Get the Results You Want!

DiZign Pty Ltd

Get the Results You Want!

START UP MATHS Year 5 Ages 10 –11 years old This book is part of the Excel Advanced Skills series, which provides students with more challenging extension work in Mathematics. The Excel Advanced Skills Start Up Maths series for Foundation to Year 7 has been specifically designed to be used as classroom or homework books in order to help students with their understanding of Mathematics. Each book in the series covers the year’s work in detail. Innovative features provide an integrated and supportive approach to learning. All units of work, review tests and Start Up sections are interrelated and cross-referenced to each other. (Please read the inside front cover for more details.) This series of books is a must for students who want to cover the year’s work comprehensively, with no gaps in their knowledge. The completion of this workbook in Year 5 will ensure that a student will be fully prepared for the work in Year 6.

In this book you will find: Over 170 units of work to complete

Year 5 Ages 10 –11

    

Thirty-five review tests for revision Over 2000 exercises to practise A Start Up section for extra help with understanding questions Comprehensive coverage of the year’s work

About the author Damon James, BEd, MSc(Ed), DipInfoTechEd, is an experienced teacher and a successful author of many primary and secondary Mathematics textbooks.

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ISBN 978-1-74125-262-0

Excel Test Zone


H Help your child prepare with our NAPLAN*-style and Australian Curriculum Tests. FREE N www.exceltestzone.com.au *This isi nott an offi *Thi fficially i ll endorsed d publication of the NAPLAN program and is produced by Pascal Press independently of Australian governments.

9781741252620 StartUpMaths Yr5 2016.indd 2,4

Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www.pascalpress.com.au

Damon James

T UP START UP START TART UP STAR UP ST T UP2 S MATHS 3 MATHS 4 MATHS 5 MATHS ART U R A T 6 S P S S P H MATHS U TAR RT S 1 MAT 7 A 7 T 7 S ATH 4 MATT UP 0 10 M HS I VI –3 3 0.5 ADVANCED SKILLS

ADVANCED SKILLS START UP MATHS

Advanced Skills

MATHS

ADVANCED SKILLS

YEAR

5

AGES 10–11

START UP MATHS

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G e t t he Re su lt s You Damon James Want !

18/05/2016 2:19 PM

UNIT 1

UNIT 2

See START UPS page 1

Numbers to 99 999 (1) 1

Complete the numeral shown on each abacus:

a Th

H

T

TTh

Th

H

T

U

TTh

Th

H

T

TTh

Th

H

T

U

Th

H

T

H

T

U

Th

H

T

U

e

U

TTh

Th

H

T

U

2

a eighty-three thousand, five hundred and sixty-three

Th

H

T

U

TTh

Th

H

T

U

TTh

Th

H

T

U

Questions 1–4: notice that each question always has exactly six exercises, i.e. a–f. This is so you will have plenty of practice of a new concept (and the same amount) so you can understand it.

f

TTh

Write the numeral for:

TTh

d TTh

f

TTh

Th

c

U

Important: turn to page 17 while you are reading this.

b

TTh

d

e

Write the numeral shown on each abacus:

a

U

c

2

1

b

TTh

Step 1: Units


Numbers to 99 999 (2)

Th

H

T

U

Write each of the following numbers in words: a 12 052

b 30 906

b twenty-five thousand, nine hundred and fifteen

c 11 042 c thirty-seven thousand, three hundred and

d 47 635

forty-five

d forty thousand, seven hundred and ninety-one

3

f 70 100 3

Write the value of the underlined digit:

a 27 385 c 40 219 e 16 190 4

e 90 020

e fifteen thousand and ninety-six f ten thousand, one hundred and fifty


a 70 000 + 2000 + 300 + 40 + 5 b 50 000 + 8000 + 600 + 90 + 8 c 60 000 + 400 + 70 + 3 d 20 000 + 800 + 90 + 5 e 10 000 + 1000 + 200 + 10 + 2 f 30 000 + 5000 + 500 + 2

b 71 867 d 55 345 f 42 612

Write each set of numbers in ascending order:

a 23 815, 41 672, 38 521 b 11 085, 12 346, 61 460 c 46 825, 45 118, 47 325 d 62 000, 63 051, 61 460 e 51 045, 51 001, 51 437 f 71 185, 76 459, 73 215

4

Questions 5–8: notice that question 5 is like question 1 repeated, question 6 is like question 2 repeated, question 7 is like question 3 repeated, and question 8 is like question 4 repeated. This is so you will revise each type of question you have just learnt.

State the value of the 8 in each of the following:

a 18 432 c 11 058 e 32 981

b 16 854 d 83 205 f 46 118

5


5


6

Write sixty-three thousand and forty-nine as a numeral.

6

Write 72 105 in words.

7

Write the value of the underlined digit: 17 851

7

Write the numeral for: 20 000 + 3000 + 500 + 6

8

Write the set of numbers in ascending order:

8

State the value of the 8 in 18 526.

9

9

61 059, 61 738, 60 476 Write the number closest to 2000, with the digits 1, 8, 4 and 2.

What is the number that is 5000 greater than thirty-two thousand, eight hundred and fifty-nine?

Th

TTh

☞

H

T

TTh

U

Th

H

T

U

Units

Answers on page 124

17

Question 9: notice that this question is a bit harder than other questions. This is so you will have a challenging problem to test yourself at the end of each unit.

Step 2: Start Ups

START UPS: Units 1 – 11 Unit 1


Page 17

Unit 5

Place value 0.01 to 99 999

1 An abacus is read as the number of discs above each letter: U = units, T = tens, H = hundreds, Th = thousands, TTh = tens of thousands. e.g.

1 2 3 4

is 42 163 Note: it can also be used to show decimals. 2 A number can be written in words or digits. e.g. 1629 is one thousand, six hundred and twenty-nine. To write in digits, write the values in place order. If there is no digit for a certain place, then a zero is written, e.g. 1072. Note: numbers can also be written with decimals. e.g. 421.89 is four hundred and twenty-one, point eight nine. 3 Look at the place of the underlined digit and this gives the value, e.g. for 325, the 3 is in the hundreds place, so has a value of 3 hundreds or 3 3 100. 4 Ordering numbers can be determined by looking at the digits in the tens of thousands place and comparing them. If these digits are the same, then look at the digits in the thousands place and so on, e.g. 32 416 is larger than 29 815. Ascending order means smallest to largest and descending order means largest to smallest.

1 See Unit 4 No. 3 2 See Unit 2 No. 4 3 See Unit 1 No. 2 4 See Unit 4 Nos 2 and 4

Unit 6 TTh

Unit 2

Th

H

T

U


Page 17

1 See Unit 1 No. 1 2 See Unit 1 No. 2 3 To write the number, take the first digit of each number and put in order of place. e.g. 70 000 + 4 000 + 800 + 20 + 4 gives the digits 7, 4, 8, 2, 4 so the number is 74 824. 4 To find the value of a certain number, look at the place of that digit and this gives the value. For the 8 in 2185, the 8 is in the tens place, so has a value of 8 tens or 8 3 10.

Unit 3

Place value 0 to 99 999 (1)

Page 18

1 A number line is a line marked with numbers in order. 0

1

2

3

4

5

6

7

8

9

10

2 To compare numbers, look at the digits in the tens of thousands place, and compare. If they are the same then look at the digits in the thousands place and so on. e.g. 24 163 is larger than 23 984 by comparing the digits in the thousands place. 3 See Unit 1 No. 2 4 A place value chart is like a numeral expander. Each digit is written in the column of place. If there is no value, a zero is written. Note: U = units, T = tens, H = hundreds, Th = thousands, TTh = tens of thousands. When there is a decimal, the decimal point is shown and Tths (tenths) and Hths (hundredths).

Unit 4

Ordering numbers

Page 18

1 See Unit 1 No. 4 2 and 4 To write a number larger than, add (or count) on. To write a number less than, count back. e.g. 64 411 is larger than 60 000 but less than 65 000. 3 < means less than and > means greater than. So 2411 < 2519 reads, 2411 is less than 2519. 0.9 > 0.6 reads 0.9 is greater than 0.6.

Page 19

Unit 7


Page 19


Page 20

1 See Unit 3 No. 4 2 See Unit 4 No. 3 3 See Unit 1 No. 3 4 The number of thousands is all of the numbers in the thousands place and to the left. e.g. 1 239 has 1 thousand 21 486 has 21 thousands 329 495 has 329 thousands

Unit 8


Page 20

Unit 9

Number patterns (1)

Page 21

1 Determine the counting pattern of units, tens, hundreds or thousands by looking at the value of the units, tens, hundreds or thousands place. Complete the pattern or write the missing numbers in the boxes. This also applies to decimals. Note: doubling or halving, multiplying or dividing can also form number patterns. e.g. 63, 66, 69 is a counting pattern of adding 3 determined by looking at the units place. The next two numbers in the pattern are 72 and 75, found by counting on. 2 1000 more is found by adding 1 to the thousands digit. 1000 less is found by subtracting 1 from the thousands digit. 3 Start at the given number and continue the counting pattern. 4 To find the tenth term, count on nine times or find the difference, multiply by 9 and add to the first number.

Unit 10

Expanding numbers

page 17 page 17 page 18 page 18

The value of the underlined digit in 43 219 is: A 3 tens C 3 hundreds

A 53 206

Unit 11

Ordinal numbers

Page 22

1 – 4 Ordinal numbers are the numbers that show place or position, such as 1st, 2nd, 3rd, and so on. They can be written in words, such as first, second, or as abbreviations, 21st, 90th.

UNIT 1 Q3

Unit 5 Place value 0.01 to 99 999 Unit 6 Place value 0 to 99 999 (2) Unit 7 Numbers to 999 999 (1) Unit 8 Numbers to 999 999 (2)

1

2 Q2 3 Q3

B 52 600

C 53 260

D 53 060

TTh

Th

H

T

True or false? 81 076 > 80 176

4 Q3

5

Write the set of numbers in ascending order: 51 204, 51 098, 51 725, 51 217

1 Q4 4 Q1

Write 20 709 in words.

2 Q2

How many thousands are there in 2476?

8

Expand: 84 229 +

86 147

+

TTh Th

5 Q4

6

Complete with < or > 462 107

8 Q2

7

Write 107 648 on the place value chart.

8

62 947

T

9

Use the set of digits to write the largest possible number in digits:

forty-two thousand, five hundred and ten

IFC_2016.indd 1

3 Q2 4 Q2

1 Q2 2 Q2 2 Q3

B 5000 + 100 + 6 D five thousand, one hundred and sixty Score =

☞ Answers on page 152

5 Q3 7 Q1

6 Q4

10 Circle the numeral that matches:

U

62 385

12 Which of these numerals does not represent 5106? A 5000 + 106 C 5106 units

461 905

U

Circle the number between 86 496 and 86 600.

42 501

63 001

T

Questions 1–12: notice that questions 1 and 2 are always multiple-choice questions and that questions 3 and 4 are always true/false questions. The rest of the questions in the test are a cross-section from the four to six units covered by the review test. This is so you are tested in a variety of ways to make sure you have fully understood the work. Unit margins: notice that each question has a unit and question reference, which is a similar question to the one given. This is so you know the exact question to go back to if you get a question wrong and need more practice to understand it.

8 Q4

one, six, three, four, eight and seven

11 Circle the numbers larger than 62 000 but less than 62 500: 62 498

5 Q2 6 Q2 7 Q3

86 454, 86 610, 86 521, 86 705

3 Q4 H

6 Q1 7 Q2

Write 104 381.25 in words.

86 937

10 Write 20 000 + 4000 + 300 + 20 + 1 on the place value chart.

7 Q4

D 54

The value of the underlined digit in 1460.17 is 7 hundredths.

+ 3 Q2

85 981

C 80

True or false?

H

Units 1–4 and 5–8: notice that each review test covers four units. This is so your knowledge is tested on several units. Notice also that you are told what units these are in case you want to revise them before doing the test.

C 46 019 D 46 190

B5

2 Q4

Circle the largest number: 85 325

B 460


UNIT 5 Q1 8 Q1

U

True or false? 41 609 > 41 610

5

2 Q3

+

T

4

HTh TTh Th

7

H

3

U

4

Th

The number of thousands in 805 429 is: A 805

1 Q1 2 Q1

The numeral of is 3617.

9

Step 3: Review Tests


The number represented on the abacus is:

A 4619 2

42 510

6 Q3 8 Q3

420 510

11 A five placed in the thousands column has more or less value than a nine in the hundreds column?

5 Q2 6 Q2 7 Q1 7 Q2 7 Q3 7 Q4 8 Q4

12 If I move a digit from one column to the column next to it on the left, I increase times. its value

5 Q3 6 Q2 7 Q1 7 Q4 8 Q4

/12 Review Tests

The student turns to the Start Ups section for Units 1–11 on page 1, then turns to Unit 1 question 4 and finds a more detailed explanation.

1

TTh

True or false?

6

A student has trouble understanding question 4 of Unit 1.

Page 21

1 See Unit 2 No. 3 2 – 3 To expand a number, break the number into its components of tens of thousands, thousands, hundreds, tens and units. Write as an addition equation. e.g. 2619 = 2000 + 600 + 10 + 9 4 See Unit 1 No. 3

B 30 thousands D 3 thousands

Fifty-three thousand, two hundred and sixty written as a numeral is:

3

For example:

See START UPS page 1 REVIEW TESTS: Units 1 – 8

UNIT 1 Unit 1 Numbers to 99 999 (1) Unit 2 Numbers to 99 999 (2) Unit 3 Place value 0 to 99 999 (1) Unit 4 Ordering numbers

2

Units 1–11: notice that each unit has extra information for questions 1–4. This is to give a more detailed explanation so you can understand a question better. Remember that questions 5–8 are just questions 1–4 repeated, i. e. question 5 is like question 1, question 6 is like question 2, etc.—so you can apply the explanations to these questions as well.

1 See Unit 1 No. 1 2 See Unit 4 No. 3 3 See Unit 1 No. 2 4 To write the largest number, find the largest digit and write it first, then the next largest and so on. Using the digits 8, 4, 1, 7, 3, the largest number is 87 431.

Start Ups

1


See Unit 1 No. 1 See Unit 1 No. 3 See Unit 3 No. 4 See Unit 1 No. 2

Score =

For example:

/12 105

A student gets question 5 of Units 1–4 wrong.

The student sees that next to the question it says: 1 Q4, i.e. Unit 1 question 4, so the student turns to Unit 1 question 4 and finds a similar question to practise.

19/05/2016 2:40 PM

MATHS

ADVANCED SKILLS

YEAR

5

AGES 10–11

START UP MATHS

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Damon James i-iv Y5Contents_2016.indd 1

18/05/2016 2:29 PM

Contents Start Ups Units 1 – 11......................................................................1 Units 12 – 20....................................................................2 Units 20 – 31....................................................................3 Units 31 – 43....................................................................4 Units 43 – 59....................................................................5 Units 60 – 71....................................................................6 Units 71 – 81....................................................................7 Units 81 – 89....................................................................8 Units 90 – 100..................................................................9 Units 100 – 110..............................................................10 Units 110 – 120..............................................................11 Units 121 – 135..............................................................12 Units 135 – 149..............................................................13 Units 150 – 163..............................................................14 Units 164 – 176..............................................................15 Geometry Unit.................................................................16

Units Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Numbers to 99 999 (1) ........................................... 17 Numbers to 99 999 (2) ........................................... 17 Place value 0 to 99 999 (1) ..................................... 18 Ordering numbers .................................................. 18 Place value 0.01 to 99 999 ..................................... 19 Place value 0 to 99 999 (2) ..................................... 19 Numbers to 999 999 (1) ......................................... 20 Numbers to 999 999 (2) ......................................... 20 Number patterns (1) ............................................... 21 Expanding numbers................................................ 21 Ordinal numbers..................................................... 22 Less than and greater than...................................... 22 Number patterns (2) ............................................... 23 Roman numerals .................................................... 23

24 25 26 27

Subtraction to 9999 (1)........................................... 28 Subtraction to 9999 (2)........................................... 29 Subtraction to 99 999 (1)........................................ 29 Subtraction to 99 999 (2)........................................ 30

Estimation and multiplication 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Estimation .............................................................. 30 Rounding numbers (2) ............................................ 31 Tables (1) ............................................................... 31 Tables (2) ............................................................... 32 Tables (3) ............................................................... 32 Tables (4) ............................................................... 33 Multiplication by tens and hundreds ....................... 33 Multiplication to 999............................................... 34 Multiplication to 9999............................................. 34 Extended multiplication (1) ..................................... 35 Extended multiplication (2) ..................................... 35 Multiples and square numbers ............................... 36 Factors ................................................................... 36 Multiplication and problem solving ......................... 37

Division 42 43 44 45 46 47 48 49 50

Division .................................................................. 37 Division of 2-digit numbers (1) ............................... 38 Division of 2-digit numbers (2) ............................... 38 Dividing numbers containing zeros.......................... 39 Divisibility............................................................... 39 Division of 3-digit numbers (1) ............................... 40 Division of 3-digit numbers (2) ............................... 40 Division by tens ...................................................... 41 Division of 4-digit numbers .................................... 41

Number lines and operations 51 Number lines........................................................... 42 52 Inverse operations and checking answers .............. 42 53 Number lines and operations................................... 43

Adding, subtracting and rounding numbers 15 16 17 18 19 20 21 22 23

ii

Addition review ...................................................... 24 Adding 3-digit numbers........................................... 24 Adding to 9999 (1) ................................................. 25 Adding to 9999 (2) ................................................. 25 Adding large numbers ............................................ 26 Mental strategies for addition ................................. 26 Subtraction review ................................................. 27 Mental strategies for subtraction ............................ 27 Rounding numbers (1) ............................................ 28

© Pascal Press ISBN 978 1 74125 262 0

i-iv Y5Contents_2016.indd 2

Averages 54 Averages (1) ........................................................... 43 55 Averages (2) ........................................................... 44

Order of operations 56 57 58 59

Order of operations (1) ........................................... 44 Order of operations (2) ........................................... 45 Order of operations (3) ........................................... 45 Operations with large numbers............................... 46

Excel Start Up Maths Year 5

Excel Advanced Skills Start Up Maths Year 5 17/05/2016 2:57 PM

Working with numbers

Symmetry

60 61 62 63

95 Symmetry .............................................................. 64

Working with numbers ........................................... 46 Missing numbers..................................................... 47 Change of units ...................................................... 47 Reasoning with numbers ........................................ 48

Negative numbers 64 Negative numbers .................................................. 48

Calculator use 65 Calculator – addition, subtraction and multiplication.......................................................... 49 66 Calculator – division................................................ 49

Fractions 67 68 69 70 71 72 73 74 75

Fractions ................................................................ 50 Fraction of a group ................................................. 50 Comparing fractions ............................................... 51 Equivalent fractions ................................................ 51 Improper fractions (1) ............................................. 52 Improper fractions (2) ............................................. 52 Fraction addition..................................................... 53 Fraction subtraction................................................ 53 Fraction addition and subtraction............................ 54

Decimals 76 77 78 79 80 81 82 83 84 85 86 87 88

Decimal place value – hundredths........................... 54 Decimals ................................................................ 55 Comparing decimals (1).......................................... 55 Decimal place value – thousandths ........................ 56 Comparing decimals (2).......................................... 56 Decimal addition (1) ............................................... 57 Decimal addition (2) ............................................... 57 Decimal subtraction (1) .......................................... 58 Decimal subtraction (2) .......................................... 58 Decimal multiplication ............................................ 59 Decimal division ..................................................... 59 Decimal multiplication and division ........................ 60 Rounding decimals ................................................. 60

Percentages 89 Percentages (1) ...................................................... 61 90 Percentages (2) ...................................................... 61 91 Fractions, decimals and percentages....................... 62

Money 92 Use of money ......................................................... 62 93 Money operations.................................................... 63 94 Money rounding ..................................................... 63

© Pascal Press ISBN 978 1 74125 262 0 i-iv Y5Contents_2016.indd 3

Contents

Angles 96 Classifying angles (1) ............................................. 64 97 Classifying angles (2) ............................................. 65 98 Comparing angles (1) ............................................. 65 99 Comparing angles (2) ............................................. 66 100 Drawing angles (1) ................................................. 66 101 Drawing angles (2) ................................................. 67 102 Drawing angles (3) ................................................. 67 103 Angles in 2D shapes................................................ 68

3D objects 104 3D objects............................................................... 68 105 Drawing 3D objects ................................................ 69 106 Views of 3D objects................................................. 69

2D shapes 107 Triangles................................................................. 70 108 Quadrilaterals ......................................................... 70 109 Polygons................................................................. 71

3D objects 110 Prisms and pyramids............................................... 71 111 Cylinders, spheres and cones ................................. 72

Parallelograms and rhombuses 112 Parallelograms and rhombuses .............................. 72

Movement of shapes 113 Movement of shapes .............................................. 73

Scale drawings 114 Scale drawings and ratios ...................................... 73

3D objects and nets 115 Sections of solids ................................................... 74 116 Nets and 3D objects ............................................... 74 117 Shapes – general review......................................... 75

Maps and directions 118 Maps (1).................................................................. 75 119 Scale....................................................................... 76 120 Maps (2).................................................................. 76 121 Compass directions ................................................ 77

Lines 122 Horizontal and vertical lines..................................... 77

Excel Advanced Skills Start Up Maths Year 5

iii 17/05/2016 2:57 PM

Maps, coordinates and grids

Chance

123 Maps (3................................................................... 78 124 Coordinates ............................................................ 78 125 Grids ...................................................................... 79

159 Chance (1).............................................................. 96 160 Chance (2).............................................................. 96 161 Chance (3).............................................................. 97

Perspective

Tables, graphs and data

126 Perspective............................................................. 79

127 Digital and analog time .......................................... 80 128 am and pm time (1)................................................. 80 129 am and pm time (2)................................................. 81 130 24-hour time (1) ..................................................... 81 131 24-hour time (2) ..................................................... 82 132 24-hour time (3) ..................................................... 82 133 Timetables and timelines........................................ 83 134 Time zones............................................................. 83

162 Picture graphs (1).................................................... 97 163 Picture graphs (2).................................................... 98 164 Line graphs (1) ....................................................... 98 165 Line graphs (2) ....................................................... 99 166 Tally marks............................................................. 99 167 Reading graphs .................................................... 100 168 Column graphs (1)................................................. 100 169 Column graphs (2)................................................. 101 170 Surveys and collecting data (1).............................. 101 171 Surveys and collecting data (2).............................. 102 172 Mean.................................................................... 102

Length

Problem solving

135 Length in mm (1)..................................................... 84 136 Length in mm (2)..................................................... 84 137 Length in km (1)...................................................... 85 138 Length in km (2)...................................................... 85 139 Length with decimals ............................................. 86

173 Problem solving (1)............................................... 103 174 Problem solving (2)............................................... 103 175 Problem solving (3)............................................... 104 176 Problem solving (4)............................................... 104

Time

Perimeter 140 Perimeter (1) .......................................................... 86 141 Perimeter (2) .......................................................... 87 142 Perimeter (3) .......................................................... 87

Area 143 Area (1) .................................................................. 88 144 Area (2) .................................................................. 88 145 Area (3) .................................................................. 89 146 Area (4) .................................................................. 89 147 Hectares................................................................. 90 148 Square kilometres .................................................. 90

Mass 149 Mass in g and kg (1) ............................................... 91 150 Mass in g and kg (2) ............................................... 91 151 Mass in tonnes (1)................................................... 92 152 Mass in tonnes (2)................................................... 92

Review Tests

Units 1 – 8....................................................................105 Units 9 – 19..................................................................106 Units 20 – 29................................................................107 Units 30 – 41................................................................108 Units 42 – 50................................................................109 Units 51 – 59................................................................110 Units 60 – 66................................................................111 Units 67 – 72................................................................112 Units 73 – 80................................................................113 Units 81 – 88................................................................114 Units 89 – 94................................................................115 Units 95 – 103..............................................................116 Units 104 – 112............................................................117 Units 113 – 126............................................................118 Units 127 – 134............................................................119 Units 135 – 142............................................................120 Units 143 – 152............................................................121 Units 153 – 161............................................................122 Units 162 – 176............................................................123

Capacity and volume 153 Capacity in mL and L (1) ......................................... 93 154 Capacity in mL and L (2) ......................................... 93 155 Cubic centimetres (1) ............................................. 94 156 Cubic centimetres (2) ............................................. 94 157 Cubic centimetres (3) ............................................. 95 158 Cubic metres........................................................... 95

iv


i-iv Y5Contents_2016.indd 4

Answers

Units..............................................................................124 Review Tests.................................................................152





Page 17

1 An abacus is read as the number of discs above each letter: U = units, T = tens, H = hundreds, Th = thousands, TTh = tens of thousands. e.g.

Unit 5 1 2 3 4

Unit 6 is 42 163 Note: it can also be used to show decimals. 2 A number can be written in words or digits. e.g. 1629 is one thousand, six hundred and twenty-nine. To write in digits, write the values in place order. If there is no digit for a certain place, then a zero is written, e.g. 1072. Note: numbers can also be written with decimals. e.g. 421.89 is four hundred and twenty-one, point eight nine. 3 Look at the place of the underlined digit and this gives the value, e.g. for 325, the 3 is in the hundreds place, so has a value of 3 hundreds or 3 3 100. 4 Ordering numbers can be determined by looking at the digits in the tens of thousands place and comparing them. If these digits are the same, then look at the digits in the thousands place and so on, e.g. 32 416 is larger than 29 815. Ascending order means smallest to largest and descending order means largest to smallest. TTh

Unit 2

Th

H

T

U


Page 17

1 See Unit 1 No. 1 2 See Unit 1 No. 2 3 To write the number, take the first digit of each number and put in order of place. e.g. 70 000 + 4 000 + 800 + 20 + 4 gives the digits 7, 4, 8, 2, 4 so the number is 74 824. 4 To find the value of a certain number, look at the place of that digit and this gives the value. For the 8 in 2185, the 8 is in the tens place, so has a value of 8 tens or 8 3 10.

Unit 3


Page 18

1 A number line is a line marked with numbers in order. 0

1

2

3

4

5

6

7

8

9

10

2 To compare numbers, look at the digits in the tens of thousands place, and compare. If they are the same then look at the digits in the thousands place and so on. e.g. 24 163 is larger than 23 984 by comparing the digits in the thousands place. 3 See Unit 1 No. 2 4 A place value chart is like a numeral expander. Each digit is written in the column of place. If there is no value, a zero is written. Note: U = units, T = tens, H = hundreds, Th = thousands, TTh = tens of thousands. When there is a decimal, the decimal point is shown and Tths (tenths) and Hths (hundredths).

Unit 4

Ordering numbers

Page 18

1 See Unit 1 No. 4 2 and 4 To write a number larger than, add (or count) on. To write a number less than, count back. e.g. 64 411 is larger than 60 000 but less than 65 000. 3 < means less than and > means greater than. So 2411 < 2519 reads, 2411 is less than 2519. 0.9 > 0.6 reads 0.9 is greater than 0.6.

1 2 3 4



Page 19

See Unit 4 No. 3 See Unit 2 No. 4 See Unit 1 No. 2 See Unit 4 Nos 2 and 4

Unit 7


Page 20

1 See Unit 3 No. 4 2 See Unit 4 No. 3 3 See Unit 1 No. 3 4 The number of thousands is all of the numbers in the thousands place and to the left. e.g. 1 239 has 1 thousand 21 486 has 21 thousands 329 495 has 329 thousands

Unit 8


Page 20

1 See Unit 1 No. 1 2 See Unit 4 No. 3 3 See Unit 1 No. 2 4 To write the largest number, find the largest digit and write it first, then the next largest and so on. Using the digits 8, 4, 1, 7, 3, the largest number is 87 431.

Unit 9

Number patterns (1)

Page 21

1 Determine the counting pattern of units, tens, hundreds or thousands by looking at the value of the units, tens, hundreds or thousands place. Complete the pattern or write the missing numbers in the boxes. This also applies to decimals. Note: doubling or halving, multiplying or dividing can also form number patterns. e.g. 63, 66, 69 is a counting pattern of adding 3 determined by looking at the units place. The next two numbers in the pattern are 72 and 75, found by counting on. 2 1000 more is found by adding 1 to the thousands digit. 1000 less is found by subtracting 1 from the thousands digit. 3 Start at the given number and continue the counting pattern. 4 To find the tenth term, count on nine times or find the difference, multiply by 9 and add to the first number.

Unit 10

Expanding numbers

Page 21

1 See Unit 2 No. 3 2 – 3 To expand a number, break the number into its components of tens of thousands, thousands, hundreds, tens and units. Write as an addition equation. e.g. 2619 = 2000 + 600 + 10 + 9 4 See Unit 1 No. 3

Unit 11

Ordinal numbers

Page 22

1 – 4 Ordinal numbers are the numbers that show place or position, such as 1st, 2nd, 3rd, and so on. They can be written in words, such as first, second, or as abbreviations, 21st, 90th.

Start Ups © Pascal Press ISBN 978 1 74125 262 0

Page 19

See Unit 1 No. 1 See Unit 1 No. 3 See Unit 3 No. 4 See Unit 1 No. 2


1

START UPS: Units 12 – 20 Unit 12 Less than and greater than 1 To find a number greater than, count on, starting at the given number. 2 To find a number less than, count back, starting at the given number. 3 See Unit 4 No. 3 4 See Unit 4 No. 3 and Unit 2 No. 3

Unit 13

Number patterns (2)

Page 22

Unit 16 Page 23

1 – 3 A rule is a simplified way of expressing a process. e.g. 3 5 means each number is multiplied by 5. This can be applied to number patterns. 4 Addition and subtraction are inverse operations. Multiplication and division are inverse operations. This means they are opposite or reverse operations, they ‘undo’ each other. e.g. 24 – 10 + 10 = 24 or 24 – 10 = 14 14 + 10 = 24 and 12 3 2 ÷ 2 = 12 or 1 2 3 2 = 24 24 ÷ 2 = 12

Unit 14

Roman numerals

Page 23

1 – 4 Roman numerals are the numerals/counting system developed by the ancient Romans. I = 1 VI = 6 XX = 20 II = 2 VII = 7 XXX = 30 III = 3 VIII = 8 XL = 40 IV = 4 IX = 9 L = 50 V = 5 X = 10 LX = 60 LXX = 70 LXXX = 80 XC = 90

Unit 15

C = 100 CC = 200 CCC = 300 CD = 400 D = 500

Addition review

4 The jump strategy is: start with the first number then add the tens, then the units. e.g. 46 + 37: 46 + 30 = 76 76 + 7 = 83 so 46 + 37 = 83

DC = 600 DCC = 700 DCCC = 800 CM = 900 M = 1000

Page 24

1 To double means to multiply by 2, so double 10 is 20. When adding two similar numbers such as 11 and 12, doubling one of them, then adding or subtracting their difference, gives the answer. e.g. 11 + 12: double 11 = 22; add 1 gives 23, so 11 + 12 = 23 2 The split strategy is splitting the numbers into hundreds, tens and units then adding together all the hundreds etc. e.g. 143 + 126 = (100 + 100) + (40 + 20) + (3 + 6) = 200 + 60 + 9 = 269 3 The compensation strategy is rounding the number to the nearest 5 or 10, adding the rounded numbers, and then counting on, or back, the difference from the rounding. e.g. 22 + 29 is about 22 + 30 = 52 As 29 was rounded up to 30 so count the answer back by 1 giving 51, thus 22 + 29 = 51.


Page 24

2 Adding three or more numbers is the same as adding two numbers. See No. 1. With quantities don’t forget the units! 3 Number patterns can be useful when completing additions. 4 To complete the addition, the number below the + sign is added to each of the numbers in the table and the answer is written underneath. +

100

200

50

(100 + 50) 150

(200 + 50) 250

Unit 17

Adding to 9999 (1)

Page 25

1 and 3 See Unit 16 Nos 1 – 2 2 Sum, total, plus and add all mean addition, the combining of two or more numbers to find a larger one. 4 To estimate is to make a sensible guess by first rounding the numbers. To round to the nearest ten, numbers 5 and greater are rounded up; numbers less than 5 are rounded down. It can then be checked with the actual calculation of the sum. The ‘actual’ is a calculated answer (a calculator could be useful). The difference is the difference between the estimation and the actual sum.

Unit 18

Adding to 9999 (2)

Page 25

1 See Unit 16 No. 1 2 Examine each solution and find the missing number by counting on or subtracting. Write the answer in the space. Can be found by e.g. 2 Found by adding 2 +3+1=6

+ 3 6

2

counting on 6, as 6 + 6 = 12 and the 1 is carried.

3 See Unit 17 No. 2 4 See Unit 16 Nos 1 – 2

Unit 19

Adding large numbers

Page 26

1, 3 and 4 See Unit 16 Nos 1 – 2 2 To find the numbers that total, trial and error can be used, or look at the units first to see which numbers total and then examine tens and hundreds.

Unit 20

Mental strategies for addition

Page 26

1 Addition of a multiple of tens, hundreds or thousands can be just added to the respective column. e.g. For 5000 + 4000, just add 5 + 4 to give 9, and then add the zeros. Thus 5000 + 4000 = 9000.


2

Adding 3-digit numbers

1 To add vertically, start at the right and add numbers together, write in the units, and carry any tens. Then move to the tens, hundreds etc. through to the left, carrying as necessary. e.g. 1 4 6 1 + 3 9 8 8 5 9


START UPS: Units 20 – 31 2 See Unit 15 No. 4 3 See Unit 15 No. 3 4 As addition and subtraction are inverse operations, they can be used to check each other. 6 5 e.g. 2 4 + 4 1 – 4 1 6 5 2 4

Unit 21

Subtraction review

Page 27

1 See Unit 17 No. 4. Subtraction is the process of taking one quantity away from another. It can be completed by counting back, horizontally or vertically. 2 To complete the table, the number below the – sign is subtracted from each of the numbers in the table and the answer written in the space. e.g. – 40 50 (40 – 10) 30

10

(50 – 10) 40

Unit 23

Rounding numbers (1)

Unit 25

Subtraction to 9999 (2)

Page 29

1 See Unit 21 Nos 3 – 4 2 Take away, minus, difference and less than all mean subtract. 3 To find the missing numbers it is possible to complete the difference or work from the bottom of the equation and complete the addition. Start with units and consider each column individually taking into account any trading. e.g. 3 8 6 ② 4 + = 8

③

5

4

= 4

① 6–5=1

Unit 26

Page 27

Page 28

Subtraction to 99 999 (1)

Page 29

1 and 3 See Unit 21 Nos 3 – 4 2 See Unit 25 No. 2 4 See Unit 22 No. 1

Unit 27


Page 30

1 and 4 See Unit 21 Nos 3 – 4 2 See Unit 25 No. 2 3 See Unit 21 No. 2

Unit 28

Estimation

Page 30

1 – 2 See Unit 23 Nos 1 – 4 3 See Unit 23 No. 4 4 See Unit 23 Nos 1 – 4. Estimation can be used as a form of checking answers.

Unit 29


Page 31

1 See Unit 23 Nos 1 – 4 2 Full price means to multiply the number by 1000. e.g. $1.3 3 1000 = $1300 3 See Unit 28 No. 4 4 See Unit 23 No. 4

Unit 30

Tables (1)

Page 31

1 – 3 Multiplication is the total of a number of groups or rows. It can be described with a number sentence such as 3 3 4 = 12 or 3 or in words. 3 4 1 2 Product, groups of, times and lots of all mean multiply. Note: anything 3 0 = 0 and anything 3 1 = itself. 4 See Unit 13 No. 4

Unit 31

Tables (2)

Page 32

1, 3 and 4 See Unit 30 Nos 1 – 3


Page 28

4 See Unit 21 No. 1. Don’t forget relevant units or signs.

1 When subtracting from numbers with zeros, it is easier to make the number end with a 9, so 2000 becomes 1999 as it is easier to subtract from 9. e.g. For 400 – 72, subtracting 1 from 400 gives 399. 399 – 72 = 327 then adding 1 gives 328, so 400 – 72 = 328 Note: these answers can also be found by counting on. 2 The jump strategy is starting with the first number, subtract the tens, then the units. e.g. 96 – 25: 96 – 20 = 76 76 – 5 = 71 so 96 – 25 = 71 3 The compensation strategy is to round the first number (and/or second) to the nearest 5 or 10, then subtract the numbers and count back the difference. e.g. 63 – 19: 65 – 20 = 45 As 63 was rounded up 2, count back 2; as 19 was rounded up 1, but subtracted, add 1. Overall, count back 1. so 63 – 19 = 44 4 See Unit 20 No. 4 1 – 4 Rounding is giving an approximate answer. For a number ending in 0, 1, 2, 3 or 4 it is rounded down to the nearest ten, and for a number ending in 5, 6, 7, 8 or 9 it is rounded up to the nearest ten, e.g. 724 is rounded down to 720. If the numbers being considered are from 0 to 49 they are rounded down to the nearest hundred and if they are from 50 to 99 they are rounded up to the nearest hundred. e.g. 485 is rounded up to 500. If the numbers being considered are between 0 and 499 they are


1 See Unit 21 No. 1 2 – 4 See Unit 21 Nos 3 – 4

3–2=1

1 6

Mental strategies for subtraction

Unit 24

– 2

3 – 4 Subtraction with trading is when a subtraction such as 5 – 9 cannot be completed so a ten needs to be traded. e.g. 3 1 A trade of ten from 4 5 the 4 makes 15 – 9. – 2 9

Unit 22

rounded down to the nearest thousand and if they are from 500 to 999 they are rounded up to the nearest thousand, e.g. 3249 is rounded down to 3000. 4 Estimation can be completed by rounding first. See also Unit 17 No. 4.


3

START UPS: Units 31 – 43 2 Missing numbers can be found by inverse operations. = 25 e.g. 5 3 25 ÷ 5 = 5 = 5 so 5 3 5 = 25 or by saying ‘25 divided by what equals five’?

Unit 32

Tables (3)

Page 32

1 – 3 See Unit 30 Nos 1 – 3 4 Multiplication grids can be completed by multiplying each number with the number below the 3 symbol. e.g. 3 3 5 (3 3 6) 18

6

(5 3 6) 30

Note: a multiplication table is on the inside back cover.

Unit 33

Tables (4)

Page 33

1 – 2 See Unit 30 Nos 1 – 3 3 See Unit 31 No. 2 4 The total amount can be found by multiplying the amounts and adding the relevant units.

Unit 34

Multiplication by tens and hundreds Page 33

1 To find the total number of tens, multiply the two numbers together, e.g. 2 3 2 tens = 4 tens. 2 – 4 For multiplying by numbers ending with zeros, multiply the digits first and then add the total number of zeros. e.g. 40 3 30: 4 3 3 = 12 Add two zeros as there are two in the question, so 40 3 30 = 1200 This can be completed horizontally or vertically. e.g. 1 5 3 2 0 2 3 15 and add 0. 3 0 0

Unit 35

Multiplication to 999

Page 34

1 and 4 See Unit 33 No. 4 2 – 3 Longer multiplication can be completed by: 6 9 3 5 4 5 + 3 0 0 3 4 5

Unit 36

(5 3 9) (5 3 60)


Page 34

Extended multiplication (1)

Page 35

1 – 2 See Unit 35 Nos 2 – 3 3 See Unit 32 No. 4 and Unit 35 Nos 2 – 3 4 See Unit 30 Nos 1 – 3 and Unit 35 Nos 2 – 3

Unit 38

Unit 39


1 See Unit 35 Nos 2 – 3 2 See Unit 30 Nos 1 – 3 and Unit 35 Nos 2 – 3

(6 3 10) 60 6 (7 3 10) 70


Page 36

Unit 40

7

(3 3 10) 30 3

3 10

4

(4 3 10) 40

Factors

Page 36

1 and 3 A factor is a number that divides evenly into another number, e.g. 3 is a factor of 6. Numbers can have many factors, e.g. 1, 6, 2 and 3 are all factors of 6. 2 See Unit 30 Nos 1 – 3 4 See Unit 39 No. 3

Unit 41

Multiplication and problem solving Page 37

1 See Unit 35 Nos 2 – 3 2 See Unit 30 Nos 1 – 3 and Unit 35 Nos 2 – 3 3 Multiplication can be checked with addition. e.g. 2 2 or 2 2 3 3 2 2 + 2 2 6 6 6 6

Page 35

Unit 42

Division

Page 37

1 – 4 Division is the sharing or grouping of a number or quantity into equal amounts. Groups of and sharing also mean division. Division can be written as 18 ÷ 9 = 2 or 2 Halving is the same as dividing by 2. 9 18 Halving twice is the same as dividing by 4. Halving three times is the same as dividing by 8.

Unit 43

Division of 2-digit numbers (1)

Page 38

1 and 4 See Unit 42 Nos 1 – 4 2 When a division or grouping is made, and there are some items or an amount left over, these are called remainders. The abbreviation for remainder is r.


4

Multiples and square numbers

1 A multiple of a number is the product of that number and any positive whole number. e.g. Multiples of 5 are 5, 10, 15, 20, … 2 See Unit 30 Nos 1 – 3 3 A squared number is the number that results from multiplying another number by itself. e.g. 32 = 3 3 3 = 9 4 Multiplication circles are completed by multiplying the number inside the circle by each of the numbers on the outside. e.g.

4 See Unit 31 No. 2

1, 2 and 4 See Unit 35 Nos 2 – 3 3 See Unit 33 No. 4

Unit 37

3 A mental strategy for larger multiplication is to break the large number into its expanded form, multiply each part, and then add the parts together. e.g. 245 3 4: 200 3 4 = 800 40 3 4 = 160 5 3 4 = 120 800 + 160 + 20 = 980 4 See Unit 30 Nos 1 – 3 and Unit 35 Nos 2 – 3


START UPS: Units 43 – 59 e.g. 13 ÷ 5 = 2 groups and 3 remainder, which can be written as 2 2r3 r 3. It can also be written as: 5 13 3 Division can be calculated by: 10 r 3 working left to right: 5 52 232 with larger numbers: 2 464 36 with trading: 1

2 72

Unit 44


Page 38

1 and 3 See Unit 43 No. 3 s See Unit 43 No. 2 4 See Unit 42 Nos 1 – 4 and Unit 43 No. 3

Unit 45

Dividing numbers containing zeros Page 39

Divisibility

4 See Unit 42 Nos 1 – 4 and Unit 43 No. 3

Division with 3-digit numbers (2)

Page 40

Page 40

1 – 4 See Unit 43 No. 3

Unit 53

Number lines and operations

Division by tens

Page 41

Division of 4-digit numbers

1 – 3 See Unit 43 No. 3 4 See Unit 40 Nos 1 and 3 and Unit 43 No. 3

65

70

75

80

85

90

Averages (1)

95

Page 43

1 – 4 The average is the sum of all numbers divided by how many numbers there are. e.g. The average of 41, 50 and 62 is: 41 + 50 + 62 = 51 3

Averages (2)

Page 44

Order of operations (1)

Page 44

1 – 4 Order of operations is the order in which the different operations should be completed. This is known as BODMAS or PEDMAS. Complete the brackets first, then multiplication and division, and finally addition and subtraction. Questions with 3 and ÷ only should be worked left to right. B – brackets P – parentheses (brackets) O – over E – exponents (powers) D – division D – division M – multiplication M – mulitplication A – addition A – addition S – subtraction S – subtraction e.g. (3 3 4) – (2 + 1) = 12 – 3 = 9 But if read without brackets: 3 3 4 – 2 + 1 = 11

Unit 57


Page 45

Unit 58


Page 45

1 – 4 See Unit 56 Nos 1 – 4

Unit 59

Page 41

Operations with large numbers

Page 46

1 See Unit 16 No. 1 2 See Unit 21 Nos 3 – 4 3 When multiplying large numbers, multiply as normal, that is, right to left and carry the tens as in addition. 4 3 8 = 32, write the 2 and carry the 3. e.g. 3 Then multiply the next number. 4 2 1 8 4 3 1 and add the excess tens, 3 4 therefore 4 3 1 + 3 = 7. 1 6 8 7 2 Then 4 3 2 = 8 amd 4 3 4 = 16. 4 See Unit 43 No. 3


Page 43

1 – 4 See Unit 3 No. 1. Operations can be performed on a number line using the jump strategy. e.g. 60 + 32 = 92

1 – 4 See Unit 56 Nos 1 – 4

1 – 3 To divide by ten, remove one zero, or move the decimal point one place to the left. e.g. 426 ÷ 10 = 426. = 42.6 Note: conventional methods can also be used. See Unit 43 No. 3 4 To divide money, divide as per with a ten, but don’t forget the $ sign!

Unit 50

Page 42

1 See Unit 13 No. 4 and Unit 20 No. 4 2 – 4 See Unit 13 No. 4

Unit 56

1 – 3 If it is not possible to divide the first digit, then divide the first two digits. See also Unit 43 No. 3. e.g. 21 6 126

Unit 49

Inverse operations and checking answers

Unit 55

Page 39


Page 42

1 – 4 See Unit 54 Nos 1 – 4

1 Numbers where the digits sum to a number divisible by 3, can be divided by 3. e.g. For 72: 7 + 2 = 9 and 9 is divisible by 3, therefore 72 is divisible by 3 and gives 24. 2 To find if a number is divisible by 7 use trial and error. 3 See Unit 13 No. 4 4 A number is divisible by 5 if it ends in a 0 or 5.

Unit 48

Unit 52

Unit 54

630=0 6 3 100 = 600 then add

Unit 47

Number lines

1 – 4 See Unit 3 No. 1

60

1 and 3 See Unit 43 No. 3 2 See Unit 43 No. 2 4 To find the missing digits use the inverse operation – multiplication: e.g. 102 102 6 3 2 = 12 6 6 612

Unit 46

Unit 51


5



Page 46

1 See Unit 13 Nos 1 – 3 2 To find the missing value, calculate the answer of the complete equation and then use inverse operations. See also Unit 13 No. 4. e.g. 433=6+

12 = 6 +

Missing numbers

Page 47

1 – 4 See Unit 13 No. 4 To find missing numbers use inverse operations. e.g. 60 = ÷ 2 or say what divided by 2 equals 60? The answer is 120.

Unit 62

Change of units

Page 47

or

3 A number line can be used to show fractions. e.g. 1 2

Unit 68

1

1 2

1

Fraction of a group

Unit 69

Page 48

Negative numbers

Page 48

Calculator – addition, subtraction Page 49 and multiplication

1, 3 and 4 A calculator can be used to find answers to equations or to check answers. 2 See Unit 17 No. 4

Page 50

Comparing fractions

Page 51

1 See Unit 67 No. 3 2 – 4 When fractions are compared with the same denominator, the fraction with the largest number as the numerator is the largest fraction. e.g. 58 is larger than 38 . If required, once compared, fractions can be written in order. Note: if fractions have different denominators, make them the same by multiplying both the denominator and the numerator by the same number (following the idea that what is done to the numerator must be done to the denominator). 2 e.g. 1 = 44 or 12 = 48 or 15 = 10

Unit 70

Equivalent fractions

Page 51

1 – 4 Equivalent fractions are fractions that have the same value or amount. e.g. all of the following fractions are equal to one half: 1 2 3 4 , , 2, 4, 6, 8,

Unit 71

Improper fractions (1)

Page 52

1 – 2 An improper fraction is a fraction that is larger than a whole. The numerator is larger than the denominator. e.g. 54 or 97 or 21 5

3 A mixed number is a number written as a whole number with a fraction. e.g. 1 14 can be shaded on a diagram or written as a number. = 1 14

Excel Start Up Maths Year 5 © Pascal Press ISBN 978 1 74125 262 0

or

1 – 3 See Unit 67 Nos 1, 2 and 4 4 The fraction of a group can be found by dividing the number in the group by the denominator of the fraction. e.g. To find 14 of 8. Divide 8 by 4 giving 2.

Reasoning with numbers

6

Page 50

Fractions can be represented with pictures or with diagrams where the fraction is the shaded/coloured part. e.g. 34 is represented by:

0

1 – 3 A negative number is a number less than zero and is represented with a – sign, e.g. – 4, – 12 , – 6.2. See also Unit 3 No. 1 4 See Unit 53 Nos 1 – 4 Note: it is possible to have a negative number answer.

Unit 65

Fractions

It can also be used for fraction equations. e.g. 1 – 12 = 12

1 – 2 See Unit 61 Nos 1 – 4 and Unit 13 No. 4 3 An array, in this case, is a rectangular shape divided into a grid to aid the process of multiplication. e.g. For the following array the equations 3 3 2 or 2 3 3 can be written so that each gives the answer of 6. 4 To complete the spaces, each section of the equation must be equal. e.g. 2 3 3 = 2 3 (2 + )= To keep each section balanced: 2 + 1 = 3, so the overall equation = 6. 2 3 3 = 2 3 (2 + 1) = 6 as 2 3 2 = 4 and 2 3 1 = 2, and 4 + 2 = 6.

Unit 64

Page 49

1, 2 and 4 The denominator is the bottom part of the fraction (the number below the line). It shows how many parts in the whole. The numerator is the top number part of the fraction (over the line); it shows how many parts out of the whole. e.g. 24 is 2 out of 4 equal parts.

0

1 and 4 To change between units of length: 10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km 2 and 4 To change between units of time: 60 s = 1 min 60 min = 1 h 24 h = 1 day 3 and 4 To change between units of mass: 1000 g = 1 kg

Unit 63

Calculator – division

1 To change a fraction to a decimal, divide the top number (numerator) by the bottom number (denominator) on the calculator, e.g. 14 is 1 ÷ 4 = 0.25 2 See Unit 40 Nos 1 and 3 3 and 4 See Unit 65 Nos 1, 3 and 4

Unit 67

12 – 6 = 6 or say 12 = 6 + what? 3 When multiplying by 10 move the decimal point one place to the right. e.g. 42.6 3 10 = 42.6 = 426 When multiplying by 100 move the decimal point two places to the right. e.g. 4.28 3 100 = 4.28 = 428 4 See Unit 49 Nos 1 – 2 When dividing by 100 move the decimal point two places to the left. e.g. 635.1 ÷ 100 = 635.1 = 6.351

Unit 61

Unit 66


START UPS: Units 71 – 81 It is possible to simplify improper fractions to mixed numbers by dividing the denominator into the numerator, to find how many whole numbers there are, and the remainder becomes the fraction. See also Unit 43 No. 2 21 e.g. 54 5 5 ÷ 4 = 1 r 1 21 ÷ 4 = 4 r 1 So 4 15 So 54 = 1 14

3 See Unit 73 Nos 1 – 4 4 See Unit 74 Nos 1, 2 and 4

Unit 76

4 A mixed number can be written as an improper fraction by multiplying the denominator by the whole number and adding the numerator. This total is placed over the denominator. e.g. 1 45 : (1 3 5) + 4 = 9 1 45

So

Unit 77

9 5

=

Unit 72


Page 52

1 – 2 See Unit 71 No. 3 3 – 4 See Unit 71 No. 4

Unit 73

Fraction addition

Page 53

1 – 4 Fraction with the same denominator can be added on a diagram or with numbers. e.g. 1 4

+

1 4

=

1+1 4

=

2 4

or

... .... ..... ...... ...... ...

1 3

+

1 3

1 2

=

Unit 78

2 3

Note: if the answer is an improper fraction, it should be changed to a mixed number. e.g. 45 + 35 = 75 = 1 25

Unit 74 Fraction subtraction

Page 53

1, 2 and 4 Fractions with the same denominator can be subtracted on a diagram or with numbers. e.g. 2 – 13 O n a diagram: Shade the subtracted part: Count the fraction e.g.

4 6

–

1 6

=

4–1 6

remaining: 1 23 =

3 6

=

1 3

So

12 4

–

1 4

11 4

Don’t forget to change to a mixed number.

Decimal place value – thousandths Page 56

3 zeros

2 and 4 See Unit 76 Nos 3 – 4 3 See Unit 1 No. 3

Unit 80

Comparing decimals (2)

Page 56

1 See Unit 1 No. 1 2 and 4 See Unit 76 Nos 3 – 4 3 See Unit 1 No. 3

Unit 81

Decimal addition (1)

Page 57

1 – 4 Decimal addition is the same as regular addition. Tens, units, tenths and hundredths all need to line up in the correct place value columns. The easiest way is to line up the decimal point first. e.g. 4 . 2 The decimal point position also continues in the answer. + 3 . 1 7 . 3


3 decimal places

➤

= 2 34

Page 55

If the number is less than 1, then a zero is written in front of the 231 decimal point, e.g. 1000 = 0.231

Fraction addition and subtraction Page 54

=


Unit 79

1 2

1 See Unit 73 Nos 1 – 4 and Unit 74 Nos 1, 2 and 4 2 To subtract a fraction from a whole number, first make the whole number a fraction with the same denominator. e.g. 3 – 14 : M ake the 3 into quarters by multiplying the top and bottom by 4. So 3 = 12 4

Page 55

1 Fractions can be written as decimals. The number of zeros in the denominator indicates the number of decimal places. e.g. 100 has 2 decimal places and 1000 has 3 decimal places.

Note: if the answer is an improper fraction it should be changed to a mixed number. 3 See Unit 67 No. 3

Unit 75

Decimals

1 See Unit 3 No. 4 2 See Unit 1 No. 3 3 A decimal is part of a whole and can be written in numbers and words, e.g. 4.26 = four point two six or four units, two tenths and six hundredths. 4 The number of tenths are found by locating the value in the tenths place and writing all of the digits to the left and including that numeral. e.g. 47.8 has 478 tenths or 478 10 1 See Unit 1 No. 1 2 See Unit 76 Nos 3 – 4 3 To find the decimal that is 5 hundredths greater, add 5 to the hundredths place, so for 3.41, add 5 to the 1, giving 3.46. If the number in the hundredths position is 5 or greater, then add as normal and carry the 1 into the tenths place. e.g. 3.59 add 5 hundredths to give 3.64 4 See Unit 77 No. 3 and Unit 76 Nos 3 – 4

1+1 3

=

Decimal place value – hundredths Page 54

1 See Unit 1 No. 1 2 See Unit 1 No. 3 3 – 4 See Unit 4 No. 3. Decimals are compared left to right. First compare whole numbers, then tenths and then hundredths; to find the largest or smallest decimal. e.g. 1.24 is larger than 1.16 which can be written as: 1.24 > 1.16


7

START UPS: Units 81 – 89 Trading is treated in the same way. e.g. 1 4 . 6 + 1 2 . 9 2 7 . 5 Note: any missing digits can have zeros added to keep the columns consistent. 4 . 2 0 e.g. 4 . 2 + 3 . 5 1 becomes + 3 . 5 1 7 . 7 1

Unit 82


Page 57

1 – 2 See Unit 81 Nos 1 – 4. Note: when working with quantities don’t forget the $ and c signs for money, or units such as m or L. 3 – 4 See Unit 17 No. 2

Unit 83

Decimal subtraction (1)

Page 58

1 – 2 Decimal subtraction is the same as regular subtraction. Tens, units, tenths, hundredths all need to line up in the correct columns. The easiest way is to line up the decimal point first. e.g. 4 . 7 The decimal point position continues in – 2 . 5 the answer. 2 . 2 Trading is treated in the same way. e.g. 6 1 1 7 . 3 – 1 2 . 9 4 . 4 Note: any missing numbers can have zeros added to keep the columns consistent. 4 . 4 9 e.g. 4 . 4 9 – 2 . 3 becomes – 2 . 3 0 2 . 1 9 3 See Unit 25 No. 2 4 See Unit 21 No. 2

Unit 84

Decimal subtraction (2)

Page 58

1 – 4 See Unit 83 Nos 1 – 2 Note: when working with money or quantities don’t forget $ and c signs, or units such as m or L.

Unit 85

Decimal multiplication

Page 59

1 – 4 When multiplying decimals, multiplication is completed as usual and then when finished, the total number of decimal places in the question is counted. This is the number of decimal places for the answer. e.g. 6 . 2 1 Two decimal places in the question. 3 3 1 8 . 6 3 Two decimal places in the answer. Therefore the answer is: 18.63 Decimal multiplication can be completed horizontally or vertically. Note: don’t forget to include the $ and c signs when working with money.

Unit 86

Decimal division

Page 59

1 – 4 When dividing a decimal by a whole number, the decimal point in the answer is lined up above the decimal point in the question, e.g. 1.26 5 6.36

If the division doesn’t go, such as 3 ÷ 6, then a zero is written as in normal division. Note: don’t forget to include the $ and c signs when working with money and units such as h or kg when working with quantities.

Unit 87

Unit 88


Rounding decimals

Page 60

1 – 2 Rounding decimals is the same as rounding whole numbers. See Unit 23 Nos 1 – 4. Numbers ending with digits 1 to 4 are rounded down, so 4.42 becomes 4.4. Numbers ending with digits 5 to 9 are rounded up, so 1.67 becomes 1.7. Note: numbers rounded to one decimal place only have one number after the decimal point. Numbers rounded to two decimal places have two numbers after the decimal point. 3 To round to the nearest whole number, any number with a decimal of 0.5 or greater rounds up, so 2.53 becomes 3. Any number with a decimal of less than 0.5 rounds down, so 47.46 becomes 47. 4 See Unit 81 Nos 1 – 4 and Unit 83 Nos 1 – 2 then round to the nearest 5c (see Unit 23 Nos 1 – 4), not forgetting the $ and c signs.

Unit 89

Percentages (1)

Page 61

1 – 3 Percentage means out of 100. It is represented with the percentage sign %. Therefore 20% is 20 out of 20 2 100 or twenty percent or 100 or 10 or 0.2 It can be represented on a diagram:

4 To find the percentage of a number, express the percentage as a fraction or decimal and then multiply by the number. 10 e.g. 10% of 50 = 100 3 50 or 10% of 50 = 0.1 3 50


8

Decimal multiplication and division Page 60

1 See Unit 85 Nos 1 – 4 2 See Unit 86 Nos 1 – 4 3 When multiplying by 10, move the decimal point one place to the right, e.g. 1.36 3 10 = 13.6 When multiplying by 100, move the decimal point two places to the right, e.g. 1.36 3 100 = 136 When multiplying by 1000, move the decimal point three places to the right. e.g. 1.36 3 1000 = 1360 Note: a zero is added if there are not enough places to move the decimal point. 4 When dividing by 10, move the decimal point one place to the left, e.g. 32.14 ÷ 10 = 3.214 When dividing by 100, move the decimal point two places to the left, e.g. 32.14 ÷ 100 = 0.3214 When dividing by 1000, move the decimal point three places to the left, e.g. 3.21 ÷ 100 = 0.0321 Note: a zero is added if there are not enough places to move the decimal point.


=5

=5

START UPS: Units 90 – 100 Page 61

1 – 3 See Unit 89 Nos 1 – 3 4 See Unit 89 No. 4

Page 62

1 To convert a fraction to a decimal: either convert the fraction to 40 one with a denominator of 100: 25 3 20 20 = 100 = 0.4; or divide the numerator by denominator as a division equation: 0.4 5 2.0

Unit 96

2 – 4 The different types of angles are: Type

1 4

4 To complete the table, first convert the fraction to one with a denominator of 100. Then write as a decimal with two decimal places, and finally a percentage can be written.

revolution (full turn)

360º

Page 65

Unit 98

Comparing angles (1)

Page 65

1 – 4 See Unit 96 Nos 2 – 4

Unit 99


Page 66

1 – 4 See Unit 96 Nos 2 – 4

Drawing angles (1) 60 0

13

70

120

110

90 100 1 10

80

100 90

80

70

120

60

13

50

0

14

0

50

70

60 0

120

80

110

90 100 11 0

100 90

80

70

120

60

13

50

0 0

13

14

0

0

0

10

20

30

80

70

60

14

40

0

0

40

14

30

150

160

20

150

10

50

120

0

13

110º

0

170 180

290º

180 170 16 0


10

10

20

Page 64

For angles larger than 180º, the protractor is turned around (don’t flip) to measure the amount of angle below the line and this is then added to 180º to give the angle: 180º = 110º = 290º or subtract the smaller angle from 360º: 360º – 70º = 290º

170 180 160

20

30

150

40

45º

30 180 170 16 0 1 40 50 14 0

10

0

10

170 180

For an angle facing left, it is possible to use the other scale. Be careful to always start from 0º.

40º

20

180 170 1 60

20

30

0

40

50

Page 66

160

1 – 2 An angle can be measured using a protractor. The centre of the protractor is placed at the vertex of the angle and the baseline is placed as one of the angle’s arms. Then the scale is read around to the other arm.

150

Unit 100


Classifying angles (2)

30

Symmetry

between 180º and 360º

150

Unit 95

reflex

40

Page 63

1 – 3 See Unit 88 Nos 1 – 2, Unit 88 No. 3 and Unit 23 Nos 1 – 4 4 See Unit 16 No. 1, Unit 81 Nos 1 – 4, Unit 83 Nos 1 – 2, Unit 85 Nos 1 – 4, Unit 86 Nos 1 – 4 and Unit 35 Nos 2 – 3 1 – 4 Symmetry is when one half of the shape is a reflection of the other, so when folded on the line (axis) of symmetry, the two halves fit exactly.

180º

0

Money rounding

straight

14

Page 63

1 See Unit 16 No. 1 2 See Unit 92 Nos 3 – 4 3 See Unit 85 Nos 1 – 4 and Unit 35 Nos 2 – 3 4 See Unit 86 Nos 1 – 4 and Unit 43 No. 3

Unit 94


1 – 4 See Unit 96 Nos 2 – 4

Page 62

Money operations

obtuse

Unit 97

1 – 2 In the Australian money system, there are six different coins: $2, $1, 50c, 20c, 10c and 5c and five different notes: $100, $50, $20, $10 and $5. 3 – 4 Change is the leftover amount of money owed back to the person after a purchase. It can be found by counting on. e.g. The change from $5 after spending $4.25 is: 5c makes $4.30, 20c makes $4.50 and 50c makes $5.00. Therefore the total change is 50c + 20c + 5c = 75c.

Unit 93

90º

90 100 11 0

Use of money

right

100 90

Unit 92


80

>

acute

110

1 2

Size

70

Then add the sign:

1 4

Diagram

120

Make both fractions:

Page 64

vertex

(see Unit 86 Nos 1 – 4). 2 See Unit 89 No. 4. Don’t forget to include the signs such as $ and quantities such as m. 3 To compare two amounts, have them in the same format, such as all fractions, or all decimals, or all percentages, and then compare them. e.g. Insert the sign, < or > : 12 0.25 1 2


1 An angle is the amount of turn between two straight lines (arms) fixed at a point (vertex). is larger than arms

60

F ractions, decimals and percentages

0

Unit 91

Note: a shape may have more than one line of symmetry. A regular shape is one where all sides and all angles are equal. See also Geometry Unit on page 16.

13

Percentages (2)

50

Unit 90

70º

9

START UPS: Units 100 – 110 3 See Unit 96 Nos 2 – 4 4 To draw an angle with a protractor, draw a horizontal line and label one end with a dot.

Unit 106

Views of 3D objects

Page 69

1 – 4 A 3D object can be viewed from the front, side or top. Note: different objects could have a view the same. top

Place the centre of the protractor on this dot, and the baseline along the horizontal line. 0

100 90

110

80

70

120

60

0

50

0

10

14 150

10

0

0

180 170 16 0

20

Read around on the scale to the desired value and mark with a dot. (60º) 60

0

120

70

110

80

90 100 11 0

100 90

80

70

Unit 107

Triangles

Page 70

1 – 2 Side lengths can be measured with a ruler and can be written in millimetres or as a decimal: 14 mm or 1.4 cm. See also Unit 100 Nos 1 – 2 3 A right-angled triangle is one which has one right angle.

13

0

30

20

160

10 0

170 180

10

50

150

0

120

60

40

20

13

0 14

30 180 170 16 0 15 40 0 14 0

50

side front

See also Geometry Unit on page 16

170 180 160

20

30

150

40

30

13

0

13

120

90 100 11 0

80

70

60

14

40

50

Join the vertex and this point to complete the second arm. Label the angle. 60º

Unit 101

Drawing angles (2)

Page 67

1 – 2 See Unit 100 Nos 1 – 2 3 See Unit 100 No. 4 4 See Unit 96 Nos 2 – 4

Unit 102

Drawing angles (3)

Page 67

1 – 2 See Unit 100 Nos 1 – 2 3 See Unit 100 No. 4 4 See Unit 96 Nos 2 – 4

Unit 103

Angles in 2D shapes

Page 68

4 Remember a quadrilateral is a 4-sided shape and has 4 angles. See also Unit 96 Nos 2 – 4, Unit 100 Nos 1 – 2 and Geometry Unit on page 16 Note: the sum of all angles in a quadrilateral is 360º.

3D objects

Unit 108

edge

corner

Drawing 3D objects

Page 69

1 – 4 3D objects are constructed of familiar 2D shapes. See Unit 104 No. 1 and Geometry Unit on page 16

Unit 109


Polygons

Page 70

Page 71

1 A polygon is a plane shape with three or more straight sides. A regular shape has all sides and all angles equal. An irregular shape does not. See Geometry Unit on page 16. 2 The side is a line on the edge of a shape joining its vertices. side

3 See Unit 96 No. 1 4 See Unit 108 Nos 2 – 3

Unit 110

Prisms and pyramids

Page 71

1 A prism is a solid shape with two identical parallel bases and all other faces are rectangles. Note: a prism takes its name from its base. triangular prism

A pyramid is a 3D shape with a polygon as a base and triangular faces that meet at a vertex.


10

Quadrilaterals

1 See Unit 107 Nos 1 – 2 2 – 3 The diagonal is a line joining one corner of a shape to other or corners, except the neighbouring corners. 4 See Unit 103 No. 4 and Geometry Unit on page 16

Page 68

1 A 3D object (solid) has three dimensions; length, breadth and height (depth). See Geometry Unit on Page 16 2 A face is the flat surface of a 3D shape. 3 An edge is where two surfaces meet. face 4 A corner (vertex) is a point where lines meet.

Unit 105

A scalene triangle is a triangle in which all three sides are different lengths.

An equilateral triangle is a triangle where all the sides are equal and all angles are equal to 60º.

1 – 2 See Unit 96 Nos 2 – 4 and Unit 100 Nos 1 – 2 3 The sum of all angles in a triangle is 180º. That is the three angles in a triangle always add up to 180º. Therefore if two angles are known, the third can be found by counting on to 180º (or subtract the total of the known two from 180º) 50º 60º + 70º = 130º 180º – 130º = 50º The missing angle is 50º. 70º 60º

Unit 104

4 An isosceles triangle is a triangle with two equal sides and two equal angles.


vertex

START UPS: Units 110 – 120 2 A cross-section is the face that is seen when a 3D object is cut through. 3 See Units 104 No. 4, Unit 104 No. 3, Unit 104 No. 2 and Geometry Unit on page 16. 4 See Unit 104 No. 2

Unit 111

Cylinders, spheres and cones

Unit 115

Sections of solids

Page 74

1 – 3 See Unit 106 Nos 1 – 4 4 See Unit 110 No. 2

Unit 116

Page 72

1, 2 and 4: A cone is a 3D object with a circular or elliptical base and a curved surface that meets at a vertex.

A cylinder is a 3D object with one curved rectangular surface and two equal circular faces.

Nets and 3D objects

Page 74

1 See Unit 106 Nos 1 – 4 2 – 4 A net is the flat pattern which can be used to make a 3D object. is the net for a triangular pyramid.

Unit 117

Shapes – general review

Page 75

1 A rotation (turn) is to turn a shape or object about one point in either a clockwise or anti-clockwise direction.

A sphere is a 3D object that is perfectly round like a ball. A translation (slide) is to move a shape or object left/right or up/down without rotating it.

3 A surface is the outer face of an object which may be flat or flat surface curved. curved surface

See also Unit 104 No. 3

Unit 112

A reflection (flip) is a shape or object as seen in a mirror.

Parallelograms and rhombuses

Page 72

1 – 2 A parallelogram is a special quadrilateral where opposite sides are equal and opposite angles are equal.

A tessellation is a repeating pattern of one or more identical shapes that fit together without any gaps.

3 – 4 A rhombus is a parallelogram with four equal sides and equal opposite angles.

2 See Unit 95 Nos 1 – 4 3 See Geometry Unit on page 16 4 See Unit 111 No. 3, Unit 104 No. 4 and Unit 104 No. 3

Unit 118 Unit 113

Movement of shapes

Page 73

1 and 4 A flip (reflection) is a shape or object as seen in a mirror. 2 and 4 A slide (translation) is to move a shape or object left/right or up/down without rotating it. 3 and 4 A turn (rotation) is to turn a shape or object about one point in either a clockwise or anticlockwise direction.

Unit 114

Unit 119

Scale drawings and ratios

Page 73

1 – 4 A scale is used to tell how large an object or item on a map or diagram really is. A scale such as 1 cm : 100 cm reads as 1 cm on the drawing represents 100 cm (1 m) in real life, i.e. the actual item is 100 times larger than in the diagram. e.g. For a scale of 1 cm : 100 cm 4 cm : 4 3 100 cm or 4 cm : 400 cm or 4 cm : 4 m

Maps (1)

Page 75

1 – 4 Coordinates (grid references) are used to show position on a grid. They are represented by pairs of letters or numbers. e.g. (A, 2) or (6, 3) or (B, C) Note: the first coordinate is the horizontal or x-value and the second coordinate is the vertical or y-value.

Scale

Page 76

1 – 2 See Unit 118 Nos 1 – 4 3 A scale on a map is used to tell how large the object shown really is. A scale such as 1 cm : 100 cm is read as 1 cm on the map represents 100 cm (1 m) in real life, meaning the land is 100 times bigger than on the map. e.g. 1 cm = 100 cm so 4 cm = 400 cm or 4 m. 4 Distance is the length between two points, objects or locations.

Unit 120

Maps (2)

Page 76

1 – 2 See Unit 118 Nos 1 – 4 3 – 4 A compass is an instrument that shows direction. Its North points are: NW

NE

West

East

SW

SE South



11


Compass directions

Page 77

1 – 4 See Unit 120 Nos 3 – 4

Unit 122

Horizontal and vertical lines

Page 77

1 and 3 A horizontal line is parallel to the horizon. 2 and 4 A vertical line is at right angles to the horizon, or straight up and down.

Unit 123

Maps (3)

Page 78

Coordinates

Page 78

1 – 3 See Unit 118 Nos 1 – 4 4 See Unit 119 No. 4. Note: the distance can be found by ounting squares.

Unit 125

Grids

Page 79

Unit 126

Perspective

Page 79

1 See Unit 119 No. 4 2 – 4 See Unit 100 Nos 1 – 2

Unit 127

Digital and analog time

Page 80

1 – 2 Time is the space between one event and the next. It is measured on a clock. To move between each number on the clock, the minute hand takes 5 minutes. When the long hand is pointing to the 6 it is stated as half past. e.g. half past 4 11 12 1 10

2

9

3 4

8 7

5

6

When the long hand points to the 3 it is stated as quarter past and when the long hand points to the 9 it is stated as quarter to. e.g. quarter past 7 11 12 1 quarter to 8 11 12 1 10

2

9

10 3

4

8 7

6

5

2

9

3 4

8 7

6

5

3 – 4 On a digital clock the time is read as so many minutes past the hour, so 7:35 is 35 minutes past 7. It can also be written as a time to the hour, so 7:35 is 25 minutes to 8.

Unit 128

am and pm time (1)

Page 80

1 and 3 am is the abbreviation for ante meridiem. It is any time in the morning between midnight and midday. e.g. 7 am or 9:35 am pm is the abbreviation post meridiem. It is any time in the afternoon or evening between midday and midnight. e.g. 8:30 pm or 11 pm 2 See Unit 127 Nos 3 – 4 4 To find the time that is one hour later add 1 to the hour of the time, e.g. 7:30 pm + 1 hour = 8:30 pm. This also applies to 24-hour time, e.g. 0319 + 1 hour = 0419. Note: if adding an hour to any time between 11:00 and 12:00 then the am will change to pm, e.g. 11:30 am + 1 hour = 12: 30 pm. For pm it will change to am, e.g. 11:30 pm + 1 hour = 12:30 am.


24-hour time (1)

Page 81

24-hour time (2)

Page 82

1 – 4 See Unit 130 Nos 1 – 4.

Unit 132

24-hour time (3)

Page 82

1 – 2 See Unit 130 Nos 1 – 4 3 See Unit 130 Nos 1 – 4 and Unit 128 No. 4 4 To find the difference between two times, check if the times are am or pm. Two possible methods are: • count on from the first time to the second time (in hours and then 5 minute intervals is probably the easiest) • convert both times to 24-hour time and find the difference.

Unit 133

Timetables and timelines

Page 83

1 – 3 A timetable is a table where times are organised for when different events happen. They are used by schools, with transport and in hospitals. 4 A timeline is a diagram (like a number line) used to show the length of time between events.

Unit 134

Time zones

Page 83

1 – 4 Time zones are the different times that occur in different states and territories. In Australia there are three time zones: • Eastern Standard Time (EST) • Central Standard Time (CST), which is 12 hour behind Eastern Standard Time • Western Standard Time (WST), which is 2 hours behind Eastern Standard Time. 3 See Unit 128 No. 4 4 In summer NSW, ACT, Vic., Tas. and SA have daylight saving. This is where clocks are moved forward one hour on the last Sunday in October and moved back on the last Sunday in March.

Unit 135

Length in mm (1)

Page 84

1 and 4 Length is the distance from one end to the other, or how long something is. It is measured with a ruler. Units include millimetres (mm) for very small lengths such as the length of an ant, centimetre (cm), metre (m) and kilometre (km) for longer lengths such as the distance between two cities. 10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km 1000 mm = 1 m


12

Page 81

1 – 4 24-hour time uses all 24 hours of the day and is expressed with four digits; am or pm is not needed. For am times, the time is written the same except times 1 to 9 o’clock which have a 0 written in front, e.g. 9:30 am is 0930 hours. For pm times 12 is added to the normal time, e.g. 2 pm is 1400 hours. Thus to write 24-hour time as pm time, 12 is subtracted from the time, e.g. 1930 hours is 7:30 pm. Midnight is 0000 hours.

Unit 131

1 – 4 See Unit 118 Nos 1 – 4

am and pm time (2)

1 – 3 See Unit 128 Nos 1 and 3 4 To find a certain number of minutes after a certain time, count on (by 5s would be the quickest) remembering to change between am and pm and cross over midday and midnight. e.g. 70 minutes after 10:30 pm is 11:40 pm.

Unit 130

1 – 3 See Unit 118 No. 1 – 4 4 See Unit 120 Nos 3 and 4

Unit 124

Unit 129


START UPS: Units 135 – 149 2 – 3 It is possible to convert between the different units. 2000 mm = 2 m e.g. 200 cm = 2 m 42 mm = 4 cm 2 mm 400 cm = 4 m

Unit 136

Length in mm (2)

Page 84

1 – 2 See Unit 135 Nos 1 and 4 3 – 4 See Unit 135 Nos 2 and 3

Unit 137

Length in km (1)

Page 85

1 See Unit 135 Nos 1 and 4 2 and 3 See Unit 135 Nos 3 – 4 4 Speed is how fast something is moving or how far it travels in a certain time. It can be written as kilometres per hour (km/h) or metres per second (m/s). Therefore an object travelling at 100 km in 2 hours is travelling at a speed of 50 km/h (divide both numbers by 2).

Unit 138

Length in km (2)

Page 85

Length with decimals

Unit 144

Page 86

Unit 147

Unit 148

2 cm

Page 87

1 – 3 See Unit 140 Nos 2 and 4 4 See Unit 135 Nos 1 and 4

Page 87

1 – 4 See Unit 140 Nos 2 and 4

Area (1)

Hectares

Page 90

Page 88

Square kilometres

Page 90

Mass in g and kg (1)

Page 91

1 Mass is the amount of matter in an object. It is measured in grams (g) for lighter objects or kilograms (kg) for heavier objects. 2 – 4 1 kilogram = 1000 grams so 4 kg = 4000 g and 1600 g = 1.6 kg Note: mass can be written as 2 kg 100 g or 2100 g or 2.1 kg.


Page 89

1 – 4 A square kilometre is equal to 1000 m 3 1000 m = 1 000 000 m2 Therefore 1 km2 = 100 ha so 5 km2 = 500 ha and 600 ha = 6 km2

Unit 149

1 Area is the size of the surface of a shape. It is measured in square units, e.g. sq cm = cm2 or sq m = m2 for larger areas. It can also be found by counting squares. 2 See Unit 140 No. 1

Area (4)

1 – 4 A hectare is used to measure large areas such as a national park. 1 hectare (ha) = 10 000 m2 so 2 ha = 20 000 m2 and conversely 40 000 m2 = 4 ha.

2 and 4 Perimeter is the distance around the outside of a shape. 3m e.g. P=2+3+2+3 2m = 10 Perimeter is 10 m. 3 To find the perimeter of a square, multiply the side length by 4. P=234 e.g. =8 Perimeter is 8 cm

Unit 143

Unit 146

Total area = 12 + 6 = 18 Total area is 18 cm2.

1 See Unit 143 No. 1 2 – 3 See Unit 143 Nos 3 – 4 4 See Unit 145 No. 2

length

Perimeter (3)

3 cm 3 3 2 = 6 2 cm

breadth

Unit 142

Page 89

4 For non-regular shapes, divide them into squares and rectangles, calculate the area of each of the shapes and then add these areas together to find the total area. e.g. 3 cm 4 cm 3 3 4 = 12

Perimeter (1)

Perimeter (2)

Area (3)

Page 86

1 Length is the longer distance of an object (see also Unit 135 Nos 1 and 4). Breadth is the width from side to side of an object.

Unit 141

Page 88

1 and 3 See Unit 143 Nos 3 and 4 2 To find the length or breadth from a given area, divide the area by the given dimension. e.g. If length = 6 cm and the area = 18 cm2, the breadth is = 18 6 = 3, so 3 cm.

1 – 2 See Unit 135 Nos 1 and 4 3 – 4 See Unit 135 Nos 2 – 3

Unit 140

Area (2)

1 – 3 See Unit 143 Nos 3 – 4 4 The area of a square can be found by squaring the side length. e.g. A= 42 4 cm = 16 (or 4 3 4) 2 Area is 16 cm .

Unit 145

1 See Unit 135 Nos 1 and 4 2 – 3 See Unit 135 Nos 2 – 3 4 To change metres to kilometres divide by 1000.

Unit 139

3 – 4 Area can be calculated by multiplying the length by breadth. 4 cm e.g. A=432 =8 2 cm Area is 8 cm2.


13



Page 91

Mass in tonnes (1)

Cubic metres

Unit 159 Page 92

1 – 4 Another measurement of mass is the tonne. 1 t = 1000 kg so 3 t = 3000 kg

Chance (1)

Mass in tonnes (2)

equal chance

Page 92 0

1 – 4 Capacity is the amount a container can hold. It is measured in litres (L) for larger capacities and millilitres (mL) for smaller capacities. 1 litre = 1000 millilitres so 3 L = 3000 mL and 2500 mL = 2.5 L Note: capacity can be written as 1 L 350 mL or 1350 mL or 1.35 L.

Unit 154

Capacity in mL and L (2)

Page 93

1 See Unit 153 Nos 1 – 4 2 Capacities can be added to find the total capacity. 2L+4L=6L 3 – 4 Displacement: when an object is placed completely under water, it displaces its own volume. As the object is placed in the water, the water level rises. 1 cm3 displaces 1 mL of water. Therefore 50 mL would be displaced by 50 cm3 and 110 cm3 would displace 110 mL.

Unit 155

Cubic centimetres (1)

Page 94

1 – 2 A cubic centimetre (centicube) is a standard unit for measuring volume. Its abbreviation is cm3. The volume of an object made of centicubes can be found by counting the number of cubes. 3 – 4 Volume can be calculated by multiplying the length by the breadth by the height. e.g. 2 cm V = 2 3 3 3 2 2 cm = 12 3 cm Volume is 12 cm3.

Unit 156


Page 94

1 See Unit 155 Nos 1 – 2 2 – 3 See Unit 155 Nos 3 – 4 Note: volume of a cube can be found by multiplying the side length by itself three times. e.g. A cube of side length of 2 cm has a volume of 2 cm 3 2 cm 3 2 cm = 8 cm3. 4 See Unit 154 Nos 3 – 4

Unit 157


Page 95

1 See Unit 155 Nos 1 – 2 and Unit 155 Nos 3 – 4 2 See Unit 155 Nos 3 – 4 3 – 4 See Unit 154 Nos 3 – 4

0.1

0.2

Unit 160


0.3

0.4

0.5

0.6

Chance (2)

1 2

0.7

0.8

0.9

1

Page 96

or 50% is equal chance and 0.01, or 1% is almost impossible.

Unit 161

Chance (3)

Page 97

1 – 3 See Unit 160 Nos 2 – 3 4 See Unit 159 Nos 1 – 4

Unit 162

Picture graphs (1)

Page 97

1 – 4 A picture graph is a graph which uses pictures to represent quantities. 9 6 3 M

T

Days of the week

Note: One picture may represent many items,

Unit 163

Picture graphs (2)

= 3 days.

Page 98

1 – 2 See Unit 162 Nos 1 – 4 3 A tally is the process of using marks to record counting. e.g. Shape Tally Number 8 7 3 Note: represents a group of 5. Information recorded as a tally in a table is often called a tally table or tally sheet. 4 A bar chart or column graph uses bars or columns to show the number of items or objects so that they can be compared. 10 8 6 4 2

red

blue

green yellow

Colour


14

likely

1 and 4 See Unit 159 Nos 1 – 4 2 – 3 Chance can be described with a fraction or decimal or 5 percentage, where 1 or 100% is equal to certain, 0.5; 10 or

Number

Page 93

Number


certain

unlikely

1 – 4 See Unit 151 Nos 1 – 4

Unit 153

Page 96

1 – 4 Chance is the probability or likelihood of something happening. It can be described in words such as certain, likely, unlikely, impossible, equal chance and never. impossible

Unit 152

Page 95

1 – 3 A cubic metre is another measurement of volume, for larger volumes. Its abbreviation is m3. 4 See Unit 155 Nos 3 – 4. Note: units are m3 in this case!

1 See Unit 149 No. 1 2 – 3 See Unit 149 Nos 2 – 4 4 Masses can be added to find the total mass. e.g. 500 g + 500 g = 1 kg

Unit 151

Unit 158



Line graphs (1)

Page 98

1, 3 and 4 A line graph joins points which represent the data. These points are often joined with lines. 3

Weight 2 in kg 1

Age in years 2

3

Line graphs (2)

Page 99

3 See Unit 25 No. 2 and Unit 30 Nos 1 – 3 4 See Unit 60 No. 2

Page 99

1 To form 1 triangle, 3 matches are used.

1 – 4 See Unit 164 Nos 1, 3 and 4

Unit 166

Page 103

4

2 See Unit 9 No. 1

Unit 165

Problem solving (2)

1 The same set of objects can be arranged in different orders. e.g. the digits 1, 2 and 3 can be arranged in the following ways: 123, 132, 213, 231, 312, and 321. 2 A cube has 6 faces. If it is joined to another cube then a total of 10 faces are showing, when looked at from any view. 6 faces 10 faces

4

1

Unit 174

Unit 175

Tally marks

Problem solving (3)

Page 104

1 – 3 See Unit 163 No. 3 4 See Unit 163 No. 4 and Unit 164 Nos 1, 3 and 4

Unit 167

Reading graphs

Page 100

1 See Unit 163 No. 3 2 See Unit 164 Nos 1, 3 and 4 3 See Unit 163 No. 4 4 A pie graph uses a circle divided into sections where each section represents part of the total.

2 See Unit 30 Nos 1 – 3, Unit 39 No. 3 and Unit 42 Nos 1 – 4 3 See Unit 30 Nos 1 – 3, Unit 42 Nos 1 – 4, Unit 25 No. 2, Unit 21 Nos 3 – 4 and Unit 16 No. 1 4 A line interval is a straight line between two points (not passing through any other point).

B Y R

Unit 168

Column graphs (1)

To form 2 triangles, 5 matches are used.

Page 100

1, 3 and 4 See Unit 163 No. 4 2 See Unit 163 No. 3

Unit 169

1st interval

Column graphs (2)

Page 101

1 – 4 See Unit 163 No. 4

Unit 170

Note: intervals can cross over.

Surveys and collecting data (1)

Page 101

1 – 2 See Unit 163 No. 3 3 – 4 See Unit 164 Nos 1, 3 and 4

Unit 171


Mean

1 – 4 Mean is the same as the average. See Unit 54 Nos 1 – 4

Unit 173

Problem solving (1)

1 – 3 See Unit 60 No. 2 4 See Unit 3 No. 1

Unit 176

Page 104

Page 102 To form 2 squares, 7 matches are used.

Page 102

Page 103

2 See Unit 25 No. 2 and Unit 30 Nos 1 – 3 3 See Unit 9 No. 1, Unit 35 Nos 2 – 3 and Unit 43 No. 3 4 See Unit 174 No. 1


Problem solving (4)

1 To form 1 square, 4 matches are used.

1 – 2 See Unit 163 No. 3 3 – 4 See Unit 163 No. 4

Unit 172

2nd interval


15

START UPS: Geometry Unit 3-dimensional objects

2-dimensional shapes

isosceles triangle

sphere

equilateral triangle

right-angled triangle

cone

scalene triangle

square

cylinder

rectangle hemisphere

rhombus parallelogram

cube

trapezium

kite

square prism

Note: quadrilaterals have 4 sides

pentagon

triangular prism

hexagon

heptagon

octagon

rectangular prism

pentagonal prism

hexagonal prism

triangular pyramid

nonagon

square pyramid

decagon

rectangular pyramid

circle oval semicircle

pentagonal pyramid

hexagonal pyramid


16 © Pascal Press ISBN 978 1 74125 262 0


UNIT 1

UNIT 2




1 Complete the numeral shown on each abacus:

a

Th

H

c

TTh

Th

H

e

1 Write the numeral shown on each abacus:

b

TTh

TTh

Th

H

d T

U

f T

U

T

U

TTh

Th

H

T

Th

H

T

U

TTh

Th

H

T

U

2 Write the numeral for:

a eighty-three thousand, five hundred and sixty-three

b twenty-five thousand, nine hundred and fifteen

c thirty-seven thousand, three hundred and forty-five

d forty thousand, seven hundred and ninety-one

e fifteen thousand and ninety-six f ten thousand, one hundred and fifty a 27 385 c 40 219 e 16 190

H

TTh

Th

H

Th

H

c

e TTh

d T

U

f T

U

T

U

TTh

Th

H

T

U

TTh

Th

H

T

U

TTh

Th

H

T

U

2 Write each of the following numbers in words: a 12 052

c 11 042

d 47 635

e 90 020

f 70 100

a 70 000 + 2000 + 300 + 40 + 5 b 50 000 + 8000 + 600 + 90 + 8 c 60 000 + 400 + 70 + 3 d 20 000 + 800 + 90 + 5 e 10 000 + 1000 + 200 + 10 + 2 f 30 000 + 5000 + 500 + 2 4 State the value of the 8 in each of the following:

a 18 432 c 11 058 e 32 981

b 16 854 d 83 205 f 46 118



Th

b 30 906

a 23 815, 41 672, 38 521 b 11 085, 12 346, 61 460 c 46 825, 45 118, 47 325 d 62 000, 63 051, 61 460 e 51 045, 51 001, 51 437 f 71 185, 76 459, 73 215

TTh

b 71 867 d 55 345 f 42 612

4 Write each set of numbers in ascending order:

b


3 Write the value of the underlined digit:

a

U

TTh


TTh

Th

H

T

U

TTh

Th

H

T

U

6 Write sixty-three thousand and forty-nine as a numeral.

6 Write 72 105 in words.

7 Write the value of the underlined digit: 17 851

7 Write the numeral for: 20 000 + 3000 + 500 + 6

8 Write the set of numbers in ascending order:

8 State the value of the 8 in 18 526.

61 059, 61 738, 60 476 9 Write the number closest to 2000, with the digits 1, 8, 4 and 2.

9 What is the number that is 5000 greater than thirty-two thousand, eight hundred and fifty-nine?

☞

Answers on page 124


Units Excel Advanced Skills Start Up Maths Year 5

17

UNIT 3

UNIT 4



Ordering numbers

1 Label each of the numbers on the number line with the letters a–f:

a 16 500 d 16 379

b 16 732 e 16 985

16 000

c 16 205 f 16 427

16 500

17 000

2998

e 84 256, 84 265, 84 296, 84 201

80 476

41 911

f 66 375, 66 357, 66 735, 66 537 2 Write six numbers larger than 60 000 but less than 65 000.

a d

d eighty-five thousand and nine e thirteen thousand, one hundred f sixty-five thousand and ninety-nine H

T

U

a 19 999 c 60 479 e 76 487

a d

3789, 3652, 3850 3600

17 852

c f

91 899 60 749 67 497

b 4006 40 208 d 18 560 16 650 f 29 562 28 562

3700

3800

3900

b e

c f

5 Place the set of numbers in ascending order: 14 281, 41 256, 40 879, 24 256

6 Write two numbers larger than 10 460 but less than 10 500. , 7 Complete the number statement with < or > to make it true:

16 832

7 Write eighty thousand, nine hundred as a numeral.

6 Circle the larger number in the pair:

b e

4 Write six numbers smaller than 95 000 but larger than 90 500.

5 On the number line, label each of the numbers:

3 Complete the following number statements with < or > to make them true:

4 Write each of the numbers on the place value chart:

c 38 049, 37 672, 38 115, 37 989

29 462

a twenty-three thousand b fifty-two thousand and sixteen c seventy thousand, four hundred and three

a b c d e f

d 42 346, 42 758, 42 675, 43 981

91 151

Number TTh Th 33 689 31 072 33 356 12 850 36 759 17 895

b 23 468, 22 475, 21 049, 24 480

8641

3 Write the following in numerals:

1 Place each of the following sets of numbers in ascending order:

a 16 487, 17 382, 15 046, 18 589

2 Circle the larger number in each of the following pairs:

a 29 006 b 85 321 c 19 151 d 29 426 e 80 172 f 42 119


10 760

1806

8 Write two numbers smaller than 25 000 but larger than 23 000. ,

8 Write the number on the place value chart: Number TTh Th H T U 58 361 9 Write the two smallest numbers that can be written using all of the following digits:

9 I am a number with the digits 1, 3, 5, 7, 9. 5 is in the tens place, 7 has the smallest value and 3 has the second highest value. Write down all the different numbers I could be.

3, 8, 5, 1, 2.

,




☞

Answers on page 124

UNIT 5

UNIT 6






1 Write true or false for each of the following:

a

b d

T

U

• Tth

T

U

•

c e

T

U

•

Hth

f

Tth

Tth

Hth

Hth

T

U

• Tth

Hth

T

U

•

Tth

Hth

T

U

•

Tth

a 67 382 < 76 489 b 23 186 > 23 816 c 10 765 < 10 675 d 81 496 > 80 529 e 34 720 < 38 475 f 42 890 > 4299 2 Write the value of the 8 in each of the following:

a 28 765 b 80 425 c 43 285 d 11 758 e 22 846 f 18 423

Hth

2 Write the value of each of the underlined digits:

a 2.79 c 17.98 e 10.06

b 41.86 d 20.48 f 132.96

3 Write the numeral for each of the following:

3 Write each number on the place value chart:

a fourteen point three six b twenty-nine point five nine c o ne hundred and fifteen

a twenty-one thousand, three hundred and six

b s ixty thousand, one hundred and ninety-five

H T U . Tth Hth

point three three

c eleven thousand and eighty d forty-six thousand, five hundred and twenty

d eighty point zero six e two hundred point nine nine f one hundred and fifty-six

e ninety thousand and fifty-five f thirty-eight thousand, one hundred and ninety-eight

4 Write each of the following numbers in words:

a 105.67 b 30 080.22 c 1046.10 d 800.46 e 99.98 f 46 050.03

4 Write six numbers between 48 325 and 48 947:

5 Write the numeral shown on

the abacus. T U • Tth 6 Write the value of the underlined digit: 1246.73 7 Write the number on the place value chart: eight hundred and twenty-five point four nine H T U . Tth Hth

Hth

a b c d e f 5 True or false? 98 760 < 98 675 6 Write the value of the 8 in 25 832. 7 Write the numeral for fifteen thousand, one hundred and eleven.

8 Write 4006.95 in words. 9 Circle the largest number:

8 Write two numbers between 68 742 and 68 954.

• one thousand, two hundred and nine point six • one thousand, two hundred and nine point eight five • one thousand, two hundred and seven point three two

☞

Answers on page 124


,

9 What is the:

a smallest 5-digit number you can write? b smallest 4-digit number you can write? Units


19

UNIT 7

UNIT 8




1 Write each of the following numbers on the place value chart:

a twenty-nine thousand, two hundred and six b one hundred and fifty thousand c nine hundred and three thousand and fifteen d five hundred and thirty-six thousand, four hundred e seven hundred and ninety thousand and eleven f four hundred thousand, two hundred and ninety-six HTh TTh Th

H

T

U

1 Draw discs on each abacus for the following numbers:

a 27 851

Th

H

T

U

c 174 236

TTh

HTh

Th

H

T

U

e 326 198

HTh

TTh

Th

H

T

U

Th

H

T

U

T

U

d 110 404 HTh

TTh

f 428 176

HTh TTh Th H 2 Complete each of the following with < or >: TTh

HTh

Th

H

T

U

a 107 429 438 467 b 140 278 104 115 c 89 426 890 375 d 92 486 98 379 e 104 600 107 900 f 913 875 913 900

2 True or false?

3 Match the correct name and numeral:

a 214 186 < 219 486 b 872 146 < 782 159 c 380 420 > 395 172 d 110 426 > 105 498 e 725 105 < 841 490 f 617 549 > 599 396

a five hundred and twenty-one thousand b five hundred thousand and twenty-one c five thousand and twenty-one d fifty thousand and twenty-one e five thousand, two hundred and ten f five hundred thousand, two hundred

a 172 385 c 117 511 e 140 135

b 493 508 d 829 376 f 915 420

4 State the number of thousands in each of the following:

b 326 421 d 46 824 f 998

6 True or false? 178 932 > 185 670 7 Write the place value of the underlined digit: 170 539

a 1, 7, 6, 3, 0 b 2, 7, 9, 8, 5, 1 c 1, 8, 3, 5, 8, 6 d 5, 9, 8, 9, 8, 7 e 4, 4, 3, 8, 6, 7 f 5, 0, 5, 1, 7, 6

HTh

TTh

T

U

190 988 1 076 176 000 176

8 Use the set of digits 2, 4, 6, 8, 0, 2 to write the largest possible number. 9 Make the largest possible number with the digits 4, 8, 7, 2, 3, 9 and write it in words.

b 11 758


H

7 Match the correct name and numeral: a one hundred and seventy-six thousand b one hundred and seventy-six c one thousand and seventy-six

9 Find half of:

20

Th

6 Complete with < or >: 109 936

8 State the number of thousands in 107 519.

and one

5 Draw the discs on the abacus for 176 051:

5 Write four hundred and seventy-three thousand, eight hundred and ninety-one on the place value chart: HTh TTh Th H T U

5 021 500 201 5 210 521 000 50 021 500 021

4 Use each set of digits to write the largest possible number:

3 Write the place value of each of the underlined digits:

a 298 360 c 490 857

TTh

HTh

b 326 285

a b c d e f

a 21 469 c 805 123 e 8 325



,

☞

Answers on page 125

UNIT 9

UNIT 10


Number patterns (1)

Expanding numbers

1 Write the next two numbers in each of the following number patterns:

a 21, 22, 23, 24, , b 4, 8, 12, 16, , c 70, 77, 84, 91, , d 410, 420, 430, 440, e 103, 106, 109, 112, f 455, 460, 465, 470,

, ,

b 995 d 496 241 f 9480

3 Write the first four terms for each of the number patterns, starting at:

a 50 and count by twos b 109 and count by ones c 30 and count by threes d 140 and count by hundreds e start at 9 000 and count by fifties

2 Expand each of the following numerals:

a 14 689 b 32 418 c 24 360 d 21 419 e 46 189 f 30 405 3 Write each of the following in expanded form as digits:

a two hundred and ninety-eight b one thousand, seven hundred and fifty-two

c four thousand, three hundred and twenty d twenty-six thousand, five hundred and seventy-one

4 Find the tenth term in the following number patterns:

a 3, 6, 9, 12, … b 100, 105, 110, 115, … c 11, 22, 33, 44, … d 1000, 990, 980, 970, … e 4860, 4859, 4858, 4857, … f 1400, 1500, 1600, 1700, …

e forty-two thousand, seven hundred and five

f eighty-nine thousand, three hundred and sixty-two 4 Write the value of the underlined digit in words:

5 Write the next two numbers in the number pattern: 12, 24, 36, 48,

a 20 000 + 4000 + 600 + 20 + 5 b 50 000 + 8000 + 200 + 30 + 2 c 10 000 + 200 + 50 + 6 d 40 000 + 900 + 70 + 6 e 80 000 + 6000 + 300 + 40 + 9 f 70 000 + 8000 + 900 + 80 + 1

f 10 006 and count by thousands

1 Write the numeral for each of the following:

,

2 Find the number 1000 more than:

a 4205 c 14 685 e 21 486

,

6 Find the number 1000 more than 109 908. 7 Write the first four terms in the number pattern starting at 1500 and counting by twenties.

a 26 385 c 20 198 e 44 687

9 Complete the table and write a rule that describes the number pattern: First term 90 80 70 60 50 40 Second term 79 69 59

☞

Answers on page 125


d 64 328 f 98 100

50 000 + 2000 + 800 + 60 + 7 6 Expand the numeral 73 490. 7 Write thirty-two thousand, eight hundred and six in expanded form as digits.

8 Find the tenth term in the number pattern: 2286, 2486, 2686, 2886, …

b 17 543



8 Write the value of the underlined digit in words:

67 851 9 What is:

a 5000 more than b 3000 less than

20 000 + 3000 + 600 + 80 + 5?


21

UNIT 11

UNIT 12


Ordinal numbers

Less than and greater than

1 Write each of the following as ordinal numbers:

a first c fourth e nineteenth

b third d fiftieth f second

a after ninth? b before third? c after 21st? d before 5th? e after 100th? f before 12th?

2 Write the number 5 less than:

3 If eight people swim in a backstroke race,

a what position is the winner? b what is last position? c what position is after 5th? d what position is before 4th? e what position are the first three swimmers? ,

,

f and the two fastest swimmers will go through to the ,

final, what positions are these? 4 Write the positions before and after:

a b c d e f

1 Write the number 5 greater than:

a 196 b 207 c 419 d 1889 e 42 950 f 36 495

2 What position comes:


10th

a 73 b 824 c 10 502 d 49 729 e 85 000 f 7200

3 True or false?

a 4100 < 4111 b 17 685 > 32 761 c 80 250 < 80 052 d 26 198 > 26 981 e 32 190 > 32 910 f 11 011 < 11 110

51st

4 Use < or > to make each of the following number statements true:

18th 12th

a 8000 + 400 + 20

2nd

b 9000 + 100 + 1

120th

c 6333

8842 9000 + 90 + 9

3000 + 600 + 30 + 3

5 Write sixteenth as an ordinal number.

d 1000 + 90 + 800 + 6

6 What position comes after 40th?

e 40 000 + 30 + 6

7 If only six people swim in a backstroke race, what is the last position?

f 75 290

4000 + 300 + 60

70 000 + 4000 + 200 + 90

5 Write the number 5 greater than 40 900.

8 Write the positions before and after: 22nd

1986

6 Write the number 5 less than 13 473.

9 There were five snails in a race. Draw in the snails and label the positions of the first three:

7 True or false? 10 765 < 10 675 8 Use < or > to make the number statement true:

Finish

Start

Finish

26 143

9 Write the number 1000 less than:

20 000 + 1000 + 40 + 600 + 3 +

90 000 + 8000 + 9 + 900 + 80




☞

Answers on page 125

UNIT 13

UNIT 14


Number patterns (2)

Roman numerals

1 Match the pattern to its rule:

1 What are the following as numerals?

a 15, 24, 33, 42 b 11, 10 34 , 10 12 , 10 14 c 2, 10, 50, 250 d 3, 9, 27, 81 e 500, 100, 20, 4 f 1.1, 2.4, 3.7, 5.0

3

3

÷5 + 1.3 +9 3

5

–

1 4

a C b DC c DCC d CM e MM f MC

2 Write the rule for each of the following patterns:

a 0.1, 0.2, 0.4, 0.8, 1.6 b 0.3, 0.6, 0.9, 1.2

e 12 , 34 , 1, 1 14 1

3

5

2 Write each of the following numbers as Roman numerals:

a 33 b 27 c 65 d 94 e 88 f 46

c 12 , 14 , 18 , 161 , d 50, 48.5, 47, 45.5

f

7

4 10 , 4 10 , 4 10 , 4 10

3 Complete the table:

a b c d e f

Starting number 112 114 110 120 115 100

Rule: 3 6 + 3

4 Find the answers to:

a 3 3 6 ÷ 6 = c 42 ÷ 7 3 7 = e 200 3 3 ÷ 3 =

b 108 + 17 – 17 = d 65 – 25 + 25 = f 96 + 37 – 37 =

5 Match the pattern to its rule:

a 13, 26, 39, 52 b 10, 20, 40, 80

3

2

+ 13

4 Write each of the following as numbers:

a LXXVI b DXV c CCIV d XCII e LXXXVII f MLIV

6 Write 93 as a Roman numeral.

Rule: 3 6 + 3

7 Write 2568 as a Roman numeral.

8 Find the answer to:

a 3000 b 300 c 400 d 691 e 585 f 747


3 Write each of the following numbers as Roman numerals:

5 What is MDC as a numeral?

6 Write the rule for: 4, 4 12 , 5, 5 12

Starting number 50

8 Write DLXXVI as a number.

90 ÷ 10 3 10 =

9 Draw a clock face using Roman numerals and add the time 3 o’clock.

9 Explain what you discovered with the answers of questions 4 and 8.


Use 100 + 72 – 72 as an example.

☞

Answers on pages 125–6



23

UNIT 15

UNIT 16


Addition review

Adding 3-digit numbers

1 Use the concept of doubles to add:

1 Complete:

a 11 + 12 = b 64 + 65 = c 73 + 74 = d 25 + 26 = e 121 + 122 = f 154 + 155 =

a 3 6 7

+ 4 5 3

+ 9 6

f 4 2 5 + 3 8 9

b 1 4 2 cm c $ 2 2 5 1 1 6 cm + 9 6 cm

$ 1 0 7 + $ 3 2 6

e 2 7 6 kg f 4 7 m 4 9 0 kg + 1 1 5 kg

4 1 2 m + 1 4 9 m

3 Complete:

a 50 + 40 =

500 + 400 =

300 + 500 =

c 20 + 90 =

200 + 900 =

600 + 700 =

e 90 + 60 =

900 + 600 =

b 84 + 96 = d 375 + 482 = f 267 + 305 =

5 Use the concept of doubles to add: 73 + 72 =

6 Use the split strategy to add:

63

70

d + 21 35 46 59 51

e + 86 27 95 72 15

58

f + 43 79 62 91

28

5 Complete: 1 0 9 + 2 9 8

6 Complete: 4 2 5 g 1 7 6 g + 3 0 2 g

145 + 23 = 7 Use the compensation strategy to add: 265 + 52 =

7 Complete: 70 + 40 =

8 Use the jump strategy to add: 425 + 136 =

700 + 400 =

8 Complete the table: 9 Find the solutions to the following and list the strategies that you used:

+ 98 43

75

52

66

9 Jodie sold 479 chocolate frogs, 156 chocolate bars, 217 fruit bars and 127 boxes of dried fruit for the fundraiser. How many items did she sell altogether?

, ,


f 80 + 30 =

800 + 300 =

35

24

d 60 + 70 =

c + 33 49 56 65

,

b 30 + 50 =

4 Complete the following tables: a + 4 15 26 32 b + 46 17 23

4 Use the jump strategy to add:

a 47 + 26 + 75 = b 92 + 92 + 83 = c 63 + 59 + 21 =

c 3 8 2

e 8 6 5

2 Complete: a 1 3 5 g 2 1 6 g + 1 0 0 g d 3 2 8 mL 1 7 6 mL + 2 3 5 mL

a 54 + 41 = b 65 + 79 = c 37 + 28 = d 256 + 39 = e 123 + 63 = f 127 + 58 =

+ 1 2 8

3 Use the compensation strategy to add:

+ 1 7 5

d 6 5 4

a 43 + 35 = b 76 + 67 = c 47 + 65 = d 81 + 53 = e 98 + 46 = f 37 + 29 =

b 4 2 6

+ 1 8 9

2 Use the split strategy to add:

a 46 + 39 = c 28 + 69 = e 265 + 179 =



☞

Answers on page 126

UNIT 17

UNIT 18


Adding to 9999 (1)

Adding to 9999 (2)

1 Find:

a $ 1 7 6 0 b $ 7 8 5 0 c $ 4 8 3 2 $ 2 1 9 5 + $ 1 3 7 6

$ 1 1 7 0 + $ 8 9 0

$ 9 7 5 + $ 3 2 1 0

d $ 5 1 1 1 e $ 4 6 7 5 f $ 3 7 8 5 $ 1 2 5 6 + $ 3 4 8 5

$ 2 4 6 8 + $ 1 0 5 9

$ 3 4 6 7 + $ 1 7 4 9

a the sum of 1765 and 3796 b the total of 4298 and 1520 c the addition of 1986, 3475 and 2486 d 4760 plus 3825 e 1176, 4893 and 3446 added together f 3851 and 2498 totalled 3 Complete: a 2 8 5 4 4 9 8 + 5 6

b 3 2 7

c 4 2 8 8

5 8 9 0 + 1 7 0

d 2 1 6 5

4 8 0 + 1 0

e 4 2 8 0

f 3 2 7

7 6 + 4 9 5

1 0 7 + 6

1 Find:

a 4 3 6 5

b 1 7 9 8 c 3 4 8 5 + 2 8 5 6 + 4 6 5 5 + 1 7 6 7 3 8 8 4 2 4 8 5 d e f 1 1 4 9 + 1 1 9 6 + 2 3 6 7 + 5 3 6 2 2 Complete the missing numbers: a 4 6 3 7 b 7 8 6 3 c 3 2

2 Find:

4 9 + 2 7 8 0

4 Complete the table by first rounding each number to the nearest ten: Question Estimate Actual Difference a 176 + 29 b 107 + 55 c 212 + 98 d 309 + 86 e 109 + 76 f 462 + 81 5 Find: $ 1 7 6 0 $ 2 5 5 0 + $ 3 7 9 0 6 Find the sum of 1750, 2176 and 3452.

7 e 6 7 f 5 6 7 + 2 1 5 + 4 3 + 2 3 5 3 0 0 7 0 5 9 8 4

d 4

3 Find the total of:

a 1785, 2630 and 1765 b 4279, 1051 and 3685 c 4356, 1079 and 1111 d 1985, 6630 and 980 e 676, 985 and 7351 f 2483, 1076 and 4385 4 Complete:

a $ 1 0 7 4 b $ 6 3 7 5 c $ 8 4 6 5 + $ 2 4 9 8 $ 3 2 6 + $ 4 9 5 $ 3 6 8 4 $ 3 9 4 5 d + $ 1 4 9 3 e + $ 4 9 9 9 f

$ 2 9 8 + $ 5 7 9 $ 3 1 5 0 $ 2 5 1 2 + $ 3 2 0

5 Find: 5 6 7 3 + 2 1 9 5 6 Complete the missing numbers: 7 8 5 + 1 2 4 3 0

8 Complete: $ 2 7 8 5 $ 1 1 9 5 + $ 4 5 0 9 a Find the total of $1065, $2990 and $3764.

b If Tom had $9999 to begin with, how much would he have left after spending the amount in part a?

9 Use three different numbers to write an equation that totals 5732. Answers on pages 126–7

+ 1 5 3 6 + 1 5 9 0 8 2

7 Find the total of 4285, 1176 and 3321.

8 Complete the table by first rounding each number to the nearest ten: Question Estimate Actual Difference 765 + 79


+ 1 2 7 9

7 Complete: 4 9 6 1 1 0 8 + 2 7

☞



25

UNIT 19

UNIT 20


Adding large numbers

Mental strategies for addition

1 Complete: a 2 0 4 6 3 8 b 6 4 1 1 2 5 c 6 0 7 8 5 + 1 4 7 9 3 5 + 2 8 4 3 1 5 + 4 9 6 3 2 d 8 5 6 3 7 e 8 1 5 6 3 f 1 1 4 3 6 0 + 4 9 1 1 2 + 7 2 9 8 5 + 5 8 3 4 1 1 2 Find which two number total:

11 765 43 021 56 662 24 985 31 764 67 050

a 43 529 = b 88 426 = c 92 035 = d 99 683 = e 36 750 = f 74 785 = 3 Find: a $ 2 6 3 1 8 5 + $ 1 7 6 4 3 9 c 1 2 8 4 9 6 m + 3 7 8 2 1 9 m

+ + + +

b $ 2 9 4 6 3 0 + $ 5 2 1 4 3 9

d 4 8 5 1 2 5 g + 3 6 4 8 2 1 g

f 8 5 8 3 2 cm

4 Calculate the total cost of:

hatchback $29 990

4WD $42 980

+ 1 1 8 6 7 5 cm

2 Use the jump strategy to complete:

b 132 + 47 = d 148 + 14 = f 256 + 15 =

a 36 + 39 = b 47 + 69 = c 242 + 51 = d 545 + 57 = e 47 + 132 = f 336 + 83 = 4 Check each of the addition equations with subtraction: a 4 3 6 b 2 2 8 – 1 2 5 – 3 9 6 + 1 2 5 + 3 9 6

sports car $37 985 minibus $65 178

d 8 5 8

+ 1 7 6

– 1 7 6

– 9 7

f

+ 2 5 7

– 2 5 7

c 5 3 1

motor bike $19 460

a 4WD + hatchback b minibus and motor bike c minibus and hatchback d sports car and motor bike e 4WD and motor bike f sports car and hatchback

a 5000 + 6000 = b 300 + 500 = c 1800 + 700 = d 900 + 2400 = e 9000 + 7000 = f 3400 + 6000 =

3 Use the compensation strategy to complete:

+

+ 9 4 2 1 8 L

1 Complete:

a 63 + 65 = c 68 + 39 = e 347 + 56 =

+

e 5 8 1 6 9 5 L


e 7 7 5

– 3 8 2

5 8 5 + 3 8 2

6 Use the jump strategy to complete: 89 + 38 = 7 Use the compensation strategy to complete:

46 725 43 189 45 852 6 Find which two numbers + total 89 041: 7 Find: 4 2 6 1 7 7 mm + 9 8 6 4 5 mm

8 Calculate the total cost of the 4WD and sports car of question 4. 7 6 4 7 8 1 4 3 7 2 9 9 Which is larger? + 6 8 5 4 6 2 8 3 4 9 or + 9 1 4 2 3

156 + 49 = 8 Check the addition equation with subtraction:

4 7 3 + 2 8 8

– 2 8 8

9 a Use the numbers 4, 6, 7 and 8 to write the largest and the smallest 4-digit numbers.

,

b Add these two numbers together.


5 Complete: 80 + 270 =

5 Complete: 1 7 8 5 9 0 + 6 2 4 3 8 5

26

+ 9 7


☞

Answers on page 127

UNIT 21

UNIT 22


Subtraction review

Mental strategies for subtraction

1 Estimate the following by first rounding each number to the nearest ten:

a 124 – 71 b 201 – 97 c 311 – 38 d 156 – 27 e 229 – 54 f 117 – 68 2 Complete the tables: – 32 58 76 45 b – 38 72 98 45 a 9 19 – 79 50 41 82 d – 37 85 72 59 c

29

11

– 53 86 75 46 f – 86 53 91 78 e

21

3 Complete: a 4 7 1 – 2 4 7

31

b 7 5 6

d 6 3 7 – 2 1 8

4 Complete: a 8 6 2 – 5 8 1 – 3 8 3

c 7 8 2

e 9 9 0

– 7 2 5

b 5 3 7 – 3 6 1

d 5 6 5

– 3 2 9

– 2 3 3

– 3 4 7

f 5 5 6

– 4 3 9

c 9 4 9 – 2 9 6

e 6 1 4

f 8 8 5

– 5 9 1

5 Estimate the following by first rounding each number to the nearest ten:

1 Complete:

a 400 – 62 = b 900 – 348 = c 9000 – 1436 = d 300 – 117 = e 4000 – 2915 = f 800 – 78 = 2 Use the jump strategy to find:

a 71 – 56 = c 91 – 58 = e 76 – 49 =

– 72 56 89 91 39

7 Complete: 9 7 5 – 3 5 7

4 7 9 8 Complete: – 2 8 5

b 87 – 35 = d 45 – 23 = f 81 – 55 =

a 63 – 19 = b 96 – 48 = c 72 – 38 = d 81 – 14 = e 62 – 46 = f 96 – 58 = 4 Check each subtraction with addition: a 4 3 7 b 5 6 2 + 2 4 8 – 2 4 8 – 3 9 5

– 4 8 3

+ 1 7 3

– 3 4 5

f 4 8 5 + 3 4 5 – 2 9 6

+ 2 9 6

e 6 2 9

+ 3 9 5

d 8 1 1 + 4 8 3 – 1 7 3

c 7 2 1

5 Complete: 4000 – 298 = 6 Use the jump strategy to find: 95 – 48 = 7 Use the compensation strategy to find:

52 – 28 =

8 Check the subtraction with addition: 6 3 2 + 3 8 5 – 3 8 5

9 Complete the wheel:

9 Draw a number line to illustrate:

3 Use the compensation strategy to find:

147 – 53 6 Complete the table:


379 – 27 =

90 34 23 65 –17 52 47 78 81

☞

Answers on page 127



27

UNIT 23

UNIT 24




1 Round each of the following numbers to the nearest hundred:

a 408 c 756 e 1181

b 289 d 647 f 2949

2 Round each of the following numbers to the nearest thousand:

a 1972 c 7156 e 12 724

b 2005 d 4358 f 16 500

E=

+

E=

E=

+

E=

+

E=

–

E=

e 3 0 0 0 – 3 7 9

–

– 1 2 7 5

– 2 3 8 5

f 11 756 – 3478 E=

–

E=

– 2 1 8 5

– 1 8 4 5

d 3 7 2 1

6 Round 14 786 to the nearest thousand: 7 Circle the following numbers that round to 6100 to the nearest hundred: 6052

5495

6352

E=

E=

+


– 4 2 6

b 4 0 0 0

c 2 0 0 0

– 2 3 4 0 e 7 0 0 0 – 4 2 8 0

– 1 4 9 6 f 3 0 0 0 – 1 7 5 8

b 1 1 0 9

c 5 8 9 5

– 2 7 5 e 2 3 6 7 – 1 4 7 5

– 3 4 8 6 f 3 0 0 0 – 1 7 5 8

5 8 7 6 – 3 2 8 9

9 John had 2756 lollipops. If he sold 1489, how many did he have left? Excel Start Up Maths Year 5

28

f 5 0 0 0

463 – 45 =

8 Find:

E=

– 5 6 0

7 Find: 4 0 0 0 – 3 2 6 5

$27 $46 $128 DVD T-shirt shoes

d 4 0 0 0

6 Find: 7 0 0 0 – 7 5 0

9 Estimate the total cost of the shopping by first rounding each amount to the nearest $10:

– 5 0 1


6181

8 Round each number to the nearest thousand then complete the estimate: 47 185 + 23 627

4 Find:

a 4 3 7 6

5 Round 1705 to the nearest hundred.

b 2 0 0 0

3 Find:

E=

– 6 4 7

d 4 0 0 0

d 7299 – 5106 E=

e 9905 – 2746

c 4 0 0 0

a 6 0 0 0

b 7385 + 11 325 E=

E=

c 5632 + 4215

– 3 9 5

4 Round each number to the nearest thousand, then complete the estimate:

a 90 – 56 = b 63 – 45 = c 42 – 38 = d 381 – 12 = e 214 – 25 = f 465 – 31 = 2 Find:

b 2595 d 2615 f 2551

a 4871 + 1986

1 Find the answers to:

a 1 0 0 0

3 Circle the following numbers that round to 2600, to the nearest hundred:

a 2714 c 2439 e 2689



☞

Answers on page 128

UNIT 25

UNIT 26


Subtraction to 9999 (2) 1 Complete each of the following: b 2 7 8 6 – 3 8 4 9 – 1 5 9 7

a 6 7 5 6 d 8 2 6 9 – 4 3 7 2

c 3 3 4 6

– 2 1 6 8 f 7 3 5 0 – 5 4 7 5

e 8 8 6 6

– 7 3 5 0

a 2 4 7 9 b 4 6 8 5 c 7 7 2 1 – 2 1 9 2

– 3 4 1 0

d 4 9 8 3 e 2

– 3 2 9 1 7

– 1 8 6 4 9

– 2 5 7 3 6

– 4 3 5 9 2

– 3 5 5 4 6

– 2 3 4 6 2

d 6 8 2 3 1 e 6 8 2 9 2 f 7 1 7 1 8

f 82 437 take away 46 832

3 Complete the missing numbers:

– 2 6 0 6

1 Complete:

a 8 5 4 7 0 b 7 5 8 3 2 c 6 7 5 5 3

a 67 329 minus 43 681 b 68 348 subtract 42 365 c 73 524 take away 38 649 d 32 405 less 17 763 e the difference between 24 983 and 37 851

a $9500 and $2754 b $8852 and $3678 c $5860 and $3983 d $9870 and $6623 e $7156 and $5249 f $4244 and $2985


2 Find:

2 Find the difference between:

– 1 4 6 7

7 f 4 6 – 1 6 8 – 2 1 9 8 3 7 1 7 5

4 a T here were 3426 tickets and 875 tickets were sold. How many were left?

b T here were 4876 apples in one bin and 3485 in

c T here are 2490 people in the hall. How many more

another. What is the difference?

people will fit if the hall holds 5000 people?

d T he cost of buying a car was $9875. If $6483 had

e A charity aimed to raise $5000. If $3264 was

been paid, how much was still owing?

collected, how much more was needed?

f James bought 2645 bricks for his paving. If he only used 1786, how many bricks were left?

5 Complete: 3 8 4 9 – 2 9 6 8 6 Find the difference between $4260 and $3852. 7 Complete the missing numbers: 7 9 3 – 2 7 4 7 3

3 Find:

a 1 0 0 0 0

9 If Mr Toe was born on 19 January 1913, how old was he on 30 January, 2006? Answers on page 128


– 2 4 8 7 c 9 0 0 0 0 – 4 8 5 2 0

b 8 0 0 0 0 – 7 8 5 2 6

d 5 0 0 0 0 – 2 7 5 0 3

f 3 0 0 0 0 – 7 9 5 – 2 8 5 2 5 4 Find the difference between 80 000 and:

e 5 0 0 0 0

a 24 326 b 48 275 c 79 350 d 975 e 4265 f 53 921 5 Complete: 4 7 2 8 3 – 2 6 4 9 1 6 Find 82 485 less 36 492. 7 Find: 2 0 0 0 0 – 1 1 3 1 5 8 Find the difference between 80 000 and 32 403. 9 Find the difference in cost between the two shopping lists:

8 There were 5287 items in the shop and 4758 items were sold. How many were left?

☞


Milk $1.75 Bread $2.95 Cereal $4.68


Cheese $3.85 Bread $2.75 Ham $3.98 29

UNIT 27

UNIT 28



Estimation 1 Round each number to the nearest ten and then complete the estimate:

1 Find:

a 8 3 4 4 5 b 5 8 2 7 6 c 5 4 5 2 9 – 6 8 4 9 3

– 3 9 1 5 4

– 2 6 3 8 5

d 3 9 0 8 8 e 4 2 9 2 1 f 3 6 2 7 7 – 2 6 4 7 2

– 2 4 8 3 5

– 1 9 4 8 5


a 56 800 km and 23 956 km b 12 356 mm and 945 mm c 72 540 m and 68 329 m d 76 273 s and 29 348 s e 46 251 L and 28 350 L f 58 011 kg and 34 756 kg 3 Complete the tables: a – 11 350 2 500 b – 4 867 1 752 c – 46 351 2 455 d – 51 456 3 847

e

f

– 40 361 – 76 451

a 172 + 49: b 309 + 258: c 174 + 232: d 179 – 52: e 523 – 78: f 426 – 81:

40 550

3 985

6 754

58 529

73 247

32 465

79 850

72 485

82 769

92 100

98 475

88 325

79 546

a 345 + 189: b 791 + 432: c 856 + 249: d 892 – 468: e 582 – 347: f 775 – 263: 3

E=

+

E=

+

E=

–

E=

–

E=

–

E=

4 Find:

– 2 4 6 0 4 – 3 1 2 5 6 6 4 0 0 0 d e 8 5 0 0 0 – 3 2 7 8 0 – 7 2 4 0 6 2 4 3 6 5 5 Find: – 1 7 4 8 7

4170

2850

+

E=

+

E=

+

E=

–

E=

–

E=

– 5450

E= 7752 9326

Which two numbers will add to give each estimate: a 7000 b 9000 c 8000 d 12 000 e 13 000 f 14 000

a 7 0 0 0 0 b 5 0 5 0 0 c 1 4 0 0 0

– 1 0 9 5 2 f 9 2 0 0 0 – 9 1 3 7 5

4 Estimate each answer in thousands and then find the exact answer: a 3 6 2 0 b 8 3 5 1 c 7 2 1 4 1 4 5 2 2 4 6 0 8 3 5 8 + 5 0 4 9 + 1 1 9 5 + 7 6 6 7 d 3 8 5 4 e 1 0 5 2 f 2 4 6 8 9 5 2 1 1 9 8 5 4 6 8 2 + 3 4 2 5 + 1 6 5 4 + 4 2 6 8 5 Round the numbers to the nearest ten and then complete the estimate:

20 004

159 + 248:

946 – 273:

11 859 7 Complete the – 2 437 table: 4 6 3 0 0 8 Find: – 2 9 3 2 5

12 015



9 Write, in words, the difference between twenty-six thousand, four hundred and ninety-five and sixteen thousand, seven hundred and twenty.

+

E=

6 Round each number to the nearest hundred and then complete the estimate:

6 Find the difference between 32 465 g and 17 357 g.

–

E=

7 Which two numbers in question 3 can be added to give an estimate of 11 000. 9 7 6 8 Estimate each answer in 1 2 4 5 thousands and then find + 1 7 7 5 the exact answer: 3 8 5 6 9 Estimate the answer in 3 4 thousands then find the exact answer of:


30

+

2 Round each number to the nearest hundred and then complete the estimate:

72 950


☞

Answers on page 128

UNIT 29

UNIT 30



Tables (1)

1 Round each of the following prices to the nearest $500:

a $9756 c $4215 e $13 249

b $2345 d $17 463 f $26 145

2 Complete the table by writing the full price: Item Price in ’000s Full price computer $4 a printer $1.2 b couch $2.5 c $3.4 d desk and chair bookcase $2.4 e $0.8 f filing system 3 Estimate each answer in thousands, then find the exact answer: a 8 6 3 4 b 4 5 8 5 c 7 9 3 6 – 2 1 9 3 – 2 8 2 6 – 5 2 2 1

d 3 7 5 1

f 6 6 7 2 – 1 8 6 3 – 2 8 9 5 4 Round each amount to the nearest $10 and estimate the total cost: a $ 4 6 3 b $ 7 8 5 c $ 4 8 5 $ 2 4 8 – $ 3 4 7 $ 2 9 9 + $ 1 9 6 + $ 3 0 2 $ 4 6 3 7 e $ 4 1 5 8 f $ 2 3 5 6 d – $ 2 4 1 8 $ 2 3 6 7 – $ 1 8 2 9 + $ 1 1 0 9 5 Round $14 780 to the nearest $500. 6 Complete the table by writing the full price: Item Price in ’000s Full price security system $1.8 – 2 1 8 7

e 2 9 4 6

7 Estimate the answer in thousands, then find the exact answer: 8 6 4 5 – 5 2 1 1 8 Round each amount to the nearest $10 and estimate the total cost: $ 6 3 4 $ 7 8 1 + $ 2 6 6 9 Estimate the total cost to build a fence: concrete poles pailings paint nails etc.

☞

1 Find:

a 3 groups of 7 c 5 groups of 10 e 8 groups of 6

Answers on page 129

b 9 groups of 7 d 6 groups of 3 f 7 groups of 5

2 Find:

a 7 3 3 = c 236= e 11 3 4 =

b 539= d 938= f 7 3 12 =

3 Find:

a 1 1 3

e 7 3

3

d 1 0 3

8

f 3

9

3

7

c 6 3

b 9

2

3

0

4 Write a division fact from each of the multiplication facts:

a 7 3 6 =

÷ ÷

c 335=

÷

d 936=

÷

e 537=

÷

=

b 11 3 8 =

= = = =

f 12 3 4 =

÷ = 5 Find 0 groups of 5. 6 Find: 12 3 10 = 7 Find: 1 0 3 6

8 Write a division fact from the multiplication fact:

9 3 5 =

$66 $179 $346 $213 $82



÷ = 9 Complete the path: 3 3

2

3

÷

8

20

÷5

34


31

UNIT 31

UNIT 32


Tables (2)

Tables (3)

1 Find the product of:

1 Find:

a 8 and 9 b 4 and 10 c 7 and 2 d 0 and 7 e 3 and 6 f 6 and 8

a 3 3 10 = b 835= c 11 3 7 = d 438= e 333= f 639=

2 Complete the missing numbers:

2 Find:

a 5 3 = 25 b 10 3 = 90 c 33 =6 d 3 10 = 0 e 3 7 = 56 f 3 4 = 12

a 2 groups of 7 b 8 times 10 c 9 lots of 2 d the product of 1 and 6 e 10 multiplied by 0 f 12 times 5

3 True or false?

3 True or false?

a 8 3 2 = 4 3 4 b 10 3 5 = 2 3 20 c 636=934 d 734=338 e 932=336 f 7 3 5 = 4 3 10

a 10 3 3 = 5 3 6 b 437=339 c 834=637 d 6 3 6 = 12 3 3 e 12 3 2 = 4 3 6 f 12 3 4 = 6 3 9

4 Find the total number of legs of:

4

a 7 spiders b 9 cows c 5 insects d 8 chickens e 10 octopuses f 6 elephants

Complete: a 3 4 5 3

6

c 3 2

8

10

e 3 10

6

5 Find the product of 7 and 10. 6 Complete the missing number:

8 Complete: 3 7 11 4

9

4 f

11

9

10

6

7

9

8

3

8

6

7

7 3

9 3

8

d 10 3


9

3 8 11 10 312 5 7 12 9


32

8

9 Complete:

b 73

c 33

3 d

8

7 3 7 = 5 3 10

Find the total number of legs of each animal:

5

7

7 True or false?

a 43

3

6 Find 3 multiplied by 9.

= 45 7 True or false?

4 3 3 = 6 3 2 8 Find the total number of legs of 11 ducks.

7 b

5 Find: 7 3 7 =

35

9



☞

Answers on page 129

UNIT 33

UNIT 34


Tables (4)

Multiplication by tens and hundreds


a 10 and 2 c 11 and 9 e 7 and 7

1 Complete:

b 7 and 4 d 4 and 5 f 5 and 3

2 Find:

a 11 3 10 = c 135= e 12 3 4 =

b 838= d 432= f 930=

a 3 3 2 = = 31 b 53 = 20 = 2 3 c 538= = 10 3 d 36= = 3 3 12 e 3 3 = 24 = 4 3 f 33= =932

tens tens tens tens tens tens

2 Complete:

3 Complete:

a 4 0

4 Find the total cost of:

3

a 4 books at $9 each b 10 hats at $5 each c 2 chocolate bars at $2 each d 6 games at $10 each e 7 lunches at $6 each f 4 drinks at $3 each

3

3

3

7 Find the missing numbers:

= 3 3 10

9 List the 9 times table and the different patterns you can find.

3

f 7 0 0

2

3

3

3

e 2 6 3

6

c 3 2

3 0

3

5

b 1 5

2 0

3

e 9 0 0

4 0

5 0

f 1 9 0 3

5 Complete: 7 3 3 tens =

8 Find the total cost of 5 toys at $8 each.

d 1 2 0

c 2 0

3

4

4 Complete: a 2 7 3 4 0

6 Find 3 3 9.

b 8 0

7

d 3 0 0

5 Find the product of 8 and 12.

=

a 4 3 2 tens = b 5 3 4 tens = c 10 3 7 tens = d 9 3 9 tens = e 4 3 8 tens = f 2 3 5 tens = a 5 3 20 = b 2 3 30 = c 4 3 40 = d 6 3 500 = e 3 3 800 = f 9 3 400 =


6 3


5 0

tens

6 Complete: 8 3 800 = 7 Complete: 3 0 3 6 8 Complete: 1 2 6 3 3 0 9 Estimate by rounding each initial number to the nearest ten before multiplying:

a 19 3 7 b 52 3 6 c 98 3 7 d 407 3 5 e 825 3 8 f 246 3 5 ☞




33

UNIT 35

UNIT 36





1 Complete:

a 7 0 0

a 4 flocks of 50 birds b 3 lots of 60 cards c 8 bunches of 30 flowers d 6 sets of 40 books e 5 rows of 90 disks f 7 boxes of 80 bananas 2 Find: a 3 9 3 3

3

d 9 8 3 5

3 Find: a 1 2 1 3 7

e 2 4 8 3

2

c 1 4

6

3

e 7 5 4

8

f 4 6 3

3

7

d 1 1 0 7

4

e 1 0 3 2

c 1 6 0 5 3 4

3 7


7

f 4 0 9 3 9

d 7 rows with 406 cabbage plants per row

5

e 5 piles with 216 bricks in each f 759 people at each of 4 performances

f 1 2 8 3

4 Find:

4 Complete:

a 5 3 $24 b 6 3 $149 c 4 3 $215 d 3 3 275 mL e 7 3 115 mL f 2 3 250 mL

a 615 3 4 = b 675 3 5 = c 709 3 8 = d 295 3 9 = e 524 3 6 = f 786 3 7 = 5 Complete: 3 4 3 3 3 6 Complete: 1 7 8 9 3 5

5 Find the total of 9 sets of 20 tools. 6 Find: 2 6 3 9

7 Find the total number of: 6 boxes with 215 DVDs in each box.

7 Find: 1 4 5 3 6

8 Complete: 3 3 824 = 9 Use the different cards to complete:

8 Find 4 3 $226. 9 Find 275 3 35 and check the answer with a calculator.

8

4

2

1

3

3

7

8

6

5

5 4


3

d 1 1 9

34

f 9 9 9

3 3

3 8

b 2 4 8 3

6

a 8 bags with 562 sweets in each b 452 people in each of 9 trams c 327 packs with 7 CDs in each pack

3

9

3 6

3

e 5 4 6

8

c 9 7 4

4

2 Complete:

3

3

a 1 0 4 1

3

3

b 8 3 2

5

d 4 0 2

b 2 3 5

6

c 1 6 3 3

3

3

b 1 8



☞

3

Answers on page 130

UNIT 37

UNIT 38


Extended multiplication (1) 1 Complete:

a 4 7 3

8

3

b 3 6

d 1 7

3

2 Complete:

a 4 3 6 3

d 3 1 2 3

6

3

6

3

c

9

81 43 20 52 d

8

3

3

2

f 1 1 9 8

50 121 14 72

5 3

26 31 49 60

3 3

71 26 32 19

b How many minutes in are there 9 hours? cW hat is the total amount in 3 bottles of 125 mL

a 546 and 3 c 727 and 4 e 7 and 619

Sydney and Melbourne. If the trip took 9 hours, how far did Dave travel?

f Sue measured a length of wood at 76 cm. If she had 9 pieces of wood all the same length, what was the total length of all the wood? 4 2 5 Complete: 3 6 6 Complete: 3 4 9 3 9 7 Complete:

3

9 Which whole numbers could be multiplied by 168 to give an answer between 600 and 1000?

Answers on page 130

9

f 5 8 6 3

3

b 295 and 9 d 6 and 351 f 5 and 256

a 393 3 4 b 732 3 5 c 454 3 6 d 707 3 9 e 356 3 8 f 241 3 7 4 a T he school had 9 rows of 72 seats. How many seats were there altogether?

b T here were 6 eggs in each of 214 egg cartons. How

c J o bought 8 packets of paper. If each packet had

many eggs were there altogether?

125 sheets, how many pieces of paper were there altogether?

d In a fundraiser, Sid collected 3 times as much as

e In a model boat there are 214 pieces. How many

Harry. If Harry collected $395, how much did Sid collect?

pieces are there in 5 model boats?

f A carpark has 7 rows with 89 parking spaces in each row. If the carpark is full, how many cars are there altogether?

5 Find: 3 9 2 3 4

512 3 7

7


3

7 Use mental and written strategies to complete:

8 If a year has 365 days, how many days are there in 4 years?

☞

e 4 2 3

7

6 Find the product of 6 and 423.

19 28 46 80

3

3 Use mental and written strategies to complete:

of drink?

d How many hours are there in 7 days? eD ave travelled at 102 kilometres per hour between

c 7 6 6

6


10

4 a How many days are there in 26 weeks?

3

8

3

3 25 41 12 70 f e

7

3

e 4 2 7

3 Complete: a 3 42 35 21 19 b

d 3 9 8

3

b 4 6 8

4

c 8 1 6

3

3

3

3

b 2 4 8

5

5

f 8 1

6

1 Find:

a 2 3 5

e 9 8

3 9

3


c 6 3

7


8 Emily had 416 five cent coins. How many cents did Emily have altogether? 9 What is the difference between the two answers? 3 2 6 and 4 5 8 3 4 3 3 Units


35

UNIT 39

UNIT 40


Multiples and square numbers

Factors

1 Write the first five multiples of each number:

a 5: b 7: c 11: d 9: e 15: f 20:

,

,

,

,

,

,

,

,

,

,

,

,

, ,

, ,

,

, ,

,

, ,

b 35 by 2 d 18 by 4 f 56 by 4

3 a 6 squared =

b 1 squared = c 3 squared = d 7 squared = e 12 squared = f 9 squared = b

7 1 6 34 8 3 4 5 2

1 2 6 37 10 9 4 5 3

c

d

8 9 4 39 5 7 6 3 10

5 6 9 33 7 10 8 1 2

e

7 8 2 36 1 10 3 4 9

5 Write the first five multiples of 12: ,

,

,

,

,

,

,

,

,

,

,

,

,

,

, ,

,

, ,

, ,

,

,

, ,

,

,

, ,

, ,

,

2 Multiply each of the following by 8:

a 7 b 12 c 15 d 20 e 25 f 62

,

,

a 6 is a factor of 28 b 4 is a factor of 50 c 7 is a factor of 49 d 3 is a factor of 90 e 12 is a factor of 34 f 15 is a factor of 60 4 a 16 =

f

9 2 7 38 3 10 0 8 4

,

3 True or false?

4 Complete: a

,

f 60:

a 14 by 2 c 43 by 2 e 22 by 4

,

,

2 Multiply:

1 List all the factors of:

a 6: b 8: c 20: d 15: e 100:

,


squared

b9= squared c 25 = squared d 100 = squared e1= squared f 81 = squared 5 List all the factors of 21:

6 Multiply 73 by 2.

,

,

,

6 Multiply 13 by 8.

7 8 squared =

7 True or false?

8 Complete: 3 10 9 35 8 4 5 7 6

25 is a factor of 100 8 64 =

squared

9 True or false?

9 Find: 32 + 42 + 52

3 is a factor of 92.




☞

Answers on page 130

UNIT 41


UNIT 42

Multiplication and problem solving

Division

1 Find the errors in the following equations and give the correct answer: a 2 4 5 b 3 0 9 c 4 2 1 3 6 3 7 3 8 1 4 6 0 2 1 0 3 3 3 6 9

d 1 1 0 2 3 9

e 1 3 2 0

1 Divide each of the following numbers by 2:

f 2 0 3 4

3 4 9 9 9 8 6 9 2 0 8 1 2 6 2 a S am earned $597 a week for 5 weeks. How much did he earn altogether?

3 6

b F red collected 322 on average stamps a year for 9 years. How many stamps did he have?

c How many days are there in 150 weeks? dH ow many balls are there in 421 boxes, if there are 8 balls in each box?

e C indy walks 825 m to and from school each day. How

f H ow much soft drink is there for the party if there

far does she walk in one week?

d 2 4 8 3 3 2

e 9 5 6

3 4 4 4 2 8

4 9 6 6 2 8 6 8 4 Find the missing numbers: a 2 4 0 b 1 2 3 3 3 7 9 2 4 7 0

c 1 8

2 1 3 5

5 Find the error in the following and give the correct answer:

9

☞

Answers on page 131


7 56

d 5 55

10 120

f

3 18

5 Divide 120 by 2.

4 3 5 0

3 7

3 0 1 5 0

6 Divide 156 by 4. 7 Divide 448 by 8. 8 Complete:

1 7 2 2 Write two different multiplication equations that gives the answer 212.

e

6 There are on average 3204 bees in a hive. How many bees are there in 3 hives? 7 Check using addition: 9 4 2 3 6 5 6 5 2 2 4 8 Find the missing numbers: 3 7

4 28

6

b

c

3 6

2

6 54

1 6 7 4

7 5 0 4

a

3 9

3

a 64 b 92 c 116 d 252 e 480 f 684

4 Complete:

d 4 2 7 e 9 3 8 f 4 3 1 3


a 128 b 360 c 568 d 200 e 152 f 504

f 1 1 0 7

3 3

a 46 b 84 c 90 d 262 e 182 f 448


are 7 bottles with 125 mL in each bottle? 3 Check each multiplication using addition: a 4 2 6 b 7 8 5 c 3 1 1 7 3 4 3 3 3 5 1 7 0 4 2 3 5 5 1 5 5 8 5


7 49

9 Draw a diagram (picture) to illustrate and solve:

4 20


37

UNIT 43

UNIT 44




1 Complete:

6 60

b

8 64

d

4 36

7 56

e

7 77

c

1 Complete with trading:

a

f

a 4 19

b

c 9 55 7 51

2 23


a 3 45

c

8 96 e 3 51

2 76

a

d

2 78

f 6 84

6 92

c

e

5 77

8 90

f

7 83

c J ordan had 52 jellybeans to share between her and a

How many cartons did she need?

friend. How many did they receive each?

d A ndrew had to put 76 sheep into 4 paddocks evenly. How many sheep did he put in each paddock?

e A ndrea used 89 pieces of paper for the week. How many pieces did she use each day?

f Jake had 54 counters to share between 4 people for a game. How many did each person receive?

5 Complete: 4 72

3 28

6 Solve: 3 81

7 This has a remainder: 6 87

8 Find one share of 70 books shared by 5.

8 Zac had 90 matchsticks to place in 8 boxes.

9 Show the equation is correct by writing a different type of equation to check the answer.

How many did he place in each box? 9 Write four number facts using the numbers: 7, 13, 91



4 76

2 54

38

f

b

3 71


e 3 45

6 72

5 60

6r4 6 40

c

b S ally had 78 eggs to place into cartons of 6 eggs.

6 This division has a remainder:

5 75

5 Complete:

b

4 85

a 66 balls shared by 6 b 70 flowers shared by 5 c 91 bricks shared by 7 d 56 pens shared by 4 e 96 cards shared by 8 f 81 coins shared by 3

3 75

4 Find one share:

f

4 a S cott had 85 apples to put in 5 baskets. How many apples were there in each basket?

4 64

d

5 95

6 90

e

7 98

b

3 84

c

3 These have remainders:

f

d

8 60

4 68

a 2 48 d

d

e

6 67

b

2 Solve:

9 45

a

2 These divisions have remainders:



☞

Answers on page 131

UNIT 45

UNIT 46


Dividing numbers containing zeros

Divisibility

1 Complete:

1 Circle the numbers which are divisible by 3:

a

b

5 525

c

7 728

d

f

4 436

8 816

e

7 714

6 624

2 Rewrite each of the following and then work out the answer:

a 105 ÷ 3 =

b 920 ÷ 4 =

d 808 ÷ 8 =

e 735 ÷ 7 =

a 3 306 c

7 708

f 981 ÷ 9 =

b

6 607

f

5 501

8 805

4 Find the missing digits:

a

c

e

301

f

102

106 5

5 Complete:


a 14 3 6 = 84 b 16 3 9 = 144 c 17 3 5 = 85 d 27 3 4 = 108 e 24 3 8 = 192 f 18 3 7 = 126 4 Divide each of the following by 5:

3

6

100

d

105

a 49 b 81 c 105 d 182 e 164 f 277

4

2

b

210 4

2 Circle the numbers which are divisible by 7:

2 806

d

e

a 6 b 102 c 91 d 76 e 115 f 123

c 630 ÷ 6 =

3 Solve:


a 320 b 125 c 160 d 490 e 261 f 378

9 927

5 Which of these numbers are divisible by 3?

6 Rewrite 505 ÷ 5 and then work out the answer:

28, 24, 87, 71 6 Which of these numbers are divisible by 7?

7 Solve:


6 612

13 3 8 = 104


8 Divide 422 by 5.

223

3

9 Find eight hundred and twenty-nine divided by four.

107, 112, 287, 807

9 Write the rule for finding if a number is divisible by 6.

☞

Answers on page 131



39

UNIT 47

UNIT 48




1 Complete:

1 Find:

a 5 575

b

c

7 784

d 6 696

8 960

e

f

9 954

a

8 424

b

6 444

f

9 342

a 750 ÷ 6 =

b 946 ÷ 8 =

e 979 ÷ 7 =

c 667 ÷ 4 =

f 763 ÷ 9 =

4 Share:

a 684 cows among 4 b 966 stickers among 6 c 426 buttons among 3 d 847 nails among 7 e 896 stamps among 8 f 765 photos among 5

c

d

5 765

7 952

e

f

4 692

6 726

b

5 912

6 812

c

d

3 775

7 824

e

f

9 852

4 786

3 True or false?

a 657 ÷ 9 = 73 b 951 ÷ 8 = 112 c 939 ÷ 7 = 134 d 216 ÷ 3 = 72 e 887 ÷ 6 = 148 f 324 ÷ 4 = 81 a

3 642

b

4 300

8 900

c

d

7 400

6 700

e

f

7 800

3 400

5 Find:

6 Divide:

8 944

4 Complete:

5 Complete:

2 374

a

5 325

b

2 Find:

d

3 Rewrite the following equations and then work out each answer:

d 552 ÷ 3 =

4 868

2 Divide:

a 4 208 c 7 581 e


6 876

6 Find:

3 174

7 Rewrite 918 ÷ 7 and then work out the answer:

4 933

7 True or false?

250 ÷ 5 = 25

8 Complete:

8 Share 819 balls among 9. 9 A box of 755 centicubes was shared among 5 students in the group. How many centicubes did each student receive?

9 800 9 Chong travelled 154 km in a week. How far did he travel each day?




☞

Answers on page 131

UNIT 49

UNIT 50


Division by tens

Division of 4-digit numbers

1 Divide each of the following by 10:

1 Divide 6452 by:

a 130 b 270 c 490 d 356 e 925 f 615

a 2 b4 c6 d5 e8 f 10

2 Find:

2 Find:

a 10 7 6 0

b 10 9 5 0

c

d

10 170

e

10 6 4 0

3 Find:

10 8 8 0

f


10 3 6 0

a

b 10 2 2 1 10 3 4 7 c d 10 8 9 6 10 7 0 5 e f 10 5 4 3 10 4 5 6

a 2 1146

6 4608

c

d 4 4784

4 1448

e

f

8 4368

3 2001

3 Find:

a

b

6 6192

9 1881

c

d

5 4000

7 7028

e

f

4 1232

4 Find how much it is for one if ten items cost:

a $50 b $180 c $240 d $36 e $179 f $298

b

8 6432

4 Find which of the numbers 3, 5, 7 and 9 are factors of:

a 3003 c 1900 e 1359

b 1881 d 4116 f 3156

5 Divide 3750 by 6. 6 Find:

5 Divide 217 by 10.

7 1995

6 Find:

7 Find:

10 4 7 0

7 Find:

8 Find which of the numbers 4, 3 and 7 are factors of:

10 6 7 8

8 Find how much it is for one if ten items cost $636. 9 There was 200 g of flour. How many times could Sara take 10 g of it?

a 1300 b 2994 c 1806 9 Fill in the missing numbers: 1 6 5

☞

Answers on page 131


7 7749

9 1


5 41

UNIT 51

UNIT 52


Inverse operations and checking answers

Number lines 1 Write the value of each letter of the number line: f

0

d 1

a 2

a d

3

c 4

e

5

6

8

b e

9

10

c f

2 Label each of the following values on the number line:

30

a 37 d 44

1 Use addition to check the subtraction. Tick the boxes for those that are correct and write the answers for those that are incorrect:

b 7

40

b 49 e 44 12

50

c 32 f 35 12

a 36 – 8 = 42 b 52 – 7 = 45 c 66 – 17 = 59 d 85 – 28 = 57 e 112 – 45 = 67 f 176 – 98 = 74 2 Use multiplication to check the divisions. Tick the boxes for those that are correct and write the answers for those that are incorrect:

3 Label each of the following values on the number line:

0

1

1 12

a

d 56

b 12

c

1 4

e 23

f

11 12

4 Estimate and label each of the following values on the number line:

1000

a 1450 d 1900

1500

b 1261 e 1007

2000

c 1735 f 1625

m

1

6 Label

3

32 12

a 28 ÷ 7 = 3 c 45 ÷ 9 = 3 e 56 ÷ 8 = 7

a 76 + 52 is more than 120 b 248 – 85 is less than 150 c 900 ÷ 6 is greater than 130 d 80 3 12 is greater than 1000 e 921 – 437 is less than 490 f 800 ÷ 5 is less than 140

on the number line:

30

40

50

7 Label 34 on the number line:

0

8 Estimate and label 1825 on the number line:

b * – 47 = 43 c * 3 7 = 777 d * ÷ 6 = 21 e * + 4 = 10 f * 3 9 = 153 5 Use addition to check the subtraction:

1

1 2

d 48 ÷ 3 = 12

f 32 ÷ 4 = 8 3 Use inverse operations to check these statements. Answer with true or false:

b 48 ÷ 6 = 8

4 Rewrite using inverse operations and find the value of the * a * + 14 = 29

5 Write the value of the letter:


247 – 83 = 164 6 Use multiplication to check the division:

72 ÷ 9 = 6 7 Use inverse operations to check the statement. Answer true or false.

1000

1500

2000

9 Draw a number line from 60 to 90 and label the points: 69, 85, 71, 66 and 78.

378 + 295 is greater than 670

8 Rewrite using inverse operations to find the value of the * * 3 6 = 114 9 Find the value of the star:

* 3 3 + 6 = 21




☞

Answers on page 132

UNIT 53

UNIT 54 UNIT 1


Number lines and operations

Averages (1)

1 Use the number lines to find:

a 712 + 18 = b 395 + 25 = c 405 + 23 = d 219 + 16 = e 114 + 17 = f 398 + 13 =

1 Find the average of each pair of numbers:

700

710

720

730

390

400

410

420

400

410

420

430

210

220

230

240

110

120

130

140

390

400

410

420

a 10 and 20 c 0 and 100 e 36 and 40

960

970

980

990

450

460

470

480

730

740

750

760

590

600

610

620

390

400

410

420

850

860

870

880

a 1, 3, 5 c 26, 28, 30 e 130, 140, 150

20

30

0

10

20

30

0

10

20

30

0

10

20

30

0

10

20

30

0

10

20

30

520

530

540

380

390

400

e T he temperature for 5 days at noon was 18ºC, 25ºC,

f Four different bags of sweets were opened and there

0

10

20

5 Find the average of 176 and 182.

550

6 Find the average of 7, 9, 14. 7 Find the average cost of $14, $17 and $20.

410

8 The ads on TV were timed and four different ads took 36 s, 48 s, 20 s and 34 s. What was the average length of a TV ad?

30

8 Draw a number line, starting at 80 and count by 6s.

9 a Find the average of 27, 35, 42, 28, 36, 27 and 40.

9 a D raw a number line from 0 to 10 and mark every half.

b Write a question based on the number line. ☞

Answers on page 132


19ºC, 21ºC and 22ºC. What was the average daily temperature at noon? were 22, 26, 24 and 24 sweets in each bag. What was the average number of sweets in a bag?

7 Use the number line to find: 13 3 2 =

the average number of eggs laid in the week?

6 Use the number line to find: 408 – 22 =

d If 4 hens laid 4, 7, 6 and 7 eggs in a week, what was

5 Use the number line to find: 526 + 23 =

cW hat is the average height of 3 students, who were 1.60 m, 1.57 m and 1.54 m tall?

a start at 2 and count by 4s b start at 6 and count by 7s c start at 200 and count by 3s d start at 100 and count backwards by 3s

f start at 200 and count backwards by 8s

bW hat is the average cost of hot food if the items cost $1.10, $1.20, $1.50 and $1.80?

4 Draw a number line to show each of the following:

b 2, 4, 6 d 19, 20, 21 f 210, 230, 250

4 a W hat is the average age of children in the family if the children are 2, 3, 5 and 10 years old?

10

e start at 47 and count backwards by 2s

a $1.20, $1.60, $1.40 b $1.10, $1.30, $1.20 c $2, $6, $4 d $10, $5, $15 e $50, $100, $150 f $120, $100, $110

0

3 Find the average cost of:


a 27 ÷ 9 = b 3 3 8 = c 30 ÷ 6 = d 4 3 7 = e 28 ÷ 4 = f 6 3 5 =

b 20 and 40 d 150 and 200 f 112 and 118

2 Find the average of each set of numbers:


a 987 – 25 = b 476 – 19 = c 753 – 18 = d 619 – 25 = e 414 – 17 = f 875 – 19 =


b Write 5 numbers that have an average of 10.


43

UNIT 55

UNIT 56


Averages (2)


1 Find the average of each set of numbers:

1 Complete:

a 4, 5, 6, 7, 8 b 10, 12, 14, 16, 18 c 10, 20, 30, 40, 50 d 7, 9, 11, 13, 15 e 100, 300, 500, 700 f 42, 48, 54, 56

a 40 – 8 + 12 = b 36 + 12 – 4 = c 59 – 14 + 6 – 3 = d 72 + 9 – 14 + 2 = e 66 – 4 – 8 + 11 = f 92 – 30 + 16 – 4 =

2 Write the average of each of the following as a decimal:

a 7, 9, 12, 14, 15 c 211, 305, 417 e 19, 27, 36, 14, 21 f 118, 210, 309, 400

b 79, 135, 113 d 8, 6, 3, 5, 7

3 Write the average of each of the following as mixed numbers:

a 12, 13 c 110, 121, 115 e 141, 152

b 42, 43, 45 d 15, 17, 19, 22 f 79, 81, 83, 84

4 a T wo fish were caught. One weighed 1.5 kg and the other 3 kg. What was the average weight?

b T hree jars held 120 g, 200 g and 250 g.

c T hree pieces of wood measure 1.60 m, 1.72 m and

d F our containers hold 1.25 L, 2 L, 5 L and 2.6 L of

e In 4 boxes there were 22, 20, 18 and 24 pencils. Find

f T here were 118, 120, 110 and 136 raffle tickets in

Find the average weight.

1.79 m. What is the average length?

water. What is the average volume of water in the containers?

the average number of pencils in the boxes.

5 6 7 8


4 books. What was the average number of raffle tickets of the books? Find the average of 27, 29, 31 and 33. Write the average of 25, 27, 29, 30 and 33 as a decimal. Write the average of 142, 140 and 130 as a mixed number. Two bottles of drink held 1.25 L and 2.0 L of soft drink. What was the average volume of the soft drink?

9 Draw a grid 6 3 4 and a grid 3 3 6. Find the average number of squares of the grids.

2 Complete:

a 4 3 2 3 6 = b 8÷239= c 20 ÷ 4 3 10 = d 24 ÷ 6 3 3 = e 4 3 6 ÷ 12 3 2 = f 4 3 12 ÷ 8 ÷ 2 = 3 Complete:

a 40 + (10 ÷ 2) = b (9 + 3) ÷ (8 – 6) = c (5 3 8) + 7 = d 50 – (4 3 8) = e 6 3 (5 + 3 + 2) = f (10 ÷ 2) 3 (12 – 3) = 4 Complete:

a 6 + 4 3 3 = b 7 3 3 – (3 3 5) = c 30 – 4 3 7 = d 50 + (2 3 6) ÷ 4 = e 20 3 2 ÷ 5 + 3 = f 60 – 8 + 4 3 2 = 5 Complete:

60 – 20 – 15 + 3 = 6 Complete:

100 ÷ 10 3 2 = 7 Complete:

(2 3 10) ÷ (4 3 1) = 8 Complete: 5 3 8 – 3 3 2 = 9 Write an equation and find the answer to:

start at 50, divide by 5, add 4, multiply by 2 and divide by 7.




☞

Answers on page 132

UNIT 57

UNIT 58




1 Put in the brackets to make the equations true:

a 6 3 4 + 2 = 36 c 54 ÷ 9 – 3 = 9 e 19 – 6 + 2 = 11

1 Complete:

b8+8÷4=4 d 100 ÷ 10 3 5 = 2 f 4 3 3 + 5 = 32

a 6 3 4 ÷ 2 = b 36 ÷ 6 3 10 = c 40 3 2 ÷ 8 = d 63 ÷ 9 3 3 = e 10 3 8 ÷ 4 = f 33435÷3=

2 Find:

a 23 – 10 ÷ 2 = c 100 ÷ (5 3 5) = e 8 ÷ (2 3 4) =

b 32 – (16 ÷ 2) = d 20 ÷ 4 + 8 = f 7+833=

2 Find:

3 Try these:

a 20 + 10 + 15 – 6 = b 27 – 13 + 12 + 9 = c 42 – 20 – 3 + 14 = d 140 – 21 + 13 – 64 = e 156 + 7 – 9 + 27 = f 198 – 121 + 32 – 14 =

a (8 + 4) ÷ 3 + 7 = b 6+8÷233= c 7 3 9 – 30 ÷ 10 = d 60 ÷ 10 + 50 ÷ 5 = e 7 – 20 ÷ (2 3 2) = f 5 + 5 3 3 – 11 = 4 a W hat is the total number of plants if there are 12 rows of 4 plants and 5 more plants in a container?

bH ow many boxes are there if there are 60 pencils with 10 in each box and 40 crayons with 5 in each box?

c I earned $7 per hour for working 3 hours on Friday and $9 per hour for working 5 hours on Saturday. How much did I get paid altogether?

a 50 + (3 3 10) – 14 = b 21 – (6 + 11) – 3 = c (4 3 8) – (8 + 2) = d (10 3 10) – (6 + 9) = e (5 + 2) 3 7 – 3 = f 10 – (6 + 2) + 27 = a 14 + 8 3 3 = b 20 + 36 ÷ 6 – 5 = c 50 – 5 3 8 = d 64 ÷ 8 – 7 = e 150 – 6 3 7 = f 3 3 4 ÷ 6 + 80 =

d T here were 3 paddocks of 8 cows and 6 paddocks of 4 horses. How many animals altogether?

e F or the party I had 6 boxes with 5 small cakes in

f D uring a sale I saved $3 on a $15 T-shirt and $8 on a

each, 8 pieces of slice and 3 tarts. How many items for sweets did I have? $36 jumper. How much did I pay in total?

3 Complete the brackets first:

4 Complete:

5 Complete: 5 3 9 ÷ 3 =

5 Put in the brackets to make the equation true: 20 3 3 – 4 + 11 = 45

8 Adam has 20 cards, but Dave has 3 more than Adam and Sean has 7 fewer cards than Adam. What is the total number of cards? (9 + 3) 3 (18 – 15) = 6 3 4 + 16

☞



20 + 47 – 3 + 15 =

10 3 9 – (40 + 5) =

7 Try: 8 – 10 ÷ (5 – 3) =

6 Find: 7 Complete the brackets first:

6 Find: 3 3 7 + 14 =

9 True or false?


8 Complete:

120 + 8 3 6 – 63 = 9 Find the missing number:

9 3 Units Excel Advanced Skills Start Up Maths Year 5

– 30 ÷ 10 = 33 45

UNIT 59

UNIT 60


Operations with large numbers


1 Find:

1 Write the rule for each of the following number patterns:

a 4 8 6 3 1 b 6 6 4 2 5 c 1 1 0 4 6 2 4 9 8 + 3 1 0 5 1

1 0 7 5 8 + 3 4 1 1 2

2 1 9 8 + 3 4 2 8 5

d 6 1 3 2 1 e 4 8 3 5 2 f 1 1 0 7 5 9 8 5 + 2 1 1 8 3

1 1 0 6 + 9 8 7 2

6 2 4 3 1 + 9 9 9 8

2 Find:

a 1 5 0 0 0 b 3 4 6 7 2 c 1 0 7 2 5 – 2 1 9 8 – 2 1 5 9 7 – 6 4 8 3 d 4 4 2 7 3 e 4 2 0 5 1 f 1 2 0 0 0 – 1 9 3 4 6 – 3 4 6 1 0 – 5 9 7 6 3 Find:

a 4 2 4 3

b 1 0 7 5

3 6

d 4 3 8 5

3 5

c 9 8 5 1

3 3

e 1 0 4 7

3 8

3 4

4 Find:

a

b

6 7524

c

5 5525

d

4 14108

3 Find each of the following:

a 6.2 3 10 = b 7.6 3 10 = c 6.85 3 10 = d 8.54 3 100 = e 3.26 3 100 = f 55.43 3 100 =

a 32 ÷ 10 = b 76 ÷ 10 = c 42.3 ÷ 10 = d 98 ÷ 100 = e 426 ÷ 100 = f 32.5 ÷ 100 =

8 7720

5 Find: 2 4 8 6 3 3 6 8 4 2 + 1 1 0 4 9 6 Find: 1 2 0 5 0 – 6 3 9 1 7 Find: 4 3 8 6 3 3

5 Write the rule for the number pattern: 21, 42, 63, 84 6 Find the missing number: 109 – 23 = 2 3 7 Find: 19.6 3 100 = 8 Find: 439 ÷ 10 =

8 Find: 3 7464

a ÷ 2 = 5 3 10 b 36 + 8 = 34 c 7 3 3 = 63 ÷ d 304 ÷ 4 = + 23 e 2 3 21 = 200 – f 115 3 3 = 69 3

4 Find each of the following:

f

9 7911

2 Find each missing number:

7 7896

e

a 70, 61, 52, 43, 34 b 621, 207, 69, 23 c 13, 52, 208, 832 d 111, 180, 249, 318 e 1.6, 4.8, 14.4, 43.2 f 70, 35, 17.5, 8.75

f 2 4 6 8 3 7

9 What is the pattern when:

9 The total cost of four televisions was $3052:

a On average, what did each television cost?

a multiplying by 10 and 100?


bW hat is the total cost of the televisions and three computers at $1946 each?

b dividing by 10 and 100?




☞

Answers on page 133

UNIT 61

UNIT 62


Missing numbers

Change of units


1 Change each of the following lengths to metres:

a 24 + = 40 b – 60 = 190 c 36 + = 52 d – 119 = 147 e 321 + = 500 f – 49 = 215

a 200 cm c 3 km e 1400 mm

a 1 hour b 3 hours

a 3 6 = 72 b 93 = 108 c 30 3 = 300 d 14 3 7 = e 3 3 = 150 f 12 3 = 144

c 2 12 hours

d 60 seconds

e 90 seconds

f 630 seconds 3 Change each of the following weights to kilograms:

a 2000 g c 6000 g e 500 g


a ÷4=8 b ÷7=5 c 81 ÷ =9 d 200 ÷ =4 e 100 ÷ =5 f ÷ 2 = 25

b 4000 g d 250 g f 468 g

4 a A dripping tap loses 200 mL of water each day. How much water is lost in one week?


a 96 = 8 3 b 101 = 42 + c 60 = ÷2 d 121 = 200 – e 460 = + 137 f 360 = 36

b S ix children shared 3 L of orange juice equally.

c I bought 2 kg of flour. Mum borrowed 250 g.

d A builder needed four lengths of 85 cm pieces of wood.

How much did they each receive?

How much did I have left?

How many metres of wood did she need to buy?

e A football game lasts for two hours. If there are

f F or a banquet at a restaurant there was 1800 g of

5 Find the missing number: 27 +

b 500 cm d 8 km f 2500 mm

2 Change each of the following times to minutes:



three breaks of ten minutes each, how long is the playing time?

rice. If each person received 200 g, how many people received rice?

5 Change 750 cm to metres.

= 75

6 Find the missing number: = 28

6 Change 1 14 hours to minutes.

7 Find the missing number:

7 Change 550 g to kilograms.

4 3

45 ÷

= 15

8 For swimming training, Daisy swam 1.5 km on Monday, 700 m on Tuesday, 900 m on Thursday and 1.2 km on Friday. How far did she swim for the week?


96 = 201 – 9 Write an equation for the following and solve it:

There were 27 people at the party and 16 more people arrived after finishing their game of cricket. How many people, in total, were at the party?

9 If a car travelled at 60 km every hour, how far did it travel each second?

☞

Answers on page 133


(Hint: you may need to use a calculator.)


47

UNIT 63

UNIT 64


Reasoning with numbers

Negative numbers


a 46 + = 85 c 3 6 = 54 e 336+ = 25

1 Record the value of each letter:

b 60 – d 90 ÷ f 73

= 22

d

= 10 + 8 = 57

2 Complete the spaces to make the number sentences true:

a 20 + 15 = 7 3 b ÷ 5 = 25 3 2 c 4 3 7 = 16 + d 54 ÷ = 92 – 86 e 27 + = 5 3 8 f 113 – 65 = 12 3

a d

b

b e

1

3

=

3

=

3

=

3

f

3

3

4

5

6

7

c f

–20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

–20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

ºC

ºC

c–20–15–10 d –20–15–10 –20–15–10 –5 –50 05 510 10 15 15 20 20 25 25 30 30 –20–15–10 –5 –50 05 510 10 15 15 20 20 25 25 30 30 –20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

–20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

ºC

ºC

e–20–15–10 f –20–15–10–5 –50 05 510 1015 1520 2025 2530 30 –20–15–10 –5 –50 05 510 10 15 15 20 20 25 25 30 30 –20–15–10 ºC ºC

–20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

ºC

ºC

3 Colour each of the thermometers to show the temperatures:

a–20–15–10 13ºC –5 –50 05 510 1015 1520 2025 2530 30 b–20–15–10 9ºC –5 –50 05 510 1015 1520 2025 2530 30 –20–15–10 –20–15–10 –20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

e

2

c

–20–15–10 –5 0 5 10 15 20 25 30

=

ºC ºC

–20–15–10 –5 0 5 10 15 20 25 30

ºC

–20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

ºC

ºC

–20–15–10 –20–15–10 e–20–15–10 –1ºC –8ºC –5 –50 05 510 10 15 15 20 20 25 25 30 30 f–20–15–10 –5 –50 05 510 10 15 15 20 20 25 25 30 30 –20–15–10 –5 0 5 10 15 20 25 30 –20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

=

–20–15–10 –5 0 5 10 15 20 25 30

ºC

–20–15–10 –20–15–10 c–20–15–10 3ºC –5 –50 05 510 1015 1520 2025 2530 30 d–20–15–10 –4ºC–5 –50 05 510 1015 1520 2025 2530 30 ºC ºC

ºC ºC

ºC

ºC

4 Show each number sentence on the number line:

4 Complete the following equations:

a 3 3 6 = 3 3 (2 + )= b 6 3 8 = 6 3 (4 + )= c 10 3 (5 + 2) = 10 3 = d 7 3 (3 + 3) = 7 3 = e 5 3 ( + )=533= f 8 3 ( + )=839=

b 3 – 5 + 4 =

–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7

c 4 + 2 – 6 – 1 =

–1 0 1 2 3 4 5 6 7 8 9 10

d 8 – 5 – 7 + 3 =

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

5 Record the value of the letter g.

g

–3

3

8 Complete: = 6 3 (5 + 3) = 6 3 9 Place the numbers 4, 5 and 6 in the correct spaces to find the answer.


–1

0

1

2

3

–20–15–10 –20–15–10 –5 –50 05 510 10 15 15 20 20 25 25 30 30 –20–15–10 –5 0 5 10 15 20 25 30 ºC ºC

ºC

7 Colour the thermometer to show the temperature –20–15–10 –20–15–10 –5 –50 05 510 10 15 15 20 20 25 25 30 30 –20–15–10 –5 0 5 10 15 20 25 30

of 8ºC. ºC ºC ºC 8 Show the number sentence –2 + 5 – 3 + 4 = on the number line:

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

9 In a quiz, Ben scored 4 points, lost 6 points and scored 5 points. What was Ben’s final score?


48

–2

6 Record the temperature of the thermometer:

= 29

–5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

equation for the array:

+

–5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10

f –6 + 5 + 4 – 2 =

2 3 + 16 = 40 6 Complete to make the number sentence true: 14 3 2 = 7 3 7 Write a multiplication

3

a 4 + 3 – 5 =

e 6 – 9 + 4 =


f

a–20–15–10 b –20–15–10–5 –50 05 510 1015 1520 2025 2530 30 –20–15–10 –5 –50 05 510 10 15 15 20 20 25 25 30 30 –20–15–10

a

2 Record each of the following temperatures:

=

3

e

–7 –6 –5 –4 –3 –2 –1 0

3 Write a multiplication equation for each of the arrays:

a b c d



☞

Answers on page 133

UNIT 65

UNIT 66


alculator – addition, subtraction and C multiplication

Calculator – division

1 Find the answer to each of the following:

a 42 + 86 + 91 + 75 = b 5876 – 925 = c 49 3 6 = d 10 + 245 +139 + 58 = e 872 – 87 = f 13 3 15 = Estimate

Actual

Numbers

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

Difference

Product

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

172 210 504 192 105 360

4 Find:

a 6.3 multiplied by 7 b the sum of 6 and 7 multiplied by 3 c 37 subtracted from 89 added to 42 d the difference of 20 and 6 multiplied by 4 e 1 4 multiplied by the difference of 8.6 and 10.7

Number sentence

Estimate

508 – 389

120

Actual

Numbers

4

5

6

d

3 8

e

4 9

f

7 8

a 60 b 144 c 72 d 160 e 48 f 92 3 Use a calculator to complete each of the following divisions:

a 8 978 c 5 987 e

8

9



4 461

d 6 777

f

5 604

a b 9 7 4 0 2 7 1107 c d 5 3201 7 3071 e f

6 4376 4 7

8 5578

to a decimal using a calculator.

6 Find all the factors of 500. 7 Use a calculator to complete:

8 265 8 Use a calculator to complete:

90

8 Find the difference between 19.3 and 7.8 multiplied by 4. 9 Find two numbers with a difference of 10 that give the , product of 231.

☞

8 958

b

4 Use a calculator to complete each of the following divisions:

Product

7

17 100

1 3

Difference

7 Circle three numbers which have the product of 90: 3

b

c

5 Change

5 Find the answer to: 19 3 14 6 Find the actual answer and work out the difference between the answer and the estimate:

f 9.8 multiplied by 40 then 17.5 is added

46 100

2 Find all the factors of each of the following:

a 563 + 291 + 476 1330 1270 b 538 – 271 1120 c 26 3 4 d 483 + 611 + 298 1390 1020 e 1623 – 598 1180 f 21 3 9 3 Circle three numbers which have the product shown in the product column: a b c d e f

1 Change each of the given fractions to a decimal using a calculator:

a

2 Find the actual answers and work out the difference between the answer and the estimate: Number sentence


6 6679 9 Jude had 1027 books to share between 4 libraries. How many books did each library receive?

Units


49

UNIT 67

UNIT 68


Fractions

Fraction of a group

1 What fraction of each shape is shaded?

a

b

1 What fraction of each group is shaded?

a

c

e

f

b d f

3 Label each of the fractions of the number line: 0

a c e

a

e

b

5 12

f

b d f

d

a 56

c 35

d 38

e 14

f

of 9

c

1 5

of 15

e

1 6

of 12

is shaded?

6 What fraction of

7 Label the fractions of the number line: a

8 Shade:

1 2

b

b

1 4

of 12

d

1 4

of 8

1 4

of 16

f

b 15 of 30

,

1

d 16 of 30 1 10

of 30

f

1 15

of 30

4 Find the fraction of each group:

is not shaded?

0

e

1 3

c 13 of 30

7 10

5 What fraction of

a

f

a 12 of 30

b 12

e

3 Use the array to find:

c

10 12

4 Shade each shape the fraction indicated:

d

2 Circle the given fraction of each group:

2 What part of each shape in Question 1 is not shaded?

c

a c e

b

d


a 14 of 20 =

b 16 of 12 =

c 19 of 18 =

d

1 10

e 17 of 28 =

f

1 3

5 What part of

1 2

of 60 = of 27 =

is shaded?

9 Draw a number line from 0 to 2 and divide into sixths.

6 Circle

1 3

of:

7 Use the array of question 3 to find 8 Find:

1 8

1 30

of 30.

of 24

9 Arthur had 48 chocolate bars to sell for fundraising. If his parents bought 18 of them, how many bars did

they buy?




☞

Answers on page 134

UNIT 69

UNIT 70


Comparing fractions

Equivalent fractions

1 Order the following fractions on the number line: 1 2

3 4

b

c

d 1 12

e 1 14

f 1

a

1 Circle the equivalent fractions:

1 4

a

0

1

2

2 Order each set of fractions from smallest to largest:

a

3 1 4, 2,

1 4

1,

b

2 1 5 7 8, 2, 8, 8

c

4 1 9 7 10 , 10 , 10 , 10

d

2 4 5, 5,

e

1 3 3 1 2, 4, 8, 8

f

1 1 1 7 2 , 5 , 10 , 10

3 Complete with < or > to make each number sentence true:

a

1 2

1 3

b

1 10

1 5

d

1 6

1 3

e

9 10

5 6

1 2

3

1 6

or

1 3

e

9 12

d

5

f

or 6

b

2 4

c

6 12

1 3

d

4 12

6 15

e

2 16

1 4

1 8

f

3 6

6 12

5 8

7 10

or

5 8

or

2 3

or

=

b

6 8

c

5 20

=

d

8 10

=

e

10 15

=

f

10 30

=

a

=

3 4

f

2 3

5 6

c

4 8

=

1 2

d

3 4

=

2 3

e

7 10

f

4 6

3 4

5 6

7 Complete with < or > to make the number sentence true:

2 8

=

b

3 6

=

c

5 8

=

d

1 3

=

e

8 10

f

2 5

=

3 9

4 6 4 12

to make the smallest equivalent fraction.

7 Answer true or false:

9 Complete with > or < to make the number statement true: five sixths nine twelfths Answers on page 134

2 3

5 12


=

6 Divide

5 12

8 Shade the larger fraction:

☞

2 3

a

1

or

=

5 Circle the equivalent fractions:

3 1 5 7 4 , 3 , 12 , 12

1 4

3 5

=

4 Write an equivalent fraction for:

0

2 5

=

7 8

6 Order the set of fractions from smallest to largest:

1 4

4 10

b

4 5

=


2 5

9 12

5 Order the fractions 34 , 14 , 23 , 13 on the number line:

3 9

a

4 8

1 2

3 6

1 2

3 4

c

b

or 8

6 8

c

4 Shade the larger fraction:

a

6 12

2 Divide to make the smallest equivalent fraction:

3 5

1,


6 12

=

2 3

8 Write an equivalent fraction for:

1 4

9 How many sixths are there in one and a half wholes? Units


51

UNIT 71

UNIT 72




1 Write the improper fraction for each of the following set of shaded shapes:

a

b

2

d

5 5

a d

b

b e

e

c

f

c f

5 4

c

4 3

d

e

10 8

b

f

7 5 13 10

f 2 45

a 1 35

b 2 14

c 1 23

d 3 103

e 2 16

f 1 58

12 5

c

7 6

d

6 4

e

9 5

f

12 8

a 4 34

c 3 107

e 1 56

a

c

a 7 Change

e

6 Write the mixed number for:

8 Write the improper fraction for: 2 13

8 Write the improper fraction that describes:

11 6

9 4

7 Write the improper fraction for: 3 18

to a mixed number.

9 Draw a diagram to show:

f

5 Shade: 2 14

b 9 5

d

6 3

b

2

b

f 4 12

6 Name the improper fractions labelled on the number line: 4 3

d 2 58

a

b 2 15

8 3

5 Write the improper fraction for:

1

b

4 Write the improper fraction to describe the shaded fractions:

7 2

4 Write the improper fraction for each of the mixed numbers:

3 Write the improper fraction for each of the following:

3 Change each of the improper fractions to mixed numbers:

a

e

1 103

a

3

10 5

d 3 12

2 Write the mixed number for each of the following:

2 Name the improper fractions labelled on the number line: a

c

1 78

1

f

b 2 13

e

a 1 34

d

1 Shade each of the following fractions:

c


9 How many sixths did Hannah eat if she ate one whole chocolate bar and 56 of another one? Excel Start Up Maths Year 5



☞


UNIT 73

UNIT 74


Fraction addition

Fraction subtraction

1 Colour each fraction addition to find the answer: 3 6

2 6

1 4

1 4

a +

=

1 5

b +

3 5

2 8

d +

5 8

1 7

4 7

1 Complete the diagrams to show:

c +

e

4 10

+

f

=

+

1 8

a + = 3 10

6 10

e 16 + 26 =

+

=

c

+

5 6

=

c

e 34 – 24 =

4 12

f

5 12

5 12

+

=

4 3

2 3

4 5

2 5

+

3 10

3 5

2 5

4 10

c

7 10

d

e

9 10

f

3 12

+

3 6

5 6

+

5 6

4 5 5 12 4 8

+

1 8

3 5

3

c 3 – 14 =

d 2 – 14 =

e 3 – 34 =

f 2 – 34 =

4

2 12

that could be subtracted to give the following answers:

4 10

4 12

3 5

7 12

5 12

4 5

9 10

7 10

1 5

b

5 10

c

1 5

d

2 10

e

2 5

f

3 12

and find the

=

7 8

–

2 8

=

0

that add to give 56 .

1 3

=

1

8 Circle the pair of fractions to give 26 .

= 2 6

1 3

2 3

=

2

7 Use the number line to find: 2 –

3 6

=

5 Complete the diagram to show: 3 –

=

8 Circle the pair of fractions

–

b 4 – 14 =

7 Complete and simplify:

3 12

–

6 Complete: 2 6

4 5

f

1

a

7 12

5 Colour boxes to show the addition answer:

6 Complete:

5 12

d

=

4 Find pairs of fractions

that could be added to give the following answers:

2 10

a 1 – 14 =

b

–

0

=

2 12

7 10

b 23 – 13 =

3 Use the number line to find:

3 5

1 5

4 Find pairs of fractions

a

1 2

f 3–

=

d 14 + 24 =

d + =

=

3 6

5 10

e2–

5 6

a 46 – 26 =

3 5

b 24 + 34 =

e + =

=

b + =

f

a 58 + 58 = 6 10

5 8

2 Complete: 2 5

3 Complete the additions, simplifying answers if possible:

5 10

= d 2 –

2 Complete the additions:

c

c1–

2 5

=

=

5 8

3 4

=

3 10

b3–

=

=

2 3

a 2 –

=


2

5 6

2 3

3 6

that subtract

9 Draw a diagram to show: 3 – 2 15 =

9 Find the sum of one fifth plus one fifth plus one fifth.

☞

Answers on page 135



53

UNIT 75

UNIT 76


Fraction addition and subtraction

Decimal place value – hundredths

1 Complete: 1 3


1 3

10 12

3 12

a + =

b

c 36 + 26 =

d 78 – 38 =

1 2


1 2

e + =

9 10

f

–

–

2 10

a

=

=

b

U

•

d

Tth

Hth

c

U

•

Tth

e

Hth

U

•

Tth

Hth

U

•

Tth

Hth

f

2 Complete:

a 4 – 15 =

b 3 – 26 =

c1–

1 10

d4–

1 12

e 2 – 14 =

f 3 – 18 =

= =

•

Tth

Hth

U

•

Tth

Hth

a 4.75 b 2.31 c 9.58 d 3.69 e 7.82 f 11.75

3 Add each of the following, writing answers as numbers:

a one third and two thirds b two fifths and one fifth c two sixths and one sixth d five eighths and two eighths e three tenths and four tenths f seven twelfths and four twelfths 4 Find the difference between each of the following, writing answers as numbers:

a three quarters and one quarter b three thirds and one third c nine tenths and seven tenths d six eighths and one eighth e four fifths and one fifth f ten twelfths and three twelfths +

2 7

=

6 Complete: 3 –

1 10

=

5 Complete:

U

2 Write the value of each of the underlined digits:

5 7

3 True or false?

a 0.6 > 0.69 b 1.45 < 1.54 c 1.5 < 5.1 d 0.32 > 0.53 e 1.06 > 1.60 f 1.19 > 1.09 4 Order the following decimals from smallest (a) to largest (f): 2.61

3.50

4.61

3.53

2.98

4.08

5 Write the numeral shown on the abacus:

U

•

Tth

Hth

6 Write the value of the underlined digit: 3.18

7 True or false? 1.76 > 1.56

7 Add six eighths and one eighth, writing the answer as a number:

8 Order the following decimals from smallest (a) to largest (c): 1.18

8 Find the difference between five tenths and two tenths, writing the answer as a number:

1.32

1.06

9 Complete the label for the hundreds grid: Units Tenths Hundredths .


a 14 +

1 12

=

b

9 12

+

4 8

=




☞

Answers on page 135

UNIT 77

UNIT 78


Decimals


1 Write each number on the place value chart:

a three tenths b o ne and fourteen

Units .

Tenths

1 Draw on each abacus the given decimals:

Hundredths

hundredths

a 32.16

c two and six tenths d o ne and nine

hundredths


e three point one

seven

T

b 42.45 U

• Tth

Hth

T

T

U

• Tth

Hth

U

• Tth

Hth

U

• Tth

Hth

c 30.65 d 61.72 T

U

• Tth

Hth

e 4.07

f 32.77

f four point seven eight 2 Write the value of each of the underlined digits:

a 124.58 c 102.46 e 46.01

b 132.89 d 516.33 f 164.23

3 Write the decimal represented by:

b 4 hundreds, 2 tens, 3 units, 3 tenths and 1 hundredth

c 4 hundreds, 6 tens, 7 units, 2 tenths and

U

• Tth

Hth

T

2 Use < or > to complete the number statements:

a 42.18 c 18.49 e 26.42

a 2 hundreds, 3 tens, 8 units, 4 tenths and 3 hundredths

T

43.81 18.51 27.35

b 63.82 d 13.24 f 12.19

63.28 13.42 9.99

3 Write the decimal that is 5 hundredths greater than:

a 3.21 c 21.15 e 60.47

b 4.63 d 42.39 f 29.09


7 hundredths

d 3 hundreds, 5 tens, 6 units, 5 tenths e 2 hundreds, 1 ten, 4 units, 8 tenths f 2 hundreds, 7 units, 3 tenths and 2 hundredths

a s ix point three five is greater than five point one eight

b s even point nine eight is greater than seven point

4 How many tenths are there in each of the following numbers:

a 246.18 d 486.99

b 347.85

c 110.72

e 431.05

f 63.46

nine nine

c two point one five is less than two point five one d two point three five is less than three point one two

e four point nine six is less than five f two point four two is greater than two point three

5 Write the number in the place value chart:

5 Draw 43.58 on the abacus:

one and seven hundredths Units .

Tenths

Hundredths

6 Write the value of the underlined digit in: 170.52 7 Write the decimal represented by:

3 hundreds, 2 tens, 1 unit and 6 hundredths 8 How many tenths are there in 14.61? 9 Of: Harry 1.52 m

Yuko 1.60 m

Grace 1.56 m Tess 1.61 m

a Who is the tallest person? b Who is the shortest person?

T

U

• Tth

Hth

6 Use < or > the complete the number statement: 25.72 28.35 7 Write the decimal that is 5 hundredths greater than: 2.78 8 Answer true or false.

four point one seven is less than four point seven one 9 Shade the hundredths grid to show: 5 tenths less than 0.86

☞

Answers on page 135



55

UNIT 79

UNIT 80


Decimal place value – thousandths


1 Write the decimal for each fraction:

a

279 1000

b

845 1000

c

324 1000

d

96 1000

e

27 1000

f

110 1000


a

2 Order the following decimals from smallest (a) to largest (f):

0.146

a c e

0.111

0.189

0.325

0.468

0.247

3 Write the value of the underlined digit:

TTth

T

U

• Tth

e

Hth

TTth

U

• Tth

U

• Tth

Hth

TTth

T

U

• Tth

Hth

TTth

T

U

• Tth

Hth

TTth

f

T

T

d

Hth

a 12.345 c 61.049 e 14.116

14.347

TTth

b 8.238 < 8.301 d 6.179 > 6.217 f 5.615 < 6.019

a 2.149 b 4.876 c 6.119 d 3.049 e 8.410 f 10.176

46.832 55.876 91.147 30.096

1.521

b 72.851 d 85.287 f 19.245

4 Circle the smaller decimal in each of the following pairs:

82.388

216 1000

6 Order the decimals from smallest (a) to largest (c):

a

c

Hth

3 Write the value of the underlined digit in each of the following:

5 Write the decimal for:

1.763

• Tth

a 6.735 < 6.617 c 4.107 > 4.701 e 9.118 < 9.985

4 Circle the larger decimal in each of the following pairs:

U

2 True or false?

a 117.643 b 248.119 c 483.472 d 864.109 e 785.273 f 832.149

a 24.318 b 83.276 c 46.785 d 55.856 e 91.245 f 30.105

b

T

b d f


c

4.785 7.248 3.020 8.509 10.719

5 Write the numeral shown on the abacus:

1.695

b

2.631

7 Write the value of the underlined digit in: 243.017

T

U

• Tth

Hth

TTth

6 True or false? 3.416 > 3.328 7 Write the value of the underlined digit: 107.219.

8 Circle the larger decimal in the pair:

8 Circle the smaller decimal of the following pair:

17.385 16.985 9 Express each of the following as a decimal:

a 2 L and 375 mL b 5 m and 249 mm c 6 kg and 759 g

7.419

9 What is the decimal that is 3 tenths larger than 14.236 and is 4 hundredths less than 14.576? Excel Start Up Maths Year 5


7.238


☞


UNIT 81

UNIT 82


Decimal addition (1) 1 Complete:

a 4 . 7 + 3 . 2

c 1 2 . 8 + 2 . 4

+ 2 . 9

d 1 3 . 9 + 2 . 4

e 3 4 . 6

+ 1 2 . 3


b 7 . 8

f 4 0 . 7 + 4 . 4

2 Add each of the following pairs of numbers:

a 5.7 and 3.8 c 10.3 and 8.5 e 20.4 and 19.7

3 Find: a 7 . 6 3 . 2 + 1 . 4 c 9 . 3 0 . 6 + 2 . 4 e 4 . 7 3 . 8 + 2 . 1

4 Complete: a 3 . 2 6 + 4 . 3 1 c 3 . 4 8 + 7 . 8 5 e 4 . 6 7 + 5 . 3 5 5 Complete:

b 4.9 and 6.5 d 7.6 and 4.8 f 32.6 and 18.5 b 1 1 . 2

7 . 8 + 3 . 5 d 8 . 5 1 . 6 + 2 . 5 f 6 . 7 4 . 3 + 2 . 4

1 Complete:

a 7 . 2 3

b 8 . 9 6

d 6 . 3 5

2 . 1 1 + 8 . 6 3 2 Complete: a $ 6 . 4 5 + $ 2 . 9 8

+ 7 . 5 4

c 7 . 3 2

+ 5 . 9 1

e 7 . 5 6

f 8 . 4 6

b $ 3 . 4 5

c $ 2 . 9 9

2 . 7 8 + 3 . 4 9 + $ 8 . 7 5

3 . 7 2 + 1 . 0 5

+ $ 6 . 4 8

$ 8 . 8 9 $ 7 . 3 5 d e f $ 4 . 7 0

$ 2 . 0 5 + $ 5 . 4 6 3 Find the sum of:

$ 2 . 4 7 + $ 3 . 0 0

$ 2 . 9 8 + $ 6 . 4 5

a 6.42 m, 3.49 m and 7.62 m b $4.35, $8.15 and $7.95 c 1.89 L, 2.46 L and 1.80 L d 3.65 kg, 4.25 kg and 1.06 kg e 7.98 cm, 2.5 cm and 0.9 cm f 1.45 s, 2.46 s and 1.08 s 4 a Find the total amount of $2.95 and $6.95.

b 6 . 4 5

6 . 2 + 3 . 5

+ 2 . 3 9

b F ind the total distance of 3.45 km, 1.78 km and

d 2 . 1 1 + 3 . 9 0

f 2 . 7 6 + 1 . 5 8

c Find the total weight of 4.62 kg, 1.08 kg and 3.95 kg. d Find the total length of 1.89 m, 3.75 m and 2.68 m. e Find the total time of 1.88 s, 4.32 s and 10.86 s. f Find the total amount of $4.15, $17.23 and $6.47.

Answers on page 136

6 Complete: $ 7 . 1 9 + $ 3 . 6 5 8 Find the total weight of 10.65 kg, 3.98 kg and 14.25 kg. 9 Anton rode his bike 4 days a week. How far did he ride in one week if he rode: 13.26 km on Monday, 19.75 km on Tuesday, 14.29 km on Thursday and 18.99 km on Friday?

9 Is the total of 3.4 and 7.6 greater than or less than the total of 2.46 and 7.54? © Pascal Press ISBN 978 1 74125 262 0

6 . 3 7 5 Complete: + 2 . 9 8

7 Find the sum of 1.98 L, 2.45 L and 3.98 L.

7 . 3 5 8 Complete: + 2 . 1 9

☞

+ 2 . 4 8

4.25 km.

6 Add: 4.8 and 19.3 7 Find: 2 . 6 3 . 7 + 4 . 8



57

UNIT 83

UNIT 84


Decimal subtraction (1) 1 Complete:

a 4 . 6

– 2 . 3

d 8 . 7 – 5 . 8

b 7 . 9 – 6 . 6

e 2 1 . 5 – 1 7 . 8

2 Complete: a 2 . 9 8 – 1 . 8 7 c 7 . 4 2 – 6 . 5 3 0 . 3 6 e – 7 2 7 . 4 1

Decimal subtraction (2) c 1 4 . 3 – 9 . 7

f 3 6 . 3 – 1 8 . 5

b 3 . 7 6 – 2 . 4 5

d 1 1 . 8 5 – 2 . 9 6

4 Complete: – 7.91 10.05 13.29 21.37 46.42 60.00 5.86 a b c d e f

a b c d e f

5 Complete: 2 1 . 8 – 1 3 . 9 6 Complete: 4 . 7 8 – 2 . 3 9 7 Find the difference between: 29.43 and 16.76 8 Complete:

– 10.67 21.14 3.25

b 6 – 4.87 d 18 – 15.18 f 9 – 3.05

2 Find:

a 5 4 . 6

– 3 1 . 2 5

c 7 0 . 8 6

e 4 2 . 0 4

– 1 1 . 9 1

b 1 7 . 5 1

– 1 9 . 6

– 2 . 9

d 1 4 . 2 8 – 7 . 6

f 9 5 . 0 3 – 7 2 . 1 8

b A t the start of the year Violet was 1.45 m tall and by

c B ob had to cut 1.35 m from a 2 m length of wood.

d S ue used 1.35 kg of potatoes from a 5 kg bag. What

e A dam saved $10.65 but needed $20 for a school

f There was 1.75 L of juice in a jug, but a recipe

the end of the year she was 1.51 m tall. How much had she grown?

How much was left over?

weight of potatoes was left over?

camp. How much more did he need to save?

required 3.4 L. How much more juice was needed?

5 Find: 30 – 23.85 6 Find: 2 1 . 0 8 – 4 . 9

$ 1 4 . 0 5 7 Find: – $ 6 . 5 2 8 4.86 kg of cement was used from a 10 kg bag. How much cement was left?

9 James had $20.00 and he spent $8.29. How much money did he have left?

a 10 – 3.42 c 7 – 2.91 e 23 – 12.46

3 Find: a $ 3 5 b $ 1 4 . 5 0 c $ 7 . 4 8 – $ 3 . 7 6 – $ 1 7 . 2 7 – $ 1 2 . 6 5 d $ 1 8 e $ 7 2 . 6 3 f $ 4 2 . 5 6 – $ 1 4 . 4 5 – $ 2 4 . 4 5 – $ 1 7 . 3 9 4 a K atie saved $90 but spent $47.66 on DVDs. How much did she have left?

a 4.26 and 2.38 b 17.45 and 12.88 c 12.72 and 4.83 d 23.12 and 14.63 e 46.29 and 23.56 f 41.46 and 35.19

1 Find:

0 . 1 5 f – 8 5 2 . 3 8



9 Write a subtraction equation that gives 3.29 as the answer.




☞

Answers on page 136

UNIT 85

UNIT 86


Decimal multiplication

Decimal division

1 Write the expression for:

1 Complete:

a 5 groups of 6.3 b 8 groups of 3.5 c 7 groups of 11.4 d 6 groups of 5.31 e 4 groups of 6.64 f 9 groups of 13.23 2 Complete: a 4 . 6 3 3 d 3 2 . 5 3 2 3 Complete: a 1 . 3 2 3 4 d 1 3 . 2 5 3 2 4 Find: a $ 4 . 2 5 3 3 c $ 5 . 9 5 3 4

e $ 4 . 6 5

3 8

a

b 1 . 8

c 9 . 3

3 7

3 5

e 1 9 . 6

f 2 1 . 5

6 63.6

c

2 44.6

5 90.5

d

e

3 75.6

f

5 73.5

4 86.4

3 6

a

3 4

b 4 . 7 9 3 5

c 6 . 8 9

e 1 7 . 2 4 3 8

f 4 3 . 0 6 3 9

b $ 6 . 4 0 3 6

d $ 1 1 . 5 5 3 5

3 7

3 7.32

c

7 9.87

5 8.15

d

e

4 7.32

f

8 9.76

6 6.54

a 6 bags? b 4 bags? c 8 bags? d 3 bags? e 10 bags? f 5 bags? 4 Find:

a

f $ 1 5 . 6 5

b

3 If I had a box of apples weighing 38.4 kg, how much would each bag weigh if the apples are placed in:

3 7

5 Write the expression for 3 groups of 21.75:

b

8 $9.76

4 $6.12

c

d

e

f

5 $3.55 3 $9.63

6 $5.82 7 $8.47

5 Complete:

6 Complete: 1 . 2 3 8

3 72.6

6 Complete:

6 7.26

7 Complete: 1 4 . 3 6 3 5

b

2 Complete:

8 Find:


7 If I had a box of apples weighing 36.6 kg, how much would each bag weigh if the apples are placed in 4 bags? 8 Find:

$ 3 . 8 5 3 7

4 $9.28 9 Mel threw a shot-put a total of 49.92 m in 3 attempts. What was the average length of each of Mel’s throws?

9 Calculate the cost of buying 6 packets of textas if one packet costs $12.15.

☞

Answers on page 136



59

UNIT 87

UNIT 88


Decimal multiplication and division

Rounding decimals

1 Find:

1 Round each of the following to one decimal place:

a 5 . 0 6

b 7 . 3 9

3 4

c 6 . 8 1

3 8

d 2 . 4 6

3 5

3 7

1 . 0 9 e 3 3 2 Find:

f 4 . 9 5 3 9

b

4 52.4

5 6.25

c

3 67.5

a 4.32 b 17.49 c 47.84 d 21.315 e 4.689 f 12.358 2 Round each of the following to two decimal places:

a

d

e

6 9.72

f

a 4.219 b 3.867 c 14.219 d 2.049 e 6.108 f 35.463

7 85.4 3 8.49 3 Find each of the following:

a 3.6 3 100 = b 8.75 3 100 = c 29.3 3 100 = d 5.75 3 1000 = e 62.758 3 1000 = f 57.521 3 1000 = 4 Find each of the following:

a 0.47 ÷ 10 = b 5.45 ÷ 10 = c 25.7 ÷ 10 = d 32.45 ÷ 100 = e 46.109 ÷ 100 = f 26.315 ÷ 100 = 5 Find: 2 . 4 6 3 7

3 Round each of the following to the nearest whole number:

a 24.35 c 4.63 e 1.079

b 2.58 d 12.435 f 36.903

4 Complete the sums and then round the answers to the nearest 5c: a $ 2 . 4 3 b $ 1 0 . 4 5 + $ 7 . 8 5 + $ 3 . 9 8 $ 1 2 . 2 5 c d $ 1 4 . 9 8 + $ 1 0 . 6 2 + $ 6 . 4 3

e $ 3 2 . 2 5

+ $ 7 3 . 4 8

f $ 1 0 0 . 0 0 + $ 7 3 . 4 8

5 Round 3.015 to one decimal place. 6 Round 4.793 to two decimal places.

6 Find:

7 Round 13.498 to the nearest whole number. 4 36.8


7 Find: 6.315 3 1000 = 8 Find: 14.215 ÷ 100 = 9 Find:

a 428.315 ÷ 1000 = b 349.205 3 1000 = c 89.315 ÷ 1000 = d 30.105 3 1000 =

8 Complete the sum and then round the answer to the nearest 5c: $ 1 4 . 8 3 + $ 2 5 . 6 8

9 Complete the multiplication and then round the answer to the nearest 5c: $ 4 . 3 7 3 4 Excel Start Up Maths Year 5



☞

Answers on page 136

UNIT 89

UNIT 90


Percentages (1)

Percentages (2)

1 What percentage of each square is coloured?

a

b

c

d

f

b

35 100

c

7 100

d

16 100

e

66 100

f

85 100

b e

c f

3 Write each of the following as a number:

c 22%

d 39%

e 83%

f 99%

a 30% = b 75% = c 9% = d 28% = e 12% = f 60% =

4 Find:

b 2%

3 Write each of the percentages as a fraction:

a twenty-six percent b nineteen percent c forty-five percent d eighty percent e seven percent f fifty-three percent a 10% of 40 c 100% of 100 e 75% of 120

10 100

2 What percentage of each square in question 1 is not coloured?

a

2 Colour each square to show the percentage:

a d

1 Write each of the following fractions as a percentage:

a 15%

e


b 50% of 60 d 25% of 16 f 20% of 50

5 What percentage of the square is coloured?

4 Find:

a 50% of 70 chickens b 10% of 30 pencils c 25% of 60 children d 10% of 40 teachers e 20% of 80 flowers f 75% of 100 shoes 5 Write

6 What percentage of the square is not coloured?

43 100

as a percentage.

6 Colour the square to show 27%: 7 Write thirty-seven percent as a number.

7 Write 54% as a fraction.

8 Find 10% of 70. 9 Draw a picture to show 50% of 10 chickens.

8 Find 25% of 80 cups. 9 Find the total if 10% is $2.

☞




61

UNIT 91

UNIT 92


Fractions, decimals and percentages

Use of money

1 Change each of the following to decimals (you may need a calculator):

a

1 2

b

1 5

c

1 8

d

1 4

e

4 10

f

3 4

1 Find the total number of each coin/note needed to make $40:

a $2 c $5 e 50c

c

75 100

e

3 4

40 100

b 30%

25%

f 90%

50%

Fraction

a

4 10

b

3 4

c

7 25

d

3 5

e

11 20

f

23 50

5 Change

7 20

0.85

Decimal

100

Percentage

b $7.50 d $4.65 f $18.75

6 Find how many drinks costing $2.50 each Owen could buy with $30? 7 If Jo had $20 and spent $6.45, how much change would she receive?

to a decimal.

8 Estimate how much change Greg would receive to the nearest $1 if he started with $100 and spent $87.35.


5 Find the total number of 10c coins needed to make $40.

0.25

Fraction

a $73.95 b $51.85 c $47.28 d $19.99 e $32.10 f $60.43

7 Add < or > to make the number statement true: 30 100

4 Estimate how much change Greg would receive to the nearest $1 if he started with $100 and spent:

6 Find 20% of 80 m.

b $10 d $20 f $50

a $14 c $8.35 e $12.90

1 4

d 0.3

0.8


3 If Jo had $20 and spent the following amounts, how much change would she receive?

3 Add < or > to make the number statement true:

a $5 c $15 e $25

a 50% of $2 b 25% of 4 m c 10% of 30 kg d 20% of 1 m e 75% of 1 hour f 10% of 90c 1 2

b $1 d 20c f $10

2 Find how many drinks costing $2.50 each Owen could buy with:

2 Find:

a


100

Decimal

Percentage

9 a Find the total cost of the items below.

b Find the change from $50.

1 4

9 Draw a picture to show 10% of a chocolate bar.

$5.75

$4.12




$3.85 Jam

$2.50

$3.25

$3.63

☞

Answers on page 137

UNIT 93

UNIT 94 UNIT 1

Money operations 1 Find the total cost of: b $ 7 . 8 5 + $ 4 . 2 6 + $ 2 . 9 8

Money rounding

a $ 4 . 6 3

d $ 3 . 1 4

1 Round each of the following amounts to the nearest $10.

c $ 1 8 . 2 9

+ $ 4 . 9 8

a $25.90 c $115.95 e $258.14

e $ 4 1 . 8 5 f $ 2 2 . 4 3 $ 7 . 5 5 $ 1 2 . 3 8 $ 1 8 . 6 9 + $ 2 . 4 8 + $ 5 . 7 9 + $ 1 2 . 1 0 2 Find the change from $7.50 if Suzie spent:


b $33.47 d $136.75 f $343.45

2 Round each of the following amounts to the nearest dollar.

a $6.32 b $9.16 c $42.74 d $97.56 e $172.85 f $114.12

a $5.25 b $6.99 c $3.45 d $7.15 e $5.85 f $4.10

3 Round each of the following amounts to the nearest 5c.

3 Find the cost of:

a 3 apples at $1.20 each b 4 books at $8.90 each c 5 newspapers at $1.35 each d 7 magazines at $5.95 each e 2 CDs at $21.45 each f 8 drinks at 95c each

a $2.43 b 71c c $4.86 d $3.99 e $143.22 f $185.58 4 Complete each of the equations and round the answer to the nearest 5c. a $ 1 4 . 2 7 b $ 4 0 . 0 0 + $ 3 . 8 5 – $ 2 7 . 3 8 c $ 2 . 1 6 d 3 3 3 $4.62 e $ 1 3 . 6 5 f $ 2 1 . 7 5 $ 2 . 9 8 3 . 5 0 – $ 1 4 . 9 9 + $ 5 Round $146.35 to the nearest $10.

4 Find how much, on average, each person spent if:

a 5 children spent $15.75 b 7 teachers spent $24.15 c 3 mums spent $37.95 d 10 dads spent $121.40 e 4 doctors spent $63.40 f 6 actors spent $137.10 5 Find the total cost of: $ 6 . 2 9 $ 4 . 8 5 + $ 3 . 2 5

6 Find the change from $9.20 if Suzie spent $8.55.

6 Round $47.83 to the nearest dollar.

7 Find the cost of 6 coffees at $2.95 each.

7 Round $52.33 to the nearest 5c. 8 Complete and round the answer to the nearest 5c. $ 4 . 6 3 3 7

8 Find how much on average each person spent if 8 friends spent $16.80. 9 26 children went on an excursion. If entry to the aquarium cost $2.50 each, the bus cost $3.50 each and lunch cost $4.15 each, what was the total cost of the excursion?

☞

Answers on page 137


9 Annita bought 3 T-shirts at $12.98 each. How much change would she receive from $40.00 to the nearest 5c?


63

UNIT 95

UNIT 96


Symmetry


1 Circle the following shapes that are symmetrical: b c

1 State the number of angles in each of the following shapes:

a

d


e

a f

2 Draw in the line(s) of symmetry for each of the following shapes:

a

b

b

d

d

e

b

a

b

d

d

e

f

3 Draw a:

a a reflex angle

b a straight angle

c

e

c

3 Complete each of the following drawings to make the shapes symmetrical:

2 Name the type of each of the following angles:

f

f

e

a

c

c

f

c a right angle

d a obtuse angle

e a acute angle

f a revolution

4 Complete the following table: Regular shape

a b c d e f

No. of axes of symmetry

No. of sides

triangle square pentagon hexagon octagon circle

5 Is

4 True or false?

a 360º is a right angle b 270º is a straight angle c 30º is an acute angle d 100º is an obtuse angle e 275º is a reflex angle f 300º is a revolution

symmetrical?

6 Draw in the line(s) of symmetry on:

5 Find the number of angles in:

7 Complete the drawing to make the shape symmetrical:

6 Name the angle:

8 Complete the table: Regular shape

No. of sides

7 Draw a right angle facing left.

No. of axes of symmetry

heptagon

8 True or false? 180º is a straight angle.

9 List the alphabet and circle all of the letters that are symmetrical.

9 Name the different types of angles in the shapes:

a b c




,

,

☞


UNIT 97

UNIT 98




1 Write the angle type of each of the following:

a

b

c

f

Diagram

e


d

2 Give the angle type for each of the following:

b 180º d 110º f 342º

3 Match the angle with the description:

a a revolution b less than a right angle c a straight angle d larger than a straight angle e a right angle f larger than a right angle but

A

B

C D E

F


7 Match the angle with the description:

c

180º f

360º

i m h j

k g

l

a 150º acute b 340º revolution c 10º obtuse d 92º right e 310º straight f 178º reflex

6 Give the angle type for 76º.

B reflex angle

Diagram

Type

straight

a

Size

b

180º – 360º

6 Name the angle type labelled m in question 2.

A straight angle

e

a acute b obtuse c right d reflex e straight f revolution

5 Complete:

b

90º

reflex revolution

a less than 360º and greater than 180º b less than 90º c greater than 90º but less than 180º d less than 360º e greater than 180º f greater than 180º but less than 270º

5 Write the angle type:

0º – 90º

obtuse d

4 Draw an angle which is:

a 45º is an obtuse angle b 89º is a right angle c 360º is a revolution d 156º is an obtuse angle e 270º is a right angle f 200º is a reflex angle

Size

right

3 Circle the larger angle of each pair:

less than a straight angle

a

c

b

2 Find which angle(s) in the diagram are:

a 5º c 90º e 280º

a

Type


7 Circle the larger angle of the pair:

C right angle

obtuse

200º

8 Draw an angle which is less than 180º but greater than 90º.

8 Answer true or false: 50º is an acute angle. 9 Draw a shape that has three right angles and two obtuse angles.

9 Draw a shape that has six obtuse angles.

☞

Answers on page 138 © Pascal Press ISBN 978 1 74125 262 0


65

UNIT 100



Drawing angles (1)

20

40 0 14

30

150

20 10 0

20 10

50

0

40

80

70

120

60

13

0

50

0 14

30

0 14

90 100 11 0

100 90

30

170 180 160 150 20 10 0

150

110

40

30

20

80

70

120

0

170 180 160 150 20 10 0

180 170 16 0

60 0

13

20

0

f

13

50

0

14

40

120

60

40

30

70

0

10

80

13

50

30

90 100 11 0

100 90

60

170 180 160 150 20 10 0

80

70

40

110

90 100 11 0 1 20 80

100 90

110

120

0

70

14

0

13

120

80

70

60 0

13

14

60

0

10

50

30

0

0

0

170 180 160 150 20 10 0

e

30 180 170 16 0 1 40 50 14 0

13

50

13

50

180 170 16 0

40 0 14

30

150

20 0

10

180 170 16 0

d 120

60

40

30 180 170 16 0 1 40 50 14 0

70

120

60

30

80

70

170 180 160 150 20 10 0

0

13

100 90

80

40

110

120

90 100 11 0

80

70

60

100 90

110

120

90 100 11 0

80

70

60 0

13

0

c

50

2 Use a protractor to measure each of the following angles to the nearest five degrees:

3 How many right angles make each of the following?

a

b

c

d

e

f

b

3 Give the angle type for each of the angles in question 2:

d

a d

e

50

0

0

a 200º is an obtuse angle b 360º is a straight angle c 90º is a right angle d 160º is a reflex angle e 14º is an acute angle f 79º is an obtuse angle

1

50

2 True or false?

13

50

14

f 300º

c

120

60

14

e 45º

70

30

d 300º

a

80

40

c 160º

b

90 100 11 0

100 90

110

170 180 160 150 20 10 0

120

30

80

70

60

50

150

a

10

0

b 100º

14

1 Record the size of each of the following angles:

0

1 Circle the larger angle in each pair:

a 80º


180 170 16 0

UNIT 99

f

b

c

e

f

4 Use a protractor to draw each of the following angles:

a 20º

b 110º

4 Draw an angle:

a smaller than 45º

b larger than 300º

c 75º

d 30º

e 155º

f 135º

c between 90º and 180º d between 270º and 360º

e between 180º and 270º f between 45º and 90º 60 0

120

70 110

80

90 100 11 0

100 90

80

70

0

10

14

10

7 Give the angle type for the angle in question 6.

8 Draw an angle less than 180º.

8 Use a protractor to draw a 15º angle.

9 Describe the different angles in the triangle by completing: I am a shape with

9 Investigate if it is possible to draw a shape with one 60º angle and three 100º angles.

0

7 How many right angles will make this angle?




0

6 Use a protractor to measure the angle to the nearest five degrees.

☞

170 180

180 170 16 0

20

5 Circle the larger angle in the pair: 6 True or false? 190º is an obtuse angle.

160

20

30

150

30

13

50

150

120

60

40

0

13

0

40

50

14

5 Write the size of the angle:

Answers on page 138

UNIT 101

UNIT 102


Drawing angles (2)

Drawing angles (3)

10 220 0

30 180 170 16 0 1 40 50 14 0

0 0

10 220 0 0

10 220 0

50

10 220 0 0

0

30 180 170 16 0 1 40 50 14 0

10 220 0 0

20 0

10

180 170 16 0

40 0 14

30

150

20 10 0

180 170 16 0

40 14

30

150

20 10

180 170 16 0

60

13 0

0

0

30 180 170 16 0 1 40 50 14 0

0

30

0 14 150

20 0

10

180 170 16 0

40 0 14

30

150

20 0

10

180 170 16 0

40 0 14

30

150

20 10

100 90 110

180

0

90 100 111 10 12 80 70 0

80 7700

b

c

d

e

f

3 Use a protractor to draw each of the following angles:

b 75º

c 30º

0 12

a

,

3 Use a protractor to draw each of the following:

60 0 13

30

180 170 16 0

50

a 80º

a 160º

13 0

1700 60 17 0 116 10 15 20

,

f

50

40

,

60

0 14

e

100 90 110

0

,

f 13 0

0

d

50

90 100 111 10 12 80 70 0

80 7700

2 Measure and record each of the following angles:

60

180

c

90 100 111 10 12 80 70 0

100 90 110

30

30

170 180 160 150 20 10 0

40

30

,

80 7700

1700 60 17 0 116 10 15 20

0

170 180 160 150 20 10 0

40

b

0 12

40

14

0

,

60 0 13

0 12

180

50

0

2 Estimate the size of the following angles and then measure with a protractor to the nearest 5º.

a

e

13

50

60 0 13

30

120

60

50

1700 60 17 0 116 10 15 20

70

d 13 0

40

80

13 0

0 14

100 90

50

50

0

110

60

60

180

90 100 11 0

80

70

90 100 111 10 12 80 70 0

100 90 110

100 90 110

30

120

80 7700

90 100 111 10 12 80 70 0

80 7700

1700 60 17 0 116 10 15 20

60 0

13

0 12

0 14

50

0

60 0 13

0 12

40

f

13

14

50

50

0

60 0 13

0 14

120

60

c

13

50

50

0

70

120

60

50

13 0

180

80

70

60

30

90 100 11 0

100 90

80

0 12

90 100 111 10 12 80 70 0

100 90 110

1700 60 17 0 116 10 15 20

80

100 90

0 13

80 7700

40

110

110

60

0 14

120

90 100 11 0

80

70

30

70

60 0

13

120

170 180 160 150 20 10 0

30

170 180 160 150 20 10 0

40

50

60 0 13

40

0

e

50

0

50

50

14

0

b

0

0

50

13

a

13

180

d 120

60

120

60

30

70

70

1700 60 17 0 116 10 15 20

80

80

40

90 100 11 0

100 90

100 90

30

80

110

170 180 160 150 20 10 0

110

14

0

13

120

0

13

90 100 11 0

80

70

40

70

60

120

0

30

50

170 180 160 150 20 10 0

40

c

60

0 14

50

0

30

50

0

30 180 170 16 0 1 40 50 14 0

13

10 220 0

120

60

0

70

40

80

30 180 170 16 0 1 40 50 14 0

b

90 100 11 0

100 90

14

0

110

14

120

13

80

70

60

14

40

50

150

a

1 Measure and record each of the shaded angles:

30 180 170 16 0 1 40 50 14 0

1 Record the size of the following angles:


b 60º

c 70º

d 130º

e 140º

f 50º

d 115º 4 True or false?

c 70

80

90 100 11 0

100 90

80

70

20

14

30

150

160

20

0

10 0

170 180



9 Draw a picture of an alien that has three angles between 90º and 180º and four angles between 0º and 90º, and label these angles on your picture.

13 0

8 True or false? 100º is an obtuse angle.

8 Name the angle type for the angle of question 7. 9 Accurately draw three angles between 70º and 90º.


50

6 Measure and record the angle:

6 Estimate the size of the angle and then measure it with a protractor , to the nearest 5º.

☞

60

30

10

5 Measure and record the shaded angle:

13

150

180 170 16 0

50

40

0

120

60

0

110

90 100 111 10 12 80 70 0

100 90 110

0

120

0

40

60 0

13

80 7700

180

50

14

5 Record the size of the angle.

0 12

30

f

60 0 13

1700 60 17 0 116 10 15 20

e

50

10 220 0

b

40

a d

0

4 Name the angle type for each of the angles in question 3:

0 14

a 80º is an acute angle b 60º is an obtuse angle c 90º is a right angle d 110º is a reflex angle e 45º is an acute angle f 180º is a straight angle

f 145º

30 180 170 16 0 1 40 50 14 0

e 90º


67

UNIT 103

UNIT 104


Angles in 2D shapes

3D objects

1 For the triangle:

1 Name each of the following 3D objects:

a name the angle type a b name the angle type b c measure angle a d measure angle b e measure angle c f add angles a + b + c

a a

c

b

a

b

c

b

45º

d

e

c

70º

f

15º

d

40º

80º 70º

f

4 For the quadrilateral:

c

and d

2 Find the number of faces for each of the 3D objects in question 1:

a c e

b d f

3 Find the number of edges for each of the 3D objects in question 1:

a c e

b d f

b d f

a

6 Find the number of faces:

b b

7 Find the number of edges:

40º

a

8 Find the number of corners:

50º

?

8 For the quadrilateral, measure angles

c

,b

f

5 Name the 3D object:

80º

a

e

a c e

d

6 For the triangle, measure angles: and b a

4 Find the number of corners for each of the 3D objects in question 1: b

5 For the triangle, measure angles: and b a

7 Find the missing angle:

d

135º

a

a measure angle a b measure angle b c measure angle c d measure angle d e name the angle type c f name the angle type d

c

55º

c

60º

60º

e

120º

b

3 Find the missing angles in each of the following triangles: a

a name the angle type a b name the angle type b c measure angle a d measure angle b e measure angle c f add angles a + b + c

b

2 For the triangle:

a


a

,

b

.

c

d

9 Complete:

The sum of the angles in any triangle is

Extension: What do the sum of the angles at the centre of a circle equal?

.

9 A number of blocks are placed end-to-end as shown below. How many faces are showing (when picked up and looked at from any direction) if there are:

a 2 blocks? b 3 blocks? c 4 blocks?




☞


UNIT 105

UNIT 106


Drawing 3D objects

Views of 3D objects

1 Complete by tracing each of the following objects:

a

b d

d triangular prism e hexagonal prism f pentagonal pyramid

e

f

1 Match the solids to one of their elevations:

a cube b cylinder c cone

c

2 Draw the top, front and side views of:

2 Draw dotted lines in each of the following to provide the hidden detail:

a

Name

b

c

d

e

f

c

c

triangular prism

d

e

f

Diagram

Top

e

a

f

4 Draw each of the following 3D objects:

a cube

Front

b rectangular prism

c triangular prism

d square pyramid

e cylinder

f triangular pyramid

5 Complete by tracing: 6 Draw a dotted line to show the hidden detail:

a

b

c

d

e

f

b

c

d

e

f

5 Match the solid to one of its views.

or 6 Draw the top view of:

7 Using the dot paper, copy the diagram. 8 Draw a cone.

7 Draw the side view of:

9 Draw a top, side and front view of:

9 For the box, measure angles a, b and c with a protractor.

8 From the shapes, identify and draw the 3D object.

☞

Side

4 From the views, identify and draw the 3D objects:

d

Side

b

Front

a

b

Top

cylinder

3 Using the dot paper, copy each of the diagrams:

a

Diagram

3 Draw the top, front and side views of:



a=


b=

c a b

c= 69

UNIT 107

UNIT 108


Triangles

Quadrilaterals

1 Measure each side and each angle of the triangle:

a b c d e f

cm

1 What is the side length of each of the following squares?

a

c

cm

b

º

º

a

cm

e

cm

a

f

º

d c

a

b

4 Label each of the following triangles as isosceles, scalene, equilateral or right-angled:

a

b

c

d

e

f

b e

c f

7 What is the length of the diagonal b of the rectangle in question 5, top left to bottom right corner?

7 Is the triangle right-angled?

8 Match the label with the quadrilateral:

8 Label the triangle as isosceles, scalene, equilateral or right-angled:

parallelogram rhombus

9 Complete by writing in the missing words:

9 Find the number of axes of symmetry of:

The sides of a square are all

All angles in a square are

The diagonals of a square are and they meet at


c f

6 What is the length of the diagonal of the rectangle in question 5, top right to bottom left corner?

6 Measure the side length marked f on the triangle. f

70

5 What are the lengths of the sides of the , rectangle?

e

a an isosceles triangle b an equilateral triangle

b e

a square b rectangle c rhombus d kite e parallelogram f trapezium

5 Measure the angle marked e in the triangle.

4 Match the label with the quadrilateral:

a d

f

f

3 What is the length of the diagonals of each of the following squares in question 1, top left to bottom right corner?

e

e

a d

c

d

d

2 What is the length of the diagonals of each of the squares in question 1, top right to bottom left corner?

º º

b

cm

c

d

f

º

3 Are the following triangles right-angled?

b

e

cm

2 Measure each side and each angle of the triangle:

a b c d e f



. angles. lengths angles.

☞


UNIT 109

UNIT 110


Polygons

Prisms and pyramids

1 Name each of the following shapes:

a c

e

b

d

f

2 Find the number of sides of each of the following shapes: a b

c

e

c

e

c

d

e

d f

5 Name the shape:

8 Find the number of diagonals of:

c pentagon

☞


c

d

e

f

3 Complete the table: No. of corners

b

No. of edges

No. of faces

c

d

e

f

5 Name the object: 6 Name the cross-section of the object. 7 Complete the table: Object

b

a

a triangle b quadrilateral

triangular prism triangular pyramid cube rectangular pyramid pentagonal prism hexagonal pyramid 4 Draw the set of faces for a pentagonal pyramid:

9 Draw an irregular:

f

a b c d e f

6 Find the number of sides of: 7 Find the number of angles of:

e

Object

4 Find the number of diagonals of each of the following shapes: a b

d

2 Name the cross-section of each of the following prisms and pyramids:

f

c

f

1 Name the following prisms and pyramids: a b

a

d

3 Find the number of angles of each of the following shapes: a b


No. of corners

No. of edges

No. of faces

square pyramid 8 Draw the set of faces of a triangular pyramid:

9 Draw a rectangular pyramid with the base facing towards you. Units Excel Advanced Skills Start Up Maths Year 5

71

UNIT 111

UNIT 112


Cylinders, spheres and cones

Parallelograms and rhombuses

1 For each of the objects, state if it is shaped like a cone, cylinder or sphere:

a volcano c drinking straw e soccer ball

b orange

a

d witches’ hat f tin of beans

b

d

c

e

No. of edges

f

b

e

d

a

c

a b c d e f

b

e d

f a

3 Measure the side length and diagonals of the rhombus:

4 Which of a cone, cylinder or sphere has:

a b c d e f

a a vertex? b one base? c two bases? d no corners? e a rectangular surface? f no flat surfaces? 5 Is a section of pipe shaped like a cone, cylinder or sphere? 6 Name the solid modelled: 7 Complete the table: Solid cone cylinder sphere

c

2 Measure the side lengths and diagonals of the parallelogram:

f

3 Complete the table: Solid No. of surfaces cone cylinder sphere

1 Measure the side lengths and diagonals of the parallelogram:

a b c d e f

2 Name the solid modelled in:


No. of corners

a d

b

e f c

4 Measure the side length and diagonals of the rhombus:

a

a b c d e f

f d

b e

c 5 Measure the angles of the parallelogram in question 1.

6 Measure the angles of the parallelogram in question 2.

8 Which of a cone, cylinder or sphere has an equal distance from the centre at all points?

7 Measure the angles of the rhombus in question 3.

8 Measure the angles of the rhombus in question 4.

9 For a cone, draw the:

a top view b side view c front view

a similarities b differences

9 What are the:

between a rhombus and a parallelogram?




☞

Answers on page 140

UNIT 113

UNIT 114


Movement of shapes

Scale drawings and ratios

1 Flip each of the following 2D shapes:

a

c

1 For the rectangle, find the total number of squares when the side lengths are made:

b

a twice as long b 3 times as long c 10 times as long d 4 times as long e 6 times as long f 5 times as long

d

e

f

2 Slide each of the following 2D shapes:

a

c

2 If a square is 2 3 2 in size, what factor has it been increased by if there are:

b

a 16 squares c 400 squares e 64 squares

d

e

f

1 cm : 10 cm

3 Turn each of the following 2D shapes in the direction of the arrow:

c

b

d

e

f

a b c d e f

5 cm 200 cm 3 cm 900 cm 1 cm 1000 cm

4 If the scale is 1 cm : 2 m, complete the following table:

1 cm : 2 m

4 Match each of the following terms with the diagrams: flip right, slide up, turn left, flip down, slide left, turn right

a

c

b

d

e

f

b 36 squares d 100 squares f 144 squares

3 If the scale is 1 cm : 10 cm complete the following table:

a


a b c d e f

4m 5 cm 12 m 3 cm 1m 10 cm

5 For the rectangle, find the total number of squares when the side lengths are made 12 as long. 6 If a square is 2 3 2 in size, what factor has it been increased by if there are 196 squares? 7 If the scale of an object is 1 cm : 10 cm, what is the actual height of a toy that is 6 cm tall on paper?

5 Flip the shape:

6 Slide the shape: 7 Turn the shape:

8 If the scale of an object is 1 cm : 2 m, what is the height on paper of a 20 m tall building? 9 On the second grid enlarge the picture.

8 Describe the following: 9 Continue the pattern by rotating the triangle:

☞



73

UNIT 115

UNIT 116


Sections of solids


Nets and 3D objects

1 Match the solids with the view:

1 Draw the shapes that make up the following solids: a b

c

d

a b

e

f a

b

c e

3 For each of the following solids draw the side view:

b

c

d

e

4 For each of the following solids draw the shape resulting from the cross-section:

c

c

e

d

e

f

5 Match the solid with its view:

f

a triangular pyramid

d

4 Draw a net for a:

3 Name the 3D objects that are made with the following nets: a b

b

f

f

a

a

e

f

d

a

f

c

d

b

d

2 Match the net with its object:

2 For each of the following solids draw the top view:

e

c

b triangular prism

c rectangular prism

d rectangular pyramid

e square pyramid

f cube

5 Draw the shapes that make up:

6 For

draw the top view.

7 For

draw the side view.

8 For

d raw the shape resulting from the cross-section.

9 If these shapes form a solid, draw the solid and name it. 74 © Pascal Press ISBN 978 1 74125 262 0

, then

6 Match the net to its object: 7 Name the 3D object that can be made with the net: 8 Draw a net for a hexagonal pyramid. 9 Look at the net of a cube. If the cube was constructed:

E A B C D F

a and if B is on the base, what letter is on the top? b what letter is opposite F? Excel Start Up Maths Year 5 ☞ Answers on page 141 Excel Advanced Skills Start Up Maths Year 5

UNIT 118


Maps (1)

a

c

d

f

2 How many axes of symmetry has:

a c e

b d f

c

e

No. of vertices

No. of edges

a b c d e f

5 Label the following as rotation, translation, reflection or tessellation. 6 How many axes of symmetry has 7 Name the shape in question 6: 8 Complete the table: No. of surfaces

State Library Parliament House

National Sydney Maritime Aquarium Museum Pyrmont Bridge

E

Hyde Park Town Hall

D C Exhibition Chinese Centre Gardents

A

Anzac War Memorial l St Liverpoo

Goulburn Street

Chinatown

1

3

2

4

5

6

7

8

9 10



No. of vertices

, ,

4 Name the road which is: a north of China Town b south of Hyde Park c west of Parliament House d south of Circular Quay e west of the National Maritime Museum f east of the Town Hall 5 What feature can be found in square 9I?

Solid

King Street Wharf

a Hyde Park , b Anzac War Memorial c Sydney Harbour Bridge d Circular Quay , e The Rocks , f Pyrmont Bridge ,

f

No. of surfaces

Australia Square

3 Give two sets of coordinates for:

4 Complete the following table: Solid

F

Government

c Exhibition Centre d Town Hall e Government House f Sydney Opera House

b

G

Circular Quay

House Museum of Contemporary Art Cahill Expressway

Sydney Observatory

Overseas Passenger Terminal

H

Sydney Opera House

bN ational Maritime Museum

d



B

3 Name each of the following shapes:

a

a K ing Street Wharf

I

d

J

aR

2 Name the coordinates of:

L K

The Rocks

Harbour Control Tower

M

ram

e

N

Pir

a 4F b 4E c 5B d 7A e 7I f 2M

b

Sydney Harbour Bridge

O

Macquarie St

1 What feature can be found in square:

1 Label each of the following as rotation (turn), translation (slide), reflection (flip) or tessellation:

Pitt St

Shapes – general review


George Street

UNIT 117

6 Name the coordinates that could be used to find the Museum of Contemporary Art.

?

7 Give two sets of coordinates for the State Library. , 8 Name the road which is west of the State Library.

No. of edges

9 Start at the Town Hall, travel North on George Street to Australia Square, turn East to Pitt Street, travel North to the end of the road. What is the museum found at the end of the road?

9 Draw the top view of the model:

☞



75

UNIT 119

UNIT 120


Scale

Maps (2)

1 Name the places found at the following coordinates: out

5

4

Flesh Fields

Hand Harbour

Curve Cove

t

3

Lifeline River

2

2 Give a set of coordinate points for each of the following locations:

The Ridge

nt Poi ky Pin

6

Nail Look

7

1 Give the coordinates of:

Digit Hut

8

Fin Swager mp

a (H, 3) b (F, 6) c (B, 5) d (D, 2) e (C, 4) f (F, 1)

a Flesh Fields c Nail Lookout e Lifeline River


oin bP

b T anzania

c K enya

d S udan

H G

Mali

F

Pores Pond

Guinea

A

B

C

D

E

F

G

H

e L ibya

f Egypt

Scale 1 cm = 100 m

b Finger Swamp d The Ridge f Pores Pond

a b c d e f

D

Angola Zamia

Mozambique Zimbabwe Madagascar Namibia Botswana

B

South Africa

A

2

3

4

Scale

7

6

5

= 700 km

b (5, H) d (2, H) f (7, B)

3 Which country is approximately:

4 Estimate the direct distance between each of the following places in metres using the scale:

a Pinky Point and Hand Harbour b Thumb Point and Pores Pond c Palm Hill and Flesh Fields d Digit Hut and The Ridge e Nail Lookout and Lifeline River f Curve Cove and Palm Hill

a 800 km south of Angola? b 800 km north of Sudan? c 1000 km west of Madagascar? d 500 km north of Gabon? e 1000 km west of Libya? f 500 km east of Mozambique? 4 Give the distance to the nearest 500 km across each of the following countries (east to west):

5 Name the place found at (D, 3): 6 Give a set of coordinate points for Pinky Point.

a Angola b Niger c Mali d Tanzania e Chad f Dem. Rep. of the Congo

7 Use the scale on the map to determine the length represented by the line below: 8 Estimate the direct distance between Thumb Point and Palm Hill. 9 Name three places to visit on the map and work out how far to travel between all three.

Chad Sudan

2 Name the country at the coordinates:

a (5, A) c (5, D) e (5, F)

Egypt

Ethiopia Cameroon Uganda Dem Rep Kenya Gabon of the Congo Tanzania

E

1

3 Use the scale on the map to determine the length represented by each line:

Niger

Nigeria

C

0

Libya

Algeria

um

Th

Palm Hill

1

a A ngola

5 Give the coordinates of Zimbabwe. 6 Name the country found at the coordinates (6, F). 7 Which country is approximately 800 km north of the Dem. Rep. of the Congo? 8 Give the distance to nearest 500 km (east to west) across Kenya. 9 Estimate the total direct distance between South Africa and Libya in kilometres.




☞

Answers on page 142

ar

UNIT 121

UNIT 122 UNIT 1


Compass directions

Horizontal and vertical lines

1 What is:

1 Circle the horizontal lines:

a s outh of the ladybird?

a

b n orth of the mosquito?

b

c

d

e

c west of the centipede? d east of the cockroach? e north of the ant? f west of the dragonfly?

f

2 Circle the vertical lines:

a

2 In which direction is the:

b

c

d

e

a bee from the butterfly? b caterpillar from the cockroach? c spider from the dust mite? d ladybird from the mosquito? e ant from the dragonfly? f butterfly from the ant?

f

3 In each of the following shapes, circle the horizontal lines:

a

3 What insect is:

c

e

b

d

f

4 In each of the following shapes, circle the vertical lines:

a N of the ant and W of the butterfly? b E of the mosquito and S of the dust mite? c W of the dust mite and N of the centipede? d S of the butterfly and E of the spider? e N of the mosquito and W of the dust mite? f S of the ladybird and W of the mosquito?

a

c

e

b

d f

5 Circle the horizontal line:

4 Where does the centipede move if it goes:

a 1 place north and 2 east? b 2 places north and 1 west? c 1 place north and 1 west? d 1 place north and 1 east? e 2 places east? f 1 place east and 2 north?

6 Circle the vertical line: 7 Circle the horizontal lines:

5 What is east of the ant? 6 In which direction is the spider from the bee?

8 Circle the vertical lines:

7 Which insect is S of the caterpillar and E of the ant?


8 Where does the caterpillar move if it goes north 1 place and 1 west? 9 Complete the compass: N

9 Write your name in capital letters and draw in red all of the horizontal lines. Then circle all of the vertical lines.

☞



77

UNIT 123

UNIT 124


Maps (3) 1 What town on the map is at:

10

Coen Cooktown

8

Cairns

7

Burketown Georgetown

ce Bru y Hw

4

3

Townsville

Finders Highway Ma tild aH wy

5

Longreach Birdsville

Brisbane

1

St George

A

B

D

C

E

F

G

H

f

O N M L e

I

a c e

d

H G

c

F E D

a

C

3 Name two points that lie on or inside each of the shapes on the grid:

a the Great Barrier Reef , b Flinders Highway , c Bruce Highway , d Whitsunday Islands , e Matilda Highway , f Southern border ,

b

B A

0

1

2

3

4

5

6

7

b d f

4 What is the distance, in units, between:

a (1, C) and (3, C)? b (4, B) and (6, B)? c (4, P) and (6, P)? d (0, P) and (3, P)? e (4, E) and (7, E)? f (3, K) and (6, K)?

4 Name a place:

a north of Georgetown b north of St George c south of Thursday Island d west of Rockhampton e south of Cooktown f south of Weipa

5 Name the shape labelled g on the grid: 6 List the coordinates of the corners of the shape labelled g on the grid:

5 What town on the map is at (F, 3)? 6 Give a grid reference for Rockhampton.

7 Name two points that lie inside the shape labelled g.

7 Write two sets of coordinates for the western border.

,

8 What is the distance, in units, between (1, R) and (3, R)?

8 Name a place east of Burketown.

9 List the towns and the direction you would travel driving from Townsville to Weipa.

g

P

a b c d e f

3 Write two sets of coordinates for:

Q

2 List the coordinates K of the corners of each of J the shapes on the grid:

Springsure

2

R

a b c d e f

Weipa

9

6

1 Name each of the shapes on the grid:

Thursday Island

ef Re

a Cooktown b Cairns c Townsville d Thursday Island e Burketown f Longreach

11

r rrie Ba

2 Give a grid reference for:

Coordinates

at Gre

a (D, 4) b (C, 7) c (C, 9) d (C, 10) e (A, 2) f (F, 1)


9 Set up a grid and list the points for a friend to draw a pentagon.




☞

Answers on page 143

UNIT 125

UNIT 126


Grids

Perspective 1 Here are two pictures as seen by an ant and a bird.

10 9

A

8

7

6

4

3 2 1 1

2

3

4

1 Draw blue dots at:

a (3, 8) c (1, 9) e (0, 2)

5

6

7

8

9

10

11

Measuring in mm, complete the following table: Width of top of container

a (4, 2) c (4, 6) e (7, 5)

12

b (2, 9) d (0, 8) f (2, 2)

b e

How many times bigger is the bottom than the top?

c f

The same rectangular prism has been drawn from different view points for questions 2, 3 and 4.

a

B C A

B C A

B b c

C A

d C

e

B A

B C A

f

B C A

2 Use a protractor to measure angle A in each of the pictures:

a d

b (4, 3) d (6, 6) f (7, 4)

b e

c f

3 Use a protractor to measure angle B in each of the pictures:

a d

3 Draw green dots at:

a (9, 2) b (9, 6) c (11, 6) d (12, 5) e (12, 3) f (11, 2)

b e

c f

4 Use a protractor to measure angle C in each of the pictures:

a d

b e

c f

5 Here is a picture as seen by a boy. Complete the following table:

4 Draw orange dots at:

Width of top of container

Picture

a (6, 3) b (7, 2) c (5, 3) d (8, 2) e (8, 4) f (8, 6)

a

Width of bottom of container

b

The cube is for questions 6, 7 and 8: 6 Measure angle A.

c C

B A

8 Measure angle C.

6 Join the orange dots that have the first coordinate as 8 to form the letter I.

9 Draw a picture of a road disappearing into the distance. Hint: the part of the road closest to you should be wider and the furthest part should be the narrowest.

7 Join the rest of the orange and red dots together to form a letter. 8 Join the green dots together to form the 4th letter of the alphabet. 9 Join the blue dots together to complete the word.

How many times bigger is the bottom than the top?

7 Measure angle B.

5 Draw blue dots at (3, 3) , (3, 5) and (1, 5).


a d

A B

Width of bottom of container

2 Draw red dots at:

☞

B

Picture

5

0


Units


79

UNIT 127

UNIT 128


Digital and analog time

am and pm time (1)

1 Write each of the following times in words:

a

11 12

b

1

10

2

9 7

4

7

11 12 10

2

9

11 12

7

6

3 5

6

11 12

7

6

5

3

7

6

5

11 12

11 12

1 2

8

4

9

3 7

6

5

11 12

1

5

6

e ten to six

3 4

8

3

6

5

f quarter past one

11 12

a

2

6

8

4

9

3

7

11 12

c

6

5

11 12

1

10

2

8

4 6

5

11 12

1

10

3

:

5

6

4 Write each of the following times as a digital time:

a quarter to

:

seven

c quarter past eight

e twenty-five minutes to five 5 Write

11 12

1

10

2

9

3

:

7

6

b half past three

11 12 10

2

9

3

as a digital time.

4

8 7

6

5

1

10

morning :

f 3

:

1 2

9

4 6

5

10

3 4

8

5

7

afternoon

11 12

2

7

6

evening

1

8

5

7

:

9

4

6

5

morning :

4 Write the time that is one hour later than:

a 9:32 pm c 11:49 am e 2:47 am 5 Is

pm

07:27

b 1:15 am d 6:52 pm f 7:23 pm

before midday or after midday? 11 12

1

10

2

8

4

9

3

2

9

7

6

5

evening

3

7 Order the times from earliest to latest time. 5:25 pm, 5:32 pm, 5:15 pm

4

8 5

6

: :

9 If lunch time finishes at twenty past one and school finishes at 3:10, how long is there between the end of lunch and the end of school?

8 Write the time that is one hour later than 4:52 am. 9 Tony started work at

am

07:25

and finished at

pm

03:15

How long did Tony work for?


11 12

3 4

8

5

10

2

9

6 Write the digital time for:

8 Write twenty-five to four as a digital time:

80

e

1 3

6

6

:

2

7

3 7

1

10

morning

11 12

8

4

5

:

2

in words. 11 12

1

6

11 12

1

10 9

afternoon

d

:

past four

7

7 Write

:

one f ten minutes

6 Draw the time twenty to ten.

:

d five minutes to

5

2:35

3

4

8

:

pm

a 4 pm, 4 am, 6 pm b 9:04 pm, 8:35 am, 9:15 am c 1:25 am, 2:30 pm, 1:45 pm d 7:51 am, 7:52 pm, 7:50 am e 6:29 am, 6:42 pm, 6:30 pm f 11:47 am, 11:42 pm, 11:30 pm

:

4 7

f

12:35

2

8

:

am

3 Order each set of times from earliest to latest time: :

3

9

5

6

1

7

f

4 7

5

10

3 8

:

2

9

6

11 12 9

4 7

e

d 3

3 7

2

8

4

1

10 9

8

9

:

5

6

2

8

4 7

5

1

10

1 1:58

11 12

2

8

4 7

11 12

b

c

1

9 3

8

11 12

10 9

2

9

4

1

10

03:19

10

3 Write each of the following times as a digital time:

e

am

8:05

1

10

5

6

4 7

3 7

8

9

2

8

5

2

11 12

9

1

10

1

10

9

6

3 7

2

7

4

11 12

10

8

9

d half past ten

11 12 2

pm

a

1

10

b

2 Write the digital time for each of the times shown: b c

2 Draw each of the times on the following clocks: a two o’clock b quarter to twelve c twenty past two 10

d

pm

4:25

4

8

am

2

9

a

1

10

3 4

8

4

f

2

9

5

8 7

1

10

3 4

8

2

e

1

10

5

6

1 For each of the following digital times, write before midday or after midday:

1

9

d

11 12

3 8

5

6

2

9

4

c

1

10

3 8

11 12



☞

Answers on page 143

UNIT 129

UNIT 130


am and pm time (2)

24-hour time (1)

1 For each of the following digital times write morning, afternoon or evening:

a

am

d

am

1 1:29

b

pm

e

pm

01:07

2:53

c

pm

f

am

1 Convert each of the following times to 24-hour time:

10:19

a 1010 c 0100 e 1400

2 Write a digital time for each of the following times: a b c 11 12

11 12

1

2

9

3

7

6

morning

d 10

e

6

5

morning :

f 4

5

6

:

6 Write a digital time for:

8

4

9

6

5

11 12

1

e

10

2

9

3 4

8

7

f

2

9

4

3

6

5

11 12

1

7

6

10

2

8

4

9

4

8

5

1

3

6

11 12 10

3 7

2

7

3

5

11 12

7

6

5

b

1

10

2 3

11 12

6

5

11 12

1

c

1

10

2

9

4 7

d

10

7

6

5

11 12

1

e 3

10

6

5

3 4

8

7

6

5

11 12

1

10

3 7

6

3 4

8

5

2

9

4

8

f

2

9

4 7

2

2

8

1

9

4

8

9

11 12 10

3

7

6

5

5 Convert 5 pm to 24-hour time. 6 Write 0900 as am or pm time. 7 Write the morning (am) time as 24-hour time.

am

04:21

8

4

1 2

9

3 4

8 7

6

5

8 Write the afternoon/evening (pm) time as 24-hour time.

3 5

11 12 10

1

9


1

c

1 2

:

morning 7 Order the set of times from earliest to latest in the day: 4:27 pm, 4:08 am, 4:01 am 8 What time is 17 minutes past 7:52 am? 9 Josh had 35 minutes of homework. If his favourite television show started at 8:15 pm, and he started his homework at 7:48 pm, did he finish in time?

☞

11 12 10

2

6

5

8

10

7

6

9

5 Write morning, afternoon or evening for: 11 12

d

a

a 25 minutes after 11:20 pm? b 20 minutes after 4:50 am? c 10 minutes after 5:54 pm? d 30 minutes after 8:18 am? e 50 minutes after 1:26 am? f 45 minutes after 3:36 pm?

3

11 12 10

4 Write each of the following afternoon/evening (pm) times in 24-hour time:

4 What time is:

8

4

8

a 1:15 am, 1:30 pm, 1:08 am b 3:49 pm, 3:35 am, 3:30 pm c 2:06 am, 2:15 pm, 1:12 am d 10:27 am, 10:26 am, 10:05 pm e 7:45 am, 7:40 pm, 7:50 am f 9:52 pm, 9:56 am, 9:54 pm

2

9

3 Order each of the sets of times from earliest to latest time in the day:

b

1

5

evening

11 12 10

7

4 7

evening :

3 8

2

9

9

1

10 3

6

a

11 12

2

7

6

:

1

8

5

afternoon

9

4

4 7

b 1615 d 2020 f 0620

3 Write each of the following morning (am) times in 24-hour time:

3

10 3

7

9

11 12

2

8

:

1

9

6

2

8

5

evening

11 12

3 7

1

10

4

8

5

:

2

9

4

8

11 12

1

10

b 9:00 pm d 11 pm f 1 pm

2 Write each of the following as am or pm time:

07:33

10

a 3 am c 7:30 am e 2:30 pm

1 5:42


11 12

1

10

2

9

3 4

8

7

6

5

9 Draw 0000 on a clock face.

11 12

1

10

2

8

4

9


3 7

6

5

81

UNIT 131

UNIT 132 UNIT 1


24-hour time (2)

24-hour time (3)

1 Use am or pm to write each of the following times:

a 0246 b 1639 c 1512 d 0719 e 2352 f 0654

2 These clocks show 24-hour time. Use am or pm to rewrite each time: a 2000 b 1730

c d 0123

e

2 Use 24-hour time to write each of the following times:

a 4:32 am c 10:52 am e 7:05 am

f

0647

11 12

b

1

10

2

9

3 7

6

2 3

pm

7

11 12

e

2

9

3 7

6

8

4

3 7

f

1 2 3

6

pm

5

pm

7

6

am

5

11 12

1

10

2

8

4

9

4

8

5

2

am

9

4

8

11 12 10

3 7

6

5

am

4 Use 24-hour time to write the time one hour later than:

a 3:15 am c 9:07 pm e 11:37 am

b 5:43 pm d 7:25 am f 6:58 pm

4 Find the difference in time between each of the following pairs:

a 9:25 am and 10:10 am b 8:56 am and 10:20 am c 4:32 pm and 5:00 pm d 7:10 pm and 8:35 pm e 11:20 am and 1:35 pm f 9:46 am and 2:14 pm 5 Use am or pm time to write this 24-hour time: 2047

5 Use am or pm to write 1942.

6 Use 24-hour time to write 5:15 am. 6 Use am or pm to rewrite:

11 12

7 Write

7 Use am or pm time to write the time which is one hour later than 1423.

0410

4-hour time.

1

10

2

9

3 4

8

b 8:12 pm d 1:43 pm f 5:21 pm

a 2257 b 0319 c 0742 d 1604 e 1827 f 0931

1

10

1

10 9

5

6

d

11 12

4

8

5

c

1

9

4

8

11 12 10

3 Use am or pm time to write the time which is one hour later than:

a

a 0217 b 1525 c 2110 d 2306 e 1146 f 0620

3 Write each of the following times in 24-hour time:

1 Use am or pm time to write each of the following 24-hour times:

2115

1017


7

6

5

8 Find the difference in time between 10:30 am and 3:47 pm.

pm

8 Use 24-hour time to write one hour later than 8:35 pm.

9 How long will it take to travel 500 km at an average speed of 80 km/h?

9 The flight from Melbourne left at 1147 and arrived in Sydney at 1310. How long was the flight?




☞

Answers on page 144

UNIT 133

UNIT 134


Timetables and timelines

Time zones

1 Use the train timetable to find the time to travel from:

a Sport Square to Sand Street

b Game Grove to Puzzle Parade

c Cards Corner to Reading Road

d Box Bend to Skate Square

1 If the time is 3:30 pm in Sydney, show the time on each clock for the different locations:

Train Timetable Sport Square

10:55 am

Cards Corner

11:12 am

Game Grove

11:26 am

Box Bend

11:37 am

Sand Street

11:43 am

Reading Road

11:58 am

Puzzle Parade

12:07 pm

Shop Street

12:19 pm

Footy Field

12:31 pm

Skate Square

12:40 pm

a

11 12

d Footy Field? f Shop Street?

b Sport Square d Reading Road f Cards Corner

6

a Melbourne c Adelaide e Perth

a

11 12

7

5

6

5

11 12

1

Adelaide

10

2

8

4

9

4

3 7

Darwin

5

6

Perth

b Brisbane d Sydney f Hobart

2 3

11 12

7

6

5

11 12

1

10

5

7

6

5

11 12

1

10

5

8

4

3 7

f

4 6

2

Hobart

3 7

6 If the train is 5 minutes early, find the time it will arrive at Skate Square?

11 12

1

Adelaide 2

9

3 4 7

Brisbane

5

6

Darwin

11 12

1

10

2

9

3 4

8 7

5

6

EST

7 Use 24-hour time to show the time in Darwin if it is 2:25 pm in Melbourne. 8 Complete the time on the clock for Melbourne if it is midday in Sydney during daylight saving.

8 In 1952 the Victa lawnmower was invented. Add this to the timeline in question 4 as letter g.

5

8

6 Complete the table: WST CST 6:00 pm

7 If the train is half an hour late, what time will it arrive at Puzzle Parade?

6

10

5 If the time is 3:30 pm in Sydney, show the time on the clock for Brisbane:

2000

1

10 9

2

8

Perth

11 12

4

9

4 6

e 3

7

3 8

2

9

2

9

Sydney

c

1

10

4

8

d

b

1

10 9

5 Use the timetable to find the time to travel from Sport Square to Reading Road.

11 12

1

10

2

8

4

9

3 7

6

5

9 When Anita woke on the first day of daylight saving the clock showed 6:30 am. What time did she change it to?

9 What is the average speed of a train that travels 120 km in 1 12 hours? Answers on page 144 © Pascal Press ISBN 978 1 74125 262 0

2

6

4 Complete the time on each of the clocks if it is midday in Sydney during daylight saving:

☞

7

f

1 3

3 4

8

2 Complete the table to show the time in each time zone: WST CST EST 9:00 am a 16:30 am b 4:15 pm c 10:05 am d 2:30 pm e 12:45 pm f

8

1950

Hobart

2

9

Melbourne

10

1

3 Use 24-hour time to show the time in each different location if it is 2:25 pm in Melbourne:

a 1996 – first plastic money b 1906 – world’s first full length feature film c 1930 – first international phone call d 1956 – TV broadcasting begins e 1912 – first public automatic phone exchange open f 1978 – first bionic ear fitted to patient

1900

11 12

8

5

11 12

EST

10

4 5

6

9

4 7

2

7

e

2

c

1 3

3

4 Some major Australian inventions are listed. Use the letters a to f to show these on the timeline:

Sydney

1

10

11 12 10

8

5

8

b Puzzle Parade?

d

6

CST 1 2 h behind EST

WST 2h behind EST

9

4 7

9

3 If the train is half an hour late, find the time it will arrive at:

a Box Bend c Footy Field e Game Grove

2 3

b

1

8

2 If the train is 5 minutes early, what time will it arrive at:

a Game Grove? c Sand Street? e Cards Corner?

11 12 10 9

e Shop Street to Footy Field f Sport Square to Skate Square



83

UNIT 135

UNIT 136


Length in mm (1)

Length in mm (2)

1 Label the following lengths as a–f on the ruler: 0

1

2

3

4

5

6

1 Name the measurement which would be used for: 7

cm

a 6 cm d 1.8 cm


b 15 mm e 20 mm

c 34 mm f 2.6 cm

2 Use decimal form to write each of the following in centimetres.

a the thickness of a finger nail b the distance between two towns c the height of a netball ring d the length of a pencil e the length of a whiteboard f the width of a computer screen 2 Measure each of the following lines to the nearest mm:

a 92 mm b 41 mm c 38 mm d 95 mm e 109 mm f 153 mm 3 Use millimetres to write each of the following:

a 1.7 cm b 2.2 cm c 8.7 cm d 4.1 cm e 12.6 cm f 15.7 cm

a b c d e f 3 Change each of the following to millimetres:

4 Select the best unit of measurement (mm, cm, m or km) to measure the:

a width of a toothpick b height of a house c length of a book d length of a basketball court e width of a piece of paper f length of a car 5 Label 14 mm as g on the ruler of question 1.

a 9 cm b 21 cm c 4.3 cm d 7.5 cm e 1.6 cm f 93 cm 4 Change each of the following to centimetres:

a 72 mm b 16 mm c 50 mm d 48 mm e 192 mm f 365 mm 5 Name the measurement which would be used to measure the length of a single train carriage.

6 Use decimal form to write 125 mm in centimetres.

6 Measure the line to the nearest mm. 7 Use millimetres to write 3.3 cm.

7 Change 102 cm to millimetres. 8 Select the best unit of measurement (mm, cm, m or km) to measure the length of the Sydney Harbour Bridge. 9 Measure to the nearest cm the length of the following line:

8 Change 127 mm to centimetres. 9 Measure the length and breadth of the rectangle in mm. What is the total length around the rectangle in mm and cm?

84


p83-104 Maths5_Unit 3-2017 updated for future reprint.indd 84


☞

Answers on page 145 17/02/2017 3:38 PM

UNIT 137

UNIT 138


Length in km (1)

Length in km (2)

1 Circle the distances that would be measured in kilometres:

1 Give the unit that would be used to measure:

a the length of a classroom b the distance between Sydney and New Zealand

a your height b the distance between Sydney and Melbourne c the length of a bus d the length of the Murray River e the width of Sydney Harbour f the length of a football field

c the distance around a house d the length of a table e the perimeter of a school fence f the distance walked in one day

2 Find how many metres in each of the following:

2 Find how many kilometres in each of the following:

a 4 km b 6 km c 1 km d 9 km e 11 km f 15 km

a 4000 m b 11 000 m c 7000 m d 23 000 m e 5000 m f 20 000 m

3 Find how many kilometres in each of the following:

3 Find how many metres in each of the following:

a 9000 m b 3000 m c 5000 m d 2000 m e 12 000 m f 17 000 m

a 6 km b 9 km c 14 km d 8 km e 3 km f 2 km

4 Write each of the following speeds as kilometres per hour (km/h):

4 Convert each of the following to kilometres:

a 2500 m b 3640 m c 1090 m d 3580 m e 2905 m f 4756 m

a 60 km travelled in 1 hour b 40 km travelled in 1 hour c 100 km travelled in 1 hour d 200 km travelled in 2 hours e 160 km travelled in 2 hours f 550 km travelled in 5 hours

5 What unit would be used to measure the length of the Nile River?

5 Would the length of a plane be measured in kilometres?

6 Find how many kilometres there are in 18 000 m.

6 Find how many metres there are in 7 km.

7 Find how many metres there are in 12 km.

7 Find how many kilometres there are in 10 000 m.

8 Convert 2385 m to kilometres.

8 Write 180 km travelled in three hours as kilometres per hour (km/h).

9 Convert the following from kilometres to metres:

9 List three objects/distances that would be measured in kilometres.

☞



a 9.610 km b 4.318 km c 6.045 km


85

UNIT 139

UNIT 140


Length with decimals

Perimeter (1)

1 Tick the most appropriate unit of measurement for the following: mm cm

m

km

a length of pool

1 Measure accurately the length and breadth of each shape: a b

b length of highway

c thickness of strand of hair

l=

b=

c

d length of calculator

b=

l=

b=

l=

b=

f thickness of mouse pad

l=

d

distance from Melbourne to e Perth


l= e

b=

f

2 Record each of the lengths marked on the ruler:

d

c a f

e

b

0

1

2

3

4

5

6

cm

a c e

mm

cm b

mm

cm

mm

cm

d cm f

mm

cm

mm

cm

mm

3 Use decimal form to write each of the following in metres:

a 837 cm c 398 cm e 1024 cm

b 149 cm f 1179 cm

4 Convert each of the following measurements to the indicated length: mm b 220 cm =

m

d 2490 m = cm f 6.5 m =

km

cm

a

c P =

e P =

f P =

2m

P=

d

b

3.2 cm

P=

12 m

P=

e

c

5.3 cm

P=

f

P=

10 m

8.1 cm

P=

4 Find the perimeter of each of the following rectangles: b c

a

4m

P=

d

3m

P=

e

6.1 cm 1.2 cm

9 cm

12 m 2m

P=

P=

f

4.1 cm 2.3 cm

4 cm

1.7 m 2.3 m

P=

P=

5 Measure accurately the length and breadth of:

6 Record the length marked on the ruler: mm

0

cm

cm

1

2

3

l=

b=

6 What is the perimeter of the shape in question 5?

7 Use decimal form to write 856 cm as metres.

7 Find the perimeter of the square:

8 Convert 3.2 m to

cm.

9 Write an appropriate measuring device for measuring:

a the perimeter of your school b the length of your drink bottle c the circumference of a bin 86

b P =

3 Find the perimeter of each of the following squares:

cm

5 Circle the most appropriate unit of measurement for the width of a refrigerator: mm cm m km

a P = dP=

d 915 cm

a 37 cm = c 8.5 m = e 32 mm =

b=

2 Find the perimeter of each of the shapes in question 1.

7

l=

8 Find the perimeter of the rectangle:


8.6 m

4.3 m 9 Anthony needs to fence his swimming pool area. The area is 15.3 m long and 8.2 m wide. How much fencing does he need?


7m


☞


UNIT 141

UNIT 142


Perimeter (2)

Perimeter (3)

1 Find the perimeter of each of the following rectangles:

a

b

6 cm 5 cm

d

8m

13 m 4m

P=

c

9m

P=

e

3m

6 cm

P=

f

10 cm

2m

P=

8 cm 3 cm

P=

P=

2 Complete the table for rectangles with the given measurements: Length Breadth Perimeter 4 cm 7 cm a 2 cm 10 cm b 8 cm 12 cm c 20 m 15 m d 25 m 10 m e 50 m 20 m f 3 Circle the correct perimeter for each of the following squares with the measurements: Length Perimeter 4 cm 16 cm 1112 cm 1120 cm a 5 cm 50 cm 1125 cm 1120 cm b 10 cm 100 cm 1150 cm 1140 cm c 9m 27 m 136 m 154 m d 20 m 200 m 100 m 180 m e 15 m 60 m 130 m 150 m f 4 Complete by measuring each side: b

a

f

c e

d

a c e

b d f

cm

10 cm

P=

d P=

b

4 cm

2 cm

c 5 cm

P=

e

P=

4 cm

f

2 cm

P=

1 cm

P=

2 Draw on the grid paper each of the following shapes:

a a rectangle with sides 4 mm and 7 mm

b a square with 2 mm sides c a rectangle with sides 9 mm and 3 mm

d a square with 3 mm sides e a rectangle with sides 2 mm and 6 mm

f a square with 5 mm sides 3 Find the perimeter of each of the shapes in question 2:

aP= dP=

bP=

cP=

eP=

fP=

4 Find the perimeter of each of the following:

a a square with side length 3.2 m b a rectangle with length 2.6 cm and breadth 1.4 cm

e an equilateral triangle with side length 2.5 cm

7m

f a regular pentagon with side length 1.2 cm

Perimeter

5 Find the perimeter of:

6 cm

6 Draw on the grid paper a square with 4 mm sides.

7 Circle the correct perimeter for a square with side length: Length Perimeter 2 12

3 cm

6 Complete the table for a rectangle with the given measurements: Breadth 4m

a

c a square with side length 4.5 cm d a rectangle with length 18.1 m and breadth 10.6 m

3m

1 Find the perimeter of each of the following shapes:

5 Find the perimeter of the rectangle:

Length 10 m


25 cm

5 cm

7 Find the perimeter of the shape in question 6. 8 Find the perimeter of a regular octagon with side lengths 2.2 cm. 9 Draw an irregular shape with a perimeter of 10 cm.

8 Add a to f of question 4 to find the perimeter of the shape. 9 Find the perimeter of the triangle:

☞



87

UNIT 143

UNIT 144


Area (1)

Area (2)

1 Find the area of each of the following rectangles (each square has a side length of 1 cm):

a

b

cm2

A=

cm2

A=

e

cm2

A=

cm2

cm2

A=

A=

f

cm2

A=

2 Measure the length and breadth of each of the following rectangles:

a

l=

b=

c

b

l=

b=

e

b=

l=

b=

l=

b=

f

l=

l=

d

b=

3 Find the area of each of the rectangles in question 2:

a A = dA=

bA=

cA=

eA=

f A=

4 Circle the correct areas for each rectangle with the following measurements:

a b c d e f

Length

Breadth

Area

16 cm

2 cm

18 cm2

10 cm2

12 cm2

10 cm

4 cm

40 cm2

14 cm2

28 cm2

19 cm

6 cm

30 cm2

54 cm2

15 cm2

17 mc

4 mc

28 m2c

24 m2c

22 m2c

12 mc

5 mc

50 m2c

60 m2c

34 m2c

18 mc

7 mc

30 m2c

44 m2c

56 m2c

5 Find the area of (each square has a side length of 1 cm):

l=

d

6m

Length 3m

Breadth 9m

Area 24

m2

27 m2

30 m2

9 What is the perimeter and area of an indoor cricket court 30 m long and 15 m wide?

2m

7m

b e

3m

2m 12 m

c

10 m

f

7m

5m 2 Circle the correct area for each square with the following side length measurements: Length (m) Area (m2) 33 12 39 336 a 37 49 328 314 b 10 40 380 100 c 39 81 336 354 d 12 36 144 392 e 20 80 200 400 f 3 Complete the following: Length Breadth Area 13 mc 14 mc a 19 mc 17 mc b 10 mc 15 mc c 18 cm 15 cm d 16 cm 11 cm e 14 cm 18 cm f

4 Calculate the area of:

a a rectangle with 6 m and 7 m sides b a square with 5 m sides c a rectangle with 9 cm and 3 cm sides d a square with 8 cm sides e a rectangle with 10 cm and 7 cm sides f a square with 2 cm sides 5 Find the area of:

4m 3m

36 m2 24 m2 12 m2 7 Complete: Length Breadth Area 2m 9m 8 Calculate the area of a rectangle with 2 m and 12 m side lengths.

b=

8 Circle the correct area for the following rectangle:

88

4m

6 Circle the correct area for a square with a side length measurement of 6 m:

7 Find the area of the rectangle in question 6:

a

cm2

A=

6 Measure the length and breadth of:

1 Find the area of each of the following:

c

d


9 Katie’s bedroom floor is 6 m by 4 m. What size rug does Katie need to completely cover the floor?




☞


UNIT 145

UNIT 146


Area (3)

Area (4)

1 What is the area of each of the following rectangles with measurements:

a l = 4 cm b = 3 cm b l = 9 cm b = 8 cm c l = 10 cm b = 7 cm dl=3m b=1m el=6m b=5m f l=7m b=2m Breadth 3m c 5 mc

Area 27 m2c 24 m2c 50 m2c c 2 cm 14 cm2 d 3 cm 18 cm2 e 4 cm 16 cm2 f 3 If the area of a shape is 24 m2, find the breadth if the length is:

a 24 m, b = c 6 m, b = e 16 m, b =

b 8 m, b = d 12 m, b = f 10 m, b =

4 Find the total area of each of the following shapes: 4 a b c 2 3

2

3 2

d

1

1

1

e

3 2

1

1

1

1

4

2

2

3

3

f

3

5 2

1

1

1 1

5 What is the area of a rectangle with measurements l = 6 m and b = 3 m? 6 Complete: Length Breadth Area 5 cm 20 cm2 7 If the area of a shape is 12 m2, find the breadth if the length equals 41 m.

1

9 Find the area of the following triangle. Hint: it is half of another shape!

5m

4m


20 m

d

80 m 50 m

e

25 m

60 m

f 200 m

30 m

90 m

3 Find the area of each of the following:

a a cow paddock b a sheep paddock c a horse paddock d a wheat field e a cow field f a house block

150 m 3 160 m 110 m 3 120 m 120 m 3 160 m 250 m 3 200 m 200 m 3 160 m 80 m 3 250 m

4 Find the length of each of the following: Length Breadth (m) 020 a 020 b 008 c 030 d 080 e 080 f

Area (m2) 00 800 00 600 16 000 02 100 32 000 40 000

5 Write the most appropriate unit of measurement (cm2 or m2) of area for a table. 6 Find the area of:

60 m 20 m

7 Find the area of a chicken pen 10 m 3 15 m. 8 Find the length of: Length Breadth (m) 8

Area (m2) 200

9 Find the total area of the farm in question 3. 3m

☞

20 m

40 m

2 1

1

2 Find the area of each of the following: 10 m a 100 m b c

3

8 Find the total area of:

1 Write the most appropriate unit of measurement (cm2 or m2) of area for each of the following:

a a classroom floor b a small garden bed c a book cover d a football field e a photo f the top of a swimming pool

2 Complete: Length c a 6 m b


Units


89

UNIT 147

UNIT 148



Square kilometres

Hectares 1 Give the unit, square metres (m2) or hectares (ha), that would be used to find the area of:

a a floor mat b a national park c a sand pit d a large beach e a kitchen f an airport 2 Find how many square metres (m2) there are in each of the following:

a 5 ha b 7 ha c 3 ha d 8 ha e 2 ha f 6 ha

1 Give the unit, of hectares (ha) or square kilometres (km2), that would be used to measure the area of each of the following:

a the Great Barrier Reef b a large playground c Western Australia d Olympic Park e a large tennis court complex f a cattle station 2 Find how many square kilometres (km2) there are in each of the following:

a 400 ha d 900 ha

b 700 ha

c 300 ha

e 100 ha

f 500 ha

3 List all of the states and territories and their areas from smallest to largest in size:

Northern Territory 1 356 176 Queensland 1 727 200 South Australia 984 381 New South Wales 801 431

Western Australia 2 525 500

3 Find how many hectares (ha) in each of the following:

Victoria 227 516

a 10 000 m2 b 40 000 m2 c 30 000 m2 d 60 000 m2 e 90 000 m2 f 20 000 m2

Tasmania 67 897

4 Complete the number statements with > or < or = :

a 100 m 3 200 m b 400 m 3 200 m c 400 m 3 25 m d 300 m 3 20 m e 350 m 3 40 m f 500 m 3 20 m

1 ha 1 ha

6 Find how many square metres there are (m2) in 9 ha. 7 Find how many hectares there are (ha) in 70 000 m2. 8 Complete the number statements with > or < or = :

60 m 3 200 m 1 ha 9 Find two different rectangles that represent fields that are exactly 1 ha in area. ,

Area (km2)

New South Wales

801 431

Western Australia

2 525 500

d e f

1 ha 1 ha

State/Territory

a b c

1 ha

1 ha 5 Give the unit, square metres (m2) or hectares (ha), that would be used to find the area of a soccer field?

Areas are in

4 Convert each of the following square kilometres (km2) to hectares (ha):

a 2 km2 = c 8 km2 = e 1 km2 =


ha ha ha

b 6 km2 = d 10 km2 = f 3 km2 =

ha ha ha

5 Give the unit, hectares (ha) or square kilometres (km2), that would be used to measure the area of a golf course? 6 Find how many square kilometres (km2) there are in 600 ha. 7 Find the total area of Australia using the information from question 3. 8 Convert 4 km2 to

ha.

9 Which is larger: 6500 ha or 62 km2?


90

Australian Capital Territory km2 2330


☞

Answers on page 146

UNIT 149

UNIT 150





1 Select the most suitable unit of measurement (g or kg) when finding the mass of:

a a brick b a pencil c a box of apples d a bag of potatoes e a CD ROM f a piece of paper

1 Select the most suitable unit of mass (g, kg or t) when measuring the weight of:

a a train c a girl e a bowling ball

b a snail d a calculator f an aeroplane

2 Find how many grams are in each of the following:

a 6 kg b 2 kg c 8 kg d 3.7 kg e 9.1 kg f 1.7 kg

2 Find how many grams in each of the following:

a 4 kg b 7 kg c 9 kg d 5 kg 320 g e 3 kg 247 g f 8 kg 693 g

3 Rewrite each of the following as kilograms and grams:

3 Rewrite each of the following as kilograms and grams:

a 1500 g b 2750 g c 6178 g d 3850 g e 4116 g f 1070 g

a 2176 g c 2122 g e 4035 g

b 4837 g d 8695 g f 1080 g

4 A cardboard box can hold a mass of 3 kg. How many of each of the following items could be packed into the box?

a

b

150 g

c

4 Write each of the following masses to the nearest 100 g:

d

a 417 g b 289 g c 851 g d 795 g e 1233 g f 2165 g

100 g

50 g

500 g

e

f

200 g

250 g

5 Select the most suitable unit of mass (g, kg or t) when measuring the weight of a bus.

5 Select the most suitable unit of measurement (g or kg) when finding the mass of a large dog.

6 Find how many grams there are in 4.6 kg.

6 Find how many grams are in 3 kg 721 g.

7 Rewrite 4619 g as kilograms and grams.

7 Rewrite 2176 g as kilograms and grams.

8 A cardboard box can hold a mass of 3 kg. How many computer keyboards weighing 400 g could be packed into the box?

8 Write 4163 g to the nearest 100 g.

9 Give the set of scales, A or B, that would be used to weigh: A 50 0 10 B 5 0 1 a a cat

9 Find the total mass of:

6.4 kg

☞

2.1 kg

3.6 kg


5.8 kg

b a strawberry


40

g

30

20

4

kg

2

3

91

UNIT 151

UNIT 152


Mass in tonnes (1)

Mass in tonnes (2)

1 Select the most suitable unit (kg or t) when measuring the weight of:

a a dad b a truck c a whale d a bag of apples e a skateboard f a helicopter

1 Complete the following table: kilograms tonnes 4 500 a 3.0 b 2.5 c 75 000 d 8 500 e 16.0 f 2 Order the following masses from lightest (a) to heaviest (f):

2 Write each of the following in kilograms:

a 9 t b5t c2t d 17 t e 21 t f 60 t

12 t

2.5 t

19 t

2143 t

84 t

52 t

3 Find how many kilograms in each of the following:

a 14 t

3 Write each of the following in tonnes:

a 3000 kg b 7000 kg c 14 000 kg d 10 000 kg e 40 000 kg f 52 000 kg

c 2 34 t

d3t

e 4 14 t

f 3 12 t

a 5.634 t b 2.186 t c 1.456 t d 6.321 t e 9.615 t f 3.80 t

a 12 t 11 000 kg b 64 000 kg 6.5 t c 700 kg 7 t d 2 t 2100 kg e 40 t 4200 kg f 19 t 18 200 kg

5 Complete: kilograms

6 Write 35 t in kilograms.

13 t

30 t

3.5 t

312 t

7 Find how many kilograms there are in 2 14 t.

7 Write 63 000 kg in tonnes. 8 Complete the number sentence with < or > :

8 Convert 3.708 t to kilograms.

50 t

9 What is the total mass of the packing crates? 3.2 t

tonnes 7.5

6 Order the following masses from lightest (a) to heaviest (d):

5 Select the most suitable unit (kg or t) when measuring 5 cabbages.

5600 kg

b 1 12 t

4 Convert each of the following from tonnes to kilograms:

4 Complete each of the following with < or > :


4.1 t

6.7 t

9 If a shipping container can hold 1 tonne, will the following boxes fit in it altogether? 624 kg




215 kg

119 kg

☞


UNIT 153

UNIT 154




1 Select the most appropriate unit (mL or L) when measuring the capacity of:

a a coffee mug b a bucket c a teaspoon d a swimming pool e a large bowl f a medicine cup b

1L

1L

1 2

1 L

c

e

1 4

f

1L

3 4L

3 Write each of the following as litres:

a 6000 mL b 1700 mL c 3000 mL d 12 000 mL e 22 000 mL f 36 000 mL a 4 L b7L

d 1 L 200 mL e 5 L 390 mL f 27 L

2L

22 000 mL

200 mL

2 12 L

2300 mL

a 200 mL + 400 mL + 300 mL b 45 mL + 125 mL + 500 mL c 800 mL + 200 mL + 450 mL d 1 L + 3 L + 8 L + 2 L e 2 L 500 mL + 3 L 450 mL f 3 L 680 mL + 200 mL + 1 L 320 mL 3 Find volume that would be required to displace each of the following:

a 40 mL b 65 mL c 75 mL d 600 mL e 125 mL f 790 mL 4 Find how much water would be displaced by each of the following:

4 Write each of the following as millilitres:

c 2 12 L

2 L 400 mL

L

1L

700 mL

1L

250 mL

L

d 1L

1 Order the following capacities from least (a) to most (f):

2 Find the total capacity of each of the following:

2 Colour to show each of the following:

a


a 20 cm3 b 90 cm3 c 120 cm3 d 310 cm3 e 500 cm3 f 850 cm3 5 Order the following capacities from least (a) to most (c):

5 Select the most appropriate unit (mL or L) when measuring the capacity of a large saucepan. 6 Colour to show 850 mL:

3 L 100 mL

3000 mL

3.2 L

6 Find the total capacity of:

1 L 375 mL + 2 L 125 mL + 3 L 250 mL

7 What volume would be required to displace 500 mL?

1L

8 Find how much water would be displaced by 450 cm3.

7 Write 10 000 mL as litres. 8 Write 2 L 490 mL as millilitres.

9 How much water would be displaced by the centicube model?

9 Find the total amount of:

1 L,

1 2

L,

0.2 L and 40 mL

☞



93

UNIT 155

UNIT 156




1 Find the volume of each of the following centicube models:

a

b

c

1 Find the volume of each centicube model:

a

b

d


e

d

f

c

e

f

2 Draw in the cubes and find the volume of each of the following prisms:

a

b

d

Breadth (cm)

Height (cm)

Volume (cm3)

a b c d e f

3 Find the volume of each of the following prisms (draw a diagram on a separate page if necessary):

a a cube with 3 cm sides b a cube with 4 cm sides c a cube with 5 cm sides d a rectangular prism with sides 3 cm, 4 cm and 5 cm

Volume (cm3)

a b c d e f

23232 13231 33231 33332 33333 43332 5 Find the volume of the centicube model:

f a rectangular prism with sides 5 cm, 3 cm and 7 cm 4 Find the capacity in mL of a prism with each of the following volumes:

a 25 cm3 c 72 cm3 e 260 cm3

b 50 cm3 d 130 cm3 f 490 cm3

5 Find the volume of the centicube model:

6 Draw in the cubes and find the volume of the model:

6 Complete the table for the prism in question 5: Length (cm)

7 Complete for the prism in question 6: Length (cm)

Breadth (cm)

Height (cm)

Volume (cm3)

8 Complete: Prism (cm)

Volume (cm3)

e a rectangular prism with sides 2 cm, 8 cm and 10 cm

Prism (cm)

Height (cm)

4 Complete the following table:

Breadth (cm)

a b c d e f

f

3 Complete the following table for each of the prisms in question 2: Length (cm)

Length (cm)

e

2 Complete the table for each of the prisms in question 1:

c

Volume (cm3)

43232 9 What are the dimensions of a cube with a volume of 1000 cm3? © Pascal Press ISBN 978 1 74125 262 0

Height (cm)

Volume (cm3)

7 Find the volume of a rectangular prism with sides of 2 cm, 4 cm and 6 cm. 8 Find the capacity in mL of a prism with a volume of 900 cm3. 9 Draw a diagram of a prism with a length of 6 cm, height of 2 cm and breadth of 4 cm.


94

Breadth (cm)


☞

Answers on page 147

UNIT 157

UNIT 158



Cubic metres 1 Select the most appropriate unit (cm3 or m3) for measuring the volume of:

1 Calculate the volume for each of the following prisms:

a

b

3 cm

3 cm

2 cm

c

2 cm

3 cm

e 6 cm

2 cm

2 cm

3 cm

7 cm

Length (cm)

Breadth (cm)

Height (cm)

Volume (cm3)

a b c d e f 3 Find the volume in cm3 of a prism with each of the following capacities:

a 40 mL c 75 mL e 263 mL

b 60 mL d 100 mL f 850 mL

4 Find the capacity in mL for each of the following prisms:

6 cm

5 Select the most appropriate unit (cm3 or m3) for measuring the volume of a DVD case. 6 Use the abbreviated form to write twenty-five cubic metres.

3 cm

6 Complete the table for the prism in question 5: Length (cm)

3 Tick the most appropriate unit for measuring: Item cm3 m3 a swimming pool a a lunch box b a match box c an airport d a farm shed e a CD case f

a 1 m 3 2 m 3 1 m b 2 m 3 3 m 3 1 m c 2 m 3 2 m 3 3 m d 4 m 3 2 m 3 1 m e 5 m 3 2 m 3 1 m f 4 m 3 2 m 3 3 m

5 Calculate the volume of the prism:

a six cubic metres b eight cubic metres c three cubic metres d eleven cubic metres e nineteen cubic metres f thirty cubic metres

4 Find the volume of a box:

a 10 cm 3 6 cm 3 4 cm b 3 cm 3 2 cm 3 5 cm c 6 cm 3 6 cm 3 6 cm d 8 cm 3 8 cm 3 5 cm e 4 cm 3 5 cm 3 4 cm f 2 cm 3 5 cm 3 9 cm 2 cm

2 Use the abbreviated form to write each of the following:

5 cm 1 cm

2 Complete the following table for each of the prisms in question 1:

a a classroom b a shoe box c a bedroom d a backpack e a supermarket f a desk draw

1 cm

3 cm

f

5 cm

4 cm

1 cm

d

2 cm

Breadth (cm)

Height (cm)

Volume

(cm3)

7 Tick the most appropriate unit for measuring:

7 Find the volume in cm3 of a prism with a capacity of 632 mL.

8 Find the capacity in mL for a prism 6 cm 3 4 cm 3 3 cm.

9 Find the capacity of the container: Answers on page 148 © Pascal Press ISBN 978 1 74125 262 0

Item a basketball stadium

cm3

m3

8 Find the volume of a box 2 m 3 4 m 3 4 m. 9 List four objects that have a volume less than 1 m3 and four objects that have a volume greater than 1 m3.

4 cm

3 cm 6 cm

☞


Units


95

UNIT 159

UNIT 160


Chance (1)

Chance (2)

1 Two dice were thrown 25 times with the results:

2

3

4

5

6

7

Which total was: a most frequent?

8

9

10

11

1 What is the chance that: 12

c most likely?

b least frequent? d e qual to a frequency of 2?

e least likely?

f greater than 10?

a Colour 10 red. b Colour 12 yellow. c Colour 8 green. d Which colour was most likely to be selected? e Which colour was least likely to be selected? f W hich colour was more likely to be selected than the red lollies?

a unlikely b likely c impossible d possible e certain f even chance 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

4 Rate the likelihood of the following events on a scale of 0 (impossible) to 1 (certain):

a it will rain tomorrow b I will clean my teeth today c the sun will set tonight d I will watch TV today e there will be school holidays this year f I will go overseas this year

Give the likelihood of drawing each coloured ball as a fraction:

a red c yellow e pink

b blue d orange f green

B

Y

Y

W

Y

O

B

G

W

G

R

W

G B

P

R

P

R

R

R

W

R

R

O

Y

G

B

W

3 Describe an event to match each of the following probabilities:

4 These are the possible totals for rolling two dice. Which total: 1 2 3 4 5 6 a is most likely? 1 2 3 4 5 6 7 b is least likely? 2 3 4 5 6 7 8 c has 2 chances in 36? 3 4 5 6 7 8 9 4 5 6 7 8 9 10 d has 5 chances in 36? 5 6 7 8 9 10 11 e is greater than 6 7 8 9 10 11 12 5 chances in 36?

f is equal to 1 chance in 18?

5 For the results in question 1, what numbers had the same frequency as the total of 5?

5 What is the chance that I toss a coin and it lands on heads?

6 For the lollies in question 2, what colours were less likely to be selected than yellow?

6 Using the information in question 2, give the likelihood of drawing out a white ball?

7 Mark on the scale in question 3: definite

7 Describe an event with a probability of 0.3

8 Rate the likelihood of ‘I will learn a new sport next year’ on a scale as 0 (impossible) to 1 (certain).

a 0.5 b 0.1 c 0 d 1 e 0.4 f 0.9

3 Mark the words on the scale:

0.1

a I will play sport next week b I will listen to the radio today c the next person to enter the room will be female d it will snow next month e I will fly a helicopter next week f I will be an astronaut when I grow up 2 There are 7 different coloured balls in a box.

2 Inside a bag were 30 lollies.

0


9 Draw a bag with coloured balls 1 that has a 4 chance of selecting a red ball and a 26 chance of selecting a purple ball.

8 Using the table from question 4, what is the chance of a total of 4? 9 List all of the different ways to arrange these shapes, ▲ ■ ● , in a straight line:




☞

Answers on page 148

UNIT 161

UNIT 162


Chance (3)

Picture graphs (1)

1 What is the chance, as a fraction, of landing on each of the following colours of the spinner?

a red c yellow e blue

0

R

b orange d green f black

Y

R

Blk

B G

B

2 For the following spinner, mark the chance on the scale for each of the different colours:

a red b green c yellow d blue e pink f orange

P

P

R R

B

G

B B

0

Y

2 Use the information from question 1 to answer:

certain

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1 The number of boxes packed at a factory are shown, = 100 boxes. Complete the numbers. where Day Boxes Number a Mon. b Tues. c Wed. d Thurs. e Fri. f Sat.

Y

impossible


0.9

1

aO n what day were 325 boxes packed? bW hich days had the same number of boxes packed?

cW ere more boxes packed on Friday or Tuesday? dH ow many more boxes were packed on Tuesday

3 True or false?

On spinner A, the chance of landing on: A

a blue is 50%. b red is less than 50%. c yellow is more than 25%.

B Y

than Monday?

R

amount of boxes packed?

On spinner B, the chance of landing on: B

d b lue is 25%. e y ellow is more than 50%. f green is the same as blue.

Y

B R G

4 Complete the diagram for the combinations of spinning the spinner two times. RR

R R

c 5 Find the chance, as a fraction, of landing on green for the spinner:

R

G B

6 For the spinner in question 2, mark the chance on the scale of landing on blue or yellow. impossible

0

0.1

certain 0.1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

7 True or false? For spinner B in question 3, the chance of landing on yellow and green is the same. 8 Complete the diagram for the combinations of spinning the spinner twice:

3 The number of boats at the docks were recorded for the week. Complete the picture graph using I = 4 boats: Day Number M Mon. 44 T Tues. 30 W Wed. 26 T Thurs. 16 F Fri. 10 S Sat. 36 = 8 apples 4 This is the number of apples sold at a school canteen over 4 weeks:

a Which week had the most sold? 1 2 3 4 Week No. b Which week had the least sold? c Which week had 24 apples sold? d F ind the difference between weeks 1 and 4? e Were more apples sold in week 2 or 3? f W hat was the total number of apples sold? 5 What does stand for in question 1? 6 True or false? There were more than 400 boxes packed on Thursday in question 1. 7 What was the total number of boats at the docks for the six days in question 3? 8 What was the total number of apples sold for the first two weeks in question 4? 9 Draw a picture graph to show the different coloured eyes in your class.

P B

9 List all of the different outcomes for spinning the spinner three times: O Y

☞

Answers on pages 148–9 © Pascal Press ISBN 978 1 74125 262 0


f W hat was the total number of boxes packed?

Number

b

a

d e f

G

R G

eW hat was the difference between the most and least

Units

97


UNIT 163

UNIT 164


Picture graphs (2)

Line graphs (1) Month Jan. Feb. March April May June

1 This is a line graph of Yuko’s height.

Number 55 80 75 60 65 90

110 100 Height in cm

1 The number of children entering a fun park is recorded. Here are the results. Complete the picture graph for the first 6 months, using  = 10 children. Month


Number of children

90 80 70 60 50

Month

90 80 70 60 50 40 30 20 10 0

T

T

W

W

T

T

F

F

d 5

e6

f 4 12

Jul. Aug. Sep. Oct. Nov. Dec.

40 30

2 Complete the table for the number of drinks supplied by a carton of milk: No. of cartons 1 12 3 4 5 6 No. of drinks 5 10 a b c d 3 Record the information from question 2 on the line graph:

Student Fred George Alayna Erin Caitlin Hannah

98

G

A

E

C

e

f

50 40 30 20

20

30

2

3

4 5 6 No. of cartons

7

8

9

4 U sing the information in questions 2 and 3, find how many drinks were supplied by:

Books read

10

F

8

60

1

a 6 cartons c 9 cartons

Find how many cartons would be needed for:

d 4 0 drinks f 28 drinks

40

50

10 0

7

10

20

6 Age in years

Find Yuko’s height when she was:

c3

 = 2 pies ▼ = 1 pie

4 Use the bar graph to complete the picture graph:

5

Day M

4

b2

3 Use the tally chart to complete the picture graph of the number of pies sold at the school canteen. M

3

Number of children

Tally

2

a 1

Day

1

No. of drinks

2 Use the bar graph on the right to complete the picture graph for the next six months of the fun park above:

No. of children

H

b 7 cartons

e 1 2 drinks

5 What was the total number of children entering the park in question 1? 6 What month had the least number of children enter the park in question 2? 7 What days had more than 12 pies sold in question 3?

5 Find how much Yuko grew between the ages of 5 and 6 in question 1.

8 What was the total number of books read by the boys in question 4? 9 Create a table of the park entries for the whole year, using the information from questions 1 and 2.

8 Would 4 cartons be enough for 23 drinks in questions 2 and 3?

6 Add 9 cartons to the table in question 2. 7 Add 9 cartons to the line graph in question 3.

9 Using the information from questions 2 and 3, calculate the number of drinks that could be supplied by 15 cartons of milk.



☞

Answers on page 149


UNIT 165

UNIT 166


Line graphs (2)

Tally marks

1 Here are a set of temperatures collected for one afternoon. Plot them on the graph:

Temp. (ºC)

noon

20

1 pm

24

2 pm

26

3 pm

28

4 pm

32

5 pm

30

1 Use tally marks to show the count of fruit eaten:

a 23 apples d 6 peaches

Time

first 30ºC?

c A t approximately what time was the temperature first 25ºC?

Find the approximate temperature at:

d 2 :30 pm? f 12:30 pm?

e 4:30 pm?

Centimeters

Tally

Number

3 Find how many cars were parked on:

a Monday b Tuesday c Wednesday d Friday and Saturday e Monday to Friday f Wednesday and Thursday

3 We can change a measurement from inches to centimetres using 1 inch = 2.5 cm (approximately). Complete the line graph for the first 6 inches: 17.5 15 12.5 10 7.5 5 2.5

4 Construct a graph from the tally sheet in question 2.

1 2 3 4 5 6 7 8

Tally

Day Monday Tuesday Wednesday Thursday Friday Saturday

b A t approximately what time was the temperature

c 14 oranges f 11 cherries

2 Complete the numbers for the tally chart of cars:

2 a At what time was the temperature 28ºC?

b 18 bananas e 19 pears

Fruit apples bananas oranges peaches pears cherries

Temp. (ºC)

Time


Inches

4 Convert to centimetres:

a 6 inches b 4 inches c 3 inches Convert to inches: d 10 cm e 12.5 cm f 5 cm


M

T

W

T

F

S

days

5 Using the information from question 1, how many fruit were counted altogether? 6 What was the total number of cars parked for the week in question 2? 7 If 17 cars were parked on Sunday, how many cars were now parked for the week in question 2?

5 Plot the temperature of 27ºC at 6 pm on your graph in question 1. 6 What was the difference between the temperature at noon and at 4 pm in question 1? 7 Add the value for 7 inches on your graph in question 3. 8 Convert 15 cm to inches. 9 Devise a conversion graph between hours and minutes.

☞

0

8 Including Sunday, what was the total number of cars parked on the weekend? 9 Create a tally chart for the number of people playing different sports in your family/class.


99

UNIT 167

UNIT 168


Reading graphs

Column graphs (1)

1 A tally of the number of whale sightings at Jervis Bay was kept:

Month June July August September

aW hat was the number

M T W T F S Su

b What was the number for September? cW hich month had 10 sightings? dW hich month had 16 sightings? eW hat was the difference between sightings in August and September?

f Find the total sightings for winter.

Runs

1 Here are the sales of a new toy for a week:

Tally

for June?

2 The runs of a cricket player for a season is shown on the graph.


70 60 50 40 30 20 10

10

20

2 Create a tally table of the information from question 1: 1 2 3 4 5 6 7 8 9 10

Game

a What was the highest number of runs? b What was the lowest number of runs? cH ow many times were there 50 or more runs? d In which game was the number of runs 25? e In which game was the number of runs 60? f W hat was the number of runs of the last game of

3 The number of hats 30 sold at a 20 surf shop 10 are shown 0 in the graph:

the season?

0

1 2 3 4 5 6

7 8 9

apples peaches

bananas

s ge an

6

pears

or

a pears b apples c bananas d oranges eW hich was the most popular

5

40

50

J

F

M

Tally

A

M

J

J

A

S

0

N

D

a Which month had the most hat sales? b Which month had the least hat sales? c How many hats were sold in November? d Which months had 10 hat sales? e How many hats were sold in spring? f How many hats were sold in summer?

4 Here is the breakdown of 64 peoples’ favourite fruit. Find how many people selected: pineapples

30

Day M T W T F S S

3 Use the information in question 2 to create a column graph of the first 6 games.

Number

a What was the number sold on Wednesday? b What was the number sold on Friday? c What days had sales more than 35? d What days had sales less than 15? e F ind the number sold on the weekend? f Find the number sold Monday to Wednesday?

fruit? f W hich fruit had a popularity of 8 people? Which month in question 1 had the greatest number of whale sightings? What was the total number of runs scored in the first five games of the season in question 2? In which game was the least number of runs scored in the column graph of question 3? What was the total popularity of apples and bananas in question 4? Use the information from question 4 to create a bar graph.

4 Create a column graph of the hat sales in the d different seasons from c b the question 3 a data: 10 20 30 40 50 60 70 80 5 Find the total number of toys sold in question 1? 6 In question 1, how many more toys were sold on Saturday than Thursday? 7 Which months had less than 10 hat sales in question 3? 8 Which season had the least number of hats sold in question 4? 9 In question 1, why would more toys be sold on the weekend than weekdays?




☞

➤ 90

Answers on page 150

UNIT 169

UNIT 170


Column graphs (2)


1 Show the information of how far Anton rode his bike during a training week on the column graph:

Monday 45 km

Tuesday 82 km

Wednesday 50 km

Thursday 70 km

Friday 25 km

Saturday 30 km

1 Here are some maths words: survey column tally data chance marks plot construct

M T W T F S S

20

30

40

50

60

70

80

90

2 a What was the furthest distance Anton rode?

b What was the shortest distance Anton rode? cW hat was the difference between the furthest and

dO n which day(s) did Anton ride over 50 km? e F ind the distance he rode Monday–Wednesday? f Find the distance he rode Thursday–Saturday?

3 1500 people were surveyed about their holiday destination and the results are shown. Complete the column graph: Country

Eur. Asia

Afr.

254

Asia

425

Africa

115 237

South America

193

Australia

350

Europe?

f– m2 t9

g3 n u

0

b used the least? d used exactly 5 times?

6 What was the total number of letters used? 7 Give a title for the graph.

f W hat was the difference between the most popular

8 What was the total number of vowels used?

and least popular destination? 5 Add Anton’s riding distance of 67 km for Sunday to the graph in question 1. 6 What was the total distance Anton rode for the week? 7 Add a title to the graph in question 3. 8 If some people said they had never been on holiday, use the information in question 3 to find out how many people this is.


e l s4 z–

5 What method was used to display the information in question 1?

Asia and Africa?

☞

d2 k r6 y2

a used the most? c not used at all? e used 5–10 times? f used 1–5 times?

dD id more people travel to Australia than Asia? eW hat were the total number of people travelling to

9 Draw a line graph of Anton’s riding distances.

c8 j– q– x1

4 Which letter(s) is/are:

b What was the most popular destination? cD id more or less people travel to North America than

b– i p3 w–

4 a How many people travelled to America?

g n u

3 Create a bar graph of the use of the vowels and t:

Number

North America

N S Aust. Amer. Amer.

a9 h2 o5 v1

Europe

picture line collecting

2 Complete the counts of letter use:

shortest distances?

axis graph reading total

Complete the tally chart of the use of letters: a b– c d e f– h i j– k l m o p q– r s t v w– x y z–

10


9 Complete from the information in question 2: No. of times Tally Number letter used 0 1 2 3 4 5 6 7 8 9


101

UNIT 171

UNIT 172



Mean

1 A six-sided die was rolled 30 times, and the following information collected on the number rolled:

1, 3, 5, 2, 4, 1, 3, 5, 6, 6, 6, 5, 4, 3, 2, 2, 1, 3, 2, 1, 4, 3, 6, 5, 2, 6, 6, 2, 5, 3

Complete each tally in the table: Number 1 2 3 4 Tally a b c d Count a b c d

5

e e

6

f f

2 Complete the count for each number in the table above.

Number of times rolled

3 Draw a column graph of the information in questions 1 and 2:

1 Find the mean of each of the following sets of scores:

a 2, 4, 6, 8, 10 b 14, 21, 15, 19, 21 c 4, 7, 8, 5 d 16, 27, 32, 21 e 30, 35, 34, 32, 31, 33 f 45, 50, 43, 52, 54, 47 2 Here is a collection of marks for students in their quick quizzes for the term. Find each student’s mean score: Student Scores Mean a Bob 7, 9, 8, 6, 5, 7, 6, 7, 9, 10 b Yuko 6, 7, 9, 5, 4, 8, 8, 4, 7, 8 Ho 8, 9, 8, 9, 10, 9, 10, 8, 8, 9 c d Fred 6, 5, 7, 8, 8, 7, 9, 8, 6, 10 e Gillian 10, 9, 10, 8, 7, 9, 8, 9, 7, 8 f Kathy 5, 6, 8, 3, 7, 5, 6, 7, 8, 6 3 Find the mean of each of the following:

0


a 13, 20, 15 b 10, 20, 15 c 12, 10, 14 d 8, 12, 10, 14 e 5, 10, 13, 20 f 15, 10, 20, 15

Number on the die

4 Write six questions that could be asked about the data in questions 1, 2 and 3:

a b c d e f

4 Find the mean cost of:

5 Draw the tally marks which represent the number 9.

a $3, $7, $8, $2 b $1, $3, $5, $3 c $20, $5, $3, $4 d $13, $17, $27, $15 e 35c, 40c, 5c, 20c f 5c, 10c, 20c, 5c

5 Find the mean of 2, 3, 4, 5, 6.

6 How many times were the numbers 1, 2 and 3 rolled in question 1?

7 What number was rolled 4 times?

8 Write a question that could be asked about the numbers on the die.

6 Find the mean score for Georgio: 7, 2, 8, 5, 7, 6, 3, 9, 8, 7 7 Find the mean of 0, 3, 5, 20.

9 Collect survey data about the number of plants in a garden, dividing them into appropriate groups.

8 Find the mean cost of $24, $30, $36. 9 Find three numbers that will add together to give a mean of 6.




☞

Answers on page 151

UNIT 173

UNIT 174


Problem solving (1)

Problem solving (2)

1 Find the number that:

1 Without using the same digit twice, find how many different 2-digit numbers can be made using:

a when doubled and 9 is added, the answer is 23 bw hen halved and 6 is subtracted, the answer is 5

cw hen multiplied by 5 and 2 is added, the answer is 32

dw hen 7 is added and then divided by 3, the answer

a 3, 4 c 3, 4, 5 e 2, 3, 4, 5

ew hen 9 is subtracted and is multiplied by 8, the

answer is 80

f w hen multiplied by 7 then divided by 3, the answer is 21

+

1 4

= 2

b3–

b 2 cubes d 5 cubes f 50 cubes

3 For each difference find two numbers that have the given product:

a ▲ + 7 = 20 – 6 b 5 3 ▲ = 27 + 8 c 100 ÷ ▲ = 21 – 16 d 63 ÷ 9 = 17 – ▲ e 83 – 47 = ▲ ÷ 2 f 6 3 3 = 45 – ▲ a

a 1 cube c 3 cubes e 10 cubes

2 Find the value of the ▲ in each of the following:

3 Find the value of the

b 1, 2, 3 d 7, 8, 9 f 6, 7, 8, 9

2 Cubes are placed end to end in a straight line. Find how many faces are visible from any view if there is/are:

is 11


a difference = 6

in each of the following: = 1 12

c

6 10

f

4 8

–

=

1 10

product = 567

numbers:

b difference = 5 product = 500

numbers:

c difference = 10

d difference = 7

product = 24

product = 408

numbers:

numbers:

e difference = 1

f difference = 9

3 68

product = 132

product = 220

4 Use the number line to find the numbers which are:

numbers:

d

– 1 18

=

2 38

e4–

=

2 107

+

0

=

10

a two units from the number 5? b five units from the number 3? c one unit from the number 10? d less than 4 units from the number 4? em ore than 2 units, but less than 5 units from the number 8?

f m ore than 1 unit, but less than 3 units from the

a * 3 2 = 8.6 b * ÷ 5 = 2.4 c * + 4.81 = 10.46 d 5 ÷ * = 1.25 e 7.25 – * = 5.47 f 6 3 * = 25.2 5 Without using the same digit twice, in any number, how many different 2-digit numbers can be made using 6

6 Find the value of the ▲ in: 21 – 15 = ▲ 3 2 7 Find the value of the

7

in: 5 +1 = 2 3

8 Which numbers are three units from the number 10?

0

8 9

10

9 Write your own ‘find the number’ (like in question 1) using at least one multiplication and division step.

2, 7, 6, 3? If 100 cubes are placed end to end in a straight line, how many faces are visible? Find two numbers that have a product of 180 and a difference of 3. Find the value of the * in: * + 6.12 = 12.05 Complete the 1 4 magic square 6 for 34: 10 11

☞



numbers:

4 Find the value of the * in each of the following:

number 7? 5 Find the number that, when doubled and 6 is subtracted, the answer is 42.


13

2 103 17/02/2017 4:00 PM

UNIT 175

UNIT 176


Problem solving (3)

Problem solving (4)

1 Matches are used to form triangles in a line, as shown: Find how many matches would be needed to form:

a 3 triangles c 5 triangles e 15 triangles

b 4 triangles d 10 triangles f 50 triangles

a multiply 3.2 by 15 b square 14 and subtract 50 c multiply 72 by 7.5 d square 19 and divide by 10 e divide 194 by 13 f multiply 2.5 by 70 and add 17 3 a A school fete raised $329, $527 and $452 from three different stalls. How much was raised altogether?

b Was the total more or less than $1000? c By how much? d If the school needed to raise $2000, how much more did they need?

e A fun run was held and 30 students raised $20 each. How much was raised altogether?

f Did the stalls and the fun run raise the $2000? 4 Using intervals, how many can be joined together in each of the following? a b c

d

e

1 Matches are used to form squares in a line, as shown:

Find how many matches are needed to form:

a 3 squares c 5 squares e 20 squares

2 Complete:

f

6 7 8

Find how many matches would be needed to form 100 triangles in a line as in question 1? Divide 200 by 7. How much more money did the principal need to add to make the $2000 in question 3? How many intervals can be drawn for 10 dots?

9 Here is part of a receipt from the school fete. What was the total cost of the items? What was the GST component?

book pens food

$16.99 $6.95 $12.95 $36.89


a 2 hours b 4 hours c 10 hours Find how long does it take to lay:

d 1032 bricks e 1462 bricks f 2580 bricks 4 Find how many 3-digit numbers can be made from the following if each digit may be used only once:

b 3, 7, 6 d 1, 4, 2, 3 f 1, 9, 3, 8, 6

5 How many matches are needed to form 85 squares, arranged as in question 1? 6 For the difference of 11, find the two numbers that give the product 476. 7 Find how much does it cost to lay 500 bricks if the bricklayer is paid $80 per hour in question 3.

8 Find how many 2-digit numbers can be made from 7 and 3 if each digit may only be used once. 9 Find the pattern and calculate the number of bricks in the tenth row.

Total includes GST of $2.62


104

b 4 squares d 10 squares f 60 squares

3 A bricklayer lays 172 bricks each hour. Find how many bricks are laid in:

a 2, 4, 7 c 1, 7, 5, 2 e 1, 2, 3, 4

2 For each difference, find the two numbers that have the product: Difference Product 65 1750 a 58 1863 b 15 1134 c 13 8330 d 63 3700 e 64 3366 f

5



☞

Answers on page 151

See START UPS page 1 REVIEW TESTS: Units 1 – 8

UNIT 1 Unit 1 Numbers to 99 999 (1) Unit 2 Numbers to 99 999 (2) Unit 3 Place value 0 to 99 999 (1) Unit 4 Ordering numbers


1 The value of the underlined digit in 43 219 is:

A 3 tens C 3 hundreds

A 53 206

2 Q2 3 Q3

B 52 600

C 53 260

H

T

A 4619 A 805

1 Q4 4 Q1

+

+

+

85 325

86 147

85 981

11 Circle the numbers larger than 62 000 but less than 62 500:

62 498

3 Q2 4 Q2

63 001 62 947 62 385

12 Which of these numerals does not represent 5106?

8 Circle the number between 86 496 and 86 600.

U

A 5000 + 106 C 5106 units

1 Q2 2 Q2 2 Q3

B 5000 + 100 + 6 D five thousand, one hundred and sixty Score =

☞ Answers on page 152 © Pascal Press ISBN 978 1 74125 262 0

7 Q4

D 54 6 Q1 7 Q2 5 Q2 6 Q2 7 Q3 5 Q4

461 905

8 Q2 5 Q3 7 Q1

U

2 Q3

6 Q4

86 454, 86 610, 86 521, 86 705 9 Use the set of digits to write the largest possible number in digits:

T

T

3 Q4 H

H

2 Q4

86 937

TTh Th

C 80

7 Write 107 648 on the place value chart.

3 Q2

10 Write 20 000 + 4000 + 300 + 20 + 1 on the place value chart.

B 5

6 Complete with < or > 462 107

+

9 Circle the largest number:

C 46 019 D 46 190

HTh TTh Th

8 Expand: 84 229

B 460

UNIT 5 Q1 8 Q1

U

The value of the underlined digit in 1460.17 is 7 hundredths.

7 How many thousands are there in 2476?

T

5 Write 104 381.25 in words.

2 Q2

6 Write 20 709 in words.

H

4 True or false?

4 Q3

5 Write the set of numbers in ascending order: 51 204, 51 098, 51 725, 51 217

Th

3 True or false? 41 609 > 41 610

U

4 True or false? 81 076 > 80 176

TTh

2 The number of thousands in 805 429 is:

1 Q1 2 Q1

The numeral of is 3617. TTh Th


1 The number represented on the abacus is:

D 53 060

3 True or false?

UNIT 1 Q3

B 30 thousands D 3 thousands

2 Fifty-three thousand, two hundred and sixty written as a numeral is:

Unit 5 Place value 0.01 to 99 999 Unit 6 Place value 0 to 99 999 (2) Unit 7 Numbers to 999 999 (1) Unit 8 Numbers to 999 999 (2)

8 Q4

one, six, three, four, eight and seven

10 Circle the numeral that matches:

forty-two thousand, five hundred and ten

42 501

42 510

420 510

11 A five placed in the thousands column has more or less value than a nine in the hundreds column? 12 If I move a digit from one column to the column next to it on the left, I increase times. its value

/12 Review Tests


6 Q3 8 Q3

Score =

5 Q2 6 Q2 7 Q1 7 Q2 7 Q3 7 Q4 8 Q4 5 Q3 6 Q2 7 Q1 7 Q4 8 Q4

/12 105

REVIEW TESTS: Units 9 – 19 Unit 9: Number patterns (1) Unit 10: Expanding numbers Unit 11: Ordinal numbers Unit 12: Less than and greater than Unit 13: Number patterns (2) Unit 14: Roman numerals

page 21 page 21 page 22 page 22 page 23 page 23

UNIT 9 Q2

1 What number is 1000 more than 40 163?

A 40 263 C 39 163

B 4163 D 41 163

11 Q2

4 True or false?

21st is the position before 22nd. 12 Q4

5 Use < or > to complete:

93 290

40 + 2000 + 200 + 90 000

13 Q2

6 Write the rule for the number pattern: 4 101 , 3 108 , 3 105 , 3 102

10 Q1 10 Q3

16 Q3

5 Complete: 3 8 4 mL 1 1 6 mL + 4 0 7 mL

16 Q1 16 Q2 17 Q1 17 Q3

6 Complete the spaces: 7 8 4 9

18 Q2

2 3

8 0 5 15 Q1

16 Q4

10 Find the sum of $5386, $1076 and $1107.

18 Q3 18 Q4

10 Q4

9 What is the difference in value between the 2s in 20 246?

11 Q3 11 Q4

10 Complete: ,

, 3rd,

, 5th,

,

, 8th 12 Q3 12 Q4

11 Complete the following with < or > to make the statement true: twenty-nine thousand six hundred and eleven twenty-nine thousand six hundred and one

9 Q1 14 Q1 14 Q4

12 Complete the number pattern: L, LV, LX,

,

,

, Score =

1176 + 1180 = 8 Complete the table: + 4 6 1 8 3 7 4 5 1 0 7 9 Estimate, by first rounding each number to the nearest ten, the answer to: 873 + 289

4 True or false? 5 + 7 = 12 50 + 70 = 120 500 + 700 = 12 000

7 Use the concept of doubles to solve:

8 Write the numeral in words for: 80 000 + 6000 + 900 + 20 + 5

15 Q3

Finding 64 + 43 by the compensation strategy equals 107.

19 Q2

B 2331 D 2739

+

9 Q3 9 Q4

7 What is the 10th term of the number pattern starting at 5 and counting by sevens?

B 3350 D 3250

3 True or false?

24 710 = 20 000 + 400 + 70 + 1

UNIT 17 Q2

2 4863 plus another number total 6592. The other number is:

10 Q2

3 True or false?

A 2250 C 3360

A 1729 C 10 445

B 610 D 565

page 24 page 24 page 25 page 25 page 26

1 The sum of 1463 and 1897 is:

14 Q1 14 Q2

2 The number for the Roman numeral DCX is: A 570 C 551

Unit 15: Addition review Unit 16: Adding 3-digit numbers Unit 17: Adding to 9999 (1) Unit 18: Adding to 9999 (2) Unit 19: Adding large numbers

11 Find the total cost of 3 people going on a holiday to New Zealand at a cost of $2385 per person.

17 Q1 18 Q1 19 Q3

12 Find the total cost of the house if: land = $35 010 house = $256 149 garden = $26 147

17 Q1 19 Q4

/12 Excel Start Up Maths Year 5


17 Q4


Score =

/12 ☞ Answers on page 152

REVIEW TESTS: Units 20 – 29 Unit 20: Mental strategies for addition Unit 21: Subtraction review Unit 22: Mental strategies for subtraction Unit 23: Rounding numbers (1)


1 757 rounded to the nearest hundred is: A 850 B 750 D 800 C 700

UNITS 23 Q1

2 700 + 800 = A 150 C 15 000

20 Q1

22 Q1

4 True or false? 4876 rounds to 4900 to the nearest hundred.

21 Q3 21 Q4

6 Check the addition with subtraction: 4 7 9

20 Q4 22 Q4

– 2 4 8

+ 2 4 8

3 True or false? The difference between $9865 and $7384 is $2481.

25 Q2 27 Q2

28 Q1 4 True or false? 375 + 246 can be estimated to be 600 when each number is first rounded to the nearest 10.

5 Complete: 4 6 8 1 9 – 2 4 7 4 3

26 Q1 27 Q1

6 Find the missing values: 4 3 1 6

25 Q3

7 Find the answer to: and round to the nearest ten.

23 Q4

20 Q2

467 + 19 + 32 21 Q2

51

11 True or false? When rounded to the nearest thousand, 14 876 > 14 299

23 Q2

12 Draw a number line and use the jump strategy to complete: 187 + 19 – 28

20 Q2 22 Q2

Score =


4

5

1

4 6 4 9 – 2 4 8 7


1479 + 1326

– 197 185 216 410

D 3023

29 Q1

831 and 97.

10 Complete:

C 3033

UNITS 24 Q2

2 17 656 rounded to the nearest 500 is: A 17 500 B 18 000 C 17 000 D 17 700

21 Q3

9 Use the jump strategy to complete:


– 2

8 Round each number to the nearest hundred and then complete the estimate to:

23 Q1 23 Q3

5 Complete: 5 6 9 – 3 8 7

7 Find the difference between

1 4000 – 967 = A 2033 B 4033

B 1500 D 5600

3 True or false? 700 – 386 = 414

Unit 24: Subtraction to 9999 (1) Unit 25: Subtraction to 9999 (2) Unit 26: Subtraction to 99 999 (1) Unit 27: Subtraction to 99 999 (2) Unit 28: Estimation Unit 29: Rounding numbers (2)

– 2000 3000 4000 5000 6000 1426

28 Q2

24 Q3 27 Q3

25 Q4 9 One box held 4873 pins and a second box held 7439 pins. What was the difference in the number of pins in the boxes?

10 Find eight thousand, seven hundred and two minus two thousand, eight hundred and eighty-five

25 Q1 25 Q2 25 Q4 27 Q2

11 Round each number to the nearest thousand to estimate the total cost of: $4789 + $3211 + $8604 + $2936

28 Q4 29 Q3

12 Which two of the following numbers will add to 28 Q3 , give approximately 6000? 4576 5431 2981 1424 2890 3721

/12 Review Tests


Score =

/12 107

REVIEW TESTS: Units 30 – 41 Unit 30: Tables (1) Unit 31: Tables (2) Unit 32: Tables (3) Unit 33: Tables (4) Unit 34: Multiplication by tens and hundreds Unit 35: Multiplication to 999 Unit 36: Multiplication to 9999

page 31 page 32 page 32 page 33 page 33 page 34 page 34

UNITS 30 Q2 30 Q3 32 Q1 33 Q2 31 Q4

1 3 3 8 = A 28

B 32

C 26

D 24

2 The number of legs on 7 octopuses is: A 49

B 56

C 42

Unit 37: E xtended multiplication (1) Unit 38: E xtended multiplication (2) Unit 39: Multiples and square numbers Unit 40: Factors Unit 41: M ultiplication and problem solving

3 True or false?

A 350 C 1545

B 1525 D 1725 39 Q3

2 10 squared = A 12

B 50

31 Q3 32 Q3

3 True or false?

34 Q2 34 Q3

4 True or false?

C 100

4 3 120 = 2400 5 Find: 2 7 4 3 4

35 Q3 36 Q1

6 Complete:

31 Q3 33 Q3

38

=

= 10 3 4

7 Find the total cost of 4 books at $6 each and 3 videos at $20 each. 8 Find twenty-six multiplied by thirty.

34 Q4

9 Complete:

34 Q1 34 Q2 34 Q3

10 Find the product of 1210 and 6. 11 Complete:

3

5

= 40 3 4

7

8

12

15

The first five multiples of 6 are: 6, 12, 24, 48, 96 5 Complete: 4 1 7 3 3

37 Q2 38 Q1

6 Multiply 43 by 4.

39 Q2 40 Q2 40 Q1 40 Q3

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20

36 Q2 36 Q4

32 Q4 35 Q2

10 Find: 42 + 32 =

39 Q3 40 Q4 37 Q3

11 Find the multiple: 34 Q3 35 Q1 35 Q2 35 Q4 36 Q3

72 432

49 294

22 132 41 Q1

12 Find the error in: 426 3 7 = 2973



15 90

Score =

108

41 Q3

37 Q4 38 Q4 41 Q2

3

3 3 $148 pairs of shoes 4 3 $35 T-shirts 1 3 $80 pants

2 3 1 4 2 3 1 4 + 2 3 1 4

9 How many days are there in 12 weeks and 4 days?

40


39 Q1

8 Write a multiplication equation from the addition and solve:

=

37 Q1 38 Q3

7 Circle the factors of 30:

33 Q4

20 3

D 20

4 6 3 7 3 0 2

4 3 10 = 7 3 7 4 True or false?

UNITS 38 Q2

1 The product of 5 and 345 is:

D 54



Score =


REVIEW TESTS: Units 42 – 50 Unit 42: Division Unit 43: Division of 2-digit numbers (1) Unit 44: Division of 2-digit numbers (2) Unit 45: Dividing numbers containing zeros Unit 46: Divisibility


A 13

B 15

C 18

D 14

A 90

B 189

C 270

42 Q1

46 Q1

43 Q2 44 Q2

4 96

B 9 D 8 48 Q3

904 ÷ 8 = 112

1

0

9

45 Q4

7 ___ ___ ___

47 Q4

312 books shared among 4 schools is 78.

5 876

756 ÷ 7 =

b4

c8

42 Q1 42 Q2 42 Q3

6 7098 47 Q3

7 Find:

9 What is the value of the remainder of:

50 Q2 50 Q3

6 Find:

a2

48 Q2

5 Complete:

44 Q3 45 Q2

7 Find the following:

45 Q3

481 ÷ 7 = 8 Find five hundred divided by six.

48 Q4

9 Divide:

49 Q1 49 Q2 49 Q3

8 721

10 There were 728 pencils to be placed in 4 containers. How many pencils were there in each container?

44 Q4 45 Q1

(100 + 49) by 10

50 Q1

10 Halve 4234.

46 Q3

11 Write a multiplication fact from:


6 84

45 Q1

12 Circle the division which has the larger answer: 45 Q3 5 520

50 Q4


8 Divide 272 by:

UNITS 49 Q4

D $16.50

4 True or false?

5 Complete:

127 is divisible by 3.

C $1.65

3 True or false?

4 True or false?

A 7 C 4

96 divided by 2 is 48.

B $16.00

2 Which of the following numbers is a factor of 702?

D 171

3 True or false?

A $17.00

46 Q2

2 The number which is divisible by 7 is:


1 Find how much it is for one, if 10 items cost $165.

UNITS 43 Q4

1 98 tools shared by 7 builders is:

Unit 47: D ivision of 3-digit numbers (1) Unit 48: D ivision of 3-digit numbers (2) Unit 49: Division by tens Unit 50: D ivision of 4-digit numbers

3 6

47 Q2

9 ___ ___ ___

12 Find how many groups of 7 total 987.

47 Q1 48 Q1

8 848 Score =


/12 Review Tests


Score =

/12 109

REVIEW TESTS: Units 51 – 59 Unit 51: Number lines Unit 52: Inverse operations and checking answers Unit 53: Number lines and operations Unit 54: Averages (1) Unit 55: Averages (2)


A 45

B 40

C 50

D 90

x

A 4 12

3

➤

2

4

B 3

5

6

D 3 12

C 4

52 Q3

A 39

54 Q2 55 Q1

D 20

B 49

56 Q1

C 32

D 25 56 Q2 58 Q1

58 Q3

(4 3 8) – (48 ÷ 4) = 20 5 Find:

5 Label each of the values on the number line: 22 14 , 21, 21 12 , 23 34 21

C 18

4 True or false?

The average of 14, 16, 18 and 20 is 18.

B 2

10 3 8 ÷ 20 = 4

92 + 48 is more than 130. 4 True or false?

A 72

3 True or false?

3 True or false?

UNITS 56 Q3 57 Q2

2 50 – 18 + 7 =

2 The value of the letter x on the number line is: 51 Q1


1 60 ÷ (5 3 6) =

UNITS 54 Q1

1 The average of 40 and 50 is:

Unit 56: Order of operations (1) Unit 57: Order of operations (2) Unit 58: Order of operations (3) Unit 59: Operations with large numbers

22

23

51 Q2 51 Q3

24

6 Use multiplication to check the equation: 68 ÷ 4 = 17

52 Q2

7 Draw a number line to show: 527 – 36

53 Q2

59 Q1

6 7 2 4 1 8 6 3 8 + 4 1 2 5 8

6 Find: 8 2 1 0 3 7

59 Q3

7 What is the total number of students if there are 3 grades with 24 students, 4 grades with 22 students and 2 grades with 26 students?

57 Q4

8 Find one hundred and fifty minus (thirty-one plus sixteen) and then add twenty-eight.

56 Q4 57 Q3

52 Q4

8 Find the value of the * in:

21 – * ÷ 2 = 6

*= 54 Q4 55 Q4 55 Q2

9 Find: 12 000 – 7289

59 Q2

10 Estimate the value marked on the number line:

51 Q1 51 Q4

10 Put in the brackets to make the equation true:

57 Q1

➤

9 Four bags of potatoes weighed 2.4 kg, 2.6 kg, 1.7 kg and 2.3 kg. What was the average weight of the bags?

1500

8 3 12 – 5 ÷ 2 – 9 = 19

2000

52 Q1

11 Write the addition equation which is used to check: 1 4 8 – 7 2 7 6 12 Write an equation for the following number line: 53 Q4

6

8

10

12

14

16

Score =

11 Find how many groups of 3 fit into 3927.


56 Q1 58 Q2

12 Complete:

14.8 + 21.7 – 3.8 ÷ 2 =


110

59 Q4


Score =


REVIEW TESTS: Units 60 – 66 Unit 60: Working with numbers Unit 61: Missing numbers Unit 62: Change of units Unit 63: Reasoning with numbers Unit 64: Negative numbers


UNITS 60 Q2

1 The missing number in 3 3 62 = 250 –

m –5 A 4000 –20–15–10 C 40 000 m

15 20 25D3064 5 C 1056

–20–15–10 –5 0 5 10 15 ºC 62 Q1 63 Q2

15400 20 25mm 30 0 5 10 B ºC

ºC

is 12. –20–15–10 –5

= 12

0 5 10 15 20 25 30

9.25 multiplied by 25 = 231.25 66 Q4

4 True or false?

289 = 6 1 7 2 8

64 Q3 ºC

Number sentence

–20–15–10 –5 0 5 10 15 20 25 30 + 246

ºC

168 785 + 137 287 – 152

ºC

65 Q2

62 Q3

Estimate

Actual

ºC 60 Q4

420 830 140

6 List all the factors of 400.

66 Q2

7 Find 729 divided by 5.

66 Q3

8 If the product of three numbers equals 126, circle the three numbers from the list:

65 Q3

10 4 9 . 7 61 Q2

8 Find the missing information: is four hundred

twenty multiplied by

9 Complete with < or > to make the number sentence true:

62 Q2

63 Q4

2, 3, 4, 5, 6, 7, 8, 9 9 Find: (10.7 – 8.5) 3 3.7 + 2.8

65 Q1

10 Find the answer to: 46 3 21 + 19

65 Q2

3600 seconds

10 Complete:

8 3 7 = 8 3 (

+

)=

11 Write the answer to: 64 Q4

11 Find: 10 – 7 + 3 – 6 = 12 Write a multiplication equation for the array:

63 Q3

66 Q4

9 9875

12 Change the fraction 58 to a decimal:

3

=

or

3

= =

ºC


66 Q1

–20–15–10 –5 0 5 10 15 20 Score 25 30


Difference

–20–15–10 –5 0 5 10 15 20 25 30

30

ºC

hours

65 Q4

false?

5 Complete:

–20–15–10 –5 0 5 10 15 20 25 30

1 12

B 42 D 406

–20–15–10 –5 0 5 10 15 20 25 30

ºC 5 Colour the thermometer to show –8ºC.

1500 6 Change –20–15–10 –5 g0to 5kilograms. 10 15 20 25

65 Q1

C 2

61 Q3

The missing number in 144 ÷

B 0.5 D 0.44

2 14 3 28 =

–20–15–10 –5 0 5 10 153 20 True 25 30 or

4 True or false?

A 2.25 20 C 25 4.4 30

ºC

4.81 3 10 = 481 ºC

UNITS 66 Q1

=

60 Q3

–20–15–10 –5 0 5 10 15 20 25 30

4 9

–20–15–10 –5 0 5 10 15 30 20 A25392

D 40 mm

3 True or false?

7 Find:

1

ºC

2 4 km equals:

is:

–5 0 A 36–20–15–10 B 46

Unit 65: C alculator – addition, subtraction and multiplication page 49 Unit 66: Calculator – division page 49

/12 Review Tests


–20–15–10 –5 0 5 10 15 20 25 30

Score =

/12 111

REVIEW TESTS: Units 67 – 72 Unit 67: Fractions Unit 68: Fraction of a group Unit 69: Comparing fractions

1 The fraction of 2

A

1 2

1 4

of 12 is:

B

A9

1 4

page 50 page 50 page 51

UNITS 67 Q1

that is shaded is: C

3 8

4 6

B3

C4

D 6 69 Q3

3 10

67 Q4

4 9

4 9

4 9

67 Q3 69 Q1

b 29

4 9

4 9

4 9

4 9

4 9

9 10

7 Colour

A

3 5

8 9

15 5

10 12

B

=

17 5

C

D

13 5

70 Q1

C

1 2

D

10 18

70 Q3

6 5

72 Q4

represents 2 12

5 Write

c 13

9 4

71 Q3

as a mixed number.

6 Write the smallest equivalent fraction for 69 Q2

7 5

67 Q4

of the shape:

10 20 .

71 Q2

on the number line. 1

2

3

71 Q1 72 Q4

8 Shade the shapes to show 83 :

67 Q1

8 What fraction of the grid has been shaded?

9 Express 69 Q2

9 Circle the fraction with the least value:

6 10

66 100

71 Q3 72 Q2

as a

mixed number.

70 Q1

10 Write three equivalent fractions for:

6 100

10 Circle 14 of 20:

70 Q2 70 Q4

7 Label

1 2

3 10

3 10

9 9

6 Order the set of fractions from smallest to largest: 4 10

B

4 True or false?

4 9

a 49

shaded is:

5 Label each of the following fractions on the number line:

10 5

3 True or false?

4 True or false?

A

2 Which of the following is an equivalent fraction of 56

8 10

1.35

5 Circle the smaller decimal in the pair: 6 Circle the pair of fractions from the list that could be added to give the answer 58 :

UNITS 76 Q2 77 Q2 79 Q3 80 Q3

76 Q3 80 Q2

4 True or false?

5 Complete the diagram to show: 2 –


B 19.25 D 14.30

3 True or false?

4 True or false?

A 5 hundredths C 5 units

75 Q2

3 True or false?

1 The value of the underlined digit in 19.25 is:

=

3 4

Unit 76: D ecimal place value – hundredths Unit 77: Decimals Unit 78: Comparing decimals (1) Unit 79: D ecimal place value – thousandths Unit 80: Comparing decimals (2)

4.6, 3.25, 3.9, 4.10

/12 Review Tests


Score =

/12 113

REVIEW TESTS: Units 81 – 88 Unit 81: Decimal addition (1) Unit 82: Decimal addition (2) Unit 83: Decimal subtraction (1) Unit 84: Decimal subtraction (2)


UNITS 84 Q1

1 4 – 2.65 =

A 2.35 C 0.45

B 1.45 D 1.35

A 4.31 kg C 6.33 kg

83 Q1

81 Q1 81 Q4 82 Q1

5 Complete:

6 Find: $ 2 4 . 9 0 – $ 1 7 . 2 5

83 Q2 84 Q2 84 Q3

6 Find:

7 Find the difference between: 70 and 56.85

83 Q3 84 Q1

9 Complete:

83 Q4 84 Q1

– 2.36

4

5

8

10

11 Circle the three numbers which add to give 11.76:

81 Q3 82 Q1

8.52

7.39

1.72 82 Q2 82 Q4

$12.55

$4.65

Score = © Pascal Press ISBN 978 1 74125 262 0

86 Q2 87 Q2

85 Q1

7 Write an equation and solve it for: 9 groups of 14.43 8 If Jodie had a 27.5 kg box of fruit, how much would each bag weigh if the fruit was divided into 5 equal bags?

86 Q3

9 Find $8.76 divided by 4.

86 Q4

10 What is the total of three groups of 1.6 and two groups of 4.2?

85 Q1 85 Q2

11 Round the answer to one decimal place.

86 Q1 87 Q2 88 Q1

12 Complete the equation $60.00 – (2 3 $21.87) and round the answer to the nearest 5c.

85 Q4 88 Q4


114

85 Q3

4 . 8 6 3 6


$29.95

87 Q4

84 Q4

2.65

3 1.92

81 Q3 82 Q1

85 Q2 87 Q1

0.26 ÷ 10 = 0.026

5 Find: 8 . 2 3 + 3 . 1 7

8 Find the total of: 6.9 + 2.8 + 3.5

88 Q2

B 38 D 37.83

4 True or false?

10 George had $50 for the show. He spent $7.50 on rides and $9.75 for lunch. How much did he have left?

A 37.82 C 37.8 3 True or false? 4 . 9 3 3 1 2 . 7

5.8 + 6.7 = 12.4

B 96.7 D 0.0967

2 37.825 rounded to one decimal place is:

81 Q2

4 True or false? 1 4 . 6 – 2 . 8 1 1 . 8

UNITS 87 Q3

A 9670 C 967

3 True or false?

82 Q3 82 Q4

B 6.34 kg D 5.85 kg


1 9.67 3 100 =

2 The sum of 2.46 kg, 1.85 kg and 2.03 kg is:

Unit 85: Decimal multiplication Unit 86: Decimal division Unit 87: D ecimal multiplication and division Unit 88: Rounding decimals


Score =

/12

☞ Answers on pages 153–4

REVIEW TESTS: Units 89 – 94 Unit 89: Percentages (1) Unit 90: Percentages (2) Unit 91: Fractions, decimals and percentages

1

19 100


UNITS 90 Q1

written as a percentage is:

A 19%

B 9%

C 90%

D 0.19%

2 The percentage shaded of the square is:

A 48% C 52%

A 20

B 10

C 40

A $9.00 C $10.00

92 Q2

8 snacks costing $1.50 each could be bought with $10.00

Eighty percent written as a number is 8%.

4 True or false?

4 True or false?

36% 2100 kg 5 Round 2935 g to the nearest 100 grams.

149 Q1 149 Q2 150 Q3

7 Complete:

1500 g =

kg

149 Q4

152 Q3

6 How many kilograms in 4 12 t?

g=

kg

8 A crate can hold a mass of 5 kg. How many 150 Q4 boxes of 700 g can be packed into the crate?

148 Q2 148 Q4

8 Complete with > or < or = : 4 km2

146 Q2 146 Q3

9 Find the area of a small acreage 90 m 3 150 m.

149 Q2

9 Order the following from lightest to heaviest: 149 Q3

8m

10 Find the total area of:

150 Q2

3 True or false?

151 Q2

A 7 kg

6 If the area of a rectangle is 20 m2, find the breadth if the length equals 10 m.

3 cm 1.5 cm

4000 ha

D ha

4 True or false?

Ct

B kg

2 7 t is equal to:

143 Q3 144 Q1 145 Q1

Length


145 Q4

2m 2m

5m

3m 10 m

11 Adjust the statement if necessary: The paddock has an area of 4 ha2.

147 Q1 147 Q2 147 Q3 147 Q4

12 True or false? This square has an area of 4 m2. If I double the length of each side, I double the area.

144 Q2 144 Q4

Score =


2m

3 kg

2 kg 100 g

2.6 kg

150 Q2 150 Q3

2400 g

10 How many grams in 1 34 t?

152 Q3

11 An empty bucket weighs 463 g. When it is full of water it weighs 6.463 kg. What is the mass of the water in the bucket?

150 Q4

12 Balance the scales by colouring the masses.

150 Q4

165 g

2m

100 g 20 g

/12 Review Tests


50 g 10 g

Score =

5g

/12 121

REVIEW TESTS: Units 153 – 161 Unit 153: Capacity in mL and L (1) Unit 154: Capacity in mL and L (2) Unit 155: Cubic centimetres (1) Unit 156: Cubic centimetres (2) Unit 157: Cubic centimetres (3) Unit 158: Cubic metres


1 The most appropriate unit when measuring a small glass is:

A kL

B mL

CL

A 5 m3

B 5 m2

D 4 cm3 153 Q3

3 True or false? 6000 mL = 6 L 4 True or false? 110 cm3 would displace 110 L of water.

154 Q3 154 Q4 156 Q4

5 Find the volume of:

155 Q1 156 Q1 157 Q1

6 Order the capacities from smallest to largest: 154 Q1 3.3 L 3000 mL 330 mL 3.9 L

10 Find the total capacity of:

154 Q2

+

500 mL

+

400 mL

12 Volume = Capacity =

3 True or false? The chance that I will fly a plane next week is definite.

159 Q4 160 Q1

4 True or false? There is a 25% chance of spinning red on the spinner.

161 Q3 green

red blue

5 Describe an event with a probability of 0.4

160 Q3

6 What is the chance of spinning orange?

161 Q1 161 Q2

R

O

G

O

B

O Y

Y

8 In a box of 12 doughnuts there are 5 chocolate, 4 strawberry and 3 pineapple. Which flavour is the most likely to be selected?

159 Q2 160 Q2

9 Complete the diagram for tossing a coin two times:

161 Q4

10 In rolling two dice what are all the possible outcomes?

159 Q1 160 Q4

155 Q1 156 Q2

11 I put 6 black, 4 brown and 2 white balls in a bag. If I draw one ball out, what colour is least likely to be selected?

159 Q2 160 Q2

154 Q2 Q3 156 Q4 157 Q3 157 Q4

12 If G = green and R = red, label the spinner so that it is most likely to land on red.

161 Q1 161 Q2 161 Q3

2 cm 154 3 cm

Score =

4 cm



D 0.6

11 Draw a cube with a volume of 1 cm3.

122

C 0.2

159 Q1 160 Q4

8 What is the volume of a container with length 155 Q2 155 Q3 4 cm, breadth 3 cm and height 5 cm? 156 Q2 157 Q3 157 Q4

B 0.5

7 If I toss two coins, what is the chance of obtaining two tails?

9 What is the capacity in mL of a container 3 cm2 3 2 cm?

A1

155 Q4 156 Q2

7 Draw a prism 2 cm 3 2 cm 3 2 cm and find the volume.

200 mL

159 Q3

UNITS 159 Q4 160 Q1

2 An even chance is equal to: 158 Q4

C 4 m3


1 The chance the sun will set tonight is: A impossible B equal chance C unlikely D definite

D kg

2 The volume of a prism 1 m 3 2 m 3 2 m is:

UNITS 153 Q1

Unit 159: Chance (1) Unit 160: Chance (2) Unit 161: Chance (3)


G

Score =

R


REVIEW TESTS: Units 162 – 176 Units 162, 163: Picture graphs (1) & (2) Units 164, 165: Line graphs (1) & (2) Unit 166: Tally marks Unit 167: Reading graphs Units 168, 169: Column graphs (1) & (2) Units 170, 171: Surveys and collecting data (1) & (2)

1

represents the value: B 20

C 10

A 28

B 18

D9

Friday

C 23

Jan.

▼▼▼▼ Feb. ▼▼▼ March ▼ ▼ ▼ ▼ ▼ ▼ = 4 boats

No. of items

4 True or false? There are 60 items in 4 boxes.

Colour blue brown green grey

40 20 4

6

No. of boxes

168 Q4 169 Q1 169 Q3 171 Q3

No. 9 6 2 3

A

soft drink

C

166 Q1 171 Q1

D

Tally

Number

Count

8 What was the most common shape?

■ ▲ ●  Shape C B A 0 kg

9 What was the total mass of A and B?

5 kg

Temp. in ºC

10 For every 8 bottle caps collected, Alex is given a sticker. How many stickers did Alex receive? 11 What was the temperature at 10 am?

15 10

5 R

B

Score = © Pascal Press ISBN 978 1 74125 262 0

168 Q1 168 Q3 169 Q2 169 Q3 163 Q3

noon

10


168 Q1 168 Q3 169 Q2 169 Q3

164 Q4 165 Q2 167 Q2

20

8am

12 What was the total number of cars?

G

B 12

C

2 4

UNITS 174 Q1 176 Q4 173 Q3

D 34

3 True or false? The square of 20 less 40 equals 0.

175 Q2

4 True or false? 15 matches are needed to form 7 triangles in a row, :

175 Q1

6 Find the number that, when it is halved and seven is added equals 45.

172 Q1 172 Q2 172 Q3 173 Q1

7 Find two numbers that give the product of 84 174 Q3 176 Q2 and have a difference of 5.

  juice  water 

B

A 14

5 Find the mean of Helen’s quiz scores: 9, 10, 6, 8, 5, 7, 3, 6, 10, 9

167 Q4

6 Here is a breakdown of people’s favourite drink. If the total number of people asked was 40, how many people preferred milk? 7 Complete the tally table:

162 Q1

164 Q4 165 Q4

60

2

5 Construct a column graph of coloured eyes in a class.

2 The value of ▲ in 2 – ▲ = 1 14 is:

D 22

3 True or false? There were 16 boats at the harbour in January.

1 The number of different 2-digit numbers that can be made from 1, 3 and 5 is: A 3 B 6 C 7 D 8

166 Q2 166 Q3

Thurs.


ilk

A 8

2 How many lunches were ordered on Friday?

UNITS 166 Q1 171 Q1

Unit 172: Mean Unit 173: Problem solving (1) Unit 174: Problem solving (2) Unit 175: problem solving (3) Unit 176: Problem solving (4)

m

page 97, 98 page 98, 99 page 99 page 100 page 100, 101 page 101, 102

W

Y

168 Q1 168 Q3 169 Q2 169 Q4

8 Write the rule that gives the number of matches that are needed to form six squares in a row, arranged: ■■■

176 Q1

9 Draw a number line to find the numbers that are more than two units away but less than six units from the number 10.

173 Q4

173 Q2 173 Q3

10 Find the value of ▲ if * = 10: ▲ ÷ 2 + * = 35 11 Find the mean cost of the items on the receipt.

book $12.50 pencils $9.70 CDs $10.30 paints $5.50

12 A brick layer lays bricks in a straight line. aH ow many faces are visible if there are 20 bricks in the line? b How long does it take for the bricks to be laid if the bricklayer lays 100 bricks per hour?

/12 Review Tests


Score =

172 Q4

176 Q3

/12 123

ANSWERS: Units 1 – 6 Unit 1

Page 17

Unit 2

Page 17

1 a 42 815 b 36 741 c 80 240 d 78 325 e 10 416 f 98 759 ● 2 a 83 563 b 25 915 c 37 345 d 40 791 e 15 096 ● 3 a 3 3 100 b 6 tens c 4 3 10 000 d 5 units e 6 3 1000 f 1 ten ● 4 a 23 815, 38 521, 41 672 f 10 150 ● b 11 085, 12 346, 61 460 c 45 118, 46 825, 47 325 d 61 460, 62 000, 63 051 e 51 001, 51 045, 51 437 5 87 650 ● 6 63 049 ● 7 8 3 100 ● 8 60 476, 61 059, 61 738 ● 9 2148 f 71 185, 73 215, 76 459 ● 2 a twelve thousand and fifty-two ●1 a 43 205 b 17 498 c 63 452 d 11 020 e 40 069 f 53 200 ●

b thirty thousand, nine hundred and six c eleven thousand and forty-two d forty-seven thousand, six hundred and thirty-five 3 a 72 345 b 58 698 c 60 473 d 20 895 e 11 212 e ninety thousand and twenty f seventy thousand, one hundred ● 4 a 8 thousands b 8 hundreds c 8 units d 8 tens of thousands e 8 tens f 8 units ● 5 17 685 f 35 502 ● 7 23 506 ● 8 8 thousands ● 9 37 859 ●6 seventy-two thousand, one hundred and five ●

Unit 3

1 ●

Page 18 c

d

16 000

f

a

b

16 500

e

2 a 29 006 b 85 321 c 91 151 d 29 462 ●

17 000

e 80 476 f 42 119 ● 3 a 23 000 b 52 016 c 70 403 d 85 009 e 13 100 f 65 099 3652 3789 3850 5 ●4 Number TTh Th H T U ● 3 689 3 6 8 9 a 3600 3700 3800 3900 1 072 1 0 7 2 b 56 5 6 ● c 6 17 852 ● 7 80 900 ● 8 Number TTh Th H 12 850 1 2 8 5 0 d 58 361 5 8 3 ● 9 12 358, 12 385 e 36 759 3 6 7 5 9 f 17 895 1 7 8 9 5

Unit 4

Page 18

Unit 5

Page 19

T 6

U 1

1 a 15 046, 16 487, 17 382, 18 589 b 21 049, 22 475, 23 468, 24 480 c 37 672, 37 989, 38 049, 38 115 ● d 42 346, 42 675, 42 758, 43 981 e 84 201, 84 256, 84 265, 84 296 f 66 357, 66 375, 66 537, 66 735 2 sample answers: a 61 000 b 62 000 c 63 000 d 61 500 e 63 900 f 64 999 ● 3 a< b< c< d> e> f> ● 4 sample answers: a 91 000 b 91 500 c 92 000 d 92 500 e 94 000 f 94 500 ● 5 14 281, 24 256, 40 879, 41 256 ● 6 sample answers: 10 470, 10 480 7 > 8 sample answers: 24 000, 24 800 9 13 957, 93 157 ● ● ● ● 1 a 41.63 b 29.05 c 84.76 d 10.52 e 15.70 f 3.98 ● 2 a 7 tenths b 1 unit c 1 ten d 8 hundredths e 6 hundredths ● 3 H T U . Tth Hth ● 4 a one hundred and five, point six seven b thirty thousand, and eighty, point two f 1 hundred ● 1 2 1 1 8 2 0 1 5

Unit 6

4 9 5 0 0 6

. . . . .

3 5 3 0 9

6 9 3 6 9

two c one thousand and forty-six, point one d eight hundred point four six e ninety-nine, point nine eight f forty-six thousand and fifty, point zero three 5 42.36 ● 6 1 thousand ● 7 ● H T U . Tth Hth 8 2 5 .

4

9

8 four thousand and six, point nine five ● 9 one thousand, two hundred and nine, point eight five ●

Page 19

1 a true b false c false d true e true f true ● 2 a 8 thousands b 8 tens of thousands c 8 tens d 8 units e 8 hundreds ● 3 a 21 306 b 60 195 c 11 080 d 46 520 e 90 055 f 38 198 ● 4 sample answers: a 48 326 b 48 426 f 8 thousands ● 5 false ● 6 8 hundreds ● 7 15 111 ● 8 sample answers: 68 750, 68 790 c 48 906 d 48 900 e 48 500 f 48 550 ● 9 a 10 000 b 1000 ●





1 ●

a b c d e f

Page 20

HTh TTh 2 1 5 9 0 5 3 7 9 4 0

Unit 8 1 a ● HTh

Th 9 0 3 6 0 0

H 2 0 0 4 0 2

Page 20

TTh

Th

H

2 a true b false c false d true e true f true ● 3 a 2 thousands b 8 units U ● 6 c 1 ten d 8 hundreds of thousands e 4 tens of thousands f 5 thousands 4 a 21 thousands b 326 thousands c 805 thousands d 46 thousands 0 ● e 8 thousands f 0 thousands 5 Th H T U ● HTh TTh 5 4 7 3 8 9 1 0 1 ● 6 false ● 7 7 tens of thousands ● 8 107 9 a 149 180 b 5879 c 245 428 12 or 245 428.5 6 ●

T 0 0 1 0 1 9

b T

U

d

c HTh

TTh

Th

H

T

U

e HTh

TTh

Th

H

T

U

HTh

TTh

Th

H

T

U

HTh

TTh

Th

H

T

U

f HTh

TTh

Th

H

T

U

2 a< b>cb< ●

b 1 3

2 3

d

2 1 5 7

1

4

7

9

2 3 4

6 ●

f 1 5 3 , 12

,

7 12

,

3 4

7 ●

1

Page 51

2 a 34 b 34 c 14 d 45 e 23 f 13 ● 3 a true b false c true ● 2 4 4 4 examples: a 14 b 12 c 10 5 23 , 46 ● 6 13 ● 7 false ● 8 example 28 ● 9 9 ● 16 d 6 e 5 f 10 ●

b 24 , 36 , 48 , c 13 , 39 d

d false e false f true Unit 71

7 1● 8 3● 9 6 bars ●

e

3 4

1 2

6 1 12 , 2

6 ●

c>d< e> f< c

1 4

Unit 70

2 3

2 a 4 , 2 , 4 , 1 b 8 , 2 , 8 , 8 c 10 , 10 , 10 , 10 d 5 , 5 , 5 , 1 ●

2

1 1 1 7 10 , 5 , 2 , 10

0

1 a ●

e

1

e 18 , 38 , 12 , 34 f

5 ●

=

f

Page 51

c

4 a ●

6 9

e

6 2 15 , 5

e

2 1 16 , 8

f 36 ,

6 12

Page 52

1 a 54 b 52 c 158 d 114 e 156 f 53 ● 2 a 75 b 125 c 155 d 85 e 135 f 165 ● 3 a 1 14 b 1 25 c 1 13 d 1 103 e 1 28 = 1 14 f 3 12 ● 13 13 4 a 85 b 94 c 53 d 33 5 138 ● 6 33 , 53 ● 7 1 45 ● 8 73 ● 9 various ● 10 e 6 f 8 ●

Unit 72 1 a ●

Page 52

b

c

d

e

21 11 9 2 a 2 25 b 2 23 c 1 16 d 1 24 = 1 12 e 1 45 f 1 48 = 1 12 ● 3 a 194 b 115 c 37 4 a 54 b 53 c 176 d 75 ● 10 d 8 e 16 f 2 ●




f

ANSWERS: Units 72 – 79 e

7 2

f

11 4

5 ●

Unit 73

6 2 14 ● 7 258 ● 8 138 ● 9 11 sixths ● Page 53

1 a 56 b 45 c 24 = 12 d 78 e 107 f 57 ● 2 a 68 = 34 b 55 = 1 c 109 d 34 e 36 = 12 f 129 = 34 ● 3 a 108 = 1 28 = 1 14 ● 1 6 8 2 1 6 1 b 54 = 1 14 c 11 4 a 15 + 25 b 122 + 125 c 103 + 104 d 15 + 35 e 104 + 105 10 = 1 10 d 3 = 2 e 6 = 1 6 = 1 3 f 5 = 1 5 ● f 122 + 123 ● 5 58 ● 6 56 ● 7 106 = 1 46 = 1 23 ● 8 36 + 26 ● 9 15 + 15 + 15 = 35

Unit 74

Page 53 3

3

3

1 a 1 13 b 2 14 c 35 d 1 38 e 1 16 f 2 12 ● 2 a 26 = 13 b 13 c 105 = 12 d 122 = 16 e 14 f 15 ● 3 a 34 b 3 4 c 2 4 d 1 4 ● e 2 14 f 1 14 ● 4 a 127 – 122 b 109 – 104 c 45 – 35 d 109 – 107 e 35 – 15 f 127 – 124 ● 5 2 23 ● 6 58 ● 7 1 23 ● 8 56 – 36 ● 9 45

Unit 75 1 a ●

Page 54

3 7 2 a 3 45 b 2 46 = 2 23 c 109 d 3 11 3 a 1 b 35 c 36 = 12 d 78 ● 12 e 1 4 f 2 8 ● e 107 f 11 4 a 24 = 12 b 23 c 102 = 15 d 58 e 35 f 127 ● 5 77 = 1 ● 6 2 109 ● 7 78 ● 8 103 ● 9 a 13 b 1 14 12 ● 2 3

b

7 12

5 6

c

d 48 = 12 e 1 f

Unit 76

Page 54

Unit 77

Page 55

7 10

1 a 3.32 b 4.63 c 5.09 d 3.15 e 7.11 f 4.2 ● 2 a 5 hundredths b 3 tenths c 9 units d 6 tenths e 2 hundredths f 1 unit ● 3 a false b true c true d false e false f true 4 a, c, f, d, b, e ● 5 3.25 ● 6 1 tenth ● 7 true ● 8 b, c, a ● 9 0.76 ● ● 1 Units . Tenths ● 0 . 3 1 . 1 2 . 6 1 . 0 3 . 1 4 . 7

Unit 78

1 a ●

T

2 a 5 tenths b 9 hundredths c 2 units d 5 hundreds e 1 hundredth f 1 hundred Hundredths ● 3 a 238.43 b 423.31 c 467.27 d 356.5 e 214.8 f 207.32 ● 4 a 2461 b 3478 ● c 1107 d 4869 e 4310 f 634 ● 5 Units . Tenths Hundredths 4 1 . 0 7 6 7 tens ● 7 321.06 ● 8 146 ● 9 a Tess b Harry ● 9 7 8

Page 55

U

• Tth

b

c

Hth

T

d

U

• Tth

Hth

e T

U

• Tth

T

U

• Tth

Hth

T

U

• Tth

Hth

f

Hth

T

U

• Tth

Hth

2 a ●

cbf> ● 4 ●

Fraction 4 10 3 4 7 25 3 5 11 20 23 50

a b c d e f

100 40 100 75 100 28 100 60 100 55 100 46 100

Decimal

Percentage

0.45

40%

0.75

75%

0.28

28%

0.65

60%

0.55

55%

0.46

46%

5 0.35 ● 6 16 m ● 7 > ● 8 ● Fraction 1 4

100

Decimal

Percentage

25 100

0.25

25%

9 various ●

Unit 92 Page 62 1 a 20 b 40 c 8 d 200 e 80 f 4 ● 2 a 2 b 4 c 6 d 8 e 10 f 20 ● 3 a $6 b $12.50 c $11.65 d $15.35 e $7.10 ● f $1.25 ● 4 a $26 b $48 c $53 d $80 e $68 f $40 ● 5 400 ● 6 12 ● 7 $13.55 ● 8 $13 ● 9 a $23.10 b $26.90 Unit 93 Page 63 1 a $7.61 b $12.11 c $23.27 d $13.17 e $60.02 f $53.22 ● 2 a $2.25 b $0.51 c $4.05 d $0.35 e $1.65 f $3.40 ● 3 a $3.60 b $35.60 c $6.75 d $41.65 e $42.90 f $7.60 4 ● ● a $3.15 b $3.45 c $12.65 d $12.14 e $15.85 f $22.85 5 $14.39 ● 6 $0.65 ● 7 $17.70 ● 8 $2.10 ● 9 $65 + $91 + $107.90 = $263.90 ●

Unit 94

Page 63

Unit 95

Page 64

1 a $30 b $30 c $120 d $140 e $260 f $340 ● 2 a $6 b $9 c $43 d $98 e $173 f $114 ● 3 a $2.45 ● b $0.70 c $4.85 d $4.00 e $143.20 f $185.60 ● 4 a $18.12, $18.10 b $12.62, $12.60 c $6.48, $6.50 d $1.54, $1.55 e $20.13, $20.15 f $6.76, $6.75 ● 5 $150 ● 6 $48 ● 7 $52.35 ● 8 $32.41, $32.40 ● 9 change $1.05 1 a, c, e ● 2 a ● 3 a ● 4 ●

a b c d e f

b

c

b

c

Regular shape

No. of sides

triangle square pentagon hexagon octagon nonagon

3 4 5 6 8 9


d

e

d No. of axes of symmetry 3 4 5 6 8 9

f e

5 yes ● 6 ●

f 7 ●

No. of axes of symmetry heptagon 7 7 9 A, B, C, D, E, H, I, M, O, T, U, V, W, X, Y ● 8 ●

Regular shape

Answers


No. of sides

137


Page 64

1 a3b4c4d5e4f4● 2 a acute b right c straight d acute e acute f obtuse ● 3 a ●

b

c

e f 4 a false b false c true d true e true f false ● 5 6● 6 revolution ● 7 ● 8 true 9 a right b acute c 2 acute and 1 obtuse ● ●

d

Unit 97 Page 65 1 a revolution b right angle c acute d obtuse e straight f reflex ● 2 a acute b straight c right angle d obtuse e reflex ● f reflex ● 3 aFbBcDdAeCfE● 4 a false b false c true d true e false f true ● 5 obtuse ● 6 acute 7 a C b B c A 8 true 9 various e.g. ● ● ● Unit 98

Page 65

1 a ●

c acute d straight e 90º – 180º f 180º – 360º ● 2 ajbickdgelfh

b

3 a 150º b revolution c obtuse d 92º e 310º f reflex ● 4 a ● e f 5 a reflex b 180º ● 6 obtuse ● 7 200º ● 8 ●

Unit 99

Page 66

1 a ● 3 ●

b 100º c

d 300º e 4 a ●

a2b3c1d2e4f1

7 2● 8 ●

c

c

d

9 various ●

2 ●

f

b

b

a false b false c true d false e true f false

d

e

5 100º ● 6 false ●

f

9 2 acute angles and 1 obtuse angle ●

Unit 100 Page 66 1 a 40º b 80º c 100º d 60º e 150º f 175º ● 2 a 90º b 45º c 35º d 10º e 150º f 175º ● 3 a right b acute c acute ● d acute e obtuse f obtuse ● 4 a b c d

40 0 14

40 0

150

30 10

14

30

150

20 0

10

180 170 16 0

40 0 14

30

150

20

0

30 20 10 0

0 14 150

20 10

180 170 16 0

0

40 0 14

30

150

20

0

0

10

170 180

180 170 16 0

20

160

20

0

30

10

10

170 180

60º

100º

150

0

0

160

0

50

40

10

0

170 180

10

170 180

180 170 16 0

0

50

0

40

13

60

14

0

70

9 yes ●

13

60

90 100 11 0 1 20 80

100 90

150

70

80

20

90 100 11 0 1 20 80

100 90

110

30

0

120

110

70

0

10

170 180

0

13

80

70

120

14

20

160

60

60

0

13

40

30

14

50

0

50

150

30

13

60

40

0

150

70

0

10

170 180

20

160

20

100 90

110

14

20

160

30

20

160

10

120

90 100 11 0 1 20 80

80

70

60

0

13

50

150

40

30

150

40

0

50

0

50

0

0

180 170 16 0

13

60

30

0

50

70

5 70º ● 6 65º ● 7 acute ● 8 ●

13

60

90 100 11 0 1 20 80

100 90

150

120

80

40

0

13

70

110

0

50

100 90

110

0

0

90 100 11 0 1 20 80

80

70

60

70

14

50

f

13

10

120

60

170 180

70

20

80

160

120

100 90

14

0

13

110

120

14

30

50

90 100 11 0

80

70

60

150

40

e

60

0

13

10

50

0

50

0

30

13

60

0

70

180 170 16 0

90 100 11 0 1 20 80

100 90

40

80

14

110

150

70

120

180 170 16 0

60

0

13

14

40

50

100º

100º

Unit 101 Page 67 1 a 90º b 50º c 110º d 20º e 35º f 135º ● 2 a 20º, 30º b 80º, 85º c 180º, 180º d 100º, 100º e 140º, 150º f 10º, 15º ● 3 a b c d e f ● 120

13

60

50

0

40 0

20 10

10 0

0

0

170 180

30 180 170 16 0 15 40 0 14 0

8 acute ● 9 various ●

13

20

120

60

50

13

0

0

30

150

40

8 true ● 9 various ●

10

10 0

170 180

0

20

160

20

70

10

0

Page 68

80

170 180

0

90 100 11 0

100 90

20

13

14

50

80

160

120

60

110

30

70

70

150

80

120

40

0

90 100 11 0

100 90

60 0

13

0

10

80

170 180

110

20

70

50

0

160

120

13

14

50

30

0

60 0

13

120

60

150

10

0

170 180

10

170 180

50

70

40

80

14 0

100 90

40

20

160

20

160

30

150

40

30

150

0

a true b false c true d false e true f true ● 5 140º ● 6 175º ● 7

Unit 103

110

120

90 100 11 0

80

70

60

0

13

30

50

0

150

13

0 14

50

20

120

60

10

70

0

80

180 170 16 0

90 100 11 0

100 90

40

80

0

110

14

70

30

120

150

60

0

13

20

50

0

10

13

0 14

50

0

120

60

180 170 16 0

70

30 180 170 16 0 15 40 0 14 0

80

40

90 100 11 0

100 90

0

80

14

110

30

70

40

10

170 180

10

120

0

20

160

0

0

60

0

13

150

50

0

20

13

14

50

10

120

60

0

70

180 170 16 0

80

20

90 100 11 0

100 90

10

80

20

110

30

10

170 180

30 180 170 16 0 15 40 0 14 0

70

150

20

160

10

120

40

30

0

60

0

13

0

50

0

30 180 170 16 0 15 40 0 14 0

13

0 14

50

150

30 180 170 16 0 15 40 0 14 0

120

60

40

20

70

0

160

80

13

50

0

50

30

90 100 11 0

100 90

120

60

150

80

70

10

120

60

40

110

0 14

4 ●

70

80

170 180

70

0

120

90 100 11 0

100 90

20

80

14

60

0

13

80

160

0

100 90

110

Unit 102 Page 67 1 a 45º b 60º c 115º d 175º e 150º f 30º ● 2 a 30º b 95º c 85º d 25º e 120º f 165º ● 3 a b c d e f ● 50

110

30

10

90 100 11 0

80

70

120

170 180

0

60 0

13

70

150

20

160

10

0

170 180

10

170 180

0

50

120

40

30

150

20

160

20

160

10

170 180

0

a obtuse b acute c acute d obtuse e right f obtuse ● 5 30º ● 6 80º, 70º ● 7

60

0

13

14

50

30

70

150

80

20

100 90

10

110

0 14

40

120

90 100 11 0

80

70

60

0

13

0

50

0

180 170 16 0

13

50

0

120

60

14

70

30

80

150

90 100 11 0

100 90

20

80

10

110

0 14

40

70

0

120

30

30

20

60

0

13

0

50

0

180 170 16 0

13

50

14

120

60

30

70

150

80

20

90 100 11 0

100 90

10

80

40

0

110

150

14

70

40

30

120

150

20

60

0

13

40

20

160

180 170 16 0

50

0

0

13

50

180 170 16 0

120

60

10

70

0 14

40

80

0 14

14

90 100 11 0

100 90

30

150

110

150

10

170 180

10

120

40

20

160

0

80

70

60

0

13

0 14

30

4 ●

150

40

30

50

0

0

13

50

30 180 170 16 0 15 40 0 14 0

120

60

150

70

20

80

10

90 100 11 0

100 90

0

110

0

120

180 170 16 0

80

70

60

0

13

0 14

40

50

1 a acute b acute c a = 40º d b = 50º e c = 90º f 40º + 50º + 90º = 180º ● 2 a acute b acute c a = 80º d b = 50º ● e c = 50º f 180º ● 3 a a = 45º b b = 60º c c = 55º d d = 20º e e = 30º f f = 30º ● 4 a a = 85º b b = 95º c c = 70º d d = 110º e acute f obtuse ● 5 a = 30º b = 60º ● 6 a = 70º b = 70º ● 7 50º ● 8 a = 55º b = 120º c = 90º d = 95º 9 180º, 360º ● 138 © Pascal Press ISBN 978 1 74125 262 0




Page 68

1 a cube b square pyramid c rectangular prism d triangular prism e triangular pyramid f pentagonal prism ● 2 a6b5 ● c6d5e4f7● 3 a 12 b 8 c 12 d 9 e 6 f 15 ● 4 a 8 b 5 c 8 d 6 e 4 f 10 ● 5 hexagonal pyramid ● 6 7● 7 12 ● 8 7● 9

a 10 b 14 c 18

Unit 105 Page 69 1 a b c ●

d

e

3 a ●

f

4 a ● 8 ●

b side

c

b c

d

e

d triangular prism e hexagonal prism

f pentagonal pyramid

5 ●

f

2 ●

cylinder cone

Diagram

6 ●

c

d e

6 ●

f 7 ●

front

cube

5 ●

d

b

Page 69

1 a ●

3 ●

2 a ●

f b

c

9 top ●

Unit 106

e

●

Top

7 ●

Front

Side

a

b

c

d

e

f

8 ●

Name

Diagram

Top

Front

Side

cylinder

a

b

c

triangular prism

d

e

f

4 a ●

square pyramid b

cube

c

square prism d

cylinder

e

cone f

pentagonal prism

triangular pyramid ● 9 a 90º b 135º c 135º

Unit 107 Page 70 1 a 4 cm b 3 cm c 5 cm d 90º e 53º f 37º ● 2 a 4 cm b 4 cm c 5 cm d 50º e 80º f 50º ● 3 a, d, e, f ● 4 a equilateral b isosceles c scalene d right-angled e isosceles f equilateral 5 20º 6 2 cm 7 no ● 8 scalene ● ● ● ● 9 a 1 b 3 ● Unit 108

Page 70

1 a 2 cm b 1.5 cm c 1 cm d 1.7 cm e 0.5 cm f 1.2 cm ● 2 a 2.8 cm b 2.1 cm c 1.4 cm d 2.4 cm e 0.7 cm f 1.7 cm ●


Answers


139

3 ●

a 2.8 cm b 2.1 cm c 1.4 cm d 2.4 cm e 0.7 cm f 3.5 cm ● 4 a square b rectangle c rhombus kite d e parallelogram f trapezium 5 1cm, 2 cm ● 6 2.2 cm ● 7 2.2 cm ● 8 ●

parallelogram

rhombus

9 equal, 90º or right, equal, right or 90º ●

Unit 109

Page 71

Unit 110

Page 71

1 a triangle b pentagon c rectangle d trapezium e octagon f hexagon ● 2 a3b5c4d4e8f6 ● 3 a 3 b 5 c 4 d 4 e 8 f 6 4 a 0 b 5 c 2 d 2 e 20 f 9 5 square 6 4 7 4● 8 2● 9 various ● ● ● ● ● 1 a pentagonal pyramid b triangular prism c square pyramid d cube e pentagonal prism f triangular pyramid ● 2 a pentagon b square c triangle d triangle e square f pentagon ● 3 ● No. of No. of Object

a b c d e f

4 a ● 7 ●

b

c

d

e

f

Object

No. of corners

No. of edges

square pyramid

5

8

Unit 111

Page 72

Unit 112

●

b

edges 9 6 12 8 15 12

2 a cylinder b cone c sphere d cone e sphere f cylinder ● ● 4 a cone b cone c cylinder d cylinder, sphere e cylinder f sphere ● 5 cylinder ● 6 sphere 7 ● Solid No. of corners cone cylinder sphere

1 0 0

Page 72

1 a 4 cm b 2 cm c 4 cm d 2 cm e 3 cm f 5.6 cm ● 2 a 2 cm b 3 cm c 2 cm d 3 cm e 2.2 cm f 4.7 cm ● 3 a 2 cm b 2 cm c 2 cm d 2 cm e 2.1 cm f 3.4 cm 4 a 3 cm b 3 cm c 3 cm d 3 cm e 3.5 cm f 4.9 cm ● ● 5 45º, 135º ● 6 45º, 135º ● 7 65º, 115º ● 8 70º, 110º ● 9 a opposite angles are equal ● b rhombus has all side lengths are equal, parallelogram has only opposite side lengths are equal


5 4 6 5 7 7

5

c

140

No. of faces

5 rectangular prism ● 6 rectangle ● No. of 8 9 ● faces ●

1 a cone b sphere c cylinder d cone e sphere f cylinder ● 3 ● Solid No. of surfaces No. of edges cone 2 1 cylinder 3 2 sphere 1 0

8 sphere ● 9 a ●

triangular prism triangular pyramid cube rectangular pyramid pentagonal prism hexagonal pyramid

corners 6 4 8 5 10 7




1 a ●

Page 73

b

c

d

c e

e

2 a ●

f b

c

b d

4 a turn left b flip down c slide left d flip right e turn right f slide up ● 5 ● 7 ●

Unit 114

e

3 a ●

f

f

6 ●

d

8 slide up ● 9 ●

Page 73

1 a 32 squares b 72 squares c 800 squares d 128 squares e 288 squares f 200 squares ● 2 a double b 3 times ● c 10 times d 5 times e 4 times f 6 times ● 3 4 ● 1 cm : 10 cm 1 cm : 2 m

a b c d e f

5 2 squares ● 6 7 times ● 7 60 cm ● 8 10 cm ● 9 various ●

Unit 115

d

e 6 ●

Unit 116 1 a ● 2 a ●

● 2 a 3 a ● 4 a ● 5 ●

c

f

a b c d e f

50 cm

20 cm

200 cm

3 cm

30 cm

90 cm

900 cm

1 cm

10 cm

100 cm

1000 cm

2 cm

4m

5 cm

10 m

6 cm

12 m

3 cm

6m

0.5 cm

1m

10 cm

20 m

Page 74

1 a ●

b

5 cm

b

c

d

b

c

d

b

c

d

e e e

f

●

f f

7 ●

8 ●

9 ●

square pyramid

Page 74

b

b

c

d d

c

e

e

f

f

3 a cube b square pyramid c pentagonal prism d hexagonal pyramid e triangular prism f triangular pyramid ● 4 a b c d e f ●

5 ●

6 ●

7 square prism ● 8 ●


9 aDbE ●

Answers


141


Page 75

1 a rotation b tessellation c rotation d translation e tessellation f translation ● 2 a4b5c0d6e3f1 ● 3 a parallelogram b trapezium c parallelogram d hexagon ● 4 ● Solid No. of surfaces No. of vertices No. of edges e rhombus f triangle a 2 1 1

5 translation or reflection ● 6 1● 7 semicircle ● 8 ●

Solid

b

4

4

6

c

5

6

9

d

3

0

2

e

6

8

12

f

5

5

8

No. of surfaces No. of vertices No. of edges

7

10

9 ●

15

Unit 118 Page 75 1 a Sydney Aquarium b Pyrmont Bridge c Chinese Gardens d Chinatown e Australia Square f Harbour Control Tower ● 2 a 4H b 3F c 4B d 7D e 10M f 9N, 9O, 10N, 10O ● 3 a 9E, 9F b 9C, 9D c 6N, 6O d 7M, 8M e 5M, 6M f 3E, 4E ● 4 a George Street or Goulburn Street b Liverpool Street c Macquarie Street d Cahill Expressway e Pirrama Road ● f George Street ● 5 State Library ● 6 7L ● 7 9I, 10I ● 8 Macquarie Street ● 9 Museum of Contemporary Art Unit 119

Page 76

1 a Thumb Point b Finger Swamp c Pinky Point d Palm Hill e Hand Harbour f Pores Pond ● 2 a (E, 4) b (F, 6) c (C, 7) d (D, 6), (E, 6) e (E, 0), (F, 1) f (D, 6), (E, 1) ● 3 a 200 m b 150 m c 300 m d 50 m e 220 m f 180 m ● 4 a 100 m b 200 m c 150 m d 50 m e 200 m f 120 m ● 5 Lifeline River ● 6 (A, 6) ● 7 400 m ● 8 220 m ● 9 e.g. Hand Harbour to Flesh Fields is 100 m ●

Unit 120 Page 76 1 a (4, C) b (6, D) c (6, E) d (5, F) e (4, H) f (5, H) ● 2 a South Africa b Egypt c Dem. Rep. of the Congo d Algeria e Sudan ● f Madagascar ● 3 a Namibia b Egypt c Zimbabwe d Cameroon e Algeria f Madagascar ● 4 a 1000 km b 1500 km c 1500 km d 1000 km e 1000 km f 2000 km ● 5 (5, B) ● 6 Ethiopia ● 7 Sudan ● 8 1000 km ● 9 6000 km Unit 121 Page 77 1 a centipede b caterpillar c ant d dragonfly e spider f cockroach ● 2 a W b S c W d NW e SW f NE ● 3 a bee ● b grasshopper c ladybird d ladybird e caterpillar f centipede ● 4 a dust mite b bee c spider d caterpillar e grasshopper N f cockroach ● 5 centipede ● 6 S● 7 mosquito ● 8 butterfly ● 9 NE

NW W

E

SW

Unit 122

5 ●

SE

Page 77

1 d, f ● 2 b, f ● 3 a ● 3 a ●

S

b

b c

c d

6 ●


d e

e

f

f 7 ●



8 ●

9 various ●


Page 78

1 a Longreach b Georgetown c Coen d Weipa e Birdsville f St George ● 2 a (D, 8) b (D, 7) c (E, 6) d (C, 11) e (A, 7) ● f (D, 4) ● 3 a (E, 8), (D, 9) b (B, 5), (C, 5) c (F, 5), (G, 4) d (F, 5), (G, 5) e (C, 5), (D, 4) f (C, 1), (D, 1) ● 4 a Coen b Springsure c Weipa d Longreach e Cairns f Coen ● 5 Springsure ● 6 (G, 4) ● 7 (A, 3), (A, 4) ● 8 Georgetown 9 Cairns, Cooktown, Coen; north to north-west ●

Unit 124 Page 78 1 a rectangle b rhombus c trapezium d square e triangle f kite ● 2 a (1, C), (3, C), (3, G), (1, G) ● b (4, B), (6, B), (7, D), (5, D) c (4, E), (7, E), (6, F), (5, F) d (3, H), (6, H), (6, K), (3, K) e (0, K), (2, K), (O, N) f (5, N), (6, P), (5, Q), (4, P) ● 3 a (2, D), (2, E) b (5, C), (6, C) c (5, E), (6, E) d (4, I), (5, I) e (1, L), (0, M) f (5, O), (5, P) 4 a 2 units b 2 units c 2 units d 3 units e 3 units f 3 units ● 5 trapezium ● 6 (0, P), (3, P), (3, R), (1, R) ● 7 (1, Q), (2, Q) ● 8 2 units ● 9 various ●

Unit 125

1 ●

Page 79

10 9 8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

9

10

11

12

Unit 126 Page 79 1 a 20 mm b 5 mm c 4 d 15 mm e 5 mm f 3 ● 2 a 120º b 100º c 135º d 230º e 105º f 155º ● 3 a 150º b 145º ● c 135º d 90º e 165º f 115º ● 4 a 90º b 115º c 90º d 40º e 90º f 90º ● 5 a 8 mm b 4 mm c 2 ● 6 120º ● 7 120º 8 120º ● 9 various ●

Unit 127 Page 80 1 a seven o’clock b half past eight c quarter to nine d quarter to eleven e five minutes to three f twenty minutes past one ● 2 a b c d e f ● 11 12

11 12

1

10

2

9

3 4

8 7

6

5

11 12

1

10

2

9

3 7

4 7

6

5

11 12

1

10

3 8

5

6

2

9

4

8

11 12

1

10

2

9

3 4

8 7

6

5

11 12

1

10

2

9

3 4

8 7

6

1

10

2

8

4

9

3

5

7

6

5

3 a 4:20 b 6:05 c 10:40 d 2:15 e 4:50 f 4:27 ● 4 a 6:45 b 3:30 c 8:15 d 10:55 e 4:35 f 4:10 ● 5 quarter to twelve ● 6 7 7:00 ● 8 3:35 ● 9 1 hour 50 minutes ● ● 11 12

1

10

2

8

4

9

3 7

6

5

Unit 128 Page 80 1 a before midday b after midday c before midday d after midday e before midday f after midday ● 2 a 2:12 pm ● b 8:43 am c 7:26 pm d 11:27 am e 2:56 pm f 2:22 am ● 3 a 4 am, 4 pm, 6 pm b 8:35 am, 9:15 am, 9:04 pm c 1:25 am, 1:45 pm, 2:30 pm d 7:50 am, 7:51 am, 7:52 pm e 6:29 am, 6:30 pm, 6:42 pm f 11:47 am, 11:30 pm, 11:42 pm 4 a 10:32 pm b 2:15 am c 12:49 pm d 7:52 pm e 3:47 am f 8:23 pm ● 5 after midday ● 6 11:13 pm ● 7 5:15 pm, 5:25 pm, 5:32 pm ● 8 5:52 am ● 9 7 hours 50 minutes ●


Answers


143


Page 81

Unit 130

Page 81

1 a morning b afternoon c evening d morning e afternoon f morning ● 2 a 9:56 am b 6:38 pm c 3:12 pm d 4:49 am ● e 6:32 pm f 8:06 pm ● 3 a 1:08 am, 1:15 am, 1:30 pm b 3:35 am, 3:30 pm, 3:49 pm c 1:12 am, 2:06 am, 2:15 pm d 10:26 am, 10:27 am, 10:05 pm e 7:45 am, 7:50 am, 7:40 pm f 9:56 am, 9:52 pm, 9:54 pm ● 4 a 11:45 pm b 5:10 am c 6:04 pm d 8:48 am e 2:16 am f 4:21 pm ● 5 morning ● 6 11:13 am ● 7 4:01 am, 4:08 am, 4:27 pm 8 8:09 am ● 9 no ● 1 a 0300 b 2100 c 0730 d 2300 e 1430 f 1300 ● 2 a 10:10 am b 4:15 pm c 1:00 am d 8:20 pm e 2:00 pm ● f 6:20 am ● 3 a 1100 b 0600 c 0530 d 0015 e 0945 f 0500 ● 4 a 1500 b 2030 c 2215 d 1630 e 1915 f 1300 ● 5 1700 6 9:00 am ● 7 0330 ● 8 1815 ● 9 ● 11 12

1

10

2

8

4

9

3 7

Unit 131

Page 82

Unit 132

Page 82

6

5

1 a 2:46 am b 4:39 pm c 3:12 pm d 7:19 am e 11:52 pm f 6:54 am ● 2 a 8:00 pm b 5:30 pm c 1:23 am d 9:15 pm ● e 10:17 am f 6:47 am ● 3 a 1631 b 0823 c 1307 d 2219 e 1152 f 0246 ● 4 a 0415 b 1843 c 2207 d 0825 e 1237 f 1958 ● 5 7:42 pm ● 6 4:10 am ● 7 2234 ● 8 2135 ● 9 1 hour 23 minutes 1 a 2:17 am b 3:25 pm c 9:10 pm d 11:06 pm e 11:46 am f 6:20 am ● 2 a 0432 b 2012 c 1052 d 1343 e 0705 ● f 1721 ● 3 a 11:57 pm b 4:19 am c 8:42 am d 5:04 pm e 7:27 pm f 10:31 am ● 4 a 45 minutes b 1 hour 24 minutes c 28 minutes d 1 hour 25 minutes e 2 hours 15 minutes f 4 hours 28 minutes ● 5 8:47 pm ● 6 0515 ● 7 3:23 pm 500 8 5 hours 17 minutes 9 = 6.25 hours (or 6 hours 15 minutes) ● ● 80

1900

➤

➤

➤ ➤

➤

➤ ➤

Unit 133 Page 83 1 a 48 minutes b 41 minutes c 46 minutes d 63 minutes e 12 minutes f 1 hour 45 minutes ● 2 a 11:21 am ● b 12:02 pm c 11:38 am d 12:26 pm e 11:07 am f 12:14 pm ● 3 a 12:07 pm b 11:25 am c 1:01 pm d 12:28 pm e 11:56 pm f 11:42 am ● 4 f a be c gd 1950

2000

km 5 63 minutes ● 6 12:35 pm ● 7 12:37 pm ● 8 see question 4 ● 9 120 ● 90 h = 80 km/h

Unit 134 1 a ●

Page 83

11 12

10

2

9

3 7

5

6

2 ●

11 12

6 ●

1

10

2

9

3 4

8 7

Sydney

6

c

1 2 3

7

6

5

Melbourne

d

1 2

11 12

6

5

6


3

11 12

7

6

2

9

3 4

8

Darwin

5

1

10

4

Hobart

7

Perth

5

6

3 a 1425 b 1425 c 1355 d 1425 e 1225 f 1425 ● 4 a b c ●

EST 6:30 pm

11 12

11 12

1

10

2

9 7

d

11 12

Sydney

e

1

10

2

9 4 7

6

5


4 7

6

2 3 4

8 6

5

5

Brisbane

9 7:30 am ●

1

10 9 7


3

Perth

7 1355 ● 8 ●

f

2

8

11 12

7

Hobart

1

10

3 4

8

5

9

3 8

6

11 12

2

9

4 7

1

10

3 8

5

6

2

9

4

8

11 12

1

10

3

5

144

2

8

5

f

1

9

4 7

Adelaide

11 12 10

3 8

EST 19:00 am 17:00 am 16:15 pm 10:35 am 12:30 pm 11:15 pm

CST 6:00 pm

2

9

4 7

e

1

10

3 8

CST 18:30 am 16:30 am 15:45 pm 10:05 am 12:00 pm 12:45 pm

WST 4:30 pm

11 12 10 9

4

8

WST 17:00 am 15:00 am 14:15 pm 18:35 am 12:30 pm 11:15 am

a b c d e f

11 12 10 9

4

8

5 ●

b

1

6

5

11 12

1

Adelaide

10

2

8

4

9

3 7

6

5

Darwin


Page 84 b de f g 2

➤

1

➤

0

a

c

➤

➤ ➤ ➤ ➤

1 ●

3

4

5

6

7 cm

2 ●

a 9.2 cm b 4.1 cm c 3.8 cm d 9.5 cm e 10.9 cm f 15.3 cm ● 3 a 17 mm b 22 mm c 87 mm d 41 mm e 126 mm f 157 mm ● 4 a mm b m c cm d m e cm f m ● 5 see question 1 ● 6 12.5 cm ● 7 33 mm ● 8 km ● 9 13 cm Unit 136

Page 84

Unit 137

Page 85

1 a mm b km c m d cm e m f cm ● 2 a 16 mm b 24 mm c 9 mm d 12 mm e 27 mm f 31 mm ● 3 a 90 mm ● b 210 mm c 43 mm d 75 mm e 16 mm f 930 mm ● 4 a 7.2 cm b 1.6 cm c 5 cm d 4.8 cm e 19.2 cm f 36.5 cm ● 5 m 6 48 mm ● 7 1020 mm ● 8 12.7 cm ● 9 l = 42 mm, b = 16 mm, P = 116 mm or 11.6 cm ● 1 b, d, e ● 2 ●

a 4000 m b 6000 m c 1000 m d 9000 m e 11 000 m f 15 000 m ● 3 a 9 km b 3 km c 5 km d 2 km e 12 km f 17 km ● 4 a 60 km/h b 40 km/h c 100 km/h d 100 km/h e 80 km/h f 110 km/h ● 5 no ● 6 7000 m

7 10 km ● 8 60 km/h ● 9 various ●

Unit 138 Page 85 1 a m b km c m d cm e m f km ● 2 a 4 km b 11 km c 7 km d 23 km e 5 km f 20 km ● 3 a 6000 m b 9000 m ● c 14 000 m d 8000 m e 3000 m f 2000 m ● 4 a 2.5 km b 3.64 km c 1.09 km d 3.58 km e 2.905 km f 4.756 km ● 5 km 6 18 km 7 12 000 m 8 2.385 km 9 a 9610 m b 4318 m c 6045 m ● ● ● ● Unit 139

Page 86

Unit 140

Page 86

1 a m b km c mm d cm e km f mm ● 2 a 21 mm, 2.1 cm b 46 mm, 4.6 cm c 16 mm, 1.6 cm d 9 mm, 0.9 cm ● e 36 mm, 3.6 cm f 25 mm, 2.5 cm ● 3 a 8.37 m b 1.49 m c 3.98 m d 9.15 m e 10.24 m f 11.79 m ● 4 a 370 b 2.2 c 850 d 2.49 e 3.2 f 650 ● 5 cm ● 6 27 mm, 2.7 cm ● 7 8.56 m ● 8 320 ● 9 a trundle wheel b ruler c tape measure 1 a 2 cm, 1.5 cm b 1.5 cm, 1 cm c 2.5 cm, 1 cm d 2.2 cm, 1 cm e 2.7 cm, 2.1 cm f 1.8 cm, 1.4 cm ● 2 a 7 cm b 5 cm ● c 7 cm d 6.4 cm e 9.6 cm f 6.4 cm ● 3 a 8 m b 48 m c 40 m d 12.8 cm e 21.2 cm f 32.4 cm ● 4 a 12 m b 30 m c 26 cm d 14.6 cm e 12.8 cm f 8 m ● 5 2.1 cm, 1.2 cm ● 6 6.6 cm ● 7 28 m ● 8 25.8 m ● 9 47 m

Unit 141 Page 87 1 a 22 cm b 34 m c 10 m d 34 m e 32 cm f 22 cm ● 2 a 22 cm b 24 cm c 40 cm d 70 m e 70 m f 140 m ● 3 a 16 cm b 20 cm c 40 cm d 36 m e 80 m f 60 m ● 4 a 0.6 cm b 1.8 cm c 1.1 cm d 0.9 cm e 0.5 cm f 0.9 cm ● 5 20 m ● 6 28 m ● 7 10 cm ● 8 5.8 cm ● 9 3.2 cm + 1.8 cm + 1.3 cm = 6.3 cm ●

Unit 142 Page 87 1 a 12 cm b 12 cm c 25 cm d 12 cm e 12 cm f 8 cm ● 2 ●

a

b

c

d

e

f

3 a 22 mm b 8 mm c 24 mm d 12 mm e 16 mm f 20 mm ● 4 ● 5 18 cm 6 7 16 mm 8 17.6 cm 9 e.g. ● ● ● ● ● 2.5

a 12.8 m b 8 cm c 18 cm d 57.4 m e 7.5 cm f 6 cm 4 3.5


Answers


145


Page 88

1 a 12 b 6 c 3 d 9 e 8 f 2 ● 2 a 16 mm, 4 mm b 6 mm, 5 mm c 15 mm, 3 mm d 7 mm, 2 mm e 25 mm, 3 mm ● 2 f 18 mm, 3 mm ● 3 a 64 mm b 30 mm2 c 45 mm2 d 14 mm2 e 75 mm2 f 54 mm2 ● 4 a 12 cm2 b 40 cm2 c 54 cm2 2 2 2 2 2 d 28 m e 60 m f 56 m ● 5 6● 6 12 mm, 7 mm ● 7 84 mm ● 8 27 m ● 9 P = 90 m and A = 450 m2

Unit 144 Page 88 1 a 8 m2 b 9 m2 c 100 m2 d 42 m2 e 24 m2 f 35 m2 ● 2 a 9 m2 b 49 m2 c 100 m2 d 81 m2 e 144 m2 f 400 m2 ● 2 2 2 2 2 3 a 12 m b 63 m c 50 m d 40 cm e 66 cm f 32 cm2 ● 4 a 42 m2 b 25 m2 c 27 cm2 d 64 cm2 e 70 cm2 f 4 cm2 ● 5 12 m2 ● 6 36 m2 ● 7 18 m2 ● 8 24 m2 ● 9 24 m2 ●

Unit 145 Page 89 1 a 12 cm2 b 72 cm2 c 70 cm2 d 3 m2 e 30 m2 f 14 m2 ● 2 a 9 m b 4 m c 10 m d 2 cm e 6 cm f 4 cm ● 3 a1m ● b 3 m c 4 m d 2 m e 1.5 m f 2.4 m ● 4 a 4 + 6, 10 square units b 6 + 4, 10 square units c 2 + 3, 5 square units d 2 + 3, 5 square units e 2 + 5, 7 square units f 1 + 1 + 9 + 3 + 3, 17 square units ● 5 18 m2 ● 6 4 cm ● 7 3m 8 1 + 1 + 6 + 3, 11 square units ● 9 6 m2 ( 12 of a rectangle) ●

Unit 146

Page 89

1 a m2 b m2 c cm2 d m2 e cm2 f m2 ● 2 a 2000 m2 b 200 m2 c 1200 m2 d 4000 m2 e 5000 m2 f 5400 m2 ● 2 2 2 3 a 24 000 m b 13 200 m c 19 200 m d 50 000 m2 e 32 000 m2 f 20 000 m2 ● 4 a 40 m b 30 m ● c 2000 m d 70 m e 400 m f 500 m ● 5 cm2 ● 6 1200 m2 ● 7 150 m2 ● 8 25 m 9 total area found by adding all areas together, i.e. 24 000 m2 + 13 200 m2 … = 158 400 m2 ●

Unit 147 Page 90 1 a m2 b ha c m2 d ha e m2 f ha ● 2 a 50 000 m2 b 70 000 m2 c 30 000 m2 d 80 000 m2 e 20 000 m2 f 60 000 m2 ● 3 a 1 ha b 4 ha c 3 ha d 6 ha e 9 ha f 2 ha ● 4 a>b> c= d< e> f=● 5 m2 ● 6 90 000 m2 ● 7 7 ha ● 8 > ●

9 various ●

Unit 148

Page 90

1 a km2 b ha c km2 d ha e ha f km2 ● 2 a 4 km2 b 7 km2 c 3 km2 d 9 km2 e 1 km2 f 5 km2 ● 3 ● 4 a 200 b 600 c 800 d 1000 e 100 f 300 ● 5 ha ● State/Territory Area (km2) 2 2 6 6 km ● 7 7 692 431 km ● 8 400 ● 9 6500 ha ● ACT 2 322 330 a

b c d e f

Tasmania Victoria New South Wales South Australia Northern Territory Queensland Western Australia

Unit 149

Page 91

Unit 150

Page 91

2 367 897 2 227 516 2 801 431 2 984 381 1 356 176 1 727 200 2 525 500

1 a kg b g c kg d kg e g f g ● 2 a 4000 g b 7000 g c 9000 g d 5320 g e 3247 g f 8693 g ● 3 a 1 kg 500 g ● b 2 kg 750 g c 6 kg 178 g d 3 kg 850 g e 4 kg 116 g f 1 kg 70 g ● 4 a 400 g b 300 g c 900 g d 800 g e 1200 g f 2200 g 5 kg ● 6 3721 g ● 7 2 kg 176 g ● 8 4200 g ● 9 6.4 + 2.1 + 3.6 + 5.8 = 17.9, 17.9 kg ● 1 a t b g c kg d g e kg f t ● 2 a 6000 g b 2000 g c 8000 g d 3700 g e 9100 g f 1700 g ● 3 a 2 kg 176 g ● b 4 kg 837 g c 2 kg 122 g d 8 kg 695 g e 4 kg 35 g f 1 kg 80 g ● 4 a 20 b 30 c 60 d 6 e 15 f 12 ● 5 t● 6 4600 g 7 4 kg 619 g ● 8 7.5, really 7 keyboards, as can’t have half a keyboard ● 9 aBbA ●

Unit 151 Page 92 1 a kg b t c t d kg e kg f t ● 2 a 9000 kg b 5000 kg c 2000 kg d 17 000 kg e 21 000 kg f 60 000 kg ● 3 a3tb7t ● c 14 t d 10 t e 40 t f 52 t ● 4 a>b> c● 5 kg ● 6 35 000 kg ● 7 63 t ● 8 7 8 86 521 ● 9 876 431 ● 10 42 510 ● 11 more ● 12 ten times ● ● HTh TTh Th H T U ● 1 0 7 6 4 8

Review Tests Units 9 – 14

Page 106

1 D● 2 B● 3 false ● 4 true ● 5 ● 12 LXV, LXX, LXXV, LXXX ●


Page 106

1 C● 2 A● 3 true ● 4 false ● 5 907 mL ● 6 7 8 4 9 ● 7 2356 ● 8 ● + 0 2 3 6 8 0 8 5

+ 4 6 1 8 6 4 3 7 8 3 4 5 9 1 1 0 7 1 5 3

9 870 + 290 = 1160 ●

10 $7569 ● 11 $7155 ● 12 $317 306 ●

Review Tests Units 20 – 23 Page 107 – 51 1 D 2 B 3 false 4 true 5 182 6 231, 231, 479 7 734 8 1500 + 1300 = 2800 9 518 1 0 ● ● ● ● ● ● ● ● ● ● 197 146 11 true ● 12 178 ● 185 134 180 190 200 210 216 165 410 359 Review Tests Units 24 – 29

Page 107

1 C● 2 A● 3 true ● 4 false ● 5 22 076 ● 6 4 3 1 6 ● – 2 7 4 5

7 2162 rounded to 2160 ●

1 5 7 1 8 ●

– 2000 3000 4000 5000 6000 1426 574 1574 2574 3574 4574


9 2566 pins ● 10 5817 ● 11 $20 000 ● 12 2981 + 2890 or 1424 + 4576 ●

Page 108

1 D● 2 B● 3 false ● 4 false ● 5 1096 ● 6 5, 40 ● 7 $24 + $60 = $84 ● 8 780 ● 9 8, 160 ● 10 7260 ● 1 1 1 2 $444 + $140 + $80 = $664 ● 3 ● 5 7 8 12 15 40

200

280

320

480

600


Page 108


Page 109


Page 109

1 D● 2 C● 3 false ● 4 false ● 5 1251 ● 6 172 ● 7 1, 2, 3, 5, 6, 10, 15 ● 8 2314 3 3 = 6942 ● 9 88 days ● 1 0 16 + 9 = 25 1 1 6 1 2 answer is 2982 ● ● ● 1 D● 2 B● 3 true ● 4 false ● 5 24 ● 6 763 ● 7 108 ● 8 a 136 b 68 c 34 ● 9 remainder = 1 (90 r 1) ● 10 182 pencils ● 1 1 14 3 6 = 84 1 2 848 ÷ 8 = 106 is larger ● ● 1 D● 2 B● 3 false ● 4 true ● 5 175 r 1 ● 6 1183 ● 7 68 r 5 ● 8 83 r 2 ● 9 14.9 ● 10 2117 ● 11 324 ● 1 2 141 groups ● 152 © Pascal Press ISBN 978 1 74125 262 0



ANSWERS: Review Tests Units 51 – 84 –20–15–10 –5 0 5 Review Tests Units 51 – 55

10 15 20 25 30 ºC

1 A● 2 D● 3 true ● 4 false ● 5 ●

21

1 2

21 12

–20–15–10 –5 0 5 10 15 20 25 30 ºC

21

9 2.25 kg ● 10 1800 ● 11 ●

–20–15–10 –5 0 5 10 15 20 25 30 ºC

Page 110

22 14 22

6 17 3 4 = 68 ● 7 491 ● 8 * = 30 ●

23 34

–20–15–10 –5 0 5 10 15 20 25 30 ºC

23

24

7 6 ● 12 6 + 2 + 2 + 2 + 1 + 1 – 8 = 6 + 7 2 –20–15–10 –5 0 5 10 15 20 25 30 ºC 1 4 8

–20–15–10 –5 0 5 10 15 20 25 30 ºC


Page 110

1 B● 2 A● 3 true ● 4 true ● 5 117 137 ● 6 57 470 ● 7 212 students ● 8 131 ● 9 4711 ● 10 8 3 (12 – 5) ÷ 2 – 9 = 19 ● 11 1309 ● 12 34.6 ● –20–15–10 –5 0 5 10 15 20 25 30 ºC


Page 111

1 D● 2 A● 3 false ● 4 true ● 5 ●

6 1.5 kg ● 7 4.97 ● 8 20 ● 9 >● 10 5 + 2 or 2 + 5, 56 ● 11 0 ●

–20–15–10 –5 0 5 10 15 20 25 30 ºC

12 6 3 4 = 24 or 4 3 6 = 24 ●


Page 111

1 D● 2 A● 3 true ● 4 false ● 5 ●

Number sentence

Estimate

Actual

Difference

246 + 168 785 + 137 287 – 152

420 830 140

414 822 135

6 8 5


Page 112

1 D● 2 B● 3 true ● 4 false ● 5 ● 10 ●

11 8 ● 12 ●

28 100

b c a

0

=

6 104 , 12 , 35 , 109 ● 7 ●

9 9

6 8 59 ● 9 100 ●

7 25


Page 112

1 C● 2 B● 3 false ● 4 true ● 5 2 14 ● 6 12 ● 7 ●

1

2

7 5

9 2 26 = 2 13 ● 10 28 = 14 = 123 = 164 ● 11 ●


12 ●

= 1 13 ● 6 3 5


8 ●

3

3 4,

1 68 ,

3 8

+

16 9 8, 4

Page 113

1 B● 2 C● 3 false ● 4 true ● 5 ● 9 49 – 29 = 29 ● 10 ●

● 6 1, 400, 2, 200, 4, 100, 5, 80, 8, 50, 7 145.8 10, 40, 16, 25, 20 ● 8 3 3 6 3 7 or 2 3 739 ● 9 10.94 ● 10 985 ● 11 1097.22 ● 12 0.625 ●

11 e.g. 68 + 18 = 78 ● 12 ● Page 113

1 A● 2 D● 3 true ● 4 false ● 5 4.203 ● 6 ●

T

U

• Tth

1 4

=

5 7 63 = 2 ● 8 126 + 124 = 10 ● 12 = 6

5 8

3 23

3

4

7 3.04, ●

3.76, 4.61, 7.19, 8.25 ● 8 40 216


Page 114

1 D● 2 B● 3 false ● 4 true ● 5 11.4 ● 6 $7.65 ● 7 13.15 ● 8 13.2 ● 9 ● 1 0 $32.75 1 1 2.65, 7.39, 1.72 1 2 $47.15 ● ● ● © Pascal Press ISBN 978 1 74125 262 0

3.25

Hth

9 nine hundred and sixty-two and eighty-five hundredths ● 10 0.19 ● 11 0.36 ● 12 ●

Answers

3.0

3.9 4.1 3.5

4.0

4.6 4.5

5.0

– 41.0 51.0 81.0 101..0 2.36 1.64 2.64 5.64 7.64


153

ANSWERS: Review Tests Units 85 – 129 Review Tests Units 85 – 88

Page 114


Page 115

1 C● 2 C● 3 false ● 4 true ● 5 29.16 ● 6 0.64 ● 7 129.87 ● 8 5.5 kg ● 9 $2.19 ● 10 13.2 ● 11 0.59 rounded to 0.6 ● 12 $16.26 rounded to $16.25 ●

96 1 A● 2 C● 3 false ● 4 true ● 5 1.2 m ● 6 100 = 24 7 ● 25 ●


Page 115

Review Tests Units 95 - 99

Page 116

62 8 0.75 ● 9 100 = 31 10 7.6 ● 11 16% ● 12 5% ● 50 ●

1 C● 2 C● 3 false ● 4 true ● 5 $25.08 ● 6 $11.15 ● 7 $11.45 ● 8 $21.17 rounded to $21.00 ● 9 $2.65 ● 10 $38.97 ● 1 1 $2, 50c, 20c, 10c, 5c; 5 coins 1 2 20 kg: 29.5c per kg; 3 kg box: 30c per kg; 20 kg box is cheaper ● ● 1 C● 2 A● 3 true ● 4 false ● 5 obtuse ● 6 ●

7 ●

10 a acute, b obtuse, c acute, d obtuse ● 11 ●

12 hexagon ●


Page 116


Page 117

1 C● 2 B● 3 false ● 4 true ● 5 125º ● 6 ● 1 1 obtuse 1 2 ● ●

1 C● 2 C● 3 true ● 4 true ● 5 ● 9 ●

,

7 obtuse ● 8 angle is 40º not 140º ● 9 110º ● 10 70º ●

6 ●

10 ●

,

8 C● 9 less than ●

7 ●

8 ●

11 6 ● 12 8 corners, 12 edges ●


Page 117

1 B● 2 D● 3 false ● 4 false ● 5 scalene ● 6 9● 7 equal length ● 8 ● 10 opposite side lengths are equal ● 11 ●


9 cylinder ●

12 ●

, sphere

Page 118

1 A● 2 90 ● 3 150 3 150 cm ● 4 false ● 5 triangular pyramid ● 6 sector ● 7 ● 10 cylinder ●

9 ●

11 4, 4, 2, 4 ● 12 ●


Page 118

1 A● 2 A● 3 true ● 4 true ● 5 SE ● 6 ● 1 1 1 2 (C, 4) ● East West South ● 

8 ●



7 500 m ● 8 ●



4 3 2 1

9 (3, B) ● 10 2 units ●

x

A B C


Page 119

1 C● 2 D● 3 false ● 4 false ● 5 4:18 am, 4:32 pm, 4:56 pm ● 6 ● 1 0 8:50 1 1 5:40 pm 1 2 ● ● ● 11 12

1

10

2

9

3

11 12

2

9

3 4

8 7

6

5

4

8 7

6

5


7 quarter to nine ● 8 1:05 ● 9 2:40 pm ●

1

10



ANSWERS: Review Tests Units 130 – 176 Review Tests Units 130 – 134

Page 119

1 D● 2 B● 3 false ● 4 true ● 5 1903 ● 6 6 hours 35 minutes ● 7 47 minutes ● 8 ●

11 12

9 3 hours 55 minutes ●

1

10

2

9

3 4

8 7

10 ●

11 12

1

10

2

9

3

11 ●

11 12

8:30 pm or

7

6

10

2

8

4

9

4

8

1 3

7

5

6

5

6

or 2030 ● 12 11:13 am

5


Page 120


Page 120


Page 121


Page 121

1 B● 2 C● 3 false ● 4 false ● 5 36.5 cm ● 6 50 km/h ● 7 9.5 cm ● 8 2.689 km ● 9 2500 m, 250 000 cm ● 10 6.4 metres ● 11 12 5.5 km ● ● 1 D● 2 A● 3 true ● 4 false ● 5 l = 3.2 cm, b = 2.3 cm, P = 11.0 cm ● 6 4.5 cm ● 7 36 cm ● 8 26 cm ● 9 3 cm ● 10 24 cm ● 11 19.18 cm ● 12 30 + 120 + 40 + 80 + 10 + 40, 320 cm ● 1 B● 2 B● 3 false ● 4 false ● 5 4.5 cm2 ● 6 2m● 7 7 cm ● 8 >● 9 13 500 m2 ● 10 40 + 6 = 46, 46 m2 ● 11 4 ha ● 12 false, it will be 4 times larger ● 1 B● 2 C● 3 false ● 4 false ● 5 2900 g ● 6 4500 kg ● 7 1 kg 500 g = 1.5 kg ● 8 7 boxes ● 3 9 2 kg 100 g, 2400 g, 2.6 kg, 3 kg ● 10 1 4 t = 1750 kg = 1 750 000 g ● 11 6 kg ● 12 ● 165 g 100 g 20 g


50 g 10 g

5g

Page 122

1 B● 2 C● 3 true ● 4 false ● 5 36 cubed units ● 6 330 mL, 3000 mL, 3.3 L, 3.9 L ● 7 V = 8 cm3 ● 8 60 cm3 ● 9 6 cm3 = 6 mL ● 10 1100 mL = 1.1 L ● 11 ●


12 24 cm3, 24 mL ●

Page 122

1 D● 2 B● 3 false ● 4 true ● 5 various ● 6 38 ● 7 14 ● 8 chocolate ● 9 ● R 10 1, 1; 1, 2; 1, 3; 1, 4; 1, 5; 1, 6 ● 11 white ● 12 G R ● 2, 1; 3, 1; 4, 1; 5, 1; 6, 1;

2, 2; 3, 2; 4, 2; 5, 2; 6, 2;

2, 3; 3, 3; 4, 3; 5, 3; 6, 3;

2, 4; 3, 4; 4, 4; 5, 4; 6, 4;

2, 5; 3, 5; 4, 5; 5, 5; 6, 5;

2, 6 3, 6 4, 6 5, 6 6, 6


1 D● 2 A● 3 true ● 4 false ● 5 ●

R

H T

T H

T

T

R R

Page 123

10

6 5 people ● 7 ●

8 Number

H

H

A

B

C

D

7

8

12

3

Tally Count

6 4 2 0

b

br

g

gry

Colour

8 ●● 9 3 + 5 = 8, 8 kg ● 10 5 stickers ● 11 15ºC ● 12 5 + 10 + 7 + 10 + 3 = 35, 35 cars ●


Page 123

1 B● 2 D● 3 false ● 4 true ● 5 7.3 ● 6 76 ● 7 12 and 7 ● 8 (number of squares 3 3) + 1 ● 9 5, 6, 7 and 13, 14, 15 ● 10 ▲ = 50 ● 11 $9.50 ● 12 a 62 b 12 minutes ● © Pascal Press ISBN 978 1 74125 262 0

Answers


155

© 2007 Pascal Press Reprinted 2008, 2009 (twice), 2010, 2011

Updated in 2012 for the Australian Curriculumm Reprinted 2014, 2015, 2016 ISBN 978 1 74125 262 0 Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www. pascalpress.com.au Publisher: Vivienne Joannou Project editor: Mark Dixon Edited by May McCool, Araya Divine and Rosemary Peers Typeset by lj Design (Julianne Billington) Cover by DiZign Pty Ltd Printed by Green Giant Press Reproduction and communication for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of the pages of this work, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that the educational institution (or that body that administers it) has given a remuneration notice to the Copyright Agency Limited (CAL) under the Act. For details of the CAL licence for educational institutions contact: Copyright Agency Limited Level 15, 233 Castlereagh Street Sydney NSW 2000 Telephone: (02) 9394 7600 Facsimile: (02) 9394 7601 Email: [email protected] Reproduction and communication for other purposes Except as permitted under the Act (for example, a fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address above.

156


p124-156 Maths(5)_Answer_2016.indd 156


Multiplication table

157

3

0

1

2

3

4

5

6

7

8

9

10 11 12

0

0

0

0

0

0

0

0

0

0

0

0

1

0

1

2

3

4

5

6

7

8

9

10 11 12

2

0

2

4

6

8

10 12 14 16 18 20 22 24

3

0

3

6

9

12 15 18 21 24 27 30 33 36

4

0

4

8

12 16 20 24 28 32 36 40 44 48

5

0

5

10 15 20 25 30 35 40 45 50 55 60

6

0

6

12 18 24 30 36 42 48 54 60 66 72

7

0

7

14 21 28 35 42 49 56 63 70 77 84

8

0

8

16 24 32 40 48 56 64 72 80 88 96

9

0

9

18 27 36 45 54 63 72 81 90 99 108

10

0

10 20 30 40 50 60 70 80 90 100 110 120

11

0

11 22 33 44 55 66 77 88 99 110 121 132

12

0

12 24 36 48 60 72 84 96 108 120 132 144


IBC-2016.indd 157

0

0

Excel Advanced Skills Start Up Maths Year 5 17/02/2017 10:04 AM

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9781741252620 StartUpMaths Yr5 2016.indd 2,4

Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www.pascalpress.com.au

Damon James

T UP START UP START TART UP STAR UP ST T UP2 S MATHS 3 MATHS 4 MATHS 5 MATHS ART U R A T 6 S P S S P H MATHS U TAR RT S 1 MAT 7 A 7 T 7 S ATH 4 MATT UP 0 10 M HS I VI –3 3 0.5 ADVANCED SKILLS

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