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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 9780190357313

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Reproduction and communication for educational purposes The New Zealand Copyright Act 1994 (the Act) allows educational institutions that are covered by remuneration arrangements with Copyright Licensing New Zealand to reproduce and communicate certain material for educational purposes. For more information, see copyright. co.nz.

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

Strand 3: Measurement Measuring

Year 3

Topic 3.1: Length, mass and capacity................. 100

Strand 1: Number

Topic 3.4: Turns ...........................................................116

Number structures

Topic 3.6: Duration....................................................124

Topic 3.2: Perimeter.................................................. 108 Topic 3.3: Area ...........................................................112 Topic 3.5: Telling the time.....................................120

Topic 1.1: Whole numbers........................................... 8 Topic 1.2: Tens and hundreds...................................12 Topic 1.3: Rounding and estimating...................... 16

Operations

Shapes Topic 4.1: Polygons.................................................... 128

Spatial reasoning

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Topic 1.4: Counting in multiples..............................20

Strand 4: Geometry

Topic 1.5: Adding and subtracting........................24

Topic 1.6: Addition and subtraction word problems.................................................... 32

Topic 4.2: Symmetry...................................................132

Pathways Topic 4.3: Following instructions.......................... 136

Topic 1.8: Family of facts......................................... 40

Topic 4.4: Maps..........................................................140

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Topic 1.7: Multiplication and division facts.........36 Topic 1.9: Multiplying................................................ 44

Topic 1.10: Dividing..................................................... 52

Strand 5: Statistics

Rational numbers

Developing knowledge from data

Topic 1.11: Reading and writing fractions........... 60 Topic 1.12: Unit fractions.......................................... 64 Topic 1.13: Equivalent fractions..............................68

Topic 5.1: Collecting data....................................... 144

Visualisation of data

Topic 1.14: Adding and subtracting fractions.... 72

Topic 5.2: Displaying data..................................... 148

Topic 1.15: Fraction of a number............................. 76

Interpretation of data

Topic 1.16: Finding the whole set.......................... 80

Financial mathematics Topic 1.17: Money....................................................... 84 Topic 1.18: Giving change.........................................88

Strand 2: Algebra Equations and relationships Topic 2.1: Number sentences...................................92 Topic 2.2: Number patterns.....................................96

Topic 5.3: Analysing data........................................152

Quick 10s........................................................ 156

For the teacher Kia ora! Thanks for choosing Mathematics and Statistics for Aotearoa New Zealand (Second edition). This programme has been purpose-written by experienced New Zealand teachers to the provide complete coverage of the NZC – Mathematics and Statistics Phases 1–3 (October 2025). Every component has been developed with real classrooms in mind – practical, curriculum-aligned, and ready to use.

How the programme works At each year level (Years 0–8), the programme includes the following components: The Teacher Dashboard is your central hub for planning and managing the programme. From here you can access: • suggested teaching and learning sequences • lesson plans • interactive teaching slides to support explicit teaching • diagnostic quizzes (both online and paper) • supporting resources such as activity sheets, blackline masters, videos, interactives • a range of formative and summative assessments.

Student Dashboard

The Student Dashboard gives students their own dedicated space to access digital activities and interactives that support and extend the learning. Designed to be intuitive and independently navigable, it keeps students engaged and on task, whether they’re working in class or at home.

Student Workbook

The Student Workbook is the core learning tool for students. It provides structured, curriculum-aligned activities across all strands, ensuring complete coverage of the curriculum.

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Teacher Dashboard

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

Element

Topic 4.3 Transformations

Strand Strand number

Topic number

Topic title

About this Student Workbook Content in this Student Workbook is organised and sequenced to align with the New Zealand Curriculum. There are six strands, and each strand is broken down into elements and topics. In every topic, questions are grouped into three levels to support students of all ability levels: Learn: T hese questions model new concepts and allow students to practice with high support. Explore: These questions consolidate understanding in different ways, with a decreasing amount of support. Deepen: T hese questions challenge and deepen understanding in new and real-world contexts with a focus on mastery.

Year 3 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 tenquestion 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.

Quick 10s / Tere Tekau Term 1

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Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

3, 6, 9, 11 + 8 = Smaller: 28 or 37? 14 − 3 = 80, 70, 60, , 17 + 2 = 15, 20, 25, 30, 8+8= Round 46 to nearest 10 Is 42 odd or even?

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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. Erin Doleman Programme consultant and author

7+7= Bigger: 63 or 36? 20, 25, 30, 35, 30, 40, 50, 6+6= 13 + 7 = 3, 6, 9, 12,

Term 70, 2 60, 50,

19 − 6 =

Round will 74 to nearest Your teacher tell you when it’s time to refresh your skills using these Quick 10 quizzes! 15, 25, 35, 45,

9+9= Is 18 odd or even? 7−5= 6+6= /10 /10 /10 Bigger: 18 or 27? 34 + 80 = 6 + 90 = Is 27 odd or even? 12, 15, 18, 21, Round 68 to nearest 10 4+4= Is 31 odd or even? 7 + 100 = 3, 5, 7, 2, 4, 6, 25, 30, 35, 8+2+6= 18, 15, 12, 9, 80, 75, 70, 20, 30, 40, 8+7= 36 + 40 = 5+9+4= 17 + 3 = 9+6= 3, 6, 9, 12, 9, 7, 5, 3, 10, 20, 30, Bigger: 52 or 25? Smaller: 90 or 9? 80, 70, 60, Round 58 to nearest 23 − 8 = 13 + 9 = 11 + 7 = 14 + 9 = 10 Bigger: 14 or 41? 8+8= 18 − 6 = Bigger: 39 or 93? 20, 30, 40, Round 67 to nearest 7 + 7/10 = /10 10 Round 32 to nearest Round 85 to nearest 10 10 10 + 10 = Is 33 odd or even? 30, 35, 40, 16 − 6 = 15 − 4 = Is 26 odd or even? Is 48 odd or even? Is 28 odd or even? 9−6= /10 /10 10, 15, 20, 25, /10 Bigger: 14 or 41? 6 + 100 = 7 + 80 = 41 + 38 = 21, 18, 15, 12, Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press 14, 19, 24, 5+5= 27 − 5 = Is 28 odd or even? Smaller: 14 or 41? 6+2+9= 4+6+8= 25 + 30 = 7+7= 10, 15, 20, 25, Round 53 to nearest Round 73 to nearest 10 10

Ngā mihi nui,

Round 58 to nearest 3 + 16 = 10 Smaller: 41 or 14? Is 29 odd or even? 3, 6, 9, 12, Quick 10s / Tere Tekau 12 + 9 = 17 + 4 =

156

/10

Is 37 odd or even? 5, 7, 9, 11, 8 + 100 = 29 + 60 = 12, 22, 32, 18 − 5 = Smaller: 15 or 51? 3+7+6= 8+8= Round 39 to nearest 10

/10

F 9+9= 46 + 90 = Is 45 odd or even? Round 74 to nearest 10 4 + 100 = 12, 15, 18, 21, 7+2+5= 8, 10, 12, 28 − 9 = Bigger: 32 or 23?

/10

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

/10 159

Hi there! I’m Hemi the Hector’s Dolphin (Upokohue).

Getting set up on Oxford Digital Scan this QR code (or visit www.oup.com.au/nzmaths_QR) to get started!

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

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PRO

PA S S P

Strand 1: Number

Number structures For me

Topic

For my teacher

Example

I feel

1.1

Recognising the place value of each digit in a three-digit number

121 = 100 + 20 + 1 534 >527

Comparing and ordering whole numbers up to 1,000 Finding the total number of objects beyond 120 by first separating them into groups

1.2

Tens and hundreds

1.4

Counting in multiples

Counting forwards and backwards in 10s and 100s from any whole number between 0 and 1,000

67 + 72 = ? Estimate = 70 + 70 = 140

30, 25, 20, 15... 8, 16, 24, 32... 27, 24, 21, 18…

Rounding numbers to the nearest 10 or 100

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230, 240, 250, ____

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Rounding and estimating

Review & date

Reading and writing whole numbers up to 1,000 and representing them using base10 structure

Whole numbers

1.3

Practices (NZC 2025)

Estimating the answer to a calculation

Counting forwards and backwards in 2s, 3s, 4s, 5s and 8s from multiples of these numbers

Operations 1.5

Adding and subtracting

1.6

Addition and subtraction word problems

1.7

34 + ___ = 100 329 - 12 = 437 + 80 =

Family of facts

Finding the complement of a number to 100 Adding and subtracting numbers up to 1,000

You have 724 stamps, you give 390 away. How many stamps do you have left?

Solving one-step addition and subtraction problems involving numbers up to 1,000

You have $60. You earn $27 more and give $15 to a friend. How much money do you have left?

Solving multi-step addition and subtraction problems involving numbers up to 100

3 + 3 + 3 + 3 = 3 × 4 = 12

Multiplication and division facts

1.8

5 × 7 = 35 7 × 5 = 35 35 ÷ 7 = 5 35 ÷ 5 = 7

Multiplying or dividing using equal sharing, grouping, repeated addition or subtraction and known facts

Memorising multiplication and corresponding division facts for 2s, 3s, 4s, 5s, 8s and 10s

Year 3 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Operations (continued)

1.9

3 × 6 = 18 4 × 78 = 312

Multiplying a one- or two-digit number by a one-digit number

1.10

9÷3=3 45 ÷ 9 = 5

Dividing whole numbers by a one-digit divisor with no remainders

Multiplying

Dividing

Rational numbers 1.11

2 = 6

Reading and writing fractions

1.12

Unit fractions

Reading, writing and representing fractions of sets, quantities and measurements on a number line, and of regions, using small denominators

1 2

Counting in unit fractions up to 1

1 3, 3, 3 — is equal to… 2 1 — 2

1 1 > 4 6

2 — 4

3 — 6

Adding and subtracting fractions

1.15

1 2 3 6 + + = 8 8 8 8

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3 5 < 7 7

Fraction of a number

1 of 15 = 15 ÷ 3 = 5 3

1.16

If 1 of a set is 3, then the whole 4 set is 4 × 3 = 12

Finding the whole set

6 — 12

Identifying when two fractions are equivalent, using representations

1 2 = 2 4

1.14

5 — 10

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1.13

Equivalent fractions

4 — 8

Comparing unit fractions with denominators up to 12

Comparing non-unit fractions with the same denominator up to 12 Adding and subtracting fractions with the same denominator within a whole

Finding a unit fraction of a whole number by connecting to division

Finding the whole when given a unit fraction by connecting to repeated addition or multiplication

Financial mathematics 1.17

Money

$2 and 50c

Making amounts of money using one- and two-dollar coins and 5-, 10-, 20-, 50- and 100-dollar notes

1.18

Giving change

Representing currency values of mixed dollars and cents without using decimal notation

Iceblock = $2 How much change from $10?

Using addition and subtraction to give change

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

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PRO

PA S S P

Strand 2: Algebra

Equations and relationships For me

Topic

Example

2.1

Number sentences

2.2

I feel

Practices (NZC 2025)

True or false: 313 < 330? 12 ÷ 3 = 5 − 2?

Checking the truth of number sentences involving direct comparisons of whole numbers up to 1,000

217 − ____ = 105 3 × ____ = 24 ____÷ 5 = 7 56 = 37 + ____

Checking the truth of number sentences and completing open number sentences involving addition, subtraction, multiplication or division

Review & date

Recognising, continuing and creating growing number patterns

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Number patterns

For my teacher

Keep swimming, you’re making great progress!

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

ESS

PRO

PA S S P

Strand 3: Measurement

Measuring For me

Topic

For my teacher

Example A

I feel B

C 4L

3.1

Length, mass and capacity

F 1 L 500 mL

500 mL

125 g 3 L

Practices (NZC 2025)

Review & date

Estimating and measuring length (cm and m), mass (g and kg) and capacity (mL and L) using tools with labelled markings and whole-number metric units

Comparing and ordering objects using whole number metric units of length, mass or capacity

15 cm 3.2

Perimeter

7 cm

Measuring the perimeter of polygons using metric units

7 cm

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15 cm

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Perimeter = 44 cm

3.3

Area

Measuring the area of rectangles using squares of equal size

Area = 9 squares Turning an object or person and describing how far they have turned, using full, half, quarter and three-quarter turns as benchmarks

3.4

Turns

Telling the time on analogue and digital clocks to the nearest 5 minutes and the nearest minute, using the language of minutes past the hour and to the hour

3.5

Telling the time

60 minutes = 1 hour 52 weeks = 1 year

3.6

Duration Time taken to brush your teeth?

Describing the differences in duration between units of time Identifying the duration of events using years, months, weeks, days, hours, minutes and seconds

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

ESS

PRO

PA S S P

Strand 4: Geometry

Shapes For me

Topic

Example

For my teacher I feel

Practices (NZC 2025)

Review & date

corner

4.1

Identifying, describing, visualising and sorting regular polygons with up to 10 sides

side

Polygons

Spatial reasoning Recognising lines of symmetry in patterns or pictures, and creating or completing symmetrical patterns or pictures

4.2

Pathways

Following instructions half turn

4.4

Maps

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4.3

Move 2 squares right, quarter turn to the left

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Symmetry

quarter turn

Describe locations on a map using words such as: above, opposite, left, right, above, below, beside, between

Following and creating a sequence of stepby-step instructions for moving people or objects to a different location, including half and quarter turns and the distance to be travelled

Using simple maps to locate objects and places relative to other objects and places.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

PRO

ESS

Strand 5: Statistics Progress passport: Statistics PA S S P

Developing knowledge from data For me

Topic

For my teacher

Example Fruit

I feel

Practices (NZC 2025)

Review & date

Collecting categorical data and sorting the responses

Vegetables

5.1

Collecting data

Collecting numerical data by asking an investigative question with a response that is a count or a discrete measurement

How many siblings do you have?

Visualisation of data Types of shapes

Number of shapes

Creating data visualisations for categorical and numerical data Square

Circle

Triangle

Star

Shapes

Interpretation of data

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7 6 5 4

5.2

Analysing data

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5.2

Displaying data

10 9 8 7 6 5 4 3 2 1

Describing data visualisations using the variable name and the context and giving the frequency for each category or number

3 2 1 Movies

Sport

Shopping

Reading

What was the most popular activity?

Answering questions about data visualisations, including which category has the most or least items and questions involving operations

I can see your progress in the data!

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Number structures

Topic 1.1 Whole numbers This is a one.

This is 12 ones This is 120 ones OR 1 ten and 2 ones. OR 1 hundred and 2 tens.

This is 1,000.

Learn 1

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AF T

In a 3-digit number, the first digit is hundreds, the second is tens and the third is ones.

How many?

Write the numbers. b

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Write the numbers

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Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Numbers with more digits are greater than those with fewer digits.

When comparing numbers, start from the left-most place value.

23 < 100

556 > 550 because 6 > 0.

> means greater than and < means less than.

Explore Insert > or <.

105

456

478

812

765

347

352

689

682

243

198

423

432

950

905

Order the numbers from smallest to biggest.

111

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920

513

101

713

902

297

349

Order the numbers from biggest to smallest. 345

When the place values match, keep going right until there is a difference.

319

357

451

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Colour the blocks to show the number.

132

b 321

231

d 123

312

What different 3-digit numbers could you make with:

1, 6, 3

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D R

f 213

Think about the place value of each digit.

Circle the largest number you made. Underline the smallest number. b

0, 3, 4? Circle the largest number you made. Underline the smallest number.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Number structures

Topic 1.2 Tens and hundreds Count forwards and backwards in 10s from 72. –10

–10

+10

102

112

Counting forwards in 10s is just like counting with 1s, except you change the 10s digit.

Count forwards in 10s.

Count backwards in 10s. 181

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226

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Learn

Count forwards and backwards in 10s from 659. 659

Count forwards in 100s. 93

Count backwards in 100s. 977

Count forwards and backwards in 100s from 535. 535

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Sorting objects into groups of 10 or 100 There are: 8 hundreds 9 tens 0 ones. In total, the number is: 8

Explore 1

There are: hundreds

Use grouping to find the number.

tens

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ones.

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There are: hundreds tens ones. There are:

hundreds tens ones.

There are: hundreds tens ones.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Represent the numbers using place value blocks.

251

760

392

577

333

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Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen A class collected 156 shells at the beach. They put them into bags of 10.

How many full bags of 10 are there?

How many shells are left over?

There are 320 stickers. They are packed into boxes of 100.

How many full boxes are made?

Are there any left over?

There are 278 blocks.

Draw your thinking.

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Draw how to group them into hundreds, tens and ones.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Number structures

Topic 1.3 Rounding and estimating Rounding numbers to the nearest 10 When finding the nearest 10, check the number in the ones column. If the number in ones is 0 to 4, round down to the nearest 10. The nearest 10 to 13 is 10.

If the number in ones is 5 to 9, round up to the nearest 10. The nearest 10 to 38 is 40.

Learn

Round each number to the nearest 10 using a number line.

33 30

The nearest 10 is 31

. 45

The nearest 10 is

68 60

The nearest 10 is

42 40

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D R

If 4 or less, round down. If 5 or more, round up!

. 65

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

When rounding to the nearest 100, look at the tens digit.

Rounding numbers to the nearest 100 Instead of checking the number in the ones, check the number in the tens. If the number in the tens is 0 to 4, round down to the nearest 100. If the number in the tens is 5 to 9, round up to the nearest 100.

Round each number to the nearest 100 using a number line.

533

137 100

351 300

520

530

540

The nearest 100 is 110

120

130

320

330

560

570

580

590

600

. 140

The nearest 100 is 310

550

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510

D R

500

The nearest 100 is

340

150

160

170

180

190

200

350

360

370

380

390

400

Round each number to the nearest 100.

585 rounded to the nearest 100 is b 143 rounded to the nearest 100 is

131 rounded to the nearest 100 is d 260 rounded to the nearest 100 is

544 rounded to the nearest 100 is f 910 rounded to the nearest 100 is

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Estimating Rounding is useful to estimate if your answer to a calculation is reasonable. Andy said “158 + 78 = 206”. Does that seem right? Round each number to the nearest 10. 158 → 160

78 → 80

Add together: 160 + 80 = 240 So, 158 + 78 is about 240. Andy’s answer doesn’t look right.

Explore 1

Round each number to the nearest 10 and add them together.

52 + 179 ≈ 230

586 + 48 ≈ 600 +

Does it seem right?

Yes

Does it seem right?

Yes

Does it seem right?

Yes

Does it seem right?

Yes

139 + 262 ≈ 500 +

628 + 50 ≈ 680 +

382 + 278 ≈ 500 +

Yes

AF T

Does it seem right?

D R

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Round each amount to the nearest 10 to estimate the total.

Ariki family:

$148 + $196

Estimate ≈

Baker family:

$202 + $327

Estimate ≈

Round each amount to the nearest 100 to estimate the total.

Chen family:

$213 + $376

Estimate ≈

Singh family:

$257 + $107

Estimate ≈

D R

AF T

Which family spent the most?

Which family spent the least?

Estimate the total amount spent by the four families by rounding to the nearest 100. Show your thinking.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Number structures

Topic 1.4 Counting in multiples A number line can help us count forwards in multiples. Multiples of 2 starting from 0. 0

9 10 11 12 13 14 15 16 17

0, 2, 4, 6, 8, 10, 12, 14, 16

Learn

Count backwards in 2s. 64

Count forwards in 5s. 0

AF T

Count forwards in 2s.

D R

Count backwards in 5s. 100

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

a b

Skip count on the number line. 57

Count backwards in 3s. 54

Circle the multiples of 3. 14

8 24

25 9

AF T

Count forwards in 3s.

D R

17 7

6 5

16 29

I am thinking of a number.

If you count in 3s starting from 0, you will say my number after 8 jumps.

What number am I?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Count forward in 4s. 0

a b

Skip count on the number line. 32

Count backwards in 4s. 76

AF T

Count forwards and backwards in 4s.

D R

How high can you count in 4s?

100

124

108

136

I am a multiple of 4. When you count in 4s, I come after 20 and before 28. What number am I?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Count forward in 8s. 0

Skip count on the number line.

a b 3

Count backwards in 8s. 96

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5 students walk on a stone path starting from 0. Start 0

1 15

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7 8

16 17

End 24

Alice steps on every 2nd stone. Label these stones with an A.

Brayden steps on every 3rd stone. Label these stones with a B.

Chen steps on every 4th stone. Label these stones with a C.

David steps on every 5th stone. Label these stones with a D.

Eru steps on every 8th stone. Label these stones with an E.

Circle the numbers which no one steps on.

Which stones are stepped on 3 times?

Which students step on the last stone?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.5 Adding and subtracting What number do we add to 34 to get 100?

We can use a 100 grid to help us work out how to get to 100.

34 + 66 = 100

Learn 1

Use the 100 grid to work out the missing numbers. b

D R

AF T

48 + 2

= 100

82 +

= 100

Colour the 100 grids to work out the missing numbers.

21 +

74 +

= 100

64 +

= 100

37 +

Complete these number pairs to 100.

80 +

+ 30

10 +

50 +

+ 60

40 +

= 100

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Find the missing numbers.

+ 37 = 100

68 +

= 100

+ 43 = 100

29 +

= 100

+ 19 = 100

+ 71 = 100

AF T

56 +

D R

74 +

= 100

Look at your answer to question 4a.

Which two numbers add together to make 100?

Add the tens digits together.

+3=

Add the ones digits together.

+7=

Check the other equations in question 4. What do you notice? The tens digits add to

The ones digits add to

and 37

How could you use this to find the missing number when adding to 100?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Column addition When using column addition, you have to regroup if the total of a place value column is more than 10. T

2 Now add the tens. 3 tens + 4 tens = 7 tens. We also need to add the regrouped ten, so we end up with 8 tens.

1 Start with the ones. 7 + 5 = 12 Regroup the 12 for 1 ten and 2 ones.

Column addition works when there are more digits.

Explore 1

Start with the ones to solve. O

d T

g H

D R

AF T

a T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Use column addition to solve these multi-step additions. The first one has been done for you.

a 2 3

7 1

5 8

2 9

D R

AF T

Sometimes you might have to regroup a bigger number.

Rewrite these as column additions and solve.

257 + 483

23 + 16 + 5

b 621 + 298

c 365 + 327

e 72 + 9 + 8

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

33 + 18 + 2

Column subtraction In column subtraction, you have to regroup when the number you are subtracting is bigger than the number you are taking away from. T

2 Now subtract the tens. We regrouped 1 ten from the first number to the ones. That leaves: 6 tens – 2 tens = 4 tens

7 6 13 –

Start with the ones to solve the subtractions. O

−

d T

D R

a T

g H

−

AF T

−

1 Start with the ones. You can’t do 3 – 6. Regroup 1 ten from the tens column for 10 ones. 13 ones – 6 ones = 7 ones

−

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Use column subtraction to solve.

4 −

7 −

−

e −

h −

c −

f −

i −

D R

−

AF T

Rewrite these problems as column subtractions and solve.

456 – 123

−

714 – 287

−

b 732 – 49

c 312 – 99

−

e 912 – 79

−

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

453 – 465

−

The Place value strategy is when you look at each digit in a number and think about what its place means.

To solve 37 + 18: Add the 10s: 30 + 10 = 40 Add the 1s: 7 + 8 = 15 Then add them together: 40 + 15 = 55

Deepen 1

Split into 10s and 1s to add.

63 + 12 =

23 + 39 =

25 + 47 =

39 + 24 =

22 + 56 =

Now try some 3-digit numbers. The first one has been started for you

247 + 235

156 + 458

513 + 226

200 + 200 = 400

40 +

So, 247 + 235 = 3

AF T

D R

Break it apart to work it out!

So, 156 + 458 =

So, 513 + 226 =

Choose a method to find the answer. 263 + 143 =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Jump method for subtraction Take away the 10s, and then the 1s. 58 – 24 –1 –1 –1 –1

34 35 36 37 38

58 – 24

–10

Use the jump method to solve.

98 – 42 =

138 – 87 =

798 – 64 =

713 – 164 =

512 – 256 =

–20

34 35 36 37 38

D R

AF T

–4

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.6 Addition and subtraction word problems A Matariki festival sold 356 tickets one day and 522 tickets another day. How many tickets were sold in total? 356 + 522 = 878

Find the relevant information, write a number sentence and then solve.

Learn

going to a eating a lunchtime friend’s house cupcake at school There were 952 lollies in a shop and Anthony bought 433 of them. How many lollies are left in the shop?

building a house

D R

AF T

Circle the relevant information, write a number sentence and then solve. A B C D A city has 579 houses and builds 222 more. How many houses will there be in total?

A theatre has 500 seats and sold 419 tickets. How many seats are empty?

A zoo has 192 lizards and 134 snakes. How many lizards and snakes are there in total?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Write a number sentence and solve.

Jamie started with 34 grapes. He bought 16 more and was given another 18 by Jessica. How many grapes does Jamie have?

Lena has 19 red flowers, Amrith d has 27 white flowers and Tony has 32 yellow flowers. Together, how many flowers do they have?

Mātua Pene printed 38 sheets for his classes, Whaea Rawiri printed 21 sheets for her class and Whaea Su printed 24 sheets for her class. How many sheets did the teachers print in total?

Simon sold 12 bikes on one day, 26 bikes the next day and 36 bikes the next day. In total, how many bikes did Simon sell?

D R

AF T

Less than 1 kg

About 1 kg

More than 1 kg

Write your own addition word problem. Give it to a friend to solve.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Write a number sentence and solve.

Michelle baked 90 cupcakes. She gave 24 to Jasmine and 34 to Awhina. How many cupcakes does Michelle have left?

A group of 72 manu (birds) d scattered into three smaller groups. One group had 33 manu and another had 25 manu. How many manu were in the third group?

Write your own subtraction word problem. Give it to a friend to solve.

There were 86 cars at a dealership. Huy sold 22 cars and Liana sold 18 cars. How many cars remain?

There were 55 pencils in a bucket. One student took 13, another student took 14 and another student took 20. How many pencils were left?

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Write a number sentence and solve.

Ciara made 66 cookies. She sold 45 and was given 3 as a gift. How many cookies does she have in total?

There were 56 passengers on a bus. At a bus stop, 17 people got off and 8 people got on. How many people were on the bus as it departed?

A museum display had 54 shells. A worker added 17 more and later moved 9 shells to another display. How many shells were left?

Write your own multi-step word problem that uses addition and subtraction. Give it to a friend to solve.

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.7 Multiplication and division facts Multiplication can be thought of as repeated addition. 3 × 4 = 4 + 4 + 4 = 12 We can show this on a number line.

Division can be thought of as repeated subtraction. 48 − 8 − 8 − 8 − 8 − 8 − 8 = 0 Subtract 6 lots of 8 48 ÷ 8 = 6

Learn Use the number lines to answer the questions.

5×6=

45 ÷ 5 =

0 36

63 ÷ 9 =

7×3=

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Grouping 2 × 5 - think of this as 2 groups of 5 objects. In total, there are 10 objects. 2 × 5 = 10

Explore Draw in the missing objects and write the answer.

3×6=

4×5=

6×3=

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Equal sharing 8÷2

Draw one object in each box at a time until you use all the objects.

This can be thought of as 8 objects equally shared between 2. Each monkey gets 4 bananas. 8÷2=4

Draw 20 balls shared between 5.

D R

b 20 ÷ 5 =

AF T

a Draw 24 balls shared between 3.

b 24 ÷ 3 = 4

a Draw a picture to find 32 shared between 4.

b 32 ÷ 4 = 38

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen If you know your 2s, 5s and 10s you can solve this page!

Use your knowledge of 2s, 5s and 10s facts to answer the following questions.

2×5=

30 ÷ 10 =

2×7=

16 ÷ 2 =

5×6=

50 ÷ 10 =

5×7=

18 ÷ 2 =

10 × 6 =

45 ÷ 5 =

Use a multiplication fact that you know to multiply the numbers. Problem

D R

AF T

Known fact

How many more?

Answer

3×4

2×4=8

4 more

6×6 11 × 8 3×9 4×7 9×7

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.8 Family of facts A family of facts is a group of related equations that use the same numbers.

15 5

Learn

AF T

Fill in the blanks for each family of facts. 40

10 ×

4 40

D R

Write the corresponding division facts for each multiplication fact. Multiplication fact

Division facts 40 ÷

40 ÷

8 × 5 = 40

2 × 8 = 16

10 × 7 = 70

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Fill in the gaps to complete the multiplication facts chart. ×

30 40

Use the times tables chart to help you fill in these families of facts.

3 =

AF T

D R

f 16

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Fill in the gaps to complete the multiplication facts chart. 0

4 8

10 40

Complete the families of facts.

6 =

7 ×

9 ×

AF T

D R

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Write as many multiplication facts as you can for each number. 24

AF T

40 × 1 = 40 5 × 8 = 40 8 × 5 = 40 = 40

= 40

Write as many division facts as you can for each number. 2

2÷1=2 4÷2=2 6÷

D R

Circle the times tables that you know. 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, 10s

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.9 Multiplying 2+2+2+2=4×2=8

10 11 12

Learn 1

Show these equations on the number lines and fill in the blanks.

3+3+3=

D R

Where would I land if I added another 3?

AF T

6+6+6+6=

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Fill in the blanks and write the answer.

There are

groups of 4. In total, there are

stars.

×4= b

groups of =

apples.

D R

. In total, there are

AF T

There are

There are ×

groups of

. In total, there are

cats.

. In total, there are

frogs.

There are ×

groups of =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

An array can be used to display a multiplication. This is 3 lots of 6. 6 + 6 + 6 = 18 3 × 6 = 18 It can also be 6 lots of 3. 3 + 3 + 3 + 3 + 3 + 3 = 18 6 × 3 = 18

Explore Fill in the blanks. +

= 15

and

D R

AF T

Draw an array to calculate each multiplication.

5×6=

6×8=

4×7=

3×9=

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

2-digit × 1-digit multiplication You can split larger numbers to make multiplying easier. 3 × 12

is the same as 3 × 10

3×2

= 30 + 6 = 36

3 numbers Use the split method to calculate these multiplications. You can larger numbers to make multiplying easier. You can split larger numbers to make multiplying easier. ers to can make multiplying easier. You split larger numbers to make multiplying easier. t larger to split make multiplying easier.

is the same as

4×

+4×

D R

b 4 × 19

AF T

is + the same as2 + the ame 3 2same = is 30 +× 610 the as 2+ same 2same =20 3 ×30 10 33+××610 2 22 is3 the same as ×as × ×310 3 ×××12 310 × 12 × 12+asis3 × 12 asisa3the = 36 = 36

c 3 × 14

is the same as

3×

+3×

+= 4+ 30 6 + 23=+× 62 = 30 2+3×=× 230

= 36 = 36

= 36=

= =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Use the ten frames to find the answer.

2 × 14 = is the same as 2 × 10 + 2 × 4 =

3 × 11 is the same as 3 × 10 + 3 ×

3 × 14 is the same as 10 × 3 + 4 ×

D R

AF T

Use the split method to calculate these multiplications.

5 × 14 = 5 ×

+5×

6 × 12 = 6 ×

4 × 21 = 4 ×

+6×

+4×

= Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Solve using the split method.

3 × 71 =

6 × 21 =

2 × 34 =

= =

D R

3 × 52 =

2 × 24 =

5 × 48 =

AF T

5 × 81 =

= =

Split up the numbers into tens and ones.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Some multiplication facts can help you with other equations. If you know that 13 × 3 = 39, then you also know that 3 × 13 = 39.

Just like addition, the order that you multiply numbers doesn’t matter.

Deepen Use any method to calculate these multiplications.

9 × 12 =

2 × 11 =

3 × 24 =

2 × 27 =

8 × 22 =

7 × 25 =

Use your answers to question 1 to fill in the blanks.

12 ×

c e

D R

AF T

= 108 × 3 = 72

22 ×

= 176

11 × 2 =

27 × 2 =

× 7 = 175

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Solve these word problems.

A movie ticket is $22. How much would it cost for a family of 6 to buy tickets for each person?

A class of 24 students have 6 pencils each. How many pencils do they have in total?

A group of 36 chickens laid 3 eggs each. How many eggs did they lay together in total?

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Operations

Topic 1.10 Dividing How many groups of 2 in 8? 8 divided into groups of 2 gives 4 groups OR 8 ÷ 2 = 4

What does “equal groups” mean?

Learn 1

AF T

Draw circles to make equal groups of:

groups.

D R

12 divided into groups of 4 gives

12 ÷ 4 =

15 divided into groups of 3 gives

groups.

15 divided by 3 is

15 ÷ 3 =

12 divided by 4 is

Equal or unequal shares?

b Equal

Unequal

Equal

Unequal

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Add more counters to make the shares equal, then solve the equations.

12 ÷

25 ÷

24 ÷

AF T

D R

Write the equation.

What is 4 × 5?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Circle the equation to show equal shares and then answer the question.

5×2= 8÷2=

12 ÷ 2 = 3×3=

12 ÷ 4 = 8–2=

How many cherries does each child get?

How many apples does each child get?

6÷2= 6÷3=

6–2= 6+3=

D R

6–2= 6+3=

AF T

How many muffins does each child get?

6÷2= 6÷3=

How many kiwifruit does each child get?

Write an equation to share the stickers among each group of children.

12 × 2 = 10 × 10 =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

How many times can you subtract 5 from 25 until you get 0? 25 – 5 = 20 20 – 5 = 15 15 – 5 = 10 10 – 5 = 5 5–5=0

1 time 2 times 3 times 4 times 5 times

Division can be thought of as repeated subtraction.

We can show this on a number line by counting the number of jumps. 0

Explore

56 ÷ 7 = b

AF T

Use number lines to answer the divisions.

D R

54 ÷ 9 = c

16 ÷ 4 = d

42 ÷ 6 = e

27 ÷ 3 = Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Draw 3 ways to equally share 16.

16 ÷

There are 4 students in each row. How many rows of students in a class of:

Show which groups can be shared equally between 3 people.

c 28?

D R

b 20

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Draw 3 different divisions whose answer is 3.

Sasha has 42 stickers to give to her friends. Each friend receives 3 stickers. How many friends does Sasha give stickers to?

Write your own division word problem and ask a classmate to solve it.

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Multiplication and division are opposites.

10 groups of 2 is 20.

There are 10 groups of 2 in 20.

10 × 2 = 20

20 ÷ 2 = 10

Deepen

Use the multiplications to complete the divisions.

11 × 5 = 55

55 ÷ 11 =

18 × 2 = 36

36 ÷ 2 =

22 × 5 = 110

110 ÷ 5 =

16 × 3 = 48

48 ÷ 3 =

14 × 12 = 168

Use the divisions to complete the multiplications.

99 ÷ 11 = 9

68 ÷ 17 = 4

21 ÷ 3 = 7

7×3=

52 ÷ 13 = 4

4×

34 ÷ 17 = 2

2 × 17 =

73 ÷ 1 = 73

73 × 1 =

D R

AF T

168 ÷ 12 =

9×

= 99 × 4 = 68

= 52

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Some division equations can help you with other equations. If you know that 54 ÷ 6 = 9, then you also know that 54 ÷ 9 = 6.

Use any method to calculate these divisions.

80 ÷ 4 =

30 ÷ 2 =

56 ÷ 8 =

35 ÷ 5 =

36 ÷ 4 =

72 ÷ 8 =

Use your answers to question 3 to fill in the blanks.

80 ÷ 20 =

30 ÷ 15 =

56 ÷ 7 =

35 ÷ 7 =

36 ÷ 9 =

72 ÷ 9 =

Complete this family of facts.

D R

AF T

6×4= 24 ÷

×6= =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

= 59

Number | Rational numbers

Topic 1.11 Reading and writing fractions The numerator tells us how many parts we are dealing with. The denominator tells us how many parts a whole or group is divided into.

2 Two-sixths or 2 parts out of 6 are shaded.

The numerator is the top number of the fraction. The denominator is the bottom number of the fraction.

Learn Shade the fractions.

1 3

D R

AF T

4 5

2 3

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

What fraction has been shaded?

Draw a line from the fraction to the matching picture.

D R

AF T

1 4

1 2

2 3

Draw a picture to represent the fraction.

3 3

3 4

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Draw lines to match each fraction with its picture.

Remember that the parts of a fraction need to be equal in size.

Divide each rectangle into the fraction shown.

quarters b fifths c

AF T

Use a ruler to divide the number line into fractions. Label the fractions on each number line.

halves 0

quarters 0

fifths 0

halves

D R

thirds d

1 Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

There are two candy jars.

Benji took half of the candies from Jar A, so he now has 12 candies. In total, how many candies were in Jar A?

Kaiji took a quarter of the candies from Jar B. He now has 6 candies. In total, how many candies were in Jar B?

Which jar had more candies?

Look at the square.

Draw a line to divide the square into 2 equal parts.

AF T

What fraction is each part? Draw another line to make 4 equal parts.

D R

What fraction is each part? c

Draw 2 more lines to make 8 equal parts. What fraction is each part?

Colour in 5 parts.

What fraction is not coloured in?

Use your answers to question 2 to order the fractions from smallest to largest. 1

What fraction is coloured in?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.12 Unit fractions A unit fraction is a fraction whose numerator is 1.

1 — 9

1 — 4

1 — 5

Learn

Colour in the unit fraction. b

1 3

1 6

D R

AF T

1 2

1 5

1 10

Based on the diagrams in question 1, order the fractions from smallest to largest. 1

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

2 2

3 3

Counting 3 in unit fractions up to3 1

To count up in unit fractions, you keep adding the same unit fraction over and 2 3 4 1 over until you get up to 1.

1 5

2 5

1 8

2 8

3 8

3 5 4

4 5 5

A fraction where the numerator 8 8 8 and the denominator are the same is equal to 1.

5 5 7 8

8 8

Fill in the blanks to count up to 1 using unit fractions.

AF T

1 8

D R

3 5

Count up to 1 using unit fractions.

1 6

1 7

1 12

Write all the fractions equal to 1 that are on this page.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Look at the fraction wall. Insert > or <.

One whole 1 2

1 2

1 3

1 4

1 5 1 6

d g

1 12

1 10 1 12

1 12

1 10

1 12

e h

1 5 1 6

1 8

1 6

1 8

1 10 1 12

c f

1 8 1 10

1 12

1 10 1 12

1 12

Circle the correct answer.

When the denominator of a unit fraction is overall fraction is smaller.

When comparing unit fractions, the one with the bigger denominator is always the smaller

1 8

AF T

1 10

1 6

D R

1 8

1 10

1 5

1 6

1 8

1 4

1 5

1 6

1 8

1 12

1 4

1 5

1 10

1 3

bigger

smaller , the

bigger one.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Shade the fractions

1 4

and

1 3

Which is bigger:

1 4

1 3

Xavier and Danielle both have some apples.

AF T

D R

Xavier

Danielle

Xavier has 6 apples. How many apples is

Danielle has 12 apples. How many apples is

Explain why

Write your own unit fraction problem

1 4

of Xavier’s apples? 1 4

Danielle’s apples?

of Danielle’s apples is more than

1 3

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

of Xavier’s apples.

Number | Rational numbers

Topic 1.13 Equivalent fractions 1 — 2

is equal to… 2 — 4

1 — 2

3 — 6

4 — 8

5 — 10

6 — 12

Learn Draw a line to match each fraction with the correct picture. Then fill in the missing equivalent fractions.

D R

AF T

2 4 4 8 6 10

4 10 8 10

2 3 5

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Equivalent means equal or the same.

Colour in the circles and complete the fractions. The first one has been done for you.

e.g.

3 = 6 4 8

AF T

1 2

1 4

D R

2 3

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

The rectangles are the same. The amount shaded is the same. The fractions are equivalent. 3 — 12

Shade the second shape to be equivalent to the first one and write the equivalent fractions. a

1 4

D R

AF T

1 — 4

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Colour in the fraction shown for each picture, then write the equivalent fraction. a

1 —= 2

3 — 6

1 —= 3

2 — 6

1 —= 4

1 —= 5

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.14 Adding and subtracting fractions Comparing fractions When two fractions have the same denominator, we can compare them by comparing the numerators. 3

11 12

and

7 12

The numerator and the denominator are the top and bottom numbers in a fraction.

4 12

Learn

Circle the correct answer.

If the denominators are the same, then the bigger fraction has the smaller

bigger numerator.

If the denominators are the same, then the smaller fraction has the smaller

AF T

Write < or >.

D R

bigger numerator. Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Write number sentences.

1 3

D R

AF T

Fill in the gaps to complete each subtraction.

–

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Check if Akira answered their homework questions correctly. If they didn’t get a question right, show the correct answer in the box.

1 1 2 a Correct Incorrect + = 3 3 6 1 1 2 b Correct Incorrect + = 4 4 4 1 1 1 c Correct Incorrect + = 5 5 10 1 1 2 d Correct Incorrect + = 8 8 8

D R

AF T

8 4 3 e Correct Incorrect − = 12 12 12 5 1 6 f Correct Incorrect − = 7 7 7 4 3 1 g Correct Incorrect − = 8 8 8 7 3 4 h Correct Incorrect − = 10 10 10 4

Try answering these three-fraction problems.

2 3 1 a + + 8 8 8

5 1 2 b − − 6 6 6

Add or subtract the numerators.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Draw each story and write a number sentence. 1 1 A cup is full of milk. Dion pours another into the cup. How much 3 3 milk is in the cup in total?

There is one quarter of a pizza left on a plate. Maia adds another quarter to the plate. What fraction of pizza is there now?

D R

AF T

+ c

There are 10 stars. One tenth of the stars are coloured in yellow. Another tenth of the stars are coloured in red. What fraction of the stars are coloured?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.15 Fraction of a number Fraction of a quantity Fractions can show a part of the whole. 1 of 4 donuts is 2 donuts. 2

Learn 1

Find the fraction of each quantity. b

1 2

of 2 dogs?

What is

D R

What is

AF T

1 4

of 8 strawberries?

What is

1 3

of 12 apples?

What is

1 8

of 8 stars?

e What is

1 5

of 10 cats?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

You can use division to work out the fraction of a group. 1

of 12 is the same

3 as 12 ÷ 3.

Halving is the same as dividing by 2.

Explore 1

Circle the objects in two equal groups. Complete the division. b

1 2

of 6 =

D R

AF T

1 2

6÷2=

of 2 =

2÷2=

1 2

of 4 =

4÷2=

1 2

of 8 =

8÷2=

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Complete the divisions.

1 2

of 10 =

= ÷

AF T

D R

e 1 6

= ÷

Draw a picture to complete the division. 1 2

of 18 = ÷

of 9 =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen There are 30 beads in the box. a

How many of each colour? Fraction

are blue

3 1

5 1 10

of 30

Number of beads

30 ÷ 3

10 blue beads

are red

3 1

Division

are green are silver

The remaining beads in the box are gold. Write the number and fraction of gold beads.

D R

gold beads or

AF T

a c e g i k

of 30.

Find the fraction in each group. 1 3 1 4 1 3 1 5 1 10 1 5

of 9 =

of 36 =

of 18 =

of 50 =

of 30 =

1 4 1 2 1 3 1 6 1 10 1 4

of 8 = of 12 = of 24 = of 30 = of 100 = of 36 =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Rational numbers

Topic 1.16 Finding the whole set 1

We can work out the whole number from a unit fraction using repeated addition.

of the objects is 4.

4 How many objects altogether?

1 — 4

4 + 4 + 4 + 4 = 16

Total number of objects is 16.

Draw the rest of the objects and find the total. 1 5

of the triangles is 2.

D R

AF T

Learn

The total number of triangles is b

1 2

of the squares is 6.

The total number of squares is 80

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Solve the problems using repeated addition.

of a pack of pens is 5 pens. How many pens are in 4 the whole pack? 5+

pens b

of a bag of strawberries is 8 strawberries. How many 3 strawberries in the whole bag? =

of a basket of bananas is 4 bananas. How many 5 bananas are there in total?

D R

AF T

strawberries

bananas d

of a tray of cupcakes is 1. How many cupcakesAare

10 there in total?

= cupcakes e

going to a friend’s house

eating a cupcake

lunchti at sch

of a pack of stickers is 12 stickers. How many stickers

5 are in the whole pack?

= stickers Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Instead of using repeated addition to find the total, we can use multiplication. 1 of the objects is 4. How many objects altogether? 4

1 — 4

4 × 4 = 16

Finish the drawing and write the multiplication.

1 — 5

× c

AF T

1 — 3

3× b

1 — 4 +

× 82

Total number of objects is 16.

D R

= Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Use multiplication to find the total number of each object.

1 6

of a box of crayons is 4 crayons. How many crayons are in the box?

4×6= crayons b

1 2

of a bag of apples is 5 apples. How many apples are there in total?

1 apple + 2 apples = 3 apples BUT

1 3

D R

AF T

apples

of a bag of feijoas is 7 feijoas. How many feijoas are in the bag?

7×

= feijoas

of the chairs in a classroom is 3 chairs. How many chairs are in the

8 classroom?

chairs

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Financial mathematics

Topic 1.17 Money

Do you know all of the New Zealand notes and coins?

How much money? Coins and notes

In words

$2 and 50 cents

Learn

Count the money and fill in the gaps.

D R

AF T

$55 and 40 cents

$3 and

cents

and

cents

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Circle coins and notes that equal the amount given.

$20

$50

$100

$37

D R

AF T

$45

$83

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Write the total value of each group of money. Cross out the one that doesn’t match.

$10

$22

$55

$124

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Draw the notes you would need to buy the following items.

a Bike: $225

More than 1 kg

AF T

Guitar: $175

Ball: $30

Shoes: $100

d Laptop: $600 2

D R

Deepen

Watch: $140

From the items in question 1, draw all the things you would buy if you had $700 to spend.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number | Financial mathematics

Topic 1.18 Giving change

Pri

I buy an

. I pay with a

note. How much change do I get?

Subtraction spent $5 −

Addition

change

spent change

$2 = ?

$2 + ?

= $3 change

= $5 = $3 change

Learn How much change do I get back if I pay with a

$5 − $1 =

D R

$1 b $1

c $4

I use a

note? $1 +

change = $

$5 − $2 =

$2 +

change = $

$5 − $4 =

$4 +

change = $

= $5

. How much change do I get if I buy these items? +

AF T

change = $

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Study the money amounts and answer the questions.

How much money?

How much change if

you spend $10?

you spend $15?

D R

AF T

How much money?

How much change if

you spend $31?

you spend $20?

How much money?

How much change if

you spend $23?

you spend $12?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

How much change would you get from $20?

1 carton of eggs

2 ice creams $8

$11

Change =

How much change would you get from $100?

18 cupcakes

r $4

D R

9 fo

3 chess boards

AF T

$33

eac

Change =

Talia buys 1 carton of eggs, 1 ice cream, 9 cupcakes and 1 chess board using one New Zealand note.

How much does Talia spend?

Which New Zealand note does Talia use?

How much change does Talia receive?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

How much?

How much would you have left over from this amount if you spent: i

$20

$45

iii

$32?

How much would you have left over from this amount if you spent:

D R

AF T

$20

$45

iii

$32?

Bronte received $18 in change after spending some money. How much did Bronte spend if she paid with a:

$50 note

Amount spent =

$100 note?

Amount spent =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Algebra | Equations and relationships

Topic 2.1 Number sentences Comparing numbers < sign

= sign

> sign

less than

both sides are the same

greater than

2 < 10

5=5

11 > 10

2 is less than 10.

5 is the same as 5.

11 is greater than 10.

The crocodile eats the larger number.

Learn

Fill in the blanks and circle true or false.

13 is

less than 17

True

False

h 18

True

False

18 < 3 3

True

i 14

False

18 is

False

10 < 14

True

1 is

f 10

10 is

1 = 19

True

2 > 10

True

17 = 18

False

2 is

False

17 is

e 20

True

14 is

14 < 20

True

20 = 20

20 is

13 > 17

AF T

D R

False

18 > 17

17 is

18 True

False

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

What would happen to the scales if 2 × 10 was replaced with 3 × 10?

The = sign shows that both sides are the same. 2 × 10 20

10 + 10

Explore Make the equations balance. 33 – 3

= 15 +

3×5

÷5

10 + 2

2×

4×5

2×

AF T

D R

Fill in the missing numbers to balance the equations.

30 +

c e

6×

g i

50 −

= 50 − 10

− 20 = 40 ÷ 4

= 36 − 6

÷ 5 = 25 − 15

= 6 × 5

40 +

= 90 − 20 − 15 = 8 × 5

7×

= 50 − 15 ÷ 4 = 24 −12

60 −

=9×4

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

Circle True or False.

50 – 29 = 8 + 13

True False

23 + 32 = 60 – 7 True False

3 × 12 = 36 ÷ 6

True False

50 ÷ 5 = 2 × 5

60 + 60 = 10 × 12 True False

43 – 29 = 60 ÷ 4 True False

40 – 20 = 19 + 19

True False

20 + 1 = 19 + 2

12 × 2 = 24 – 0

True False

100 ÷ 10 = 9 + 1 True False

13 + 4 = 19 – 10

True False

7+7=6+6

Fill in the missing gap with >, < or =.

911

912

238

374

279

671

761

473

331

661

531

378

677

766

749

810

217

419

853

831

True False

D R

AF T

True False

Which number is bigger? Which number is smaller?

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

Deepen 1

Fill in the gaps to complete the number sentences.

+ 15 > 30

48 −

= 44

− 23 = 61

35 +

< 89

× 8 = 48

7×

< 28

45 ÷

÷ 5 = 11

26 + 34 > 100 −

78 − 46 = 19 +

147 −

Check these number sentences. Tick if they are true or false.

429 + 287 = 716

Working out

True

False

D R

Number sentence

+ 83 > 180 − 32

AF T

= 96 + 15

152 + 672 = 814

217 − 135 = 183

945 − 273 = 672

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

Algebra | Equations and relationships

Topic 2.2 Number patterns Here is a number pattern counting up by fives: 5, 10, 15, 20, 25, 30, 35, 40.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Learn 1

Find the pattern and continue it to the end of the number line.

Counting by twos

0, 2, 4,

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

AF T

D R

Counting by threes

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0, 3,

Counting by tens

0, 10,

Can you continue the number patterns?

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

Explore 1

Continue this pattern. 4

The pattern is counting by: Number patterns can also go down.

Continue this pattern. 80

AF T

The pattern is going down by:

Find the missing numbers.

D R

b c

d e

Rule: 60

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

Join the dots by following the pattern.

3 0

18 21

30 27

Use the rule to help you complete the number pattern.

Rule: up by 4s.

50, 45, 40, 35, d

Rule: up by 3s. 17, 20, 23, 26,

D R

Rule: down by 5s.

Rule: down by 10s. 86, 76, 66, 56,

Complete the pattern and write the rule.

Rule: 8, 10,

b , 14,

, 110,

Rule: 21, 18,

Rule: 90,

AF T

6, 10, 14, 18,

, 12,

Rule: 9, 18, 27,

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

Deepen 1

9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Circle the numbers counting by 5 from 3.

What is the biggest number in this pattern?

Colour the numbers counting by 3 from 2.

What is the biggest number in this pattern?

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Write the numbers you get when you start at 6 and count in 4s.

AF T

Use these numbers to make a pattern. 37 57 7 27 47 67 17

D R

What are you counting by?

Make two of your own number patterns and ask a friend to find the rules.

Rule:

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

Measurement | Measuring

Topic 3.1 Length, mass and capacity Metres

We measure the length of long items in metres (m).

What are some things we might measure in metres?

Learn 1

First estimate, then use a metre ruler to find:

the length of your classroom

the width of a bookcase

D R

AF T

Estimate: Measurement: c

metres

the height of the door

Estimate: Measurement: 100

metres

metres metres

Estimate: Measurement: d

metres metres

the width of the whiteboard.

Estimate: Measurement:

metres metres

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Centimetres

30 cm

We measure the length of small things in centimetres (cm).

How many centimetres tall do you think I am?

13 cm 5 cm

There are 100 cm in 1 m. A child that is 3 or 4 years old is about one metre tall.

100 cm

First estimate, then use a 30 cm ruler to find:

the length of your pencil

the width of this book. Student Workbook

D R

centimetres

Measurement:

centimetres

for Aotearoa New Zealand

3 Erin Doleman

Programme consultant

Micah Hocquard Vicki Lewis Nikki Ollis Annie Facchinetti

Estimate: Measurement:

Draw something in your classroom that is about:

15 centimetres long

Phase 1

Year

Student Workbook

AF T

Mathematics and Statistics

Estimate:

Mathematics and Statistics

centimetres centimetres

1 metre long.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

101

Would you measure these items in metres or centimetres?

D R

102

AF T

Which of the items in question 4 do you estimate is the longest?

Order the objects from shortest to longest.

How long might the couch be?

How long might the banana be? Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Mass The base unit for measuring mass is the kilogram (kg). Many everyday items are measured in kilograms.

The mass of the dog is 15 kg.

The mass of the laptop is 1 kg.

Explore 1

Estimate whether each item has a mass of less than 1 kg, about 1 kg or more than 1 kg. Draw lines to show your answers.

D R

AF T

Less than 1 kg

About 1 kg

More than 1 kg

Which item do you estimate has the heaviest mass?

Many everyday items, such as groceries, are labelled in kilograms. Find and draw three items that are packaged and labelled in kilograms.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

103

The mass of lighter objects is measured in grams (g). There are 1,000 g in 1 kg.

125 g

250 g

Estimate first, then find the mass of these items to the nearest 100 grams. You will need to use scales. Item

Estimate

Actual

Stapler

A workbook

D R

A cup of water

AF T

Your lunchbox

Rugby ball

104

Think about the items in question 3.

Which item is the heaviest?

Which item is the lightest?

Write the items in order from lightest to heaviest.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

How many of each item could be packed in a box that holds 24 kg?

4 kg 2 kg 12 kg

3 kg

AF T

Read the scales and record the mass.

D R

6 kg

5 4

kg 1

Mass:

kg 1

Mass:

90 80

60 50

Mass:

20 3090 40 80

60 50

20 90 30 80 40

60 50

90 80

20 40

Mass:

kg 1

60 50

20 3090 40 80

60 50

Mass:

20 90 30 80 40

60 50

20 30

60 50

20 3090 40 80

60 50

20 90 30 80 40

20 30

60 50

Mass:

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

105

Capacity Capacity is how much a container holds. A litre (L) is a unit of capacity. This milk cartoon holds 1 litre (1 L). 1 L is equal to 1,000 millilitres (1,000 mL).

Deepen 1

Find similar containers and estimate their capacity. Then measure the actual capacity using a measuring jug. Estimate

Actual

D R

AF T

Container

106

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Number these containers 1 to 6 from smallest to largest capacity.

C 4L

2L 1L

F 1 L 500 mL

500 mL

D R

AF T

Write the letters of the items that hold 1 L or less.

Write the letters of the items that hold more than 1 L.

What is the capacity of the detergent and spray bottle together?

What is the capacity of the watering can and the juice bottle together?

What is the capacity of the paint can and the detergent together?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

107

Measurement | Measuring

Topic 3.2 Perimeter Perimeter To find the perimeter of a shape, measure all the sides and add them up.

This shape is 6 cm in length and 2 cm in height. The perimeter is 6 + 6 + 2 + 2 = 16. The perimeter is 16 cm.

Learn Use a ruler to find the perimeter of each shape. b

D R

AF T

108

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Measure the perimeter of each shape.

Pentagon

b Rectangle

cm 3

c Triangle

Order the perimeters of the shapes in question 2 from longest to shortest. Perimeter

Measure the perimeter of the following polygons using a ruler. b

D R

Triangle

cm 5

Shortest

AF T

Longest

Hexagon

Octagon

Order the perimeters of the shapes in question 5 from shortest to longest.

Shortest

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Longest

109

Explore 1

Find the perimeter of the shapes.

10 cm

15 cm 7 cm

10 cm

7 cm

10 cm

15 cm

10 cm

5 cm

2 cm

3 cm

2 cm

10 cm

AF T

5 cm

13 cm 8 cm

D R

10 cm

10 cm 5 cm

3 cm

8 cm

14 cm

13 cm

14 cm

m 2c

2 cm

18 cm

2 cm

14 cm

2 cm

18 cm

2 cm

110

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Find the perimeter of the following shape. 10 cm

5 cm

Perimeter = 10 cm

5 cm

Measure these shapes to find their perimeters in cm.

a cm

Perimeter =

AF T D R

Perimeter =

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

111

Measurement | Measuring

Topic 3.3 Area

This laptop screen has an area of 12 sticky notes.

This book has an area of 12 sticky notes.

Learn

AF T

Circle the item with the smallest area.

Tick the item with the biggest area.

D R

How many sticky notes do you think would cover the area of:

a book

Student Workbook Mathematics and Statistics

Mathematics and Statistics

your table

another item?

Phase 1

Year

for Aotearoa New Zealand

Student Workbook

3 Erin Doleman

Programme consultant

Micah Hocquard Vicki Lewis Nikki Ollis Annie Facchinetti

sticky notes

Circle the right word. Area is the space

112

sticky notes

inside

outside a shape.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Find the area of each rectangle by counting the squares.

squares

What else could you use to measure area with?

AF T

squares

D R

squares

Circle the shape in question 1 with the smallest area.

Find the area of each shape by counting the squares.

squares squares

squares

Circle the shape in question 3 with the largest area.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

113

Draw 1 cm squares on the rectangles. Record the area of each rectangle.

How many rectangles can you find with an area of 12 squares?

squares

Using blocks, draw a rectangle with an area of:

7 squares

12 squares.

6 squares

D R

AF T

114

18 squares.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Use the grid paper to draw:

a blue square with an area of 9 squares

a red rectangle with an area of 10 squares

2 different green rectangles, each with an area of 12 squares

a yellow square with an area of 4 squares.

In words, what is the total area of the shapes in question 1?

Find the area of the blue square.

D R

AF T

Estimate the area of the shape.

squares

squares c Find the area of the red rectangle. squares d

What is the total area? squares

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

115

Measurement | Measuring

Topic 3.4 Turns

half-turn half turn 1 — turn 2

quarter turn quarter turn to tothe the right right 1 — turn 4

three quarter three-quarter turn to the the right right 3 — turn 4

full full turn turn

When we turn something around to the right, this is also known as clockwise, as it’s the same direction that the hands go around a clock.

Learn 1

quarter quarter turn turn totothe left the left 1 — turn 4

Identify each turn. b

Half turn

D R

AF T

Quarter turn

Full turn

Quarter turn

Half turn

Quarter turn

Half turn

Full turn

Three-quarter turn

Full turn turn Full

116

Half turn

Half turn turn Half

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Decide whether the pattern is showing half turns or quarter turns, then continue the pattern. Half turn

Quarter turn

Half turn

Quarter turn

D R

AF T

Write the name of each turn – quarter turn, half turn, three-quarter turn or full turn.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

117

Draw what happens if you do a:

half turn

three-quarter turn to the left

quarter turn to the right

full turn.

Draw the shapes after a:

D R

i half turn

118

AF T

quarter turn

i t hree-quarter turn to the right

full turn.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Describe the turn used to make the pattern.

Continue the pattern.

Describe the turns used to make the pattern.

Continue the pattern.

D R

AF T

Circle the shapes that show a quarter turn.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

119

Measurement | Measuring

Topic 3.5 Telling the time

2 : 00

2 : 15

2 : 30

Learn

2 : 45

Why do we say “quarter past” and “quarter to”?

What number is the minute hand pointing to?

5 o’clock

Draw a line to match the clocks to the times.

quarter to 6

quarter past 11 d

half past 8

D R

AF T

quarter to 11 120

half past 4

9 o’clock

quarter past 6

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Draw in the minute hands and write the digital time.

half past 3

quarter past 1

: d

quarter past 12

quarter to 7

: f

Draw in the hour hands and write down the digital time.

quarter past 3

D R

half past 5

8 o’clock

: d

half past 6

AF T

7 o’clock

quarter to 9

quarter to 10

: f

12 o’clock

: Why do you think it is called the “hour hand”?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

121

This clock helps us read the time as

10 minutes past 5 or 5:10.

5 minutes to 8 or 7:55.

Explore 1

Fill in the digital clock and write the time in words.

b :

AF T

25 minutes past 4 d

D R

f :

122

What number is the minute hand pointing to at these times?

25 minutes to 6

5 minutes past 2

10 minutes to 9

20 minutes past 12

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

We can read time on analogue clocks to the nearest minute. These clocks both show the time is 4:37.

4 : 37

Deepen Match the clocks that show the same time.

D R

AF T

2 : 27

7 : 17

Write the time past or to the hour.

9 : 08

8 : 39

6 : 26

3 : 53

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

12 : 42

123

Measurement | Measuring

Topic 3.6 Duration JANUARY

FEBRUARY

Sun Mon Tues Wed Thur Fri

Sat

10 11 12 13

MARCH

Sun Mon Tues Wed Thur Fri

6 4

Sat

APRIL

Sun Mon Tues Wed Thur Fri

Sat

10 11 12 13 14

14 15 16 17 18 19 20

11 12 13 14 15 16 17

15 16 17 18 19 20 21

21 22 23 24 25 26 27

18 19 20 21 22 23 24

22 23 24 25 26 27 28

28 29 30 31

25 26 27 28

25 26 27 28 29 30 31

29 30

MAY

JUNE

Sun Mon Tues Wed Thur Fri

JULY

AUGUST

Sat

Sun Mon Tues Wed Thur Fri

Sat

Sun Mon Tues Wed Thur Fri

Sat

10 11 12 13 14

10 11 12

Sun Mon Tues Wed Thur Fri

10 11

10 11 12 13 14 15 16

15 16 17 18 19 20 21

12 13 14 15 16 17 18

17 18 19 20 21 22 23

22 23 24 25 26 27 28

19 20 21 22 23 24 25

27 28 29 30 31

24 25 26 27 28 29 30

29 30 31

26 27 28 29 30 31

NOVEMBER

Sun Mon Tues Wed Thur Fri

Sat

Sun Mon Tues Wed Thur Fri

14 15 16 17 18 19 20

11 12 13 14 15 16 17

10 11 12 13 14 15

16 17 18 19 20 21 22

21 22 23 24 25 26 27

18 19 20 21 22 23 24

16 17 18 19 20 21 22

23 24 25 26 27 28 29

28 29 30 31

25 26 27 28 29 30

23 24 25 26 27 28 29

10 11 12 13 14 15

10 11 12 13

Sat

Sun Mon Tues Wed Thur Fri

Sat

Sun Mon Tues Wed Thur Fri

DECEMBER

Sat

1 4

seconds, minutes, hours, days, weeks, months and years.

20 21 22 23 24 25 26

OCTOBER

We can measure time in:

Sat

13 14 15 16 17 18 19

SEPTEMBER

There are 12 months in a year. There are 7 days in a week.

30 31

AF T

Learn

124

Sat

Fill in the blanks.

There are

There are 14 days in

Use the calendar to help answer these questions.

One week from Saturday 10 March is

One week from Sunday 3 June is

Two weeks from Tuesday 4 September is

Two weeks from Monday 8 January is

September has

July has

D R

days in one week. months in one year. weeks.

March. June. September. January.

days. days.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore Circle whether each activity takes seconds, minutes, hours, days, weeks or months to complete.

Brushing your teeth

days

weeks months

seconds minutes hours

days

weeks months

seconds minutes hours

days

weeks months

seconds minutes hours

days

weeks months

seconds minutes hours

days

weeks months

days

weeks months

Growing a lettuce

Blinking your eyes

Reading a book

D R

seconds minutes hours

AF T

Painting a house

Celebrating a birthday party

seconds minutes hours

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

125

Duration

watching a movie

eating a banana

sleeping at night

Summer

The things we do take time.

Write the activities (A, B, C, D) in order from the shortest to the longest time they take.

Shortest time

Write these units of time from shortest to longest. minute, second, day, hour

Think about these activities.

D R

reading a chapter book

126

AF T

Longest time

brushing your teeth

washing your hands

Which would your measure in seconds?

Which would you measure in minutes?

Which would you measure in hours?

Draw or write something that you measure in each unit of time.

weeks

months

years

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

This calendar shows the month of May.

If today is the 4th, what will be the day and date in 2 weeks?

What day is 9 days after the 13th of May?

May Sun Mon Tues Wed Thur Fri

Sat

Which days are there 5 of in the month?

If you went on holidays on the 3rd of May for 11 days, on which day would you get back?

How many days is it from the 17th to the 23rd of May?

If today is the 23rd of May, how many days are left in the year? Use the calendar at the start of the topic to help you. Show how you worked out the answer.

D R

AF T

Does May always start on a Wednesday?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

127

Geometry | Shapes

Topic 4.1 Polygons corner

side

The shape has 4 corners and 4 sides. The sides are straight lines.

How else could you describe this shape?

Learn 1

A hexagon has:

AF T

sides.

D R

corners

128

A pentagon has:

These 2D shapes are also called polygons.

corners

sides.

corners

sides.

An octagon has:

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

These shapes are regular polygons.

What features do regular polygons have in common?

Explore 1

Name the polygons. b

D R

AF T

Draw and name the shapes.

Regular polygon with 3 sides

Regular polygon with 4 sides

Regular polygon with 5 sides

Regular polygon with 6 sides

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

129

Cross out the shapes which are not polygons.

Name the regular polygons and label them with their number of sides.

Match the shapes to their names and descriptions.

D R

AF T

heptagon

hexagon

square

6 corners, 6 equal sides and 6 equal angles

4 corners, 4 equal sides and 4 equal angles

7 corners, 7 equal sides and 7 equal angles

triangle

3 corners, 3 equal sides and 3 equal angles

Can you name these shapes in te reo Māori?

130

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Write a description of each shape. Can a friend guess the shape from your description? a

D R

AF T

What is your favourite shape? Why?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

131

Geometry | Spatial reasoning

Topic 4.2 Symmetry

A shape is symmetrical if one side is a mirror image of the other.

The square is symmetrical. The left side of the black line is exactly the same as the right side. This line is called a line of symmetry.

Learn

D R

Draw 1 line of symmetry on each shape.

AF T

132

Circle the shapes that have a line of symmetry. Draw the symmetry lines.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Reflect these shapes across a line of symmetry. Use the dot on each shape as a starting point. b

D R

AF T

Reflect these shapes across the line of symmetry.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

133

Use the grid and the lines of symmetry to create symmetrical pictures.

134

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen Shapes can have more than one line of symmetry.

Tick the shapes that have more than one line of symmetry.

Draw lines between shapes with the same number of lines of symmetry.

Circle the shape with the most lines of symmetry.

Draw your own shape with 3 lines of symmetry which is not a triangle.

D R

AF T

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

135

Geometry | Pathways

Topic 4.3 Following instructions Directions depend on the orientation of the observer. Blue and red are told to go forward one space. They end in different places because they are facing different directions.

Learn Always remember which way you are facing!

1 Wall

Wall

AF T

Wall

136

D R

Wall

Fill in the instructions to help the detective red path to get to the hammer. •

Quarter turn right.

•

Move forward

•

Quarter turn

•

Move forward

walk along the

spaces. . spaces.

Write instructions for another path from the detective to the hammer

Write instructions for the detective to get to the glove.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

B C

D R

AF T

Draw the path the kiwi will follow by reading the instructions. 1 Move forward 2 spaces.

5 Move forward 2 spaces.

2 Quarter turn left.

6 Quarter turn left.

3 Move forward 3 spaces

7 Move forward 1 space.

4 Quarter turn left. b

Where does the kiwi end up?

Write instructions for the kiwi to get from B to C.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

137

Your classmate is a robot. Robots only follow exact instructions!

Plan a route. (e.g. Door → Reading corner, Whiteboard → Sink) Starting place: Finishing place:

Write your instructions Write a set of instructions to guide your robot classmate. Use quarter turns, half turns and forward steps.

Test your instructions by swapping with a partner. Could your partner follow the instructions successfully? Yes

Not quite

AF T

Rewrite any instructions that were unclear.

Write instructions to guide your robot to three different classroom locations.

D R

138

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Write two different sets of instructions to get to the milk starting from .

Fridge

D R

AF T

the

Write instructions of how to get to from the arrow to the donut. Then from the donut to the apple.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

139

Geometry | Pathways

Topic 4.4 Maps There are four cardinal directions: north, east, south and west. On maps, these directions are used to describe the position of objects.

North West

East

AF T

South

140

D R

Learn

“Never Eat Soggy Weetbix” is one way to remember the directions.

Use the map and circle true or false.

The playground is east of the soccer field. True False

The soccer field is north of the running track. True False

The running track at the west of the basketball court. True False

The playground is west of the basketball court. True False

Which place is:

the furthest north

the furthest west

the furthest east? Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore

Hairdresser

Department store

Shoe shop

Toilets

Play area

Food court

Jewellery shop

Surf shop

Muffin shop

Clothes shop

Book shop

Pet shop

AF T

Toy shop

Circle the correct direction using the map.

The shoe shop is

The book shop is north south of the toy shop.

The food court is west

south of the department store.

The play area is south

west of the food court.

The pet shop is west

east

Which place(s) are:

north of the muffin shop

east of the hairdresser

south of the shoe shop

west of the play area?

west of the hairdresser.

D R

east

of the shoe shop.

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

E S

We can use the cardinal directions to describe locations on a map.

141

pūkeko

kākāpō

seal

takahē

ruru

kereu

sheep

tıeke ¯

kiwi Entrance

Use the map to fill in the blanks.

The kiwi is

of the entrance.

The kereu is

of the sheep.

The kākāpō is

of the tīeke.

The kiwi is

The entrance is

142

AF T

of the seal.

D R

of the takahē.

Which bird(s) are the furthest east in the park?

Which bird(s) are the furthest north in the park?

Which bird(s) are the furthest south in the park?

Which bird(s) are the furthest west in the park?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen N W

AF T

On the map, draw:

a rock to the west of the tree

a whare (house) that is 3 squares south of the rock

a treasure that is 4 squares east of the tree

a crab that is on the southernmost side of the island

a sheep north of the treasure.

Compare your map with someone else. Did you draw your objects in the same places?

Draw three more objects on the map. Describe their location so there is only one possible square for each new object.

D R

Object 1: Object 2: Object 3:

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

143

Statistics | Developing knowledge from data

Topic 5.1 Collecting data

Categorical data is information we can group or name.

What is your favourite ice-cream flavour?

Responses Chocolate, Vanilla, Strawberry, Hokey

pokey, Chocolate, Raspberry, Vanilla, Strawberry, Chocolate, Hokey pokey, Vanilla, Mango, Strawberry, Chocolate, Hokey pokey, Vanilla, Chocolate, Strawberry, Vanilla, Hokey pokey

Learn Complete the table using the responses from the example.

Vanilla Chocolate

Number of students (ticks)

AF T

Ice-cream flavour

Tally marks

Total

D R

Strawberry Hokey pokey Other

144

Which flavours are in the “Other” category?

What is the most popular flavour?

What is the least popular flavour?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Explore 1

Write a yes/no question to ask your classmates.

What do you think the data will show?

Ask 12 people your question and record their answers.

✓ or ✗

Name

✓ or ✗

D R

AF T

Name

Record the results in a tally chart.

Yes

What do you notice? What is the most common answer?

What did you find out from your survey?

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

145

How many hours did you sleep last night? Responses

8, 9, 10, 9, 11, 10, 9, 8, 10, 9, 11, 10, 9, 8, 10, 9, 11, 10, 9, 8

Deepen 1

Complete the table using the responses in the example. Hours slept last night

Number of students (ticks)

Tally marks

Total

D R

AF T

Numerical data is information we can count or measure.

146

Do these questions collect numerical or categorical data?

How many pets do you have?

Numerical

Categorical

What is your favourite colour?

Numerical

Categorical

How many books did you read last year?

Numerical

Categorical

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Questions starting with “How many…” collect numerical data.

Write a question you can use to collect numerical data from your classmates.

What are the possible responses to your question? Try to limit it to five.

What do you think the data will show?

Ask 12 people your question and record the data.

D R

AF T

Responses

Number of students (ticks)

Tally marks

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Total

147

Statistics | Visualisation of data

Topic 5.2 Displaying data A bar graph can help us understand the data.

Shapes

Types of shapes

Number of shapes

10 9 8 7 6 5 4 3 2 1 Square

Circle

Triangle

Star

Shapes

AF T

Learn Sort the data using the table and then create a bar graph.

10 9 8 7 6 5 4 3 2 1

Number of shapes

D R

Title:

How many whetū (stars) are there?

Square

Circle

Triangle

Star

Shapes

Circle

Triangle

Star

Ticks Tally Total 148

Year 3 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Choose a way to sort the shapes into four different categories.

What are the four groups?

Category 1:

Category Tally marks Total

AF T

Category 2:

D R

Category 3: Category 4: c

Record your categories in a table.

1 2 3 4

Use the data to make a bar graph.

Title:

Frequency

10 910 89 78 67 6 5 5 44 33 22 11 Categories