Year 6 Full Workbook Sample by OUPANZ

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Mathematics and Statistics for Aotearoa New Zealand Second edition

Lead author: Erin Doleman

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Rich tasks designed by Marie Hirst Dr Jo Knox

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Cultural author and reviewer: Moana Jarden-Osborne

Name: Class:

Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship and education by publishing worldwide. Oxford is a registered trademark of Oxford University Press in the UK and in certain other countries. Published in Australia by Oxford University Press Level 8, 737 Bourke Street, Docklands, Victoria 3008, Australia © Oxford University Press 2027 The moral rights of the author have been asserted. First published 2025 Second edition All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, transmitted, used for text and data mining, or used for training artificial intelligence, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence, or under terms agreed with the reprographics rights organisation. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. ISBN 9780190357344

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Contents For the teacher...............................iv Progress Passports.........................2

Strand 3: Measurement Measuring Topic 3.1: Estimating, measuring and converting..................................................112

Year 6

Topic 3.2: Area and volume....................................120 Topic 3.3: Measuring and drawing angles........128

Strand 1: Number

Topic 3.4: Angle rules............................................... 133 Topic 3.5: Time............................................................138

Number structures Topic 1.1: Whole numbers......................................... 10 Topic 1.2: Rounding.....................................................15 Topic 1.3: Factor pairs, squares and cubes........20

Strand 4: Geometry Shapes

Operations

Topic 4.1: 2D shapes, prisms and pyramids....... 146

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Topic 1.4: Adding and subtracting........................ 25

Topic 1.5: Multiplying................................................. 33

Spatial reasoning

Topic 1.6: Dividing.......................................................38

Topic 4.2: Transformations..................................... 153

Rational numbers

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Topic 1.7: Order of operations............................... 46

Topic 1.8: Converting fractions, decimals and percentages......................................51 Topic 1.9: Equivalent fractions................................56

Topic 1.10: Comparing and ordering fractions and decimals........................ 61 Topic 1.11: Mixed numbers and improper fractions....................................................66 Topic 1.12: Multiplying and dividing by 10, 100 or 1,000......................................69 Topic 1.13: Adding and subtracting fractions...... 72 Topic 1.14: Adding and subtracting decimals...... 77 Topic 1.15: Using fractions........................................82 Topic 1.16: Using percentages.................................87

Financial mathematics

Pathways Topic 4.3: Positions and pathways...................... 158

Strand 5: Statistics Developing knowledge from, visualising, and interpreting data Topic 5.1: Time series................................................163 Topic 5.2: Mean and range.................................... 168 Topic 5.3: Data visualisations................................173

Strand 6: Probability Experimental probability Topic 6.1: Chance.......................................................178

Topic 1.17: Money........................................................ 92

Strand 2: Algebra Equations and relationships Topic 2.1: Number sentences................................... 97 Topic 2.2: Growing patterns..................................102 Topic 2.3: Coordinate planes................................ 107

Quick 10s........................................................ 183

For the teacher Kia ora! Thank you for choosing Mathematics and Statistics for Aotearoa New Zealand (Second edition). This programme has been purpose-written by experienced New Zealand educators to provide complete coverage of the New Zealand Curriculum (2025). Every component has been developed with real classrooms in mind, offering practical support for teachers, engaging learning experiences for students, differentiated activities and an easy-to-implement structure.

The three components of the programme This is your central hub for planning and implementing the programme. From here you can access: • Suggested year planners • Topic plans • Interactive teaching slides to support explicit teaching • Weekly pre- and post-topic quizzes (both online and paper) • Supporting resources such as rich tasks, activity sheets and interactives • An interactive assessment builder • Various achievement reports

Student Dashboard

This gives students easy access to digital activities and interactives that support and extend learning. Designed for independent use, it keeps students engaged both at school and at home.

Student Workbook

This is the core learning resource for students. It provides engaging, curriculumaligned activities organised by topic and includes all strands and elements, ensuring complete curriculum coverage.

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Teacher Dashboard

Here is an example of the workbook numbering system: Geometry | Pathways

Strand

Topic 4.3 Positions and pathways

Topic number

Element

Topic title

Topics Our programme organises curriculum practices into clear topics. Each topic typically runs for one week (with the exception of a few double or half topics), with everything you need as a teacher provided. Each topic follows a three-stage progression: Learn, Explore, Deepen. Learn: D evelop the foundational knowledge and skills for the topic. Explore: Extend understanding by investigating different aspects of the topic and introducing new concepts and ideas. Deepen: B uild on learning through increased challenge and complexity, encouraging deeper mathematical thinking. For clarity, all topic plans, topic teaching slides and supporting workbook pages are aligned with these three stages. iv

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

New features added to the student workbooks: Progress passport These checklists include illustrated examples to help students understand their goals and self-assess their confidence as they progress. Teachers can track progress, add comments or stickers and celebrate achievement. Progress Passports also support meaningful learning conversations between students, teachers and whānau.

Quick 10s Located at the back of the workbook, these ten-question number knowledge checks draw on practices from the previous year level. They are ideal for lesson starters and provide regular opportunities to consolidate number knowledge skills.

Ngā mihi nui, Erin Doleman Programme consultant and author

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Our goal for this programme is to support and empower confident teaching, meaningful mathematical learning and success for every student. Above all, we hope that you and your students enjoy the learning, discovery and mathematical thinking it inspires.

Kia ora! I’m Koa the Kiwi.

Getting set up on Oxford Digital Scan this QR code (or visit www.oup.com.au/nzmaths_QR) to get started! Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

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PRO

ESS GR

PA S S P

Strand 1: Number

Number structures and operations For me

Topic

1.3 Factor pairs, squares and cubes

Practices (NZC 2025)

782,813 > 782,684 379 = 300 + 70 + 9

Reading, writing, comparing and ordering any whole number and representing them using base 10 structure

4, 9, 14, 19,... 54, 50, 46, 42... −6, −8, −10, −12...

Counting forwards and backwards with positive whole numbers, including working with negative numbers

38,932 rounded to nearest 1,000 = 39,000

Rounding whole numbers to the nearest million, hundred thousand, ten thousand, thousand, hundred or ten

2.83 rounded to nearest tenth is 2.8 Factor pairs of 18: 1 and 18, 2 and 9, 3 and 6 42 = 16 102 = 100 23 = 8 53 = 125

1.4 Adding and subtracting

56,139 + 3,287 = 8,267 − 4,291 =

1.5 Multiplying

2,392 × 7 = 542 × 12 =

1.6 Dividing

I feel

Rounding hundredths to the nearest whole number or tenth

Finding factor pairs for numbers that result from multiplying any two whole numbers between 1 and 12

Recognising square and cube numbers and the notation for squared (^2) and cubed (^3) Memorising the square numbers to 144 and cube numbers to 125

Adding and subtracting any whole numbers

Dividing up to five-digit whole numbers by a one-digit divisor, with a remainder

1,283 ÷ 5 = 256 r 3 19,628 ÷ 3 = 6,542 r 2

Connecting finding unit fractions of whole numbers to division (with remainders)

1 1 of 31 = 31÷ 6 = 5 6 6 53 ÷ 4 = 13 r 1 or 13.25 or 13

Review & date

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1.2 Rounding

Example

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1.1 Whole numbers

For my teacher

1 4

Representing remainders from division as whole numbers, fractions or rounded decimals, as appropriate to the context

G Grouping E Exponents 1.7 Order of operations

M A

Multiply (and) Divide

Calculating expressions using the order of operations

Add (and) Subtract

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Rational numbers For me

0.7 =

7 10

0.64 =

64 100

0.328 =

328 1,000

0.2

0.8

3 4

1 5

4 5

1.9 Equivalent fractions

1.12 Multiplying and dividing by 10, 100 or 1,000

1.13 Adding and subtracting fractions

Converting decimal tenths and hundredths to fractions and percentages

9 3 = 12 4

Finding equivalent fractions

3 1 > 8 4

Comparing and ordering fractions where at least one denominator is a common multiple of all the others

Compare 70% and

18 25

18 72 = = 72% 25 100

4 19 = 5 5

0.63 × 10 = 6.3 5.4 × 100 = 540 781 ÷ 100 = 78.1 672 ÷ 1,000 = 0.672 5 4 17 + = 18 6 18 2

Review & date

Memorising decimal and percentage equivalents of common fractions ( 1 , 1 , 2 4 3 , 1 , 2 , 3 , 4 ) including fractions with 4 5 5 5 5 denominators that are 10 or 100

31 = 31 100

6.824 > 6.515

1.11 Mixed numbers and improper fractions

Practices (NZC 2025) Reading, writing and representing tenths, hundredths and thousandths as fractions and decimals

0.75

0.31 =

1.10 Comparing and ordering fractions and decimals

I feel

3 11 3 1 − = =1 4 8 8 8

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1.8 Converting fractions, decimals and percentages

Example

For my teacher

Comparing and ordering numbers with up to three decimal places

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Topic

Reasoning proportionally with fractions, decimals and percentages to compare two quantities and determine missing values

Converting between mixed numbers and improper fractions

Multiplying and dividing numbers by 10, 100 or 1,000 to make decimals and whole numbers (e.g. 1.3 × 10 = 13) and to identify tenths, hundredths and thousandths places

Adding and subtracting fractions and mixed numbers when one denominator is a multiple of the other

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

For me

Topic

Example

1.14 Adding and subtracting decimals

1.15 Using fractions

1.16 Using percentages

For my teacher I feel

Practices (NZC 2025)

2.678 + 4.84 = 8.345 − 3.721 =

Adding and subtracting decimals to three decimal places

3 of 240 = 180 4

Finding a non-unit fraction of a whole number, using multiplication and division facts and where the answer is a whole number

2 of the set is 90, what is the 3 whole set?

Review & date

Finding a whole set or amount when given a non-unit fraction, using multiplication and division facts

If you win 75% of 20 games, how many games do you win?

Finding common percentages (1%, 10%, 20%, 25%, 50%, 75%) of whoe numbers

50% of a number is 10. What is the number?

Finding the whole (100%) when given a percentage

Financial maths For me

For my teacher

Example

I feel

Practices (NZC 2025)

Review & date

Calculating 10%, 25% and 50% of whole dollar amounts

How much is 10% of $90? If one book costs $12.90 and another costs $13.10, is $25 enough to pay for both?

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1.17 Money

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Topic

Investigating questions involving purchases (e.g. ensuring there’s enough money)

Small steps every day. That’s the kiwi to success.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Strand 2: Algebra

PRO

ESS GR

PA S S P

Equations and relationships For me

Topic

Example

I feel

15 + ____ = 4 × 5 6 × 3 > 4² (3 + 4)² − 10 = ____ True or false: 8 × 7 ≤ 8 × 5 + 4² ?

2.1 Number sentences

2.2 Growing patterns

For my teacher Practices (NZC 2025)

Review & date

Checking the truth of and completing open number sentences that involve all four operations and that include the use of inequalities, respecting the order of operations Developing a rule for a growing pattern in words and making conjectures about further elements in the pattern

Step 1

Step 2

Locating coordinate points on a coordinate plane, including points found on the x- or y-axis

Step 3

How many sticks are in the 10th term? Monthly savings y

120

Generating a table of values from a rule for a growing pattern and plotting these points on a coordinate plane

100 80 60 40 20 0

Month

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Savings

2.3 Coordinate planes

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140

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

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Strand 3: Measurement

PRO

PA S S P

Measuring For me

Topic

For my teacher

Example

3.1 0 Estimating, kg 2 1 measuring and converting 500

44 cm 55 cm

0 500 kg 500

500

0 500 kg 500 2

500

1 500

2 hours and 30 minutes

4 cm

1 cm 3 cm 8m

3.2 Area and 5m volume

110

30 150 20

160

170

180

100 80

30 150

160 20

15 10

180

170

35º

27º

3.4 Angle rules

72 min = 1 hr 12 min FROM BELGRAVE Belgrave

3.5 Time

CUBE

Calculating, estimating and comparing the volumes of cubes and rectangular prisms using standard units, including cubic centimetres and cubic metres

Identifying and describing angles at a point, angles on a straight line and vertically opposite angles, using angle notation Reasoning about and finding unknown angles in situations involving angles at a point, angles on a straight line and vertically opposite angles

80º

Visualising, estimating and calculating (using multiplication) the areas of rectangles and right-angled triangles and the volumes of rectangular prisms

Classifying, measuring and constructing angles up to 360°, using a protractor

160

30 150 160

170

180 40

100

30 150

110

160 20

160

180

3 cm

170

3m 170

track

180

Read the

V = 12 × 3 × 2 = 72 m3

160 20

180

12 moutside

110

170

100

100 80

160 20

100

110

100

110

3.3 Read the and Measuring inside track drawing angles 0

Read the inside track 10 m

4 cm

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110

170

100 80

100

180

110

4 cm

1 A= × 8 × 4 = 16 m2 2

10 cm

3 cm 4 m

Accurately measuring length with a ruler, mass (weight) with scales, capacity with measuring jugs, temperature with a thermometer and duration with a timer, using appropriate metric or time-based units or a combination of units

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4 cm

Review & date

Converting metric units of length, mass and capacity, including combining mixed units to produce units with up to 2 decimal places

3 kg and 550 g = 3.55 kg 2 cm

Practices (NZC 2025) Estimating length, mass (weight), capacity, temperature and duration using appropriate metric or time-based units or a combination of units

0 500 kg 500 Milk

500

I feel

Train 1

Train 2

dep:

10:30

11:10

Menzies Creek arr:

10:53

11:33

Menzies Creek dep:

11:05

11:35

Emerald

dep:

11:20

11:53

Lakeside

arr:

11:30

12:08

Converting between units of time Finding elapsed time in minutes across an hour Using and interpreting timetables to calculate the duration of events

How long is the train trip? 18:00 = 6:00 pm

Measuring duration in both 12- and 24-hour time systems

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

ESS

Strand 4: 6: Probability Geometry

PRO

PA S S P

Number of bases

3D object

Shapes

For me1

e.g.

Topic

Example

Base shape

Side face shape

The object is sitting on:

hexagon

triangles

the base

I feel

Hexagonal pyramid

Practices (NZC 2025)

Review & date

Identifying, classifying and explaining similarities and differences between 2D shapes (including different types of triangles and quadrilaterals) and between prisms and pyramids

40°

4.1 2D shapes, prisms and pyramids

For my teacher

120° 120°

? Square pyramid

Identifying and describing the interior angles of triangles and quadrilaterals

b Triangular prism

Spatial reasoning c

For me Example Triangular prism

I feel

Practices (NZC 2025)

Review & date

Identifying shapes with rotational symmetry and determining their order of rotational symmetry

d Rectangular prism

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4.2 Transformations

For my teacher

AF T

Topic

Visualising, creating and describing 2D geometric patterns and tessellations using rotation, reflection and translation, and identifying the properties of the shapes that do not change Predicting the results of two-step transformations on 2D shapes

Pathways For me

Topic

Example N 3

4.3 Positions and pathways

I feel

Scale: 100 m

2 1

0 0

S T 2

For my teacher

Practices (NZC 2025)

Review & date

Interpreting and creating grid references and simple scales on maps, using directional language including the four main compass points, turn (in degrees) and distance (in m, km) to locate and describe positions and pathways

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

ESS

Strand 5: Statistics

PRO

PA S S P

Developing knowledge from, visualising, and interpreting data For me

Topic

For my teacher

Example

I feel

Temperature in Te Anau

°C

Creating time-series graphs

Day

Identifying whether a time-series graph shows a trend

Calculating the range for numerical data

Range = 8 Minimum

Maximum

4+8+3 =5 3

Number of ice creams sold in one week Key: = 10 ice

5.3 Data visualisations

creams

Mon

Tues

Wed

Thurs

Fri

Calculating an average and a range for continuous numerical data

AF T

Mean:

Calculating the mean for numerical data

Choosing and creating an appropriate data visualisation for a given set of data

D R

5.2 Mean and range

Review & date

Collecting time-series data (e.g. how the mass of a kilogram of carrots varies over 5 days)

5.1 Time series

Practices (NZC 2025)

Interpreting data visualisations, including those from contemporary media

The trend is clear: you’re getting there!

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

ESS

PRO

PA S S P

Strand 6: Probability

Experimental probability Topic

For me Example

For my teacher I feel

Practices (NZC 2025)

Review & date

Listing the sample space of an event B

R B

6.1 Chance

Calculating the probabilities of individual outcomes

P(red) =

Calculating probabilities using a spinner, where each event is a fraction or combination of fractions on the spinner

1 8

Answering questions about the probability of combinations of outcomes, including checking that the sum of all the probabilities is 1

D R

AF T

Sum of probabilities = 1 2 2 3 + + + =1 8 8 8 8

The odds of your success are in your favour!

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Number structures

Topic 1.1 Whole numbers Place value

In a number, the value of each digit depends on its position, or place.

923856 is easier to read if we write it as 923,856. It also makes it easier to say the number: nine hundred and twenty-three thousand, eight hundred and fifty-six.

Learn

a b

Ones

Tens

Hundreds

700,000

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Thousands

Write the number, using commas if necessary

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Ten thousands

e.g.

Hundred thousands

Look at this number: 725,384. The 7 is worth 700,000. Show the value of the other digits on the place value grid.

Remember to use a zero as a space filler.

c d e

If we write thirty-two thousand, five hundred and nine in numerals, we use a zero to show there are no tens: 32,509 Write as digits:

nine thousand, three hundred and seven

twenty-five thousand and forty-six

one hundred and two thousand, seven hundred and one.

Write in words:

2,860

13,465

28,705. Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

What is the value of the red digit in each number? e.g.

85,306:

80,000

53,207:

48,005:

29,425:

135,284:

2,399,517:

Write each number from question 4 in words. e.g. 85,306: eighty-five thousand, three hundred and six

a b c d

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Write these numbers as numerals.

Eighty-six thousand, two hundred and thirty-one

One hundred and forty-two thousand

Six hundred and fifty-six thousand, three hundred and eight

Four million, one hundred and five thousand, nine hundred and twenty-one

Circle the number that is one more than 25,789.

D R

25,800 8

25,780

25,799

25,790

Circle the number that is one less than 34,000. 33,900

33,990

33,999

40,001

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Look at this number: 4,785,321.

Ten thousands

Thousands

Hundreds

Tens

Ones

4,000,000

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Hundred thousands

Write the number using commas if necessary

Put the numbers in ascending order.

4,605,924

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Millions

Show the value of each digit on the place value grid.

4,087,845

4,591,043

4,605,812

984,142

Of the following pairs in the first column, circle the larger number. In the second column, find the difference between the two numbers. Which number is larger? 156,782 and 156,791

Difference between numbers 9

2,345,600 and 2,346,000 1,234,567 and 1,234,576 345,021 and 345,210 999,999 and 1,000,001 600,002 and 600,020 789,999 and 790,002 456,789 and 456,799 3,456,001 and 3,455,999 12

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Expand these numbers. e.g. 14,217:

10,000 + 4,000 + 200 + 10 + 7

25,123:

6,563,382:

6,004:

125,381:

860,094:

Use the digits on the cards to make: 6

20,000 +

Remember to use commas between the digits where necessary.

the largest number using all the cards

the smallest number if “5” is in the ones place

the largest number if the “7” is in the hundreds of thousands place

the smallest number if the “1” is in the thousands place.

Shade the triangle on the number line that is at the approximate position of the number shown. 3,427

D R

AF T

2,000

10,000

20,000

41,132 0

1,000

98,775 0

50,000

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

In the table, look at the given starting number and whether to count forwards or backwards. In the specified multiples, what are the first five numbers you reach? The first one has been done for you. Start at:

Count forwards or backwards

In multiples of:

First five numbers

forwards

17, 22, 27, 32, 37

backwards

186

forwards

289

backwards

345

forwards

836

backwards

100

Negative numbers Sometimes numbers can be negative. These are numbers that are less than zero.

AF T

e.g. In winter, an outside temperature may drop below zero, to −5°C.

–5

–2

–8 –7 –6 –5 –4

–1

–2 –1

9 10

Place the following numbers on the number line: 30, 60, –40, –80, 90, –10 –100

–3

Fill in the missing numbers on the number line. –10

–4

D R

On a number line, negative numbers are to the left of zero.

–60

100

Count forwards or backwards using the information given. The first one has been done for you. Start at:

Count forwards or backwards

In multiples of:

First five numbers

–6

forwards

–6, –4, –2, 0, 2

backwards

–13

backwards

–100

forwards

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Number structures

Topic 1.2 Rounding Rounding numbers

Before a number is rounded, you need to know which place value column you are rounding to. For example, if you wanted to round 32,828 to the nearest thousand, you focus on the digit to the right of it. Here’s how:

Tth th h t o 3 2 8 2 8 If the digit is 5 or more, round UP

If the digit is 4 or less, round DOWN

AF T

We can see that the circled digit is more C than 5. So, we round up to the nearest thousand. 32,828 rounded to the nearest thousand is 33,000. (All the columns to the right are now empty. So, a zero goes in each empty space.)

The ABC of rounding B Decide on Circle the the column digit to the you are right. rounding to.

Learn

Round the numbers below to the nearest 100.

492

Round these numbers to the nearest 1,000.

5,793

12,629

Round these numbers to the nearest 10,000.

92,639

231,000

A factory makes roughly 5,000 cars in one day (rounded to the closest thousand).

D R

357

4,098

8,527

77,777

29,856

35,102

174,521

481,394

98,911

923

Using the numbers, list three possible numbers that could be the actual number of toy cars produced at this factory. 1, 5, 6, 4, 7, 2

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Round these numbers to the nearest thousand.

1,875

4,125

19,235

56,852

996

3,599

32,828

824,721

Round 32,828 to the nearest:

hundred

thousand

ten

ten thousand.

If a prize of $22,935 had to be rounded, would you prefer it to be rounded to the nearest ten thousand, thousand, hundred or ten? Give a reason for your answer.

Round to the nearest ten thousand.

38,759

52,811

41,445

97,624

25,555

872,923

451,445

375,172

Round to the nearest hundred thousand.

178,280

292,321

413,633

928,872

298,729

562,837

1,132,405

7,234,116

D R

AF T

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Round to the nearest tenth.

1.82

5.32

0.48

2.87

37.09

3.55

7.99

0.82

4.47

34.21

21.18

98.78

In New Zealand, our smallest coin is 10 cents. Round these money amounts to the nearest 10 cents (tenth).

$7.82

$4.57

$6.91

$2.34

$56.69

$87.25

Scientists say that the Moon is an average of 384,399 kilometres away from Earth.

What would be your rounded distance to the Moon? Give a reason for the way you have rounded the distance.

Why do you think the average distance is given and not the exact distance?

D R

AF T

Rounding to the nearest million! 4

Circle the correct rounding, from either the left or the right column. 2,000,000

2,873,974

3,000,000

8,000,000

8,321,783

9,000,000

5,000,000

5,678,204

6,000,000

9,000,000

9,412,831

10,000,000

7,000,000

7,520,024

8,000,000

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

This table shows unusual record-breaking activities. Place

Activity

Record number

USA

Number of dogs on a walk together

New Zealand

People performing the Haka

Poland

People ringing bells together

Hong Kong

People playing percussion instruments together

Singapore

People line dancing together

Portugal

People making a human advertising sign

Mexico

People doing aerobics at the same time

India

Trees planted by a group in one day

USA

People in a conga line

England

The longest scarf ever knitted (in centimetres)

AF T

Complete the number column in the table by rewriting the numbers in order, from the lowest to the highest number. The events are in order from low to high.

D R

Record numbers 80,241 10,021 119,986 38,633 322,000 3,117

34,309 6,531

11,967 10,102

The following numbers are from the list in question 1. They have been rounded in various ways. Write the actual number for each.

80,000

40,000

3,000

300,000

10,100

10,000

100,000

12,000

7,000

35,000

Rounded to the nearest ten thousand, the 2024 population of New Plymouth in the North Island was 50,000 people. The actual number can be made by using each of these digits once: 1 4 6 8 9 List as many of the 18 numbers that could be the actual population as you can.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Improving your estimating and rounding skills can help you save time with mental calculations.

Look at these facts and figures. Show how you would round the numbers by underlining or highlighting one of the numbers. World fact

Metres

Rounded number

2,191 m

2,100 or 2,200?

b Cehi: the tenth-deepest cave in the world

1,502 m

1,500 or 1,600?

c Mont Blanc: the highest mountain in Europe

4,807 m

4,800 or 4,900?

d Mont Maudit: the tenth-highest mountain in Europe 4,466 m

4,400 or 4,500?

e Mt Everest: the highest mountain in the world

8,850 m

8,800 or 8,900?

f Aoraki/Mount Cook, the highest mountain in NZ g Mammoth Cave: the longest cave in the world

3,754 m

3,700 or 3,800?

h Wind Cave: the fourth-longest cave in the world

212,500 m 200,000 or 300,000?

AF T

a Krubera: the deepest cave in the world

590,600 m 500,000 or 600,000?

Circle the number that will make the information correct.

The total of the depths of Krubera and Cehi caves is about 3,500 m, 3,700 m, 3,600 m, 3,400 m.

Mont Blanc is about 20 m, 200 m, 30 m, 300 m taller than Mont Maudit.

If you walked the lengths of the Mammoth Cave and the Wind Cave, you would have travelled about 700 km, 70 km, 80 km, 800 km.

Sarah goes shopping in a bargain shop. She has $11 to spend. She goes to the checkout with the following items.

D R

Paint set: $1.99

Ball: 99c

Calculator: $1.99

Cuddly toy: $1.99

Pen set: $1.25

Notebook: 49c

Geometry set: $1.99 Stickers: $1.29

To the nearest dollar, how much more than $11 is the total?

Which item should Sarah put back to be closest to a total of $11?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Number structures

Topic 1.3 Factor pairs, squares and cubes A factor is a number that will divide evenly into another number: 2 is a factor of 4. 1 is a factor

of every whole number.

Learn 1

Circle the factors of each number. 2

6 6

The factors of 8 are:

The factors of 5 are:

The factors of 9 are:

The factors of 6 are:

The factors of 2 are:

The factors of 4 are:

The factors of 7 are:

The factors of 3 are:

Identify the factor pairs for each number. e.g.

The factors of 10 are: 1

AF T

e.g.

18:

24:

30:

50:

D R

factor pairs for 10 are: 1 and 10, 2 and 5.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Write the factors of each number.

Which numbers between 20 and 30 have exactly:

two factors

four factors

three factors

six factors?

List all eight factors of 24.

b Which number between 30 and 40 has even more factors than 24?

The number 2 is a factor of every even number. Factors that are the same for more than one number are called common factors.

AF T

List its factors. The factors of 16 are:

The factors of 20 are:

The common factors of 10 and 20 are:

D R

The factors of 4 are:

The factors of 6 are:

The factors of 8 are:

The common factors of 4 and 8 are:

The common factors of 6 and 8 are:

The factors of 14 are:

The factors of 12 are:

The factors of 21 are:

The factors of 18 are:

The highest common factor (HCF)

The HCF of 12 and 18 is:

of 14 and 21 is:

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Numbers can be arranged in patterns 4 is a square number because 2 × 2 = 4. 9 is a square number because 3 × 3 = 9.

A small 2 to the right of a number indicates that the number is squared. For example, if you see 32, it means 3 multiplied by itself: 32 = 3 × 3 = 9.

Explore These are the first six square numbers. Fill in the gaps. 4

1 × 1 = 12 12 = 1

2 × 2 = 22 22 = 4

AF T

4×4=

3 × 3 = 32

D R

Can you find the following square numbers?

72 =

82 =

92 =

102 =

112 =

122 =

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Complete the grid to show the first ten square numbers. Write the information as you have done previously. 4

D R

AF T

Use your answers from question 3 to complete the following.

What is the next number in the square number pattern?

How does the digit in the ones column change in the square number pattern?

Circle one answer. The 100th square number is: 100 1,000 10,000 100,000

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Cube numbers A cubed number is the result of multiplying a whole number by itself three times. e.g. 23 = 2 × 2 × 2 = 8 2×2×2=8 23 = 8

Deepen 1

Can you work out the first 6 cubed numbers?

D R

AF T

13 = 1 × 1 × 1 = 1 23 =

= 2

Steve is building a cube-shaped garden shed. If each side of the shed is 3 metres long, how much space will it occupy in cubic metres? Show your working.

Jack is hiring a cube-shaped storage unit to store his spare things. Its side length is 6 metres long. How much space will it have in cubic metres? Show your working. Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.4 Adding and subtracting Learn Rounding and compensating is an addition strategy. For example, in 74 + 19, you can round 19 to 20 and calculate 74 + 20. Then adjust (compensate) by subtracting 1. Fill in the rest of the table. Problem

Using rounding it becomes:

Now I need to:

e.g. 74 + 19

74 + 20 = 94

take away 1

56 + 41

56 + 40 = 96

add 1

25 + 69

25 + 70 = 95

take away 1

125 + 62

125 + 60 = 185

add

136 + 198

136 +

195 + 249

1,238 + 501

1,645 + 1,998

Answer 93

AF T

Use the rounding and compensating strategy to solve the following.

35 + 99

D R

24 + 101

173 + 198

1,407 + 1,002

1,451 + 1,499

1,562 + 1,004

Try these trickier numbers. Round one number, add together and then adjust your answer.

125 + 38 =

279 + 45 =

164 + 47 =

497 + 82 =

1,193 + 842 =

1,204 + 347 =

2,585 + 1,321 =

3,410 + 1,996 =

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Use the place value strategy to solve the following problems.

e.g. 125 + 132

173 + 125

237 + 462

389 + 462

7,114 + 2,365

2,564 + 4,236

62,873 + 25,184

100 + 100 + 20 + 30 + 5 + 2

Answer 257

Sometimes you will add numbers with a different number of place value columns. Make sure you add the correct columns together. Problem

Join the place value columns

AF T

Problem

D R

628 + 53

4,329 + 582

2,783 + 925

Join the place value columns

Answer

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Use the place value strategy to solve the following.

147 + 232

184 + 415

747 + 551

1,552 + 732

3,267 + 642

6,564 + 4,426

Use rounding and compensating to solve the following.

745 + 299

364 + 401

276 + 598

847 + 302

958 + 190

902 + 304

Choose a method to solve these. Explain how you got each answer.

649 + 249 =

1,253 + 199 =

1,750 + 1,750 =

14,578 + 410 =

D R

AF T

Look out for the ones that involve trading!

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

T 1

Column addition Set the numbers out vertically, start with the ones + and add each column in turn. Sometimes you need to regroup from one column to the next.

Deepen Complete the following. Try rounding to estimate your answers first.

a +

T 1

AF T

T 1

Start with the ones and add each column in turn.

a +

D R

Complete the following.

b +

Ten Th

c +

Ten Th

Hun Ten Th Th

You need to regroup with these.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Look for a pattern in the answers.

a +

d +

f +

Look for pairs of numbers which add to 10 to save time in written addition.

+ 1

+ 2

+ 1

+ 6

+ 5

D R

AF T

Rewrite these problems as column additions, then solve them.

114 + 137 H

b O

5,547 + 49

2,739 + 278

173 + 38

827 + 138

1,637 + 829

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Subtraction in parts Splitting numbers up into their place value parts can make subtraction easier. For example, 479 – 135 = ? • Split (expand) the number you are taking away: 135 becomes 100 + 30 and 5 • First, take away 100: 479 – 100 = 379 • Next, take away 30: 379 – 30 = 349 • Then, take away 5: 349 – 5 = 344 • So, 479 – 135 = 344

Learn 1

Use the subtraction in parts strategy. Fill in the gaps.

Take Take away Problem away the Answer the 2nd part 3rd part 349 – 5 = e.g. 479 – 135 135 = 100 + 30 + 5 479 – 100 = 379 379 – 30 = 349 344 344 a 257 – 126 126 = 100 + 20 + 6 257 – 100 = b 548 – 224 224 = c 765 – 442 d 878 – 236 e 999 – 753 Take away the 1st part

D R

AF T

Expand the number

Use subtraction in parts to solve these.

45 – 24

464 – 343

676 – 254

5,727 – 3,325

8,958 – 5,635

The subtraction in parts can be used on an open number line. Fill in the gaps.

What is 776 – 423? – 3 – 20

– 400

What is 487 – 264? –

–

– 200 487

776

Answer: 776 – 423 = 30

Answer: 487 – 264 =

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Some written subtractions involve regrouping. Here is a reminder of how it works, using place value blocks and small numbers, such as 54 – 25. Step 2 Regroup a ten for 10 ones.

Step 4 Take away 5 ones.

When you write the algorithm, you regroup in the same way.

Step 6 Take away There aren’t enough ones. 2 tens. Regroup a ten. That leaves 4 tens.

T O 45 14 Step 1 Step 3 Step 5 Start with 54. There are still 54 That leaves (You cannot take (4 tens and 14 ones). 49. away 5 ones.)

Step 7 The answer is 29.

–

Now there are 10 + 4 ones = 14.

2 9

Explore

T 7

O 3

– 2

– 1

e Th H T O

– 1

i –

l –

H T O 2 34 13

T O 1 9

T 1

O 8

– 2

T O 5 14

H 7

T 2

O 5

– 3

O 1

g Th H T O 5

– 3

– 2

Tth Th H 4 3 7

T 2

O 4

k Tth Th H T O

–

H 4

T 6

Th H 4 3

Hth Tth Th H 8 1 3 5 4

– 1

Tth Th H 8 3 4

AF T

You could use place value blocks to help with the regrouping as you complete these algorithms.

D R

h Th H T O

Subtraction with larger numbers works in the same way. Start with the ones column.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Practise regrouping with subtraction.

4 1 0

–

5 0 8

7 4

–

g –

8 1 2

8 7 2

9 5 3

3 3

–

2 7 4

–

1 8 5

–

1 7 6

–

Sometimes when you regroup, there is nothing in the next column. Here’s what to do:

More ones are needed …

AF T

Regroup a hundred. Regroup a ten. That leaves 2 hundreds. That leaves 9 tens.

… but there are no tens H

1 4 7

–

23 10

23 109 15

D R

3 0 5

–

1 4 7

–

1 … so regroup FROM the hundreds TO the tens first.

5 8

Now there are 15 ones.

Practise regrouping across two columns with these subtractions.

4 0 2 –

1 3 4

3 2

–

Now there are 10 tens.

5 0 6

6 0 2

4 0 6

9 0 3

–

2 4 8

–

h Hun Ten

Ten Th

–

1 7 7

2 5 8

–

5 3 4

–

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.5 Multiplying Grid method

If there is a larger number, then a larger grid is needed.

62 × 45 ×

2,400

300

518 × 23

62 × 45 = 2,400 + 80 + 300 + 10

500

10,000

200

160

1,500

518 × 23 = 1 0,000 + 1,500 + 200 + 160 + 30 + 24

= 2,790

= 11,914

AF T

Learn Fill in the grids and complete the multiplication.

74 × 21 = ×

D R

63 × 95 = ×

20 1

283 × 45 = ×

618 × 92 = ×

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Column multiplication If you need to regroup, you can do it like this.

3 tens × 4

3 tens × 4 = 12 tens There is another 1 ten. That makes 13 tens.

4×4

4 × 4 = 1 ten and 6 ones 1 ten goes in the tens column.

Learn 1

Complete the algorithms. Regroup if necessary.

Solve these problems in the same way.

1 2 5

h ×

2 5 3 3

D R

1 4 2

8 4

It works the same with larger numbers. Start at the ones and complete each column in turn.

AF T

2 8

0 7

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

To multiply by two digits, split the number you are multiplying by.

( 36 × 5 ones ) + ( 36 × 2 tens )

3 6 5

What is 36 × 25? There are two multiplications.

1 8 0

Add the two answers to find the total.

What is 24 × 23? b

7 2 0

1 8 0 + 7 2 0

9 0 0

3 6 2 0

What is 23 × 35?

36 × 25 = 900

What is 35 × 28?

Make two multiplications.

× 2

2 ×

× 3

3 ×

24 × 23 =

23 × 35 =

What is 37 × 24? b

× 2

D R

AF T

35 × 28 =

What is 39 × 27?

What is 42 × 26?

Make two multiplications.

37 × 24 =

39 × 27 =

42 × 26 =

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

What is 36 × 25?

Previously, you looked at a way of multiplying 36 × 25. You can make this shorter by putting both multiplications into one algorithm: (36 × 5) + (36 × 20).

3 6 ×

2 5

36 × 5

1 8 0

36 × 20

+ 7 2 0

Don’t forget to put a zero as a space-filler.

9 0 0

2 9 ×

4 2 ×

2 5

3 9 ×

2 7

1 9

29 × 5

d ×

29 × 20

3 3

D R

2 6

2 0 7

5 4

Use the working out space to answer the following.

At Mount Waialeale in Hawaii, it rains 335 days a year. If you lived there for 35 years, how many rainy days would you have?

Amy blinked 2,700 times a day for two years. How many times did she blink in the month of January?

6 4 ×

1 5

1 2 3 ×

7 5 ×

4 3

AF T

3 7

3 9 6 ×

4 7

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen

Distance from Melbourne to:

An aeroplane flies millions of kilometres in its lifetime. This table shows the distances from Melbourne Tullamarine airport to other airports around the world.

Adelaide, Australia

651 km

Bangkok, Thailand

7,363 km

Chicago, USA

11,559 km

Darwin, Australia

3,143 km

Edmonton, Canada

13,993 km

Frankfurt, Germany

16,308 km

Glasgow, Scotland

16,962 km

Honolulu, USA

8,870 km

Istanbul, Turkey

14,619 km

Johannesburg, South Africa 10,326 km Kuala Lumpur, Malaysia

6,360 km

Los Angeles, USA

12,764 km

Choose an efficient multiplication method to find the answers. You may need extra paper for your calculations.

What is the distance of a return trip to Istanbul?

How far does a plane fly if it makes three return trips to Bangkok?

If a plane flies to and from Chicago eight times, how far does it fly?

A plane flies from Melbourne to Darwin and back twice a day for two weeks. What distance does it cover?

If a plane travelled to and from Johannesburg 50 times, would it have flown a million kilometres?

People can earn points for the distances they travel on certain airlines. ABC Airlines offers one point for every kilometre that its passengers fly.

Aria flies from Melbourne to Adelaide on business each day and back home again from Monday to Friday. How many points does she earn in two weeks?

Aiman travels from Kuala Lumpur to Melbourne once a month to visit his family. How many points does he earn in a year?

How many points does a family of four people earn by going on a holiday to Frankfurt?

A plane flies from Melbourne to Adelaide and back twice a day. How many kilometres does it fly in one week?

D R

AF T

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.6 Dividing Division can be set out in an algorithm. You put the number in a “box” and split it up. This is called short division. Imagine the problem is 42 ÷ 3. This is how it works:

Step 1 4 tens split into groups of three makes 1 group of three tens and 1 ten left over.

14 3 412

The answer to a division is called a quotient.

Step 3 12 ones split into groups of three makes 4. Step 2 Regroup the ten for 10 ones. Now there are 12 ones.

Learn

Solve these division problems using the short division method. b

3 72

6 78

5 60

5 75

4 68

These problems contain larger numbers, but you can solve them in the same way.

7 252

5 360

6 816

4 924

3 714

9 882

6 288

8 672

3 378

8 864

7 756

5 315

m 9 252

9 936

5 495

6 468

D R

a 68 4

AF T

8 88

7 91

3 81

896

6 72

342

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Sometimes, the number you are dividing will not split equally. When this happens, you have a remainder. This can be shown using “r” for remainder. For example, 13 ÷ 3 = 4 r 1.

Solve the division problems. Use “r” to show the remainder. b

2 51

5 77

6 80

6 693

3 952

5 582

7 782

5 72

7 1842

3 46

4 915

9 672

7 58

6 832

5 3265

4 85

2 485

5 363

3 248

9 4391

7 628

w 3 756

6 92

3 517

7 184

aa 5 1 9 8

ab 6 5 7 2 8

AF T

4 57

D R

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Here are two ways of showing a remainder at the end of a division problem: 35 ÷ 2 = 17 r 1

35 ÷ 2 = 17 1 2

Explore

Write the remainder in two ways.

14 ÷ 3

47 ÷ 5

39 ÷ 4

65 ÷ 8

77 ÷ 9

61 ÷ 7

84 ÷ 9

58 ÷ 6

Complete each algorithm, showing the remainder in two ways.

4 4 6 7

6 197

AF T

3 2 7 2

6 197

5 7 4 2

3 2 5 7 5

9 1 6 8 4

6 4 1 6 5

7 2 3 1 9

In a real-world division problem, we have to decide what to do with a remainder. Do we leave it as a remainder, or divide it into a fraction? Give a real-world answer to each of these problems.

Two children share a bag of 125 marbles. How many do they each get?

Two children share 15 doughnuts. How many do they each get?

D R

4 4 6 7

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

If two people shared $25, we would not leave the remainder as $1, nor would we call it 1 a dollar. We would use a decimal: $25 ÷ 2 = $12.50 2

To write an algorithm, we need to put a decimal point and show “zero cents”. $ 12. 50 2 25.100

Put in the decimal point and the zeros to complete these.

$ . 2 5 3.0 0

$ 4

We can use decimals for other remainders.

7 3

$ 4

$ 8 1 3 2

7 4

$ 8

9 2

$ 6

1 2 9

AF T

17 , 18 , 19 and 15 in four tests, For example, if Dom scores 20 20 20 20

D R

1 7. 2 5 his average score is the total (69) ÷ 4 = 17 r 1, or 17 1 or 4 629.1020 4

5 9 5 . 0 0

6 2 8

5 0 6

6 8 4

4 1 3 4 7

9 8 5 2

17 1 9 3

5 2 1 8 6

Solve the following problems. Think of the most appropriate way to deal with the remainders.

145 marbles are divided between four people. How many do they each have?

Four people share a prize of $145. How much does each person receive?

11 5 9 8

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Remainders can be shown in different ways. Here are three examples: Whole number: 35 ÷ 2 = 17 r 1

Fraction:

Decimal: 35 ÷ 2 = 17.5

35 ÷ 2 = 17 1 2

35 people split into 2 teams. 35 chocolate bars shared Each team has 17 people, between 2 people. Each with 1 person left over. person gets 17 bars, with another half a bar each.

Write the answer with the remainder in 3 different ways.

e.g. 19 ÷ 4 =

4.75

95 ÷ 4 = Answer Whole

Whole Fraction Decimal

AF T

Decimal

78 ÷ 3 = Answer

D R

Fraction

Answer 4r3 4 3 4

Whole

61 ÷ 2 = Answer Whole

Fraction

Decimal

878 ÷ 4 =

357 ÷ 4 =

Answer

Whole

Fraction

Decimal

74 ÷ 5 =

470 ÷ 8 =

Answer

$35 split between 2 people is $17.50 each.

Answer

Whole

Fraction

Decimal

Decimal Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Use division to find the unit fraction of a number! 1 6 of 31 = ?

This is asking you to split 31 into 6 parts (to find 1 6 ). So, 31 ÷ 6 = 5 r 1, or 5 1 6

Deepen 1

Solve the following problems in this way.

1 5 of 47 =

Solve the following word problems. Show the remainder in the most appropriate way using a whole number, a fraction or a decimal.

77 cards are split across 6 binders. How many marbles are there in each binder?

31 chocolate bars are split among 5 friends. How many bars does each friend get?

You want to run 27 km over 6 days. If you split it evenly, how many kilometres do you need to run each day?

$54 is split between 4 people. How much does each person get?

29 students are divided into 3 teams. How many students are in each team?

Write your own remainder word problems for a friend to solve.

1 3 of 38 =

1 9 of 65 =

$86 is divided among 5 friends. How much money do they each receive?

AF T

D R

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Not every number can be divided equally by other numbers. Write algorithms for these. Use remainders where necessary in the answers.

97 ÷ 5

72 ÷ 3

145 ÷ 6

386 ÷ 7

What is the best way to express the answers in these real-life situations?

Seven doughnuts shared between two people.

Two people are given nine marbles. How many can each person have?

Two sisters share $13. How much do they each get?

Tana and Chanel are cooking pancakes. Their friends are coming over, so they need to make enough for eight people!

D R

AF T

Find the missing values and complete the pancake recipe table. 1 person Flour

36 g

Eggs

1 egg

Baking powder Sugar

8 eggs 16 g

25 g

Butter Maple syrup

8 people

128 g 12 g

At a chicken farm, 3,000 eggs a day are packaged and put into boxes. Each box can hold 8 eggs. How many boxes are needed for 3,000 eggs?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Solve the following word problems. A teacher has 45 books that he wants to divide equally between himself and the teacher next door. How many books will each person get, and how many will be left over?

c Anahera has 511 stickers that she d wants to divide equally among her 3 children. How many stickers will each child receive, and how many stickers will Lucia keep for herself?

A baker made 675 cupcakes for a large function and wants to package them into boxes that hold 8 cupcakes each. How many full boxes can they fill, and how many cupcakes will remain?

D R

AF T

a Jahrome has 78 coloured pencils b that he wants to share equally amongst his 5 friends. After giving out the pencils, how many pencils will each friend receive, and how many will Jahrome have left over?

e A library has received a donation f of 932 new books. They plan to organise the books onto 8 shelves. How many books will fit on each shelf, and how many books will be left over?

A charity organisation is distributing 254 blankets to families in need by placing them in bags that can hold 6 blankets each. How many full bags will they have, and how many blankets will be left over?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.7 Order of Operations Ordering

Pay attention to the order of operations!

Working with number sentences is a bit like putting on your clothes. Sometimes the order of doing things does not matter, and sometimes it does! Changing the order of putting on clothes … Left then right, or right then left …

✓

Sock then shoe …

Shoe then sock…

✓

✘

Learn Try changing the number order with each operation.

Addition

14 + 2 = ?

20 + 12 = ?

15 + 10 = ?

2+3=?

Yes

AF T

e.g. 3 + 2 = ?

Change Same the order answer?

D R

Number sentence

Subtraction

Multiplication

Number sentence e.g. 3 × 2 = ?

e.g. 3 – 2 = ?

14 – 2 = ?

20 – 12 = ?

15 – 10 = ?

Change Same the order answer? 2–3=?

Division

Change Same the order answer? 2×3=?

Yes

Number sentence e.g. 3 ÷ 2 = ?

14 × 2 = ?

14 ÷ 2 = ?

20 × 12 = ?

20 ÷ 12 = ?

15 × 10 = ?

15 ÷ 10 = ?

Complete these sentences.

The answer is the same if you change the order of the numbers for addition and

Number sentence

Change Same the order answer? 2÷3=?

Can you see how addition and multiplication are connected?

The answer is not the same if you change the order of the numbers for . Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

An equation is a number sentence with 2×3 parts separated by an = symbol. The parts balance each other. 3

4+2

The parts on either side of the = symbol are called expressions.

Complete these equations.

a 4×2 = d

– 14 = 3 + 7

g 2×7 =

÷2 = 3+6

16 ÷ 2 = 2 ×

40 ÷ 2 = 4 ×

9×2 =

– 20 = 5 × 6

÷2

30 ÷ 3 = 100 ÷

AF T

You can use equations to make calculations simpler. 4

Which of the following expressions would not balance 17 + 19?

2×3×6

Which of these expressions is not correct?

4 × 15 = 15 × 4 b

Imagine each expression in the first column is sitting on the left side of a scale (like in question 3). Write three possible expressions you could use to balance the scales. An example has been done for you. e.g.

2×3×5

5 + 20 + 8

50 ÷ 2

72 – 25

6 × 2 × 10

3 + 23 + 12

40 ÷ 5 ÷ 2

12 + 2 + 12

D R

4 + 15 = 15 + 4 c

60 ÷ 2

56 – 20

15 + 4 = 4 + 15 d

5 + 15 + 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

360 ÷ 10

15 ÷ 4 = 4 ÷ 15

100 − 50 − 20

Order of Operations To solve math problems correctly, we use the Order of Operations. GEMA G

Grouped operations inside backets, ()

Exponents such as squaring, a2

Multiplication and division, from left to right

Addition and subtraction, from left to right

Explore 1

Solve these questions.

5+3×2 =5+6 =

Solve these questions.

3 × (8 − 5) = =

Write the answers to these pairs of number sentences.

36 ÷ (9 − 3) = =

(7 + 1) × 2 + 3 d = =

3 × 12 ÷ 4 = =

36 ÷ 9 – 3 = =

AF T

(5 + 3) × 2 = =

D R

24 ÷ 8 + 11 = =

Problem 1

Problem 2

a 14 – 13 + 7 =

14 + 7 – 13 =

Look for the problem in each b 49 – 24 + 25 = pair that is easier to solve.

These pairs of number sentences look similar, but the answers are different.

25 – 24 + 49 =

c 35 – 10 + 25 =

35 + 25 – 10 =

d 175 – 50 + 25 =

175 + 25 – 50 =

Problem 1

Problem 2

a 7+2×3=

(7 + 2) × 3 =

b 10 – 8 ÷ 2 =

(10 – 8) ÷ 2 =

c 15 ÷ 3 + 2 =

15 ÷ (3 + 2) =

d 10 × 5 + 15 =

10 × (5 + 15) =

What would you need to enter on a calculator to get the answer to 4 + 3 × 5?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

When you read a word problem, things need to be done in the right order so that you arrive at the correct answer. Here is an example: Leka had ten $1 coins. He lost four coins at playtime (so he had $6). His aunty felt sorry for him and doubled the amount he had left ($6 × 2). How much did he have? ($12) To solve the problem, we could write a number sentence. However, doing the following calculation will not give the right answer: 10 – 4 × 2. Why?

Write a number sentence that would solve the problem correctly.

Write a story to suit this number sentence: (12 + 6) ÷ 3.

Join up each word problem to the correct number sentence, then solve it.

D R

AF T

A team is preparing for a tournament. Each player needs 2 bottles of water, and there are 8 players on the team. If they plan to bring 4 extra bottles for the coach, what is the total number of water bottles they need? A baker sells muffins in boxes of 8. If she prepares 7 boxes and adds 4 more muffins for display, how many muffins does she have in total? A family is planning a picnic and needs 4 sandwiches for each of the 5 family members. They also want to prepare 2 extra sandwiches for guests. How many sandwiches do they need in total? A dance class has 6 groups, with 5 dancers in each group. If 3 more dancers join the class, how many dancers are there in total? Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

(4 × 5) + 2

(6 × 5) + 3

(2 × 8) + 4

(8 × 7) + 4

Circle the important information in the problem, write the number sentence and then solve.

Each book at the fair costs $15, and you buy 3 books. If there is a discount of $10 on your total purchase, how much do you spend in total?

Maggie has 5 bags of rice, and each bag has 2 kg of rice. If she buys 4 more kilograms, how many total kilograms of rice does she have in total?

During Matariki celebrations, a d class makes 6 rows of harakeke stars, with 8 stars in each row. They weave 4 more stars to finish the display. How many harakeke stars are there altogether?

A movie theatre sells tickets for $12 each. If 7 tickets are sold and then $18 is spent on popcorn, what is the total amount earned by the movie theatre?

A farmer has 4 fields, and each field produces 20 kg of kumara. If the farmer keeps 10 kg for herself, how many kilograms of kumara does she have to sell?

D R

AF T

A school is travelling to Zealandia. Each bus carries 25 students. Four buses are used, and 5 extra adults join the trip. How many people are travelling altogether?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational Numbers

Topic 1.8 Converting fractions, decimals and percentages If you split one whole into 10 equal parts, each part is a tenth. If you split one whole into 100 equal parts, each part is a hundredth. You can show tenths and hundredths as fractions and as decimals.

one whole

one-tenth

one-hundredth

0.1

0.01

1 10

1 100

Learn Write the shaded part in words, as a fraction and as a decimal. e.g. a b 1

two-tenths

two-hundredths

2 10

AF T

0.2 d

Shade the diagrams to match the decimals.

0.4

Write these as decimals. 23 3 b 100 10

Write these as fractions.

0.6

D R

0.04

0.15

0.77

tenths

0.7

3 100

0.08

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

0.99

Write the following decimals in the place value columns, then convert each decimal into a fraction. ones

tenths

hundredths

thousandths

c 0.012

d 0.345 =

e 0.678

f 0.901 =

g 0.234

b 0.789 =

D R

a 0.456

0.319

319 1,000

AF T

Hint: The column the number ends in tells you the denominator to use. For example, 0.319 ends in the thousandths column, so it can be written as a fraction out of 1,000.

Write the following fractions as decimals.

629 = 1,000

54 100

6 10

792 1,000

67 100

24 1,000

403 = 1,000

9 1,000

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

The amount shaded is:

The symbol % stands for per cent. It means out of a hundred. 1% means one out of a hundred. It can be written as a fraction, as a decimal or as a percentage.

1 fraction 100

0.01 decimal 1%

percentage

Explore

Fraction

Decimal

Percentage

Fraction

Percentage

Fraction

100

Decimal

AF T

Write each shaded part as a fraction, as a decimal and as a percentage.

Fraction

D R

Another way of saying 100% is 1, or one whole.

Fraction

Decimal

Percentage

Shade the grid. Fill the gaps. Fraction

20 100

Fraction

Decimal

Percentage

Fraction Decimal Percentage

Fraction

15%

55 100

Decimal

75%

Percentage

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Fill in the gaps to match the percentages, decimals and fractions. 30%

1 0.5

0 0

1 10

Complete the table. Fraction a

Decimal

5 100

25%

c d

0.75 99 100

AF T

e f

40% 2 100

0.3

10% =

0.01 < 1%

0.2 = 25

35% = 35

7 < 75% 10

0.9 > 9%

2 > 20% 100

1 10

100 100

95% = 0.95

100% > 1

Compare the fractions and percentages.

1 of this square 2

of this square is shaded.

Write true or false.

100%

is shaded.

of this square is shaded.

Percentage

D R

Shade the same amount of this square. Shade the same amount of this square. Shade the same amount of this square.

1 is the same 2

is the same as

% is the same

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Fill in the gaps in the table. Make sure the fractions are in their simplest form. For example,

2 1 in its simplest form is . 10 5

Fraction

Decimal

Percentage 50%

3 4

0.2 1 5

60%

D R

AF T

4 5

0.84

Write the position of the triangle on each number line.

0.06

0.04

0.07 0.05

There are 100c in $1. So, one cent is 1 of a dollar. It can also be 100 written as $0.01. Write five cents with a dollar sign and as a decimal.

Follow the instructions to colour these circles. 30% red, 0.4 blue, 30 yellow 100

Write the fraction of triangles that are green as a decimal, as a fraction and as a percentage.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational Numbers

Topic 1.9 Equivalent fractions Learn One whole

1 6 1 7 1 8 1 9 1 10 1 11 1 12

1 5

1 4

1 3

1 2

The fraction wall shows that 2 is equivalent to 1 .

What other fractions on the fraction wall are equivalent to 1 ?

Write a fraction that is equivalent to 1 but is not on the fraction wall.

Find a fraction that is equivalent to:

2 10

Shade the diagrams to show the equivalent fractions. Write the number sentences.

6 is equivalent to 3 8 4

AF T

D R

3 12

= 56

4 5

3. 9

4 is equivalent to? 5

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Divide and shade the shapes to show that: 3 is equivalent to 1 6 2

6 is equivalent to 3 . 8 4

5 0

The circle is 1 of the way along the number line. Write another fraction 4

that describes its position. b

Apart from 9 , what other fraction describes the position of the pentagon?

Write two equivalent fractions to describe the position of the hexagon.

Draw a star 2 of the way along the line.

Annie and Bridget are comparing the amount of pizza they have each eaten.

D R

AF T

Annie says she ate 3 out of the 12 equal slices, while Bridget says she ate

1 of the pizza. 4

Draw a picture to show the slices of pizza and how much Annie and Bridget ate.

Annie thinks she ate more pizza because 3 is greater than 1 (the numerator in Bridget’s fraction). Explain why Annie is incorrect.

Write the amount of pizza leftover as a fraction in 2 different ways.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

÷2 2 1 If you look at an equivalent fraction such as = , you can see that 2=1 4 2 there is a connection between the numerator and denominator. 4 2

What is the connection between the numerator and the denominator in each of these pairs of fractions? b

÷4 4 = 1 2 8

h 2 = 4 5 10

4 = 2 5 10

9 = 3 4 12

5 = 1 2 10

i 3 = 6 8 4

j 1 = 4 3 12

4 9

i 10

m 6

q 12

f 18 9

90 18

30 50 60

r 180

4 = 8 5 10

40 8

121 21

o 4

13 60

f 8 = 2 3 12

s 200

d 8

63 30

39 32

150

40 9 40

2 = 8 3 12

Equivalent fractions... Whatever you do to the top, you must do to the bottom!

49 7

l 1 = 6 2 12

AF T

Find the missing number in these equivalent fractions.

3 = 1 3 9

D R

÷2

t 500

8 24 45 50 5 30 40 45 7 50

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Show the connection between the numerators and denominators in each pair of equivalent fractions. Fill in each box. a

÷2 12 6 = 6 3

c 3 6 = 6 12

d 5 1 = 10 2

Choose a method to find two equivalent fractions for each of the following.

e 9 = 12

4 6

1 3

15 20

9 18

8 20

2 14

8 10

25 100

This robot has malfunctioned. Your task is to check whether the robot has made a correct equivalent fraction pair. If it has not, explain the mistake that has been made.

D R

AF T

Robot says: 1 4=8 Circle: Correct / Mistake Reasoning:

Robot says: 3 4 = 16 Circle: Correct / Mistake Reasoning:

Robot says: 5 = 15 Circle: Correct / Mistake Reasoning:

16 Robot says: 4 6 = 22 Circle: Correct / Mistake Reasoning:

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Divide the numerator and denominator by their highest common factor (HCF) to simplify the fractions.

16 40

÷8

Factors of 16: 1, 2, 4, 8, 16 Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 b

18 30

18 = 30

Factors of 18: Factors of 30:

Simplify the fractions. b ÷ 4 8

3 9

6 = 10

5 = 100

D R

AF T

16 = 40

Use factors to help you find the biggest number that goes into both numbers. The first question has been done for you. Fraction 8 12

Factors

Factors of 8: 1, 2, 4, 8 Factors of 12: 1, 2, 3, 4, 6, 12

Simplified fraction Divide both by 4:

2 3

15 20 18 24 4

Circle True or False. Statement

True or False

3 1 simplifies to 9 3

True

False

8 3 simplifies to 10 5

True

False

16 2 simplifies to 24 3

True

False

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational Numbers

Topic 1.10 Comparing and ordering fractions and decimals Learn 1

a b

Fill in the gaps on the number lines. 0

1 5

4 5

9 10

1 5

3 1 10

c 1 4

3 8

e f

AF T

1 3

D R

4 6

2 4

1 8

1 6

g 0

Which is closer to 1 in each pair? Use the number lines in question 1 to help.

1 3 or 4 8?

1 3 or 6 ?

1 1 or 4 8?

1 1 5 or 10 ?

1 1 or 2 3?

3 1 or 1 4 2?

1 or 9 ? 5 10

5 1 or 8 2?

7 or 7 ? 8 10

Which fractions are the same distance along the number line as 2 ?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Use the number lines from question 1 to help you order each group from smallest to largest.

1 1 , 4 , 1 , 1, 3 , 2 5 5 5 5 5 7 , 3 , 1, 9 , 2 , 6 10 10 10 10 10 1, 1, 13, 1 , 1 2 4 8 10 5 3, 3 , 3, 3, 3 8 10 4 6 3 2, 2, 2, 2 , 2 5 8 3 10 6

b c d e

Use the symbols > (greater than), < (less than) or = (is equal to) to complete these number sentences.

3 4 2 3 9 10

e h

1 4 3 8 3 5

1 8 1 2 6 10

AF T

D R

7 8 2 6 4 5

f i

13 6 2 4 15 6

11 2 5 8 12 3

b c

Circle the two fractions that describe the position of the triangle on the number line. 6 and 6 6 and 1 6 and 3 8 10 8 4 8 4 Circle the fraction that describes how far from 1 the triangle is. 2 2 2 3 8 4 3 Draw a diamond that is of the way from 0. 8

Circle the largest fraction in each pair.

13 or 6 30 15 3 or 10 8 24

c 62

b d

17 or 9 40 20 5 or 17 14 42

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

When comparing decimals, look at the tenths place first, then the hundredths (then the thousandths, if needed)

Comparing decimals

Which is bigger: 0.135 or 0.55? Many people think 0.135 is bigger than 0.55 because 135 is bigger than 55. Think about it carefully. 0.55 means 5 tenths and 5 hundredths. 0.135 means only 1 tenth, 3 hundredths and 5 thousandths. Therefore, 0.55 > 0.135.

Explore Compare these decimals using <, > or =.

0.412

0.421

2.005

2.05

0.8

0.799

1.250

1.25

0.037

0.073

3.142

3.14

0.600

0.6

0.287

0.278

7.305

7.35

0.004

0.04

1.003

1.03

2.750

2.705

0.450

0.405

8.230

8.23

9.207

9.027

Order these fractions from smallest to largest.

D R

Mixed list

AF T

Ordered list (Smallest to largest)

2.3, 2.03, 2.30, 0.23 4.005, 4.5, 4.05, 4.500 0.807, 0.78, 0.8, 0.708 5.6, 5.06, 5.606, 5.60 7.09, 7.9, 0.709, 7.090 1.234, 1.24, 1.204, 1.2 3

Explain why these statements are true or false. Statement

Your explanation

6.70 < 6.7 0.513 > 0.8 5.093 < 5.12 Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

A marine biologist measured the lengths of five baby green sea turtles/honu at a coastal rescue centre. Look at the data table to answer the questions. Name

Length (m)

Koru

0.745

Rangi

0.701

Hina

0.75

Moana

0.748

Tui

0.695

Who is longer: Koru or Moana? Explain how you know this using place value.

Order the turtles from shortest to longest by numbering them in the “Order” column.

A new turtle, Manu, is measured and found to be longer than Moana but shorter than Hina. Give one possible length (to three decimal places) Manu could have.

True or False: Moana is the longest turtle because it has the biggest number after the decimal points (748). Explain why or why not.

Four swimmers raced in a 50-metre freestyle. Their times were recorded.

Swimmer

Time

Who was the fastest swimmer?

Noah

24.306

Tama

24.152

Kiran

24.300

Fine

24.159

D R

AF T

Order the swimmers from fastest to slowest. Write their name and time in the boxes. 1st place

Order

2nd place

3rd place

4th place

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Two friends played a video game. Their accuracy scores are:

• Marcello: hit 8 out of 25 targets • Mia: hit 15 out of 20 targets. Who had the higher accuracy percentage? Hint: Convert both fractions to percentages to compare. Marcello

Mia

Fraction: 18 25

Fraction: 15

Percentage: 2

Percentage:

A jacket originally costs $80. Shop A offers “

1 off the price”. Shop B offers 4

“20% off the price”. Does A or B give the bigger discount in dollars?

AF T

Extra for experts: Can you work out how much money you would save at

D R

each shop?

A shop is selling two brands of orange juice. • Brand A: 3 litres for $6.30 • Brand B: 2 litres for $4.80

Which brand is the better value? Show your working to compare the price per litre.

Order each row from smallest to largest.

0.03

20%

2 100

0.05

1 2

55 100

1 4

40%

70%

0.07

10%

0.01

3 4

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

0.5

0.04 11 100 65

Number | Rational numbers

Topic 1.11 Mixed numbers and improper fractions Mixed numbers and improper fractions A mixed number is a mix of a whole number and a fraction. An improper fraction (sometimes called a “topheavy” fraction) has a numerator that is greater than or equal to the denominator.

1 2— 2

5 — 2

Learn For the following images, write the shaded fraction as both a mixed number and an improper fraction. Mixed number

Improper fraction

D R

Shaded shape

AF T

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Changing a mixed number to an improper fraction Each whole has 4 quarters, and you have 5 wholes. 5 × 4 = 20 (quarters) 1 1 21 Plus, the original : 5 = 4 4 4

How many quarters 1 are there in 5 ? 4

Explore 1

Convert these mixed numbers into improper fractions.

3 4

1 3

1 2

2 7

6 8

2 5

Improper fraction

D R

Working out

AF T

Mixed number

At a class party, the teacher sliced the pizzas into 8 slices each. At the end of the party, there were 19 slices left over. Write this amount as an improper fraction and a mixed number.

Write the missing mixed numbers and improper fractions on the number line. 4 4 1

6 4 1

1 4

7 4 1

3 4

9 4 2

1 4

11 4 2

2 4

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

12 4

3 4 67

Changing an improper fraction to a mixed number 10 3 = 2 (wholes) with left over 5 5 13 3 How many wholes are there =2 5 5 in the improper fraction? How much is leftover?

Convert these improper fractions into mixed numbers. Improper fraction

Working out

Mixed number

11 4 16 3 25 6

AF T

24 7

D R

15 2 33 5

Mrs Hamilton bought 3 whole blocks of chocolate and one-half block for a baking project. She needs to break them all into halves to melt them easily. How many half-blocks (improper fraction) does she have in total?

Write the missing mixed numbers and improper fractions on the number line. 5 5 1

6 5

7 5 1

8 5

9 5

11 5

3 5

4 5

1 5

2 5

13 5

14 5

15 5

3 5

4 5

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational Numbers

Topic 1.12 Multiplying and dividing by 10, 100 or 1,000 When you multiply a decimal by 10, the digits shift one place to the left, making the number ten times greater. ×10 It is important that you ESTIMATE your answer. 3.45 × 10 = 3 .45 = 34.5

The digits move left one place.

3 × 10 equals 30, so you would expect your answer to be in the 30s. We don’t usually put a zero unless it is necessary.

Learn a 45 × 10 =

b 4.5 × 10 =

a 74 × 10 =

b 7.4 × 10 =

a 375 × 10 =

b 37.5 =

a 629 × 10 =

b 62.9 × 10 =

AF T

D R

When you divide a decimal by 10, the digits shift one place to the right, making the number ten times smaller. ÷10 It is important that you ESTIMATE your answer. 96.4 ÷ 10 = 96. 4 = 9.64

The digits move right one place.

90 equals 9, so you would expect your answer 10 to start with a 9.

a 350 ÷ 10 =

b 35 ÷ 10 =

a 740 ÷ 10 =

b 74 ÷ 10 =

a 870 ÷ 10 =

b 87 ÷ 10 =

a 930 ÷ 10 =

b 93 ÷ 10 =

a 32.6 × 10

b 2.35 × 10

c 7.892 × 10

d 65.2 × 10

a 23.5 ÷ 10

b 42.75 ÷ 10

c 3.5 ÷ 10

d 0.2 ÷ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

When you multiply a decimal by 100, the digits shift two places to the left, making the number one hundred times greater. ×100 It is important that you ESTIMATE your answer. 3.45 × 100 = 3 .45 = 345

The digits move left two places.

3 × 100 equals 300, so you would expect your answer to be in the 300s. If there is no number to “jump over”, add in a zero.

Explore Solve these multiplication problems. a 3.5 × 10 =

b 3.5 × 100 =

a 6.7 × 10 =

b 6.7 × 100 =

a 5.38 × 10 =

b 5.38 × 100 =

a 4.09 × 10 =

b 4.09 × 100 =

AF T

96.4 ÷ 100 = 96. 4 = 0.964

The digits move right two places.

D R

When you divide a decimal by 100, the digits shift two places to the right, making the number one hundred times smaller. ÷100 It is important that you ESTIMATE your answer. 90 equals 0.9, so you would expect your answer 100 to be near this.

Solve these division problems. 5

4.5 ÷ 10 =

b 4.5 ÷ 100 =

7.9 ÷ 10 =

b 7.9 ÷ 100 =

54.5 ÷ 10 =

b 54.5 ÷ 100 =

62.7 ÷ 10 =

b 62.7 ÷ 100 =

Solve these multiplication problems. a 2.45 × 100 =

Solve these division problems. a 3,416.1 ÷ 100 =

b 17.37 × 100 = b 0.1 ÷ 100 =

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

If we just added a zero to multiply $1.50 by 10, the answer would be $1.500 – and that’s not correct!

The ten trick Multiplying by 10 in your head is easy, but you don’t just add a zero! 14 7

140

$1.50

35 725

× 10

70 350

Deepen

Complete the table.

100

1,000

e.g.

370

3,700

37,000

124

6.38

$1.25

750

÷ e.g.

7,250

120

AF T

Complete the table.

$15.00

100

1,000

120 ÷ 100 = 1.2

120 ÷ 1,000 = 0.12

4.5

45 ÷ 100 = 0.45

45 ÷ 1,000 = 0.045

D R

820

370

4,700

258

$22.50

5,432.169

Look at the number and answer the questions.

Which digit is in the thousandths place?

Which digit is in the tenths place?

Which digit is in the hundredths place?

If you divide this number by 1,000, what is the new place value of the digit “5”?

A 3,500 metre racetrack is divided into 1,000 equal sections for marking. How long is each section in metres?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.13 Adding and subtracting fractions Working with fractions is like working with numbers when you first started school.

How many? 3 What are they called? apples

A fraction such as 1 4 tells you the name of the fraction (denominator) and the number of parts that you have (numerator).

numerator 4 denominator

number name

How many? What are they called?

It works in the same way for subtraction.

Learn You can add and subtract fractions with the same denominator just as you do with ordinary objects. = +

2 apples

Fill in the gaps.

1 quarter + 1 quarter = +

+ 1

2 quarters

1 4

2 4

1 eighth + 2 eighths = +

fifths

1 4

3 4

eighths

2 sixths + 3 sixths =

3 quarters

–

e 3 4

1 quarter

3 apples

quarters

2 fifths + 2 fifths =

1 4

AF T

1 apple

D R

3 4

3 quarters

sixths

–

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Write the number sentence.

e.g.

+ 1 4

2 4

3 4

= =

Use two colours to shade each diagram, to match the number sentence. a

1 3 5+5=

3 4 8+ 8 =

2 5 + 10 10 =

AF T

1 3 e.g. 2 4+4=4 2 2 6+ 6 =

1 2 3+3=

Use the diagrams to help complete the subtraction sentences.

D R

e.g. 3 – 2 = 1 4

✕✕

5 2 8–8=

9 3 10 – 10 =

6 5 6–6=

3 1 5–5=

2 1 3–3=

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Adding and subtracting like fractions (such as 3 – 1 ) 4

is as easy as working out 3 jelly beans – 1 jelly bean. With unlike fractions, we need to make the denominators the same before we can add or 4

subtract. In the example, we turn 4 into 8 by multiplying both parts of the fraction by 2.

5 2 8 + 4

5 4 8 + 8

3–1=2 4 4 4

9 1 8 or 1 8

Explore Change the first fraction so both fractions have the same denominator. Then add or subtract the fractions to find the answer.

Answer

AF T

Add together 1 3 2+4 4 1 + 5 10 2 1 3−6 1 7 6 − 12 4 5 6 + 18

D R

Whatever we do to the bottom, we must do to the top!

3 +2= 16 8

5 + 3 = 10 20

2 2 5 + 25 =

3+ 2 = 7 35

7 3 12 + 6 =

2 5 18 + 9 =

1+4= 6 3

5 + 5 = 10 40

4 = 3 8 + 16

7–3= 8 4

8–2= 9 3

11 – 1 = 12 4

3–1= 4 2

11 – 3 = 14 7

9 – 3 = 10 5

2–4= 3 9

5–1= 6 3

4 – 3 = 5 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Solve the following.

7+1= 8 4

9 +1= 10 5

12 +5= 3 6

23 +5= 4 8

1 7 +4 = 5

37 +2= 9 3

Solve the following.

15 –3= 8 4

2 3 –1 = 2

1 5 –1 = 2

12 –5= 3 6

23 – 11 = 4 2

1 1 –2 = 3

Shade the diagram to solve the addition problem. Write a number sentence that matches the problem.

AF T

D R

Use improper fractions and mixed numbers if the answer is

7+5= 8 8

5+7= 9 9

8 + 8 = 12 12

3+3= 4 4

5 + 4 = 6 6

5+3= 8 8

greater than one whole. For example, 3 + 2 = 5 = 11 . 4 4 4 4

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

You could use pictures or number lines to help with these.

Deepen From the way this cake is arranged, it is obvious that the slices will add together to make a whole cake.

5 18

2 9

1 6

Prove that these pieces can also be added together to make a whole cake. (Hint: Look at the size of each fraction.)

1 3

AF T

Write each answer in its simplest form.

9 +3= 10 5

5= 31 – 1 4 8

15 + 7 = 6

1 13 – 1 =

2 5 +3 4 = 12

32 – 21 = 3 6

21 +1 1 = 3 6

3 = 54 – 3 10 5

At a party, there are parts of four pavlovas left over. One pavlova was split into quarters, but the others were split into different fractions. The total amount left is one and one-sixth. What fraction of each pavlova might be left?

D R

100

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.14 Adding and subtracting decimals You can add or subtract decimals just like you do with whole numbers. 3

+ 1

4 8 7

But if there is a different number of columns, it is important to line up the numbers according to their place value. 2

+ 1

D R

Find the answers. 3

+ 5

2 9

8 2 8 7

The decimal point doesn’t make much difference to the way you work, but it makes a BIG difference to the answer.

AF T

Learn

23 + 60 = 83, so the answer will be close to 83.

3 + 2 = 5, so your answer will be close to 5.

Round 23.17 to 23. Round 59.7 to 60.

Round 3.14 down to 3. Round 1.73 up to 2.

4 8 7

Use rounding and estimating to check your answers.

+ 1

Use place value to line up the numbers and calculate the answers. Use estimating or rounding to help check your answers.

16.5 + 12.4

85.6 − 20.3 –

12.47 + 11.9

5.86 − 2.3 –

24.74 + 8.64 +

36.25 − 9.27 –

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Calculate the answers.

+ 2

– 2

65.45 – 5.24

+ 3

– 1

Add $323.79 and $107.35.

Find the total of 2.54 m, 17.7 m and 34.67 m.

+ 2

– 3

46.7 – 29.28 –

D R

–

68.72 – 32.8

–

AF T

Subtract $329.65 from $400.

By how much is 3.463 kg less than 5 3 kg? 4

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Use rounding to help you estimate the answer for each problem (to the nearest whole number), then use column addition to solve each one.

24.07 + 7.54

Estimate:

829.29 + 73.78 Estimate:

Actual:

Actual: d

607.24 – 23.17 Estimate:

–

490.23 − 164.64 Estimate:

AF T

−

Actual:

D R

Actual:

Find the answer to each problem.

365.12 + 189.62 =

734.18 – 408.41 =

−

154.32 – 87.58 =

−

276.47 – 150.82 =

−

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Solve the following word problems. Show your working. Problem Show your working here The rainfall in Alexandra was measured over 3 days: 58.2 millimetres on Monday, 44.5 millimetres on Tuesday and 78.6 millimetres on Wednesday. What was the total rainfall over these three days? Wil went on a bike ride. He travelled 20.1 kilometres in the morning and 14.25 kilometres in the afternoon. The next morning, he rode another 7.82 kilometres. How far did Wil travel in total?

AF T

Isla went shopping for her school supplies. She bought a notebook for 75c, a pack of pens for $3.20 and a ruler for $1.45. How much did she spend in total?

D R

A school raised money through a bake sale. They made $120.50 on the first day, $95.75 on the second day and $82.40 on the third day. How much money did the school raise in total?

Some cafés show their prices using just one decimal place. Using the normal way of writing money, find the cost of:

a small coffee and a large muffin

a large coffee and two fruit scones

a small and a large coffee, a small muffin and two plain scones

a large coffee and one plain scone

two large coffees, one plain scone and two fruit scones.

Menu Coffee Small: $3.2 Large: $3.9 Muffins Small: $2.4 Large: $4.7 Scones (2 per serve) Plain: $3.7 Fruit: $4.2

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

The answer to this equation is 9.18. Try to find at least two ways of filling the gaps to complete the equation.

+4.

. 36 = 9.18

+4.

. 36 = 9.18

Did you know that your skin weighs almost as much as your bones? This table lists the mass of the eight largest organs in an adult who weighs 68 kg.

ewrite the table, listing the R organs from heaviest to lightest. Organ

Mass 0.315 kg

Lungs

1.09 kg

Skin

10.886 kg

Pancreas

0.098 kg

Brain

1.408 kg

Spleen

0.17 kg

Liver

1.56 kg

Kidneys

0.29 kg

D R

Heart

Mass

AF T

Organ

Find the total mass of the heart and lungs.

How much heavier is the skin than the brain?

The mass of which organ is closest to the mass of the kidneys?

The right lung is 0.07 kg heavier than the left lung (to make space for the heart). What might the two masses be?

What is the difference between the mass of the lungs and the mass of the pancreas?

The mass of an adult male gorilla is about 240 kg, but his brain weighs only 0.465 kg. How much heavier is a human brain than a gorilla’s brain?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.15 Using fractions Find a non-unit fraction of a whole number When asked to find a fraction of a whole number, find the “unit fraction” first, then multiply. e.g. Find

3 of 32 8

1 of 32 = 4 8 3 So, of 32 = 12 (because 4 × 3) 8

Learn Fill in the table. Question

Find the unit fraction

Solve

2 of 18 3

1 of 18 = 6 3 (18 ÷ 3 = 6)

2 of 18 = 12 3 (2 × 6 = 12)

AF T

D R

5 of 36 6 3 of 32 8 4 of 50 5 2 of 48 3 3 of 56 7 2

Match the question with the correct answer. 3 of 28 4

2 of 75 5

7 of 81 9

4 of 54 6

5 of 60 10

3 of 42 6

8 of 90 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Solve these fractional word problems.

A wildlife sanctuary

A marae prepared

A school made 48

is caring for 45

60 pākete kai

panikeke (Samoan

kororā (little penguin). 2 of 9 them are chicks.

(food parcels) for a

pancakes) for a

How many kororā

festival. Volunteers delivered 4 of 5 them before

school fair. By midday, 3 of them 4 had been sold. How

chicks are there?

lunchtime. How

many panikeke were

many pākete kai

sold?

were delivered?

A ferry can carry 120 passengers. On a busy day 5 it was filled to 6 of its capacity. How many passengers were on board?

A school library

has 200 books about New Zealand history and pūrākau. Students have borrowed 3 10 of them. How many

A science class

sorted 36 fossils. 2 of them were 3 plant fossils. How

Scientists found 90 alpine buttercup

were there?

were not flowering?

AF T

many plant fossils

plants on Mt Ruapehu. 1 were 5 flowering. How many

D R

A concert venue sold 800 tickets. 7 of the tickets 8 were sold before the weekend. How many tickets were sold early?

A charity packed 150 care parcels. Volunteers completed 2 of the parcels 5 before lunchtime. How many parcels were finished by lunch?

books have been borrowed?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Finding a whole set from a fractional part of a set

Sometimes we know a part of a group, but we need to find the whole amount. 8 Example 8 is 2 of a set. What is the whole set?

6 Find 1 : Since 2 parts = 8, we divide 8 ÷ 2 = 4. 6

Find 6 : Since 1 part 6

(6) 1

Total = ?

is 4, the whole set is 4 × 6 = 24.

Explore Fill in the table.

9 is 3 of a number. 4 16 is 2 of a number. 5

Find what 1 part is

AF T

The problem

3 = 9, so 4

1 must equal 3. 4

D R

Multiply to full number

3 × 4 = 12

27 is 3 of a number. 4 24 is 4 of a number. 7 18 is 2 of a number. 3 40 is 5 of a number. 8 14 is 7 of a number. 10 36 is 3 of a number. 5 45 is 3 of a number. 4 84

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Find the whole set from the fractional part.

Akira received 1 of the prize, which meant she received $24. What was 3

the total prize amount? b

Ken used ribbon to wrap a present. He used 2 of the ribbon, which was 5 40 cm. How long was the original ribbon?

Farmer Mere lost her records. Calculate the whole flock size for the known flocks, then create your own puzzle for the last flock. The clue

Whole flock size

3 of the flock is 24 sheep. 5

D R

4 of the flock is 32 sheep. 6

AF T

2 of the flock is 18 sheep. 3

4 A kiwifruit packing shed has filled some crates, but

the total order isn’t finished. Calculate the total order size based on what is already packed.

The workers have packed 45 crates, which is 5 of 8 the total order. a

What is the total number of crates needed?

They have sorted 420 kg of fruit, which represents 7 of the morning’s 8

harvest. How much does the total morning harvest weigh? 5

The All Blacks have played 60 minutes of a game. This is 3 of the total game time. 4

How long is the total game in minutes?

How many minutes are left to play?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Find the non-unit fraction of these whole numbers.

Find the whole set or amount of the following.

3 of 32 = 4 5 of 30 = 6 3 of 40 = 8 4 of 27 = 9 3 of 35 = 5

2 of a number is 10. 5 3 of a number is 21. 4 5 of the class is 25 students. 6 4 of a number is 20. 9 2 of a number is 14. 3

A shearer has finished 3 4 of a flock of 24 Romney sheep. How many sheep have been shorn?

c d e

A photographer edited 1 of the 4

photos from a shoot. This was 13 images. How many photos were taken in total?

D R

AF T

A teacher prepared 45 science kits. 2 of the 3

kits were handed out to students. How many kits were given out?

Find the mystery numbers. a I am thinking of a number. 3 of my number is 24.

A painter completed 2 of a mural, 3

which measured 14 metres of painted wall. How many metres is the whole mural?

What is 1 of my number? 2

b I am thinking of a number. 2 of my number is 16. 3

What is 3 of my number? 4

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.16 Using percentages Finding percentages Use these tricks to find them quickly! 1 . To find it, divide by 2. (2) • 25% is the same as one quarter 1 . To find it, divide by 4. (4)

• 50% is the same as one half

• 10% is the same as one tenth

1 . To find it, divide by 10. ( 10 )

Learn Complete this table.

40 120 80 160

Find 50%

Find 25%

Find 10%

AF T

Number

D R

28 76 52 2

Follow the instructions to colour these diamonds. 30 yellow, 5% green, 5% white 40% red, 20% blue, 100

There are 20 beads on the string. Colour them in these percentages: 50% red, 25% blue, 25% yellow.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Calculate the new prices of these objects after being discounted. Object

Discount

Pants $60

50%

Earrings $40

25%

Cap $45

10%

AF T

Trampoline $900

The store manager needs to decide which discount is the best deal for the customer. Look at the options and determine the final price. Item

D R

New price

Option A

Option B

Skateboard $120

Take 50% off

Take $55 off

Sneakers $200

Take 25% off

Take $40 off

Video game $80

Take 10% off

Take $10 off

Which is the better deal?

A bike shop has 240 helmets in stock. They put 25% of the helmets on clearance. How many helmets are on clearance?

A fundraiser raised $1,200. They plan to give 10% of the money raised to a local shelter. How much money will the shelter receive?

A school ordered 180 juice boxes for a sports day. The students drank 50% of them by lunchtime. How many juice boxes were drunk? Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Finding percentages Use these tricks to find them quickly: • 1% is the same as 1 . Divide by 100. 100

• 20% is double 10%. Find 10%, then double it. • 75% is 50% + 25%. Find half, find a quarter, and add them together. Or, find a quarter and subtract it from the whole (100% − 25% = 75%).

Explore Fill in the table. Number

Find 1%

Number

Find 20%

Number

450

390

240

270

420

700

100

900

600

AF T

200

D R

Find 75%

The local rugby team played 20 games this season. They won 75% of their games. How many games did they win?

Of 400 people, 20% were sick. How many people were sick?

A garden centre has 240 flower pots. They discount 20% of the pots for a clearance sale. How many pots are on clearance?

A bookstore received an order of 300 new novels. They set aside 1% for a special display. How many novels are in the display?

A catering company prepared 600 sandwiches for an event. Of the sandwiches, 1% were vegetarian. How many vegetarian sandwiches did they make?

A hotel has 160 rooms. During a renovation, 75% of the rooms are closed for repairs. How many rooms remain available?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

If someone offers you 50% of their apple, it’s the same as offering a half. Complete the table to show what you would get if you were offered these items. Item

Percentage offered

Box of 20 doughnuts

50%

Pack of 50 pencils

10%

Tin of 80 lollies

25%

Bag of 1000 marbles

Fraction

Number

In some situations it is possible to have more than 100%.

If you cut a 1-metre piece of string and Sally said she needed a second piece that was 50% of the length of the first one, how long would it be?

If Sally asked for another piece that was 100% of the length of the first one, how long would it be?

If Sally asked for a fourth piece that was 200% of the length of the first one, how long would it be?

Draw a line to connect the percentage calculation with the correct answer.

D R

AF T

50% of 80

25% of 80

10% of 80

1% of 800

75% of 80

You are organising a class party for 30 students. 50% of the class wants pizza, 20% wants sushi and the rest want burgers.

How many students want pizza?

How many students want sushi?

How many students want burgers?

A giant bag of lollies contains 500 pieces. 1% of the lollies are blue. How many blue lollies are in the bag?

A baker made 60 cupcakes. He sold 20% of them in the first hour. How many cupcakes did he sell?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Finding the whole (100%) 50% is the same as 1 (half). 2

To find the whole (100%), multiply the part by 2. 25% is the same as 1 (one quarter). 4

To find the whole (100%), multiply the part by 4. 10% is the same as

1 (one tenth). 10

To find the whole (100%), multiply the part by 10.

Deepen

100% = ? 50% = 12

100% = ?

50% of a number is 12. What is the number?

AF T

Answer the following questions.

D R

25% of a number is 9. What is the number?

25% = 9

100% = ?

10% of a number is 6. What is the number?

10% = 6

50% of a number is 104. What is the number?

10% of a number is 30. What is the number?

The price of a game has been lowered by $15. This is a 25% discount. What was the original price of the game?

Cirie has read 40 pages of her book. This is exactly 20% of the book. How many pages are in the whole book?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Financial mathematics

Topic 1.17 Money

“Percent of” questions about money Percentage as a fraction

Example

50% =

1 2

Find 50% of $280 (

25% =

1 4

10% =

1 10

Calculation

1 of $280) 2

$280 ÷ 2 = $140

Find 25% of $80 (

1 of $80) 4

$80 ÷ 4 = $20

Find 10% of $60 (

1 of $60) 10

$60 ÷ 10 = $6

Learn What is 50% of…?

$20

$100

$84

$102

$264

$520

What is 25% of…?

$100

$44

$60

$28

$240

$888

What is 10% of…?

$80

$200

$68

$490

$93

$745

Fill in the gaps in the following table. Amount

D R

AF T

50%

$40

25%

10%

$10 $120 $110

$168 $5 92

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

A bookstore has the following six books newly available. Little Train

Bear

The Kite

Why?

Alien Dancer

My Pony

$9.50

$5.60

$12.80

$9.40

$14.30

$17.60

If you bought “The Kite”, how much change would you get from $20?

Is $35 enough money to buy the two most expensive books?

You have $20 and buy two books. You get 10c change. Which two books did you buy?

If you have $20, do you have enough money to buy books C and D?

How much more does “Little Train” cost than “Bear”?

Hine bought three native trees from the nursery. They cost $45.60, $65.10 and $31.30. Estimate, then calculate how much Hine spent.

What is the difference between the estimated cost and actual cost of Hine’s plants in question 2?

D R

AF T

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Year 6 want to raise money for an end-of-year party. They decide to buy fruit, cut it up and sell 100 fruit salads at a stall on “Fruit Salad Friday”. They want to make a profit. This means that they sell the fruit for more than it costs to buy it. The less it costs to prepare the fruit salad, the more profit they will make.

Look at the sign. How much money will Year 6 take at the stall if they sell all 100 fruit salads?

If the fruit costs $150 to buy, Year 6 will not make any profit. How much profit will they make if the cost of the fruit is:

$100?

Year 6 decide to cut up five fruits into the fruit salads. How much would it cost if they bought:

1 kg of each fruit

$50?

$25?

AF T

$75?

D R

Oranges $3/kg

Bananas $2/kg

2 kg of each fruit

500 g of each fruit

5 kg of each fruit?

Flora’s Fruit Shop offers a 10% discount if Year 6 buy 10 kg of each fruit.

What would be the total price before discount if Year 6 bought 10 kg of each fruit?

What is the 10% discount?

What would be the new price of the fruit?

If Year 6 bought 5 kg of each fruit, how much profit would they make?

Grapes $10/kg

Pears $2.50/kg

Apples $4/kg

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Year 6 want to make a profit of at least $50, so they don’t want to spend more than $100. If they buy 5 kg of each fruit, how much over their budget are they?

Year 6 need to spend less on the fruit. They decide to buy only 2.5 kg of grapes.

Circle the amounts that describe 2.5 kg compared to 5 kg. 50%

a quarter

a half

How much do 2.5 kg of grapes cost?

Flora’s Fruit Shop send the fruit along with an invoice to show how much Year 6 owe.

Write the total price of all the fruit.

Year 6 can get a 10% discount. Fill in the amount of the discount.

25%

Quantity

Price per kg

Cost

Apples

5 kg

$4.00

$20.00

Pears

5 kg

$2 .50

Oranges

5 kg

$3.00

Bananas

5 kg

$2.00

Grapes

2.5 kg

$10.00

Description

AF T

Write the cost for each type of fruit.

0.75

Flora’s Fruit Shop

D R

0.5

Total 10% discount if you pay on time. Discount

Write the new discounted total.

How much under their $100 budget will Year 6 be after buying the fruit?

Cups: $16.5 The students need to buy 100 bamboo 0 for 100 spoons and either 100 bamboo bowls or 100 bamboo cups. Calculate the price and profit for each option.

Discounted total

0 Bowls: $22.0 for 100

Spoons: $5.5 0 for 100 Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

GST is a tax that has to be paid for some purchases. In New Zealand, GST is 15% but other countries have different percentages. For example, GST in Australia is 10%. A percentage of the cost is added to the price. The percentage can change.

Bo’s Bamboo Item

Quantity

Unit price

Cost

Spoons

100

$5.00

Cups

100

15c

$15.00

Total price of goods

$20.00

GST (10%) Total:

Deepen The class used spoons and cups. On Fruit Salad Friday, GST was 10%. Fill in the GST amount and total on the receipt.

Two furniture shops are selling the same tables and chairs. One shows the price without GST. The other shows the price including GST.

AF T

D R

Fill in the amounts to see which shop has the better price for a table and four chairs.

Table $120 plus GST

Chair $20 plus GST

Furniture World Item

Quantity Unit price Cost

Table $130

Chair $21.50

Furniture For You Item

Quantity Unit price Cost

Table

$120.00

Table

$130.00

Chairs

$20.00

Chairs

$21.50

Price of goods

Total price of goods (including GST)

GST (10%) Total:

Both shops have an end-of-year sale. They offer 10% off the final prices. What is the new price for a table and four chairs at each shop?

Furniture World:

Furniture For You:

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Algebra | Equations and relationships

Topic 2.1 Number Sentences Learn 1

Fill in the gaps to complete the number sentences.

+ 17 = 32

58 –

= 44

– 23 = 61

35 +

= 89

× 8 = 48

7×

= 56

= 9

÷ 5 = 11

78 – 46 = 19 +

= 96 + 15

63 ÷

26 + 34 = 100 –

147 –

Find the missing number to make the sentence true. Write the missing number in the box.

15 +

20 − 3 =

e 3

+ 83 = 180 – 32

D R

AF T

= 45

62 –

= 30

+ 2

3 × (

+ 2) = 18

÷ 2 = 14 + 1

50 −

Identify the accuracy of each equation. If it is incorrect, write a new equation by changing only one number to make it true. Equation

True / False?

Correction (if false)

8 × 5 = 20 + 25 36 ÷ 6 = 12 ÷ 2 100 − 25 = 50 + 15 7 × 3 = 30 − 8 64 ÷ 8 = 3 × 2 Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Order of Operations and inequalities Greater than

GEMA

Grouped operations inside backets, ()

Exponents such as squaring, a2

Multiplication and division, from left to right

Addition and subtraction, from left to right

Less than <

Remember the alligator always wants to eat the larger food

Solve these equations using GEMA.

5+3×4=

20 ÷ (2 + 3) × 2 =

(10 − 2) ÷ 4 =

4² + 6 ÷ 3 =

6² − 10 =

(3 + 4)² − 10 =

20 − 2 × 3 =

40 ÷ 4 + 3 =

Circle true or false.

8 + 2 × 4 < (8 + 2) × 4

True False

24 ÷ 6 − 3 > 24 ÷ (6 − 3)

True False

3 × 10 – 5 > (3 × 10) – 5

True False

(12 + 6) ÷ 3 + 3 < 12 + (6 ÷ 3) + 3

True False

Place the correct symbol (<, > or =) between the two expressions to make the statements true.

6×3

30 − 5 × 2

2+3×6

4×5+1

3×7

D R

AF T

4²

(10 + 2) ÷ 2

8² ÷ 8

2×3 2³

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Investigate the number sentences. Do the calculation for each side to see if the statement is True or False. Circle your answer. Number sentence

Your calculations

True

False

5² – 5 > 20

True

False

2 × (3 + 4) = 14

True

False

8 × 7 < 8 × 5 + 4²

True

False

100 ÷ 10 ÷ 2 = 5

True

False

6 + 4 × 3 = 18

True

False

7² − 6 > 40

True

False

84 ÷ 7 ÷ 2 = 6

True

False

10² − 15 > 80

True

False

7×5>6×6+2

True

False

8² − 7 < 60

True

False

Two other inequality symbols are:

≥ greater than OR equal to.

D R

≤ less than OR equal to 2

Verdict

4 + 3 × 2 = 14

AF T

Evaluate each side of the number sentence using the order of operations. Then decide if the statement is correct. Number sentence

Solve left side

Solve right side

Correct? (✓/✕)

8 × 7 ≤ 8 × 5 + 4² 15 + (3 × 2) ≥ 7 × 3 100 ÷ 10 + 5 ≤ 3 × 5 6² ÷ 4 ≥ 5 + 4 3

Fill in the missing number to make each statement true. There might be more than one correct answer, but just find one that works. 4×

+ 2 ≤ 22

(20 ÷

) + 8 ≥ 12

3² +

=5×4−2

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Rewrite as number sentences and solve.

When this number is added to 42, the answer is the same as 31 plus 27. What is the number? Number sentence: 42 +

When this number is subtracted from 73, the answer is the same as 26 + 23. What is the number? Number sentence: Create your own number sentence using at least three operations (choose from +, −, ×, ÷ exponents) that results in the following answers.

24 15

Number sentence

AF T

Answer

D R

120

Write number sentences to show the following statements.

The answer remains the same if you change the order of numbers in addition.

The answer remains the same if you change the order of numbers in multiplication.

Addition and subtraction are related. One “undoes” the other.

Multiplication and division are related. One “undoes” the other.

100

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Can you think of more than one way to solve each problem?

Write number sentences to solve.

Sua had 12 boxes with 6 eggs in each. How many eggs in total?

Rosalia wrote a poem of 8 lines with 9 words in each line. How many words altogether?

Manaia collected 15 football cards. Cruz has 6 times more cards than Manaia. How many cards does Cruz have?

Each classroom shelf holds 7 books. If the teacher puts 49 books away, how many shelves has he filled?

AF T

The chef made 54 grams of meringue mix. How many meringues can she make if each one uses 6 grams of the mix?

D R

Wairangi completes 28 pieces of a puzzle on Sunday and 32 on Monday. She still has 10 times as many pieces left. How many pieces has she got to go?

Write your own word problem for the following.

110 ÷ 11 = 10

6 × 32 = 192

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

101

Algebra | Equations and relationships

Topic 2.2 Growing patterns 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Coming, ready or not!

We use number patterns every day. You probably learned your first number pattern before you started school.

Learn

Rule: Increase by 2 each time. Continue the pattern. Position

Number

Find the rule, then continue each number pattern. Write a rule for each pattern using the words increase or decrease. a

Position

Number

100

Position

Number

1 2

D R

Rule:

AF T

Rule: 3

Read the rule to complete each table.

Start at 5 and increase by 4 each time.

102

Term

Number

Start at 10 and decrease by 0.5 each time. Term

Number

9.5

Write the next four terms. Write a rule for each pattern.

0, 0.2, 0.4, 0.6,

Rule:

3 , 1 1 , 2 1 , 3, 2 4 4

Rule: Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Write the next four terms in each sequence by following the stated rule.

Rule: add 7

6 → 13 → 20 →

Rule: subtract 20

Rule: multiply by 4

These patterns follow a constant rule, but some information is missing. Use the clues to find the rule and fill in the missing terms.

→

200 → 180 → 160 →

→

2 → 8 → 32 →

→

Sequence 54,

Identify the rule

, 84,

3.5,

Add , 8.0

Add

AF T

, 10.4, 10.6,

Step 1 is 4.0, Step 5 is 5.0 ,

145,

, 105,

18.5,

, 15.5, 14,

1, 3,

120, 7

, 11

D R

23, 20,

→

Add Add Subtract Subtract Subtract

, 81

, 30,

Multiply by

, 7.5

Divide by

Fill in the gaps and identify the rule. Sequence 16, 24, 5,

Identify the rule

, 40, 48, , 17,

, 29,

, 81,

, 65,

, 49

, 3.5,

, 2.5,

, 1.5

, 12,

, 24,

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

103

Finding the “general rule” for a pattern Step number (n)

Matchsticks (m)

5 Step 1 3 sticks

Step 2 5 sticks

Step 3 7 sticks

Step 2

Step 3

D R

AF T

→ → +2 +2 You want to write a rule that links the number of matchsticks (m) to the step number (n). 1 Look at how the pattern is changing (it increased by 2 in this example). 2 Write a general rule. m = 2 × n 3 Check if you need to adjust the rule using step number 1 (n = 1). m = 2 × 1 = 2 But step number 1 has 3 matchsticks, not 2. So, we need to add 1 to the general rule. New rule: m = 2 × n + 1 4 Check the rule using another step number (e.g. n = 3). m=2×3+1 =7 This is correct. There are 7 matchsticks in step number 3. 5 How many matchsticks will there be in step number 10? m = 2 × n + 1 = 2 × 10 + 1 = 21 matchsticks in step number 10.

Explore 1

104

House pattern.

Step number (n)

Matchsticks (m)

11 16

5 Step 1

Draw the next step in the pattern.

What is this pattern increasing by?

Find the general rule.

Using your general rule, how many matchsticks will there be in step number 10? Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Squares pattern.

Step number (n)

Matchsticks (m)

Step 1

Step 2

Step 3

Complete the table. What is this pattern increasing by?

Find the general rule.

Using your general rule, how many matchsticks will there be in step number 10?

Fish pattern.

Step 1

Step 2

Step 4

Step 3

Step number (n)

Matchsticks (m)

10 14

AF T

Complete the table. Draw the next step in the pattern.

What is this pattern increasing by?

Find the general rule.

Using your general rule, how many matchsticks will there be in step

D R

number 10? 4

Triangle pattern.

Step number (n)

Matchsticks (m)

Step 1

Step 2

Step 3

Complete the table. Draw the next step in the pattern.

What is this pattern increasing by?

Find the general rule.

Using your general rule, how many matchsticks will there be in step number 10?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

105

Deepen 1

Your boss wants you to deliver advertising leaflets in a town with 1,000 houses. She knows that some houses will have a No Junk Mail sign. This table gives information about whether the houses accept junk mail.

House number

10 11 12 13 14 15

Junk mail OK? yes yes yes yes no yes yes yes yes no yes yes yes yes no

Circle the rule that describes the pattern. The number of houses that do not accept junk mail is: 5 out of 5

1 out of 5

4 out of 5

1 out of 2

Out of 10 houses, how many do not want junk mail?

Out of 100 houses, how many would not want junk mail?

Out of 1,000 houses, how many would not want junk mail?

How many leaflets will you need to deliver?

There are two different rules in these patterns.

D R

AF T

Number Is it even?

• R ule 1: If the number is even, Answer you divide by 2. • R ule 2: If the number is odd, you take away 1 and then you divide by 2. Follow the two rules to complete the table.

106

1 out of 4

Yes, ÷ 2 5

Is it even?

No, – 1, ÷ 2

Answer

Is it even?

Yes, ÷ 2

Answer

Is it even?

No, – 1

Answer

It takes four steps to get to zero for the starting numbers in question 2. How many steps does it take to get to zero if the starting number is:

25?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Algebra Topic xx| Equations and relationships

Topic xxxx 2.3 Coordinate planes 6 5 4

(5, 3)

3 2 1 0

x-axis

6 x

Crawl before you climb! Always move along the x-axis (sideways) first, then move up the y-axis.

Learn 1

y-axis

A coordinate plane is like a map. To find a specific spot, we use an address called a coordinate pair: (x, y). • The x-axis is the horizontal line (left to right). • The y-axis is the vertical line (up and down). • The origin is the starting point at (0, 0).

Find the coordinates of the points on the coordinate plane. Point

y 10

AF T

9 8

D R

7 6

Coordinate pair (x, y)

C E

D E

2 1

B 1

10 x

On the axes, draw the following points: F (1, 5)

G (4, 0)

H (0, 7)

I (6, 6)

J (9, 2)

Points that land directly on the lines (the axes) can be tricky. Answer these quick questions to show you are an expert!

If a coordinate is (0, 8), which axis is it on?

If a coordinate is (4, 0), which axis is it on?

Describe where the point (0, 0) is located. What is its special name?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

107

Linear relationships

y 140

Sometimes, it’s a good idea to show number patterns in different ways, such as in a graph. Felicia is saving $20 per month. The table shows how much savings she would have after each month. The relationship between the number of months and the amount of savings is shown on the graph. Month

Savings ($)

100

120

Savings

120 100 80 60 40 20 0

y 32

Complete the table to show how much it costs to buy each number of doughnuts.

Cost ($)

Plot the results on the coordinate plane.

If Bella buys 8 doughnuts, how much will it cost?

Marco has started working at a café. He earns $10 per hour.

Earnings ($) 10

20 16 12 4 0

8 x

Number of doughnuts

y 80 70

Complete the table to find out the earnings for the number of hours worked. Hours

Month

Earnings ($)

D R

Cost ($)

A doughnut shop sells a jam doughnut for $5.

AF T

No. of doughnuts

60 50 40 30 20 10 0

Plot the results on the coordinate plane.

If Marco worked 14 hours in total, how much would he earn?

Hours

Look carefully at the scale on the y-axis.

108

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Sometimes the graph does not start at (0, 0). This happens when there is a fixed amount added or taken away before you start counting. For example, you might pay a fixed fee to hire a bike and then pay an extra amount per hour.

Explore

An e-bike rental shop charges $5 to hire their e-bike, plus $2 for every hour you ride.

Complete the table to show the total cost for each number of hours.

16 15 13 12 11

Hours

Total ($)

y 18

10 9 8 7

Plot the results on the coordinate plane.

How much would it cost to hire the e-bike

6 x

D R

y 22 21 20

Complete the table to show the bill per week.

19 18

Week

Bill ($)

Plot the results on the coordinate plane.

How much will the bill total after 7 weeks? How much will the bill total after 10 weeks?

Hours

A phone company charges a hire fee of $4 plus $3 per week of use.

How much would it cost to hire the e-bike for 9 hours?

17 16 15 14 13

Bill ($)

AF T

for 7 hours?

12 11 10 9 8 7 6 5 4 3 2 1 0

Week Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

109

A café sells muffins for $4, but there is a one-time $2 service fee at the café. Complete the table to show the total cost for the number of muffins that you buy. Number of muffins

Total ($)

A toy company is ordering wheels for toy cars. Each car has four wheels.

Complete the table for the first ten terms of the pattern. Number of cars Number of wheels

50 cars

100 cars

y 32 28

Number of wheels

A toy company decides it needs to have extra wheels in case some get lost. They decide to get an extra wheel for every 25th car. Re-calculate the number of wheels that need to be ordered for:

D R

Plot all the points from the table and then connect all the points with a line.

AF T

24 20 16 12 8 4 0

8 x

Number of cars

iii

110

350 cars

1,250 cars.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Battleship is a game that involves coordinate planes. In this case, there is a letter used in the coordinate pair e.g. H5. 1 Let’s practise. Here is your battleship board, with your ships shaded in black. Circle “hit” or “miss” if the coordinates listed in the table hits or misses one of your ships.

Coordinate

Hit or Miss?

Hit or Miss

10 9 8 7 6 5 4 3 2 1 A

Play with a classmate This game is for two players. Each player will need their workbook (keep it hidden!). 1. Deploy: Draw your 5 ships on the My Fleet grid. You can place them horizontally or vertically, but not diagonally. The ships are 1, 2, 3, 4 and 5 squares long (same as the sample image).

D R

AF T

Battle: Take turns calling out coordinates (e.g. B4).

• If your opponent hits a ship, say “HIT”. They mark an X on their Enemy Radar. • If they miss, say “MISS”. They mark an O. 3. Win: The first person to sink all enemy ships wins. My Fleet

Enemy Radar

1 A

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

111

Measurement | Measuring

Topic 3.1 Estimating, measuring and converting When you are measuring, it is important to be as accurate as possible. The length of this pencil is 0 0 1 1 2 2 not 8 cm. Can you explain why?

44 cm 55 cm

6 6

Learn 1

Write the length of each red line. Include units.

Write the length of the red lines in centimetres and millimetres.

b 2

D R

AF T

e.g. 5.2 cm or 52 mm

Estimate and then use a ruler to measure these red lines. Write the lengths as you did in question 2.

a b c

112

a This line is 3.2 cm long. Increase the length by 12.3 cm.

Write the total length of the line in two different ways.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Mass tells us how heavy something is. We use four units of mass.

Milligrams (mg)

Grams (g)

Kilograms (kg)

Dog

Each unit of mass is 1,000 times heavier than the one before it.

Tonnes (t)

Apple

Under each picture, estimate the most likely unit of mass.

Complete the tables to convert between units of mass. × 1,000

Tonnes Kilograms

1,000 kg

4,000 kg

1,500 kg

Grams Milligrams

÷ 1,000

e.g. 1 kg

1,000 g

e.g. 1 g

2,000 g

D R

Kilograms Grams

÷ 1,000

e.g. 1 t

× 1,000

AF T

× 1,000

Grains of sand

Train

5 kg

3.5 kg

3.5 t

1.25 t

÷ 1,000

1,000 mg

5g 3,000 mg 1.5 g

1,250 g

0.5 kg

2,500 mg 0.5 g

Write the mass of each box in grams. Write the mass of each box in both grams and kilograms. a

0 00

500 kg 500 500 500 500 500 500 kgkg kg500

500 kg 500 500 500 500 500 500 500 kgkg kg

2 22 1

1 11

500 500 500 500

2 22 1

1 11

500 500 500 500

2 22 1

1 11

500 500 500 500

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

2 22 1

1 11

500 500 500 500

113

Complete this table. Kilograms and fraction

Kilograms and decimal

Kilograms and grams

2 2 kg

2.5 kg

2 kg 500 g

1.5 kg

1 kg 500 g

e.g. a

2 4 kg

4.75 kg

1.3 kg

Not all scales have the same increments (markings). Write the masses in kilograms and grams, and in kilograms with a decimal. A

B 0 kg

1 500

500

0 500 kg 1

0 kg

500

500 3 500

D R

D 5

500 kg 500

500

Look at the scales in question 9. Would you use scale A, B, C or D if you needed to have: a 100 g of b 650 g of c 4.25 kg of d 2.5 kg of butter flour kumara apples?

Draw pointers on the scales to show the mass of each box. a

1 kg 500 g

0 kg 2

114

AF T

1 2 kg is the 2 same as 2.5 kg or 2 kg 500 g.

850 g

1.6 kg

0 kg 1

500 kg 500 500

1 500

3 kg 3— 4

5 500

0 500 kg 1

500

500 3 500

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

A cup has a capacity of about 250 mL. Circle the best estimate for the capacity of the following containers.

6 mL 60 mL 600 mL 6 L

2 mL 20 mL 30 mL 300 mL 200 mL 2 L 3 L 30 L

80 mL 800 mL 8 L 80 L

What is something that has a capacity of about a litre?

The capacity of the milk carton could also be written as 1,000 mL, because there are 1,000 mL in a litre.

AF T

D R

Complete the table to convert between millilitres and litres.

× 1,000

Milk

Litres Millilitres ÷ 1,000

e.g.

a b

2,000 mL 3L

c 1L

9,000 mL 5.5 L

e f

2,500 mL 1.25 L

Order each row from smallest to largest.

2 L, 400 mL, 2.5 L, 2,350 mL

1 2 L, 450 mL, 0.35 L 3 1,850 mL, 14 L, 1.8 L 1 4 L, 200 mL, 20 mL

0.3 L, 1.2 mL, 320 mL, 15 L

1,000 mL

3,750 mL

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

115

Record the temperature shown on each thermometer. Write one thing that could be that temperature.

a ºC

100

100 90

°C

40 30

°C

40 30

–10

100

ºC

100

ºC

°C

10 0 –10

D R

°C

30 20

–10

28°C

−4°C ºC

Draw the temperature given on each thermometer. b

°C

100

ºC

116

100 90

ºC

AF T

°C

66°C ºC

100

–10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

You will need a timer for this activity. 7

Time how long it takes you to do 20 star jumps. Record your time in the chart to the nearest whole second. Ask four classmates to complete the star jumps challenge. Record their times in your chart. Who

Classmate 1

Classmate 2

Classmate 3

Classmate 4

Name Time

Plot each person’s time on the graph. a

y 60

Which student completed the 20 star jumps in the shortest time?

55 50

What is the average time taken by all five students to complete the challenge? How can you calculate that?

40 35 30 25 20 15 10 5 0

D R

What is the difference between the fastest and slowest times recorded?

AF T

Time (seconds)

x Classmate’s initials

Design your own timer activity. Be precise about the details needed for your activity. If you have time, complete your activity.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

117

Deepen 1

Solve the following single-step measurement word problems. Remember to include units in your answers.

b a For Matt’s treehouse he needs 6 metres of wood for the floor and 3 metres for each of the four walls. How much wood in total does he need?

A water tank can hold 500 litres of water. If it is currently filled with 275 litres, how much more water does it need to be completely full?

c The temperature in Ōtautahi is 15°C in the morning. If the temperature rises by 7°C in the afternoon, what will the temperature be?

d A running track is 400 metres long. If Takina runs 3 laps around the track, how many metres has she run in total?

e A juice jug holds 2.5 litres. If you have 5 jugs, how much juice do you have in total in litres?

D R

AF T

The temperature is 28°C. If the temperature drops by 10°C by evening, what temperature will it be?

h g The school is selling soup. Each pot holds 8 litres of soup, and they need to serve 150 students with each serving being 200 millilitres. How many pots of soup do they need?

118

In a greenhouse, the temperature is set to 20°C. The temperature increases at a rate of 2°C every hour during the day. If the greenhouse is opened after 4 hours, what will the temperature be? Additionally, if the temperature drops by 5°C at night, what will the temperature be by morning?

A new hiking trail is being built that is 12.5 kilometres long. A group of hikers decides to complete the trail by hiking 3 kilometres each day. How many days will it take them to finish the trail? If they hike an extra 1.5 kilometres on the last day, how many days will it actually take? Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Look at the table of the record-breaking masses of fruits and vegetables.

Record-breaking fruit or vegetable

Where and when?

Mass

Apple

Japan, 2005

1.849 kg

Cabbage

UK, 1999

57.61 kg

Lemon

Israel, 2003

5.265 kg

Peach

USA, 2002

725 g

Pumpkin

USA, 2009

782.45 kg

Strawberry

UK, 1983

231 g

Pear

Australia, 1999

2.1 kg

Blueberry

Poland, 2008

11.28 g

Order the fruits and vegetables from lightest to heaviest.

How much heavier than the cabbage is the pumpkin?

How much heavier than the pear is the lemon?

Which fruit is 1,124 grams heavier than the heaviest peach?

If strawberries like the heaviest one were sold in boxes of around a kilogram, how many would there be in a box?

By how many grams is the heaviest strawberry heavier than the heaviest blueberry?

A group of seven Year 6 students found that they had a total mass of 283.854 kg.

Round the total mass to the nearest 10 kg.

Divide the rounded number by the number of students to find the average mass of a student in the group.

Sol bought three apples. The first had a mass of 125 g. The second had a mass of 133 g and the third had a mass of 117 g. Find the average mass of one apple.

D R

AF T

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

119

Measurement | Measuring

Topic 3.2 Area and Volume To find the area of a rectangle, you need to know: •

how many squares fit on a row

•

how many rows there are.

2 rows 3 squares on a row Area = 3 cm2 × 2 Area = 6 cm2

e.g.

Learn Find the areas of these rectangles.

rows

Area =

squares on a row ×

= c

rows

D R

AF T

squares on a row Area =

rows squares on a row Area =

e Area =

× Area =

= f

Area = = 120

Area =

= Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

If you know the length and width of a rectangle, you can find the area by imagining how many squares will fit on a row and how many rows there are. You can see how it happens on this rectangle. 4 cm

4 cm

2 cm

Length and width

Centimetre marks

4 × 2 cm2

Find the area of each rectangle. Include units in your answer. b

5 cm

Area = d

2 cm

5 cm

Area =

Area = 3 cm

3 cm

4 cm

7 cm

Area =

D R

5 cm

f 2 cm

AF T

Area =

4 cm

Area = 8 cm g

12 cm

Area =

Use the dimensions of each rectangle to help find its area. They are not drawn to actual size.

3 cm

4 cm

Area =

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

121

To find the area of a right-angled triangle, imagine it as half of a rectangle. The area of triangle ABC is half of rectangle ABCD. Half of 8 cm2 is 4 cm2.

Record the area of each shape.

Area of rectangle ABCD =

Area of triangle ABC = D

2 cm B

Area of rectangle EFGH = E

AF T

Area of rectangle IJKL = Area of triangle JKL =

Area of rectangle MNOP = Area of triangle NOP =

D R

4 cm

Area of triangle EFG =

M M

Find the area of these right-angled triangles.

4 cm

8m 7 cm

122

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Find the area of these triangles.

A 10 m

14 cm

24 m

14 cm

16 m 88 cm 9m

AF T

D R

e A local adventure centre has a f climbing wall shaped like a rightangle triangle. The height of the wall is 10 metres and the base is 6 metres. What is the area of this climbing wall?

10 cm

A gardener is designing a flower bed in a park that is shaped like a right-angle triangle. The base of the flower bed will be 12 metres long, and the height will be 5 metres. What will be the area of the flower bed?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

123

Volume is the space something takes up. It is measured in cubes. This centimetre cube model has a volume of 6 cubic centimetres (6 cm3). Volume can also be measured in cubic metres (m3).

Explore Write the volume of each centimetre cube model. b

Volume =

cm3

Volume = e

Volume =

cm3

AF T

D R

Volume =

cm3

Volume =

cm3

Volume =

cm3

a H ow many centimetre cubes would be needed to make this model? b What is the volume? c I f there were three layers the same, what would the volume be?

a H ow many centimetre cubes are on the bottom layer of this box? b How many layers does the box hold? c What is the volume of the box?

124

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

How do you know that the volume of this box is 8 cm3?

1 cm 2 cm 4 cm

What would the volume of the box in question 4 be if the height were:

2 cm

3 cm

4 cm

5 cm?

What is the volume of this rectangular prism? 3 cm

b E xplain why you can find the volume by multiplying the length by the width by the height.

AF T

2 cm 2 cm 4 cm

2 cm

1 cm

2 cm

Volume: 4 cm

4 cm

2 cm 2 cm

2 5mm

4 cm

4 cm 4 cm 4 cm 4 cm 4 cm 10 cm 2 m10 cm 4 cm 10 cm 3 cm 3 cm 3 m 122mm 3 cm CUBE 2 33m cm cm 3 cm 3 m3 m 4 cm 4 cm 4 cm

1 cm

10 m 3 cm

12 m 12 m

Volume:

CUBE 3 cm 3 cmCUBE cm 44cm

5m 5m

10 m

12 m 10 m 10 m

Volume:

4 cm

Volume:

4 cm1 cm

102 m 10 m m

10 cm

3 cm 3 cm 5m

5 m5 m 1 cm

3 cm 3 cm

2 m2 m

4 cm

3 cm 4 cm 4 cm 10 cm 10 cm 3 cm

1 cm 1 cm

4 cm 4 cm

5 cm

Calculate the volume of each rectangular prism. Show your working.

D R

2 cm

12 m

Volume:

4 cm 4 cm

2m 3m 3m 12 m 33 cm CUBE m

3 cm

CUBE

Volume:

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

125

Deepen Measure each rectangle to find its area.

b Area =

c Area =

Area =

If you can split a shape into rectangles, you can find its area. Find the area of each shape. 3 cm a b 2 cm

2 cm

4 cm

B 5 cm

D R

Area of B =

Total area =

c 2 cm

2 cm

Area of B = Total area =

2m 1m

B 2 cm

Area of B = Total area =

2 cm

3 cm

2 cm

Area of A = Area of C =

Area of A =

B 4 cm

Area of A = Area of B = Area of C =

Total area =

Area of triangle: 3 cm 10 cm 6 cm

126

3 cm

4 cm Area of A =

AF T

Area of rectangle: Total area:

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

3 If you can split a shape into rectangular prisms, you can find its volume.

Find the volume of each shape.

2 cm

4 cm

2 cm

10 cm

4 cm

3 cm

Volume of prism A =

Volume of prism B =

Total volume =

Total volume = d

D R

2 mm

4 mm

AF T

6 mm

1 mm

Volume of prism A = Volume of prism B = Total volume =

The volume of this shape is 39 cm3. Find possible side lengths that give this volume. Diagrams are not always drawn to scale, so you can’t rely on what they look like.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

127

Measurement | Measuring

Topic 3.3 Angles

Angles are measured in degrees (°).

There are six types of angles. Acute angle from 1° to 89°

Straight angle 180°

Right angle 90°

Obtuse angle from 91° to 179°

Reflex angle from 181° to 359°

Full turn 360°

Learn Write the name of each type of angle and estimate its size in degrees.

128

D R

AF T

How do you know that this is an obtuse angle?

Use a pencil and ruler to draw each angle from the dot on its base line.

An acute angle

A right angle

An obtuse angle

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

10 20 170 160

180 10 20 20 180 180 170 170 160 16030 30 150 1504 0 40 14 14 0 0

100

Read the Read the outside outside track track

angle 70

100 80 100

90 90

100

110 80 12 100 70 0 110 60 13 80 12 0 05 70 0 60 13 0 50

010

180 180 170 170 160 160 0 10 100 0 0 15 15 20 20 0 0 30 14 3 40

110 0 70 12 50 0 06 110 13 0 12 50 0 3 1

10 20 20 180 180 170 170 160 16030 30 150 1504 0 40 14 14 0 0

110

80 12 100 70 0 110 60 13 80 12 0 05 70 0 60 13 0 50

010

100 80

AF T

0 010 10 20 20 180 180 170 170 160 16030 30 150 1504 0 40 14 14 0 0

110 0 70 110 20

12 0 60

Read the Read insidethe track inside track

110 80 12 100 70 0 110 60 13 80 12 0 05 70 0 60 13 0 50

D R

100

0 010 10 20 20 180 180 170 170 160 16030 30 150 1504 0 40 14 14 0 0

100 80

110 0 70 12 50 0 06 110 13 0 12 50 0 3 1

100

180

angle

180 180 170 170 160 160 0 10 100 0 0 15 15 20 20 0 0 30 14 3 40

An 60

angle 80

Read the track that starts at 0

180 180 170 170 160 160 0 10 100 0 0 15 15 20 20 0 0 30 14 3 40

Read the Read insidethe track inside track

80 12 100 70 0 110 60 13 80 12 0 05 70 0 60 13 0 50

0 13

100

100 80

110 0 70 110 20

12 0 60

110

Make sure the protractor is positioned properly

100

170

An acute angle 90

110

160

100 80

Write the type and size of each angle.

b °

0 12

100

110

0 15

30 150

40 14 0

0 14 40

Angles are measured with a protractor. The base line of the protractor needs to be on the base line of the angle. You have to make sure you read the correct track. This angle is on the inside track.

Write the type of angle. Circle the best estimate for the size of the angle.

Acute angle

b 100°

angle

c 100°

angle

20°

80º

140º

120º

40º

170º

60º

e 20°

angle

f 80°

angle

70°

60º

90º

80º

100º

110º

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

129

Write an estimate for the size of each angle. Name the type of angle.

e °

D R

AF T

130

Use a protractor to measure each angle in question 6.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Complete the angles. Check where “0” is and read the angle size from there. Name the angle type.

100

100 80

110

0 50

13 0

100 80

30 150

0 50

13 0

180

10 20 170 160

180

170

35°

110

160 20

10 20 170 160

100

110

0 15

180

0 13

0 12

0 14 40

0 13

0 12

110

0 14 40

40 14 0

180

150°

Angle type:

Use a protractor, pencil and ruler to draw the angle on each line. Start at the dot.

70°

Draw the following angles.

AF T

115°

45°

170°

100°

20°

D R

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

131

Deepen This diagram shows one method you can use to find the size of a reflex angle. 1

40º

Without using a protractor, write the size of

?º

the reflex angle in this diagram. 2

Use a method of your choice to find the size of these reflex angles.

b °

d °

D R

AF T

There are two angles shown here.

Estimate the size of each angle. A

Angle A estimate:

Angle B estimate: b

Explain how you estimated the size of each angle.

Measuring just one of the angles, write the sizes of both angles. Angle A =

132

Angle B =

Explain how you found the size of the angle that you did not measure.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Measurement | Measuring

Topic 3.4 Angle rules Learn Calculate the size of each unknown angle without using a protractor. e.g. ? = 100º (180 – 80)

? 86º

80º

67º

45º

120º

1º

D R

AF T

160º ?

89º

20º

We can work out the size of some angles using known rules.

?= 152º

111º

Finish the sentence. Angles on a straight line add

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

. 133

Calculate the size of each unknown angle without using a protractor.

240º ? 90º

27º

320º

? 80º

D R

AF T

190º 100º

200º

280º

350º

300º

Finish the sentence. Angles at a point add

134

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Calculate the size of each unknown angle without using a protractor.

130º ? 50º 130º

35º

110º

100º 40º

AF T g

D R

20º

90º ?

130º

We can use rules to find unknown angles. Can you remember them all?

Finish the sentence. Vertically opposite angles

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

135

Explore 1

Calculate the size of each missing angle. Show your working, include the rules you are using.

a b

46º

56º

a= 150º

150º

D R

AF T

57º

119º

86º x

62º 62º

136

46º

c 76º 58º

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Use a ruler to draw 4 straight lines right across the box. They must all intersect (cross) at exactly the same central point. Your lines will create a starburst pattern with many angles around the central point. Colour each section using a different colour to create a geometric masterpiece!

Now, let’s analyse the angles in your masterpiece!

Pick one straight line. List the colour sections that add to make 180°.

Name two colours with angles that are equal in size.

D R

AF T

and How do you know?

Measure or work out the size each colour angle and list them in the boxes.

What will the total be if you add up all of your angles?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

137

Measurement | Measuring

Topic 3.5 Time

Converting units of time 60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

7 days = 1 week

Learn Fill in the table by converting between minutes and hours. Minutes

Hours

2 hr

45 minutes

3 hr 11 hr

210 minutes

D R

78 minutes

Fill in the table by converting between seconds and minutes. Seconds

Minutes and seconds

Seconds

62 seconds

Minutes and seconds 11 minutes

2 minutes

100 seconds

1 minute 17 seconds 90 seconds

Hours

30 minutes

1 hr 30 min

Minutes

AF T

6 minutes 5.5 minutes

a How many hours are there in: i

2 days

ii 3 days? b How many days are there in 3 weeks? c How many weeks are there in a year? 138

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Write, in words, the time shown on the clocks, or write the time given onto the clocks.

13 minutes past 4

14 minutes to 6 o’clock g

11 12 1 2 10 3 9 8 4 7 6 5

AF T

11 12 1 2 10 3 9 8 4 7 6 5

D R

11 12 1 2 10 3 9 8 4 7 6 5

1112 1 2 10 3 9 8 4 7 6 5

10 minutes to 9

13 minutes to 2

Quarter past 7 What is your favourite time of day? Can you show it on a clock? Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

139

Explore

4 am 1 am

3 am

6 am

5 am

10 am

7 am

9 am

2 pm

1 pm

3 pm

Wednesday AM

Tues

6 pm 5 pm

8 pm

7 pm

9 pm

11 pm

Wednesday PM

0400 0600 0800 1000 0500 0700 0900

1200 1400 1600 1300 1500

1800 2000 1900

Thurs 2200 0000 2300

Convert these times to 24-hour times. For example, 8:15 am becomes 0815.

10 am

3:30 pm

9:48 pm

7:11 pm

Record the am/pm time and 24-hour time of these everyday activities.

D R

AF T

0000 0200 0100

Event

2:20 pm

9:48 am

am/pm time

7:11 am

12:29 am

24-hour time

The time I leave for school

The time I eat lunch

The time I leave school

The time I eat dinner

Owen’s football match starts at 1420 and lasts for 45 minutes. Show the starting and finishing times on the analogue and digital clocks. Starting time 11 12 1 2 10 3 9 8 4 7 6 5

140

Noon

11 am

Midnight

On a 24-hour clock, the times continue past 12 to 13, 14 and so on. 24-hour times are usually written as four digits with no spaces. Midnight is 0000. Fill in the 24-hour and am/pm times on this timeline. Midnight

11 12 1 2 10 3 9 8 4 7 6 5

Finishing time

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Fill in the gaps to show these times in four different ways. b

11 12 1 2 10 3 9 4 8 7 6 5

am/pm

3:37 pm 24-hour

The red circle means pm time.

am/pm 24-hour

d 11 12 1 2 10 3 9 4 8 7 6 5

am/pm 24-hour

11 12 1 2 10 3 9 4 8 7 6 5

am/pm

8:37 am 24-hour

Literacy session

10:00 11:00 11:20

Reading groups 12:15

D R

Maths Recess

AF T

This is Sam’s timetable for Friday at school. Use the information to complete the activities. a At what time does the Maths lesson begin? Friday 9:00 (Use am/pm time.) Sport

When does the lunch break start? (Use am/pm time.)

How long does Recess last?

Lunchtime starts with 10 minutes “eating time”. How much playtime does Sam have after that?

How long does the Literacy session last?

Estimate the time that Story reading begins. (Use 24-hour time.)

Journal writing 13:00

Lunch 14:00 Art & craft Story

15:00

Digital clocks are used for 24-hour time as well as am/pm times. Rewrite the times on these 24-hour clocks.

am/pm

24-hour

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

141

Deepen 1

Complete the table. Time in words

24-hour clock

12-hour clock

Analogue clock

11:00 pm

11 12 1 2 10 3 9 8 4 7 6 5 11 12 1 2 10 3 9 8 4 7 6 5

1515

Using the information in the schedule, answer the questions. Monday

Tuesday

Wednesday Thursday

Friday

8:00 - 9:00

Maths

Science

English

History

Geography

9:00 - 9:40

Art

Music

Technology

Drama

9:40 - 10:00

Morning Tea Morning Tea Morning Tea Morning Tea Morning Tea

D R

10:00 - 11:00 English

AF T

Time

Maths

Science

Geography

History

11:00 - 11:40 PE

Art

Technology

Music

Maths

11:40 - 12:40 Lunch

Lunch

12:40 - 1:40

Science

History

Geography

English

1:40 - 2:20

Technology

Drama

Art

Maths

Technology

2:20 - 3:00

Drama

Geography

Drama

English

How many days a week does this student have PE?

Which day is the latest Maths class, and what time does it start?

How many hours is a student in class if they attend every class for the whole week?

142

Write your own question about the schedule.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Use the timetable to answer the questions. Community Centre workshops Time

Harakeke Weaving

1.5 hours

$25

10:30 am - 11:00 am

Coffee Break

30 minutes

Free

11:00 am - 12:00 pm

Yoga Basics

1 hour

$15

12:00 pm - 1:00 pm

Cooking Class: Italian

1 hour

$30

1:00 pm - 2:00 pm

Lunch Break

1 hour

Free

2:00 pm - 3:30 pm

Pottery Wheel Basics

1.5 hours

$40

3:30 pm - 4:00 pm

Refreshment Break

30 minutes

Free

4:00 pm - 5:00 pm

Creative Writing

1 hour

$20

5:00 pm - 6:00 pm

Dance Fitness

1 hour

$15

6:00 pm - 7:30 pm

Advanced Weaving

1.5 hours

$35

If a person starts the “Pottery Wheel Basics” workshop at 2:00 pm, what

D R

If someone arrives at the community centre at 9:00 am to attend the “Harakeke Weaving” workshop and stays until the end of the “Advanced Weaving” workshop, how many total hours will they spend at the centre?

Cost

9:00 am - 10:30 am

time will the workshop end? b

Duration

AF T

Workshop Title

Calculate the total time spent on breaks (coffee, lunch and refreshment) if someone attends all workshops for the day.

If someone decides to attend both the “Harakeke Weaving” and the “Creative Writing” workshops, what will their total cost be for these two sessions?

If someone had $100 to spend on the day, give an example of the workshops they could attend.

Write your own question about the timetable and ask a classmate to solve it.

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143

Puffing Billy 4

There is a famous train in Victoria, Australia called Puffing Billy. It was built over 100 years ago. Puffing Billy got its name because it is a steam engine. This image shows part of a timetable for people who want to take a ride on Puffing Billy. Use the information to complete the following activities. FROM BELGRAVE Train 1

Train 2

dep:

10:30

11:10

Menzies Creek arr:

10:53

11:33

Menzies Creek dep:

11:05

11:35

Emerald

dep:

11:20

11:53

Lakeside

arr:

11:30

12:08

Lakeside

dep:

…

12:20

Cockatoo

arr:

…

12:35

Gembrook

arr:

…

13:00

144

AF T

Belgrave

How long does the 10:30 train take to get from Belgrave to Menzies Creek?

How long does the 11:10 train wait at Menzies Creek?

How much longer does the 10:30 train take to get from Belgrave to Lakeside?

How long does the 11:10 train wait at Lakeside?

How long does the journey take from Belgrave to Gembrook?

If I need to get to Lakeside by 11:20 am, can I take either train? Explain.

D R

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

The ferry from Bluff to Stewart Island takes 40 minutes.

Outbound Trip: Bluff to Stewart Island Day

Departure Times

Monday

8:00 am, 12:00 pm, 4:00 pm

Tuesday

9:00 am, 1:30 pm, 5:00 pm

Wednesday

8:30 am, 12:00 pm, 3:45 pm

Thursday

10:15 am, 12:30 pm, 4:00 pm

Friday

8:45 am, 12:15 pm, 4:15 pm

Saturday

9:15 am, 1:00 pm, 5:30 pm

Sunday

8:00 am, 11:45 am, 4:15 pm

Return Trip: Stewart Island to Bluff Departure Times

Monday

10:00 am, 2:00 pm, 6:00 pm

Tuesday

11:00 am, 3:30 pm, 7:00 pm

Wednesday

10:30 am, 2:00 pm, 5:00 pm

Friday Saturday Sunday

12:15 pm, 2:30 pm, 6:00 pm 10:45 am, 2:15 pm, 6:15 pm

D R

Thursday

AF T

Day

11:15 am, 3:00 pm, 7:30 pm 10:00 am, 1:45 pm, 6:15 pm

Ilisa lives in Bluff and goes on the 8:30 am ferry on Wednesday. What time will she arrive on Stewart Island?

If it takes her 25 minutes to drive from her house to the ferry terminal, what time should she leave home?

Her friend Hannah is arriving on the last ferry that same day. What time will she arrive on Stewart Island?

They plan on staying two nights and need to be back in Bluff before 4 pm. What ferry and on what day should they take?

On which day does the ferry have the latest departure time from Bluff to Stewart Island? What is that specific time?

If someone completes three return trips in a week, how long do they spend on the ferry?

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145

Geometry | Shapes

Topic 4.1 2D shapes, prisms and pyramids A 3D shape has height, width and depth. A polyhedron is a 3D shape that has flat faces and straight sides. A cube is a polyhedron but a Cube Cylinder Cube (a polyhedron) Cylinder (not a polyhedron) Cube Cylinder cylinder is not. (The plural of (a polyhedron)(not(not a polyhedron) (a polyhedron) a polyhedron) polyhedron is polyhedra.)

Learn 1

Prisms and pyramids are two types of polyhedra. They get their names from the shapes of their bases. Use the word bank to help you write the names of these polyhedra.

A cube has three sets of parallel (or opposite) faces. Word bank

hexagonal

prism

octagonal

pyramid

pentagonal rectangular

146

e.g. hexagonal pyramid

D R

AF T

triangular

e.g. square prism

The side faces of prisms are always rectangles. What 2D shape can you see on the side faces of all pyramids?

Can you think of examples of polyhedra that you see in real life?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Apex

A pyramid has one base. The top is called the apex. A prism has two bases but may sit on one of the side faces.

One hexagonal base

Complete this table. 3D shape

f. e.g. Hexagonal

Two hexagonal bases

Number Base shape Side face The shape is Number Base Side face The objectsitting is of bases shape on:

3D object

of bases

pyramid

e.g.

Hexagonal prism

Hexagonal pyramid

shape

sitting on:

hexagon triangles the base hexagon triangles the base

Hexagonal pyramid

Square pyramid

Triangular prism

Square pyramid

D R

AF T

3D object

Triangular pyramid

Triangular prism e.g.

Number of bases

Base shape

Side face shape

The object is sitting on:

hexagon

triangles

the base

3D object

Hexagonal pyramid

e.g.

Triangular prism Square pyramid

Numb of bas

1 Hexagonal pyramid

Draw the d 2D net of the 3D shapes shown. The first one has abeen done Triangular prism for you. Square pyramid Square pyramid

Rectangular prism c

Rectangular Triangular prism prism

Triangular pyramid

Triangular b prism Triangular prism

d Rectangular prism

c Triangular prism

d Rectangular prism

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147

A circle is a 2D shape, but it is not a polygon.

A polygon is a closed shape with three or more straight sides. None of the sides cross over each other.

This is not a polygon.

This is a polygon.

a Shade the polygons. A

b Explain why the unshaded shapes are not polygons.

is not a polygon because

•

is not a polygon because

AF T

•

Most polygons are named after the number of angles in the shape. Write each polygon’s name. Use the word bank to help with spelling.

D R

• B is not a polygon because

triangle

pentagon

octagon

quadrilateral

hexagon

A polygon is either regular or irregular. Regular shapes have all sides and angles the same. Irregular ones do not. Shade the regular polygons. Draw stripes on the irregular polygons. A

148

Word bank

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

All triangles have three sides. Triangles can be named according to the lengths of their sides and the sizes of their angles. Isosceles triangle: Two sides are the same length. Two angles are equal.

Right-angled triangle: There is a right angle in the triangle.

Equilateral triangle: All sides are the same length. All the angles are equal.

This rectangular pattern is made from triangles. Colour it according to the types of triangles: •

green for scalene triangles

•

yellow for right-angled triangles

•

blue for isosceles triangles

•

red for equilateral triangles.

D R

AF T

Scalene triangle: No sides are the same length. No angles are equal.

Some triangles are two different types. Write the two types of triangles for these.

Isosceles and

and

Name the quadrilateral and complete its description. Shape

Name

Description

• sets of parallel lines • equal sides • opposite angles are

• • •

set of parallel lines sides equal angles

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149

Interior angles of triangles Interior angles in a triangle add to 180°. For example, this right-angled triangle is 30° at the bottom. 90° 30° 180° – (90° + 30°) = 60° The top corner is 60°. To find an unknown angle, add two of the angles and subtract it from 180.

Explore 1

Find the missing angles.

P 70°

130° 30°

180° –

° +

180° –

20°

° +

° =

AF T

D R

40°

° –

100°

Isosceles triangles have two equal angles. We can find the two missing angles if we know the third one. 180° – 40° = 140° Two of the missing angles are equal, so we halve 140°. 140° ÷ 2° = 70° Find the missing angles using this method.

80°

180° −

150

° +

° =

° ÷2=

40°

76°

180° −

° =

° ÷2=

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Interior angles of quadrilaterals The interior angles in a quadrilateral add to 360°.

Rectangle • Opposite sides are equal • All interior angles are 90°

Special quadrilaterals have their own properties in terms of angles.

C Parallelogram • Opposite sides are equal and parallel • Opposite interior angles are equal

Rhombus

• All four sides are equal

• Opposite interior angles

are equal

Find the internal angles in an equilateral triangle.

AF T

Square • All four sides are equal • All interior angles are 90°

D R

All the angles in an equilateral triangle are equal. °. Therefore, 180° ÷ = Find the indicated unknown angle in each of the quadrilaterals. b 120°

70° 120°

360° – (2 × 120°) = ÷2=

50°

360° – (

+ 90°)

= 360° – =

? 60°

360° – (

100° 95°

) = 360° –

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

° 151

Deepen 1

Identify each polygon from its description.

This polygon has three sides, one right angle and two equal angles. It is

This polygon has six equal angles. It is

This polygon has four sides. It has one pair of sides that are parallel. It

has another pair of sides that are not parallel. It is d

This polygon is a parallelogram. It has two acute angles and two obtuse angles. It has four equal sides. It is

What is the size of the two acute angles in an isosceles right-angled triangle?

Write down some information about this polygon.

This picture is made from:

D R

AF T

152

•

two right-angled triangles

•

an irregular pentagon

•

a trapezium

•

a rectangle.

Draw a polygon picture. Write the names of the polygons that you use. (Remember: a polygon has no curved sides!)

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Geometry | Spatial reasoning

Topic 4.2 Transformations An object has rotational (turning) symmetry if it turns around its middle and fits on top of itself before it gets back to the beginning. Can you think of a letter that has line symmetry and rotational symmetry?

Learn Circle the letters that have rotational (turning) symmetry.

Draw lines of symmetry on each shape with rotational symmetry. b

D R

AF T

I magine you can rotate this pattern. Count the starting position as “1”. How many times will it fit on top of itself before it gets back to the beginning?

b C olour the shapes to make a pattern with 2 lines of symmetry. c 4

Draw in the lines of symmetry.

Create a picture or pattern with rotational symmetry on the grid.

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153

Transformations include translations, reflections and rotations. Patterns can be made by transforming shapes horizontally, vertically or diagonally. Translation

Reflection

vertical

horizontal

diagonal

horizontal

vertical

diagonal

Explore 1

Describe these patterns. Pattern

Description

e.g.

The triangle has been reflected vertically.

AF T

D R

b c d

154

Continue this pattern and describe the way it grows.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Look at the way these patterns grow. Complete each pattern, then describe it.

AF T

D R

esign a transformation D pattern using this shape.

b D escribe the way you made your pattern.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

155

Deepen Continue the following patterns and then colour them in a way that creates a colour pattern too. Create your own pattern in the space at the bottom.

Put a tick beside which patterns are tessellating patterns. Explain why.

D R

AF T

156

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

You can create designs in a few minutes with the help of a computer and a program such as Microsoft Word (or similar).

Open a blank document. Make sure you can see the Insert menu bar.

Click on the Shapes icon and choose an interesting 2D shape.

Draw the shape at the top of the page by clicking and dragging.

Copy the shape.

Paste the shape.

Use the arrow keys to move the shape so that its left edge joins the right edge of the first shape, like this:

Repeat steps 1–6 as many times as you like.

This activity involves rotating copies of a simple shape on top of the original shape.

Open a new blank document.

Click on the Shapes icon and choose a double arrow.

Draw the arrow on the page by clicking and dragging.

Copy and paste the shape as you did in question 1.

Use the arrow keys to move the shape so that it is exactly over the top of the first shape.

Select the shape to change it. Then click on the Shape Format menu.

Click on the Rotate menu and then on the More Rotation Options.

Change the rotation amount from 0° to 30° and click OK.

D R

AF T

Rotate__________________ Rotation:

30º

Copy, paste and move the new shape by repeating steps 5–8.

10 Repeat, increasing the angle of rotation by 30° each time.

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

157

Geometry | Pathways

Topic 4.3 Positions and pathways Coordinate points are often written using two numbers, rather than a letter and a number. You read the number going across first (x-axis) then the number going up (y-axis). The numbers are written in brackets and separated by a comma. The circle is at (1,0).

Learn

Grid E

Write the grid references for:

a the star

b the triangle

the diamond.

Draw the following on Grid E. a

A square at (2,3)

Stars at (1,2), (2,2) and (3,2)

Circles at (1,4) and (3,4) c

AF T

a Write the first letter of your first name on an empty grid point.

D R

b What is the grid reference for the letter you wrote? 4

When two coordinate points have an arrow between them, it means that you join them with a straight line. Complete the following. y

a The coordinate points for drawing the

8 7

triangle are: (1,5)

(3,5)

(2,8)

5 4

b The coordinate points for drawing

3 2

the square are: (4,5)

0 0

Draw a large rectangle on the grid below the triangle and the square.

b Write the coordinate points for drawing the rectangle. 158

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Rabbit Way

Use this map to answer questions 6 to 9.

Bus stop

Hospital

Cat Road

Bird Street

Car park Crab Court Shopping centre

Swimming pool Goat Street

Lan

Bear Street

e ors

School

Giraffe Road

Tiger Street

Bus stop

Dog Road

Skate park Lion Lane

a Which 2 roads is the skate park on?

AF T

b Which 2 roads is the hospital on?

Follow the directions.

Start at the Bird St bus stop.

Walk along Bird St to Cat Rd.

Turn left onto Cat Rd.

Keep walking until you reach Goat St.

Turn left and walk to the corner of Dog Rd.

Where are you now?

Write your own directions from the swimming pool to the school.

Choose your own starting point and destination. Write the directions and ask a classmate to follow them. Were they able to reach your destination?

D R

Remember to consider where you are on the map when turning left or right.

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159

Explore

City Fun Run course Sports stadium

City Road

6 5

Johns Street

F Riv

ers

Bou

lev

3 Botanical gardens

ard

Station

ide

Bingo Road

City square

Riv

Art gallery

Boundary Road

Scale: 1 cm = 50 m

Legend:

AF T

Toilets

Fun Run course

First aid

Start

Information

Water station

About how long (in metres) is the Fun Run course?

D R

b Describe where the course goes. c Write directions from the city square to the sports stadium.

160

What is at:

What is the grid reference for:

first aid

Add S (south), E (east) and W (west) to the compass.

the station

C3?

the finish line?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

A legend (or key) gives information about places on a map. If a map has a scale, you can work out real-life distances. On this map, the treasure is at (4,1) and is 50 metres from the snake pit. b

Write a coordinate for the campsite.

N 3

Scale: 100 m

2 1

0 0

S T 2

Legend S = Snake Pit C = Crocodiles P = Poisonous Plants N = Nest of Scorpions T = Treasure

AF T

D R 6

Scale: 1 cm = 1 km

Snakesville

How far is the campsite from the treasure?

P P P

Legend T = Treasure S = Snake Pit C = Campsite

a M ark these on the map: Big Bug Beach has a nest of scorpions near it. Tin Pot Cave is 6 km south-east of Snakesville. Spider Head is 4 km south of Snakesville. Cockroach Cliff is 7 km north of Spider Head. b S hark Point is 5 km west of Snakesville. Mark its position with a dot and write “Shark Point” on the map. c T here is a curved track from Snakesville to Shark Point that misses the poisonous plants by going to the south of them. Draw the track on the map. d E stimate the distance from Snakesville to Shark Point along the track you drew. e T he Treasure is buried along a straight track 500 m south-east of Goanna Gorge. Mark it on the map with the letter T.

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161

Deepen This is O’Brien’s Farm. Legend

162

Using a scale of 1 cm = 5 m, draw and label:

a paddock that is 30 m long and 20 m wide

a shed that is 10 m long and 5 m wide

a farmhouse that is 15 m wide and 20 m long

an orchard that is 15 m long and 10 m wide.

Create symbols in the legend and add the following items to the map.

5 trees

b 2 water tanks

7 cows

e An arrow to show north

Draw a track the length of the farm.

How long is your track in metres?

How will you decide where to place each item?

D R

AF T

c A windmill

If the scale was 1 cm = 10 m, what would be the dimensions of:

the paddock

long and

wide

the shed

long and

wide

the farmhouse?

wide and

long

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Statistics | Developing knowledge from, visualising, and interpreting data

Topic 5.1 Time-series Learn

Temperature in Te Anau 10

°C

A time-series graph shows how data changes over time (e.g. days, months, years, hours). What was the temperature on Day 4?

b On which day was the temperature the lowest?

Day

c Between which two days did the temperature drop the most? 2

hich month had W the most rainfall?

Rainfall per month 300

300 250

ow many people H were at the gym at 12 pm?

b W hat time of the day were the most people at the gym? Why do you think this is?

100 50

250

AF T

150

150 100

100

D R

c W hy do you think that is?

200

50 50

0 Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

Month People at a gym during a weekday 40

Number of people

b W hich four months had the least rainfall?

Rainfall (mm)

250

35 30

25 20

15 10

0 6am 7am 8am 9am 10am 11am 12pm 1pm 2pm 3pm 4pm 5pm 6pm

Time of day

c W hy do you think a significant number of people go to the gym at 7 am? Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

163

What is a trend? When we look at graphs, we usually see one of three things. 1 Upward trend: The values are generally increasing (getting bigger). 2 Downward trend: The values are generally decreasing (getting smaller). 3 No trend: The values go up and down randomly without a clear direction. Look at each of these graphs and identify if it shows a trend or not. a D escribe the trend you see.

b W hat do you think made the population drop in 2020–2021?

No trend

30,000 27,500 25,000 22,500 20,000 17,500 15,000 12,500 10,000 7,500 5,000 2,500 0 2015

Week 2

Week 3

Week 4

Week 5

Week 6

Week

Population of Queenstown 2015-2025

D R

a Describe the trend you see.

Population

50 45 40 35 30 25 20 15 10 5 0 Week 1

AF T

b W hy do you think this happened?

Downward

Waste collected at local beach Amount of waste (kg)

Upward

2016

2017

2018

2019

2020

2021

2022

2023

2024

2025

Year

a D escribe the trend you see. b W hat day did this person read the most pages?

Number of pages read each day 30

Number of pages read

25 20 15 10 5

164

ay nd Su

rd ay tu Sa

ay Fr id

ay ur sd Th

W ed ne sd

ay Tu es d

da y

Day

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Problem: A teacher wonders: Are there any patterns in classroom attendance?

Plan: She collected attendance data over the last three weeks of Term 2 by recording the number of students present each day.

Data: Mon

Tue

Wed

Thu

Fri

Week 8

Week 9

Week 10

The line graph shows her data for Weeks 8. Add the data for Weeks 9 and 10 to the graph.

AF T

Classroom attendance 25

D R

Number of attendees

20 15 10 5 0 Mon

Tue

Wed

Thu

Fri

Day

Tue

Wed

Thu

Fri

Analysis: Describe the trends shown in this time-series graph.

Give a possible reason for such low attendance on Friday of Week 10.

Conclusion: Answer the investigation problem.

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165

Problem: A canteen manager wants to know how sushi sales change during the lunch hour so that she can organise staffing rosters.

Plan: She recorded the number of sushi packs sold during each 10-minute interval across the lunch hour (60 minutes) for three consecutive school days.

Data: 12:00– 12:09

12:10– 12:19

12:20– 12:29

12:30– 12:39

12:40– 12:49

12:50– 12:59

Day 1

Day 2

Day 3

Label the axes and plot the values for each day on the graph. Use a different coloured pen for each day. You should have three lines on your time-series graph. Sushi sales 50

D R

AF T

40 35 30 25 20 15 10 5 0 12:00–12:09

12:10–12:19

12:20–12:29

12:30–12:39

12:40–12:49

12:50–12:59

Analysis: Describe the trends shown in this time-series graph.

Give a possible reason for the high number of sales at the start of lunchtime.

Conclusion:

166

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Deepen 1

You are going to record how many star jumps you can do in 20 seconds, repeated over five trials. Take only a short rest between each trial. Trial

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Number of star jumps

Using the data you have collected, create a time-series graph in the grid. Remember to: 1.

Label your axes (x-axis = Trial number, y-axis = Number of star jumps)

Plot your points carefully

Connect the dots with a ruler Star jumps 36 33

AF T

30 27 24 21 18

D R

15 12 9 6 3 0

Reflection: Look at your graph. Did your number of star jumps go up (increase), down (decrease) or stay the same (constant) over time? Why do you think that happened?

Repeat the test on some classmates and add their data to your graph. What trends do you notice?

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167

Statistics | Developing knowledge from, visualising, and interpreting data

Topic 5.2 Mean and range What is the range?

Range = 8

The range is the difference between the highest (maximum) and lowest (minimum) values in a data set. It shows how spread out the data is.

Minimum

Maximum

Learn 1

Fill in the table. Data set

Maximum

Minimum

Range

3, 9, 4, 12, 6 20, 15, 10, 25, 30

7, 14, 3, 21, 10 11, 22, 33, 44, 55 90, 60, 30, 120 54, 78, 21, 36 2

D R

100, 50, 25, 75

AF T

8, 8, 8, 8, 8

Five pupils scored the following marks out of 200: 158, 172, 189, 145, 176. What is the range of the scores?

Three friends counted their steps for the week: 18,000 steps, 22,000 steps, 20,000 steps. What is the range of their step counts?

Two rugby players, Ardie and Beauden, practised kicking goals. Here are the number of successful kicks they made over five training sessions. Ardie: 5, 25, 8, 30, 2

Beauden: 12, 14, 13, 12, 14

Calculate the range for both players. Who has the smaller range?

If you were the coach, who would you pick to kick for the team? Explain why.

Hint: A smaller range usually means the data is more consistent (staying the same). A larger range means the results are more unpredictable. 168

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

What is the mean?

Data set: 2, 3, 4

The mean is a type of average. It gives us a central value for a set of data.

Add up values: 2 + 3 + 4 = 9 Divide by the number of values (3). 9 ÷ 3 = 3. The mean is 3.

Fill in the table to calculate the mean for each data set. The first one has been done for you. Sum (Add them up) 3, 5, 10

Count Mean (How many numbers?) (Sum ÷ Count)

3 + 5 + 10 = 18

18 ÷ 3 = 6

4, 8, 12, 16

100, 200, 300

AF T

9, 2, 5, 2, 7

Find the mean of the following problems.

In their last 5 games, Auckland FC scored the following number of goals: 2, 8, 4, 6, 5. What is their mean number of goals per game?

Over four days a food truck sold 8, 10, 12 and 10 bowls of chop suey. What was the mean number of bowls sold each day?

While exploring rock pools, Anika counted sea snails. On Day 1 she found 6, on Day 2 she found 8 and on Day 3 she found 7. What was the mean number of sea snails she found each day?

Let’s try some larger numbers. Find the mean of each data set.

D R

a 120, 150, 210

b 60, 90, 120

c 50, 70, 80, 100

d 18, 19, 20, 21, 22

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169

Explore 1

Liana and her five friends had a sleepover. She asked them a series of questions about their week so far: how many books they had read, hours of sleep, netball goals they had scored, hours of exercise and how much water they drank. Here are the results for each question. Calculate the range and mean of each data set. Data

Range

Mean

Books Read: 4, 10, 8, 6, 4, 4 Hours Sleep: 38, 32, 30, 38, 22, 20

Hours of Exercise: 2, 6, 8, 10, 4, 0

D R

Goals Scored: 4, 2, 0, 6, 6, 0

AF T

Daily Water Intake: 2, 8, 4, 6, 6, 4

Which data set has the biggest range? Explain what that means.

A cricket player wants her mean score to be 50 for her first three matches. She has played 2 games so far. Her scores are 40 and 45. What must she score in the third game to achieve a mean of 50?

A set of data has a range of 15. The smallest number is 10. What must the largest number be? Explain how you know.

170

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The table shows the number of points scored by each player (including the substitute) on a basketball team.

Player

Total Mean Points in Points in Points in Points in Points in number points Game 1 Game 2 Game 3 Game 4 Game 5 of points per game

Hemi

Aaliyah

Fehi

Minh

Lily

Noah

Divide the total for each player by the number of games to find their mean number of points per game. Write the average scores in the table.

Whose mean score was the highest?

Who scored the most points in a single game?

Use the data to create a picture graph on this grid, showing the mean points per game.

D R

AF T

Key: 1 basketball = 2 points 18 16 14 12 10 8 6 4 2 H.

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171

Continuous data is information that can be measured (e.g. height, weight, time or temperature). It’s different from discrete data, which consist of counted values (e.g. things you can count, like number of pets).

Deepen 1

A group of Year 6 students held a paper plane throwing contest. They measured the distance of each throw in metres. Here are the results for the group. Throw 1

Throw 2

Throw 3

Throw 4

Throw 5

4.5 m

6.2 m

3.8 m

5.5 m

5.0 m

Calculate the mean distance for the group. Show your working.

Calculate the range of the distances.

The daily rainfall (in millimetres) was recorded for one week in Te Whanganui-a-Tara/Wellington. Analyse the data to answer the questions. Tues

Wed

0 mm

12 mm

5 mm

D R

Mon

AF T

Thurs

Fri

Sat

Sun

0 mm

22 mm

8 mm

2 mm

What is the range of rainfall for the week?

Calculate the mean daily rainfall for this week.

If it rained 0 mm on the following Monday, would the new mean be higher, lower or the same? Explain why without calculating.

Meteorologists use range to see how much the temperature changes in a week. Look at the forecast for two cities. City

Mon

Tues

Wed

Thurs

Fri

Tāmaki Makaurau/Auckland

18.5°C

20°C

19.8°C

21°C

17.5°C

Tāhuna/Queenstown

5°C

12.5°C

8°C

15°C

4°C

Calculate the temperature range for Tāmaki Makaurau/Auckland.

Calculate the temperature range for Tāhuna/Queenstown.

Which city has more changeable weather? Use your answers to explain why.

172

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Statistics | Developing knowledge from, visualising, and interpreting data

Topic 5.3 Data visualisations Primary data is data gathered by you.

A survey is an example of primary data. Data collected from the internet or a library is an example of secondary data.

Secondary data is data gathered by someone else.

Learn The two main types of data that are collected are numerical and categorical. Numerical data can be counted (or measured). Categorical data (such as where we like to go on holidays) is not numerical. Write “N” (for numerical) or “C” (for categorical) for the type of data that will be collected.

What is your favourite pet?

How many pets do you have?

How tall are you?

What is your favourite sport?

If you asked “How many snacks do you eat a day?”, you would be collecting numerical data. Write a survey question about food that would enable you to collect categorical data.

If you asked “What type of music do you like?”, you would be collecting categorical data. Write a survey question about music that would enable you to collect numerical data.

Year 6T took the noon temperature in degrees Celsius for 20 days.

D R

AF T

19, 18, 19, 20, 19, 20, 20, 20, 19, 18, 20, 19, 20, 19, 18, 20, 18, 17, 19, 20 a

What type of data did they collect?

Complete the frequency table for the data.

Complete the dot plot for the temperature data.

Is the temperature data primary or secondary? How do you know?

Temp. (°C)

Tally

Frequency

Total Noon time temperatures for 20 days

17º Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

18º

19º

20º 173

How much money was in my piggy bank? $25

Key: = $5

$20 $15 $10 $5 $0

2 Week

2 3 Week

The example graphs show that the amount of money Tamaiti had in week 1 was $5.

By how much did it go up in week 2?

In which week did Tamaiti have the most money?

Estimate the amount of money Tamaiti had in week 4.

Which graph is easier to interpret? Why?

These are the amounts Tamaiti had in weeks 5 to 8. Use the information How much money was in Key: to make a line graph How much money was in my my piggy bank? piggy bank? and a picture graph. Week 5: $15

•

Week 6: $20

•

Week 7: $3

•

Week 8: $18

= $5

$25 $20

Amount

•

D R

AF T

$15 $10 $5 $0

How many birds came on Friday?

b What was the total number of birds that visited?

174

Picture graph

Line graph

Amount

Two types of graphs used to represent data are line graphs and picture graphs. A line graph is only used to show how something changes over time, such as the amount of money in a piggy bank.

6 7 Week

28 24 20 16 12 8 4 0

7 Week

Number of birds that visited the class bird feeder

Mon Tues Wed Thu

Fri

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

These are Blair’s spelling scores out of 20 during the term. Represent the data on a line graph.

Week

Score

Complete the numbering for the vertical axis and the horizontal axis. Write a title for the graph.

Write appropriate labels for the horizontal and vertical axes.

Plot the data, then join up each point.

D R

AF T

Look at your graph in question 8. a

In which weeks did Blair score 100%?

b Describe the change in scores between weeks 5 and 7.

c In which week do you think Blair did not do her homework? d True or false? Blair’s average score was more than 16 out of 20. Explain.

e Between which weeks was the rise in scores the biggest?

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175

A Year 5 class held an ice cream stall to raise money for the Year 6 Farewell.

Number of ice creams sold in one week Key: = 10 ice

How many ice creams were sold on Monday?

By how much did sales increase between Wednesday and Thursday?

What is the different between the days with the most and least sales?

Write a sentence about the ice cream sales on Tuesday.

What was the total number of ice creams sold during the week?

The ice creams were 50c each. How much money did they make?

There are a lot of vowels used in the 40 words of this joke.

creams

Tues

Wed

Thurs

Fri

D R

AF T

Mon

A monkey goes into a café and points to a picture of a cheese sandwich. “That’s strange!” says one waitress to another. “A monkey is ordering a cheese sandwich.” “I know!” says the monkey. “I usually order a hot dog.” a

Find out how often each vowel is used. Make an accurate tally of the number for each vowel. Vowel

Frequency

176

How reliable do you think this data is as an indicator of the most frequently used vowels? Why?

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Data about people's favourite colour is shown. Circle and label the mistakes in the graph. Colour

Frequency

Favourite colour

20 18 16 14 12 10 9

Black

Blue

Green

Pink

Orange

8 7 6 4 2 Black

Blue

Look at the pie chart.

Is the chart misleading? Why or why not?

Pink

Dogs

AF T

Number of birds that visited the bird feeder

D R

Green

Represent the data in the pie graph in two ways which are more appropriate.

Friday

Thursday

Wednesday

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Monday

Tuesday

177

Probability | Experimental probability

Topic 6.1 Chance Probability

The sum of all probabilities is 1.

The sample space is a list of all possible outcomes.

When flipping a fair coin:

If you are rolling a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.

1 P(Heads) + P(Tails) = 1 + 2 2

= 1.

Learn This is a spinner. Colour the spinner so that the following probabilities are true. •

There is 1 chance for yellow.

•

There is 0 chance for white.

• •

There is 2 chance for blue.

10 There is 4 of a chance for green. 10 There is 3 chance for red. 10

Look at your completed spinner in question 1.

List the sample space for the spinner.

Add the probabilities for the colours together. What do you notice? Why do you think this is?

There is 1 of a chance that the spinner will land on red. 4 What fraction describes the chance of the spinner landing on blue?

This spinner has a 90% chance of landing on red. What is the percentage chance of it landing on blue?

R B

178

AF T

•

D R

The chance of this spinner landing on yellow is 0.1. What chance is there that it will land on:

blue

green

white?

B G

B R

R R R R R

R Y R B R

R R R

G R

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Tupou spins two wheels. For each wheel, write the likelihood of each outcome as a fraction.

a b Y Green: B Y B

Blue:

Yellow:

Green:

R B

Red:

Blue: Yellow: Red:

The Jellybean Company always puts 100 jellybeans in each pack: 20 red ones, 10 green ones, 25 white ones, 20 yellow ones, 10 purple ones, 10 pink ones and 5 black ones.

Joel loves the yellow ones. He takes one from his pack without looking. What is the chance that he will take a yellow jellybean?

Which colour is there a quarter of a chance Evie will take out?

Lachlan’s favourites are red and green. What fraction of a chance does he have of getting one of his favourites?

Which colour jellybean has a 1-in-20 chance of being chosen by Chryss?

Kaipo invented a board game. The number of squares you move depends on the colour of the spinner you land on. The less chance of landing on a colour, the more squares you get to move! This is how it works:

Red:

D R

AF T

•

Land on red: Move 1 square

•

Land on green: Move 4 squares

•

Land on blue: Move 2 squares

•

Land on gold: Move 6 squares

Colour the spinner so that there is the greatest chance of landing on red, less chance for green, even less chance for blue and the least chance of all for gold.

Describe the chance of landing on each colour as a fraction and a decimal. Blue:

Green:

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Gold:

179

Chance experiments There is a 1-in-2 chance of choosing correctly when a coin is tossed. That means that if you toss the coin four times the chances are that it will land twice on heads and twice on tails. However, does that mean it will happen?

1st toss

2nd toss

3rd toss

4th toss It’s sure to land on tails next time, isn’t it?

Explore 1

Imagine a coin lands on heads 10 times in a row. Circle the chance of it landing on tails next throw. 100%

90%

75%

50%

25%

a Predict the result if you toss a coin 10 times.

Heads:

Tails:

8th

10th

Toss

1st

4th

5th

6th

7th

9th

D R

H or T?

2nd 3rd

AF T

b Toss a coin 10 times. Record the results.

c C ompare your prediction with what actually happened. Explain the difference. 3

There is not a 1-in-2 chance of rolling a 4 on a 6-sided die.

Give a number value for the chance of the die landing on 4.

If a dice lands on 4 ten times in a row, what is the chance of it landing on 4 on the eleventh throw?

a Predict the result if you roll a die 12 times. One:

Two:

Three:

Four:

Five:

Six:

b Roll a die 12 times. Record the results. Toss

1st 2nd 3rd 4th 5th

6th

7th

8th

9th 10th 11th 12th

Result

c W as it more difficult to predict the results for the coin or the die? Try to give an explanation.

180

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For this experiment, you will need two coins. There are three results that can occur. Fill in the table to show the possible results. When you toss two coins the result can be: They both land on heads.

Predict the results after 40 tosses of the coins. Two heads:

Two tails:

Heads and tails:

Carry out the experiment. Tally and record the results in the table. Ways the coins landed

Two heads

Two tails

Heads and tails

AF T

Tally of the number that combination occurred

D R

Total

Write a few sentences commenting on the results of your experiment.

Each result did not have the same chance of occurring in the last experiment. Explain why by looking at the diagram.

Result: heads and tails

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Result: two tails

Result: two heads

181

For this experiment, you will need a spinner with 4 equal segments split into four numbered sections. You could make a spinner or use an online one.

Deepen

a C ircle the number values that describe the chance of the spinner not landing on number 4. 3 7 out of 10 3 out of 4 75% 0.75 4 b If you spin the spinner four times it should land on each number once. Do you think that will happen? Give a reason for your answer.

Decide on the number of spins that is necessary to obtain accurate results. 12? 20? 40? (The number needs to be a multiple of 4.) Operate the spinner and tally the results in the table.

Number on the spinner

AF T

Tally of the number of times it occurred

D R

Total

If you made five-sided spinners and numbered them like this, which one would you more likely land on a 4? Explain.

1 4

Write a few sentences about the results of the experiment. Think about things such as: • Why did it not land the same number of times on each number? • If I started from the beginning again, would the results be the same? • If I doubled the number of spins, would it be very different?

182

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Quick 10s / Tere Tekau Term 1 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

33, 44, 55,

9×5=

235 + 379 =

0.34 = 100

81 ÷ 9 =

0.25 = 1? 6×

88, 77, 66,

12, 24, 36, 9× = 42

= 63

351 ÷ 5 =

7×8=

923 − 361 =

0.7 = 10

24 ÷ 3 =

/ 10

D 7×6=

0.58 = 100

0.5 = 1?

× 6 = 24 6×7=

? 0.3 = 10

743 ÷ 4 = 0.75 = 4?

901 − 458 =

/ 10

22, 33, 44,

6×8=

508 + 167 =

0.19 = 100

48, 36, 24,

63 ÷ 9 =

8×

4×

= 64

72 ÷ 8 =

/ 10

D R

824 − 241 =

AF T

562 × 4 =

835 ÷ 4 =

416 + 205 =

312 × 5 =

231 + 723 =

234 × 6 =

15, 27, 39, = 28

7×

= 49

742 ÷ 6 =

8×6=

639 ÷ 4 =

0.6 = ?

0.9 = 10

902 − 358 =

145 × 4 =

18 ÷ 3 =

36 ÷ 3 =

652 ÷ 3 =

418 + 529 =

790 − 356 =

0.4 = ?

815 − 267 =

304 × 5 =

/ 10

63 0.63 = ?

357 + 468 = 215 × 6 =

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

/ 10 183

Quick 10s / Tere Tekau Term 1

77, 66, 55,

4×9=

327 + 489 =

0.72 = 100

419 + 278 =

60, 48, 36,

36 ÷ 9 =

6×

8×

54 ÷ 6 = 7×

= 49

11, 22, 33,

= 42

= 56

9×8=

856 ÷ 7 =

5×7=

0.2 = 10

734 − 289 =

0.6 = 10

918 ÷ 5 =

? 0.5 = 2

27 ÷ 3 =

845 − 392 = ?

765 ÷ 4 =

289 + 634 = 418 × 3 =

/ 10

J 8×7=

? 0.41 = 100

932 − 487 =

/ 10

99, 88, 77,

3×9=

256 + 319 =

0.63 = 100

33, 45, 57,

45 ÷ 5 =

5×

6×

= 40

0.75 = ?

/ 10

D R

0.25 = 4

312 × 6 =

AF T

236 × 7 =

72, 60, 48, = 36

4×

= 28

967 ÷ 8 =

4×8=

731 ÷ 5 =

845 − 376 =

0.4 = 10

0.1 = ?

835 ÷ 6 =

30 ÷ 3 =

21 ÷ 3 =

421 × 3 =

512 + 389 = 236 × 4 = 3

0.3 = ?

72 0.72 = ?

710 − 265 =

/ 10 184

/ 10

912 − 458 = 427 + 316 = 125 × 7 =

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

44, 55, 66,

5×8=

387 + 146 =

0.27 = 100

512 + 263 =

11, 23, 35,

63 ÷ 7 =

9×

0.75 = ?

27 ÷ 9 = 3×

= 24

66, 55, 44,

= 72

7×6=

685 ÷ 6 =

0.8 = 10

903 − 417 =

8×5=

235 × 5 =

45 ÷ 3 =

923 ÷ 4 =

0.5 = 2

0.1 = 10

/ 10

P 2×9=

? 0.86 = 100

96, 84, 72,

= 21

164 × 6 =

318 + 649 =

745 ÷ 3 =

209 × 3 =

690 − 358 =

AF T

802 − 419 =

= 35

/ 10

D R

0.25 = 4

3×

7×

55, 66, 77,

6×7=

294 + 381 =

0.51 = 100

0.84 = ? 81 ÷ 9 =

19, 31, 43, 8×

= 56

758 ÷ 4 =

6×

821 − 356 =

3×9=

834 − 469 =

42 ÷ 3 =

0.5 = 10

33 ÷ 3 =

318 × 4 =

412 + 579 =

234 + 587 =

862 ÷ 5 =

312 × 5 =

777 − 422 =

0.9 = 100

0.2 = ?

/ 10

= 48

947 ÷ 3 =

145 × 8 =

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

/ 10 185

Quick 10s / Tere Tekau Term 2 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

= 42

512 + 189 =

418 + 267 =

6×

72 ÷ 8 =

235 + 379 =

63 ÷ 7 =

835 ÷ 4 =

8×

6×9=

81 ÷ 9 =

9×6=

0.3 × 10 =

87 ÷ 10 =

0.7 × 10 =

312 × 4 =

824 − 241 =

421 × 3 =

743 ÷ 5 =

7×8=

34 = 4

8.4 × 10 =

15 = 5

905 − 468 =

234 × 6 =

790 − 356 =

528 ÷ 10 =

23 = 3

349 ÷ 10 =

/ 10

= 56

653 ÷ 4 =

AF T

= 35

/ 10

D R

5×

905 − 468 =

304 + 528 =

421 × 3 =

4×

54 ÷ 6 =

63 ÷ 7 =

= 28

7×

46 = 6

8×7=

418 + 267 =

0.5 × 10 =

512 + 189 =

64 ÷ 10 =

258 × 5 =

8×

743 ÷ 5 =

918 ÷ 7 =

653 ÷ 4 =

6×7=

845 − 392 =

93 ÷ 10 =

9.2 × 10 = 312 × 5 =

/ 10

= 49

72 ÷ 8 = 3

186

28 = 8

7.5 × 10 =

3 ? 2 10 = 10

672 ÷ 10 =

/ 10

= 56

790 − 356 = 9×6=

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

623 + 145 =

52 ÷ 10 =

517 + 268 =

45 ÷ 5 =

845 − 392 =

36 ÷ 4 =

258 × 5 =

4×

9×

= 63

6×8=

918 ÷ 7 =

4 ? 25 = 5

304 + 528 =

= 28

1 ? 24 = 4

7×9=

0.2 × 10 =

6.1 × 10 =

0.9 × 10 =

346 × 6 =

8×7=

519 × 2 =

932 − 487 = 415 ÷ 10 =

54 ÷ 6 = 7×

= 49

710 − 265 = 628 ÷ 10 =

/ 10

346 × 6 =

401 + 359 =

517 + 268 =

932 − 487 =

27 ÷ 3 =

835 ÷ 6 =

81 ÷ 10 =

3×

623 + 145 =

5×7=

710 − 265 =

0.6 × 10 =

3 10 = 10

J 1 ? 26 = 6

D R

/ 10

835 ÷ 6 =

AF T

765 ÷ 4 =

2 ? 43 = 3

= 24

5.9 × 10 = 4

3.7 × 10 =

235 × 5 =

45 ÷ 5 =

923 ÷ 4 =

4×

6×8=

802 − 419 =

519 × 2 =

746 ÷ 10 =

47 ÷ 10 =

38 = 8

7×9=

7×

= 42

765 ÷ 4 =

/ 10

36 ÷ 4 =

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

= 28

/ 10 187

Quick 10s / Tere Tekau Term 2

612 + 278 =

802 − 419 =

329 + 184 =

63 ÷ 9 =

38 ÷ 10 =

81 ÷ 9 =

923 ÷ 4 =

6×

3×

9×5=

8×

= 64

6×7=

2 ? 13 = 3

0.4 × 10 = 164 × 6 = 745 ÷ 3 = 2 ? 54 = 4

= 24

235 × 5 =

264 × 8 =

5×7=

862 ÷ 5 =

27 ÷ 3 =

35 = 5

589 ÷ 10 =

8.6 × 10 =

AF T

401 + 359 =

777 − 422 = 913 ÷ 10 =

/ 10

D R

= 48

0.1 × 10 =

690 − 358 =

/ 10

164 × 6 =

415 + 267 =

777 − 422 =

4.2 × 10 =

42 ÷ 6 =

264 × 8 =

63 ÷ 9 =

7×

690 − 358 =

8×6=

745 ÷ 3 =

0.9 × 10 =

81 ÷ 9 =

6×7=

36 = 6

9×

318 × 4 =

329 + 184 =

953 ÷ 7 =

862 ÷ 5 =

864 − 397 =

8×5=

735 ÷ 10 =

59 ÷ 10 =

612 + 278 = 8×

= 64

1 ? 5 10 = 10

76 ÷ 10 =

/ 10 188

= 49

68 = 8

2.8 × 10 = ?

/ 10

= 36

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Quick 10s / Tere Tekau Term 3 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

329 − 231 =

2 6 of 36?

1.56 + 0.78 = 4.92 × 10 =

8.3 × 10 =

418 + 275 = 845 − 367 = 164 × 5 =

/ 10

D 845 − 367 = 6.7 × 10 =

592 + 322 = ×

= 24

283 × 4 =

AF T

= 42

9.23 − 5.87 =

1.56 + 4.28 = 418 + 275 = 8.41 − 3.16 = 4 1 + 6 3 =

= 35

/ 10

= 56

736 + 128 = 902 − 458 = 215 × 6 = 1 3 5 + 5 =

9.18 × 10 = 745 ÷ 10 = = 63

523 + 389 = 1 2 8 + 8 =

164 × 5 =

8×

3 10 of 60?

9×

914 ÷ 10 =

/ 10

7.54 − 3.18 =

45 ÷ 10 =

7.64 × 10 =

/ 10

5.43 + 0.26 =

4 6 of 36?

5 6 of 48?

6.82 − 1.49 =

1 2 4 + 8 =

D R

8.41 − 2.35 =

C 3.27 + 1.15 =

27 ÷ 10 =

2 3 + 7 7 =

2 8 of 24?

2.34 + 7.42 =

563 ÷ 10 =

7×

710 − 265 = 324 × 3 =

215 × 6 = 63 ÷ 10 = 3.72 + 2.15 = 3 8 of 48?

736 + 128 = 9.4 × 10 = 902 − 458 = ×

= 42

7.82 − 1.49 = 2 4 5 + 10 =

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

/ 10 189

Quick 10s / Tere Tekau Term 3

710 − 265 =

2 8 of 72?

4.61 + 2.33 = 6.07 × 10 =

864 − 397 = 438 × 2 =

/ 10

J 4.61 + 3.33 = 864 − 397 = 612 + 247 =

5.43 + 1.26 = ×

= 56

7.8 × 10 = 2 5 4 + 8 =

9.45 − 4.27 = = 63

6 3 − 7 7 =

8.93 − 5.47 = 5×

= 35

401 + 359 = 932 − 487 = 126 × 7 =

2.49 + 0.88 =

2 1 6 + 3 =

= 21

517 + 268 = 777 − 422 = 257 × 4 =

/ 10

952 ÷ 10 =

/ 10

3 7 of 56?

3×

5.2 × 10 =

7.28 + 1.64 =

/ 10

6.71 − 2.46 =

91 ÷ 10 =

190

84 ÷ 10 =

481 ÷ 10 =

438 × 2 =

5 2 8 + 8 =

523 + 389 =

5.84 × 10 =

4 9 of 72?

2 3 of 33?

3.56 × 10 =

AF T

= 28

612 + 247 =

324 × 3 =

D R

9.45 − 4.27 = 4×

6.54 − 2.18 = 2 3 of 60?

638 ÷ 10 = 2 3 5 + 5 =

/ 10

126 × 7 = 3.9 × 10 = 8.93 − 5.47 = 1 2 of 38? 1 8 5 + 10 =

401 + 359 = 932 − 487 = 58 ÷ 10 = 7.28 + 1.64 = ×

= 28

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

M 257 × 4 =

3 10 of 80?

1.75 + 3.14 = 8.26 × 10 = 7.82 − 1.93 = = 36

329 + 184 = 802 − 419 =

73 ÷ 10 =

6.52 + 0.39 =

1 2 6 + 3 =

777 − 422 = 2.49 + 6.88 = 2 8 of 56?

7.71 − 2.46 =

AF T

4.6 × 10 =

145 × 8 =

/ 10

P 145 × 8 =

= 48

329 + 184 = 1.75 + 5.14 =

3.68 + 1.27 = 7.35 × 10 =

3 4 of 80?

4×

= 54

/ 10

= 56

415 + 267 = 4 1 5 − 5 =

690 − 358 = 312 × 5 =

8.62 − 3.49 =

8.1 × 10 =

7×

846 ÷ 10 =

6.82 − 1.93 =

9.14 − 4.88 =

/ 10

5 1 + 7 7 =

802 − 419 =

728 ÷ 10 =

/ 10

5 6 of 54?

39 ÷ 10 =

4.71 × 10 =

D R

1 7 4 + 8 =

O 4 6 of 42?

517 + 268 =

369 ÷ 10 = 6×

= 36

538 + 274 = 921 − 456 = 4 3 − 5 10 =

264 × 4 =

312 × 5 = 7.4 × 10 = 690 − 358 = 415 + 267 = 2 4 + 8 8 =

9.14 − 4.88 = 68 ÷ 10 = 6 7 of 42?

6.52 + 2.39 = ×

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

= 72

/ 10 191

Quick 10s / Tere Tekau Term 4 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

1.56 + 0.38 =

283 × 6 =

945 ÷ 5 =

418 − 207 =

25% of 64 =

3.14 + 0.58 =

126 × 3 =

Round 4.78 to nearest whole number =

56 ÷

418 + 257 =

50% of 40 =

Round 742 to nearest 100 = 50% of 18 =

8×3=

25% = ?

648 ÷ 4 =

672 ÷ 4 =

256 × 5 =

36 ÷

5, 10, 15,

4×8=

25% = ?

10% of 110 =

/ 10

512 + 189 =

3.08 + 0.67 =

690 + 245 =

Round 8.21 to nearest whole number =

690 − 245 =

283 × 3 =

214 × 5 =

312 × 4 =

25% of 92 =

Round 859 to nearest 100 =

Round 3.49 to nearest whole number =

8×7=

50% of 42 =

D R

10% of 64 =

642 − 319 =

1.56 − 0.38 =

AF T

36 ÷

Round 781 to nearest 100 =

10% = ?

7×6=

/ 10

10 = 40

3.45 − 0.97 = 945 ÷ 5 = 3 = 30

54 ÷

6, 12, 18,

816 ÷ 4 = %

9×3=

54 ÷ ,

/ 10 192

25% of 76 = 9×4= 2.88 − 0.41 = 816 ÷ 4 = 10% = 8

10% of 78 =

/ 10

42 ÷

7, 14, 21,

=6 ,

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

0.92 + 1.45 =

8, 16, 24,

804 − 357 =

327 + 418 =

864 ÷ 4 =

145 × 6 =

60 ÷

589 − 274 =

Round 267 to nearest 100 =

25% of 48 =

318 × 3 =

50% of 26 =

6×8=

6×9=

283 × 4 =

50% of 22 =

924 ÷ 6 =

Round 9.62 to nearest whole number =

Round 452 to nearest 100 =

6×7=

1.74 − 0.56 =

54 ÷

25% = 1

735 ÷ 5 =

10% of 95 =

/ 10

10% = 9 ?

0.47 + 2.36 =

25% = 25

10% of 75 =

D R

42 ÷

AF T

/ 10

Round 5.18 to nearest whole number =

8×7=

512 + 267 =

25% of 88 =

2.09 + 0.88 =

3, 6, 9,

147 × 6 =

283 × 5 =

760 − 395 =

25% of 52 =

50% of 60 =

864 ÷ 4 =

702 ÷ 6 =

Round 7.74 to nearest whole number =

245 + 376 = 9×7= 2.63 − 0.84 = 30 ÷

214 × 6 =

Round 906 to nearest 100 =

648 ÷ 4 =

42 ÷

9, 18, 27,

10% = ?

100

/ 10

25% = 25

10% of 98 =

8×6= 4.12 − 1.09 = 48 ÷

10% = ?

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

/ 10 193

Quick 10s / Tere Tekau Term 4

7×5=

36 ÷

2.75 + 0.84 =

905 − 468 =

418 + 309 =

731 − 428 =

1.63 + 0.29 =

Round 2.66 to nearest whole number =

237 × 3 =

198 × 4 =

1.95 − 0.48 =

Round 614 to nearest 100 =

Round 338 to nearest 100 =

6×7=

50% of 50 =

4 = 16

945 ÷ 5 =

9×5=

672 ÷ 3 =

25% of 68 =

5×9=

30 ÷

10, 20, 30,

10% of 86 =

648 ÷ 8 =

/ 10

11, 22, 33,

10% of 140 =

/ 10

735 ÷ 5 =

327 + 512 =

7×8=

8×4=

12, 24, 36,

690 + 318 =

48 ÷

25% of 96 = 283 × 2 =

10% of 120 = 2.41 + 0.59 =

Round 6.51 to nearest whole number =

Round 8.49 to nearest whole number =

523 − 186 =

816 ÷ 4 =

214 × 5 =

7×7=

3.76 − 1.22 =

Round 391 to nearest 100 =

25% of 72 =

50% of 30 =

42 ÷

672 ÷ 4 = 54 ÷

10% = ?

/ 10

45 ÷

D R

5 = 50

12 = 48

AF T

50% of 12 =

194

25% = ?

/ 10

2.19 − 0.67 =

9×6= 10% = ?

100

/ 10

Year 6 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

D R AF T

D R