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! Page 10
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
Test Yourself! Page 13
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
Topic 4: Multiplication 1 Page 15
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
Test Yourself! Page 16
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°
Test Yourself! Page 19
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 Page 20
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
Test Yourself! Page 22
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
Topic 7: Fractions 1 Page 24
D Numerator – the number above the
line in a fraction. Improper fraction – the numerator is
larger than the denominator.
231Planet Maths Teacher Resources • 6th Class
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)
Test Yourself! Page 25
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
Topic 8: 2D Shapes Page 27
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
Test Yourself! Page 28
1. 2. Trapezium 3. Scalene 4. No 5. Octagon 6. Polygons 7. 49 8. Teacher Check 9. Equilateral 10. A protractor
Topic 9: Fractions 2 Page 29
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 Page 30
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
Test Yourself! Page 31
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
232 Planet Maths Teacher Resources • 6th Class
G 1. (a) €18 (b) €54 2. 608 3. 2,550 4. €304.52 5. (a) €36 (b) €60
Test Yourself! Page 34
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
Test Yourself! Page 37
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
Topic 12: Multiplication 2 Page 38
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
Topic 12: Multiplication 2 Page 39
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! Page 40
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
Test Yourself! Page 43
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
Topic 14: Division 2 Page 44
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
233Planet Maths Teacher Resources • 6th Class
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
Topic 14: Division 2 Page 45
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.)
Test Yourself! Page 46
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%
Topic 15: Percentages 1 Page 48
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
Test Yourself! Page 49
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 Page 50
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
Test Yourself! Page 52
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
Topic 17: Percentages 2 Page 53
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%
Topic 17: Percentages 2 Page 54
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
234 Planet Maths Teacher Resources • 6th Class
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
Test Yourself! Page 55
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.
3. 5cm2 approx. 4. 35cm2 approx.
5. 15cm2 approx. 6. 3cm2 approx.
7. 18cm2 approx. 8. 2cm2 approx.
F
1. 1,360m2
2. bowling 112m2
horse riding 216m2
archery 160m2
badminton 160m2
swimming 192m2
3. 520m2
4. horse-riding
Test Yourself! Page 58
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 Page 60
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
Test Yourself! Page 61
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
Test Yourself! Page 64
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
235Planet Maths Teacher Resources • 6th Class
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
Test Yourself! Page 67
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! Page 70
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
Test Yourself! Page 73
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.
Test Yourself! Page 76
1. €150 2. €120 3. 10% 4. 20%
5. 12 6. €24
7. €75 8. €32 9. €669.50 10. €52.80
236 Planet Maths Teacher Resources • 6th Class
Topic 25: 3D Shapes Page 77
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
Topic 25: 3D Shapes Page 78
D n/aE Teacher Check
Test Yourself! Page 79
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 Page 80
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.
Test Yourself! Page 82
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
Test Yourself! Page 85
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
Test Yourself! Page 88
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
237Planet Maths Teacher Resources • 6th Class
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! Page 91
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!
Test Yourself! Page 94
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
Test Yourself! Page 97
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
Topic 32: Problem Solving 2 Page 98
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
Topic 32: Problem Solving 2 Page 99
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
Test Yourself! Page 100
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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