basic skills - Blake Education

Basic Skills

Get the Results You Want! Year 6 Ages 11–12 years old This book has been revised and updated for the Year 6 Australian Curriculum. Mental Maths is the Maths we do in our heads without the use of calculators and without writing down the calculation. Mental Maths strategies are the ‘tricks’ we use to do Maths in our heads. There are different ways of finding the answer to any Mental Maths problem, and such strategies are the focus of this series. Even though electronic devices play an enormous role in the modern world, we still need to go back to the basics—we do need to know how to check that the sales assistant at the counter is giving us the right change! Mental Maths has become more important than ever and the Australian Curriculum for primary years reflects this. All states have placed an emphasis on Mental Maths in the primary syllabus, and the NAPLAN Tests for secondary years (Years 7 and 9) have a non-calculator section.

Features of this book  Thirty-two double-page units of Mentals are included—eight units for each school term. Each unit is divided into four sets (A, B, C and D) of 20 questions each.

 Each numbered question covers a particular Maths topic throughout the book: for example, Question 1 always covers addition, while Question 20 always covers geometry.

 A special Help Section at the front of the book gives different strategies and explanations to help students

solve Mentals problems. These are also numbered so they link to the question numbers in each Mentals unit.

 A Fun Spot! unit, containing fun activities, and a Revision unit are included at the end of each eight units.  Extra practice sections which reinforce particular strategies appear in the lower part of each page.  The answers to all questions are in a lift-out section in the centre of the book.

About the authors

Alan Parker has been writing textbooks for more than 30 years. As a primary school teacher for over 40 years, he taught in several Australian states and gained experience at all levels of primary teaching, including ESL, remedial and extension classes. He was a primary school principal for 13 years and is the author of many successful educational books, including the successful Signpost Maths textbooks and (with Jan Faulkner) Signpost Maths Mentals Workbooks. Jan Faulkner has been a classroom teacher for over 30 years. She has taught both mainstream and gifted and talented classes in schools across Australia, and is currently the Assistant Principal of a large school in Sydney. With Alan Parker, Jan also co-authored the best-selling Signpost Maths Mentals Workbooks.

Other books in the Excel Mental Maths Strategies series: Bookseller reference

Books

Level



Mental Maths books

978-1-74125-184-5 978-1-74125-185-2 978-1-74125-180-7 978-1-74125-182-1 978-1-74125-182-1

Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies

Year 1 Year 2 Year 3 Year 4 Year 5 ISBN 978-1-74125-183-8

Excel Test Zone

Get the Results You Want!

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.

9781741251838 EBS MentalMaths Yr6 NSACE 2015.indd 1

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

9 781741 251838

B A S IC S K ILLS MEN TA L MATH S STR ATE G IE S Year 6 Ages 11–12

Mental Maths Strategies

MENTAL BASIC SKILLS MATHS 6 STRATEGIES

MATHS

Excel

YEAR AGES 11–12

G e t t he Re su lt s Alan Par k er & You Want ! J an Faulk ner 12/01/2015 4:05 pm

What is in this book?  There are 32 units of work, with eight units of work for each school term. The last two units for each term are comprised of a fun unit and a revision unit. The fun unit presents fun activities and the revision unit contains questions that test the student’s understanding of the term’s work.  Each unit is broken up into 4 sets: A, B, C and D. The sets are graded in terms of difficulty so that Set A is the easiest and Set D is the hardest. Each set is numbered Question 1 to 20.  Each set has a score box to fill out. The student can then go to the back of the book to complete a score sheet that provides valuable feedback on progress.  You will notice illustrations at the top of nearly every page. These characters are used to convey an important strategy or step in Mental Maths.  Each page of Mentals has an extra practice section in the lower part which will give the student further practice in a concept. The illustrations help explain the concepts and strategies that could be used to answer the questions.  Answers are provided in the middle of the book. These pages may be removed if required.

What is special about the Mental Maths questions? The questions are set out in a special order. Each question will cover only selected topics in Mental Maths.  If you look at the questions in Question 1, you will see only different types of addition questions, while Question 4 has only different types of division questions. Then, if you look at Question 6, you will see a selection of questions on only a few concepts, such as place value, expanded notation and numerals in words.  This is our innovative approach to learning, as a student will have the opportunity to practise a few concepts again and again in a question until they are understood. This is the essence of Maths learning and will develop the student’s confidence and mastery.

What is the Help section?  This section is not just a list of explanations or strategies—it has been carefully put together to relate directly to the appropriate question in each Unit.  It is divided into sections that match the numbered questions—1, 2, etc. An explanation is supplied to help the student answer each type of question. For example: A student has difficulty with Unit 3, Set B, Question 17. Litres in 3 000 mL.  Go to the Help section and turn to section 17  Under the section on Capacity you will see an example in bold type: e.g. Litres in 12 000 mL This is a similar question to the one the student is unsure about.  Read the explanation on Capacity to find out how to solve this type of problem.  The  icon tells you books in the Excel series which can provide further practice in each particular concept.  An index for the Help section can be found on the back page.

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MATHS

MENTAL BASIC SKILLS MATHS 6 STRATEGIES YEAR AGES 11–12

G e t t he Re su lt s You Want ! A lan P arker & Jan Faulk ner TP 2015.indd 1

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Copyright © 2005 Alan Parker Reprinted 2007, 2008 (twice), 2009, 2010, 2011, 2012 Updated in 2013 for the Australian Curriculum Reprinted 2015, 2016 ISBN 978 1 74125 183 8 Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www.pascalpress.com.au Publisher: Vivienne Joannou Project editors: Emma Driver and May McCool Edited by May McCool, Jeremy Billington and Valerie McCool Answers checked by Valerie McCool Indexed by Jeremy Billington Original page design by Jelly Design Additional design and typesetting by Precision Typesetting (Barbara Nilsson) Cover by DiZign Pty Ltd Cover photos by Brand X, Image Source and photos.com 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 the body that administers it) has given a remuneration notice to 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 E-mail: [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.

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Contents Help Section . . . . . . . . . . . . . . .

2

Unit 18 . . . . . . . . . . . . . . . . . . . . . 56

Unit 1 . . . . . . . . . . . . . . . . . . . . . . 22

Unit 19 . . . . . . . . . . . . . . . . . . . . . 57

Unit 2 . . . . . . . . . . . . . . . . . . . . . . 24

Unit 20 . . . . . . . . . . . . . . . . . . . . . 60

Unit 3 . . . . . . . . . . . . . . . . . . . . . . 26

Unit 21 . . . . . . . . . . . . . . . . . . . . . 62

Unit 4 . . . . . . . . . . . . . . . . . . . . . . 28

Unit 22 . . . . . . . . . . . . . . . . . . . . . 64

Unit 5 . . . . . . . . . . . . . . . . . . . . . . 30

Unit 23 — Fun Spot! . . . . . . . . . . 66

Unit 6 . . . . . . . . . . . . . . . . . . . . . . 32

Unit 24 — Revision . . . . . . . . . . . 68

Unit 7 — Fun Spot! . . . . . . . . . . . 34

Unit 25 . . . . . . . . . . . . . . . . . . . . . 70

Unit 8 — Revision . . . . . . . . . . . . 36

Unit 26 . . . . . . . . . . . . . . . . . . . . . 72

Unit 9 . . . . . . . . . . . . . . . . . . . . . . 38

Unit 27 . . . . . . . . . . . . . . . . . . . . . 74

Unit 10 . . . . . . . . . . . . . . . . . . . . . 40

Unit 28 . . . . . . . . . . . . . . . . . . . . . 76

Unit 11 . . . . . . . . . . . . . . . . . . . . . 42

Unit 29 . . . . . . . . . . . . . . . . . . . . . 78

Unit 12 . . . . . . . . . . . . . . . . . . . . . 44

Unit 30 . . . . . . . . . . . . . . . . . . . . . 80

Unit 13 . . . . . . . . . . . . . . . . . . . . . 46

Unit 31 — Fun Spot! . . . . . . . . . . 82

Unit 14 . . . . . . . . . . . . . . . . . . . . . 48

Unit 32 — Revision . . . . . . . . . . . . 84

Unit 15 — Fun Spot! . . . . . . . . . . 50

Index to Help Section . . . . . . . . 86

Unit 16 — Revision . . . . . . . . . . . 52

Answers . . . . . . . . (lift-out section)

Unit 17 . . . . . . . . . . . . . . . . . . . . . 54

© Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_pp00_01_title_new2725.indd 3

Excel Basic Skills Mental Maths Strategies Year 6 11/09/13 8:02 AM

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 Help Section

Question 2

Question 1

Subtraction

Addition

Addition is combining or putting together two or more numbers. We use the sign + to show addition. 29 e.g. 6 + 7 = 13 + 17 46

Subtraction is taking away one number from another number. We use the sign – to show subtraction. e.g. 13 – 7 = 6 51 – 18 33

Hint: Other words for addition include add, plus, sum, more and total (the answer when we add two or more numbers together). e.g. 19 and 26 more (answer is 45)

Hint: Other words for subtraction include minus, subtract, take away, less than, difference (the answer when we subtract one number from another). e.g. 56 minus 29 (answer is 27)

Addition strategies You can add numbers in your head using strategies (or little tricks) to help you. Let’s look at some of them. The jump strategy e.g. 58 + 23

58

68

Subtraction strategies You can subtract numbers in your head using strategies (or little tricks) to help you. Let’s look at some of them. The jump strategy e.g. 81 – 23

78 79 80 81

we say 58 + 10 + 10 + 3 = 78 + 3 to give 81

The split strategy e.g. 56 + 27 we say 50 + 20 + 6 + 7 = 70 + 13 to give 83 The compensation strategy e.g. 25 + 59 we say 25 + 60 – 1 = 85 – 1 to give 84 Bridging the tens e.g. 57 + 15 we say 57 + 10 + 5 = 67 + 5 to give 72 Changing the order of addends e.g. 14 + 8 + 6 we say 14 + 6 + 8 = 20 + 8 to give 28 Using patterns to extend number facts e.g. 2 + 3 = 5 so 20 + 30 = 50

58 59 60 61

71

81

we say 81 – 10 – 10 – 3 = 61 – 3 to give 58

The split strategy e.g. 89 – 56 we say 80 – 50 + 9 – 6 = 30 + 3 to give 33 The compensation strategy e.g. 100 – 46 we say 99 – 46 + 1 = 53 + 1 to give 54 Bridging the tens e.g. 72 – 15 we say 72 – 10 – 5 = 62 – 5 to give 57 Using patterns to extend number facts e.g. 9 – 6 = 3 so 90 – 60 = 30  Excel Basic Skills Addition and Subtraction Years 5–6

 Excel Basic Skills Addition and Subtraction Years 5–6

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© Pascal Press ISBN 978 1 74125 183 8

MMS_yr6_pp02_21_new2725.indd 2

Excel Basic Skills Mental Maths Strategies Year 6

11/09/13 8:02 AM

Factor strategy e.g. 6 × 33 (answer is 198) You know 6 is 2 × 3. So 33 × 6 is the same as 33 × 3 × 2. That is 99 × 2 = 198.

Question 3

Multiplication Multiplication is repeated addition of the same number. We use the sign × to show multiplication. e.g. 6 + 6 + 6 + 6 + 6 0

6

12

18

24

Factorising large numbers e.g. 6 × 45 (answer is 270) You know 45 is 40 + 5. So 6 × 45 is the same as 6 × 40 + 6 × 5. That is 240 + 30 = 270.

30

Here we added 5 lots of 6 to make 30. 5 × 6 = 30 6 × 5 30

Hint: Other words for multiplication include multiply, times, lots of, groups of, product (the answer when we multiply two or more numbers together). e.g. 9 times 14 (answer is 126) Here is a tables chart to help you with multiplication. × 1 2 3 4 5 6 7 8 9 10

1 1 2 3 4 5 6 7 8 9 10

2 2 4 6 8 10 12 14 16 18 20

 Excel Basic Skills Multiplication and Division Years 5–6

Question 4 Division

3 3 6 9 12 15 18 21 24 27

4 4 8 12 16 20 24 28 32 36

5 5 10 15 20 25 30 35 40 45

6 6 12 18 24 30 36 42 48 54

7 7 14 21 28 35 42 49 56 63

8 8 16 24 32 40 48 56 64 72

9 9 18 27 36 45 54 63 72 81

10 10 20 30 40 50 60 70 80 90

30

40

50

60

70

80

90

100

Division is repeated subtraction of the same number. We use the sign ÷ to show division. e.g. 30 – 6 – 6 – 6 – 6 – 6

Multiplication strategies You can multiply in your head using strategies (or little tricks) to help you. Let’s look at some of them. Skip counting allows us to count on our fingers. e.g. 8, 16, 24 so 3 × 8 is 24

Multiply tens then units e.g. 7 × 84 (answer is 588) 7 × 80 = 560 7 × 4 = 28 So 7 × 84 = 560 + 28 = 588

Using patterns to multiply e.g. 2 × 3 = 6 1·34 × 1 = 1·34 so 2 × 30 = 60 so 1·34 × 10 = 13·4 so 2 × 300 = 600 so 1·34 × 100 = 134 Reverse operations If you know one table fact, you also know three others. e.g. 7 × 8 = 56 so 8 × 7 = 56 and 56 ÷ 8 = 7 and 56 ÷ 7 = 8

0

6

12

18

24

30

Here we were able to take away 6 five times so there are 5 sixes in 30. 5 30 ÷ 6 = 5 6 30

)

Hint: Other words for division include divide, share, quotient (the answer when we divide one number by another). e.g. 68 divided by 4 (answer is 17)

Remainder

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When we divide one number into another number we don’t always get a whole number for the answer. Sometimes we have a little bit left over and we call this a remainder. e.g. 31 – 6 – 6 – 6 – 6 – 6

01

7

13

19

25

31

Here 6 can be subtracted five times but there is still one left over. The answer is 5 r 1 (5 remainder 1). 5r1 31 ÷ 6 = 5 r 1 6 31

)

 © Pascal Press ISBN 978 1 74125 183 8



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 Hint: If we write the remainder (here 1) over the

1 divisor (here 6) we get a fraction (here ) so the 6 1 answer to our question can be written as 5 . 6 1 e.g. 456 ÷ 5 (answer is 91 ) 5

Divisible by 10 The last digit must be 0. 64 780 ÷ 10 = 6 478 e.g. 790 ÷ 10 = 79 Here 790 and 64 780 end in 0.

 Excel Basic Skills Multiplication and Division Years 5–6

Division strategies You can divide numbers in your head using strategies (or little tricks) to help you. Let’s look at some of them. Using patterns to divide e.g. 56 ÷ 8 = 7 so 560 ÷ 8 = 70 Reverse operations If you know one table fact, you also know three others. e.g. 7 × 8 = 56 so 8 × 7 = 56 and 56 ÷ 8 = 7 and 56 ÷ 7 = 8

Tests for divisibility Divisible by 2 The number must be even. e.g. 98 ÷ 2 = 49 274 ÷ 2 = 137 Here 98 and 274 are even numbers. Divisible by 3 The sum of the digits must be divisible by 3. e.g. 10 212 ÷ 3 = 3 404 Here the digits 1 + 2 + 1 + 2 = 6 and 6 can be divided by 3. Divisible by 4 The number made by the last two digits must be divisible by 4. e.g. 868 ÷ 4 = 217 20 676 ÷ 4 = 5 169 Here 68 and 76 are both divisible by 4. Divisible by 5 The last digit must be a 5 or a 0. e.g. 190 ÷ 5 = 38 3 285 ÷ 5 = 657 Here 190 and 3 285 end in 0 or 5. Divisible by 6 Must be divisible by 2 and 3. e.g. 24 is even and can be divided by 3, so it can be divided by 6. Divisible by 8 The number made by the last three digits must be divisible by 8. e.g. 2 616 ÷ 8 = 327 3 944 ÷ 8 = 493 Here 616 and 944 are both divisible by 8. Divisible by 9 The sum of the digits must be divisible by 9. e.g. 11 736 ÷ 9 = 1 304 Here the digits 1+1+7+3+6 = 18 and 18 can be divided by 9.

Question 5 Money—addition & subtraction We use the same strategies to add or subtract money that we use to add or subtract ordinary numbers but we have to remember to write the dollar sign ($) and include the decimal point. e.g. $3.25 + $6.45 we say $3.25 + $6 is $9.25 and 40c is $9.65 and 5c is $9.70 e.g. $5.65 + $7.45 (answer is $13.10)

Money—multiplication & division We use the same strategies to multiply or divide money that we use to multiply or divide ordinary numbers but we have to remember to write the dollar sign ($) and include the decimal point. e.g. $3.35 × 3 we say $3.00 × 3 is $9.00 and 3 × 40 – 15 is $1.05 making $10.05 e.g. $3.25 x 5 (answer is $16.25)

Changing dollars and cents To change dollars to cents, we multiply by 100. e.g. $16.85 = 16.85 × 100 = 1 685 cents Hint: You can just remove the dollar sign and the decimal point to get the same answer. e.g. $12.95 as cents (answer is 1 295c) To change cents to dollars, we divide by 100. e.g. 1 685 cents = 1 685 ÷ 100 = $16.85

Addition & subtraction of decimals We add and subtract decimals just like money. We have to be careful to keep the decimal points in the right place. 3·5 e.g. 3·5 + 1·8 = 5·3 + 1·8 5·3

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11/09/13 8:02 AM

Hint: If you write the numbers vertically, make sure that the decimal points are in a straight line. e.g. 6·5 + 9·9 (answer is 16·4) 13·8 – 8·3 (answer is 5·5)

Problem solving with money To solve problems with money, we first need to understand what operation is involved. It may be addition, subtraction, multiplication or division. Key words can help us understand what to do. e.g. Change from $20 if $12.95 is spent. ‘Change’ indicates subtraction so $20.00 – $12.95 = $7.05

Cost of 5 at $3.25 each Cost ‘at’ indicates multiplication so $3.25 x 5 = $16.25 Share $16.35 between 5 people ‘Share’ indicates division so $16.35 ÷ 5 = $3.27

 Excel Basic Skills Addition and Subtraction Years 5– 6  Excel Basic Skills Multiplication and Division Years 5–6

e.g. 8 256 has 8 256 ones or units 825 tens 82 hundreds 8 thousands e.g. Tens in 36 478 (answer is 3 647)

Numerals in words

Sometimes we need to write a numeral in words. e.g. sixty-five thousand three hundred and forty-two Here we write the numeral just the way it sounds when we read it as a number. e.g. Numeral for seventy thousand four hundred and ten (answer is 70 410)

Digits A digit is a symbol used to write a numeral. We use digits from 0 to 9 to write all of our numerals. e.g. 364 829 1 496 207 e.g. How many digits in 6 305 194? (answer is 7 digits)  Excel Basic Skills Addition and Subtraction Years 5–6

Question 6 Place value Place value tells us the value of each digit depending on where it is placed in a number. e.g. 38 256 3 is 3 ten thousands (30 000) 8 is 8 thousands (8 000) 2 is 2 hundreds (200) 5 is 5 tens (50) 6 is 6 units (6) e.g. Place value of 9 in 49 281 (answer is 9 thousands or 9 000)

Expanded notation Expanded notation is a way of writing numerals to show the place value of each digit. e.g. 60 000 + 5 000 + 900 + 40 + 3 Here: 6 is in the ten thousands column 5 is in the thousands column 9 is in the hundreds column 4 is in the tens column 3 is in the units column e.g. Expanded notation for 65 943 (answer is 60 000 + 5 000 + 900 + 40 + 3)

Reading place value By reading place value carefully, we can find how many tens, hundreds, thousands, etc. there are in a number.

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Question 7 Fractions A fraction is any part of a whole or group. The common fraction is written as

a where: b

a (numerator) is the number of equal fraction parts b (denominator) is the number of equal parts that the whole has been divided into. e.g.

3 shows 3 out of 5 equal parts 5

3 < numerator 5 < denominator

The denominator is the bottom number of a fraction. The numerator is the upper number. 5 6

e.g. 5 out of 6 as a fraction (answer is )

Decimal fractions A decimal fraction is a fraction that uses a decimal point. Decimal fractions show the number of equal parts out of ten, one hundred, one thousand, etc. e.g. 25 out of 100 equal parts or

25 100

so the decimal fraction is 0·25




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 e.g. 6 parts out of 10 as a decimal (answer is 0·6)

Percent

25

A percentage is a special fraction that is always out of one hundred. e.g.

35 is 0·35 = 35% 100

e.g. 75 parts out of 100 as a percentage (answer is 75%)

Converting a percentage to a fraction To change a percentage to a fraction, write it as a part out of 100. e.g. 65% is 65 parts out of 100 =

65 100

e.g. 25% as a fraction (answer is

Here are some percentage equivalents that you should know:

10% = 20% = 25% =

Converting a decimal to a fraction To change a decimal to a fraction, look at the number of digits after the decimal point. If there is one digit the fraction will be tenths. If there are two digits, the fraction will be hundredths, etc. e.g. 0·7 has one digit after the decimal so 0·7 =

7 10

so 0·75 =

75 100

e.g. 0·64 as a fraction (answer is

64 ) 100

Converting a decimal to a percentage To change a decimal to a percentage, multiply by 100. e.g. 0·48 = 0·48 × 100 = 48% 0·06 = 0·06 × 100 = 6% e.g. 0·05 as a percent (answer is 5%)

= 0 ⋅ 01

50% = 50 = 0 ⋅ 5

Equivalent decimal fractions

= 0 ⋅1

75% =

= 0 ⋅2

100% =

Fractions, decimals and percentages can appear to be different but they are equivalent if they have the same value.

100 75 100 100 100

= 0 ⋅ 75 = 1⋅ 0

= 0 ⋅ 25

Converting a fraction to a percentage To change a fraction to a percentage, we have to change the denominator to one hundred. 90 9 (×10) e.g. = 10 (×10) 100 = 90% e.g.

3 as a decimal (answer is 0·3) 10

e.g.

0·75 has two digits after the decimal

25 ) 100

To change a percentage to a decimal, divide by 100. e.g. 48% = 48 ÷ 100 = 0·48 6% = 6 ÷ 100 = 0·06 e.g. 25% as a decimal (answer is 0·25)

1 100 10 100 20 100 25 100

= 25 ÷ 100 100 = 0·25

Converting a percentage to a decimal

1% =

6

e.g. = 6 ÷ 10 10 = 0·6

3 as a percentage (answer is 30%) 10

Converting a fraction to a decimal We can change a fraction to a decimal if it has a denominator of ten or one hundred.

e.g. 0·45 =

45 = 45% 100

They all have the same value. e.g. Is 0·8 the same as 70%? (answer is no)

Place value in decimals Place value tells us the value of each digit depending on where it is placed in a number. e.g. 8·375 8 is 8 ones (8) 3 ) 10

3 is 3 tenths (

7 is 7 hundredths (

7 ) 100 5 ) 5 is 5 thousandths ( 1000

e.g. 2 +

7 4 9 + + as a decimal 10 100 1000

(answer is 2·749)

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e.g. 3 units + 5 tenths + 2 hundredths as a decimal (answer is 3·52)

Words for decimals Sometimes we need to write a decimal numeral in words. e.g. One point three four = 1·34 Here we write the numeral just the way it sounds when we read it as a number. e.g. Numeral for five point three seven (answer is 5·37)

Decimal to the nearest whole number We can round off decimals in the same way that we round off counting numbers. e.g. 6·75 is closest to 7 and 6·35 is closest to 6 e.g. 8·58 to the nearest whole number (answer is 9)  Excel Basic Skills Fractions, Decimals and Percentages Years 3–6

Rounding off to the nearest thousand

To round 4692 to the nearest thousand we look at the hundreds digit (6) which is above 5 therefore we round off upwards so 4 692 rounds off to 5 000 e.g. Round off 35 468 to the nearest thousand (answer is 35 000)

Greater than and less than

We use the symbol > to show that one number is bigger than another. e.g. 6 942 > 5 942 We read this as 6 942 is greater than 5 942. e.g. Is 75 892 > 75 882? (answer is yes) We use the symbol < to show that one number is smaller than another. e.g. 6 942 < 8 942 We read this as 6 942 is less than 8 942. e.g. Is 75 892 < 75 882? (answer is no)

Ascending and descending order When we place things in ascending order, we arrange them from smallest to largest. e.g. 3 567, 4 069, 6 921, 8 004 1·2, 1·5, 1·9

Question 8 Rounding off Rounding off numbers allows us to estimate answers. We round off digits 5 and above up to the next number and we round off digits below 5 down to the lower number.

Rounding off to the nearest ten To round 4 692 to the nearest ten we look at the ones digit, which is 2 (below 5, therefore we round off downwards), so we round down to 9 tens. Then we write a zero in the place of the last digit so 4 692 rounds off to 4 690. e.g. Round off 35 468 to the nearest ten (answer is 35 470)

Rounding off to the nearest hundred To round 4 692 to the nearest hundred we look at the tens digit, which is 9 (above 5, therefore we round off upwards), so we round 6 up to 7. Then we write a zero in the place of the last two digits so 4 692 rounds off to 4 700. e.g. Round off 35 468 to the nearest hundred (answer is 35 500)

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When we place things in descending order, we arrange them from largest to smallest. e.g. 6 589, 4 318, 3 950, 3 007 9·5, 7·9, 5·6, 1·4 e.g. Arrange 35, 68, 27 and 56 in ascending order (answer is 27, 35, 56, 68)

Largest and smallest possible number To make the largest possible number from a group of digits, we write the largest digit first, followed by the next largest and so on until all the digits have been used. e.g. Largest possible number using 6, 4, 8, 5 (answer is 8 654) To make the smallest possible number from a group of digits, we write the smallest digit first, followed by the next smallest and so on until all the digits have been used. e.g. Smallest possible number using 6, 4, 8, 5 (answer is 4 568)  Excel Basic Skills Addition and Subtraction Years 5–6  Excel Advanced Skills Start Up Maths Year 6




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 Mixed numbers

Question 9

Equivalent fractions

A mixed number is a fraction that has a whole number and a common fraction written together.

Equivalent fractions are fractions that look different but are equal in value.

e.g.

e.g.

3 6 is equivalent to 5 10 3 5

6 10

Here we have multiplied both the 3 numerator and denominator of by the 5 same number (× 2). 6 3×2 = 10 5×2

Simplify a fraction 2 1 e.g. can be simplified to 6 3

2 6

1 3

Here we have divided both the numerator and 2 denominator of by the same number (÷ 2). 1 2÷2 = 3 6÷2

1 is coloured 3

1 3

2 is a mixed number

1 4

e.g. 2 is a mixed number

Changing a mixed number into an improper fraction We can change a mixed number into an improper fraction by multiplying the whole number by the denominator and adding the numerator. 1 3

e.g. 2 is 2 × 3 +1 = 7 thirds

To simplify a fraction, we reduce it to the lowest equivalent fraction.

2

6

=

3 4

7 3

e.g. 2 as an improper fraction (answer is

11 ) 4

 Excel Basic Skills Fractions, Decimals and Percentages Years 3–6

Question

10

Finding a fraction of a whole number

Improper fractions An improper fraction is a fraction where the numerator is bigger than the denominator.

To find a fraction of a whole number, we multiply the fraction by the whole number.

e.g.

e.g.

7 is coloured 5

7 is an improper fraction 5

e.g.

8 is an improper fraction 3

Changing an improper fraction to a mixed number We can change an improper fraction to a mixed number by dividing the denominator into the numerator and writing down the remainder over the denominator. 7 e.g. is 7 ÷ 5 5

= 1 remainder 2 parts of the whole

=1

2 5

1 of 15 is the same as 15 ÷ 3. That is 5. 3

Hint: Here we say that one third of 15 is 5. 2 2 × 15 e.g. × 15 = 3

3

30 = 3

= 10 Hint: Here we could have said one third of 15 is 5 so two thirds (twice as much) is 10. 5 e.g. of 24 (answer is 20) 6

Multiplying a fraction We can multiply a fraction by using repeated addition. 3 3 3 3 e.g. 3 × = + + 8

3 11 e.g. as a mixed number (answer is 2 ) 4 4

8 9 = 8

=1

8

8

1 8

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 We can also multiply a fraction by multiplying the numerator by the whole number. 7 3×7 e.g. 3 × =

Roman numerals

Adding and subtracting fractions

Roman numerals use letters instead of digits. They are not often used today but we still see them on clocks and in books. The letters used in Roman numerals are: I = 1 V=5 X = 10 L = 50 C = 100 D = 500 M = 1 000

With the same denominator We can add and subtract fractions if they have the same denominator. 1 3 4 7 4 3 e.g. + = – =

Most Roman numerals join up to three of each letter to show numbers. e.g. XXXII = 32 LXXXIII = 83 CCXXXI = 231 DCCCXIII = 813

With a different denominator If the fractions have different denominators we can change one (or both) to equivalent fractions to make the denominators the same.

The fours and nines are a little more difficult and are shown by two letters: IV = 4 XL = 40 CD = 400 IX = 9 XC = 90 CM = 900 e.g. Roman numeral for 276 (answer is CCLXXVI)

10

10 21 = 10 1 = 2 10

5

5

5

8

8

8

7 1 7 5 1 1×2 + = + – = 10 5 10 5 × 2 6 3 7 2 = + = 10 10 9 = = 10

e.g.

5 1×2 – 6 3×2 5 2 – 6 6 3 6

Finding a percentage of a whole number To find a percentage of something we change the percentage to a fraction and then work it out as shown above. e.g. To find 25% of 80 25 1 change 25% to = 100

and

4

1 of 80 is 20 4

e.g. 10% of $70 (answer is $7)

Finding the percentage off a price To find the percentage off a price, we find the percentage of the amount (as shown above) and subtract that amount from the full price. e.g. To find 25% off a price of $80

change

and

25% to

25 1 = 100 4

1 of $80 is $20 4

then $80 – $20 = $60 e.g. Cost if 10% off $300 (answer is $270)  Excel Basic Skills Fractions, Decimals and Percentages Years 3–6

Question

11

Hindu-Arabic numerals

These are the ordinary numbers that we use every day. By using the digits 0 to 9, we can make any counting number. e.g. 6, 96, 127, 2 705, etc. Hint: These are sometimes known as digital numbers. e.g. Hindu-Arabic numeral for CCLXXVI (answer is 276)

Bigger and smaller numbers We can find a bigger or smaller number than a given number by adding or subtracting. e.g. Number 500 bigger than 3 768 is 3 768 + 500 = 4 268 e.g. What is the number after 27 899? (answer is 27 900)

Negative numbers

A negative number is any number less than zero. e.g. 5 less than 2 is –3. 2 – 5 = –3 –4 –3 –2

–1

0

1

2

3

Hint: Imagine a thermometer in a very cold climate where the temperature is –4°C. Here the negative number is –4. e.g. What is the number 10 less than 3? (answer is –7)  Excel Basic Skills Whole Numbers, Decimals, Percentages and Fractions Year 7


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Prime numbers

12

Divisible A number is divisible if it can be divided exactly by another number. e.g. 75 ÷ 5 = 25 so 75 is divisible by 5 Hint: Use the tests for divisibility in section 4 e.g. Is 75 divisible by 8? (answer is no)

Factors A factor is any whole number that can be divided into another number. e.g. 2, 3, 4 and 6 are factors of 12 because each number will divide evenly into 12. (12 ÷ 6 = 2, 12 ÷ 3 = 4 etc.) e.g. All the factors of 6 (answer is 1, 2, 3 and 6)

Highest Common Factor (HCF) The highest common factor is the largest factor found in two or more given numerals. e.g. Factors of 6 are 1, 6, 2, 3. Factors of 9 are 1, 9, 3. The highest factor common to both is 3.

Products

A product is the answer obtained when two or more numbers are multiplied. e.g. 12 is the product of 3 and 4 because 3 × 4 = 12 e.g. Product of 5 and 6 (answer is 30)

Multiples A multiple is any number that can be divided by a given number. e.g. 3, 6, 9 and 12 are multiples of 3 because 3 will divide into each one.

Hint: When we write the 3 times tables we write the multiples of 3. i.e. 1 × 3 = 3, 2 × 3 = 6, 3 × 3 = 9, 3 × 4 = 12 Here 3, 6, 9 and 12 are multiples of 3. e.g. What are the first 3 multiples of 5? (answer is 5, 10 and 15)

Lowest Common Multiple The lowest common multiple is the smallest numeral that is a multiple of two given factors. e.g. What is the lowest common multiple of 4 and 5? Multiples of 4 are 4, 8, 12, 16, 20, 24, ... Multiples of 5 are 5, 10, 15, 20, 25, ... The lowest multiple common to both is 20.

A prime number is any number that only has two factors (itself and one). e.g. 3 = 1 × 3 3 has only has two factors so it is a prime number. Prime numbers include 2, 3, 5, 7, 11, etc. e.g. Is 19 a prime number? (answer is yes)

Composite numbers A composite number has more than two factors. e.g. 8 = 1 × 8 = 2 × 4 8 has more than two factors so it is a composite number. Hint: Because1 has only one factor it is neither a prime number nor a composite number. e.g. Is 12 a composite number? (answer is yes)

The average The average is the total of the scores divided by the number of scores. e.g. Scores: 36, 47, 29, 40 Average = (36 + 47 + 29 + 40) ÷ 4 = 152 ÷ 4 = 38 Here, the average is 38. Hint: To find the average first add the scores together. Count the number of scores and divide the total by the number of scores. e.g. Average of 12, 15 and 21 (answer is 16)  Excel Basic Skills Multiplication and Division Years 5–6

Question

13

Odd numbers An odd number is any number that cannot be exactly divided by 2. e.g. 1, 3, 5, 7, 9 etc. e.g. Is 257 an odd number? (answer is yes)

Even numbers An even number is any number that can be exactly divided by 2. e.g. 2, 4, 6, 8, 10, etc e.g. Is 356 an even number? (answer is yes)

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Ordinal numbers

Number patterns

We use ordinal numbers to order things from first to last. We use digits and abbreviations to write ordinal numbers. e.g. 1st (first), 2nd (second), 3rd (third) etc. e.g. Ordinal number for twenty-fifth (answer is 25th)

A number pattern is a regular pattern made by counting or by using operations. e.g. 250, 350, 450, … Counting by hundreds 4, 8, 16, … Doubling each number 1·5, 2, 2·5, 3, ... Counting by 0·5

Square numbers A square number is the answer obtained when a number is multiplied by itself. e.g. 2 × 2 = 4 5 × 5 = 25 Here, 4 and 25 are square numbers. Square numbers may be represented by dots in the shape of a square.

A geometric pattern shows a pattern of numbers that you can get from multiplication or division. e.g. ∆, ∆∆, ∆∆∆, ... Here the number of sides on the triangles show the pattern 3, 6, 9, … These are multiples of 3. Number patterns are often shown as grids. e.g. Number of hexagons 1 2 3 4 5 6 Number of sides

4

9

16

Hint: We use a small number (called an index) if we want to show a number has been squared. e.g. 22 ← index is 2 × 2 which is equal to 4. e.g. Is 64 a square number? (answer is yes)

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6

12

18

24

30

36

e.g. 375, 325, 275, ____ (answer is 225)

Order of operations

Triangular numbers are numbers that are obtained by adding successive numerals starting at 1. e.g. 1 + 2 = 3 1+2+3=6 Here 3 and 6 are triangular numbers. Triangular numbers may be represented by dots in the shape 1 3 6 10 of a triangle. e.g. Is 10 a triangular number? (answer is yes as 1 + 2 + 3 + 4 = 10)

When we have more than one operation to complete in the same problem, we complete them in a set order: 1 Complete any operations inside brackets. 2 Complete any multiplication or division in the order they appear. 3 Complete any addition or subtraction in the order they appear. e.g. 6 + (3 × 4) – 2 × 5 We do inside the brackets first: 6 + 12 – 2 × 5 We do multiplication next: 6 + 12 – 10 We do addition and subtraction: 6 + 12 – 10 = 18 – 10 = 8 e.g. 6 + 9 – 16 ÷ 4 (answer is 11)

 Excel Basic Skills Whole Numbers, Decimals, Percentages and Fractions Year 7

 Excel Basic Skills Multiplication and Division Years 5–6  Excel Basic Skills Problem Solving Years 5–6

Triangular numbers

Question

Question

14

Length

Number sentences A number sentence uses a shape to represent a missing numeral. e.g. 3 × = 27 To solve a problem like this we say 3 times what equals 27. Here, the missing numeral is 9. e.g. 35 +

15

= 72 (answer is 37)

When we talk about length, we are talking about how long something is, the distance between two points or the circumference of a circle. Units of length millimetre (mm) centimetre (cm) metre (m) kilometre (km)


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Question

10 mm = 1 cm 100 cm = 1 m 1 000 mm = 1 m 1 000 m = 1 km

Perimeter The perimeter of a shape is the total length of its boundary.

Converting different lengths To convert centimetres (cm) to metres (m), we divide by 100. e.g. 300 cm = 300 ÷ 100 =3m

478 cm = 478 ÷ 100 = 4·78 m

To convert metres (m) to centimetres (cm), we multiply by 100. e.g. 3 m = 3 × 100 = 300 cm

16

4·78 m = 4·78 × 100 = 478 cm

To convert metres (m) to kilometres (km), we divide by 1 000. e.g. 5 000 m = 5 000 ÷ 1 000 = 5 km To convert kilometres (km) to metres (m), we multiply by 1 000. e.g. 5 km = 5 × 1 000 = 5 000 m e.g. Metres in 5·5 km (answer is 5 500 m)

Speed Speed tells us how quickly something is moving. To find the (average) speed, we divide the distance travelled by the time taken to cover that distance. e.g. 60 km travelled in two hours Speed is 60 ÷ 2 = 30 so speed is 30 km/h (kilometres per hour)

Distance To find the distance travelled, we multiply the (average) speed by the time taken to cover that distance. e.g. How far travelled in two hours at an average speed of 60 km/h. Distance is 60 × 2 = 120 so distance is 120 km  Excel Advanced Skills Start Up Maths Year 6

e.g. The perimeter of this shape is 4 + 2 + 4 + 2 = 12 cm

4 cm 2 cm

2 cm 4 cm

Hint: To find the perimeter of any shape, first draw a diagram, write the dimension of each side and then add all the lengths together. 5 cm e.g. Perimeter = 5 + 4 + 5 + 4 = 18 cm 4 cm 4 cm 5 cm

Perimeter = 4 + 4 + 4 + 4 = 16 cm

4 cm 4 cm

4 cm 4 cm

Formula for perimeter of a rectangle Another way to find the perimeter of a rectangle is add the length to the width and then double that. e.g. Perimeter = 2 × (length + width) 5 m 4m = 2 × (5 + 4) =2×9 = 18 m To find the perimeter of a regular polygon A regular polygon has all sides the same length. You can find the perimeter of any regular polygon by multiplying the length of one side by the number of sides. e.g. Perimeter = 3 × length 5 cm =3×5 = 15 cm Perimeter = 6 × length =6×3 = 18 cm

3 cm

Circumference The perimeter of a circle has a special name. It is called a circumference

Area Area is the amount of space covered or enclosed by a shape. We divide area into square units and then count the number of squares. Units of area square centimetre (cm2) square metre (m2) hectare (ha) square kilometre (km2)

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You should know this table:




 10 000 m2 = 1 hectare 1 000 000 m2 = 1 km2 100 ha = 1 km2

1 000 000 cm3 = 1 m3 1 mL of water takes up 1 cm3 of space 1 L of water takes up 1 000 cm3 of space

Formula for area of a rectangle or square A formula for finding the area of a rectangle is: Area = length × width e.g. Area = length × width 5 cm = 5×4 4 cm = 20 cm2

Volume of a rectangular prism To find the volume of a rectangular prism we can count the number of cubes in each layer and multiply by the number of layers. e.g.

Area = length × width = 6×6 = 36 cm2

6 cm

6 cm

Area of a triangle The area of a triangle is half the area of the rectangle in which the triangle can be drawn. 6 cm e.g. Area = length × width = 6×4 4 cm = 24 cm2 So the area of the triangle is 12 cm2. A formula for finding the area of a triangle is: 1 Area = of base × perpendicular height 2

e.g. Area =

1 of 6 × 4 2

=3×4 = 12 cm2

4 cm 6 cm

There are 15 cubes in each layer and there are 3 layers. The volume is 45 cm3

Formula for volume of a rectangular prism A formula for finding the volume of a rectangular prism is: Volume = length × width × height e.g. Volume = 5 × 3 × 3 3 cm 3 = 45 cm

Capacity

5 cm

3 cm

Capacity is the amount of space inside a container.

Hectare A hectare is a unit of area that is equal to 10 000 m2. To change square metres (m2) into hectares (ha), we divide by 10 000. e.g. 30 000 m2 = 30 000 ÷ 10 000 = 3 ha To change hectares (ha) into square metres (m2), we multiply by 10 000. e.g. 3 ha = 3 × 10 000 = 30 000 m2  Excel Advanced Skills Start Up Maths Year 6

Question

e.g.

There are 12 cubes in each layer and there are 3 layers. The volume is 36 cm3

17

Volume

Volume is the space taken up by an object. We divide the space into cube units and then count the number of cubes. Units of volume cubic centimetre (cm3) cubic metre (m3)

Units of capacity millilitre (mL) You should know this table:

litre (L)

1 000 mL = 1 L 1 cm3 of space can hold 1 mL of water 1 000 cm3 of space can hold 1 L of water Converting different capacities To change millilitres (mL) into litres (L), we divide by 1 000. e.g. 5 000 mL = 5 000 ÷ 1 000 = 5 L To change litres (L) into millilitres (mL), we multiply by 1 000. e.g. 3 L = 3 × 1 000 = 3 000 mL e.g. Litres in 12 000 mL (answer is 12 L)  Excel Advanced Skills Start Up Maths Year 6




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Question

18

19

Mass

Time

Mass measures the amount of matter in an object but weight is commonly used in place of mass. Units of mass gram (g) kilogram (kg) tonne (t)

Units of time second (s) minute (min) hour (h) You should know this table:


1 000 g = 1 kg 1 000 kg = 1 t 1 mL of water has a mass of 1 g 1 L of water has a mass of 1 kg

Converting different masses Converting grams and kilograms To change grams (g) into kilograms (kg), we divide by 1 000. e.g. 5 000 g = 5 000 ÷ 1 000 = 5 kg

To change kilograms (kg) into grams (g), we multiply by 1 000. e.g. 3 kg = 3 × 1 000 = 3 000 g e.g. Kilograms in 7 000 g (answer is 7 kg) Converting kilograms and tonnes To change kilograms (kg) into tonnes (t), we divide by 1 000. e.g. 8 000 kg = 8 000 ÷ 1 000 =8t To change tonnes (t) into kilograms (kg), we multiply by 1 000. e.g. 3 t = 3 × 1 000 = 3 000 kg e.g. Kilograms in 6 t (answer is 6 000 kg)

Problems with mass To solve problems with mass, we first need to understand what operation is involved. It may be addition, subtraction, multiplication or division. Key words can help us understand what to do. e.g. 1·5 kg at $4.00 per kilogram ‘at’ indicates multiplication so 4 × 1·5 = $6.00  Excel Advanced Skills Start Up Maths Year 6

60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day 365 days = 1 year 366 days = 1 leap year

We use several different types of clocks to tell the time. Here are the most common ones.

Analog time Analog times uses a clock with hands to tell the minutes and hours (and seconds). 11 12 1 e.g. 11 12 1 10 2 10

2

9 8

3 4 7

6

5

time is 10 past 6

9 8

3 4 7

6

5

time is 20 to 3

Hint: If the minute hand (long one) is moving from 12 towards 6 we read the time as past the last hour. If the minute hand is moving from 6 towards 12 we read the time as to the next hour.

Digital time Digital time uses numerals to tell hours and minutes. It shows hours from 1 to 12 and uses am to show morning (from midnight to midday) and pm to show afternoon (from midday to midnight). time is 10:16 am e.g. am

10:16

24-Hour time 24-Hour time uses numerals to tell hours and minutes. It shows all 24 hours with 00:00 being midnight and 12:00 being midday. Sometimes, the colon is left out and we write 1200 for midday. e.g. pm am

8:16

time is 08:16

10:33

time is 22:33

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Converting analog time to digital time To change analog time to digital time we write the hour that has passed then count the minutes after that hour. We add ‘am’ for before noon or ‘pm’ for after noon. e.g. 20 to 9 morning the hour is 8 40 minutes have passed from 8 o’clock so it is 8:40 am e.g. Give the digital time for 17 to 6 evening (answer is 5:43 pm)

e.g. Minutes from 7:36 to 8:15 Count on from 7:36 to 8:00 is 24 minutes Count on from 8:00 to 8:15 is 15 minutes Giving a total of 39 minutes e.g. Minutes from 6:14 to 7:10 (answer is 56 minutes)

Days in each month Here is a rhyme to help you to remember how many days in each month. Thirty days has September, April, June and November. All the rest have thirty-one except February alone, which has twenty-eight days clear and twenty-nine each leap year.

Converting digital time to analog time To change digital time to analog time, we count the minutes past the last hour. If it is less than 30 minutes past the last hour, we write that number of minutes past the hour. e.g. 7:26 the minutes past 7 are less than 30 so it is 26 past 7

Time zones

If it is more than 30 minutes past the last hour, we write 60 minus that number of minutes to the next hour. e.g. 7:36 the minutes past 7 are more than 30 so it is 24 to 8 e.g. What is the analog time for 10:39? (answer is 21 to 11)

The western part (WA) uses Western Standard Time (WST) which is two hours behind EST. e.g. When EST is 9:30 am CST is 9:00 am and WST is 7:30 am

Converting digital time to 24-hour time To change digital time to 24-hour time we write the hours in the morning as 01, 02, 03, …,12 and write the hours in the afternoon as 13, 14, 15, …, 23. e.g. 7:45 am is 07:45 7:45 pm is 19:45

Converting analog time to 24-hour time To change analog time to 24-hour time we first change to digital time and then write the digital time as 24-hour time. e.g. 20 to 6 evening is 5:40 pm is 17:40

Working out minutes between times To find the number of minutes between two times, we use the counting on strategy.

Australia is divided into three time zones. The eastern part (NSW, Qld, Vic & Tas) use Eastern Standard Time (EST).

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The central part (SA & NT) use Central Standard Time (CST) which is half an hour behind EST.

Timetables

A timetable shows the expected times of events. e.g. A train timetable shows the times that trains are expected to arrive or leave different stations. Station

Concord Stanley Chisholm

Arrive

Depart

0927 0945 1004

0931 0948 1007

 Excel Advanced Skills Start Up Maths Year 6

Question

20

Angles

An angle is the amount of turning between two lines. We use a protractor to measure angles and to draw angles of a given size. There are different types of angles: Right angle Acute angle less than 90° is 90°




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Obtuse angle more than 90° but less than 180°

Straight angle is 180°

Reflex angle more than 180° but less than 360°

Revolution is 360°

To find the number of diagonals first draw a diagram and draw a diagonal from one corner to every other possible corner. Move to the next corner and do the same. Continue until all the corners have been covered. Count the diagonals as you draw them.

Symmetry We have symmetry when one half of a shape is a mirror image of the other half. e.g. axis of symmetry

Compass points

Compass points are used to N show direction. The main NW NE compass points are north (N), south (S), east (E) and west W E (W). Other main points include SE SW north-east (NE), south-east (SE), north-west (NW) and S south-west (SW). Hint: The four main compass points are at right angles to one another so there is 90° between N and E, etc.

Parallel lines Parallel lines are pairs of lines that always remain the same distance apart. e.g. Hint: Imagine two lines like straight railways lines that appear to go on forever and always remain the same distance apart. They never meet.

Perpendicular lines

Hint: Some shapes have more than one line of symmetry.

Plane shapes A plane shape is a two-dimensional (flat) shape. It only has length and width. Plane shapes include the: triangle, circle, parallelogram, rhombus, rectangle, square and other polygons. Plane shapes may be regular or irregular.

Regular shapes Regular shapes have all sides and all angles equal. e.g.

Irregular shapes Irregular shapes do not have all sides and angles equal. e.g.

Circles

umferen irc

Hint: Imagine that you are standing in the corner of a basketball court. The line markings are perpendicular.

Circumference The circumference of a circle is the distance around the outside. Hint: You can find the circumference of a round object by wrapping a piece of string around it and measuring the length of the string.

A diagonal is a line that can be drawn to join any two opposing corners of a polygon. e.g.

diameter

s radiu

Diagonals

c

A circle is a plane shape that has a curved line as its boundary. Various parts of the circle have different names.

ce

Perpendicular lines are lines that meet at right angles. e.g.

Diameter A diameter is the distance across a circle through the centre point. The diameter is twice the length of the radius. e.g. If the diameter is 3 cm the radius is 1·5 cm

 16




11/09/13 8:03 AM

Radius A radius is the distance from the centre of a circle to the circumference. The radius is half the length of the diameter. e.g. If the radius is 1·5 cm the diameter is 3 cm.

Semicircle

Quadrilaterals

A quadrilateral is any plane shape with four straight sides. Quadrilaterals include the square, rectangle, parallelogram, rhombus, etc. e.g.

A semicircle is a half of a circle.

Quadrant

Parallelograms

A quadrant is a quarter of a circle.

A parallelogram is a plane shape that has opposite sides equal and parallel. Opposite angles are also equal.

Sector A sector is the shape formed between any two radii of a circle.

Polygons A polygon is a plane shape having three or more straight sides. e.g. Triangle (3 sides), square (4 sides), rectangle (4 sides), pentagon (5 sides), hexagon (6 sides), heptagon (7 sides), octagon (8 sides), nonagon (9 sides), decagon (10 sides). Hint: Polygons such as hexagons, pentagons, octagons etc. may be regular or irregular.

Types of triangles A triangle is a plane shape with three sides. There are various types of triangles: Scalene triangle This type of triangle has no equal sides and no equal angles. Right-angled triangle This type of triangle has one angle of 90°. Isosceles triangle This type of triangle has two equal sides and two equal angles. Equilateral triangle This type of triangle has three equal sides and three equal angles. Sum of angles in a triangle When we add the three angles in any triangle together we find an interesting fact. e.g. 70°

60°

50°

60° + 50° + 70° = 180°





A rectangle and square are a special kind of parallelogram because all of the angles are right angles.

Solid shapes A solid is a three-dimensional object. It has length, width and height. A solid cannot be drawn so that all parts can be seen at the same time. e.g. Hint: Solids include the prism, pyramid, cone, sphere, cylinder, etc.

Cross-section

A cross-section is the face that we see when we cut a solid in two. Hint: Imagine that you have cut a banana into pieces. If you cut straight across the banana the cross-section will be a circle. If you cut at an angle the cross-section will be an oval.

Views of solids

When we look at a solid from different angles we see different shapes. e.g. A cone top view side view front view

Hint: The views of solids are always plane shapes like you would see it you took a photograph of the solid from that angle.

The sum of the angles in any triangle is always 180°.




17

11/09/13 8:03 AM



 Cones, cylinders and spheres

A surface is another name for a face but is often used when we talk about circular objects such as cones, cylinders and spheres. A cone has one curved surface and one flat surface. A total of 2 surfaces.

Hint: Pyramids are named according to their bases.

Faces, edges and corners of pyramids The number of faces, edges and corners of common pyramids are shown in the table below. Faces

Pyramid

Edges Corners

Triangular

4

6

4

A cylinder has one curved surface and two flat surfaces. A total of 3 surfaces.

Rectangular

5

8

5

Pentagonal

6

10

6

Hexagonal

7

12

7

A sphere has only a curved surface.

Heptagonal

8

14

8

Octagonal

9

16

9

Hint: Cones, cylinders and spheres are all solids.

Decagonal

11

20

11

Prisms A prism is a solid that has any polygon as its base. A prism has two identical bases (one at each end) and all other faces are rectangles. e.g. Triangular prism

Net A net is a flat pattern that can be folded to make a solid. e.g. Net of a cube

corner

edge

face

base

Hint: Rectangular prisms are shown in section 17 . A cube is a special rectangular prism that has all sides of the same length. Prisms are named according to their bases.

Hint: Imagine a breakfast cereal box opened out flat. That would be the net of a rectangular prism.  Excel Advanced Skills Start Up Maths Year 6

Faces, edges and corners of prisms The number of faces, edges and corners of common prisms are shown in the table. Prism

Faces

Edges Corners

Triangular

5

9

6

Rectangular

6

12

8

Pentagonal

7

15

10

Hexagonal

8

18

12

Heptagonal

9

21

14

Octagonal

10

24

16

Decagonal

12

30

20

Coordinates Coordinates are pairs of letters or numbers used to show a position on a grid. e.g. 4 3

2 1

0 A

Pyramids A pyramid is a solid with any polygon as its base. All other faces are triangles which meet at one corner (vertex or apex). e.g. Octagonal pyramid

Extra practice

vertex corner

B

C

D

 is at B2  is at C3

E

We always read the horizontal coordinate before the vertical coordinate. Hint: A map in a street directory uses coordinates to help you find various places. You run your finger along the two coordinates until they meet at a single point.

base

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11/09/13 8:03 AM

Number plane

On a number plane, negative numbers are placed to the left of zero on the horizontal axis and below zero on the vertical axis. e.g. Point A is (1, 2) Point B is (–1, 1) Point C is (1, –2) Point D is (–2, –2) y -axis 3 2 B 1 –3

–2 –1 0 –1 D –2

Pie graph A pie graph uses a circle divided into segments of different sizes to represent information. e.g. Rainfall Apr May

1

2

3

x -axis

C

Apr

Different types of graphs Column graph A column graph uses blocks of different lengths to represent information. e.g. Here, the blocks are arranged vertically.

Jun

Jul

Dot plot A dot plot is a graph that uses dots to compare the sizes of different groups. e.g.

60

mm

May

Hours worked

Rainfall

80

40

Jan Feb Mar Apr May Jun Jul

Rain

20

Month

Chance

0

Apr

May Jun

Jul

Month e.g. Here, the blocks are arranged horizontally. Rainfall Month

Jul

Bar graph A bar graph uses a rectangle (or bar) divided into different sections to represent information. e.g. Rainfall

–3

Apr May Jun Jul

Rain

Probability tells us the chance that something may happen. Frequency is the number of times that a chance event actually occurs. e.g. If you toss a coin in the air it will land on either a head or a tail. Here, the probability or chance that the coin will land on heads is one in two. This can be written as

0

20

40

60

80

mm Line graph A line graph uses a continuous line to show how one set of information varies in relation to fixed events. Daytime temperature e.g. 30 Temperature (°C)

Jun

A

28 26 24 22 20 18 16

6 am

7 am

8 am

9 am

Time





10 am 11 am 12 noon

1 or 50%. 2

We can list the possible outcomes for an experiment. e.g. The possible outcomes for tossing two coins are: HH (two heads) HT (head and tail) TH (tail and head) TT (two tails) So the chance of getting: 1 or 25%) 4

two heads is 1 in 4 (i.e.

two tails is 1 in 4 (i.e.

a head and a tail is 2 in 4 (i.e.

1 or 25%) 4 1 or 50%) 2




19

11/09/13 8:03 AM



 Scale

Scale is used to show that a drawing or diagram has not been drawn to actual size. The scale on a diagram tells us the real size of the object being represented. Scale drawings are frequently used on maps to reduce the actual size to something that can be shown on a page. e.g. 0

50

100 150 kilometres

200

Here the scale tells us that 1 cm represents 50 km. Hint: To use the scale, find the distance on the diagram and convert that to the actual size. For example 5 cm on the diagram would be 250 km in real life.

Problem solving strategies

Guess and check e.g. What two numbers add together to give 23 but multiply to give 126? Solution: Guess 1: 16 + 7 = 23 but 16 × 7 = 112 Guess 2: 15 + 8 = 23 but 15 × 8 = 120 Guess 3: 14 + 9 = 23 and 14 × 9 = 126 So the numbers are 14 and 9 Draw a diagram e.g. How many marbles can be placed along a 30 cm ruler if each marble is 6 cm apart? Solution: 0 cm

5

10

15

20

25

30

There are six marbles. Work backwards e.g. I sold 35 stamps, bought 12 more, sold another 19 and ended up with 27. How many did I have to begin? Solution: Start 27 add 19 gives 46 minus 12 gives 34 add 35 equals 69. I started off with 69 stamps. Make a list e.g. How many two-digit numbers can be made using the digits 1, 5, 7 and 0?

Solution: Start with 1: 11, 15, 17, 10 Start with 5: 51, 55, 57, 50 Start with 7: 71, 75, 77, 70 Twelve two-digit numbers can be made.

Act it out e.g. Five stacks of money were placed in a row with 20c in the first stack, 40c in the second, 80c in the third and so on. How much money altogether? Solution:

20 40 80 160 There was $6.20 altogether.

320

Use a ratio e.g. One car was provided for every 4 people. How many cars were needed for 128 people? Solution: 128 ÷ 4 = 32 so 32 cars were needed. Solve a simpler problem e.g. How many matches are needed to make 20 of these squares?

Solution: One box uses four matches. Two boxes use 4 and 1 lot of 3 matches. Three boxes use 4 and 2 lots of 3 matches. So twenty boxes use 4 and 19 lots of 3 matches i.e. 61 matches.

Eliminate possibilities e.g. A brick has a mass between 1 kg and 2 kg. Could the mass of 4 bricks be: A 3·2 kg? B 9·5 kg? C 7·9 kg? Solution: The least mass for 4 bricks would be 4 kg so answer A is wrong. The greatest mass for 4 bricks would be 8 kg so answer B is wrong. So the mass of 4 bricks is 7·9 kg i.e. answer C

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11/09/13 8:03 AM

Look for patterns e.g. What will be the next tile?

Solution: The pattern is to colour one more segment each time. The next tile will be

 Excel Basic Skills Problem Solving Years 5–6  Excel Advanced Skills Start Up Maths Year 6








21

11/09/13 8:03 AM

Unit 1

22

A 1 2 3 4 5 6 7 8 9

20 + 12 40 – 9 5×4 30 ÷ 6 $1.50 + $1.25 Place value of 7 in 3 756 0·31 as a fraction Round off 1 654 to nearest hundred Tenths in

B

3 10

1 2 3 4 5 6 7 8

19 + 24 37 – 8 7×6 35 ÷ 5 $1.35 + $2.20 Place value of 4 in 4 367 0·47 as a percentage Round off 7 890 to nearest thousand

9

Is 1 = 3 ? 4

8

10 1 of 24

10 1 of 16

2

2

11 Roman numeral for 150 12 Is 9 divisible by 3? 13 Next odd number after 31 14 6 +

To add 19, I add 20 then subtract 1.

= 18

15 Centimetres in 6 m 16 Perimeter of rectangle 4 m by 7 m

17 Litres in 6 000 mL 18 Kilograms in 4 000 g 19 25 past 7 as digital time 20 Are opposite sides equal on a rectangle?

20

11 What number is 7 more than 3 896? 12 Is 6 a factor of 30? 13 Last even number before 92 14 8, 16, 24, 15 Millimetres in 4·2 cm 16 Area of square with 5 cm sides 17 Millilitres in 3 L 18 Grams in 7 kg 19 Use am or pm to write 3:47 morning 20 How many sides has a hexagon?

20

Complete the addition grids.

1

+

22

26

33

35

41

46

23

25

32

34

45

47

19 29

To add 29, I add 30 then subtract 1. To add 39, I add 40 then subtract 1 etc.

39 49

2

+ 19 29 59 69

Excel Mental Maths Strategies Year 6—Unit 1

© Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_pp22_33_new2725.indd 22


C

38 + 6 52 – 9 6×8 42 ÷ 6 $1.30 + $5.40 Place value of 7 in 75 916 65% as a decimal Round off 8 568 to nearest thousand

9

Is 1 = 2 ? 5

D

To add 99, I add 100 then subtract 1.

1 2 3 4 5 6 7 8

Answers on page A1

10

1 2 3 4 5 6 7 8

99 + 27 96 – 14 90 × 4 270 ÷ 3 $3.35 + $4.45 Place value of 6 in 368 951 0·1 as a percentage Round off 52 498 to nearest thousand

9

Is 3 the same as 6 ? 5

10

10 1 of 32

10 3 of 20

11 12 13 14 15 16 17 18 19

11 Hindu-Arabic numeral for CCXCVI 12 Is 6 a factor of 48? 13 6 squared

8

4

Roman numeral for 347 All factors of 40 Is 409 an odd number? 7, 14, 21, Millimetres in 3·8 cm Area of square with 3 cm sides Millilitres in 8 L Grams in 5 kg Use am or pm to write 4:57 evening 20 How many sides has a pentagon?

14 35 + 15 16 17 18 19

= 68

Centimetres in 9·5 m Area of rectangle 5 cm by 9 cm Millilitres in 4·5 L Grams in 6·5 kg Use am or pm to write 3:47 morning

20 How many vertices has a sphere?

20

20

In magic squares, each row, column and diagonal add up to the same number. Complete the following magic squares. 1 2 3 3 1 4 3 3 8 5 5 6

5 6

5

8

1

3

9

7

6

13 7 5

9

15 10 3

6

13 14 3

6 5

Let’s look at an example. 3 + 5 + 7 = 15 so 6 + 7 + = 15 The missing number is 2.

6

2 15

12 6 2 15

2

7

10

7

0

9 16

4

14 3 13

Hint: Begin with the row, column or diagonal that has all the numbers.



23


A

24

1 2 3 4 5 6 7 8

Unit 2

30 + 16 60 – 8 5×9 45 ÷ 5 $1.30 + $2.55 Place value of 6 in 6 029 0·61 as a fraction Round off 2 449 to nearest hundred

B

1 2 3 4 5 6 7 8

9 Is 3 = 5 ? 6

9 1 =

10

3

10 1 of 15

6

10 3 of 20

3

5

11 Roman numeral for 164 12 Is 3 a factor of 12? 13 Ordinal number for sixteenth 14 15 –

To subtract 29 + 35 19, I subtract 32 – 19 20 then add 1. 9×6 42 ÷ 7 $1.65 + $3.40 Place value of 3 in 69 321 0·65 as a percentage Round off 8 345 to nearest thousand

11 Number 100 after 5 739 12 All factors of 20 13 Is 55 a square number?

=8

14 42, 35, 28,

15 Millimetres in 9 cm

15 Millimetres in 3·6 cm

16 Perimeter of rectangle 6 m by 4 m

16 Area of square with 4 cm sides 17 Millilitres in 9 L

17 Litres in 8 000 mL

18 Grams in 5 kg

18 Kilograms in 5 000 g

19 Use am or pm to write 6:35 evening

19 20 past 6 as digital time 20 Are the angles equal in a square?

20

20 How many faces has a rectangular prism?

20

Complete the subtraction grids.

1

72

76

81

85

93

97

64

68

73

76

81

85

–19 –39 –59 –69 This is called the compensation strategy.

To subtract 39, first subtract 40 then add 1.

2 –19 –29 –39 –49




C

1 59 + 7 2 52 – 14 3 8 × 6

4 36 ÷ 6

D

360 is 36 tens so 360 ÷ 4 is 9 tens. i.e. 360 ÷ 4 = 90

1 2 3 4 5 6 7 8

5 $1.65 + $1.40

6 Place value of 4 in 74 589 7 0·53 as a percentage 8 Is 1 516 less than 1 416?

9 Is 2 the same as 6 ? 5

10 1 5

of 45

Answers on page A1

89 + 36 65 – 19 80 × 7 280 ÷ 4 $3.40 – $1.36 60 000 + 7 000 + 400 + 60 + 3 0·7 as a percentage Round off 28 537 to nearest thousand

9 9 as a mixed number

10

10 5 of 40

12 All factors of 18

11 50 more than 9 476?

13 92

14 123, 133, 143,

14 1 475, 1 575, 1 675,

15 Centimetres in 7·5 m

16 Area of square with 6 cm sides

16 Area of rectangle 4 cm by 8 cm

17 Millilitres in 9 L

17 Millilitres in 6·5 L

18 Grams in 7 kg

18 Grams in 9·5 kg

19 Use am or pm to write 3:29 morning

12 Is 5 a prime number?

13 Ordinal number for fifteenth 15 Millimetres in 5·6 cm

8

11 What number is 6 more than 8 358?

20 A cylinder has surfaces.

4

curved

19 Use am or pm to write 4:38 evening

20

20 A cone has surfaces.

curved 20

1

Name each solid shape. a b

_________ _________ _________

d

e

Prisms and pyramids are named according to their bases.

c

f

pentagonal prism

base is a pentagon

hexagonal pyramid

_________ _________ _________

2

Which solids have curved surfaces? __________________

3

Which solids have only flat surfaces? __________________

base is a hexagon



25


A

26

1 2 3 4 5 6 7 8

If I know one

Unit 3

table fact, I also know

B

1 39 + 26 2 54 – 28

40 + 36 90 – 8 5×7 40 ÷ 8 $3.45 + $2.35 Place value of 3 in 2 309 0·84 as a fraction Is 9 642 greater than 9 462?

3 8 × 7 4 63 ÷ 9

8 × 7 = 56 7 × 8 = 56 56 ÷ 8 = 7 56 ÷ 7 = 8

7 0·54 as a percentage

8 Round off 25 683 to nearest thousand 9 10 as a mixed number

10 1 of 24 4

11 What number is 9 less than 2 456?


= 59

13 62

15 Millimetres in 7 cm

14 120, 140, 160, 180,

16 Perimeter of rectangle 8 m by 3 m 17 Millilitres in 6 L 18 Grams in 9 kg

3

11 Roman numeral for 139 12 Is 35 divisible by 7? 13 Even number after 699 14 25 +

6 8 000 + 500 + 40 + 9

5

of 24

5 $2.45 + $3.95

9 Fifths in 4 10 1 2

three related facts.




19 28 past 11 as digital time 20 How many right angles has a rectangle?

15 Centimetres in 39 mm

19 Minutes from 2:37 to 3:04 20

20 A triangular pyramid has faces.

20

Write the decimal for the part coloured in each hundred square.

1

2

3

4

5

6

28 out of 100 is the same as 0·28

Hint: final zeros in a decimal may be omitted, e.g. 0·60 is 0·6. 60 hundredths is the same as 6 tenths. Excel Mental Maths Strategies Year 6—Unit 3



C

1 2 3 4 5 6 7 8

D

58 + 6 35 – 19 8×8 72 ÷ 9 $2.95 + $1.35 Place value of 4 in 64 297 0·95 as a percentage Round off 45 678 to nearest thousand

9 2 3 as improper fraction

1 2 3 4 5 6

154 + 20 245 – 30 6 × 7 = 42 so 90 × 6 6 tens × 7 = 42 tens = 420 320 ÷ 8 $6.20 – $1.35 Expanded notation for 15 729 7 0·9 as a percentage 8 Round off 457 964 to nearest ten thousand

5

9 14 as a mixed number 3

10 1 of 90 10

10 3 of 35

14 14 +

11 What number is 100 more than 8 457? 12 Is 6 a composite number? 13 82

= 35


14

16 Area of rectangle 3 cm by 9 cm 17 Millilitres in 8 L

18 Kilograms in 7 000 g 19 Use am or pm to write 6:51 evening 20 A hexagonal pyramid has faces.

5

11 What number is 20 more that 3 645? 12 All factors of 40 13 3 squared

20

+ 28 = 52

15 Millimetres in 9·6 cm 16 Area of rectangle 3 cm by 8 cm 17 Millilitres in 7·5 L 18 Grams in 4·8 kg 19 Write 2:24 am in analog time 20 A cube has corners.

20

Complete the multiplication grids. 1 8 6 9 5 7 ×

4

6

When I know 2×3=6 I also know 20 × 3 = 60

8 9 7

2

×

9

4

7

5

8

6

10

2×3=6 so 2 tens × 3 = 6 tens or 20 × 3 = 60

20 30 40



Answers on pages A1-A2

27


A

Unit 4

1 2 3 4 5 6 7 8

36 + 9 60 – 8 5×6 42 ÷ 7 $2.95 – $1.55 500 + 40 + 8 0·65 as a fraction Round off 3 579 to nearest thousand

9 Quarters in 3

B

1 2 3 4 5 6 7 8

5

10 1 of 30

5

5

11 What number is 5 less than 14 082?

11 Is 6 795 less than 6 975? 12 Is 5 a factor of 30? 13 Ordinal number for twelfth 14 5 ×

The factors of 12 are

59 plus 37 1, 12, 2, 6, 3 and 4. 1 × 12 = 12, 2 × 6 = 46 minus 8 12, 3 × 4 = 12 9 times 8 56 divided by 7 $6.45 – $2.80 Place value of 9 in 69 485 0·7 as a percentage Round off 98 456 to nearest thousand


4

10 1 of $20

12 All factors of 36 13 Ordinal number for twenty-fifth

= 35


14 8 ×

16 Perimeter of rectangle 8 cm by 3 cm


17 Millilitres in 9 L


18 Grams in 6 kg


19 Minutes from 4:21 to 4:57


20 How many sides has a rhombus?

= 64


20

20 How many faces has a triangular prism?

20

Complete the factor wheels. 2

1 Factor wheels show all the factors of a number.

28

1

8

20

18

10

2

3

8

4

1×8=8 2×4=8

4

5 28

6 30

24




C

Answers on page A2

D

1 79 plus 4

1 Sum of 97 and 35

surface

2 63 minus 8

2 Difference between 96 and 38

face

A face is a flat surface.

3 7 times 5 4 81 divided by 9

3 70 × 9 4 450 ÷ 5

5 $1.55 + $2.95

5 $9.35 – $6.75

6 Numeral for sixty-five thousand and forty

6 Place value of 7 in 367 594

7 97% as a decimal


8

8 Is 9 076 greater than 9 760?

Is 45 639 < 45 963?

9 1 7 as improper fraction 8


10 5 of $60 10

10 1 of $24 3

11 What number is 200 after 5 824?

11 Roman numeral for 297 12 Is 40 divisible by 6?

12 Is 16 a composite number?

13 Ordinal number for thirty-first

13 102

14

14 10 + 5 × 7

+ 29 = 57



16 Area of a square with 9 m sides

16 Area of a square with 12 m sides


17 Volume of cube with 2 cm sides


18 Kilograms in 8 500 g 19 25 to 4 in digital time

19 Minutes from 4:21 to 4:59 20 How many surfaces has a cylinder? 20

20 A rectangular prism has corners.

20

Use three of the numerals 3, 4, 5, 12 or 15 to complete each number sentence. Use any numeral only once in each question. 1

( ____ – ____ ) ÷ ____ = 3

2

( ____ – ____ ) × ____ = 8

3

____ + ____ + ____ = 12

4

( ____ – ____ ) × ____ = 24

5

____ ÷ ____ + ____ = 10

6

( ____ – ____ ) × ____ = 9

7

____ ÷ ____ + ____ = 6

8

( ____ + ____ ) × ____ = 27

Follow the steps.

Step 1: Do operations inside grouping symbols. Step 2: Do × and ÷ as they occur. Step 3: Do + and – as they occur.



29


A

30

1 2 3 4 5 6 7 8

Unit 5

45 + 23 70 – 12 8 × 5 36 ÷ 6 $10.00 – $4.85 9 000 + 700 + 30 + 6 0·3 as a fraction Round 12 685 to nearest thousand

9 Is 2 the same as 3 ? 5

B

1 To 84 add 16 2

35 less than 67

3 10 times 17

23rd is the ordinal number for twenty-third.

4 56 divided by 7 5 5·6 + 2·9 6 80 000 + 5 000 + 30 + 8

7 Is 95% equivalent to 0·95? 8 Is 35 647 closer to 35 000 or 36 000? 9 4 1 as an improper fraction

10

4

10 1 of 21

10 1 of 160

3

10

11 Hindu-Arabic numeral for CLXI 12 Is 3 a factor of 37? 13 Ordinal number for twentieth 14 645, 545, 445, 15 Millimetres in 3·5 cm 16 Perimeter of square with 6 cm sides 17 Litres in 9 000 mL 18 Kilograms in 3 000 g 19 20 to 8 morning as digital time 20 A square has diagonals.

11 Roman numeral for 392 12 Next prime number after 7 13 32 + 2 14 20 – (3 × 4)

15 Metres in 6·5 km 16 Area of rectangle 5 m by 8 m 17 Millilitres in 3·5 L

20

18 Grams in 7·5 kg 19 9:26 pm as analog time 20 How many degrees in a right angle?

20

Complete the table to show the number of faces, edges and corners on each pyramid. Pyramid

Faces

Edges

7 faces, 12 edges and 7 corners

Corners

corner

Triangular

edge

Rectangular Pentagonal

face

Hexagonal Heptagonal Octagonal Decagonal




C

D

1 46 plus 27

1 2 3 4 5 6 7 8

2 65 minus 38 3 10 times 16 4 72 divided by 9 5 2·9 + 5·8 6 90 000 + 6 000 + 800 + 70 + 3 7 Is 80% equivalent to 0·8? 8 Is 6 875 > 6 785?

For 76 – 28 175 + 89 say 76 – 20 = 56 364 – 38 then 56 – 8 = 48 73 × 10 840 ÷ 10 $12.00 – $9.70 Place value of 9 in 937 291 95% as a decimal Round off 57 368 to nearest hundred


9 Improper fraction for 3 2

10 1 8

10 3 × 2

6

3

of 40

5

11 Hindu-Arabic numeral for CCLXXVII

11 What number is 500 before 9 468?

12 Is 21 a composite number?

12 Are 3 and 9 both factors of 36? 13 82 – 36 14 3 700, 3 800, 3 900, 15 Centimetres in 5·4 m 16 Area of rectangle 7 cm by 11 cm 17 Volume of cube with 4 cm sides

13 Is 3 457 an odd number? 14 6 × (4 + 7) 15 Centimetres in 25 mm 16 Area of rectangle 4 m by 7 m 17 Litres in 9 500 mL 18 Kilograms in 7·5 t 19 Is 4:57 am before noon? 20 Degrees in two right angles

20

18 Grams in 3·6 kg 19 8:47 am in 24-hour time 20 How many faces has a triangular prism?

20

8 faces, Complete the table to show the number of faces, edges and corners on each prism. Prism

Faces

Edges

18 edges and 12 corners

Corners

Triangular Rectangular Pentagonal Hexagonal

corner

Heptagonal edge

Octagonal Decagonal face




31


A

Unit 6

B

2 46 minus 27 3 10 times 14 4 64 divided by 8 5 Double $4.55

6 50 000 + 8 000 + 400 + 30 + 8 7 Is 75% the same as 0·70? 8 Is 35 647 less than 35 764?

9 How many thirds in 1 1 ?

4

4

10 1 of 32

5

8

11 Roman numeral for 164 12 All factors of 15 13 Ordinal number for thirteenth 14

9 Is 3 3 equivalent to 14 ?

3

10 1 of 40

A revolution is one complete turn or 360°

1 77 plus 19

24 + 45 80 – 14 8×8 54 ÷ 9 $10.00 – $5.45 6 000 + 900 + 40 + 5 0·9 as a fraction Is 6 752 closer to 6 700 or 6 800?

11 Roman numeral for 348

12 Is 35 a prime number? 13 82 14 (4 + 8) × 4

× 5 = 45

15 Metres in 9·5 km

15 Millimetres in 7·5 cm 16 Perimeter of square with 12 m sides 17 Litres in 7 500 mL 18 Kilograms in 8 000 g 19 4:05 in analog time 20 What shape is the face of a cube?

16 Area of rectangle 5 cm by 9 cm 17 Millilitres in 6·5 L

18 Grams in 9·5 kg

19 8:47 am as analog time

20 How many flat surfaces has a cone?

20

20

Use a protractor to measure each angle. 1

60

14

4

50

01

6

0

17 0 1 80

20 10

180 170 16

5

160

20

2

30

10

01

100 1 10 12 01 80 7 30 0 60 5

3

50

0

13

90 0 100 1 1 0

2

01

0

80

40

30

40

50

70

0

32

1 2 3 4 5 6 7 8

14

The angle is 35° Excel Mental Maths Strategies Year 6—Unit 6



Answers on page A3

C

D

1 64 plus 27 2

1 2 3 4 5 6 7 8

95 minus 68

3 10 times 13 4 72 divided by 8 5 8·4 + 7·9 6 70 000 + 4 000 + 200 + 90 + 6 7 Is 80% the same as 8 ? 10

8 Is 9 521 < 9 251? 8

10 1 10

62 = 6 × 6

186 + 97 = 36 232 – 49 35 × 10 950 ÷ 10 $11.40 – $7.60 Place value of 5 in 158 407 35% as a decimal Is 64 219 > 64 218?

9 Mixed number for 14

5

9 Is 15 equivalent to 1 3 ? 8

10 3 × 3

4

of 40

11 What number is 300 after 6 897?




13 112

13 5

2

14 95 – 7 × 8 – 9

14 9 + 12 – 2 × 4



16 Area of rectangle 8 m by 9 m


17 Volume of cube with 3 cm sides

17 Litres in 6 500 mL 18 Kilograms in 4·5 t

18 Grams in 6·5 kg

19 Days in one year

19 10:29 pm in 24-hour time

20 Degrees in a straight angle

20

20 Degrees in three right angles

20

Complete the table for each geometric pattern. 1

2

3

Number of hexagons

1

Number of sides

6

Number of heptagons

1

Number of sides

7

Number of decagons

1

3

4

5

6

I see the pattern. 2

3

4

5

6

4 sides 2

3

4

5

6

Number of pentagons

1

Number of sides

5

8 sides 12 sides

10

Number of sides

4

2

2

3

4

5

6



33


Unit 7 Fun Spot! 1

Use the four shapes to complete the grid so that the same shape does not appear twice in any row, in any column, and in either of the diagonals.

2

Move only three dots to invert this triangular pattern of dots.

3

A bee wants to fly, without stopping, over these nine flowers. How can she do this by flying in only four straight lines?

4 Tile A

To make this pattern, has Tile A been: a flipped? b slid? c turned?

5

34

Draw this shape so that it tessellates and fills the square.




Answers on page A3

6

These matches have been arranged into 5 squares. Remove three matches to leave only 3 squares.

7

Trace over this geometric shape in one continuous movement without tracing over any line more than once.

8

Arrange the numbers 1 to 9 (inclusive) in the circles so that the sum of the numbers along each side of the triangle is 20.

9

Draw 12 stars on the grid so that there is: a one in each corner and b two in each row and c two in each column and d two along each diagonal.

10 Arrange these shapes in order of size (from smallest to largest area).

A


B

C

D


35


Unit 8 Revision A 1

2

3

4

5

6

7

8

36

9

Place value of 6 in: a 3 675 b 26 491 c 654 892 Roman numeral for: a 232 b 197 c 378 d 359 Write: a 0·65 as a percentage b 75% as a fraction c 0·4 as a percentage a b c d

45 plus 36 92 minus 37 9 times 40 45 divided by 9

a 6 + 9 × 4 b 3 × 8 + 4 × 9 c 3 × 5 – 18 ÷ 6

10 Write: a 23 to 6 as digital time b 29 past 11 as digital ime c 3:55 as analog time 11 How many: a millilitres in 3·5 L? b kilograms in 2 500 g? c metres in 456 cm? d kilometres in 5 500 m? 12 What is the perimeter of each shape? a b c 3 cm

4 cm

Round off to nearest thousand: a 4 679 b 26 368 c 376 521 Write all factors of: a 24 b 36 c 45

What is: a half of 38? b half of 48?

_________ _________ _________

13 How many surfaces has each shape? a b c

Write the number that is: a 100 after 23 468 b 1 000 before 478 569

2 cm

_________

_________ _________

14 What is the area of each shape? a b 4 cm

5 cm

4 cm

_________

8 cm

_________




Answers on page A4

Revision B 1

a 6 000 + 500 + 40 + 9 b 5 000 + 20 + 1 c 20 000 + 9 000 + 50 + 3

9

2

Write as a decimal:

10 Complete the number patterns. a 45, 54, 63, 72, , b 32, 40, 48, 56, ,

a

9 10

b 1 and 45

100

c 5 tenths and 7 hundredths 3

4

What number follows: a 7 958? b 26 394? c 68 599? a 39 +

= 73

b 94 –

= 56

c 7 ×

5

6

11 How many: a litres in 3 500 mL? b grams in 6·5 kg? c millimetres in 4·6 cm? d metres in 9·5 km? 12 What is the volume of each shape? 3m

a

b

__________

= 56

d 63 ÷

Write as 24-hour time: a 10:45 am b 3:18 pm c 9:51 pm d 1:39 am

= 21

How many: a days in 5 weeks? b months in 3 years? c weeks in a year? a Is 3 the same as 6 ? 4

8

4 cm

__________

13 How many sides has each shape? a a hexagon b a pentagon c an octagon d a trapezium 14 Which angles are more than 30°? a b c d

b Is 1 2 equal to 5 ? 3

c Is

9 4

d Is

7 3

3

a mixed number? equal to

2 1 3

?

15 Record each length shown. a cm 0

7

8

Write the number that is: a 100 after 46 954 b 1 000 before 961 347

1

2

3

4

5

b

cm 0

1

2

3

4

5

List the first five multiples of: a 6 b 9



37


A

Unit 9

1 2 3 4 5 6 7 8

38 plus 24 56 minus 39 Double 16 Halve 34 Cents in $8.68 8 000 + 500 + 40 + 9 0·72 as a percentage Is 14 589 > 14 859?

9 Is 1 greater than 2 ? 2

Did you sail

B 1 2 3 4 5 6 7

through the revisions?

39 plus 56 72 minus 39 10 times 16 54 divided by 9 Spent $3.55, change from $10 Tens in 36 754 3 units + 4 tenths + 9 hundredths as a decimal 8 Round off 38 658 to nearest thousand

5

10 1 of 18

9 Is 4 equal to 2 ?

11 Hindu-Arabic numeral for CCXXI

10 1 of 15

12 Is 7 a factor of 35? 13 7 squared

11 Roman numeral for 351 12 Is 139 divisible by 3? 13 Ordinal number for twenty-third

10

3

14 24 +

= 56

15 Centimetres in 59 mm 16 Perimeter of rectangle 6 m by 7 m 17 Millilitres in 3·5 L 18 Grams in 4·5 kg 19 Days in 5 weeks 20 How many sides has a quadrilateral? 20

3

3

14 7 ×

= 63

15 Kilometres in 8 500 m 16 Perimeter of a square with 12 cm sides 17 18 19 20

Litres in 4 580 mL Kilograms in 3 590 g Minutes from 9:29 to 11:16 An hexagonal prism has faces. 20

38

1 2 3

Complete the following. a 1 + 2 = b 1 + 2 + 3 = c 1 + 2 + 3 + 4 = d 1 + 2 + 3 + 4 + 5 = Is this a triangular number? a 3 b 10 c 21 d 15 e 35 f 28 g 48 h 66 What triangular number follows: a 21? b 15? c 28? d 10? e 45? f 55?

Do you see the pattern? Triangular numbers

1

3

6




Answers on page A4

C

D

1 2 3 4 5 6 7

9 Is 10

1 5

3 4

equal to

3 tenths and 9 hundredths is 0·39

1 459 and 85 more

45 plus 62 81 minus 35 10 times 13 45 divided by 5 Cents in $10.45 60 000 + 7 000 + 400 + 30 + 9 1 unit + 4 tenths + 7 hundredths as decimal 8 Is 54 689 closer to 54 000 or 55 000?

2 329 take away 78 3 65 times 10 4 690 divided by 10 5 14·5 + 6·8

6 Place value of 2 in 425 617 7 75% as a decimal 8 Is 46 304 < 46 430? 9 Is 1 1 equal to 6 ? 5

6 ? 8

5

10 1 of $32 8

of 30

11 Number 500 after 3 875



12 Are 4 and 5 both factors of 30?

13 Is 6 a triangular number?

13 Next odd number after 97

14 4 + 6 × 5 ÷ 10

14 5 × 6 + 3 × 6




16 Area of a square with 9 cm sides




18 Grams in 4·5 kg

19 9:53 am as analog time

19 Minutes from 11:34 to 12:06 20 How many sides has a parallelogram? 20

20 A pentagonal prism has faces.

20

Complete the number patterns and write the rule for each. 1

2

3

4

First number

42 52 62 72 82 92

Second number

56

First number

37 47 57 67 77 87

66

76

_____________ _____________

Second number

74

First number

78 68 58 48 38 28

Second number

53

43

33

First number

1

2

3

Second number

1

4

9

_____________ _____________

94 114

_____________ _____________ 4

5

The rule in the first pattern is ‘add 14’.

42 + = 56 42 + 14 = 56 52 + = 66 52 + 14 = 66 etc.

6

_____________ _____________



39


Unit 10

A

1 2 3 4 5 6 7 8

39 plus 53 76 minus 48 Double 27 Halve 56 546 cents as dollars and cents 90 000 + 4 000 + 700 + 20 + 5 0·76 as a fraction Round off 35 499 to nearest thousand

9 Is 1 equal to 3 ? 2

B 1 2 3 4 5

is equivalent

75 added to 68 to because 38 less than 92 × 8 lots of 30 How many eights in 56? Spent $4.35, change from $10

6 Tens in 96 537 7 2 units + 8 tenths as decimal 8 Is 56 835 < 56 735? 9 3=

10

4

10 1 of 24 6

11 Hindu-Arabic numeral for CCCXLIV

8

10 1 of 36 12

11 Number 500 after 35 894 12 Average of 19, 24 and 23

12 Is 42 divisible by 6? 13 Is 9 a square number?

13 122

14 38 +

14 18 ÷ 3 + 6 × 4

= 92

15 Kilometres in 8 500 m

15 Centimetres in 3·69 m 16 Area of square with 10 m sides 17 Litres in 6 500 mL 18 Kilograms in 3 500 g 19 Months in 5 years 20 How many faces on a rectangular prism?

16 Perimeter of triangle with 5 cm sides 17 Litres in 7 500 mL 18 Kilograms in 4 500 g 19 Is 10:46 the same as 14 to 10?

20

20 Direction between north and west 20

40

For each solid, draw the front, side and top view. l For the front view, imagine that you are looking at it face on. l For the top view, imagine that you are looking at it from the sky. l For the side view, imagine that you are looking at it side on.

front

1 front

side

top

2

side

top

front

side

top




D

C

1 To 687 add 94 2 From 721 take 97

1 52 and 29 more 2 25 less than 81

10% is 1

3 24 multiplied by 4

10

3 35 times 10 so 10% of $40 is $4 4 670 ÷ 10 5 $3.40 + $3.29 + $2.35

4 How many fours in 36? 5 Halve $10.86 6 Tens in 46 532 7 0·3 as a fraction

6 Expanded notation for 86 391 7 0·73 as a percentage 8 Is 164 584 > 165 971?

8 Is 68 642 > 68 542? 9 5 = 10

10

1 6



2

8

of 30

10 11 12 13 14 15 16

11 Number 500 before 37 381 12 Average of 21, 18 and 15 13 62 14 3 × 4 + 15 ÷ 3 15 Metres in 6·5 km

16 Perimeter of square with 20 m sides

17 Millilitres in 9·5 L 18 Kilograms in 8 t 19 05:46 as analog time 20 Is an obtuse angle less than 90°? 20

17 Litres in 9 500 mL 18 Grams in 3·5 kg 19 16 to 7 as digital time 20 Direction opposite SE

10% of $90 Number is 1 000 after 25 962 All factors of 56 Is 12 a triangular number? (9 + 8) × (7 – 5) Kilometres in 4 500 m Perimeter of regular hexagon sides 5 cm

20

Write the digital time for each time shown. 1 2 3 11 12 11 12 11 1

10

2

9 8

6

8

5

_________ 4 10

11 12 1

8

2

10

4 6

8

5

_________

8

5

11 12 1

9

3 7

6

10 3

4 7

6

5

_________

2 3 4

7

6

5

_________ 6

2

1

9

3 4 7

12

10

_________ 5

9

2

9

3 4 7

1

10

11 12 1

9 8

3:24 2 3 4

7

6

Digital clocks only show digits.

e.g. 24 past 3 in digital time is 3:24

5

_________ Excel Mental Maths Strategies Year 6—Unit 10


41


A

Unit 11

1 12 + 13 +18

B

68 + 23 = 60 + 20 + 8 + 3 = 80 + 11 = 91

1 67 plus 29

2 79 – 46

2 86 minus 47

3 Double 28

3 67 times 5

4 Half of 52

4 72 divided by 9

5 How many 5 cent coins in $1?

5 Spent $6.85, change from $10

6 6 000 + 400 + 80 + 3 7 65% as a decimal

6 Thousands in 13 684

8 Is 8 675 > 8 567?

7 9 tenths as a decimal

9 Is 1 2 less than 1 3 ? 3

10

1 10

8 Is 95 289 < 95 298?

4

9 Is 1 4 less than than 1 7 ? 5

of 80


10

10 Is 2 of 12 equal to 9? 3

12 Is 7 a factor of 27?


13 Next even number after 65


14 7 ×

13 92

= 63

15 Centimetres in 4 m

14 6 + (3 × 8) – 14

16 Perimeter of a square with 5 m sides

15 Kilometres in 5 500 m 16 Area of rectangle 7 cm by 5 cm

17 Millilitres in 3·5 L 18 Grams in 6·5 kg


19 Days in a leap year


20 How many degrees in a right angle? 20

19 Minutes from 5:07 to 5:59 20 Direction opposite SW

20

42

1

Find the highest common factor for each pair of numbers. a 3 and 6 b 5 and 10 c 8 and 12 d 6 and 10 e 14 and 21 f 12 and 16 g 9 and 18 h 4 and 24 i 6 and 24 j 6 and 27

2

Find the lowest common multiple for each pair of numbers. a 3 and 6 b 2 and 5 c 4 and 5 d 8 and 3 e 5 and 3 f 6 and 12 g 9 and 18 h 4 and 18

The highest common factor is 2.

Factors of: 2 are 1, 2 6 are 1, 6, 2, 3




C

3 can be 5 written as

1

1 49 added to 38

the improper 8 fraction . 5

2 From 92 take 68 3 34 times 6

Answers on page A5

D

1 249 and 34 more 2 From 749 take 68 3 147 times 10

4 How many sevens in 63?

4 790 divided by 10

5 9·6 – 6·7

5 $2.53 + $1.60 + $3.78

6 60 000 + 7 000 + 400 + 30 + 2

6 How many thousands in 469 301?

7 5 tenths as a decimal 8 Round off 56 357 to nearest hundred 9

13 4

7 0·73 as a fraction 8 Is 456 920 > 456 819?


as an improper fraction

3

10 10% of $80

10 Is 2 of 15 equal to 10? 3


11 Number 1 000 after 63 872

12 Average of 45, 67, 39 and 57

12 Highest common factor of 8 and 10

13 Triangular number after 3

13 82

14 21 + 5 × 7 – 39

14 5 × 8 – 3 × 7



16 Perimeter of pentagon with 4 cm sides

16 Area of rectangle 5 cm by 4 cm 17 Litres in 7 500 mL


18 Grams in 8·5 kg

18 Kilograms in 9 t

19 Minutes from 6:21am to 7:03 am 20 Are opposite sides of a parallelogram equal? 20

19 1:24 pm as 24-hour time 20 Is a straight angle 180°?

20

To move 30 m north we move

Plot this course on the grid. Move: 30 m north 110 m east 90 m north 40 m west 60 m south 120 m west 50 m north 70 m east 30 m south At which point did you arrive? ________

3 squares up.

N

A

C B

0 START

50 metres



43


Unit 12

A 1 2 3 4 5 6

7

B 1 2 3 4 5

46 + 29 78 – 49 6+6+6+6 Divide 35 by 7 Cents in $9.45 Tens in 5 692 65 100

163 + 25 194 – 63 To multiply by 4, 34 × 4 double then double 305 ÷ 5 again. Cost of 6 at $1.20 each 6 60 000 + 3 000 + 900 + 30 + 7 7 Decimal for one point seven six

as a decimal

8 Is 4 675 > 4 575?

9 Is 1 4 an improper fraction? 5

8 Is 87 256 > 87 526?

10 1 of 32


11 Hindu-Arabic numeral for CCCXLII

10 3 of $15

4

8

5


12 Is 3 a factor of 19? 13 Last odd number before 200 14 156, 166, 176,

12 Is 6 a factor of 24? 13 52 + 4 14 7 × 3 + 10 ÷ 2

15 Metres in 750 cm 16 Perimeter of a square with 4 m sides 17 Litres in 8 500 mL 18 Kilograms in 3 500 g 19 Minutes in 3 hours 20 Degrees in two right angles 20

15 Centimetres in 6·35 m 16 Perimeter of rectangle 6 cm by 5 cm 17 Litres in 7 500 mL 18 Kilograms in 4 375 g 19 Seconds in 2 1 minutes 2

20 Is 75° an acute angle?

20

44

Here is the net of a cube. Which cube below could not be made from this net? _____ A net is a flat pattern that can be folded to make a solid shape.

A C B




We can add fractions with the same denominator.

C

1 145 + 34 2 187 – 26 3 102 × 4 4 5 1 + = 6 6 6

4 369 ÷ 3 5 $3.60 + $1.30

D

1 2 3 4 5 6

Answers on page A5

567 and 49 more 683 minus 39 872 × 10 670 divided by 10 $1.97 + $1.59 + $3.68 400 000 + 70 000 + 6 000 + 500 + 20 + 8

6 Thousands in 54 987

9 7 Decimal for 5 units + 9 tenths 7 10 as a percentage + 4 hundredths 8 Is 4 654 857 > 4 652 875? 8 Is 78 563 > 78 562? 9 2 5 as improper fraction 6

9 0·6 as a fraction

3 + 2 8 8

10 2 of 18 candles

10

11 Number before 269 361

11 Roman numeral for 647 12 Lowest common multiple of 3 and 5

3

12 Is 8 a factor of 32? 13 52 – 4 14 6 × (4 + 16) 15 Metres in 956 cm 16 Area of square with 7 cm sides 17 Millilitres in 4·5 L 18 Grams in 3·125 kg 19 Minutes in 3 1 hours 4

20 Degrees in a straight angle 20

13 14 15 16

62 – 31 8 × 4 – 3 × 5 Metres in 4·5 km Perimeter of triangle with 7 cm sides

17 18 19 20

Litres in 6 500 mL Kilograms in 12 t 7:59 am as 24-hour time How many edges on 20 a square prism?

Here are two In different ways, colour half the area of each rectangle.

different ways.



45


A

1 2 3 4 5 6 7 8

Unit 13

B 1 2 3 4 5 6 7

15 + 14 + 25 67 – 32 5+5+5+5+5 Half of $5 50c coins in $3 7 000 + 900 + 60 + 5 0·5 as a percentage Is 4 629 < 6 429?

92 plus 46 74 minus 39 Multiplication is the same 35 × 6 as repeated addition. 147 ÷ 7 $1.65 + $3.70 + $2.45 Place value of 4 in 34 600 Decimal for 5 units + 7 tenths + 9 hundredths 8 Is 67 954 > 76 945?

9 Quarters in 2 3 4

10

2 3

9 2 3 as an improper fraction 5

of 12

10 5 + 1 10


10


12 Are 3 and 5 factors of 15?

12 List all the factors of 60

13 2 squared

13 42 + 3

14 36 ÷ 6 + 3

14 9 + 4 × 6 – 8

15 Centimetres in 7 1 m 2

15 Metres in 1 1 km

16 Perimeter of a rectangle 3 cm by 7 cm 17 Millilitres in

1 4

4

16 Area of a square with 6 cm sides 17 Litres in 1 255 mL 18 Kilograms in 1 750 g 19 Time 15 minutes after 6:42

L

18 Grams in 1 kg 4

19 Days in December 20 Is 69° less than a right angle? 20


20

46

What is the perimeter of each shape?

1

2 12 m

8 cm

Perimeter is the distance around the boundary of a twodimensional shape.

12 m

6 cm

3

4 cm

4 cm

6 cm

3 cm

4

3·5 cm

Perimeter = 6 + 4 + 6 + 4 = 20 cm

4 cm 3 cm

2 cm 5 cm




C

1 234 + 65 2 196 – 47

1 2 3 4 5 6

mixed number 1 2 . 4

3 316 × 10 4

D

9 can be 4 written as the

609 divided by 3

5 $10.00 – $6.35 6 50 000 + 4 000 + 600 + 80 + 2

9

10

8 Round off 1 654 376 to nearest thousand

Is 95 201 < 95 120? 14 3

Sum of 627 and 94 Difference between 943 and 76 72 × 100 679 ÷ 10 6·8 + 3·5 + 7·4 Place value of 7 in 174 569

7 7 as a percentage

7 Decimal for 6 units + 6 tenths + 9 hundredths 8


as a mixed number

4

5 – 3 = 8 8

10 25% of 80

10

11 Number 500 before 29 387

11 Number 2 000 after 658 726

12 First three multiples of 8

12 Are 3, 4, 6 and 7 all factors of 42?

13 7 – 4 2

14 64 ÷ 8 × 3 15 Metres in

13 Ordinal number for seventy-fifth 13 4

14 240, 280, 320, km


16 Area of a rectangle 5 m by 9 m

16 Name for perimeter of a circle




18 Tonnes in 7 000 kg

19 Minutes from 12 to 7 until 23 past 7

19 19:21 as 12-hour digital time

20 Is 145° an obtuse angle?

20 Are opposite sides of a rectangle parallel? 20

20

Use the labels and angle measurements to complete the table. revolution

reflex

straight

acute 360°

120°

300°

obtuse 50°

180°

Angle

Do you have an angle for remembering names?

Name Size




47


A

Unit 14

B

1 21 + 32 + 27

92 – 35 = 92 – 30 – 5 = 62 – 5 = 57

1 35 + 16 + 43 2 164 – 58 3 463 × 10

2 96 – 67 3 8+8+8+8

8 Round off 4 763 to nearest hundred

4 5 6 7 8

9 Tenths in 2 3


10 3 of 40

10 10% of 60

4 How many threes in 24? 5 20c coins in $4 6 Place value of 5 in 3 562 7 60% as a decimal

How many sixes in 126? Cost of five at $3.25 each 60 000 + 8 000 + 300 + 90 + 1 0·4 as a percentage Is 87 569 closer to 87 000 or 88 000? 3

10

10

11 1 000 after 46 351

11 Number after 13 469 12 Is 4 a factor of 26? 13 Next odd number after 1 797 14 35 +

12 Is 39 a multiple of 6? 13 82 + 6 14 7 + (3 × 4) – 6

= 97

15 Metres in 1 km 4

15 Centimetres in 9 1 m

16 Area of a square with 12 cm sides

2

16 Perimeter of a square with 9 m sides 17 18 19 20

17 Millilitres in 4·725 L 18 Grams in 3·625 kg 19 Minutes from 8:53 am to 9:46 am

Litres in 4 500 mL Grams in 3·5 kg Days in June and July Is 106° less than a right angle? 20

20 How many faces on a hexagonal prism?

20

48

In each row, circle the factors of the given products. Possible factors

Product

1

6

7

4

8

3

15

9

16

2

36

2

8

5

4

3

7

15

12

9

17

45

3

3

2

9

6

5

8

18

4

17

64

4

5

4

7

16

2

9

15

13

12

92

5

6

5

9

4

2

17

3

16

15

105

6

8

2

6

3

5

4

12

10

21

124

7

9

3

5

2

10

6

15

13

16

156

A product is the answer when numbers are multiplied.

A factor is a whole number that can be divided exactly into another number.




learn these facts.

C

2 326 – 43 3 126 × 10

D

1 = 0·25 4 1 = 0·50 2 3 = 0·75 4

1 167 + 39

Answers on page A6

1 2 3 4 5 6

Sum of 34, 48 and 67 Difference between 523 and 98 30 × 40 358 ÷ 10 Cost of one if 6 cost $8.70 Numeral for sixty-four thousand and seventy 7 4 tenths 9 hundredths as a decimal 8 Round off 3 861 459 to nearest million

4 340 ÷ 10 5 Change from $5 if $3.45 is spent 6 Hundreds in 35 465 7 3 as a decimal 10

8 Is 69 521 > 69 621?


9 Is 10 the same as 5 ?

5

12

10 10% of $120

6

10 9 – 5

11 2 000 before 35 968

10 10


11 12 13 14 15 16

13 32 + 3 14 5 × 3 + 6 × 3 15 Metres in 3 km 4

16 Area of a rectangle 6 cm by 2 cm

17 Litres in 4 250 mL 18 Tonnes in 4 750 kg 19 06:43 as analog time 20 How many edges on a triangular prism? 20

17 Litres in 3 950 mL 18 Kilograms in 7 355 g 19 16 minutes after 9:53 am 20 Is 180° a straight angle?

Is –7 a negative number? First 4 multiples of 8 40th in words 360, 450, 540, Centimetres in 3·75 m Perimeter of a square with 30 m sides

20

The unit digit in 32 is 2.

Some of the multiples of 8 are 8, 16, 24, 32, 40, 48. The unit digits are 8, 6, 4, 2, 0. When joined in order, these make a unit digit pattern. Draw the unit digit patterns for the multiples of 3, 4, 6 and 7. 1

9

0

2

1

9

0

3

1

9

0

4

1

9

0

1

8

2

8

2

8

2

8

2

7

3

7

3

7

3

7

3

6

5 3

4

6

5 4

4

6

5 6

4

6

5 7

4

9

1

8

2

7

3 6

0

5

4

Excel Mental Maths Strategies Year 6— Unit 14


You should

49


Unit 15 Fun Spot! Draw a diagram

1

A welder can cut a metal bar into 3 pieces in six minutes. At the same speed, how long will it take to cut the same bar into 6 pieces?

2

A snail is climbing a brick wall which is 15 m high. It climbs up 3 m every day but slides down 1 m every night. How long will it take to reach the top?

3

Nine children join hands to form a chain. How many hands are held?

Act it out

5

4

Ten blocks were placed in a line at 10 cm intervals. 10 cents was placed between the first two blocks, 20 cents between the next two, then 30 cents, then 40 cents and so on. How much money was used to fill the spaces?

Find the least number of colours needed to colour this pattern if touching shapes have different colours.

6

On a skiing holiday there are five people but only three pairs of skis. How many different groups of three could ski?

7

Mia has a bag full of 10c and 20c coins. In how many different ways can she pay for a drink that costs $1.10?

Make a list

50




Answers on page A6

Trial and error

9

8

Some classrooms have 35 chairs while others have only 30. The total number of chairs in ten classrooms is 330. How many classrooms have 35 chairs?

Mark had twice as much money as Karen. When Mark gave Karen $10 they both had the same amount. How much did Karen originally have?

10 Two numbers have a sum of 31 and a product of 228. What are the numbers?

Work backwards

11 Jan doubled her starting number, added 5, subtracted 7, divided by 3 then squared the result. If her final answer was 36, with which number did she begin?

12 An explorer walked 1 km west, 3 km south, 5 km west, 4 km north, 3 km east, 2 km north, 6 km west and 4 km south to reach point D. At which point did he begin?

N

A

C

B

D 0 1 2 3 kilometres

Use a ratio


13 At a conference, one car was provided for every 4 people. a If there were 17 cars, how many people were there? b I there were 76 people, how many cars were needed? c I there were 91 people, how many cars were needed? Excel Mental Maths Strategies Year 6—Unit 15 51 Excel Basic Skills Mental Maths Strategies Year 6 11/09/13 8:06 AM

Unit 16 Revision A 1 Place value of 6 in: a 6 897 b 36 592 c 637 459

9

b

= 63 × 8 = 64

c 6+

2 Complete: a 4 × 5 + 15 ÷ 5 b (4 + 6) × 3 + 8

5 Round off to the nearest thousand: a 5 694 b 37 290 c 164 531 6 Write the first five multiples of: a 6 b 9 c 7

8 Write the improper fraction for:

12 What is the perimeter of each shape? a b c 3 cm

5 cm

6m

3 cm

3m

________

4 cm

3 cm

________

________

13 How many edges has each shape? a b c

________

________

________

14 What is the area of each shape? a b

a 1 3 4

b 2 3

9 cm

9m

5

c 2 6

9m

10

d 17

____________

8

52

11 How many: a millilitres in 3·575 L? b grams in 2·525 kg? c centimetres in 5·64 m? d kilometres in 6 250 m?

135 + 48 142 – 67 124 × 10 369 ÷ 3

7 Write the number that is: a 100 before 28 674 b 1 000 after 175 639

= 92

10 Write: a 11 to 8 as digital time b 14 past 12 as digital time c 2:54 as analog time

3 Write: a 0·4 as a percentage b 25% as a fraction c 39% as a decimal 4 a b c d

a 7 ×

12 cm

____________





Revision B 1 a 40 000 + 9 000 + 400 + 70 + 6 b 50 000 + 9 000 + 70 + 5 c Place value of 8 in 58 462

10 Roman numeral for: b 164 a 251 c 375 d 299

2 Write as a percentage: a

3 10

b 0·5

c 0·65 3

12 How many: a litres in 3 950 mL? b kilograms in 6 575 g?

Average of: a 22, 28, 31 b 16, 19, 28, 29

c metres in 3 km? 4

4 Use > or < to show the bigger number. a 5 964 5 694 b 25 430 25 410 c 94 236 93 236 5

6 What is the time half an hour after: a 25 to 9? b 3:42 am? c 11:56 am? 7 Write the mixed number for: 5

c

11 8

b 23 10

d

7 3

8 List the first five multiples of: a 8 b 6 c 4 9 Write as 24-hour time: a 9:26 am b 11:26 pm c 11:49 am d 8:59 am © Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_pp52_53_new2725.indd 53

d centimetres in 6 1 m? 2

13 Match each angle with its name: acute angle reflex angle,

obtuse angle

a

List all the factors of: a 12 b 24 c 30

a 13

11 Complete the number patterns. a 108, 208, 308, ___ , ___ b 2 065, 2 165, 2 265, ____ , ____

straight angle

b

__________ __________ c d

__________

__________

14 Write as digital time. a 25 past 7 b 11 to 5 c 19 past 12

15 Record each length shown. a cm 0

1

2

3

4

5

1

2

3

4

5

b cm 0


53


A

Unit 17

1 23 + 42 +13 2 84 – 67 3 9 + 9 + 9 + 9+ 9 4 How many sixes in 24? 5 $5.00 – $3.75 6 60 000 + 7 000 + 400 + 90 + 7 7 0·75 as a percentage

8 Round off 12 864 to nearest thousand 9 Is 3 1 a mixed number? 10

B 1 2 3 4 5 6

To take away from 100, I subtract from 99 then add 1.

35 + 29 + 45 100 – 67 100 × 10 Divide 72 by 8 9·6 – 5·8 How many digits in 346 579?

7 9 units + 5 tenths + 3 hundredths as decimal 8 Is 352 857 > 353 857? 9 Is 2 3 the same as 11 ?

4

3 10

4

of 30

4

10 7 – 3

11 Number 100 before 9 107 12 Is 72 divisible by 4? 13 5 squared 14 105, 155, 205, 15 Millimetres in 3·5 cm 16 Perimeter of square with 8 cm sides 17 Millilitres in 6·5 L 18 Grams in 4·5 kg 19 Days in March and April 20 Is 123° more than a right angle? 20

8

8

11 12 13 14 15 16

Number 2 000 before 89 257 Is 336 divisible by 9? Ordinal number for thirty-ninth 6 × 5 – 20 ÷ 4 Kilometres in 9 650 m Perimeter of a square with 4·2 cm sides 17 Millilitres in 3·5 L 18 Grams in 2·375 kg 19 Two hours after 11:54 am 20 Shape of base on a hexagonal pyramid 20

Coordinates tell us the position on a

54

1

What shape is located at: a F4? b G1? c C3? d E5? e D1? f B4?

2

What are the coordinates of: a ? b ?

c e

? ?

d f

? ?


grid. We read the horizontal coordinates first e.g. is at G2.

5 4 3 2 1

A

B

C

D

E

F

G

H



C

2 200 – 86 3 94 × 10 4 147 divided by 7

D

To find the average, add all the scores and divide by the number of scores.

1 43 + 38 +16

Answers on page A7

1 Sum of 97 and 385 2 From 372 take 186 3 Product of 40 × 70 4 Quotient of 720 and 8 5 $3.95 + $2.60 + $4.85 6 Place value of 6 in 169 378 7 0·2 as a percentage 8 Smallest 3-digit numeral using 4, 9, 3

5 $1.45 + $1.15 + $1.55 6 40 000 + 9 000 + 60 + 8 7 75% as a decimal 8 Is 49 392 > 49 329 9 3 7 as an improper fraction

9 Which is not equivalent: 0·3, 30%, 3 ?

10 3 + 5

10 4 × 3

11 Is –5 a negative number?

11 Number 4 less than 2 12 Lowest common multiple fo 4 and 5

100

10

8

8

4

12 Are 7 and 8 both factors of 64? 13 62 + 5

13 32 + 52 14 8 × 5 ÷ 10 + 8 15 Centimetres in 15·56 m 16 Hectares in 10 000 m2 17 Volume of cup if it holds 250 mL 18 3·5 kg in grams 19 2 hours after 20:36 20 Shape of a cross-section of a sphere 20

14 1 107, 1 057, 1 007, 15 Metres in 9·5 km 16 Perimeter of a square with 3·5 m sides 17 Litres in 3 275 mL 18 Grams in 3·455 kg 19 Minutes from 10:37 am to 12:16 pm 20 Name for bottom of a pyramid 20

Regular shapes have all sides equal and all angles equal.

1 Colour the regular shapes. 2

1

3

4 6

5

7 8

9

regular 10

irregular



55


A

1 2 3 4 5 6 7 8

Unit 18

B

1 2 3 4 5 6

Add 38 and 46 61 take away 39 10 × 20 How many eights in 32? $5.00 + $2.95 Place value of 6 in 69 742 35% as a decimal Round off 18 578 to nearest hundred

A prime number has

38 + 29 + 32 only two factors. e.g. factors of 3 200 minus 94 are 1 and 3 63 × 5 128 divided by 4 $2.35 + $2.55 + $2.45 Place value of 4 in 247 890

7 61 as a percentage 100

8 Is 326 487 < 328 487?

9 Eighths in 1 1

9 4=

10 2 of 12

10 2 of 40

11 Roman numeral for 358 12 Average of 20, 30, 40 13 4 squared

11 Number 1 000 after 968 127 12 All prime numbers between 0 and 10

5

8

14 7 ×

10

5

3

13 32 + 22 14 2 × 3 + 2 × 10 15 Metres in 6·7 km 2 16 Is 36 cm the area of a 6 cm square? 17 Millilitres in 6·8 L 18 Kilograms in 4·7 t

= 56

15 Millimetres in 6·7 cm 16 Area of square with 5 cm sides 17 Millilitres in 3 1 L 2

18 Grams in 1 1 kg 2

19 Days in Australian winter 20 Angle between south and east 20

19 Minutes in 1 3 hours 4

20 Shape of base on a pentagonal pyramid 20

A column

56

graph shows information in blocks.

This graph shows the number of students travelling by bus in one week.

50

Number of students

40 30 20 10 19

20

21

Date

22

23

1

How many travelled by bus on: a 20th? ________ b 23rd? ________

2

On which date did: a 50 students travel? ________ b 45 students travel? ________

3

How many students travelled on 21st and 22nd? ________

4

How many students travelled by bus during the week? ________




C 1 2 3 4 5

1 371 + 45 2 283 – 197 3 80 × 30

Ouadrilaterals have four sides.

4 450 ÷ 9 5 16·5 + 7·8 + 5·9

6 How many digits in 6 947 201?

6 80 000 + 7 000 + 400 + 60 + 1


7 Is 4 = 40%? 100

8 Is 5 647 389 > 5 637 389?

8 Round off 245 689 to nearest thousand 9

D

35 + 27 + 38 400 – 78 36 × 5 Remainder when 125 is divided by 8 4 kg of apples at $1.35 per kilogram

12 5

Answers on page A7

9 4·55 as a mixed number 10 3 of 16

as a mixed number

4

11 Number 9 less than 4

10 25% of $120


11 Hindu-Arabic numeral for DLXXIV

13 Last odd number before 800 000

12 Is 27 a prime number? 13 Last even number before 900 000

14 35 ÷ 7 + 3 × 4

14 2 175, 2 125, 2 075,



16 Area of rectangle 3·2 cm by 5 cm

16 Area of square with 9 m sides 17 Litres in 5 275 mL

17 Volume of rectangular prism with sides 5 m, 3 m and 2 m

18 Grams in 3 1 kg

18 Mass of 3 L water

19 6:38 am as analog time 20 Does a cube have eight faces? 20

19 2:49 pm as 24-hour time

4

20 Name a triangle with three equal sides 20

Find the volume of each prism. 5 cm 1 2

Each cube is 1 cm3.

4 cm 2 cm

3 cm 7 cm

6 cm

________________

3

________________ 4

7 cm

12 cm 2 cm

3 cm

3 cm 4 cm

________________

6 cubes in one layer 2 layers, so Volume = 2 × 6 = 12 cubes

________________



57


A

Unit 19

1 Sum of 45 and 39

2·1, 2·3, 2·9

2 From 264 take 89

3 6 × 14

3 40 times 6

4 How many nines in 45?

4 360 divided by 6

5 $10.00 + $7.85

Ascending order is from smallest to largest.

5 13·8 – 6·9

6 How many digits in 35 920?

6 70 000 + 9 000 + 500 + 20 + 4


7 One point six three as a decimal

8 Is 45 632 > 45 532?

10

B 1 Add 257 and 64

2 Take 46 from 84

9 Halves in

8 Arrange in ascending order: 6·8, 6·3, 6·5

3 1 2


5 3 + 10 10

4

10 75% of 60

11 Number 1 000 after 9 867

11 Is a negative number less than zero?



13 3 squared

13 42 + 22

14 1 560, 1 660, 1 760, 15 Centimetres in 3·9 m

14 30 ×

16 Perimeter of square with 10 cm sides 17 Millilitres in 7·5 L

= 600

15 Kilometres in 6 800 m 16 Is 49 cm2 the area of a 7 cm square? 17 Litres in 4 725 mL

18 Grams in 1 1 kg

18 Kilograms in 3·9 t

19 Days in Australian spring

19 Two hours before 9:06 pm

20 Is a sphere a plane shape? 20

20 Do parallel lines meet at 90°?

4

20

58

1 How many wins were there in: a August? b June? c March? d May? e April? f July?

Dot plot Football wins

Mar

Apr

May Jun Month

Jul

Aug

2 Were there more wins in: a March or August? b June or April? c July or May? d August or April?




C 1 2 3 4 5 6


D 1 2 3 4 5 6

24 + 25 + 26 400 – 67 36 × 5 Remainder when 134 is divided by 9 $3.90 + $4.85 + $3.65 How many digits in 5 497 208?

7 Is 60 = 60%?

53 + 268 294 – 188 30 × 70 63 + = 135 350 ÷ 7 We say 135 – 63 = = 72 $20.00 – $14.85 600 000 + 50 000 + 8 000 + 300 + 60 + 4

8 Round off 467 279 to nearest thousand

7 Zero + 5 tenths + 8 hundredths 8 Largest 4-digit number using: 6, 3, 0, 8

9 1·58 as a mixed number


100

6

10 5 × 2

10

3

11 3 – 4

1 + 2 2 6

11 Roman numeral for 794 12 Is 163 divisible by 7? 13 60th in words 14 3 + 4 × 5 × 2 15 Metres in 7·625 km 16 Perimeter of rectangle 3·4 m by 5·7 m

12 First five multiples of 9 13 Last odd number before 300 000 14 4 + 6 × 7 + 3 15 Kilometres in 9 300 m 16 Area of rectangle with sides 3·5 cm by 6 cm 17 Millilitres in 7·8 L 18 Grams in 4·7 kg 19 16 to 5 morning as digital time 20 Does a rectangular prism have six faces? 20

17 Volume of rectangular prism sides 3 m, 5 m and 4 m 18 Kilograms in 3·25 t 19 06:27 as digital time 20 Can the top view of a sphere be a circle? 20

An axis of symmetry divides a shape into two halves.

How many axes of symmetry in each shape? 1 2 3

______

______ 5

4

______ 6

Each half is a mirror image of the other. axis of symmetry

______

______

______



59


A

Unit 20

1 2 3 4 5 6 7 8

B 1 2 3 4

90 + 50 93 minus 48 Double 39 How many eights in 64? $10.00 + $6.90 3 000 + 700 + 90 + 5 45% as a decimal Round off 26 937 to nearest thousand

5 $2.40 × 3 6 Place value of 3 in 378 910 7 9 as a percentage 10

8 Round off 865 201 to nearest ten thousand 9 4 × 2·5 10 10% of 50 11 Is 15 a negative number? 12 Lowest common multiple of 4 and 6

9 Eighths in 1 3 8

10 8 – 2 10

10

11 Roman numeral for 259 12 Are 5 and 3 both factors of 35? 13 2 squared 14 326, 276, 226, 15 Centimetres in 5·2 m

Sum of 28, 39 and 57 Take 69 from 237 63 × 10 Remainder when 130 is divided by 6

13 52 – 15 14 56, 64, 72, 15 Metres in 3·8 km 16 Area of rectangle 4·3 cm by 3 cm 17 Litres in 1 439 mL 18 Kilograms in 3 595 g 19 7:53 as analog time 20 Does a square pyramid have six faces?

16 Area of square with 7 cm sides 17 Litres in 7 500 mL 18 Grams in 1 3 kg 4

19 Minutes from 3:09 am to 3:56 am 20 Is a right angle more than 75°? 20

20

24-hour time does not need am or pm.

60

Write each time as 24-hour time. 1 2 3 am

5

pm

am

4

pm

2:43

4:39

9:42

8:56

________

________

________

________

am

6

7

pm

am

8

pm

5:14

11:27

10:47

1 0:32

________

________

________

________

6:35 am is 06:35 6:35 pm is 18:35




C

To share, we divide. $1.40 shared between two is $1.40 ÷ 2 = $0.70

1 2 3 4 5

Add 37, 46 and 54 Take 89 from 274 35 × 10 23 ÷ 5 Share $6.90 among three girls 6 80 000 + 2 000 + 400 + 6 7 Is 8

4 6 + 10 100

D

1 Add 170 and 47 2 Subtract 169 from 328 3 40 × 60 4 280 ÷ 4 5 $35.65 – $17.95 6 Place value of 4 in 405 378 7 Which is not equivalent: 0·6, 60%, 6 ? 8 Round off 356 895 to nearest thousand


10

9 Improper fraction for 3 2 3

of 120

10 Cost if 25% off $400

11 Number 6 less than 1


12 HIghest common factor of 4 and 20

12 Is 9 a factor of 1 665?

13 4 + 10

13 Is 81 a square number?

14 4 + 6 × 7 – 9

14 5 × 6 + 4 × 5

2

15 Metres in 2·6 km 16 Is 77 cm2 the area of a 7 cm square? 17 Millilitres in 9·4 L 18 Grams in

100

= 0·45?

Is 208 901 > 207 901? 1 3

Answers on page A8

11 2

kg +

3 4

kg

15 Distance in 3 hours at 60 km/h 16 Hectares in 20 000 m2 17 Volume of glass if it holds 750 mL 18 Grams in 2·5 kg + 3·2 kg

19 28 to 5 afternoon as digital time

19 4:53 am as 24-hour time

20 Is a rectangle a quadrilateral? 20

20 Name triangle with two equal angles 20

You have to visualise the cube from all directions.

Here are five views of the same cube.

Draw the shape that is opposite: 1

2

3



61


A

Unit 21

1 16 + 27 + 34 2 84 minus 56 3 7 times 30 4 Half of 78 5 $10.00 + $9.85 6 How many digits in 67 392? 7 Is 60% the same 0·65? 8 Is 56 729 > 56 279? 9

3 = 4

8

equivalent fractions.

B

1 Sum of 35, 48 and 47 2 285 minus 97 3 10 × 39 4 53 divided by 9 5 2·13 × 4 6 How many digits in 329 601? 7 3 + 5 + 6 + 8 as decimal 10

100

1000

8 Smallest four-digit numeral using: 5, 9, 3, 8 5

11 Hindu-Arabic numeral for CCXLVII 12 Lowest common multiple of 6 and 18 13 4 squared

10

9 – 3 10 10

11 1 – 8 12 Average of 51, 53, 55 and 57 13 62 – 11 14

+ 95 = 162

15 Millimetres in 5 1 cm

15 Metres in 624 cm 16 Area of square with 9 m sides 17 Litres in 3 500 mL

6


10 25% of 12 candles

14 50 – (5 × 6)

3

and are 5 10

18 Kilograms in 1 t 19 28 to 10 evening as digital time 20 How many sides has a quadrilateral? 20

2

16 Area of square with 20 m sides 17 Litres in 8 450 mL 18 Grams in 2·5 kg 19 Minutes from 11:45 pm to 1:10 am 20 Shape of base on a hexagonal pyramid 20

62

1

Draw and label the factors of 12.

A factor is a number that will divide exactly into another number.

Factors of 6 are 1, 6, 2 and 3. 6 1 2 3

2

Draw and label the factors of 16.




Answers on page A8

C

0·62 We read this as ‘zero point six two’.

1 28 + 39 + 47 2 362 – 68 3

10 × 24

4

46 ÷ 6

5 Share $20.50 among 5 friends 6 Expanded notation for 56 729 7 Numeral for seven point zero nine 8 Is 467 345 < 476 345? 9 3= 5

D 1 2 3 4 5 6

Sum of 164, 50 and 53 Take 139 from 456 4 × 600 Remainder when 197 ÷ 20 6·8 × 5 Expanded notation for 348 109

7 8 + 7 + 9 + 7 as decimal 10

100

1000

8 Largest four-digit numeral using: 2, 7, 9, 6 9 Simplify 8

12

10

10 7 – 2

10 3 × 20

10

4

11 Hindu-Arabic numeral for DCCXLVI 12 Is 35 a composite number? 13 Are 36 and 49 both square numbers? 14 (4 + 7) × 3

5

11 Number 12 less than 3 12 Add prime numbers between 30 and 45 13 52 + 62 14 4, 9, 16,



16 Area of rectangle 6 m by 3 m

16 Area of square with 7·5 cm sides


17 Volume of a cube with 5 cm sides

18 Kilograms in 4·5 t 19 Minutes from 3:27 am to 5:13 am 20 Name of triangle with two equal sides 20

18 Kilograms in 4·75 t 19 3 hours after 10:48 pm 20 Sum of angles in a triangle

20

A parallelogram has four sides.

Circle the parallelograms. B

A

E

D

C

F

I G

4 cm 2 cm

H

J

2 cm 4 cm

A parallelogram has opposite sides equal and opposite angles equal. Excel Mental Maths Strategies Year 6—Unit 21


63


A

Unit 22

1 24 + 32 + 45 2 100 minus 69 3 4 times 40 4 Half of 92 5 Two boxes at $2.75 a box 6 How many digits in 136 579? 7 0·35 as a percentage 8 Is 19 472 > 19 306? 9 6 = 10

B 1 2 3 4 5 6 7 8

Before we can add

180 + 97 fractions we have to make the denominators 325 – 39 the same. Multiply 6 and 50 149 ÷ 5 $15.00 + $9.45 Place value of 6 in 641 579 Five point eight six as a decimal Is 459 368 closer to 459 000 or 460 000?


5

10 2 + 3 + 1

10 7 + 1

11 Number 1 000 after 35 378

11 Next number after 348 799 12 All prime numbers between 10 and 20

8

8

12

8

12 Is 15 a prime number? 13 62 14 5 × 6 + 4 × 5 15 Metres in 825 cm 16 Perimeter of triangle with 7 m sides 17 Litres in 4 500 mL

62 + 52 + 22 25, 36, 49, Millimetres in 13·9 cm Is 63 m2 the area of 8 m by 7 m rectangle?

17 Volume of cup if it holds 250 mL 18 Kilograms in 1·25 t 19 Minutes from 9:45 am to 11:06 am

18 Tonnes in 2 000 kg 19 11:36 pm as analog time 20 How many faces on a pentagonal prism?

13 14 15 16

6

20

20 Do parallel lines meet at 30°?

20

64

1

If EST is 6:29 am, what is the time in: a Perth? _________ b Darwin? _________ c Hobart? _________ d Adelaide? _________

2

If it is midnight in Perth, what is the time in: a Sydney? _________ b Adelaide? _________ c Brisbane? _________ d Darwin? _________

3

If EST is 12:21 pm, what is the time in: a Adelaide? _________ b Perth? _________

Eastern Standard Time (EST) Central Standard Time (CST) half an hour behind EST Western Standard Time (WST) 2 hours behind EST




1 243 + 168 + 76

1 290 + 64 To find the 2 236 – 19 product we multiply. 3 30 multiplied by 8

2 Difference between 841 and 358 3 Product of 78 and 6 4 738 divided by 9

4 95 ÷ 7 5 6·7 + 3·8 + 6·4 6 40 000 + 6 000 + 200 + 40 + 5 7

5

Share $66.16 among four people

6 How many digits in 367 289? 7 7 + 5 + 3 as decimal

as a decimal

100

8

8 Is 356 792 < 366 792? 9 2·38 as a mixed number 10

1000

Is 6 789 561 < 6 689 561?

9 Which is not equivalent: 6 , 6%, 0·6? 10

3 – 2 5 10

10 Cost if 10% off $350

11 Number before 230 000



12 Is 394 a multiple of 4?

13 Odd number before 86 380

13 Even number before 93 240

14 80 – (63 – 13) + 7

14 (35 – 29) × 8

15 Metres in

D

C

9 10

Answers on pages A9

8 1 2

km


16 Is 64 cm2 the area of an 8 cm square? 17 Millilitres in 3·755 L

16 Hectares in 30 000 m2

17 Volume of a cube with 4 m sides 18 Grams in 5·725 kg


19 23:37 as digital time

19 Two hours after 11:43 am 20 Does a parallelogram have four sides? 20

20 Name triangle with three equal angles 20

Complete each parallelogram. B

A

D

E

G

C Parallelograms have opposite sides equal and parallel.

F

H



65


Unit 23 Fun Spot! 1

Work backwards

2

A farmer sold 250 of his sheep, bought 35 and then bought 68. After 3 died, he sold another 260. If he now had 190, with how many did he begin?

3

On a bus, Mia watched 8 people get off and 4 get on at the first stop, 3 get off and 10 get on at the second, 5 get off and 7 get on at the third. If there were now 25 passengers, how many were on the bus when Mia started counting? 4

Trial and error

Con has $3 more than Chi and $2 more than Cher, while Jan has $1 less than Cher. Together they have $28. How much has Con?

5

Mr Right is five times as old as his daughter but in two years time he’ll be four times as old as his daughter. How old is Mr Right now?

6

A collection of chickens and pigs has a total of 70 legs and 26 heads. How many chickens are there?

7

Without using the same digit twice in any number, how many two-digit numbers can be made using 1, 2, 3 and 4?

8

If I write the numbers from 1 to 43, how many digits do I write?

9

If I use 141 digits, to which number will I write if I begin with 1?

Make a list

66

Peta started with a number, added 3, multiplied the result by 4, then subtracted 6 and multiplied that result by 3. If her final answer was 90, with which number did she begin?




Answers on page A9

Solve a simpler problem

10 Eight people were at a party. If each person shook hands with every other person, how many handshakes were there?

11 How many matches would be needed to form 40 large triangles?

12 If this pattern is continued until there are 50 rhombuses, how many matches will form the perimeter of the whole pattern?

Eliminate possibilities

13 Eight boxes each hold the same number of machine parts. Only one answer below shows the total number of parts. Which is it? a 135 b 138 c 136 d 133

14 If I have 12 coloured pencils which vary in length from 10·5 cm to 12·7 cm. Could the total of their lengths be 120·5 cm, 125·6 cm, 134·9 cm or 153·7 cm?

15 Mindy banks more than $12.70 each week. In five weeks could she bank $61.50, $63.00, $62.90 or $64.20?

16 Choose the correct tile to complete each pattern.

Look for patterns

a

A


A

B

B

C

C


b


67


Unit 24 Revision A 1 Place value of 2 in: a 2 597 b 49 238 c 290 168

2 Complete: a 4 + 9 × 3 – 10 b (2 × 3) + 5 × 8

3 Write: a 0·38 as a percentage b 35 as a decimal

100

c 0·58 as a fraction 4 a 268 + 54 b 200 – 74 c 40 × 20 d 171 ÷ 9

7 Write the number that is: a 1 000 after 67 206 b 1 000 before 569 358 8 Write the improper fraction for: c 2 7

8

9 a 34 +

= 92

_______

13 How many faces has each solid? a b c

______

______

______

14 What is the area of each shape? a 6m 6m

__________

b 6 cm 12 cm

__________

15 Lowest common multiple of: a 2 and 7 b 3 and 6

+ 39 = 101

c 7× 68

_______

d 2 5

10

b

b

2 3 4

7m

7m

5 cm

6 Write the first five multiples of: a 8 b 9 c 6

a

7m

8 cm

5 Round off to the nearest thousand: a 25 375 b 49 621 c 378 502

15 6

10 Write: a 3:16 pm as 24-hour time b 08:39 as digital time c 11:37 as analog time 11 How many: a millilitres in 7·5 L? b grams in 3·6 kg? c metres in 5·275 km? 2 d hectares in 20 000 m ? 12 What is the perimeter of each shape? a b

= 63




Answers on page A9

Revision B 1 a 80 000 + 4 000 + 700 + 20 + 1 b 500 000 + 90 000 + 4 000 + 50 + 8 c Place value of 6 in 165 937 2 Write as a percentage: a 7

b 0·9

10

c 0·84 3 Highest common factor of: a 4 and 6 b 15 and 20 4 Use > or < to show the bigger number. a 38 439 38 349 b 94 627 94 687 c 107 385 108 385 5 Circle the factors of: a 16 (4, 6, 8, 9, 12) b 20 (4, 5, 6, 9, 10) c 30 (5, 6, 7, 8, 10) 6 What is the time two hours after: a 5:39 pm? b 11:41 am? c 13:27? d 05:52? 7 Write the mixed number for: a 11

b 16

6

c 17

5

d 11

8

3

8 a 3 + 2 8

8

b

7 5 – 10 10

9 List the first five multiples of: a 7 b 4

10 Write as 24-hour time: a 3:37 am b 10:17 am c 6:58 pm d 9:26 am 11 Roman number for: a 307 b 589 c 767 d 684 b 5 squared 12 a 3 squared c 42 d 62 13 How many: a litres in 7 500 mL? b kilograms in 9 250 g? c metres in 1·5 km? d centimetres in 629 mm? e metres in 7·25 km? 14 Match each triangle with its name: isosceles

a


right-angled

b

__________ c

__________

__________ 15 Write as digital time. a 06:45 b 15:12 c 11:57 d 21:28 16 Record each length shown. a

cm 0

1

2

3

4

5

6

1

2

3

4

5

6

b


equilateral

cm 0


69


A

Unit 25

1 25 + 26 + 47 2 100 minus 57 3 5 times 30 4 Half of 76 5 $10.75 shared among 5 boys 6 How many digits in 369 472? 7 55% as a decimal 8 Is 11 457 < 11 657?

1 2 3 4 5 6 7

1 t = 1 000 kg

To 258 add 65 where t = tonne and kg = kilogram 582 minus 97 Multiply 5 and 30 164 divided by 8 $20.45 + $3.65 Place value of 5 in 459 237 Numeral for three point five eight

8 Round off 358 962 to nearest ten thousand

9 Quarters in 2 1 4

10

B


1 + 2 + 1 5 5 5

11 Number 1 000 after 39 503 12 All prime numbers between 0 and 10 13 Is 16 a square number? 14 2 × (50 – 35) 15 Metres in 5 km 16 Area of rectangle 4 m by 8 m 17 Millilitres in 3·7 L 18 Kilograms in 3 t 19 25 to 9 morning as digital time 20 How many sides has a trapezium? 20

10 60% of 30 11 3 – 12 12 Circle the prime numbers: 63, 71, 81, 91 13 42 – 15 14 6 × 4 + 6 × 5 15 Metres in 973 cm 16 Area of rectangle 4·2 m by 5 m 17 Volume of rectangular prism with sides 5 m, 4 m and 3 m 18 Tonnes in 3 955 kg 19 Minutes from 11:17 am to 1:39 pm 20 Circle the obtuse angle: 20 48°, 169°, 295°

70

Circle the correct cross-section for each solid. 1

2 crosssection

3

4 A cross-section is the face that we see when we slice a piece off a solid.




possible number is 9640.

C

D

1 2 3 4 5

1 2 3 4 5 6 7 8

97 + 180 325 – 39 Multiply 6 and 50 6 4 149 ÷ 5 9 0 Change from $20 if I spend $12.75 6 How many digits in 1 654 327? 7 Numeral for seven point zero three 8 Largest 4-digit numeral using: 3, 6, 8, 4 9

Sum of 345, 271 and 196 Difference between 461 and 49 Multiply 60 by 40 77 ÷ 8 9·86 – 6·59 Place value of 2 in 2 378 459 3·78 to the nearest whole number Arrange in descending order: 2·4, 2·7, 2·1 9 12·95 as a mixed number

Improper fraction for 4 3

10 5 of 144

5

12

10 3 + 1 5

11 Hindu-Arabic numeral for DCCXCVI

10

11 Numeral 6 less than 2 12 All factors of 36 13 82 + 9 14 48 ÷ (4 + 4) ÷ 2 15 Centimetres in 8·37 m 16 Perimeter of a square with 9·5 cm sides 17 How many cm3 in 950 mL of water? 18 Tonnes in 2 575 kg 19 9:26 pm as 24-hour time 20 Does a decagon have ten sides? 20

12 Average of $1.30, $1.90, $1.60 13 112 14 320, 400, 480, 15 Distance covered in 5 hours at 85 km/h 16 Area of rectangle 5·5 cm by 6 cm 17 Volume of cup if it holds 500 mL 18 5·5 kg at $2.20 per kilogram 19 Time in Adelaide if EST is 3:40 am 20 Are all angles in a regular hexagon equal? 20

Daily bridge traffic Sun Mon

Day

Tue Wed Thu Fri Sat 2

4

6

8

10

12

14

Number of vehicles (in hundreds)

1

On which day were there: a 600 vehicles? ____________ b 1 100 vehicles? ____________ c 800 vehicles? ____________ d 1 400 vehicles? ____________

2

How many vehicles crossed the bridge on: a Monday? ______ b Thursday? _______ c Tuesday? ______ d Saturday? _______

3

What was the total number of vehicles on: a Monday and Tuesday? ____________ b Thursday and Friday? ____________ c Saturday and Sunday? ____________

4

How many more vehicles used the bridge on Friday than on: a Tuesday? ____________ b Saturday? ____________ c Wednesday? ____________



Answers on pages A9–A10 The largest

71


A

Unit 26

1 32 + 46 + 28

B

A line of symmetry divides a shape into two mirror images.

1 148 + 35

2 100 minus 78

2 263 – 147

3 3 times 40

3 40 × 50

4 Half of 58

4 180 ÷ 3

5 $6.90 + $5.65

5 $10.00 – $4.75

6 30 000 + 5 000 + 900 + 80 + 2

6 How many digits in 7 469 023?

7 Numeral for four point nine

7 7 as a percentage 10

8 Round off 67 104 to nearest ten thousand

8 Largest possible number using 6, 5, 9, 3



3

8

10 50% of 50

10 20% of $60

11 Roman numeral for 529 12 Highest common factor of 2, 4 and 6


13 3 squared

13 42 + 52

14 8 × 4 – (3 × 4)

14 160, 240, 320,


12 Is 56 a prime number?

15 Metres in 1 567 cm


16 Square metres in 7 ha 17 Volume of cube with 5 cm sides

17 Millilitres in 4·5 L 18 Tonnes in 5 000 kg


19 Minutes in 1 1 hours

19 Two hours before 10:07 pm

20 Is a rectangle a quadrilateral?

20 Does a rectangle have a line of symmetry? 20

2

20

72

1

Which bird was seen most often? __________

2

Were more magpies seen than: a mudlarks? ___ b sparrows? ___ c finches? ___

3

Were more parrots seen than: a starlings? ___ b sparrows? ___ c magpies? ___

4

Together, were more finches and magpies seen than: a parrots? ___ b starlings? ___ c others? ___

5

What fraction of the birds seen were either parrots or sparrows?__________

Finches

s rk dla u M Other

rli

Use the pie graph to answer the following.

ng s

Magpies

Sta

Parrots Sparrows

A pie graph uses parts of a circle to show information. Excel Mental Maths Strategies Year 6—Unit 26



C 1 2 3 4 5 6 7 8

25 km/h means a speed of 25 kilometres per hour.

169 + 78 234 – 168 20 × 60 250 ÷ 5 $3.30 + $4.65 + $2.95 Place value of 1 in 178 469 6·7 to nearest whole number Largest number using 6, 4, 8, 2, 7

D

1 2 3 4 5 6 7 8

Answers on page A10

1 430 + 300 Subtract 263 from 596 Multiply 120 by 300 Quotient of 140 and 10 Five DVDs at $19.95 each Thousands in 1 456 389 Is 45% the same as 0·4? Smallest possible number using 4, 6, 5, 9, 3


9 Simplify 6

10 7 – 3

10 Add 1 and 1

11 Next negative number after –2

11 Negative number before –7 12 Add prime numbers between 12 and 20

10

6

8

6

8

12 Are 9 and 6 both factors of 36? 13 52 – 15 14 40 ÷ 5 + 25 15 Distance covered in 2 hours at 70 km/h 16 Square metres in 2 ha 17 Volume of cup if it holds 500 mL 18 Kilograms in 1·75 t 19 01:48 as digital time 20 Is a quadrant a quarter of a circle? 20

3

13 Triangular number after 10 14 56 ÷ 8 – 36 ÷ 6 15 Average speed if 480 km covered in 6 h 16 17 18 19 20

Hectares in 20 000 m2 Volume of a cube with 6 cm sides Tonnes in 3 250 kg 2 hours before 22:17 Diameter of a circle with radius 3·45 cm 20

Answer the following by looking at the diagram. 1 Which line is parallel to: a D? ____ b H? ____ c G? ____ 2

Which line is perpendicular to: a I? ____ b C? ____ c D? ____

A I

Perpendicular lines meet at right angles.

Parallel lines always remain the same distance apart and never meet.

B H C D E

F

G



73


A

Unit 27

1 75 + 156 2 Take 64 from 192 3 Double 38 4 How many fours in 120? 5 How much for 10 L of petrol at 85c a litre? 6 How many digits in 385 604?

B 1 2 3 4 5 6

350 mL of water takes up a space of 350 cm3.

Add 168 and 43 Subtract 135 from 382 Product of 40 and 60 240 ÷ 6 11·5 – 6·9 300 000 + 60 000 + 5 000 + 700 + 40

7 Which is not equivalent:

7 60% as a decimal

0·65, 60%, 65 ?

8 Is 34 967 < 34 957?


100

8 Largest number using 8, 4, 9, 2, 5 9 1·07 as a mixed number 10 Cost if 25% off $200 11 Number 25 less than 14 12 Highest common factor of 6, 9 and 12

3

10 50% of 90 11 Negative number before –5 12 Are 4 and 6 both factors of 48? 13 42 14 23 + 12 – 8 15 Metres in 7 km 16 Perimeter of square with 6 m sides

13 32 + 42 14 810, 900, 990, 15 Kilometres in 5 725 m 16 Perimeter of square with 3·5 cm sides

17 Millilitres in 6·5 L 18 Kilograms in 4 t 19 10:09 am as analog time 20 Is a straight angle > a right angle?

20

17 Volume of cup if it holds 750 mL 18 Tonnes in 5 750 kg 19 21:38 as digital time 20 Sum of angles in a triangle

20

74

1

a throw a die. _______________________________

b spin the spinner. _______________________________

c draw one marble from the hat. _______________________________

d draw two marbles from the hat. _______________________________

List the possibilities you can get when you: When we toss a coin we have only two possible outcomes: a head or a tail. 5 6 1 4 3 2

If we toss two coins we can get: 2 heads, 2 tails or a head and a tail




C 1 2 3 4 5 6

a fraction we divide the top and the bottom by the same number.

Add 140 and 69 Subtract 143 from 478 30 × 70 280 ÷ 4 $30.00 – $16.45 Place value of 8 in 864 539

7 Which is not equivalent: 0·4, 4%, 4 ? 8 Smallest number using 8, 1, 0, 4

10

D

1 2 3 4 5 6 7 8

Add 147 to 652 Subtract 135 from 216 Multiply 145 by 20 4 790 ÷ 10 Change from $100 if $64.95 spent Place value of 6 in 3 681 294 4·39 to the nearest whole number Is 2 567 389 > 2 557 389?

9 Is 3 > 10 ?

9 Simplify 1 4

10 2 + 7

10 Cost if 25% off $800 11 Number before 3 000 000 12 Is 364 a multiple of 7? 13 10 squared

4

5

12

12

10

11 Number 10 less than zero 12 Average of $3.60, $3.90, $4.50, $5.40

14 36 ×

13 Is 64 a square number? 14

15 Distance in 4 hours at 130 km/h

– 49 = 25

16 Square metres in 4 ha


17 Volume of container if it holds 1 L

16 Hectares in 30 000 m

18 Mass of 3·5 L of water

17 Volume of rectangular prism 6 cm, 4 cm, 2 cm sides?

19 Time in Perth if EST is 4:35 am 20 How many edges on a hexagonal prism?

18 Mass of 2 L water 19 14:29 as digital time 20 Name polygon with six sides

= 3600

20

20

The diameter is twice as long as the radius.

Use a pair of compasses to draw these circles.

diameter

radius 15 mm

diameter 34 mm

radius

radius 1·9 cm



Answers on pages A10–A11 To simplify

75


A

Unit 28

1 106 + 64

1 Sum of 146, 29 and 37

2 137 – 58

We can write remainders as fractions

2 Take 108 from 273 3 6 × 300

3 10 times 20 4 How many sixes in 180?

4 Is 148 ÷ 7 = 21 2 ?

5 $1.55 + $2.35 + $1.65

7

6 Place value of 5 in 35 690

5 6 7 8

7 Numeral for eight point six three 8 Smallest number using 6, 3, 8, 4 9 Sixths in

B

Share $24.60 among six people 800 000 + 60 000 + 4 000 + 300 + 6 3·51 to nearest whole number Is 348 952 < 284 952?

9 Simplify 6 9

15 6

10 50% of 60 11 Roman numeral for 762 12 All composite numbers between 11 and 19 13 Ordinal number for thirty-eighth 14 16 + 4 × 6 15 Kilometres in 4 000 m 16 Area of rectangle 9 m by 5 m 17 Litres in 4 500 mL 18 Tonnes in 6 000 kg

10 20% of 250 11 Hindu-Arabic numeral for MCXIV 12 Lowest common multiple of 3 and 7 13 32 + 5 14 1025, 975, 925, 15 Kilometres in 2 975 m 16 Square metres in 1 ha 17 Volume of cube with 3 cm sides 18 Mass of 3 L water 19 6:18 pm as 24-hour time 20 Tick the quadrant: A

19 7:53 pm as analog time 20 Is 68° an acute angle?

C

20

B

20

76

On a number plane the x-coordinate comes before the y-coordinate.

y -axis 5

E A

4 3

I

G

N B D

1 1

K F

2

0

M

J

2

L O

2

P

H 3 4

C 5

6

7

1 Write the letter at each point. a (3, 1) b (4, 3) c (5, 1) d (1, 4) e (3, 4) f (7, 3) g (1, 1) h (3, 0)

x -axis

Write the coordinates for each point. a L b P c K d B e N f G g E h I




Answers on page A11

C 1 2 3 4 5 6

D

Sum of 154, 38 and 49 Take 136 from 378 3 × 500 Remainder when 187 ÷ 5 8·64 – 3·78 Place value of 7 in 1 753 849

7 Which is not equivalent: 0·5, 50%, 5 ? 100

8 Smallest possible number using: 5, 8, 4, 3, 9 9 Is 25% less than 0·3? 10 Cost if 10% off $150 11 Number 12 more than –7 12 Lowest common multiple of 5 and 8

7 =7×7 1 576 + 132 = 49 381 – 163 Product of 90 and 8 Remainder when 511 ÷ 6 Share $84.35 among 5 friends Expanded notation for 1 350 607 Numeral for five point six four Arrange in descending order: 3·8, 3·4, 3·9 2

9 Simplify 6

12

10 Cost if 10% off $750 11 Hindu-Arabic numeral for MDCCLIV 12 Average of $4.55, $2.35, $3.90

13 Is 21 a triangular number? 14 3 064, 3 014, 2 964, 15 Distance covered in 3 hours at 60 km/h 16 17 18 19 20

1 2 3 4 5 6 7 8

13 6 squared 14 10 × 10 – 72 ÷ 9 15 Average speed if 300 km covered in 4 h 16 Square metres in 3 ha

Area of square with 9 cm sides Volume of cube with 4 cm sides Kilograms in 3·5 t Two hours after 11:01 pm A B Tick the sector:

17 Mass of 4·75 L of water 18 Tonnes in 2 475 kg 19 4 hours after 13:29 20

20 Radius of a circle with diameter 4·56 m

20

Use the bar graph to answer the following. men

women

boys

girls

1

Were there more boys than: a women? _____ b girls? _____

2

Were there fewer men than: a boys? _____ b women? _____

3

Was the total of men and women the same as the total of boys and girls? _____

4

Order the size of each group from largest to smallest. __________________________________

A bar graph uses parts of a bar to show information.



77


A

Unit 29

1 124 + 35

We use ha for hectare. 1 hectare = 10 000 m2

1 137 + 165 + 39 2 249 – 168 3 Product of 34 and 6 4 192 divided by 5 5 $15.30 – $9.85 6 Place value of 2 in 2 569 385 7 7·04 as a mixed number 8 Arrange in ascending order: 3·5, 3·8, 3·6

2 Difference between 163 and 87 3 20 × 30 4 120 ÷ 6 5 $2.50 × 3 6 How many digits in 906 500? 7 0·6 as a percentage 8 Round off 259 368 to nearest thousand

9 Is 5 the same as 6 ?


10

2

10 11 12 13 14 15

10 25% of 80 11 Next number after 156 789 12 First four multiples of 6 13 90 – 82 14 63 ÷

B

=7


25% of $200 Number 25 more than –8 Is 504 a multiple of 9? 52 + 10 3 096, 3 146, 3 196, Distance covered in 5 hours at 50 km/h

16 Square metres in 9 ha 17 Volume of container if it holds 350 mL

16 Perimeter of rectangle sides 3·2 m by 4·2 m 17 Litres in 7 500 mL

18 Mass of 1·5 L water 19 Time in Perth if EST is 8:47 am 20 Shape of base on a triangular prism

18 Kilograms in 2·5 t 19 6:38 am as analog time 20 Name the triangle with all angles 60°

12

20

20

The area of each

78

Find the area of each triangle. 4 cm 2 1

4 cm

2 cm

3

3 cm

A = __________

3 cm

A = __________

4

5 cm 3 cm

3 cm

triangle is half the area of each rectangle.

A = __________

A = __________

A rectangle has sides 4 cm by 2 cm. Area = length × width =4×2 = 8 cm2 Therefore area of triangle is 4 cm2.




C

32 + 11 = 3 × 3 + 11 = 9 + 11 = 20

1 236 + 124 + 47 2 369 – 276 3 Product of 25 and 5 4 Is 137 ÷ 4 = 34 1 ? 4

5 6 7 8

Ten toys at $6.95 each Expanded notation for 367 005 6·37 to nearest whole number Arrange in descending order: 1·4, 1·6, 1·3

Answers on page A11

D 1 2 3 4 5 6 7

3 267 + 245 From 311 take 185 400 × 60 Quotient of 1 496 and 10 12·75 – 9·8 Place value of 9 in 9 174 682 Numeral for nineteen point zero eight

8 Is 4 245 789 < 4 245 145? 9 Simplify 1 8

9 Simplify 4

12

10

10 50% of 640

10 3 of $84

11 –2 + 5

4

11 Number before 290 000 12 First four multiples of 12

12 Product of 45 and 6 13 92 + 9

13 72 +

14 81, 64, 49,

= 60

14 20 × 9 ÷ 3 15 Metres in 3·65 km 16 Hectares in 30 000 m2 17 Volume of container if it holds 250 mL

15 Distance in 7 hours at 150 km/h 16 Square metres in 5 ha 17 Volume of vase if it holds 2 L 18 Mass of 3·25 L of water

18 Grams in 3·725 kg 19 10:31 am as 24-hour time 20 Diameter of a circle with radius 3·5 cm 20

19 Time in Melbourne if EST is 2:19 pm 20 Is the top view of a cone a circle? 20

Number plane—four quadrants The x-coordinate comes before the y-coordinate. y -axis 6 L I A 4 E D J B 2 C K –6 –4 N

–2 0 M

–2 –4

O

2 G

4 F

6

H

1 Write the letter at each point. a (2, 4) b (3, 1) c (0, 3) d (4, –2) e (–2, 4) f (–5, 1) g (–3, 2) h (–2, –2)

x -axis

2

Write the coordinates for each point. a B b D c G d H e L f N g O h M

–6 Excel Mental Maths Strategies Year 6—Unit 29


79


A

Unit 30

1 145 + 57

B 1 2 3 4 5 6

2 From 158 take 96 3 50 × 30 4 150 ÷ 5 5 $2.50 × 4 6 Place value of 7 in 378 391 7 Is 0·75 the same as 57%?

2

7 Numeral for sixteen point zero nine

8 Is 567 290 < 576 290?


8 Smallest number using 8, 5, 2, 6

10 50% of 64

9 Simplify 4


10 Cost if 10% off $300 11 Number before 500 000 12 Is 683 divisible by 7? 13 42 + 50

6

16

12 Is 248 divisible by 4? 13 32 + 5 14

2÷2

Simplify = 143 + 260 + 28 10 10 ÷ 2 589 – 251 =1 5 Product of 45 and 5 167 divided by 6 12·5 × 9 600 000 + 10 000 + 5 000 + 400 + 30 + 5

× 8 = 160


14

16 Area of square with sides 10 m

15 Metres in 4·375 km 16 Hectares in 60 000 m2 17 Volume of container if it holds 950 mL

17 Litres in 9 500 mL 18 Kilograms in 4·5 t 19 20 past 4 morning as am or pm time 20 How many faces has a square prism?

20

× 32 = 160

18 Mass of 1·625 L water 19 23:57 as digital time 20 How many edges on an hexagonal prism?

20

To change millimetres to centimetres we Complete each table. divide by 10.

80

Millimetre

50

Centimetre Centimetre

7

3·5

300

Metre

87

120

450 6

192

7·5

mm ÷ 10 = cm cm ÷ 100 = m

Metre

4 000

Kilometre

6 500 8

4 725

m ÷ 1000 = km

8·5




C

1 2 608 + 139 2 Difference between 906 and 178 3 70 × 500

4 Is 196 ÷ 6 = 32 5 ?

4 Quotient of 5 627 and 10

5 Change from $20 if $16.45 spent 6 Expanded notation for 475 926

5 Share $59.55 between three

6

7 6+

6 How many digits in 26 789 201? 7 One point two five six as a decimal

5 6 4 + + 10 100 1000

8 Is 6 389 514 > 6 388 514?

8 Is 345 498 closer to 345 000 or 350 000?

9 Simplify 1 15

9 Simplify 12

10 Cost if 10% off $650

24

20

11 Number before 67 000 000

10 25% of $640

12 Product of 54 and 4

11 Number 30 more than –16

13 Is 28 a triangular number?

12 Is 3 050 divisible by 5?

14 (9 + 7 + 5 × 8) ÷ 2

13 6, 10, 15, 14

D

One point five six is 1·56

1 228 + 132 + 69 2 246 – 178 3 64 multiplied by 6

Answers on page A12

15 Distance in 8 hours at 360 km/h

÷ 8 = 25

16 Square metres in 12 ha


17 Volume of container if it holds 2·375 L

16 Hectares in 60 000 m

2

17 Volume of glass if it holds 375 mL

18 Mass of 5·625 L of water

18 Grams in 6·125 kg


19 08:52 as am or pm time

20 Are opposite sides of a rectangle parallel?


20

20

Complete each table. Gram Kilogram

9 000 2

6 275 To change grams to kilograms we divide by 1 000.

7·5

5

Gram Kilogram

4 500

3 000

8 500

1 625 3·85

To change kilograms to grams we multiply by 1 000.



81


Unit 31 Fun Spot! 1

Peta stacked small cubes into the corner of this box. How many: a cubes are in the stack? b cubes altogether would stack into the box?

2

Tile A

3

Arrange the numbers 1 to 9 (inclusive) in the circles so that the sum of the numbers in a straight line across the centre of the circle is 18.

4

A palindromic number is a number that is the same when read backwards or forwards, for example 242. Complete the table to find these palindromic numbers. Addition

82

To make this pattern has Tile A been: a flipped? b slid? c turned?

Palindromic number

Addition

a

56 + 65

e

423 + 324

b

132 + 231

f

514 + 415

c

623 + 326

g

314 + 413

d

235 + 532

h

142 + 241

Palindromic number




Answers on page A12

Blaise Pascal discovered some interesting facts about numbers arranged in a triangular pattern like this:

Sum of numbers: 1 2 4 ___ ___ ___ ___ ___ ___

Row:

1

1

1

2

1

3

1

4

1

5 6

1

1 2

3

1 3

1

4 6 4 1 5 10 10 5 1

7 8 9 5

Find the pattern and complete the next three rows of the pattern.

6

Find the sum of the numbers in each row.

7

What will be the sum of the numbers in the: a 10th row? b 11th row? c 15th row?

8

Look for a pattern in the second numbers in the rows. What will be the second number in the: a 10th row? b 15th row? c 18th row?

9

What will be the third number in the: a 10th row? b 11th row? c 20th row?

Blaise Pascal was a French mathematician of the seventeenth century.

10 Use a calculator the find the value of 112, 113 and 114. Can you find these numbers in the above pattern? © Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_pp82_83_new2725.indd 83


83


Unit 32 Revision A 1 a b c d

Sum of 190 and 54 To 258 add 74 486 minus 94 Difference between 274 and 109

e 40 × 60 f 6 × 400

2 Write: a 0·6 as a percentage b 90% as a fraction c 3 a

7 10

as a percentage

3 2 + 8 8

8 Round off to the nearest thousand: a 24 782 b 68 496 c 159 704 9 Use > or < to show the bigger number: a 64 389 46 389 b 105 549 107 459 c 857 294 587 294 10 a b c d

11 How many: a metres in 3·75 km? b square metres in 3 ha? c tonnes in 4 575 kg? d litres in 6 500 mL?

b

9 4 – 10 10

c

5 1 – 6 3

d

1 2 3 + + 10 10 10

e Simplify 9

12 If EST is 1:30 pm, what is the time in: a Brisbane? b Adelaide? c Perth? d Darwin?

12

4 Largest possible number using: a 6, 0, 3, 9 b 4, 6, 1, 8 Arrange in ascending order. c 1·6, 1·9, 1·4 5 Hindu-Arabic numeral for: a DCLXVII b MCDLXXIX Roman numeral for: c 468 d 1 279

13 Tick the regular shapes. a b c

d

7 Write the improper fraction for: a 1 7

b 3 2

c 4 1

d 3 2

2

84

3 5

e

f

14 What is the volume of each solid? b a 5m

5 cm

6 Write the first five multiples of: a 4 b 8 c 6

8

3:27 am as 24-hour time 6:39 pm as 24-hour time 13:19 as digital time 08:57 as digital time

3 cm

2 cm

__________

15 What is the mass of: a 2 L of water? b 750 mL of water?

3m

4m

__________




Answers on page A12

Revision B 1 Place value of 8 in: a 37 849 b 685 721 c 4 892 306 2 Write in extended notation. a 359 278 b 950 307 3 What is: a 20% of 75? b 75% of $400? c Price if 10% off $190? 4 Product of: a 56 and 4 b 64 and 3 c 43 and 4

10 Write the digital time for: a 23:49 b 06:38 11 How many: a kilometres in 3 550 m? b kilograms in 2·75 t? c millilitres in 4·275 L? 12 What is the area of each shape? a b 5m 7m

5 What is: a 5 squared? b 82? c triangular number after 10? 6 Complete: a 20 + (3 × 5) b 5 × 8 + (24 ÷ 6) c 35 – (4 × 8) 7 Smallest possible number using: a 4, 8, 2, 0 b 6, 3, 8, 1 Arrange in ascending order: c 2·5, 2·8, 2·6 8 Write the number that: a is 1 000 after 59 307 b is 1 000 before 389 201 c follows 689 593 d follows 927 599 9 Write true or false for each: a 367 297 > 357 297 b 987 206 < 988 206 c 1 589 346 < 1 689 346

3 cm

________ ________ 13 How many faces has each solid? b c a

________ ________ ________ 14 How many hectares in: a 30 000 m2? b 50 000 m2? c 40 000 m2? 2 d 70 000 m ? 15 What is the capacity of a container holding: a 275 mL of water? b 3 L of water? 16 Record the length shown.

6


7

8

9

10

11


9 cm


85


Index to help section A acute angle 15 addition 2, 4 fractions 9 money 4 analog time 14–15 angles 15–16 in triangle 17 apex 18 area 12–13 ascending order 7 average 10 axis of symmetry 16 B bar graph 19 base of solid 18 breadth 13 bridging the tens 2 C capacity 13 centimetre 11–12 Central Standard Time 15 chance 19 circle 12, 16–18 circumference 12, 16 column graph 19 compass points 16 compensation strategy 2 composite numbers 10 cones 17–18 converting units see units coordinates 18–19 corners of solids 18 cross-section of solid 17 cube, solid 17 cubic metre 13 cylinders 17–18 D days in months 14–15 decimals 5–7 denominator 5–6, 8–9 descending order 7 diagonal lines 16 diameter of circle 16 difference see subtraction digital time 14–15 digits in numbers 5 distance 12 divisibility 4, 10 division 3–4 dot plot 19 E east 16 Eastern Standard Time 15 edges of prisms 18 equilateral triangle 17 equivalent fractions 8 even numbers 10 expanded notation 5

F faces of solids 18 factors 3, 10 fractions 5–9 frequency 19 G grams 14 graphs 19 greater than 7 grids 18–19 H hectare 12–13 height of solid 13, 17–18 highest common factor 10 Hindu-Arabic numerals 9 hours 14–15 I, J, K improper fractions 8 irregular shapes 16 isosceles triangles 17 jump strategy 2 kilograms 14 kilometre 11–12 L larger number 7, 9 leap year 14–15 length 11–13 less than 2, 7 see also subtraction line graph 19 lines 16 litre 13 lowest common multiple 10 M map 18 mass 14 metre 11–12 millilitre 13 millimetre 11–12 minus see subtraction minutes 14–15 mirror image 16 mixed numbers 8 money 4–5 percent off price 9 months 15 multiples 10 multiplication 3, 4, 10 fractions 8, 9 N negative numbers 9 net of solid 18 north 16 number patterns 2, 11 number plane 19 number sentences 11 numerals 9 in words 5, 7 numerator 5–6, 8–9

O obtuse angle 16 odd numbers 10 order of numbers 7 order of operations 11 ordinal numbers 11 outcomes 19 P parallel lines 16 parallelograms 17 patterns 11, 21 extend number facts 2 for multiply/divide 3–4 to solve problems 19 percent 6, 9 perimeter 12 perpendicular lines 16 pie graph 19 place value 5, 6 plane shapes 16–18 plus see addition polygons 12, 16–18 prime numbers 10 prisms 12–13, 17–18 probability 19 problem solving 20–21 mass 14 money 4 product of factors 10 see also multiplication pyramids 17–18 Q, R quadrant of a circle 17 quadrilaterals 17 quotient 3–4 radius of circle 17 ratios 20 rectangles 12–13, 17 rectangular prisms 13, 17–18 reflex angle 16 regular shapes 16 remainder 3–4 reverse operations 3 revolution 16 right angle 15–16 right-angled triangle 17 Roman numerals 9 rounding off 7

speed 12 spheres 17–18 split strategy 2 square, geometry 13, 17 square metre 12–13 square numbers 11 straight angle 16 subtraction 2, 4 fractions 9 sum see addition sum of angles 17 surfaces of solids 18 symmetry 16 T tables percent/fractions/ decimals 6 times table 3 tests for divisibility 4 three-dimensions see solid time 14–15 times table 3 timetables 15 time zones 15 tonnes 14 triangles 13, 16–18 triangular numbers 11 triangular prism 11 twenty-four-hour time 14–15 two-dimensional shapes 16–18 U, V, W units area 12–13 capacity 13 length 12 mass 14 speed 12 time 14–15 volume 13 vertex 18 views of solids 17 volume 13 weight 14 west 16 Western Standard Time 15 words for numerals 5, 7 year 14–15

S scale drawing 20 scalene triangle 17 seconds 14 sector of circle 17 semicircle 17 shapes, flat 16–18 simplify fraction 8–9 smaller number 7, 9 solid shapes 13, 17–18 nets 18 south 16

86 © Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_pp84_86_new2725.indd 86


A 1 32

2 31

13 33

B 1 43

12 yes

3 20

14 12

45

5 $2.75

15 600 cm

16 22 m

17 6 L

7

18 4 kg

31 100

8 1 700

19 7:25

93

10 8

11 CL

12 yes

20 yes

2 29 3 42 4 7 5 $3.55 6 4 thousands (4 000) 7 47% 8 8 000 9 no 10 12 11 3 903 13 90 14 32 15 42 mm 16 25 cm2 17 3 000 mL 18 7 000 g 19 3:47 am 20 6

Extra practice section: 1

6 7 hundreds (700)

2

+

22

26

33

35

41

46

+

23

25

32

34

45

47

19

41

45

52

54

60

65

19

42

44

51

53

64

66

29

51

55

62

64

70

75

29

52

54

61

63

74

76

39

61

65

72

74

80

85

59

82

84

91

93

104

106

49

71

75

82

84

90

95

69

92

94

101

103

114

116

Answers

Unit 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 22

C 1 44

2 43 3 48 4 7 5 $6.70 6 7 ten thousands (70 000) 7 0·65 8 9 000 9 yes 10 4 11 CCCXLVII 12 1, 40, 2, 20, 4, 10, 5, 8 13 yes 14 28 15 38 mm 16 9 cm2 17 8 000 mL 18 5 000 g 19 4:57 pm 20 5

D 1 126

2 82 3 360 4 90 5 $7.80 6 6 ten thousands (60 000) 7 10% 8 52 000 9 yes 10 15 11 296 12 yes 13 36 14 33 15 950 cm 16 45 cm2 17 4 500 mL 18 6 500 g 19 3:47 am 20 none


2

3

4

8

3

4

1

6

5

10 3

8

1

5

9

8

6

4

8

4

0

5

9

6

7

2

7

2

9

3

2

7

6 11 4

3 10 5

7

5

1

8 13 12

6

7

7

5

2 15 5 16

6

8

6 11

2 15 1 12

9 12 6 11

5 16 9

4

15 10 3

13 8 10

14 3 17 4

7

14 11 2

9

4 10 7

14 3 13 0

Unit 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 24 A 1 46

3 45

12 yes 13 16th

B 1 64

2 52

2 13

49 14 7

3 54

15 90 mm

46

12 1, 20, 2, 10, 4, 5

61 100

8 2 400

9 no

18 5 kg

19 6:20

20 yes

5 $3.85 6 6 thousands (6 000) 16 20 m

17 8 L

7

5 $5.05 6 3 hundreds (300) 7 65% 8 8 000 9

13 no

14 21


15 36 mm

16 16 cm2

2 6

11 CLXIV

10 12 11 5 839

17 9 000 mL

2

10 5

18 5 000 g

19 6:35 pm

72

76

81

85

93

97

64

68

73

76

81

85

–19

53

57

62

66

74

78

–19

45

49

54

57

62

66

–39

33

37

42

46

54

58

–29

35

39

44

47

52

56

–59

13

17

22

26

34

38

–39

25

29

34

37

42

46

–69

3

7

12

16

24

28

–49

15

19

24

27

32

36

20 6

C 1 66

2 38 3 48 4 6 5 $3.05 6 4 thousands (4 000) 7 53% 8 no 9 no 10 9 11 8 364 12 1, 18, 2, 9, 3, 6 13 15th 14 153 15 56 mm 16 36 cm2 17 9 000 mL 18 7 000 g 19 3:29 am 20 1

D 1 125

2 46

3 560

11 9 526 12 yes

4 70

13 81

5 $2.04 14 1 775

6 67 463 15 750 cm

7 70%

8 29 000

16 32 cm2

9 2

1 4

10 25

17 6 500 mL 18 9 500 g 19 4:38 pm 20 1

Extra practice section: 1a cone b hexagonal prism c square pyramid d rectangular pyramid e cylinder f triangular prism 2 a and e 3 b, c, d and f

Unit 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 26 A 1 76

2 82

13 700

3 35

14 34

45

5 $5.80

15 70 mm

6 3 hundreds (300)

16 22 m

17 6 000 mL

7

84 8 yes 100

18 9 000 g

94

10 12

19 11:28

11 CXXXIX

12 yes

20 4

A1 A1 © Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_answers_middle_2725.indd 1


Answers

B 1 65

2 26 3 56

47

5 $6.40

12 1, 30, 2, 15, 3, 10, 5, 6 13 36 14 200

Extra practice section: 1 0·36

C 1 64

2 16

3 64

48

2 0·84

5 $4.30

8 26 000 9 3

15 3·9 cm

3 0·59

4 0·7

10 6 11 2 447

17 3 L

16 64 cm2

5 0·4

1 3

18 9 kg

19 27 minutes 20 4

6 0·1

6 4 thousands (4 000)

7 95%

8 46 000

13 5

9

10 9 11 3 665

12 1, 40, 2, 20, 4, 10, 5, 8 13 9 14 21 15 47 mm 16 27 cm2 17 8 000 mL 18 7 kg 19 6:51 pm 20 7

D 1 174

6 8 549 7 54%

2 215

11 8 557

3 540

12 yes

4 40

10 64


5 $4.85 6 10 000 + 5 000 + 700 + 20 + 9 7 90% 8 460 000

14 24

15 96 mm

16 24 cm2

17 7 500 mL

2

18 4 800 g

9 4

2 3

10 21

19 24 past 2 20 8

×

8

6

9

5

7

4

×

9

4

36

54

30

42

24

10

90

40

5 50

6

48

7 70

8

6

80

60

8

64

48

72

40

56

32

20

180

80

140

100

160

120

9

72

54

81

45

63

36

30

270

120

210

150

240

180

7

56

42

63

35

49

28

40

360

160

280

200

320

240

Unit 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 28 A 1 45

3 30

46

15 4 cm 16 22 cm

B 1 96

2 52

2 38

3 72

5 $1.40

6 548

17 9 000 mL 48

8 4 000

93

10 $4

19 36 minutes

11 yes

12 yes 13 12th 14 7

20 4

6 9 thousands (9 000) 7 70%

8 98 000

9

17 5

10 6 11 14 077

12 1, 36, 2, 18, 3, 12, 4, 9, 6 13 25th 14 8 15 5·8 cm 16 49 cm2 17 5 L 18 4 kg 19 47 minutes 20 5 2

2 10

1

10

C 1 83

2 55

3 35

14 28 15 5·8 cm

D 1 132

2 58

49

4 90

12 yes 13 100 14 45

6 65 040

17 9 L 5 $2.60

15 950 cm

5

20 10

7 63%

18 6 kg

4

2

1

3

18

16 81 m2

3 630

2

18

9

5 $4.50

3

1 6

5

65 100

18 6 000 g

5 $3.65


7

4

28

7

20

8 no

12 5

19 38 minutes

17 8 cm3

10

30

15

6

2

30

3

1

6 8 12

5

10 $8 11 CCXCVII

2

24 24

3 4

12 no 13 31st

20 3

6 7 thousands (7000) 7 0·97 16 144 m2

4

1

6

28

14

9

5

2

1

8 yes

18 8·5 kg

9

19 3:35

15 8

10 $30

11 6 024

20 8

Extra practice section: 1 (12 – 3) ÷ 3 = 3 2 (5 – 3) × 4 = 8 3 3 + 4 + 5 = 12 4 (12 – 4) × 3 = 24 5 15 ÷ 3 + 5 = 10 6 (15 – 12) × 3 = 9 7 12 ÷ 4 + 3 = 6 8 (4 + 5) × 3 = 27

Unit 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 30 A 1 68

14 345

B 1 100

2 58

3 40

46

15 35 mm 2 32

13 11 14 8

16 24 cm

3 170

48

17 9 L

7

3 10

8 13 000

18 3 kg

6 85 038

7 yes

16 40 m2

17 3 500 mL

Faces

Edges Corners

Pyramid Triangular

4

6

4

Rectangular

5

8

5

Pentagonal

6

10

6

Hexagonal

7

12

7

Heptagonal

8

14

8

Octagonal

9

16

9

Decagonal

11

20

11

© Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_answers_middle_2725.indd 2

6 9 736

5 8·5

15 6 500 m

Extra practice section:

A2A2

5 $5.15

9 no

19 7:40 am 8 36 000

10 7

11 161

12 no

13 20th

20 2 9

18 7 500 g

17 4

10 16

19 26 past 9

11 CCCXCII

12 11

20 90°


2 27

14 66

D 1 264

3 160

48

15 2·5 cm 2 326

6 1 or 1 5 5

10

19 08:47 or 0847

17 9·5 L

16 28 m

2

3 730

5 8·7 6 96 873

4 84

11 8 968

5 $2.30

7 yes

8 yes

18 7 500 kg

11 6

9

19 yes

10 5

11 277

15 540 cm

13 yes

20 180°

6 9 hundred thousand (900 000)

12 yes 13 28 14 4 000

12 yes

Answers

C 1 73

7 0·95

16 77 cm2

8 57 400

17 64 cm3

9

11 3

18 3 600 g

20 5


Faces

Prism

Edges Corners

Triangular

5

9

Rectangular

6

12

8

Pentagonal

7

15

10

Hexagonal

8

18

12

Heptagonal

9

21

14

Octagonal

10

24

16

Decagonal

12

30

20

6

Unit 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 32 A 1 69

2 66

14 9

3 64

15 75 mm

46

5 $4.55

16 48 m

6 6 945

17 7·5 L

9 10

7

18 8 kg

8 6 800

94

19 5 past 4

10 8

11 CLXIV

12 1, 15, 3, 5 13 13th

20 square

B 1 96

2 19 3 140 4 8 5 $9.10 6 58 438 7 no 8 yes 9 no 10 4 11 CCCXLVIII 13 64 14 48 15 9 500 m 16 45 cm2 17 6 500 mL 18 9 500 g 19 13 to 9 20 1

12 no

Extra practice section: 1 70o 2 50o 3 60o 4 45o 5 80o 6 40o

C 1 91

2 27 3 130 4 9 5 16·3 6 74 296 7 yes 8 no 9 no 10 4 11 CCXCVI 12 1, 48, 2, 24, 3, 16, 4, 12, 6, 8 13 25 14 13 15 65 mm 16 30 cm2 17 6·5 L 18 4 500 kg 19 365 days 20 180°

D 1 283

2 183

3 350

4 95

5 $3.80

11 7 197 12 1, 35, 5, 7 13 121 19 22:29 or 2229 20 270°


3

6 5 ten thousands (50 000)

14 30

15 370 cm

16 72 cm2

Number of hexagons

1

2

3

4

5

6

Number of sides

6

12

18

24

30

36

Number of decagons

1

2

3

4

5

6

10

20

30

40

50

60

Number of sides

2

4

7 0·35

8 yes

17 27 cm3

9 2

4 5

10

9 1 or 2 4 4

18 6 500 g

Number of heptagons

1

2

3

4

5

6

Number of sides

7

14

21

28

35

42

Number of pentagons

1

2

3

4

5

6

Number of sides

5

10

15

20

25

30

Unit 7 ... Fun Spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 34 1

2

7

8

4

3

3 start

7 start

1

6

5

9

5

2

3

6

9

1

6

10 B, C, A, D

7

4 8

4 Turned (rotated) 5

2

8



Answers

Unit 8 ... Revision A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 36 1a 6 hundreds (600) c CCCLXXVIII

b 6 thousands (6 000)

d CCCLIX

3a 65%

c 6 hundred thousands (600 000)

75 b c 40% 100

4a 81

b 55

c 360

2a CCXXXII b CXCVII

d 5 5a 5 000

b 26 000

c 377 000 6a 1, 24, 2, 12, 3, 8, 4, 6 b 1, 36, 2, 18, 3, 12, 4, 9, 6 c 1, 45, 3, 15, 5, 9 7a 23 568 b 477 569 8a 19 b 24 9a 42 b 60 c 12 10a 5:37 b 11:29 c 55 past 3 or 5 to 4 11a 3 500 mL b 2·5 kg c 4·56 m d 5·5 km 12a 20 cm b 18 cm c 16 cm 13a 5 b 3 c 6 14a 16 cm2 b 40 cm2

Unit 8 ... Revision B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 37 1a 6 549 b 5 021 c 29 053 2a 0·9 b 1·45 c 0·57 3a 7 959 b 26 395 c 68 600 4a 34 b 38 c 8 d 3 5a 35 days b 36 months c 52 weeks 6a yes b yes c no d yes 7a 47 054 b 960 347 8a 6, 12, 18, 24, 30 b 9, 18, 27, 36, 45 9a 10:45 (1045) b 15:18 (1518) c 21:51 (2151) d 01:39 (0139) 10a 81, 90 b 64, 72 11a 3·5 L b 6 500 g c 46 mm d 9 500 m 12a 18m3 b 16 cm3 13a 6 b 5 c 8 d 4 14a yes b yes c yes d no 15a 38 mm or 3·8 cm b 56 mm or 5·6 cm

Unit 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 38

A 1 62

2 17 3 32 4 17 5 868c 6 8 549 7 72% 8 no 9 yes 10 6 15 5·9 cm 16 26 m 17 3 500 mL 18 4 500 g 19 35 days 20 4

B 1 95

12 no

11 221

12 yes

13 49 14 32

2 33 3 160 4 6 5 $6.45 6 3 675 tens 7 3·49 8 39 000 9 no 10 5 11 CCCLI 13 23rd 14 9 15 8·5 km 16 48 cm 17 4·58 L 18 3·59 kg 19 107 minutes 20 8

Extra practice section: 1 a 3 b 6 c 10 d 15 2 a yes b yes c yes d yes e no f yes g no h yes 3 a 28 b 21 c 36 d 15 e 55 f 66

C 1 107

13 99

2 46 3 130 4 9 5 1 045c 6 67 439 7 1·47 8 55 000 9 yes 10 6 11 CCXCIX 14 48 15 8·7 cm 16 81 cm2 17 5 600 mL 18 4 500 g 19 32 minutes 20 4

12 no

D 1 544

2 251 3 650 4 69 5 21·3 6 2 ten thousands (20 000) 7 0·75 8 yes 9 yes 10 $4 11 4 375 12 1, 64, 2, 32, 4, 16, 8 13 yes 14 7 15 3 500 m 16 45 cm2 17 6·5 L 18 8·5 kg 19 7 to 10 20 7


First number

42 52 62 72 82 92

Second number

56

66

76

Rule: add 14 to first number

3

First number

78 68 58 48 38 28

Second number

53

33

2

96 106

86

43

23

13

First number

37 47 57 67 77 87

Second number

74

94 114 134 154 174

Rule: double first number

4

3

Rule: subtract 25 from first number

First number

1

2

3

4

5

6

Second number

1

4

9

16

25

36

Rule: square first number

Unit 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 40 A 1 92

2 28

4 28

5 $5.46

14 54 15 369 cm 16 100 m2

B 1 143

3 54

14 30

2 54

3 240

15 8·5 km

47

6 94 725

17 6·5 L

5 $5.65

16 15 cm

7

19 25

18 3·5 kg

6 9 653 tens

9 no

10 4

19 60 months

20 6

7 2·8

17 7·5 L 18 4·5 kg


8 35 000

19 no

8 no

9

20 NW

6 8

11 344

10 3

12 yes

11 36 394

13 yes

12 22

13 144

2 front

side

top

front

side

top

A4A4 © Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_answers_middle_2725.indd 4


3 96

13 36 14 17

D 1 781

2 56

5 $5.43

15 6 500 m

2 624

11 26 962 19 14 to 6

49

3 350

6 4 653 tens

16 80 m

4 67

17 9·5 L

3 10

8 yes

1 2

9

18 3 500 g

10 5

19 6:44

5 $9.04 6 80 000 + 6 000 + 300 + 90 + 1

12 1, 56, 2, 28, 4, 14, 7, 8 20 no

Extra practice section: 1 1:22

7

2 6:43

13 no 14 34 15 4·5 km

3 5:11

4 5:51

5 12:14

11 36 881

12 18

Answers

C 1 81

20 NW 7 73%

16 30 cm

8 no

21 8

9

17 9 500 mL

10 $9 18 8 000 kg

6 4:39

Unit 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 42

A 1 43

2 33 3 56 4 26 5 20 6 6 483 7 0·65 8 yes 9 yes 10 8 11 5 991 15 400 cm 16 20 m 17 3 500 mL 18 6 500 g 19 366 days 20 90°

B 1 96

12 yes

12 no

13 66 14 9

2 39 3 335 4 8 5 $3.15 6 13 thousands 7 0·9 8 yes 9 no 10 no 11 35 265 13 81 14 16 15 5·5 km 16 35 cm2 17 10·5 L 18 6·5 kg 19 52 minutes 20 NE

Extra practice section: 1 a 3 b 5 c 4 d 2 e 7 f 4 g 9 h 4 i 6 j 3 2 a 12 b 10 c 20 d 24 e 15 f 12 g 18 h 36

C 1 87

3 204

14 19 15 7.5 km

D 1 283

2 24

12 52

2 681 13 6

49

5 2·9

16 20 cm2

3 1 470 14 17

4 79

6 67 432 17 7·5 L

7 0·5

8 56 400

18 8 500 g

16 20 cm

7 4

10 yes

19 42 minutes

5 $7.91 6 469 thousands

15 9·5 km

9

17 8 500 mL

12 2

13 64

20 yes

73 8 yes 100

7

11 64 872

9

18 9 000 kg

8 3

10 $8 11 DLXXXIX

19 13:24 or 1324

20 yes

Extra practice section: Arrived at point B

Unit 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 44

A 1 75

2 29 3 24 4 5 5 945c 6 569 tens 7 0·65 8 yes 9 no 10 4 11 342 14 186 15 7·5 m 16 16 m 17 8·5 L 18 3·5 kg 19 180 minutes 20 180°

B 1 188

2 131

13 29 14 26

3 136

4 61

15 635 cm

5 $7.20

6 63 937

16 22 cm

7 1·76

8 no

17 7·5 L 18 4·375 kg

91

1 4

10 $9

12 no 13 199

11 45 889

19 150 seconds

12 yes

20 yes

Extra practice section: Cube B cannot be made

C 1 179

3 408

4 123

12 yes 13 21 14 120

D 1 616

2 161

2 644

13 5 14 17

5 $4.90

6 54 thousands 7 5·94 8 yes 9

6 10

10 12 candles 11 269 360

15 9·56 m 16 49 cm2 17 4 500 mL 18 3 125 g 19 195 minutes 20 180°

3 8 720

4 67

15 4 500 m

5 $7.24

16 21 cm

6 476 528

17 6·5 L

7 90%

8 yes

18 12 000 kg

9

17 5 10 6 8

11 DCXLVII

19 07:59 or 0759

12 15

20 12

Extra practice section: Answers will vary

Unit 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 46

A 1 54

2 35 3 25 4 $2.50 5 6 coins 6 7 965 7 50% 8 yes 9 11 quarters 10 8 13 4 14 9 15 750 cm 16 20 cm 17 250 mL 18 250 g 19 31 days 20 yes

B 1 138

2 35

3 210

4 21

5 $7.80

12 1, 60, 2, 30, 3, 20, 4, 15, 5, 12, 6, 10 19 6:59 20 no

6 4 thousands (4 000) 13 19

14 25

7 5·79

15 1 250 m

8 no

9

16 36 cm2

13 5

10

11 35 901 6 3 or 10 5

12 yes

11 D

17 1·255 L 18 1·75 kg



Answers

Extra practice section: 1 28 cm

C 1 299

2 149

3 3 160

13 45 14 24

D 1 721

2 1 or 8 4

10

17 8 500 mL

4 203

15 1 750 m

2 867

2 48 m

3 7 200

5 $3.65

16 45 m2

4 67·9

11 660 726

3 10·5 cm 6 54 682

17 1·75 L

5 17·7

7 6·69

8 no

18 2·25 kg

9 4

13 75th

14 360

2 3

10 20

19 35 minutes

6 70 thousands (70 000)

12 no, 4 is not

18 7 t 19 7:21 pm

4 14 cm

7 70%

15 9 500 m

11 28 887 12 8, 16, 24

20 yes

8 1 654 000

9 4

1 4

16 circumference

20 yes

Extra practice section: 1 acute angle, 50° 2 obtuse angle, 120° 3 straight angle, 180° 4 reflex angle, 300° 5 revolution, 360°

Unit 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 48

A 1 80

2 29 3 32 4 8 5 20 coins 6 5 hundreds (500) 7 0·6 8 4 800 9 23 tenths 10 12 13 1 799 14 62 15 950 cm 16 36 m 17 4·5 L 18 3 500 g 19 61 days 20 no

B 1 94

2 106

12 no

3 4 630

13 70 14 13

4 21

15 250 m

5 $16.25

16 144 cm2

Extra practice section: 1 6, 4 , 3, 9, 2

C 1 206

12 3

D 1 149

2 283 13 12

3 1 260 14 33

2 425

12 8, 16, 24, 32

4 34

4 35·8

13 fortieth

Extra practice section: 1 3

9

2 5, 3, 15, 9

10 3

10 6

6 354 hundreds

7 0·3

8 no 9 3

17 3·95 L

6 64 070

2 4

9

18 7·355 kg

7 0·49

8 4 000 000

3 6

1

9

6 2, 4 1 5

7 3, 2, 6, 13

10 $12 11 33 968

9 yes

20 yes 4 2 or 10 5

11 yes

19 17 to 7

20 9

10

18 4·75 t 0

12 no

20 8

19 10:09 am

16 120 m 17 4·25 L 0

11 47 351

19 53 minutes 5 5, 3, 15

15 375 cm

1

9

4 4, 2

5 $1.45

0

8 88 000

3 2, 8, 4

16 12 cm2

14 630

7 40%

17 4 725 mL 18 3 625 g

5 $1.55

15 750 m

3 1 200

6 68 391

11 13 470

4 7

1

0

9

1

8

2

8

2

8

2

8

2

7

3

7

3

7

3

7

3

6

4

5

6

4

5

6

4

5

6

4

5

Unit 15 ... Fun Spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 50 1 15 minutes 2 7 days 13a 68 b 19 c 23

3 16 4 $4.50

53

6 10

76

86

9 $20

10 12 and 19

11 10

12 B

Unit 16 ... Revision A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 52 1a 6 thousands (6 000) b

25 1 or 100 4

b 6 thousands (6 000)

c 0·39 4a 183

b 9, 18, 27, 36, 45

b 75

c 1 240

c 7, 14, 21, 28, 35

c 6 hundred thousands (600 000)

d 123

7a 28 574

5a 6 000 b 176 639

c 86 10a 7:52 b 12:14 c 6 to 3 11a 3 575 mL b 2 525 g c 12 cm 13a 9 b 8 c 18 14a 81 m2 b 108 cm2

b 37 000 8a

7 4

b

c 564 cm

2a 23 b 38

c 165 000 13 5

c

26 10

d

d 6·25 km

3a 40%

6a 6, 12, 18, 24, 30 15 8

9a 9

12a 12 cm

b8 b 18 m

Unit 16 ... Revision B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 53 1a 49 476 b 59 075 c 8 thousands (8 000) 2a 30% b 50% c 65% 3a 27 b 23 4a 5 964 > 5 694 b 25 430 > 25 410 c 94 236 > 93 236 5a 1, 12, 2, 6, 3, 4 b 1, 24, 2, 12, 3, 8, 4, 6 c 1, 30, 2, 15, 3, 10, 5, 6



b 4:12 am

c 12:26 pm

7a 2

3 5

3 10

b 2

c1

3 8

d 2

1 3

8a 8, 16, 24, 32, 40

b 6, 12, 18, 24, 30

c 4, 8, 12, 16, 20 9a 09:26 (0926) b 23:26 (2326) c 11:49 (1149) d 08:59 (0859) 10a CCLI b CLXIV c CCCLXXV d CCXCIX 11a 408, 508 b 2 365, 2465 12a 3·95 L b 6·575 kg c 750 m d 650 cm 13a acute angle b obtuse angle c reflex angle d straight angle 14a 7:25 b 4:49 c 12:19 15a 34 mm or 3·4 cm b 47 mm or 4·7 cm

Unit 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 54

A 1 78

2 17 3 45 4 4 5 $1.25 6 67 497 7 75% 8 13 000 9 yes 10 9 11 9 007 14 255 15 35 mm 16 32 cm 17 6 500 mL 18 4 500 g 19 61 days 20 yes

B 1 109

2 33

3 1 000

49

5 3·8 6 6

13 39th 14 2·5 15 9·65 km

Extra practice section: 1a

C 1 97

3 940

12 no, 7 is not

D 1 482

2 114

2 186

11 –2 12 20

16 16·8 cm

8 no

9 yes

4 1 or 8 2

10

17 3 500 mL 18 2 375 g

b c

d

5 $4.15

6 49 068

4 21

13 41

7 9·53

e

f 2a B2

7 0·75

8 yes

9

11 87 257

19 1:54 pm b F3

37 10

12 yes

c C5

Answers

6a 5 past 10

13 25

12 no

20 hexagon d E2

e D4

f G5

8 or 1 11 yes 8

10

14 957 15 9 500 m 16 14 cm 17 3·275 L 18 3 455 g 19 99 minutes 20 base

3 2 800 13 34

4 90

5 $11.40


7 20%

8 349

14 12 15 1 556 cm 16 1 ha 17 250 cm3 18 3 500 g

Extra practice section: 1 yes 2 no 3 no 4 yes 5 no 10 no (1, 4, 6 and 8 are coloured)

6 yes

7 no

9

37 12 10 or 3 10 4

19 22:36 or 2236

8 yes

20 circle

9 no

Unit 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 56

A 1 84

2 22 3 200 4 4 5 $7.95 6 6 ten thousands (60 000) 7 0·35 8 18 600 9 9 eighths 10 8 11 CCCLVIII 12 30 13 16 14 8 15 67 mm 16 25 cm2 17 3 500 mL 18 1 500 g 19 92 days 20 90°

B 1 99

2 106

3 315

4 32

5 $7.35 6 4 ten thousands (40 000) 7 61% 8 yes

12 2, 3, 5, 7 (1 is neither a prime number nor a composite number) 13 13 17 6 800 mL 18 4 700 kg 19 105 minutes 20 pentagon

Extra practice section: 1a 40

C 1 100

13 899 998

D 1 416

2 322

3 180

b 35

2a 19th

4 remainder 5

14 2 025 15 5·4 km

2 86

3 2 400

4 50

Extra practice section: 1 90 cm

3

5 $5.40

16 81 m2

5 30·2

13 799 999 14 17 15 8 475 m

1 21st

3 70

6 7 7 60%

16 16 cm2

2 56 cm

3

8 yes

17 30 m3

3 84 cm

3

8 10 16 11 969 127 10

14 26 15 6 700 m

16 yes

4 195

6 87 461 7 no 8 246 000 9 2 17 5·275 L

9

18 3 125 g

2 10 $30 11 574 12 no 5

19 38 past 6 or 22 to 7

55 11 or 4 100 20

9 4

10 12

11 –5

20 no

12 yes

18 3 kg 19 14:49 or 1449 20 equilateral triangle

4 72 cm3

Unit 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 58 A 1 84

3 84

45

5 $17.85

65

7 64%

14 1 860 15 390 cm 16 40 cm 17 7 500 mL

B 1 321

2 38

2 175

3 240

4 60

13 20 14 20 15 6·8 km

5 6·9

16 yes

6 79 524

8 4 or 10 5

8 yes 9 7 halves 10 18 1 250 g 7 1·63

19 91 days

8 6·3, 6·5, 6·8

11 10 867

12 no

13 9

20 no

9 2

17 4·725 mL 18 3 900 kg 19 7:06 pm

1 4

10 45 11 yes 12 5 20 no



Answers

Extra practice section: 1a 5

C 1 75

2 333

c 2

4 remainder 8

d 5

e 3

5 $12.40

f 4 67

2a August 7 yes

b June

8 467 000

91

c May

d August

58 10 1 10 or 3 100 3 3

11 –1

12 9, 18, 27, 36, 45 13 299 999 14 56 15 9·3 km 16 21 cm2 17 7 800 mL 18 4 700 g 19 4:44 am 20 yes

D 1 321

3 180

b 4

2 106

12 no

3 2 100

13 sixtieth

4 50

5 $5.15

6 658 364

14 43 15 7 625 m

Extra practice section: 1 one

2 one

3 two

7 0·58

16 18·2 m 4 one

8 8 630

17 60 m3

5 two

9 2

5 6

5 6

10

18 3 250 kg

11 DCCXCIV

19 6:27

20 yes

6 two

Unit 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 60 A 1 140

2 45

3 78

12 no, 3 is not

48

13 4

5 $16.90

14 176

6 3 795

9 11 eighths 10

17 7·5 L

18 1 750 g

6 3 or 11 CCLIX 10 5

19 47 minutes

20 yes

B 1 124

2 168 3 630 4 remainder 4 5 $7.20 6 3 hundred thousands (300 000) 7 90% 8 870 000 9 10 10 5 11 no 12 12 13 10 14 80 15 3 800 m 16 12·9 cm2 17 1·439 L 18 3·595 kg 19 7 to 8 20 no

C 1 137 12 4

D 1 217

8 27 000

15 520 cm 16 49 cm2

Extra practice section: 1 02:43 (0243) 6 23:27 (2327)

7 0·45

2 185 13 26

3 350 14 37

2 159

2 16:39 (1639) 3 09:42 (0942) 7 10:47 (1047) 8 22:32 (2232)

4 4 remainder 3 15 2 600 m

3 2 400

4 70

16 no

5 $17.70

5 $2.30 each 17 9 400 mL

2

7 no

18 2 250 g

8 yes

15 180 km

16 2 ha

9

5 05:14 (0514) 9 5

19 4:32 pm

6 4 hundred thousands (400 000) 7

10 $300 11 357 087 12 yes 13 yes 14 50 19 04:53 or 0453 20 isosceles triangle


6 82 406

4 20:56 (2056)

11 –5

20 yes

6 100

17 750 cm3

10 40

8 357 000

9

11 3

18 5 700 g

3

Unit 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 62 A 1 77

2 28

3 210

4 39

5 $19.85

65

7 no

12 18

13 16

14 20

15 6·24 m 16 81 m2

B 1 130

2 188

3 390

4 5 remainder 8

12 54

13 25 14 67

15 55 mm

C 1 114

2 294

3 240

6 10 15 11 746 10

9

19 106 minutes

D 1 267

2 317

2 9 3

3 10 10

18 4 750 kg

17 3·5 L

5 8·52

16 400 m2

Extra practice section: 1 1, 12, 2, 6, 3, 4

8 yes

66

9

6 8

10 3 candles

18 1 000 kg 7 3·568

19 9:32 pm

8 3 589 9

17 8·45 L 18 2 500 g

11 247

18 5

10

20 4 6 3 or 10 5

19 85 minutes

11 –7

20 hexagon

2 1, 16, 2, 8, 4

4 7 remainder 4

5 $4.10 each

12 yes 13 yes 14 33

6 50 000 + 6 000 + 700 + 20 + 9

15 256 mm

16 18 m2

17 8 625 mL

7 7·09

8 yes

18 4 500 kg

20 isosceles triangle 3 2 400 4 remainder 17

11 –9

5 34

12 152 (add 31, 37, 41, 43)

19 1:48 am

6 300 000 + 40 000 + 8 000 + 100 + 9 13 61

14 25

15 6·25 km

7 8·797

16 56·25 cm2

8 9 762 17 125 cm3

20 180°

Extra practice section: A, C, E , H and I are circled



A 1 101

14 50

B 1 277

2 31

3 160

4 46

5 $5.50

15 8·25 m 16 21 m 2 286

15 8 459 000 9 8

3 300

66

17 4·5 L

7 35%

18 2 t

4 29 remainder 4

9 3 10 or 12 4

17 250 cm3 18 1 250 kg

8 yes

19 81 minutes

3 5

10

11 36 378

12 no

6 6 hundred thousands (600 000)

7 5·86

12 11, 13, 17, 19 13 65 14 64

2 217

3 240

4 13 remainder 4

11 229 999 12 3 13 86 379

14 37

13 36

15 139 mm

16 no

20 no

Extra practice section: 1a 4:29 am b 5:59 am c 6:29 am d 5:59 am d 1:30 am 3a 11:51 am b 10:21 am

C 1 354

6 3 or 8 4

19 24 to 12 20 7

5 $24.45

11 348 800

9

Answers

Unit 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 64

5 16·9 6 46 245

15 8 500 m

7 0·9

16 yes

2a 2:00 am

38 100

8 yes

17 3 755 mL

b 1:30 am

9 2

10

c 2:00 am

4 2 or 10 5

18 2 250 kg 19 1:43 pm 20 yes

D 1 487

2 483 3 468 4 82 5 $16.54 each 6 6 7 7·053 8 no 9 6% 10 $315 11 DCLXXIX 12 no 13 93 238 14 48 15 8·575 km 16 3 ha 17 64 cm3 18 5 725 g 19 11:37 pm 20 equilateral triangle


B

A

D

E

C

F

G

H

Unit 23 ... Fun Spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 66 1 6 2 600 3 20 4 $9 15 $64.20 16a B b B

5 30

6 17 7 12

8 77

9 75

10 28

11 201 12 102

13 136

14 134·9 cm

Unit 24 ... Revision A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 68 1a 2 thousands (2 000)

b 2 hundreds (200)

58 29 or b 0·35 c 100 50

4a 322 b 126

b 9, 18, 27, 36, 45

c 6, 12, 18, 24, 30

c 800

c 2 hundred thousands (200 000) d 19

7a 68 206

2a 21

5a 25 000

b 50 000 c 379 000

b 568 358

11 8a 6

10a 15:16 (1516) b 8:39 am c 23 to 12 11a 7 500 mL 13a 7 b 5 c 6 14a 36 m2 b 72 cm2 15a 14 b 6

11 b 4

b 3 600 g

27 c 10

c 5 275 m

b 46

3a 38%

6a 8, 16, 24, 32, 40 d

21 8

d 2 ha

9a 58

b 62

c9

12a 26 cm b 21 m

Unit 24 ... Revision B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 69 1a 84 721 b 594 058 c 6 ten thousands (60 000) 2a 70% b 90% c 84% 3a 2 b 5 4a 38 439 > 38 349 b 94 627 < 94 687 c 107 385 < 108 385 5a 4, 8 b 4, 5, 10 c 5, 6, 10 6a 7:39 pm b 1:41 pm c 15:27 (1527)

d 07:52 (0752)

7a 1

5 6

b 3

1 5

c 2

1 8

d 3

2 3

8a

5 8

b

2 1 or 10 5

9a 7, 14, 21, 28, 35

b 4, 8, 12, 16, 20 10a 03:37 (0337) b 10:17 (1017) c 18:58 (1858) d 09:26 (0926) 11a CCCVII b DLXXXIX c DCCLXVII d DCLXXXIV 12a 9 b 25 c 16 d 36 13a 7·5 L b 9·25 kg c 1 500 m d 6·29 cm e 7 250 m 14a equilateral triangle b right-angled triangle c isosceles triangle 15a 6:45 am b 3:12 pm c 11:57 am d 9:28 pm 16a 52 mm or 5·2 cm b 49 mm or 4·9 cm

Unit 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 70 A 1 98

2 43

3 150

4 38

5 $2.15

66

7 0·55

8 yes

12 2, 3, 5, 7 (1 is neither prime nor composite) 13 yes 18 3 000 kg 19 8:35 am 20 4

9 9 quarters 14 30

10

4 5

11 40 503

15 5 000 m 16 32 m2

17 3 700 mL



Answers

B 1 323

2 485 3 150 4 20 remainder 4 5 $24.10 6 5 ten thousands (50 000) 7 3·58 8 360 000 9

10 18

11 –9

12 71 13 1

C 1 277

3 300

3

4

4 29 remainder 4

5 $7.25

67

7 7·03

8 8 643

23 5

9

10

7 10

11 –4

12 1, 36, 2, 18, 3, 12, 4, 9, 6 13 73 14 3 15 837 cm 16 38 cm 17 950 cm3 18 2·575 t 19 09:26 (0926) 20 yes

D 1 812

2 286

14 54 15 9·73 m 16 21 m2 17 60 m3 18 3·955 t 19 142 minutes 20 169°

2


8 3

95 100

2 412

3 2 400 4 9 remainder 5 5 3·27 6 2 millions (2 000 000) 7 4 8 2·7, 2·4, 2·1 9 12

10 60 11 796 20 yes

12 $1.60 13 121 14 560 15 425 km 16 33 cm2

17 500 cm3

Extra practice section: 1a Sunday b Saturday c Wednesday d Friday 2a 900 3a 1 900 b 2 600 c 1 700 4a 400 b 300 c 600

18 $12.10 b 1 200

19 3:10 am

c 1 000

d 1 100

Unit 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 72 A 1 106

14 20

B 1 183

14 400

2 22

3 120

4 29

5 $12.55

15 6 km 16 18 cm2 2 116

3 2 000

15 15·67m

17 4 500 mL

4 60

5 $5.25

16 70 000 m2

Extra practice section: 1 sparrow

C 1 247

11 –3

D 1 1 730

6 35 982

7 4·9 8 70 000

18 5 t

67

19 90 minutes

7 70%

8 9 653 9

17 125 cm3 18 3 575 kg

2a yes

b no

c no

5 3

9

10 25

12 2

19 8

10 $12

b no

c yes

11 357 037

2 333

3 36 000

12 49 (13, 17, 19) 20 6·9 cm

4 14

13 15

Extra practice section: 1a A

15 140 km 16 20 000 m2 17 500 cm3

14 1 bC

5 $99.75

6 1 456

15 80 km/h cE

2a B

7 no

16 2 ha

bF

12 no 13 41

20 yes 4a yes

b yes

2 66 3 1 200 4 50 5 $10.90 6 1 hundred thousands (100 000) 7 7 8 87 642 9 12 yes 13 10 14 33

13 9

20 yes

19 8:07 pm

3a yes

11 DXXIX

c yes

17 4 1 10 or 6 8 2

18 1 750 kg 19 1:48 am

8 34 569 9

17 216 cm3

3 5

10

18 3·25 t

3 1 or 6 2

5 50%

20 yes

11 –6

19 20:17 (2017)

c E and G

Unit 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 74 A 1 231

14 27

B 1 211

2 128

3 76

4 30

5 $8.50 6 6

7 0·6

15 7 000 m 16 24 m

17 6 500 mL

2 247

5 4·6 6 365 740

3 2 400

13 25 14 1 080

4 40

15 5·725 km

16 14 cm

8 no

9 2

18 4 000 kg 7 60%

2 3

10 45

11 –4

19 9 past 10 8 98 542

17 750 cm3 18 5·75 t

91

12 yes

13 16

20 yes 7 100

10 $150

19 9:38 pm

11 –11

12 3

20 180°

Extra practice section: 1a 1, 2, 3, 4, 5, 6 b 1, 2, 3, 4, 5, 6 c black, pink d black, black (BB); black, pink (BP); pink, pink (PP)

C 1 209

2 335

11 1 or 1 10 10 10

20 hexagon

3 2 100

4 70

5 $13.55 6 8 hundred thousands (800 000)

11 –10 12 $4.35 13 yes 14 74

7 4%

8 1 048

9 no

15 4·125 km 16 3 ha 17 48 cm3 18 2 kg 19 2:29 pm



2 81

3 2 900

11 2 999 999 20 18

4 479

5 $35.05 6 6 hundred thousands (600 000) 7 4 8 yes 9 1

12 yes 13 100 14 100

15 520 km 16 40 000 m2

1 3

10 $600

17 1 000 cm3 18 3·5 kg 19 2:35 am

Extra practice section: 1 circle is 30 mm (3 cm) in diameter 2 circle is 34 mm (3·4 cm) in diameter 3 circle is 38 mm (3·8 cm) in diameter

Answers

D 1 799

Unit 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 76

A 1 170

2 79 3 200 4 30 5 $5.55 6 5 thousands (5 000) 7 8·63 8 3 468 9 11 sixths 10 30 11 DCCLXII 12 12, 14, 15, 16, 18 13 38th 14 40 15 4 km 16 45 m2 17 4·5 L 18 6 t 19 7 to 8 20 yes

B 1 212

2 165

14 875

3 1 800 4 no

15 2·975 km

5 $4.10

16 10 000 m2

6 864 306

74

8 no

17 27 cm3 18 3 kg

9

2 3

10 50

11 1 114

19 18:18 (1818)

12 21 13 14

20 B

Extra practice section: 1a O b F c C d A e M f J g D h H 2a (4, 2) b (6, 3) c (5, 4) d (2, 2) e (1, 3) f (2, 4) g (6, 5) h (0, 3)

C 1 241

2 242

3 1 500

9 yes 10 $135 11 5 19 1:01 am 20 A

D 1 1 708

2 218

8 3·9, 3·8, 3·4

17 4·75 kg

3 720 1 9 2

4 remainder 2 12 40 13 yes

14 2 914

4 remainder 1

10 $675

18 2·475 t

5 4·86 6 7 hundred thousands (700 000) 15 180 km

5 $16.87

11 1 754

16 81 cm2

7

5 100

8 34 589

17 64 cm3 18 3 500 kg

6 1 000 000 + 300 000 + 50 000 + 600 + 7 7 5·64

12 $3.60

13 36

14 92

15 75 km/h

16 30 000 m2

19 17:29 (1729) 20 2·28 m

Extra practice section: 1a no

b yes

2a yes

b yes

3 yes

4 women, boys, girls, men

Unit 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 78

2 76

3 600

13 26

14 9

15 7 km 16 14·8 m 17 7·5 L 18 2 500 kg 19 22 to 7 20 equilateral triangle

B 1 341

4 20

5 $7.50 6 6

7 60%

8 259 000

9 3

11 156 790 12 6, 12, 18, 24

4 8 3·5, 3·6, 3·8 100

10 $50 11 17 12 yes 13 35 14 3 246 15 250 km 16 90 000 m2 20 triangle

C 1 407

2 93

3 125

4 yes

2 6 cm2

3 4·5 cm2

D 1 3 512

2 126

10 320

91

18 3·25 kg

3 24 000 11 3

6 10

4 149·6 (or 149 )

12 270

13 90

9 yes

17 350 cm3 18 1·5 kg 19 6:47 am

4 7·5 cm2

5 $69.50 6 300 000 + 60 000 + 7 000 + 5

10 $63 11 289 999 12 12, 24, 36, 48 13 11 19 10:31 (1031) 20 7 cm

2 3

10 20

2 81 3 204 4 38 remainder 2 5 $5.45 6 2 millions (2 000 000) 7 7

Extra practice section: 1 4 cm2

1 2

A 1 159

14 60 15 3 650 m 5 2·95

76

16 3 ha

8 1·6, 1·4, 1·3 17 250 cm3

6 9 millions ( 9 000 000)

14 36 15 1 050 km

16 50 000 m2

7 19·08

9

2 5

18 3 725 g 8 no

17 2 000 cm3

19 2:19 pm 20 yes

Extra practice section: 1a A b C c E d F e I f K g J h M 2a (5, 2) b (4, 3) c (2, –3) d (5, –5) e (–5, 5) f (–5, –3) g (–4, –6) h (–2, –2)



Answers

Unit 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 80 A 1 202

12 yes

B 1 431

2 62

3 1 500

13 14

14 20

2 338

11 499 999

3 225 12 no


4 30

4 27 remainder 5 13 66

14 5

5 112·5

15 4 375 m

18 4 500 kg

6 615 435

16 6 ha

50

70

120

35

87

Centimetre

5

7

12

3·5

8·7

7 no 8 yes

9

17 6

10 32

11 DCXXIX

19 4:20 am 20 6

7 16·09

8 2 568

17 950 cm3

1 4

18 1·625 kg

Centimetre 300 Metre

9

3

10 $270

19 11:57 pm 20 18

600

750

450

192

6

7·5

4·5

1·92

4 000 8 000 6 500 8 500 4 725 8

4

6·5

8·5

4·725

1

C 1 429

2 68 3 384 4 no 5 $3.55 6 400 000 + 70 000 + 5 000 + 900 + 20 + 6 7 6·564 8 345 000 9 2 10 $160 11 14 12 yes 13 21 14 200 15 4 750 m 16 6 ha 17 375 cm3 18 6 125 g 19 8:52 am 20 yes

D 1 2 747

17 9·5 L

Millimetre

Kilometre


15 9 km 16 100 m2

Metre

5 $10

2 728

3 35 000

4 562·7

5 $19.85

68

7 1·256

8 yes

91

3 4

10 $585

11 66 999 999

12 216 13 yes 14 28 15 2 880 km 16 120 000 m2 17 2 375 cm3 18 5·625 kg 19 151 minutes 20 yes


Gram

3 000 5 000 4 500 7 500 6 275

Kilogram

5

3

4·5

7·5

6·275

Kilogram Tonne

2 000 9 000 8 500 1 625 3 850 9

2

1·625 3·85

8·5

Unit 31 ... Fun Spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 82 1a 10

b 64

2 flipped

3

7 4

6 9

8

3

4a 121 b 363 c 949 d 767 e 747 f 929 g 727 h 383 5 1, 6, 15, 20, 15, 6, 1; 1, 7, 21, 35, 35, 21, 7, 1; 1, 8, 28, 56, 70, 56, 5 28, 8, 1 6 8, 16, 32, 64, 128, 256 7a 512 b 1 024 c 16 384 8a 9 b 14 c 17 9a 36 b 45 c 171 10 121, 1 331, 14 641 2

1

Unit 32 ... Revision A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 84 1a 244 d

b 332

6 3 or 10 5

e

c 392 3 4

6a 4, 8, 12, 16, 20

d 165

e 2 400

4a 9 630 b 8 641 b 8, 16, 24, 32, 40

f 2 400

c 1·4, 1·6, 1·9

2a 60% 5a 667

c 6, 12, 18, 24, 30

b

9 10

c 70%

3a

5 8

b

5 1 or 10 2

c

3 1 or 6 2

b 1 479 c CDLXVIII d MCCLXXIX

15 7a 8

b

11 3

c

9 2

d

17 8a 25 000 5

b 68 000

c 160 000 9a 64 389 > 46 389 b 105 549 < 107 459 c 857 294 > 587 294 10a 03:27 (0327) b 18:39 (1839) c 1:19 pm d 8:57 am 11a 3 750 m b 30 000 m2 c 4·575 t d 6·5 L 12a 1:30 pm b 1.00 pm c 11:30 am d 1:00 pm 13a yes b yes c no d no e yes f yes 14a 30 cm3 b 60 m3 15a 2 kg b 750 g

Unit 32 ... Revision B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 85 1a 8 hundreds (800) b 8 ten thousands (80 000) c 8 hundred thousands ( 800 000) 2a 300 000 + 50 000 + 9 000 + 200 + 70 + 8 b 900 000 + 50 000 + 300 + 7 3a 15 b $300 c $171 4a 224 b192 c 172 5a 25 b 64 c 15 6a 35 b 44 c 3 7a 2 048 b 1 368 c 2·5, 2·6, 2·8 8a 60 307 b 388 201 c 689 594 d 927 600 9a true b true c true 10a 11:49 pm b 6:38 am 11a 3·55 km b 2 750 kg c 4 275 mL 12a 35 m2 b 27 cm2 13a 6 b 8 c 5 14a 3 ha b 5 ha c 4 ha d 7 ha 15a 275 cm3 b 3 000 cm3 16 106 mm or 10·6 cm



 Mentals Score Sheet

Write down your scores for each set of Mentals here. How did you go? Unit

Set A

Set B

Set C

Set D

Unit

Set A

Set B

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Unit 22

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Unit 9

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Unit 25

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Unit 26

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Unit 28

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Unit 29

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Unit 30

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 © Pascal Press ISBN 978 1 74125 183 8 MMS_yr6_IBC.indd 1


Basic Skills

Get the Results You Want! Year 6 Ages 11–12 years old This book has been revised and updated for the Year 6 Australian Curriculum. Mental Maths is the Maths we do in our heads without the use of calculators and without writing down the calculation. Mental Maths strategies are the ‘tricks’ we use to do Maths in our heads. There are different ways of finding the answer to any Mental Maths problem, and such strategies are the focus of this series. Even though electronic devices play an enormous role in the modern world, we still need to go back to the basics—we do need to know how to check that the sales assistant at the counter is giving us the right change! Mental Maths has become more important than ever and the Australian Curriculum for primary years reflects this. All states have placed an emphasis on Mental Maths in the primary syllabus, and the NAPLAN Tests for secondary years (Years 7 and 9) have a non-calculator section.

Features of this book  Thirty-two double-page units of Mentals are included—eight units for each school term. Each unit is divided into four sets (A, B, C and D) of 20 questions each.

 Each numbered question covers a particular Maths topic throughout the book: for example, Question 1 always covers addition, while Question 20 always covers geometry.

 A special Help Section at the front of the book gives different strategies and explanations to help students

solve Mentals problems. These are also numbered so they link to the question numbers in each Mentals unit.

 A Fun Spot! unit, containing fun activities, and a Revision unit are included at the end of each eight units.  Extra practice sections which reinforce particular strategies appear in the lower part of each page.  The answers to all questions are in a lift-out section in the centre of the book.

About the authors

Alan Parker has been writing textbooks for more than 30 years. As a primary school teacher for over 40 years, he taught in several Australian states and gained experience at all levels of primary teaching, including ESL, remedial and extension classes. He was a primary school principal for 13 years and is the author of many successful educational books, including the successful Signpost Maths textbooks and (with Jan Faulkner) Signpost Maths Mentals Workbooks. Jan Faulkner has been a classroom teacher for over 30 years. She has taught both mainstream and gifted and talented classes in schools across Australia, and is currently the Assistant Principal of a large school in Sydney. With Alan Parker, Jan also co-authored the best-selling Signpost Maths Mentals Workbooks.

Other books in the Excel Mental Maths Strategies series: Bookseller reference

Books

Level



Mental Maths books

978-1-74125-184-5 978-1-74125-185-2 978-1-74125-180-7 978-1-74125-182-1 978-1-74125-182-1

Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies Excel Basic Skills Mental Maths Strategies

Year 1 Year 2 Year 3 Year 4 Year 5 ISBN 978-1-74125-183-8

Excel Test Zone

Get the Results You Want!

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.

9781741251838 EBS MentalMaths Yr6 NSACE 2015.indd 1

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

9 781741 251838

B A S IC S K ILLS MEN TA L MATH S STR ATE G IE S Year 6 Ages 11–12

Mental Maths Strategies

MENTAL BASIC SKILLS MATHS 6 STRATEGIES

MATHS

Excel

YEAR AGES 11–12

G e t t he Re su lt s Alan Par k er & You Want ! J an Faulk ner 12/01/2015 4:05 pm