green arrow points to centre black arrow points to circumference

red arrow points to radius blue arrow points to diameter 2. Teacher Check 3. none of these 4. 75.36cm 5. infinite number 6. around 7. inside 8. n/a 9. 28.26cm 10. 23.55m or 2,355cm

Topic 24: Using Percentages Page 74

A 1. 27 2. 28 3. 30 4. 48 5. 12 6. 18 7. 19.2 8. 21.6B

1. 10%, 20%, 50%, 25%, 1212%, 100%

30%

2. 3313%, 162

3%, 25%, 75%, 20%, 1212%,

70% 3. 7 seconds 4. 40% 5. Profit €50 €100 €60 €160 €140 €270 €31

Percentage 25% 25% 10% 20% 50% 75% 5%

Topic 24: Using Percentages Page 75

C

Bought for Sold for

Guitar €80 €120

Accordion €250 €300

Piano €1,200 €1,020

Banjo €300 €390

Trumpet €450 €405

Flute €550 €880

Violin €600 €552

Cello €720 €990

€ Profit / Loss

% Profit / Loss

Guitar €40 50% profit

Accordion €50 20% profit

Piano €180 loss 15% loss

Banjo €90 30% profit

Trumpet €45 10% loss

Flute €330 60% profit

Violin €48 loss 8% loss

Cello €270 profit 3712% profit

D 1. (a) €9 (b) €13.50 (c) €18 (d) €22.50 (e) €27 2. €900 3. €400 4. €50E Two years ago its value fell to

€200,000. When its value rose last year by 50%, the calculation is on its present value – 50% of €200,000 – bringing its value to €300,000.


1. €150 2. €120 3. 10% 4. 20%

5. 12 6. €24

7. €75 8. €32 9. €669.50 10. €52.80



A 1. (a) cube (b) pentagonal pyramid (c) hexagonal prism 2. A, C, E and F 3. 3, 5, 3B 1. false 2. true 3. true 4. falseC 1. cuboid 2. cylinder 3. sphere 4. cube 5. cuboid 6. cone 7. sphere 8. cylinder


D n/aE Teacher Check


1. When sliced, a pyramid’s cross-sections get smaller, while those of a prism remain the same.

2. cuboid (among others) 3. 5 vertices 4. hexagonal prism 5. square pyramid 6. cylinder 7.

8. a slice 9. cuboids and cylinders stack

spheres and pyramids won’t stack 10. 1 more

Topic 26: Weight 0

A 1. bicycle, van, lorry, aeroplane 2. pip, grape, apple, pineapple 3. pea, mushroom, carrot, cabbage 4. mouse, kitten, cow, elephant 5. strand of hair, stick of chalk,

calculator, full lunchboxB 1. (a) 4.236kg (b) 8.98kg (c) 2.103kg (d) 7.015kg (e) 9.003kg (f) 8.06kg (g) 8.23kg (h) 4.8kg (i) 7.047kg 2. (a) 4kg 128g (b) 3kg 119g (c) 5kg 496g (d) 7kg 700g (e) 3kg 30g (f) 4kg 9g (g) 120g (h) 900g (i) 7g 3. (a) 6.475kg (b) 3.056kg (c) 3.257kg (d) 7kg (e) 6.525kg (f) 8.6kg (g) 4.09kg (h) 3.747kg

(i) 89.28kg (j) 109.989kg (k) 0.335kg (l) 0.587kg (m) 2.75kg

Topic 26: Weight Page 81

C Camel 1: 40kg Camel 2: 44kg Camel 3: 30.9kg Camel 4: 28.0kg Camel 5: 25.0kg Camel 6: 0.5kg Camel 7: 60g Camel 8: 0.02kg Camel 9: 10g Camel 10: 0.001kgPuzzle Place the elephant (carefully!) in the

boat. Use the paint to mark the level to which the boat drops in the water. Take out the elephant. Fill the boat with stones until it drops to the same point. Take out the stones and weigh each of them. Add the weights.


1. approx. 300g 2. 6.64kg 3. 110g 4. none of these 5. 8.29kg 6. 3.07kg 7. 1.5kg 8. 13kg 9. €26.25 10. 0.34kg

Topic 27: Number Rules Page 83 & 84

A Teacher CheckB 1. (a) 29 (b) 2 (c) 40 (d) 48 (e) 35 (f) 0 2. (a) 14 (b) 17 (c) 13 (d) 12 (e) 11 (f) 20 (g) 16 (h) 20 3. (a) 14 (b) 29 (c) 25 (d) 36 (e) 93 (f) 94 (g) 91 (h) 92D 1. (a) 60, 72, 84 (b) 375, 450, 525 (c) 495, 594, 693 (d) 4,007, 3,998, 3,989 (e) 6, 0, –6 (f) 3, –4, –11 (g) –8, –5, –2 (h) –6, 2, 10 2. (a) 2.51, 2.56, 2.61 (b) 3.099, 3.103, 3.107 (c) 6.311, 6.305, 6.299 (d) 0.06, 0.03, 0.015 3. (a) 16 (b) 36 (c) 81 (d) 256 (e) 576 (f) 3,600 4. Brackets, of, multiply, divide, add,

subtract


1. 99, 110, 121 2. 3, –5, –13 3. 2.998, 3.004, 3.01 4. 7 5. 36 6. none of these 7. (12 + 10) + (20 – 6) = 36

Topic 28: Averages and Charts Page 86

A 1. 13 2. 21 3. 15 4. 51 5. 5 6. 10 7. 4 8. 7 9. 6C 1. (a) 31 (b) 47.5 (c) 33 (d) 24 (e) 27 (f) 45 (g) 30 (h) 26 (i) 45

2. (a) 14 (b) 20 people

(c) 8 people (d) 8 people (e) 24 people

Topic 28: Averages and Charts Page 87

D Teacher CheckE 1. 1.45¬ 2. €113.25 3. €84 4. Bill 5. 2.99km 6. Doris and Bill 7. 3.24km 8. 72 minutes 9. 96 minutes


1. 64 2. Josh (Josh averaged 55% and Jenny

averaged 54%) 3. 95 4. 54 5. none of these (316) 6. 24 7. 222 8. 79 students

Topic 29: Variables Page 89

B 1. (a) 8 (b) 13 (c) 18 (d) 13 (e) 11 (f) 12 2. (a) 3 (b) 4 (c) 6 (d) 8 (e) 2 (f) 3 3. (a) 6 (b) 7 (c) 12 (d) 20 (e) 14 (f) 72 4. (a) 16 (b) 2 (c) 10 (d) 23 (e) 32 (f) 4 (g) 3 (h) 12C 1. (a) €24.20 (b) €48.40 (c) €90.75 (d) €106.48 (e) €110.11 (f) €127.05 2. (a) €50 (b) €60 (c) €80 (d) €100 (e) €111 (f) €120

Topic 29: Variables Page 90

D

Nero 414 faults

Tiberias 412 faults

Constantine 16 faults Julius 13 faults

Romulus 114 faults

Tacitus 12 faultsE 1. Barbara €8.40 Maeve €5.60


Fred €11.20 Ricky €16.80 Julie €16.80 Tony €28 2. Let x be the amount of money

Rebecca had yesterday. 2x + 5 = 25 so x = €10F 8

Test Yourself! 1

1. x = 8 2. x = 6 3. Let x be the number. x/5 = 10 x=50 4. 1 5. none of these 6. 9 7. €16 8. €17 9. €3 10. Teacher Check

Topic 30: Capacity and Volume Page 92

A 1. 8¬ 127m¬ 2. 2¬ 367m¬ 3. 1¬ 150m¬ 4. 2¬ 80m¬ 5. 3¬ 600m¬ 6. 9¬ 100m¬ 7. 4¬ 250m¬ 8. 5¬ 200m¬ 9. 2¬ 100m¬ 10. 3¬ 1m¬ 11. 1¬ 10m¬ 12. 7¬ 375m¬ 13. 5¬ 800m¬ 14. 2¬ 17m¬ 15. 8¬ 230m¬ B 1. 900¬ 2. 10¬ 3. 20¬ 4. 950¬C 1. (a) 8 (b) 125 (c) 512 (d) 1,331 (e) 8,000 (f) 1,000,000 2. (a) 6.345¬ (b) 3.354¬ (c) 16.498¬ (d) 25.314¬ (e) 36.003¬ (f) 10¬ 3. (a) 5¬ 971m¬ (b) 6¬ 321m¬ (c) 7¬ 920m¬ (d) 4¬ 24m¬ (e) 4¬ 648m¬ (f) 5¬ 404m¬ 4. (a) 13¬ 680m¬ (b) 41¬ 24m¬ (c) 102¬ 960m¬ 5. (a) 912m¬ (b) 1¬ 595m¬ (c) 392m¬

Topic 30: Capacity and Volume Page 93

D 1. (a) reject (b) accept (c) reject (d) accept (e) reject (f) reject 2. (a) accept (b) accept (c) accept (d) reject (e) accept (f) accept (g) reject (h) reject 3. (a) reject (b) reject (c) reject (d) accept (e) accept (f) accept (g) accept (h) reject (i) reject (j) accept (k) accept (l) reject (m) reject (n) reject (o) reject

4. (a) accept (b) reject (c) accept (d) accept (e) accept (f) reject (g) accept (h) accept (i) reject (j) accept (k) accept (l) reject (m) accept (n) reject (o) accept (p) rejectE 1. Must provide customer with amount

specified. 2. Measure the weight or capacity and,

if it’s wrong, bring it to the attention of the maker.

3. If the tolerance was very big, then bottles that were less than half full, for example, would be sent to the shops for sale. Lots of unhappy customers!


1. 2.967¬ 2. 230m¬ 3. 350m¬ approx 4. none of these 5. 6.206¬ 6. 4.9¬ 7. 4.5¬ 8. 3.25¬ 9. 512

Topic 31: Co-ordinates Page 95 & 96

A and B Teacher CheckC 1. (5,5) 2. (a) (1,10) (b) (4,7) (c) (9,9) (d) (10,5) (e) (7,3) (f) (9,2) 3. (1,1) (2,8) and (3,2) 4. Sunless Crater (and Hades Chasm) 5. South-West


1. – 4. (0,5)(3,6)(0,10)(4,7)(5,10)(6,7)(10,10) (7,6)(10,5)(7,4)(10,0)(6,3)(5,0)(4,3)

(0,0)(3,4)(0,5) 5. – 8. Teacher Check 9. and 10. Teacher Check


A 1. navy / crew 2. clothes 3. French 4. .ie 5. look 6. safe 7. strand, shore, beach 8. antarctic 9. sidewalk 10. fuinneogB 1. (a) 36 (b) prime (c) range / plus-minus (d) backward slash (e) heart 2. (a) spade (b) difference (c) product (d) reflex

(e) 000,000,000

3. (a) ¬ (b)

(c)

(d) Mars (e) software


C 1. €75 and €45 2. ring all 10 of the possible numbers 3. (a) minor (b) 2 minutes 11 seconds (131

seconds) 4. €62.50 5. €37.60 6. €1,560 7. €39,600D


1. 2 hours 5 minutes 2. €1,074.80 3. €90 4. 14:55 5. empty blue square 6. none of these (31 games) 7. €2.30 8. Alan 20%, Amy 25% 9. €288

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