Year 4 Full Workbook Sample by OUPANZ

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Mathematics and Statistics for Aotearoa New Zealand Second edition

Lead author: Erin Doleman

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Rich tasks designed by Marie Hirst Dr Jo Knox

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Cultural author and reviewer: Moana Jarden-Osborne

Name: Class:

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

Strand 3: Measurement Measuring

Year 4

Topic 3.1: Estimation and measuring................... 101

Strand 1: Number

Topic 3.4: Volume.......................................................119

Topic 3.2: Perimeter...................................................109 Topic 3.3: Area .......................................................... 114 Topic 3.5: Angles........................................................124

Number structures

Topic 3.6: Time .......................................................... 127

Topic 1.1: Whole numbers........................................... 8 Topic 1.2: Rounding.....................................................13 Topic 1.3: Counting in multiples.............................. 18

Strand 4: Geometry Shapes

Operations

Topic 4.1: 2D shapes................................................. 135

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Topic 1.4: Adding and subtracting........................ 23

Spatial reasoning

Topic 1.6: Multiplying.................................................36

Topic 4.2: 3D Shapes................................................ 143

Topic 1.7: Dividing...................................................... 44

Topic 4.3: Transformations.....................................148

Rational numbers

Pathways

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Topic 1.5: Multiplication and division facts........ 31

Topic 1.8: Fractions and decimals......................... 52

Topic 4.4: Grid references....................................... 153

Topic 1.9: Comparing and ordering fractions.... 57 Topic 1.10: Adding and subtracting fractions....65 Topic 1.11: Unit fractions and scaling....................70 Topic 1.12: Adding and subtracting decimals....78 Topic 1.13: Multiplying and dividing decimals....83

Financial mathematics

Strand 5: Statistics Developing knowledge from, visualisation of and interpretation of data Topic 5.1: Dot plots................................................... 158

Topic 1.14: Using money............................................86

Topic 5.2: Statistical investigations......................163

Strand 2: Algebra

Quick 10s.........................................................171

Equations and relationships Topic 2.1: Number sentences................................... 91 Topic 2.2: Growing patterns....................................96

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

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

Student Dashboard

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

Student Workbook

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

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Teacher Dashboard

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

Strand

Topic 4.3 Transformations

Topic number

Element

Topic title

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

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

New features added to the student workbooks: ESS

Strand 1: Number

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.

PRO

Progress passport

PA S S P

Number structures For me

Topic

For my teacher

Example

I feel

1.1 Whole numbers

Thousands

Hundreds

Tens

Ones

Bigger: 394 or 349? 253

353

Quick 10s

800

Rounding whole numbers to the nearest thousand, hundred or ten 900

7.6

1.3 Counting in multiples

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

Review & date

Counting in 10s, 100s and 1,000s from any whole number up to 10,000

874

1.2 Rounding

Practices (NZC 2025) Reading, writing, comparing and ordering whole numbers up to 10,000 and representing them using base 10 structure

Place value house

Rounding tenths to the nearest whole number

21, 28, 35, 42… 48, 40, 32, 24… 50, 75, 100, 125…

Counting forwards and backwards in 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, 25s and 50s from multiples of the counting unit

1.4 Adding and subtracting

3,452 + 1,934 = 8,274 – 682 =

Adding and subtracting up to four-digit numbers

1.5 Multiplication and division facts

7 × 8 = 56 56 ÷ 8 = 7 17 × 0 = 8×1= 63 ÷ 1 =

Operations

1.6 Multiplying

T 1

O 9 5

Memorising multiplication and corresponding division facts for 2s to 10s Using place value and known and derived facts to multiply and divide mentally, including multiplying by 0 and 1 and dividing by 1

200

438

ten

7 3

1.7 Dividing

Multiplying two-digit and three-digit numbers by a one-digit number

Dividing up to a three-digit whole number by a one-digit divisor, with no remainder

Rational numbers 1 1.8 Fractions and decimals

Bigger: 1 2

6 10

or 0.4?

= 0.5

Reading, writing and representing tenths as fractions and decimals Comparing and ordering tenths as fractions and decimals Memorising and using the decimal 1 and fractions with equivalent of 2 denominators of 10

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

OM_MASNZ_Y4_57320_PPS_NG.indb 2

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.

Term 1

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

Erin Doleman Programme consultant and author

56 + 9 =

83 – 9 =

63 – 7 =

135 + 8 =

30 +

= 100

32, 42, 52, 62,

Bigger: 254 or 245?

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Ngā mihi nui,

28-Jul-26 15:53:23

Quick 10s / Tere Tekau

Smaller: 827 or 872? 12, 10, 8, 6, 230, 330, 430,

600, 500, 400,

50 +

23 + 46 =

87, 77, 67, 57,

98 – 12 =

78 + 21 =

3, 6, 9, 12,

94 – 13 =

25, 20, 15, 10,

4, 8, 12, 16,

/10

= 100

74 + 8 = 59 − 6 = 40 + = 100 14, 24, 34, 44, Bigger: 312 or 319? 450, 350, 250, 38 + 27 = 85 − 14 = 2, 4, 6, 8, 30, 25, 20, 15,

/10

/10 Quick 10s / Tere Tekau

Term 2

91 − 7 =

46 + 7 = 82 − 5 = Your teacher 77 − 9 = 165 + 8 will = tell you when it’s time to refresh your skills using these Quick 10 quizzes! 60 + = 100 Smaller: 765 or 756? Smaller: 598 or 859? 11, 21, 31, 41, 14, 12, 10, 8, 12, 14, 16, 18, Bigger: 428 or 482? 410, 510, 610, 45 +620, 78 =520, 420, 340, 440, 540, 37 + 52 = 720, 620, 520, 60 + = 100 = 100 65 + 103 − 48 = _ = 100 29 + 34 = 86 – 70 43 += 93, 83, 73, 63, 84,57 94,to104, 114, Round 49 to nearest 78 + 43 = 91 − 18 = Round nearest 10 98 – 67 = 49 + 28 = 5, 10, 15, 20, 10 37 + 48 = Round 916 to nearest Round 631 to nearest 40, 38, 36, 34, 86 − 14 = 95 123 − 12to= nearest Round 100 100 4, 8, 12, 16, 100 4, 8, 12, 16, 483 + 300 = 40, 32, 24, 16, 16, 24, 32, 40, /10 /10 /10 Smaller: 829 or 819? Bigger: 578 or 587? Bigger: 345 or 364? 347 – 60 = + 23 = 100 + 67 = 100 Round 89 to nearest 298 + 70 = Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University 359 + Press 80 = 10 171 812 − 300 = 92, 82, 72, 62, 12, 15, 18, 21, 564 – 200 = 142 + 9 =

23, 33, 43, 53,

OM_MASNZ_Y4_57320_PPS_NG.indb 171

/10

28-Jul-26 15:58:55

/10

Mōrena! I’m Maia the Morepork (Ruru).

480, 380, 280, 42 + = 100 64 + 37 = 105 − 58 = Round 742 to nearest 100

79 + 28 = 144 − 72 = Round 47 to nearest 10 Round 915 to nearest 100

330, 430, 530, 37 + _ = 100 71 + 28 = 129 − 47 = Round 689 to nearest 100

391 + 600 = Smaller: 714 or 741? 412 − 70 = Round 34 to nearest 10 8, 12, 16, 20,

72, 62, 52, 42, Bigger: 847 or 874? + 36 = 100

478 + 500 = Smaller: 592 or 529? 645 − 90 = Round 57 to nearest 10 64, 56, 48, 40,

/10

174

OM_MASNZ_Y4_57320_PPS_NG.indb 174

389 + 60 = 1230 − 400 = 44, 48, 52, 56,

/10

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

28-Jul-26 15:58:56

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

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

ESS

Strand 1: Number

PRO

PA S S P

Number structures For me

Topic

For my teacher

Example

I feel

1.1 Whole numbers

Hundreds

Tens

Ones

Bigger: 394 or 349? 253

Counting in 10s, 100s and 1,000s from any whole number up to 10,000

353 874

1.2 Rounding

800

Rounding whole numbers to the nearest thousand, hundred or ten 900

7.6

1.3 Counting in multiples

Rounding tenths to the nearest whole number

Counting forwards and backwards in 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, 25s and 50s from multiples of the counting unit

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21, 28, 35, 42… 48, 40, 32, 24… 50, 75, 100, 125…

1.4 Adding and subtracting

3,452 + 1,934 = 8,274 – 682 =

1.5 Multiplication and division facts

7 × 8 = 56 56 ÷ 8 = 7 17 × 0 = 8×1= 63 ÷ 1 =

1.7 Dividing

T 1 ×

O 9 5

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Operations

1.6 Multiplying

Using place value and known and derived facts to multiply and divide mentally, including multiplying by 0 and 1 and dividing by 1

200

Adding and subtracting up to four-digit numbers

Memorising multiplication and corresponding division facts for 2s to 10s

7 3 6

Review & date

Reading, writing, comparing and ordering whole numbers up to 10,000 and representing them using base 10 structure

Place value house Thousands

Practices (NZC 2025)

6 438

Multiplying two-digit and three-digit numbers by a one-digit number

Dividing up to a three-digit whole number by a one-digit divisor, with no remainder

Rational numbers 1 1.8 Fractions and decimals

Bigger: 1 2

6 10

1 or 0.4?

= 0.5

t te n h

Reading, writing and representing tenths as fractions and decimals Comparing and ordering tenths as fractions and decimals Memorising and using the decimal 1 equivalent of and fractions with 2 denominators of 10

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

Rational numbers (continued) 2 5

1.9 Comparing and ordering fractions

Comparing and ordering fractions with the same numerator or same denominator

4 5

Identifying when two fractions are equivalent, using representations

Relating fractions, improper fractions and mixed numbers to their position on a number line

1 2

7 3 4 − = 8 8 8

1.10 Adding and subtracting fractions

Adding and subtracting fractions with the same denominators, including beyond a whole

2 3 2 7 + + = 5 5 5 5

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

1 If is 6, what is the whole 4 amount? Can you halve the cookie recipe?

3 +

1 8

1– 3 7

– 3

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

4 3

Using known multiplication and division facts to scale a quantity

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1.12 Adding and subtracting decimals

1 of 18 = 3

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1.11 Unit fractions and scaling

Adding and subtracting decimals to one decimal place

Multiplying decimal tenths by 10 1.13 Multiplying and dividing decimals

9.4 × 10 = 94 5 ÷ 10 = 0.5 68 ÷ 10 = 6.8

Dividing one- and two-digit whole numbers by 10 to make decimals and identify tenths

Financial maths Representing amounts of currency using different combinations of denominations 1.14 Using money $3.00

Calculating the total cost of several items costing whole-dollar amounts and with different prices, or of multiples of the same item, including giving change

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

ESS

PRO

PA S S P

Strand 2: Algebra

Equations and relationships For me

Topic

Example 35 ÷ 5

147 − 65

Checking the truth of number sentences and completing open number sentences involving addition and subtraction

True False

Checking the truth of number sentences and completing open number sentences involving multiplication and division

= 96 + 15 61

Practices (NZC 2025)

60 + 60 = 10 × 12

I feel

Review & date

57 Recognising, continuing, creating and describing growing patterns (including numerical and non-numerical patterns) that change by adding, subtracting or multiplying by a constant whole number

2.2 Growing patterns

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AF T

2.1 Number sentences

For my teacher

I’m counting on you!

Year 4 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

I feel 1000 ml 900 ml 800 ml 700 ml 600 ml 500 ml 400 ml 300 ml 200 ml 100 ml 0 ml

30 cm

Practices (NZC 2025)

Review & date

Using familiar objects (e.g. body parts) and experiences to create estimation benchmarks

50 40

3.1 Estimation and measuring

Using the appropriate tool for measuring length, mass (weight) and capacity in mixed units

20 10

0 500 kg 1

500

500 3 500

Measuring temperature in degrees Celsius 0 CM

7 cm

18 cm

5 cm

B C

3.3 Area

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Measuring the perimeter of polygons using metric units

3 cm

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3.2 Perimeter

Measuring the areas of irregular shapes covered with squares and half squares

Calculating the areas of rectangular figures (including squares) using multiplication of side lengths

7 cm 2 cm

Area =

cm2

3.4 Volume 36 cm3

3.5 Angles

Measuring the volumes of rectangular prisms (cuboids) by filling them with identical 3D blocks

Estimating the size of angles by comparing them to 90, 180 and 360 degrees 90°

5 hours =

minutes

Measuring duration in hours, minutes and seconds, including mixed time units Finding equivalent durations of time using different units

3.6 Time

9 : 00

Telling the time on analogue and digital clocks to the nearest minute

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

ESS

Strand 4: Geometry

PRO

PA S S P

Shapes For me

Topic

4.1 2D shapes

Example

Regular polygon

For my teacher I feel

Practices (NZC 2025)

Review & date

Identifying, classifying and describing the attributes of regular and irregular polygons of up to 12 sides, using edges, vertices and angles

Irregular polygon

Identifying the number of lines of symmetry in 2D shapes

Semicircle

Spatial reasoning Visualising 3D shapes and connecting them with 2D diagrams, verbal descriptions and the same shapes drawn from different perspectives

Top view

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4.2 3D shapes

Side view

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Front view

4.3 Transformations

Performing one-step transformations (reflections, translations, rotations) on 2D shapes

Pathways 4

4.4 Grid references

Using alphanumeric and general grid references to identify regions and plot positions on a grid map

3 2 1 A

Year 4 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, Visualisation of data and Interpretation of data For me

Topic

For my teacher

Example

I feel

Practices (NZC 2025)

Review & date

Answering questions about the frequency of a particular value in dot plots

Hours of sleep

Answering questions about individual values in a dot plot, while referring to the context

5.1 Dot plots 6

Distinguishing between when to use a particular value or the frequency for a given value when answering questions about dot plots

How many people slept 6 hours?

How we got to school

title

8 6 5 4

Creating dot-plot or bar-graph data visualisations

3 2 1 0

y-axis

Collecting numerical data and, if needed, rounding to an appropriate unit or part of a unit, based on the context

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5.2 Statistical investigations

Walk

Car

Bike

Bus

Scooter

Transport method

x-axis

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Number of students

Interpreting data visualisations

The more-pork you know, the further you’ll go!

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

Number | Number structures

Topic 1.1 Whole numbers Place value 5,367 can be broken into:

5 thousands, 3 hundreds, 6 tens and 7 ones (5,000 + 300 + 60 + 7) or 53 hundreds, 6 tens and 7 ones (5,300 + 60 + 7) or 536 tens and 7 ones (5,360 + 7)

Numbers can be broken into lots of different combinations

or 5,367 ones (5,367)

Learn 1

Show these numbers on the numeral expanders.

2,431 hu

te ns

n dre d s

te ns

n dre d s

te ns

8,276

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us an d s

ones

D R

tho

ones

tho

us an d s

ones

te ns

n dre d s

te ns

ones

Answer these place value questions.

How much is the 7 worth in the number 2,785?

How much is the 9 worth in the number 9,103?

How many hundreds are in all of 4,168?

How many tens are in all of 3,496?

How many ones are in all of 6,219?

te ns

n dre d s

ones

te ns

n dre d s

te ns

ones

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

Write each number:

in words

4,568

on the place value house. Place value house Thousands

8,043

iii

7,109

How many?

Tens

Ones

How do the numbers in words connect with the place value house?

D R

AF T

Hundreds

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

Explore 1

Rewrite the number of votes in the table from largest to smallest. Bird number

New Zealand’s bird of the year votes 2024 Bird number

Number of votes

Bird Kea

4,206

Ruru/morepork

4,467

Hoiho

6,328

Kākāpō

4,548

Pīwakawaka/fantail

4,205

Karure

5,442

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Number of votes

Make the largest number possible with 1, 7, 8 and 0.

Make the smallest number possible with 3, 8, 2, 1 and 3.

Count on and back from the number you made in question 2.

10 more

10 less

25 more

25 less

50 more

50 less

100 more

100 less

1,000 more

1,000 less

D R

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

Circle the number in which:

4 has the greatest value

3,472

6,324

4,012

9 has the smallest value

6,889

3,914

1,900

5 has the smallest value.

19,875

2,536

6,851

A hiker records the distances travelled on three different walking trails. • Trail X: 5,430 metres • Trail Y: 6,215 metres • Trail Z: 4,800 metres

Write down the distances of each trail in words. Trail X:

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Trail Y: Trail Z:

Order the trails from shortest to longest.

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b c

How much longer is Trail X than Trail Z?

Circle the bigger number in each of these pairs.

345 or 354

2,369 or 2,198

5,592 or 5,679

983 or 1,276

4,309 or 4,390

214 or 241

396 or 369

507 or 570

842 or 824

1,204 or 1,240

2,368 or 2,386

3,107 or 3,170

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

Deepen 1

Complete the following number patterns.

Start at 742 and count forwards in 10s. 742

Start at 253 and count forwards in 100s. 253

752

353

Start at 482 and count forwards in 1,000s. 482

1,482

What do you notice about these patterns? Which place value column is changing in each pattern? Go back and circle the numbers that changed when either 10, 100 or 1,000 was added.

Riley is collecting stickers. She currently has 256 stickers. If Riley adds 100 stickers to her collection each week, how many stickers will she have after 3 weeks?

D R

AF T

Dave has $153 in his account. His Mum says she will pay him $10 to mow the lawns each week. How many weeks will it take for Dave to save more than $200?

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

Number | Number structures

Topic 1.2 Rounding

Rounding to the nearest 10

Every number lives between two multiples of 10. 40

Example: Is 47 closer to 40 or 50?

We can use a number line to help us round. The number 47 is nearer to 50 than it is to 40. So, 47 rounded to the nearest ten is 50. Rounding rules: 4 or less: Round down. 5 or more: Round up.

Learn 1

Mark each number on the number line and circle the nearest ten it would round to.

675

729

Solve these rounding problems.

Mike read 27 pages of his book one day. If he rounded that number to

670

680

720

730

348

384

AF T

D R

340

350

380

390

the nearest ten, how many pages would he say he read? b

Yasmin spent a total of $48 on groceries. If she rounds this amount to the nearest ten, what amount will she say she spent?

The zoo has 152 animals in total. If the zookeeper rounds that number to the nearest ten, how many animals are at the zoo?

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

Round down

Rounding to the nearest 100 When we round to the nearest 100, we are looking for which multiple of 100 (e.g. 100, 200) the number is closest to on a number line.

140

100

200 170

Round up

100

Locate the following numbers on each number line and circle the nearest 100.

670

600

d 400

300

874 800

900

D R

230 200

350 300

Look at the tens digit: If the tens digit is 4 or less → Round down. If the tens digit is 5 or more → Round up.

AF T

700

200

Complete this table and identify which “100” is the nearest. The first one has been completed for you. Lower 100

Number

Upper 100

Nearest 100

500

527

600

500

792 436 389 258 117

The Smyth family drove around New Zealand on holiday. Read the distances they travelled and round them to the nearest 100 km.

Auckland to Gisborne, they drove 495 km. This is approximately

Napier to Wellington, they drove 325 km. This is approximately

Clyde to Mosgiel, they drove 186 km. This is approximately

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

Rounding to the nearest 1,000

Look at the hundreds digit. If the hundreds digit is 4 or less → Round down. If the hundreds digit is 5 or more → Round up.

To round to the nearest 1,000, you must look at the hundreds digit. Example: 3,700 sits between 3,000 and 4,000.

Round up

It is closer to 4,000, so 4,000 is the nearest 1,000.

3,700

3,000

3,500

4,000

Explore 1

Locate the following numbers on each number line and circle the nearest 1,000.

8,900

8,000

34,790

35,000

3,000

56,202 56,000

57,000

D R

34,000

2,000

AF T

9,000

2,480

Complete this table and identify which “1,000” the number is nearest to. Two examples have been done for you. Lower 1,000 6,000

Number 6,427 8,992 5,136 4,689 52,317 87,924

Upper 1,000 7,000

Hundreds digit Nearest 1,000 4 6,000

Solve these rounding problems.

Aoraki/Mount Cook is 3,724 metres high. Rounded to the nearest 1,000, the height is metres.

Rakaia Bridge is the longest road bridge in New Zealand. It is 1,756 m long. Rounded to the nearest 1,000, it would be m.

Spark Arena in Auckland can hold 12,200 people. Rounded to the nearest 1,000, the capacity is .

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

Rounding tenths to the nearest whole number

6.8

To round decimal numbers to the nearest whole number, you need to look at the tenths digit. For example, 6.8 sits between 6 and 7. On the number line, 6.8 sits closer to 7, so 6.8 rounded to the nearest whole number is 7.

Look at the tenths digit: If the tens digit is 4 or less → Round down. If the tens digit is 5 or more → Round up.

Place each decimal number on the number line, and circle the nearest whole number.

7.4 7

29.3

3.9 3

Complete this table.

D R

15.7 16

AF T

Whole number before

Decimal number

Whole number after

Tenths digit

Nearest whole number

3.6

35.5 15.9 0.7 68.2

a A conservationist weighs a Little Spotted Kiwi. The scale shows 1.29 kg. What is its weight rounded to the nearest whole number? b S arah ran 5.62 kilometres in her morning jog. If she rounds that distance to the nearest kilometre, how far did she run?

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

Deepen 1

Round up or down to the nearest 10.

Round up or down to the nearest 100.

491

Round up or down to the nearest 1,000.

6,088

Complete the table by rounding each number to the nearest 10, 100 and 1,000.

1,802

34,470

Nearest 10

34,137

12,988

83,808

Nearest 100

Nearest 1,000

AF T

Number 3,491

2,164

8,693 7,208

D R

4,975 25,793 78,345 89,614

Play this game with a classmate. You will need 3 dice and some colour pencils each. One person rolls all 3 dice and arranges them into a number e.g. 325, 532, 523, etc. Round your number to the nearest 10, and colour in that number on the board. If you get 4 counters in a row, you get a point. 10

120

130

140

150

160

170

220

230

240

250

260

270

320

330

340

350

360

370

420

430

440

450

460

470

520

530

540

550

560

570

620

630

640

650

660

670

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

Number | Number structures

Topic 1.3 Counting in multiples Counting in multiples This number line shows counting forwards from 0 in multiples of 2.

This number line shows counting backwards from 16 in multiples of 2.

9 10

9 10 13 14 15 16

Learn 1

Write the numbers in the patterns shown on the number lines.

24, 26, c

78 79 80 81 82 83 84 85 86 87 88

AF T

24 25 26 27 28 29 30 31 32 33 34

34 35 36 37 38 39 40 41 42 43 44

D R

14 15 16 17 18 19 20 21 22 23 24

This activity is about counting in multiples. Pick a colour pencil.

Colour in all the multiples of 3 (e.g. 3, 6, 9…) on the number chart.

Pick a different colour and colour in the multiples of 4 (e.g. 4, 8, 12)

c d

What numbers are coloured in by both colours? Can you describe any patterns you notice in the multiples of 3?

How about in the multiples of 4?

Circle the multiples of 5. What pattern do you notice?

100

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

Counting forwards and backwards in 100s, 50s and 25s. Fill in the empty boxes. The first one has been completed for you. 100

200

400

500

900 150

300

500

600

800 700

500

200

400

650

500

700

750

450

900 150 400

350

700

800

AF T

675

400

Complete the word problems.

Rico is collecting stamps. He starts with 100 stamps and adds 50 stamps each week to his collection. How many stamps will he have after 5 weeks?

Matt has a savings account. He starts with $200 and saves $25 every week. How much money will he have after 3 weeks?

A library is adding books. It starts with 400 books and gets 100 new books each week.

How many books will it have after 5 weeks?

How many books will it have after 6 weeks?

How many books will it have after 9 weeks?

D R

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

Explore 1

List the multiples of 6 (from 6 to 60). 6, 12,

Find and circle the multiples of 6 in the box. 12

37 24

11 73

48 60

91 66

99 58

A concert organiser is setting up rows of seats. The rows get smaller as they get further from the stage. The first row at the front has 42 seats, and each following row has 6 less seats than the previous row.

AF T

Write the number of seats in the: First row: 42

D R

Second row:

What is 6 × 6?

Third row: Fourth row:

What is the total number of seats? 4

Complete this table. −7

Multiple of 7 21 42

A farmer has 49 apples. He gives 7 apples to every person that he sees on his walk home. He sees 5 people. How many apples does he have left once he gets home?

56 35 7 63

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

List the multiples of 8 (from 8 to 80). 8, 16,

23 48

80 64

54 11

45 12

×8

×7

67 72

×5

×1 ×2

×6

×3 ×4

Complete the table. List the multiples of 9

Add together its digits 0+9=9

What number is in the tens column? 0

What number is in the ones column? 9

9 18

1+8=9

AF T

8 Complete the wheel by writing in the correct multiple of 8.

Find and circle the multiples of 8 in the box.

D R

10 What do you notice about the multiples of 9?

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

Deepen 1

Write the first 10 multiples of each number. Example: 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.

For each row, circle the numbers that are multiples of the red number. 3

100

AF T

e.g.

D R

Write the next 2 numbers.

40, 45, 50, 55…

9, 12, 15, 18…

20, 24, 28, 32…

18, 16, 14, 12…

60, 54, 48, 42…

×7

21, 28, 35, 42…

×6

48, 40, 32, 24…

54, 45, 36, 27…

25, 50, 75, 100…

450, 400, 350, 300…

Complete the wheel by writing in the correct multiple of 25.

×8

×1 ×2

25 ×5

×3 ×4

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

Number | Operations

Topic 1.4 Adding and subtracting Jump method for addition Start with the larger number. Add the 10s, and then the 1s. 22 + 43

22 + 43 +10

+10

63 64 65

+20

63 64 65

Learn Solve these equations using the jump method.

72 + 25 =

112 + 57 =

231 + 63 =

320 + 41 =

25 + 414 =

D R

AF T

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

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.

Explore Solve using regrouping in the ones column.

a H

d H

g H

D R

AF T

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

Rewrite these as column additions and solve.

28 + 47

63 + 19

358 + 22

Remember to line the numbers up in their place value columns.

46 + 25

168 + 206

D R

AF T

432 + 19

Write these as column additions and solve.

Serena counted 328 cars on the way to school and 453 cars on the way home. How many did she count altogether?

Arjun drove 236 km on Saturday and 607 km on Sunday. How far did he travel on the weekend?

Identify the numbers in worded questions.

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

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

To solve 47 + 28: Add the 10s: 40 + 20 = 60 Add the 1s: 7 + 8 = 15 Then add them together: 60 + 15 = 75

Split into 10s and 1s to add.

23 + 12 =

26 + 31 =

45 + 42 =

34 + 58 =

43 + 27 =

D R

Deepen

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

147 + 231 =

AF T

349 + 238 =

100 + 200 = 300

40 + 30 = 70

7+1=8 So, 147 + 231 = 3

Break it apart to work it out!

635 + 236 =

= =

So, 349 + 238 =

+ +

= =

So, 635 + 236 =

Choose a method to find the answer. 324 + 548 =

Year 4 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

–4

–20

34 35 36 37 38

Learn Use the jump method to solve.

98 – 34 =

360 – 43 =

798 – 51 =

598 – 125 =

372 – 203 =

D R

AF T

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

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

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

7 6 13

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

–

Explore Solve by starting with the ones column.

–

D R

–

AF T

Solve using regrouping from the tens to the ones column.

a H

d H

–

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

Rewrite as column subtraction and solve.

34 – 17

–

51 – 33

–

182 – 163

85 – 36

–

793 – 447

–

891 – 206

–

D R

AF T

–

Remember to line the numbers up in their place value columns.

Write as column subtraction and solve.

Betty the baker made 97 cupcakes. She sold 58 of them. How many are left?

–

Suresh had $644. He spent $415. How much does he have left? Subtract the smaller number from the bigger number.

–

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

You can use the Subtraction in parts strategy by splitting up the number you are subtracting by its place value parts.

437 – 129 =

317 – 9 = 308

437 – 100 = 337 337 – 20 = 317

Take away 100, then 20, then 9.

Deepen 1

Take away the 10s, then the 1s to subtract.

35 – 13 =

48 – 15 =

−

52 – 21 =

−

67 – 34 =

−

96 – 25 =

−

124 – 13 =

−

389 – 257 =

−

478 – 235 =

−

Choose any method to find the answer.

−

AF T

−

D R

962 – 457 =

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

Number | Operations

Topic 1.5 Multiplication and division facts 4 groups of 3

We use the x sign for “groups of ” or multiplication, and the ÷ sign for sharing or division.

3 groups of 4

4 × 3 = 12 3 × 4 = 12

Learn Complete the multiplication facts to match the pairs of arrays.

D R

AF T

Complete the families of facts.

3 × 9 = 27

10 × 2 = 20

= 27

= 20

27 ÷

20 ÷

27 ÷

20 ÷

8×5= 5×

7 × 10 =

÷5=

= 5

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

Multiplication facts can help with division. 15 ÷ 3

Think

3×

= 15.

The answer is 5.

= 26,

so 26 ÷ 2 =

Solve these sums.

26 ÷ 2

Think

2×

27 ÷ 3

Think

3×

= 27,

so 27 ÷ 3 =

45 ÷ 5

Think

5×

= 45,

so 45 ÷ 5 =

55 ÷ 5

Think

5×

= 55,

so 55 ÷ 5 =

120 ÷ 10

Think

10 ×

= 120,

so 120 ÷ 10 =

Fill in the missing lines in each family of facts house. The first one is completed for you. b

2×7=4 7 × 2 = 14 14 ÷ 7 = 2

D R

AF T

6 × 9 = 54

7 × 8 = 56

5 × 4 = 20

54 ÷ 9 = 6

56 ÷ 8 = 7

20 ÷ 5 = 4

14 ÷ 2 = 7 e

3 × 8 = 24

4 × 6 = 24

24 ÷ 8 = 3

24 ÷ 6 = 4

9 × 2 = 18

8 × 5 = 40

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

Explore 1

There are 5 chocolates in each box. How many in:

3 boxes

6 boxes

7 boxes

10 boxes?

Write the first 10 numbers in the 3 times table. The numbers are: all odd.

The table shows the number and cost of each item sold at the school fair.

Complete the table to show how much money each student raised.

Who sold the most items?

B all even.

C a mix of odd and even.

AF T

Number of items sold

Cost per item

Mika

Andy

Serena

$10

Sophia

Hao

D R

Name

Who raised the most money?

How much money would Serena have raised if she sold 8 items?

How many items would Sophia have sold if she raised $63?

According to the table, what was the total amount raised?

Amount raised

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

Explore 1

Multiply the number in the centre of the wheel by the numbers around it. Write the answer in the outer sections of the wheel. The first one has some examples for you.

10 5 4

5 7

6 3

4 2

h 5

3 7

6 8

9 6

8 5

D R

AF T

f 7

Complete the following multiplication wheels which have 0 or 1 in the centre. 5 4

7 6

2 3

1 6

Complete this family of facts house.

8×1=8

10 8

8÷8=1 a

What do you notice happens when you multiply by 1? What do you notice happens when you multiply by 0?

What happens when you divide by 1?

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

Deepen 1

To multiply by 4: double, then double again. 7×4=7×2×2 =

14 × 2

Use double, then double again to solve these sums. a

8×4=8×2×2=

20 × 4 =

×2×2=

12 × 4 =

30 × 4 =

To divide by 4: halve, then halve again.

AF T

Halve

×2=

24 ÷ 2 = 12

D R

24 ÷ 4

×2=

Halve again

12 ÷ 2 = 6

So 24 ÷ 4 = 6

Use halve, then halve again to solve. Halve a 16 ÷ 4

Halve again Halve

b 40 ÷ 4

Halve again Halve

c 60 ÷ 4

Halve again

16 ÷ 2 = ÷2=

So 16 ÷ 4 =

40 ÷ 2 = ÷2=

So 40 ÷ 4 =

60 ÷ 2 = ÷2=

So 60 ÷ 4 =

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

Number | Operations

Topic 1.6 Multiplying The grid method involves splitting the numbers up into their place value parts and replacing them inside the grid. Add the two answers 6 × 23 =

120

at the bottom of the grid to find the total.

= 138

Learn

Solve with the grid method. 4 × 27 =

5 × 53 =

D R

b 6 × 36

AF T

5 × 84 =

d 3 × 62 =

× 3

= 2

= e

4 × 48

× 4

There are 3 bags of kumara, with 29 kumara in each bag. Use the grid method to find out how many kumara there are in total.

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

The grid method also works for larger numbers, you just need a larger grid.

219 × 5 =

200

1,000

Solve with the grid method.

239 × 4 = ×

200

= 219 × 5 = 1,000 + 50 + 45 = 1,095

b 30

734 × 6 = ×

= d

378 × 4 =

300

= f

348 × 2 = ×

D R

376 × 8 =

AF T

556 × 9 = ×

= g

482 × 5 =

261 × 7 = ×

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

Place value strategy is a strategy where you break the larger number into its place value parts.

3 × 20 and 3 × 6 added together = 60 + 18

3 × 26 =

= 78

Explore 1

Use the place value strategy to solve these multiplications.

2 × 27

is the same as

2×

+2×

4 × 14

is the same as

4×

D R

AF T

3 × 19

is the same as

3×

+4×

+3×

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

Solve with the place value strategy.

5 × 13 = 5 × =

4 × 32 = 4 ×

5 × 45 =

8 × 33 =

3 × 58 =

+4× +

+6× +

7 × 24 = 7 ×

+7× +

× Split up the 2-digit number using place value.

D R

6 × 21 = 6 ×

AF T

+5×

× +

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

The place value strategy can be used for larger numbers too. 7 × 329 = 7 × 300 + 7 × 20 + 7 × 9 = 2,100 + 140 + 63 = 2,303

Solve these problems that multiply 1-digit numbers with 3-digit numbers.

5 × 278 =5×

+5×

4 × 825 =

2 × 836 =

3 × 924 =

8 × 274 =

9 × 183 =

7 × 229 =

6 × 581 =

D R

AF T

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

Column multiplication Column multiplication (an algorithm) is a shorter way to multiply larger numbers. 4 × 53 = ?

2 Now multiply the tens. 4 groups of 5 tens or 4 × 50 = 200. Also, add the regrouped ten to end up with 21 tens, or 210. So, 4 × 53 = 212.

× 2

1 Start with the ones. 4 groups of 3 ones or 4 × 3 = 12. Regroup the 12 for 1 ten and 2 ones and record the numbers in their place value columns.

This method is similar to the column addition algorithm. Start at the ones and work left.

Deepen

AF T

Solve using short multiplication.

D R

2 3

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

8 4

Rewrite as short multiplication and solve.

4 × 32 H

b T

Namrita bought 8 games that each cost $109. How much did she spend? H

× $

marbles

Match the equations with their answers. 45 7

602

AF T

D R

Antony bought 9 boxes of marbles with 47 in each. How many does he have altogether? T

5 × 152

9 × 265

6 × 54

8 × 68

7 × 41

86 ×

368

53 ×

315

45 ×

318

92 ×

360

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

Solve using your choice of written methods. Show how you got your answer. You may need to do some working on another sheet of paper.

4 × 37

Taine bought 5 sets of football cards. Each pack costs 90 cents. How much did he spend? Write the answer in dollars and cents.

Nouf ordered 1 doughnut for each of her birthday guests and 3 extras, in case more guests arrived. She bought 4 boxes with 26 doughnuts in each. How many guests was she expecting?

Use your choice of method to solve.

Four teams with 16 people in each were going to the stadium. How many seats were needed on the bus?

The front section of the stadium has 5 rows with 123 seats in each. How many people can sit there?

6 groups of 16

D R

AF T

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

Number | Operations

Topic 1.7 Dividing You can set out division problems like 64 ÷ 4 using this symbol: 4

2 Write the 1 on the answer line above the tens and regroup the 2 tens left over to the ones column. 1 Start with the biggest place value column. 6 (tens) divided by 4 is 1 (ten) with 2 (tens) left over.

1 6 4

6 4

Solve these divisions.

D R

Learn

For division, set the quotient out this way, and start from the left and work your way right.

AF T

4 Write the 6 on the answer line above the ones. So, 64 ÷ 4 = 16.

3 Now divide the ones by 4. 24 (ones) divided by 4 is 6.

5 55

4 84

2 68

3 69

2 46

3 93

5 75

6 84

8 96

3 54

7 91

4 92

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

Rewrite and solve.

87 ÷ 3

98 ÷ 2

88 ÷ 8

84 ÷ 7

78 ÷ 3

95 ÷ 5

Solve and rewrite.

AF T

D R

76 ÷

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

Dividing 3-digit numbers

7 3 1

6 43 8 Questions to ask yourself: How many times does 6 go into 4? It doesn’t. So, how many times does 6 go into 43? 7 times. Write a 7 above the 3 on the answer line. There is 1 ten left over, write this 1 beside the 8. How many times does 6 go into 18? 3 times. Write a 3 above the 8 on the answer line. 438 ÷ 6 = 73

Rewrite and solve these divisions.

342 ÷ 6

864 ÷ 8

648 ÷ 9

723 ÷ 3

576 ÷ 8

912 ÷ 4

792 ÷ 9

258 ÷ 6

561 ÷ 3

384 ÷ 4

735 ÷ 5

672 ÷ 8

914 ÷ 7

528 ÷ 4

486 ÷ 6

D R

AF T

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

Division in parts Another way to solve division problems is by dividing them in parts (or chunks!). For example: 96 ÷ 8 Instead of dividing 96 in one go… Split it up and divide 80 and 16 separately by 8, then add the answers.

96 ÷ 8 = 12

80 16 ÷ 8 ÷8 = 10 = 2 10 + 2 = 12 Divide the biggest “chunk” of the number you can first, divide whatever is left over as well. Then add the answers together.

Solve

78 ÷ 3 60 ÷ 3 = 20 18 ÷ 3 = 6

98 ÷ 7

68 ÷ 4

D R

AF T

Explore

78 ÷ 3 = 20 + 6 = 26 d

72 ÷ 6

95 ÷ 5

81 ÷ 3

54 ÷ 3

84 ÷ 7

92 ÷ 4

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

Division in parts with 3-digit numbers Division in parts also works with 3-digit numbers. For example:

384 ÷ 4 = 96

384 ÷ 4

360 24 ÷ 4 ÷4 = 90 = 6

360 ÷ 4 = 90 24 ÷ 4 = 6

90 + 6 = 96

384 ÷ 4 = 96 Solve

462 ÷ 6

924 ÷ 4

756 ÷ 3

816 ÷ 8

378 ÷ 9

504 ÷ 7

840 ÷ 7

936 ÷ 9

672 ÷ 3

486 ÷ 3

390 ÷ 5

542 ÷ 2

D R

AF T

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

Deepen Solve using a division method of your choice.

84 students were staying in rooms of 3 on their school trip. How many rooms did they need?

95 sheep were divided equally into 5 pens. How many were in each?

Te Aroha divided her 96 football cards into 4 equal piles. How many cards in each pile?

How many cards in each pile if Te Aroha divided them into 3 equal piles?

78 people in the audience sat in rows of 6. How many rows were there?

D R

AF T

Could 77 people sit in rows of exactly 7? Why or why not?

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

Solve using a division method of your choice.

A factory makes 864 toys in a b day. If each worker makes 8 toys, how many workers are there in the factory?

A bookstore has 756 books. If there are 7 shelves, how many books are on each shelf?

An orchard harvests 912 apples. d They are packed into trays holding 8 apples each. How many trays are needed?

A principal has 540 pencils. If she distributes them equally among 6 classes, how many pencils does each class get?

Students have made 594 flower garlands for a Pasifika dance festival. If they are packed into bags holding 9 garlands each, how many bags are needed?

D R

AF T

A garden shop has 672 plants. If each planter can hold 6 plants, how many planters are needed to hold all the plants?

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

Solve using a division method of your choice.

A concert hall has 240 seats. If b each row has 8 seats, how many rows are there in the concert hall?

A school has 168 students participating in a Maths competition. If each group can have 7 students, how many groups are formed?

An orchard harvests 968 kiwifruit. If the fruit is sold in bags of 8, how many bags are needed?

Students have made 432 lanterns for a Matariki celebration. If each container holds 6 lanterns, how many containers are needed to move the lanterns?

D R

AF T

A bakery produces 99 cookies. If each box can hold 9 cookies, how many boxes are needed to package all the cookies?

A recipe requires 48 grams of sugar. If you have 4 grams of sugar per serving, how many servings can you make?

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

Number | Rational numbers

Topic 1.8 Fractions and decimals

= 0.1

es on

( )

te ns

re ds

hu nd

Zero point one (0.1) can also 1 be read as one-tenth . 10 1 You can write as the decimal 0.1. 10 1 = 10

te nt hu hs nd re dt th hs ou sa nd th s

Tenths

10 10

is the same as 1 or one whole.

Learn Shade the boxes and write each fraction as a decimal.

2 10

6 10

9 10

4 10

Complete the number line.

AF T

D R 0 0 10

0.1

0.2 2 10

0.4 3 10

0.5

0.6

5 10

6 10

0.8 7 10

1 9 10

10 10

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

Write these numbers as fractions.

three-tenths

five-tenths

nine-tenths

six-tenths

Write these fractions in words.

2 10

7 10

4 10

8 10

Write these numbers as decimals.

four-tenths

seven-tenths

nine-tenths

two-tenths

Write these decimals in words.

0.1

0.8

0.6

0.2

Shade in the grids and write the fractions as decimals.

1 2

5 10

What do you notice about the two values in question 7?

Five tenths = 9

D R

AF T

half

What is a simpler way to write

10 ? 10

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

Explore 1

Circle the larger number in each pair. Circle both numbers if they are equal.

1 6 or 2 10

Put the fractions in order from biggest to smallest:

4 1 or 10 2

1 or 0.5 2

1 7 3 4 2 9 , , , , , . 10 10 10 10 10 10

Circle the larger fraction in each pair.

3 5 or 10 10

Find a fraction that sits between each pair shown.

2 10

Put the decimals in order from biggest to smallest: 0.2, 0.5, 0.8, 0.6, 0.3, 0.9.

Circle the larger decimal in each pair.

0.2 or 0.8

Find a decimal that sits between each pair shown.

0.6

0.9

0.2

0.4

0.1

0.5

0.6

0.9

6 4 or 10 10

5 10

D R

AF T

3 10

7 10

0.9 or 0.3

7 9 or 10 10

7 10

10 10

0.5 or 0.6

0.5

0.8

Fractions and decimals can be used to represent the same values. 54

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

Which is bigger? Circle the larger number.

3 or 0.4 10

Order these numbers from smallest to biggest: 0.4,

Write a fraction or decimal that sits between each pair shown.

0.2

Fill in the gaps.

6 10

0.3

1 10

4 or 0.8 10

0.5

6 7 2 , 0.1, , 0.9, . 10 10 10

8 10

0.5

AF T

0.2

3 10

D R

7 or 0.2 10

0.6

4 10

Order these numbers from smallest to biggest.

2.3, 2.7, 1.6, 1.9, 3.4

2 8 6 5 9 , 3 , 2 , 1 , 3 10 10 10 10 10

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

9 10

Deepen Solve these word problems involving tenths.

Juni has three ribbons of different lengths: 0.5 metres, 0.3 metres and 0.7 metres. Arrange the ribbons from shortest to longest.

In a cooking competition, four chefs used different amounts of salt in their dishes: 0.6 grams, 0.2 grams, 0.7 grams and 0.4 grams. Arrange the dishes by the amount of salt used from most to least.

At a bakery, three types of cupcakes have different icing weights: 0.4 kilograms, 0.6 kilograms and 0.2 kilograms. Order the cupcakes from lighest to heaviest based on the icing weight.

A smoothie shop offers different sizes of smoothies: 0.5 litres, 0.8 litres, 0.3 litres and 1 litre. Arrange the sizes from largest to smallest.

A gardener watered three plants with different amounts of water: 0.8 litres for the first plant, 0.5 litres for the second and 0.9 litres for the third. List the plants in order of the amount of water they received, from least to most.

D R

AF T

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

Number | Rational numbers

Topic 1.9 Comparing and ordering fractions Same denominator When fractions have the same bottom number (denominator), you can compare them by looking at the top numbers (numerators). For example,

3 8

3 5 is smaller than . 8 8

5 8

Learn 1

Order these fractions from smallest to largest.

4 1 3 6 5 , , , , 6 6 6 6 6

5 1 4 7 2 , , , , 7 7 7 7 7

Write the correct inequality sign (< or >) between the images.

3 1 5 2 4 , , , , 5 5 5 5 5

AF T

3 7 1 5 2 , , , , 8 8 8 8 8

D R

Write the correct inequality sign between the fractions.

2 5

4 5

7 7

3 7

9 16

14 16

3 4

1 4

4 10

8 10

19 25

17 25

Create your own inequality questions using the circles. Write the fraction beside each circle.

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

Same numerator

1 5

When fractions have 1 1 1 1 1 1 1 1 the same numerator, 8 8 8 8 8 8 8 8 you can compare them by looking at the denominators. The fraction with the smaller denominator represents a larger part of the whole. For example,

2 2 is larger than . 5 8

When a fraction has a 1 on top (numerator) it is called a unit fraction. 1 1 1 1 1 1 1 1 1 , , , , , . 9 2 5 10 3 4 6 7 8

AF T

Order these unit fractions from smallest to biggest: , , ,

Order the fractions from smallest to biggest.

5 5 5 5 , , , 11 6 9 7

3 3 3 3 , , , 10 6 4 8

Write the correct inequality sign, < or >, between the images.

D R

4 4 4 4 , , , 12 20 9 5

2 2 2 2 , , , 9 5 3 8

Write the correct inequality sign between the fractions.

4 8

4 5

7 8

7 10

3 3

3 5

8 10

8 9

5 9

5 6

2 3

2 6

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

Equivalent fractions =

1 2

= 2 4

= 3 6

4 8

Explore Circle the equivalent fraction.

1 4

2 3

2 8

4 8

2 3

3 4

1 2

4 6

6 8

3 4

3 6

8 10

Label each pair of equivalent fractions.

D R

AF T

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

Colour and label an equivalent fraction.

1 2

4 6

a c e

Write <, > or =. 1

0.4

D R

2 8

AF T

8 10

b d f

0.2

10 3

0.2

< means less than, > means greater than and = means the same.

Fill in the boxes to show equivalent fractions. 1 4 3 10

1 b = 6 12

21 7 e = 10

1 8 5 10

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

Improper fractions and mixed numbers An improper fraction has a numerator bigger than or equal to the denominator. You can change an improper fraction into a mixed or whole number. 6 = 4 Improper fraction

1 2 Mixed number

1 4 0

2 4

3 4

1 2

4 4

5 4

6 4 1

7 4

8 4

1 2

Why do you think they are called mixed numbers?

Deepen Fill in the gaps.

AF T

a 2 4

4 4

8 4

5 4

D R

1 4

1 2

b 2 2

3 3

1 2

c 4 3

4 2

5 3

1 2

7 3

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

1 2

9 3

Change the improper fractions to mixed or whole numbers. 1 5

2 5

3 5

4 5

5 5

6 = 5

9 5

2 6

3 6

4 6

5 6

10 = 5

c 6 6

7 6

8 6

9 6

10 6

11 6

e 2 10

3 10

4 10

5 10

8 = 6 6 10

7 10

11 = 10

12 = 10

Order from smallest to biggest.

D R

12 6 2

f 8 10

AF T

7 = 6

10 5 2

1 10

9 10

10 10

11 10

11 = 6 12 10

13 10

14 10

14 = 10

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

Smallest

Biggest

4 2 3 5 1 2 , 1 , , 1, , 1 , 6 6 6 6 6 6 Smallest

8 5

8 = 5

7 5

1 6

6 5

Biggest

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

Draw a line from each fraction to the correct place on the number line.

3 1 2 1 1 2 4 4 4

a 0 b

How do you know where to put each fraction?

2 3

1 3

Write the improper fraction and a mixed number for the diagrams.

Mixed number

D R

AF T

Improper fraction a

c d

How can you check your answers? Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Change these improper fractions into mixed numbers.

5 = 2

7 = 4

16 = 5

17 = 4

13 = 2

25 = 6

18 = 7

35 = 8

Change these mixed numbers into improper fractions.

1 = 2

3 = 4

2 = 3

5 = 8

2 = 7

2 = 5

1 = 3

Circle the bigger fraction. Convert one of the numbers to prove why.

1 7 or ? 2 2

2 4 or ? 6 6

1 9 or ? 5 5

3 12 or ? 10 10

1 10 or ? 4 4

7 1 or 7 ? 3 3

10 1 or 5 ? 8 8

9 1 or 2 ? 3 3

AF T

D R

2 = 6

Convert one first, then compare!

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

Number | Rational numbers

Topic 1.10 Adding and subtracting fractions We can add or subtract fractions with the same denominator. Numerator

Denominator

Learn

+ 1 4

= 1 4

AF T

Write the number sentences.

D R

Use 2 colours to shade each diagram, to match the addition number sentence.

2+2= 6 6

2+5= 8 8

1+2= 3 3

4 + 4 = 10 10

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

Subtract the fractions.

b 3 4

−

1 4

− =

3 5

−

1 5

Write the number sentences. b

−

D R

−

AF T

Solve these number sentences.

8 – 2 = 10 10

6–5= 6 6

4–3= 5 5

2–1= 3 3

1+2= 5 5

2+4= 7 7

5–2= 8 8

7 – 3 = 10 10

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

Explore 1

Add the fractions.

1 1 1 + + = 4 4 4

5 2 2 + + = 10 10 10

2 1 1 + + = 5 5 5

1 1 1 + + = 3 3 3

3 2 1 + + = 6 6 6

2 1 2 + + = 6 6 6

3 2 1 + + = 8 8 8

3 3 1 + + = 10 10 10

Write the missing fractions to make 1.

2 + 4

2 2 + + 6 6

4 2 + + 8 8

Write the missing fractions.

2 − 4

2 + 3

1 2 + + 5 5

7 1 + + 10 10

1 4

2 – 3

1 2 = 5 5

3 8

D R

=1 =1

= –

1 3

2 3 = 6 6

7 − 8

Match up each equation with the correct answer.

3 6 + = 10 10

4 10

1−

3 = 10

9 10

9 5 − = 10 10

7 10

AF T

–

Why would we write 1 instead of 3 ?

1−

9 10

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

Add these fractions together. Write your answer as an improper fraction and a mixed number. The first problem has been solved for you.

Fractions to add a

2 1 2 + + 3 3 3

Improper Mixed

5 3

2 3

Fractions to add b

5 2 1 + + 6 6 6

1 1 3 + + 2 4 4

4 3 5 + + 10 10 10

3 1 2 + + 4 4 4

3 1 2 + + 5 5 5

Improper Mixed

Solve these word problems. Write your answer as an improper fraction and a mixed number.

a A bucket contains

3 litres of water. 4

AF T

1 of a litre is added, and then 4 2 another of a litre is added, how 4

D R

much water is in the bucket now? 2 of a kilogram of flour 3 1 to make panakeke and 1 kilogram 3 1 for bread, plus kilogram for buns. 3

b A baker used

How much flour did the baker use in total? c A blueberry farm covers 1 hectares of land.

4 6

5 of a hectare had 6

wildflowers to attract bees. How

much land remained for blueberries?

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

Deepen 1

Each pair of blocks totals to the block above them. Use addition and subtraction to fill in the missing fractions and complete the steps.

c 3 8

4 12

2 12

2 9

1 9

3 9

2 8

7 7

9 10

3 10 2 10

11 12 3 12

1 5

4 10

4 5

3 6

1 5

15 12

4 12

5 12

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

18 9

3 5 1 5

2 10

4 6

1 12

4 7

D R

1 7

AF T

4 10

6 9

5 9

Number | Rational numbers

Topic 1.11 Unit fractions and scaling Fractions and division You can use division to work out the fraction of a group. 1 of 9 is the same 3 as 9 ÷ 3.

Halving a quantity is the same as dividing by 2.

Learn

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

AF T

D R

1 of 4 = 2

1 of 8 = 2

1 of 6 = 2

8÷2=

6÷2=

4÷2= d

1 of 12 = 2 12 ÷ 2 =

1 of 16 = 4

1 of 12 = 4

16 ÷ 4 =

12 ÷ 4 =

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

Complete the divisions.

1 of 18 = 3

1 of 20 = 2 ÷

1 of 4

= ÷

1 of 6

D R

AF T

= ÷

1 of 5

= ÷

1 of 8 = 4

1 of 24 = 8 ÷

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

There are 20 beads in this bag. How many beads are there 20 of each colour? beads Fraction 1 are red 4

1 of 20 4

Can you explain the link between unit fractions and division?

Division

Number of beads

20 ÷ 4 = 5

5 red

1 are yellow 4 1 are blue 5

The remaining beads in the bag in question 3 are purple. Write the number and fraction of purple beads.

D R

AF T

1 are green 10

purple beads or

of 20

Find the fraction in each number.

1 of 8 = 4

1 of 12 = 4

1 of 24 = 4

1 of 6 = 3

1 of 12 = 3

1 of 18 = 3

1 of 40 = 5

1 of 30 = 5

1 of 45 = 5

1 of 60 = 10

1 of 90 = 10

1 of 100 = 10

1 of 420 = 2

1 of 200 = 3

1 of 250 = 10

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

Draw lines to join the matching equations. 1 of 30 6

1 of 50 10

1 of 80 8

1 of 36 6

80 ÷ 8

30 ÷ 6

50 ÷ 10

36 ÷ 6

Solve the problems from question 6.

1 of 30 = 6

1 of 50 = 10

There are 20 players in Tim’s rugby union team. In one 1 match, of the players 5 scored tries. How many players scored a try?

Amiria saved $250 for a new mountain bike.

1 of 36 = 6

D R

AF T

1 of 80 = 8

She bought her bike on sale 1 and only spent of her money. 2 How much did she spend? 10

Heath picked 78 feijoas. He kept 1 for himself and gave the rest 6 to his aunty for jam. How many feijoas did Heath keep?

Lawrence has 280 alpacas on his lifestyle block. He needs to move 1 of them to a new paddock. 4 How many alpacas does he move?

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

Finding the whole set, when given the unit fraction 1

Find 1 part using the unit fraction. Example: 1 2 Multiply by the number of parts, If = 7, then there are 4 equal parts. 4 to find the whole set or amount. So, 7 × 4 = 28. The whole set is 28.

Explore 1

Draw the rest of the images in each set. Use multiplication of parts to find the whole set. 1 3 stars is of the total stars in the set. 3

Total stars (whole amount) =

1 of the total hearts in the set. 5

AF T

2 hearts is

D R

Total hearts (whole amount) = 1 4 triangles is of the total triangles in the set. 4

Total triangles (whole amount) = 1 5 arrows is of the arrows in the set. 6

Total arrows (whole amount) = 2

Solve the following questions.

b c 74

1 is 20, what is the whole amount? 2 1 If is 6, what is the whole amount? 4 1 If is 8, what is the whole amount? 5 Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Draw a line to match the unit fraction statement to the correct whole amount. 1 is 10 2

1 is 9 4

1 is 5 10

1 is 7 3

The whole is 36

The whole is 20

The whole is 21

The whole is 50

Complete the following problems.

1 This group of apples represents of 5 the box.

Working out space

D R

apples

AF T

How many apples are in the whole box? 1 of a class is 4 students. 6 How many students are in the whole class? students c

1 of the cookies. She 8 ate 3 cookies. Aimee ate

How many cookies were in the jar to start with? cookies d

1 of a garden is planted with 6 tomatoes, which amounts to 8 plants. How many plants are in the garden in total? plants

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

Scaling a quantity To double (make twice as much): multiply by 2. To halve (make half as much): divide by 2.

Deepen 1

This recipe makes 1 batch a of cookies. We need to make 2 batches, so we must double the recipe.

Multiply the ingredients by 2 to find the new amounts.

Ingredients: • 2 cups of flour • 1 cup of sugar

D R

• 100 chocolate chips

AF T

• 3 eggs

You check the fridge and find you have 10 eggs. Do you have enough to make 4 batches? Explain why or why not.

Mere and Sione are a making a smoothie recipe with 8 servings, but only want 4. They need to halve the recipe.

Divide the ingredients by 2 to find the new amounts.

Ingredients: • 4 cups of milk • 2 bananas • 10 strawberries

If we halve the recipe and then decide to add an extra banana, how many bananas will we use in total for the new recipe?

• 1 cup of yoghurt

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

This soup is made from the following ingredients:

You only have 2 onions at home so have to halve the recipe. List the new amounts.

• 12 carrots • 8 potatoes • 4 onions • 2 litres of broth

This pasta recipe serves 8 people. Ingredients:

We need to serve 16 people. How much of each ingredient will we need?

• 1 cup of grated cheese

This cupcake recipe makes 24 cupcakes. Ingredients: 1 • 1 cups of flour 2 • 1 cup of sugar 1 • cup of butter 2 • 3 eggs

D R

• 2 cups of marinara sauce

AF T

• 3 cups of pasta

We only want to make 12 cupcakes. Write the halved recipe.

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

Number | Rational numbers

Topic 1.12 Adding and subtracting decimals You can show tenths as fractions and decimals. +

4 is the same as 10 0.4.

2 10

4 10

0.2

0.4

Learn Write the tenth fractions as decimals, then add or subtract.

4 10

+ +

–

5 10

4 10

D R

AF T

−

= 3

−

= =

Add or subtract the following decimals.

0.3 + 0.4 =

0.4 – 0.3 =

0.5 + 0.2 =

0.8 − 0.7 =

0.2 + 0.2 =

0.6 – 0.4 =

0.2 + 0.6 =

0.7 − 0.5 =

0.4 + 0.5 =

0.4 + 0.8 =

1.5 − 0.9 =

0.7 + 0.8 =

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

Place value strategy for addition To solve 1.3 + 2.9, we can do the following: 1

Add the whole numbers: 1 + 2 = 3

Add the tenths: 0.3 + 0.9 = 1.2

Combine to get the total answer: 3 + 1.2 = 4.2

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

2.3 + 1.5 =

3.2 + 1.7 =

To solve 3.6 – 1.9 =

0.1

• Rearrange as an addition problem

1.9 +

4.6 + 2.5 =

D R

Jump method for subtraction

3.9 + 1.7 =

AF T

1.9

= 3.6

1 2

0.6 3

3.6

• Jump along number line 0.1 + 1 + 0.6 = 1.7

Use the jump method to solve the following subtraction problems.

4.3 – 1.5 =

b 8.7 – 4.9 =

3.4 – 1.8 =

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

d 92.5 – 43.8 =

Adding decimals using column addition You can add decimals just like you do with whole numbers. 3

+ 1

4 8 7

Use estimating and rounding to check your answers. Round 3.1 down to 3. Round 1.7 up to 2.

4 8 7

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

Explore Add the decimals.

d 7.5 + 4.3 =

g 19.5 + 6.7 =

b 2.8 + 4.5 =

e 9.3 + 6.8 =

h 26.6 + 12.6 =

c 6.3 + 2.9 =

AF T

a 3.1 + 4.7 =

D R

23.4 + 8.9 =

i 34.8 + 45.6 =

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

Subtracting decimals using column subtraction You can subtract decimals just like you do with whole numbers. 8

– 3

Use rounding and estimating to check your answers. Round 8.2 down to 8. Round 3.9 up to 4.

4 3

Subtract the decimals.

–

12.8 – 9.6 =

–

g 89.4 – 67.8 =

–

b 8.7 – 2.5 =

c 9.7 – 3.9 =

–

AF T

a 9.8 – 3.4 =

e 34.7 – 2.5 =

D R

8 – 4 = 4 so your answer will be close to 4.

–

h 76.3 – 23.6 =

–

45.2 – 17.9 =

–

i 99.4 – 47.6 =

–

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

Deepen 1

Solve the word problems using a method of your choice.

a A whānau travelled from Nelson to Kaikōura over two days. They drove 120.5 km on the first day and 154.8 km on the second. What is the total distance travelled?

A family used 150.8 litres of water d on Monday and 136.5 litres on Tuesday. How much water did they use over the 2 days?

A plant grew 4.5 cm in the first week and 3.7 cm in the second week. How much did the plant grow in total?

A fuel tank had 45.8 litres of petrol. After a trip, it now has 29.6 litres. How much fuel was used during the trip?

D R

AF T

A pet store sells 1.5 kg of dog food and 4.9 kg of cat food. How much pet food did they sell in total?

The temperature was 21.7ºC in the morning. If it drops to 16.4ºC by the evening, what is the decrease in temperature?

2 Use six of the digits 0 to 9 to fill in the boxes so that the sum is as close

to 10 as possible. Digits can only be used once.

· 82

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

Number | Rational numbers

Topic 1.13 Multiplying and dividing decimals Multiplying decimals by 10 0.3 × 10 = 3 is shown visually. If you were to add up 0.3 ten times, it would equal 3. 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 = 3

Learn Solve these multiplication problems.

0.2 × 10 =

0.6 × 10 =

0.9 × 10 =

0.1 × 10 =

0.5 × 10 =

1.2 × 10 =

2.5 × 10 =

3.3 × 10 =

5.8 × 10 =

Write the missing decimal in each equation.

× 10 = 7

D R

AF T

× 10 = 35

× 10 = 12

× 10 = 8

× 10 = 65

× 10 = 87

× 10 = 3

× 10 = 49

× 10 = 2

Write the missing number in each equation.

× 10 = 2

0.6 ×

× 10 = 9

0.1 × 10 =

1.2 × 10 =

5.4 × 10 =

× 10 = 25

3.3 ×

× 10 = 58

9.4 × 10 =

× 10 = 924

63.8 × 10 =

= 33

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

Explore 1 Match up the division equation with its answer. Then multiply all of the

answers by 10.

25 ÷ 10 68 ÷ 10 40 ÷ 10 5 ÷ 10 9 ÷ 10 99 ÷ 10 13 ÷ 10 81 ÷ 10

0.5 1.3 2.5 4.0 6.8 8.1 9.9 0.9

Write these division equations as a fraction, and then a decimal. The first one has been done for you.

9 ÷ 10 =

7 ÷ 10 =

5 ÷ 10 =

If you divide 10 by 10 will you get a decimal? Explain.

We can use a number line to visualise tenths.

4 ÷ 10 =

AF T

= 0.9.

D R

9 10

× 10

3 ÷ 10 =

2 ÷ 10 =

Which decimal is the arrow pointing to?

Draw another arrow at 0.2.

Draw your own number line and show where 2.3 is on it.

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

Deepen 1

Write the equation for each of these word problems and then solve. The first one has been started for you. Word problem

Equation

a A pencil lead is 0.9 mm thick. If you stack 10 pencil leads on top of each other, how thick is the stack in mm?

0.9 × 10 =

Solution

b O ver 10 days, Sam runs a total of 23 kilometres. If he ran the same distance each day, how far did he run per day?

AF T

c A bucket holds 4.5 litres of water. A large tank holds 10 times as much as the bucket. How many litres does the tank hold?

D R

d A bag of apples costs $1.50 per kilogram. If you buy 10 kilograms, how much will you spend in total? e If a car consumes 2.1 litres of fuel for every 10 kilometres, how much fuel does it consume over a distance of 100 kilometres? f A household uses the same amount of water each day. They use 42 litres over 10 days. How much water do they use each day?

g S mall lollies cost $0.20 each. You have $2.50 in your pocket. Do you have enough money to buy 10 candies? Show why or why not. h A child has 25 chocolate bars and wants to share them equally among 10 friends. How many chocolate bars will each friend receive?

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

Number | Financial mathematics

Topic 1.14 Using money Coins In New Zealand we have 5 different coins.

You can make 50c in different ways.

Could you make $1.70 in different ways?

Learn

Draw any coins to show 3 ways to make these amounts.

70c

$1.40

$2.30

D R

AF T

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

Draw 3 coins to make these amounts.

30c

90c

$1.20

$2.10

Show the smallest number of coins you could use to buy these items.

$2.5 0

60c

AF T

$1.2 0

c $5.1 0

D R

$1.9 0

80c

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

Notes In New Zealand we have 5 notes.

Explore 1

Match the cash to the correct cash register. $ 72.80

D R

AF T

$ 58.30

$ 85.20

$ 34.90

$ 12.40

$ 95.10

$ 25.70

$ 47.70

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

How much change would you get from $10?

ice ch r P a .0 0 $3

.0 0 $2

ice ch r P a e

ice ch r P a .0 0 $4

D R

AF T

.0 0 $1

ice ch r P ea

How much change would you get from the above questions if you had paid $20? a

How much change would you get?

b $1.00

$3.00 c

$2.00 $2.00

$5.00 Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

How much change do these people receive? b Angela buys 5 pairs of scissors at $4 each and 3 packs of pens at $2 each. She pays with $30 cash.

c At the movies, a family buys 4 adult tickets at $10 each and 2 child tickets for $6 each. They pay with a $100 note.

d Sina’s restaurant meal totals $47. She gives a $10 tip. Sina pays $60 cash.

D R

AF T

a X avier buys 2 books priced at $15 each and a magazine for $5. He pays with a $50 note.

Three friends use money from their piggy banks to buy each other Christmas presents. Work out how much money they each have left after they have done their shopping. Name Kauri

Mele

Nella

Piggy bank amount

Spent

$57

$31

$88

$64

$79

$58

Who has the most money left after shopping?

Who has the least money left after shopping?

Amount left

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

Algebra | Equations and relationships

Topic 2.1 Number sentences Balancing number sentences

2 × 10

The = sign shows that both sides are the same. A balance helps us see that both sides must be equal.

10 + 10

5 × 10

25 + 25

Learn 1

Complete the number sentences.

3×6

6×3

D R

AF T

Use +, −, × or ÷ to complete the equations.

4 = 24

2=9

7 = 70

9 = 45

5=9

6=4

8=1

0=0

6 = 14

7 = 18

7=4

12 = 36

8 = 26

9 = 10

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

Make the equations balance.

33 – 3

= 15 +

3×5

÷5

10 + 2

2×

4×5

2×

If you added 3 to both sides of the equations in question 3, what would happen to the balance? Explain why.

Sometimes two sides are not equal, so we use inequality symbols. Fill in the missing symbols (less than < or greater than >).

15 + 10

17 + 15

50 – 5

75 – 10

5 + 50

90 + 20

105

300 – 50

200 + 70

80 – 25

12 + 9

26 – 4

28 + 14

55 – 12

400 – 80

250 + 70

94 – 20

60 + 15

19 + 18

45 – 9

D R

AF T

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

Explore Analyse the equations and 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

True False

60 + 60 = 10 × 12 True False

43 – 29 = 60 ÷ 4

True False

Fill in the gaps to complete the number sentences.

+ 15 = 30

48 –

= 44

– 23 = 61

35 +

= 89

× 8 = 48

7×

= 28

AF T

÷ 5 = 11

78 – 46 = 19 +

45 ÷

26 + 34 = 100 –

147 –

48 + 12 = 5 ×

72 ÷ 8 =

−1

6 × 7 = 50 −

90 − 30 =

÷2

Analyse the equations and circle true or false.

32 + 34 < 13 × 4

True False

45 − 12 > 5 × 6

True False

8 × 7 < 60 − 2

True False

72 ÷ 8 > 5 + 3

True False

9 × 6 > 100 − 40

True False

81 ÷ 9 < 3 × 4

True False

28 + 39 < 17 × 4

True False

96 ÷ 8 > 10 + 4 + 2

True False

= 96 + 15

D R

+ 83 = 180 – 32

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

4 a

Check if each number sentence is correct by working out the answer. Then tick true or false. Number sentence

Working out

True

False

Working out

True

False

True

False

234 + 167 = 401 356 + 482 = 738 5,432 + 326 = 5,758 6,789 + 2,154 = 8,923

Number sentence

AF T

152 – 38 = 116 875 – 243 = 632 8,725 – 146 = 8,589

D R

7,621 – 2,385 = 5,236

Number sentence

Working out

7 × 12 = 86 128 ÷ 8 = 12 88 ÷ 11 = 8 6 × 14 = 78

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

Writing a number sentence A number sentence is a maths sentence that helps us solve a word problem. It uses numbers and symbols to show what we need to do. Example: Raukawa wants to buy 150 soccer balls for a sports event. One box can fit 30 soccer balls. How many boxes does he need to purchase? 30 ×

= 150

150 ÷ 30 =

Deepen Write a number sentence for each problem, and then solve it.

Nadine wants 100 balloons at her birthday party. Each pack contains 25 balloons. How many packs of balloons does she need to buy?

Aroha bought 4 cartons of eggs. Each carton contains 12 eggs. How many eggs does she have in total?

William read 42 pages of his book on Monday, 14 on Tuesday and 28 on Wednesday. How many pages did he read in total?

The school is trying to raise $1,200 for new playground equipment. So far, they have raised $850. How much more money do they need to raise?

When this number is added to 78, the answer is the same as 200 minus 32. What is the number?

There were 35 boys and 54 girls at a concert. 40 people had seats, the rest had to stand. How many people had to stand?

D R

AF T

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

Algebra | Equations and relationships

Topic 2.2 Growing patterns Recognising and continuing patterns +3

Rule: Add 3 2

Follow the rule to finish the pattern.

Rule: Add 5

D R

Rule: Add 9 3

Rule: Add 12 3

Rule: Multiply by 2 2

Rule: Subtract 20 97

Rule: Subtract 4 65

Rule: Divide by 2 80

Rule: Subtract 10 94

Rule: Subtract 3 54

Rule: Add 10 24

Rule: Add 6 6

AF T

Find the rule by looking at the size of each “jump”.

Learn

−4

Rule: Subtract 4

Rule: Multiply by 3 1

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

Write a rule for the number patterns.

Rule:

3 13 23 33 43 53 63 73 c

90 85 80 75 70 65 60 55 d

Rule:

4 11 18 25 32 39 46 53 e

Rule: 1

125

78 j

120

27 81 243 729

Out

Rule:

AF T

240

Rule:

625

Rule:

46 h

Rule:

10 100 1,000 10,000

Rule:

In Out

D R

Fill in the missing numbers and write the rule. Out

b Out

Rule:

c Out

Out

Rule:

d Out

Out

Rule:

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

Explore

The numbers in addition patterns get bigger and the numbers in subtraction patterns get smaller.

1 a

Complete the diagram and number pattern.

1 b

What is the rule?

18 b

What is the rule?

AF T

Complete the diagram and number pattern.

D R

3 a

Make your own addition patterns.

Make your own subtraction patterns.

Rule:

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

Continue the pattern.

What is the rule?

This type of pattern is called a repeating pattern.

Complete the pattern.

What is the rule?

Circle the error.

How could you fix the pattern?

Circle the error.

How could you fix the pattern?

AF T

D R

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

Deepen 1

These patterns have 2-step rules. Rule: Add 4, subtract 2 0

Rule: Subtract 5, add 3

Write the 2-step rules. a

0 c

Rule: 5

Rule: 20

D R

AF T

20 d

Rule:

Follow the rule to finish the pattern.

Rule: Add 1, add 3 1

Rule: Subtract 2, subtract 3 56

Make your own 2-step pattern. Rule:

100

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

Measurement | Measuring

Topic 3.1 Estimation and measuring Body parts and everyday experiences can help with estimating!

Learn 1

Create your own personal measures for the lengths in the table. For example, 30 cm might be equal to two of your handspans. 1 m might be equal to 6 of your foot lengths. Length

Personal measure

2 handspans = 30 cm

30 cm 50 cm

30 cm

Use your personal measures to help you find classroom items that match the lengths in the table.

Record the items in the table.

Now measure the items and record the actual lengths.

D R

AF T

Length

Item

Actual length

10 cm 50 cm 1m 1 m 50 cm

Chloe estimates it takes 15 minutes to walk to school. Anna lives twice as far from school. Estimate how long it takes Anna to walk to school.

Write a possible temperature if you would describe the weather as:

cool

warm and comfortable

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

hot. 101

Length Shorter lengths are measured in centimetres (cm). Longer lengths are measured in metres (m). There are 100 cm in 1 m.

The length of the eraser is 4 cm. 0 CM

100

The length of the guitar is 100 cm or 1 m.

Use a ruler to find the lengths of these items.

cm cm

AF T

b d

D R

Would you use cm or m to measure the length of:

the classroom

this book

your house

a chocolate bar?

Write the lengths of the objects shown. a

0 CM

102

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

Temperature We measure temperature in degrees Celsius.

Explore Read the temperatures on the thermometers.

a 100º

100º

100º 90º

80º

70º

60º

°C

50º 40º

60º

°C

50º

40º

30º

20º

10º

0º

Shade the temperatures shown on the thermometers.

a 50

b 50

20 10

15°C

50 40

D R

50°C

90º

AF T

30 20

Which temperature in questions 1 and 2 is the highest?

Which is the lowest?

What is the difference between the highest and lowest temperatures?

Which 2 temperatures have a difference of exactly 20°C?

Which 2 temperatures have the smallest difference?

31°C

On Monday, the temperature in Wellington was 18°C degrees Celsius. On Tuesday, it got colder by 5 degrees. Then, on Wednesday, it got warmer by 8 degrees.

What was the temperature on Tuesday?

What was the temperature on Wednesday?

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

103

Mass

The mass of heavier objects is measured in kilograms (kg).

The mass of lighter objects is measured in grams (g).

15 kilograms or 15 kg

15 grams or 15 g

There are 1,000 g in 1 kg. Remember to use units in your answers.

Explore 1

Write the item letters in order from lightest to heaviest.

a 110 g

410 g

b 2 kg

4 kg

32 kg

250 g

F heaviest

215 kg

lightest

104

40 g

D R

lightest

11 g

AF T

125 g

1 kg

65 kg

F heaviest

Look at the mass of all the items in question 1.

Which item is the heaviest?

Which item is the lightest?

How much heavier is the boy than the cat?

What is the total mass of the banana and butter? Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Read the scales and record the mass.

0 500 kg 1

500

0 500 kg 1

500

500 3 500

Mass:

500 g

AF T

200 g

Mass:

D R

Mass: 4

Look at the scales in question 3. What is the mass of:

1 orange

1 strawberry

How much heavier are:

the pineapples than the oranges

the bananas than the strawberries

the oranges than the bananas

the pineapples than the bananas?

g g

1 pineapple

1 banana?

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

kg g

Which units should you use?

105

Capacity Millilitres (mL) and litres (L) are two units of capacity.

375 mL

A soft drink can A large paint tin holds holds less than 1 L. more than 1 L.

There are 1,000 mL in 1 L.

How is capacity different from volume?

Explore 1

A B

200 mL

4L 1L

E F 1,250 mL

1,000 mL

500 mL

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

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

Write the letters of the items that hold exactly 1 L.

Which item has the biggest capacity?

Which item has the smallest capacity?

D R

AF T

C 50 mL

250 mL 500 mL

750 mL Detergent

106

350 mL

180 mL

600 mL

Which 2 items together have a capacity of 1 L?

Which 2 items together have a capacity of more than 1 L?

What is the capacity of the sunscreen and the yoghurt?

What is the capacity of the detergent and the milk? Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

Deepen 1

Fill in the missing values.

0.5 m =

3m=

g 2

cm cm

cm = 2.6 m

m = 100 cm

1.3 m =

m = 450 cm

0.8 m =

cm = 0.3 m

0.75 cm =

Write the mass letters in order from lightest to heaviest. There are 1,000 g in 1 kg. 1,200 g

1 kg

960 g

4 kg

2 kg 100 g

F heaviest

AF T

lightest

Write the capacity of each jug, in both mL and L. b

15 ml

400 ml

1000 ml 900 ml 800 ml 700 ml 600 ml 500 ml 400 ml 300 ml 200 ml 100 ml 0 ml

10 ml

5 ml

0 ml

mL or

D R

mL or

300 ml 200 ml 100 ml 0 ml

f 1000 ml 900 ml 800 ml 700 ml 600 ml 500 ml 400 ml 300 ml 200 ml 100 ml 0 ml

1000 ml 900 ml 800 ml 700 ml 600 ml 500 ml 400 ml 300 ml 200 ml 100 ml 0 ml

mL or

1000 ml 900 ml 800 ml 700 ml 600 ml 500 ml 400 ml 300 ml 200 ml 100 ml 0 ml

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

mL or

L 107

Read through each problem, highlighting or circling the important information. Circle which problem type it is. Show your calculations and answer in the final column. Word problem

108

Problem type Length Mass Capacity Temperature

Apples A bag of apples weighs 1.5 kilograms. If each apple weighs 150 grams, how many apples are in the bag?

Length Mass Capacity Temperature

Hot chocolate Meri made hot chocolate that is initially 85°C. After it sits for 15 minutes, it cools down to 60°C. By how many degrees Celsius did it cool down?

Length Mass Capacity Temperature

AF T

Baking cookies Ailine is baking cookies and needs 250 grams of flour for each batch. If she wants to make 4 batches, how many grams of flour does she need in total?

Calculations

D R

Water bottles Will has a water bottle that holds 750 millilitres. If he fills it up 5 times, how many litres of water has he used?

Length Mass Capacity Temperature

Create your own word problem:

Length Mass Capacity Temperature

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

Measurement | Measuring

Topic 3.2 Perimeter Perimeter is the distance around a 2D shape. It can be worked out by adding up the lengths of each side of the shape. For example, this square has four sides, and each side is 2 cm.

2 cm 2 cm

2 cm

2 cm + 2 cm + 2 cm + 2 cm = 8 cm

2 cm

The perimeter of the square is 8 cm.

Learn 1

3 cm

D R

AF T

Calculate the perimeter of the shapes. Remember to show your working in the boxes.

Perimeter = c

3 cm

Perimeter = d

5c m

3 cm

4 cm 3 cm

Perimeter = e

Perimeter =

2 cm

6 cm

7 cm 3 cm 5 cm

Perimeter =

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

109

Explore 1

Use a ruler to measure the side length of these shapes and add them together to find the perimeter of each shape.

Perimeter =

AF T

Side lengths:

D R

Side lengths:

When a shape is regular (each side is the same length), you can just measure one side length and multiply by the number of sides. Use this method to work out the perimeter of the shapes. Perimeter = Shape name: Number of sides: Length of one side:

Perimeter = Shape name: Number of sides: Length of one side:

110

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

Estimate which shape from question 4 will have the greatest perimeter.

Find the perimeter of each shape in cm.

7 cm 3 cm

5 cm

3 cm

5 cm

7 cm

cm c

4 cm

2 cm 1 cm

3 cm

1 cm

AF T

2 cm

3 cm

1 cm

1 cm 2 cm

D R

4 cm

2 cm

There are 10 mm in 1 cm.

Find the perimeter of each shape in mm. 1 cm

2 cm

8 cm

2 cm

1 cm

2 cm

3 cm 1 cm

1 cm

4 cm

3 cm

9 cm

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

111

Deepen 1 Perimeters can also be large. The examples have perimeters in metres. Calculate the perimeter of each and then add your own real-life perimeter example. Place

Dimensions

Calculations

Swimming pool Length = 50 m Width = 25 m Perimeter = Garden bed

AF T

Length = 3 m Width = 2 m

D R

Netball court

Perimeter =

Length = 30 m Width = 15 m Perimeter =

Playground Length = 15 m Width = 15 m Perimeter = Create your own problem here:

Perimeter =

112

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

On the grid paper create a shape with a perimeter of:

10 cm

20 cm

18 cm

8 cm.

22 cm

State the perimeter beside each shape and ask a friend to check your work. Two example shapes with perimeters of 12 cm and 16 cm have been drawn to show you how to shade and label your shapes. Perimeter = 16 cm

D R

AF T

Perimeter = 12 cm

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

113

Measurement | Measuring

Topic 3.3 Area Area

1 cm

A square centimetre is 1 cm wide and 1 cm high. We use square centimetres to measure area.

1 cm

The abbreviation of square centimetres is cm2. Area = 10 cm2

Learn 1

What does area mean?

Record the area of each shape.

cm2

D R

AF T

cm2

114

cm2

Write the letter of the shape in question 1 that has:

the largest area

Which 2 shapes in question 1 have the same area?

the smallest area.

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

Area measures the space a shape takes up, in square units like square centimetres (cm²). Some irregular shapes don’t fit neatly into whole squares and might cover part of a square, like half a square (0.5 cm²). We measure their area by adding the whole and half squares they cover.

Find the area of the following irregular shapes.

B C

AF T

Shape A Area =

Area = 5

b cm2

Shape D

Shape B Area =

e cm2

D R

c cm2

Shape E Area =

Area = f

cm2

Shape C cm2

Shape F Area =

cm2

In the grid provided, draw your own shape (made up of squares and half squares) and calculate its area. Area =

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

115

Explore 1

The shapes have square centimeters drawn on them. Write the areas of the shapes. 3 cm

6 cm 2 cm

3 cm ×

Area = c

Area =

cm2 d

3 cm

cm2

7 cm 2 cm

AF T

7 cm

Area =

cm2

D R

Area =

cm2

Label the side lengths of these rectangles and then write their area. e.g. Area = 6 cm2

Area =

cm2

Area =

cm2

Area =

cm2

3 cm 2 cm

116

Area =

cm2

Area =

cm2

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

Use the cm2 grid paper to draw and label the side lengths of:

a blue square with an area of 9 cm2

a red rectangle with an area of 10 cm2

2 different green rectangles, each with an area of 12 cm2

a yellow square with an area of 4 cm2.

What is the total area of the shapes in question 3? Area =

cm2

D R

AF T

5 a

Estimate the area of this shape:

Find the area of the blue square. × Area =

= cm2

Find the area of the red rectangle. × Area =

cm2

= cm2

What is the total area? ×

cm2

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

117

Deepen 1

Square metres are used for measuring large areas. A square metre (m2) is 1 m by 1 m (or 100 cm by 100 cm)

100 cm or 1 m

Plan of my backyard

10 m 100 cm or 1 m

1 m2 cubby

Record the area of: a

the cubby m2

path

the picnic table m2

the path. m2

D R

AF T

picnic table

pool

How much bigger is the cubby than the picnic table?

Solve each word problem by circling important information, drawing and labelling a diagram and calculating the area.

Mātua Rauru wants to plant a flower garden that is 4 metres long and 3 metres wide. What is the area of her garden in square metres?

Area = 118

the pool

The playground has a grassy area that is shaped like a rectangle. It is 8 metres long and 2 metres wide. What is the area of the grassy area in square metres?

Area =

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

Measurement | Measuring

Topic 3.4 Volume Volume 1 cm

1 cm 1 cm

This centicube is 1 cm high, 1 cm wide and 1 cm long. It is also called a cubic centimetre or 1 cm3. Volume: Space inside a shape Capacity: How much it can hold

This 3D shape has a volume of 8 cubic centimetres or 8 cm3.

Learn Write the volumes of these 3D shapes. b

AF T

D R

cubic centimetres or c

cm3 or cm3 d

cubic centimetres or e

cubic centimetres

cm3 or cm3 f

cubic centimetres or

cubic centimetres

cm3 or cm3

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

119

Find the volume of these 3D shapes by counting how many 1 cm³ cubes are in them. Writing the number of cubes in each “stack” is a good strategy. The first one has been done for you. b

Volume =

D R

Volume =

2 1

Volume =

AF T

2+3+3+2+1+1 = 12 cm3

120

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

Explore Use the layers to find the volumes of the following shapes. 1

] 1 layer ] 1 layer

How many layers?

How many cubic centimetres in each layer?

Total volume:

How many layers?

How many cubic centimetres

cm3

in each layer? Total volume:

cm3

AF T

D R

How many layers?

How many cubic centimetres in each layer?

Total volume:

cm3

4 a

Circle which colour shape from questions 1 to 3 has the biggest volume? Blue

Pink

Green

Circle which colour shapes from questions 1 to 3 have the same volume? Blue

Pink

How much greater is the volume of the green shape than the pink shape?

If one more layer was added to the green shape, what would the total volume be?

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

Green

121

These rectangular prisms (cuboids) are made up of 1 cm3 cubes. Label each cuboid with its length, width and height. Use this information to work out the volume of each cuboid. Hint: Work out how many cubes are in one layer and then multiply that by the number of layers.

Rectangular prisms (cuboids)

Length × Width × Height

Volume = b

cm³ ×

Volume = c

D R

AF T

× Volume = ×

× Volume =

122

= cm³

Volume = f

= cm³

Volume = ×

= cm³

A teacher has a cuboid box that measures 10 cm in length, 5 cm in width and 4 cm in height. She wants to fill this box with centicubes (1 cm³ cubes).

Draw the cuboid and label its length, width and height.

Calculate the volume of the cuboid in 1 cm³ cubes. How many centicubes can fit inside the box?

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

Deepen 1

Use centicubes to make a rectangular prism with a volume of 12 cm3.

Draw your shape.

D R

AF T

Draw your shape.

Use centicubes to make a rectangular prism with a volume of 10 cm3.

Create the following shape out of centicubes. What is its volume?

Volume =

3 cm

cm³

2 cm 4 cm

Use centicubes to make your own rectangular prism. Draw it and calculate its volume. Shape

Volume

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

123

Measurement | Measuring

Topic 3.5 Angles

An angle is the amount of turn between 2 arms. A square corner angle is known as a right angle. A right angle is a quarter of a full turn. A full turn (revolution) = 360°

A straight angle = 180°

90°

Rectangles and squares have four right angles!

Learn

Tick whether each angle is smaller, larger or equal to a right angle. Smaller

Smaller

Larger

Equal

D R

AF T

Smaller Larger

Smaller 90°

Equal 2

124

Larger Equal

Find and draw 3 things in your classroom that have a right angle.

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

Explore 1

Which is closest to each angle: 90 (right angle), 180 (straight angle) or 360 (full turn) degrees? Write 90, 180 or 360 in the answer box. a b c

degrees

d e f

AF T

degrees

Look at the angles marked between the clock hands.

A a

degrees

D R

degrees

At what times do the hands make a right angle?

Which clock shows the closest angle to 180 degrees? What is the time shown?

Which clock shows the closest angle to 360 degrees? What is the time shown?

What would the angle look like if it were 6 o’clock?

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

125

Deepen 1

Circle whether each angle is smaller, larger or equal to a right angle. a

Smaller Smaller

Smaller

Larger Larger

Larger

Equal Equal Circle the shapes that have 90 degree angles. b

AF T

D R

Equal

Find and draw 4 angles in the classroom.

b Use less than (<) or greater than (>) or equal to (=) symbols to compare each angle to 90°, 180° and 360° angles. Angle 1

Angle 2 90°

90° 180°

180°

360°

Angle 3

Angle 4 90°

90°

180°

180° 360° 126

360°

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

Measurement | Measuring

Topic 3.6 Time

The marks between each number on a clock represent 1 minute.

There are 60 minutes in 1 hour. Each of the numbers on the clock is 5 minutes apart. You can count by 5s to tell the time more quickly.

25 mins

The minute hand is pointing to the thirty-fifth minute so the time is 3:35 or 25 minutes to 4. 35 mins

Learn 1

Write the analogue and digital times. b

D R

AF T

past :

to :

past :

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

127

Draw minute hands to show the times.

1 to 5 4 d

7:22 e

12:15

7 past 5 f

10 to 12

12:43

Draw hour hands to show the times. b

25 past 2

25 to 9

4:40

Draw the hour and minute hands to show the times.

1 past 11 2 d

128

D R

AF T

1 to 10 4

17 past 7 e

25 past 9 f

10 to 2

28 past 11

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

How many minutes until:

20 past 2

b 10 to 3

1 past 3 4

d 3:00?

8:00

1 past 9 4

5 to 8?

What time is shown on the clock?

How long until 1 past 8? 4

How long until 9 o’clock?

What time is shown on the clock?

How long until 5 to 11?

How long until 11:30?

What time is shown on the clock?

How long until 1 past 12? 2

How long until 1 o’clock?

How long until:

D R

AF T

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129

Going to a friend’s house

Eating a cupcake

Lunchtime at school

Building a house

Duration The things we do take time.

Explore 1

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

Shortest time

Longest time

D R

minute, second, day, hour

AF T

Write these units of time from shortest to longest.

Think about these activities.

2, 3, 4, 4, 5, 5, 1, 2, 1, 3,1, 4,2, 5,3, 7, 8, 9, 9, 1010 6, 7, 6, 8,6, 9,7, 108,

Growing long hair Growing long Growing long hairhair

Counting 10 Counting toto10 Counting to 10

Which would take a few seconds to do?

Which would take a few minutes to do?

Which would take a few months to do?

Draw or write something you do that matches each time.

It takes about 1 hour. 130

Eating one pizza Eating pizza Eating oneone pizza

It takes about 1 minute.

It takes 10 minutes.

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

Seconds, minutes and hours To change minutes to seconds, multiply by 60.

To change hours to minutes, multiply by 60.

5 minutes = 5 × 60 = 300 seconds

10 hours = 10 × 60 = 600 minutes

Match up the equivalent durations of time 1 minute

60 minutes

1 hour

52 weeks

1 day

365 days

1 week

7 days

Fill in the gaps.

2 minutes =

3 hours =

1 1 minutes = 2

48 hours =

49 days =

24 hours

D R

1 year 1 year

How would you change minutes to hours?

AF T

60 seconds

6 minutes =

5 hours =

2 1 hours = 2

days

3 days =

hours

weeks

5 weeks =

days

seconds minutes seconds

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

seconds minutes minutes

131

The race times for 6 students from Year 4B were recorded.

Complete the times in the table.

Rank the students from fastest (1) to slowest (6). Name

Time in seconds

Wiremu

75 seconds

Time in minutes and seconds

Jemima

2 mins 20 seconds

Jessica

1 min 40 seconds 90 seconds

Alby

120 seconds

AF T

Mario

Rank

1 min 10 seconds

D R

Hana

Circle the longer duration in each pair.

3 weeks or 27 days

700 days or 2 years

3 days or 70 hours 3 1 hours or 200 minutes 2

97 minutes or 2 hours 660 minutes or 10 1 hours 2 10 years or 4,000 days

1 hour or 400 seconds

132

How many:

days in 5 weeks

minutes in 5 hours

seconds in 5 minutes

months in 5 years

days in 2 years

hours in 2 days

weeks in 1 year

weeks in 2 years?

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

Deepen 1

Use hours or minutes to describe the duration of each activity in the table. In the last row, write the start and finish time as well as the duration. Activity

Start

Finish

Duration

Walking a dog

minutes Dinner party

6 : 15

9 : 00

D R

Your school lunchtime

AF T

Flight from Auckland to Christchurch

Rangi and his friends are planning a visit to the Ngāruawāhia River. They will leave their house at 10:15 am to start their adventure. The drive to the river takes 45 minutes. Once they arrive, they want to spend 1 hour exploring and playing by the water. After their exploration, they plan to have a picnic lunch that will take 30 minutes.

What time will they finish their picnic lunch?

How long will they spend from the time they leave until they finish their picnic?

James and his family are planning a visit to Te Papa Museum in Wellington. They arrive at the museum at 11:15 am after a drive that takes 1 hour and 30 minutes. They spend 2 hours exploring the exhibits before having lunch at a nearby café for 45 minutes.

What time did they leave home?

What time will they finish their lunch?

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

133

Draw the hands on these clocks to show the time.

3:40

11:55

07:05

02:20

a Willow starts her homework at 3:30 pm. If it takes her 1 hour and 15 minutes to finish, what time will she complete her homework?

b Tua starts baking a cake at 2:45 pm. If the baking time is 45 minutes, and he needs an additional 30 minutes to cool the cake, at what time will it be ready to eat?

AF T

c Eponi’s netball practice ends at 6:30 pm. It was a 1 hour and 30 minutes practice. What time did practice start?

134

D R

Use the movie schedule to answer the questions. Movie title

Showtime 1 Showtime 2

Showtime 3

Duration

Adventure Zone

10:00 am

1:00 pm

4:00 pm

1 hour 30 min

Bella’s Kingdom

11:30 am

2:30 pm

5:30 pm

1 hour 45 min

Dino’s Journey

12:00 pm

3:00 pm

6:00 pm

1 hour

Space Mission

11:00 am

2:00 pm

5:00 pm

2 hours

Which movie has the longest duration?

If you go to the 11:30 am viewing of Bella’s Kingdom, what time will the movie finish?

If you arrive at the theatre at 2:45 pm, what are the next two movies that are showing?

Your movie finished at 5:30 pm, which movie did you see?

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

Geometry | Shapes

Topic 4.1 2D shapes Polygons Polygons are flat shapes that have straight sides. They are closed shapes, which means all the sides join up and there are no gaps.

Is a circle a polygon?

Learn

Match each polygon to its name and number of sides. 9 sides

Hexagon

4 even sides

Dodecagon Pentagon

AF T

Triangle

D R

12 sides 6 sides

Octagon

3 sides

Rectangle

8 sides

Nonagon

5 sides

Square

10 sides

Decagon

7 sides

Heptagon

4 sides

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

135

Complete the polygons crossword. 1

2 3

5 6

7 8

136

D R

AF T

A polygon with 11 sides in called a hendecagon!

Across

Down

I have 9 sides and 9 corners.

A stop sign is shaped like me.

Most doors are shaped like me.

I am a polygon with 12 sides.

I am a polygon with 11 sides.

10 I have 4 equal sides and 4 equal corners.

I am a polygon with 3 sides and 3 corners.

I am a polygon with 10 sides.

11 I am a polygon with 7 sides.

My name starts with “penta”, meaning five.

Honeycomb cells are shaped like me.

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

Lines of symmetry A line of symmetry is a line you can draw through a shape to divide the shape into two halves that are mirror images of each other.

Semicircle

Explore 1

Draw 1 line of symmetry for each shape. b

Draw the lines of symmetry for each shape.

D R

AF T

Which shape in question 2 has exactly 3 lines of symmetry?

Which shapes have exactly 4 lines of symmetry?

c Which shape from question 1 has an infinite (endless) number of lines of symmetry? Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

137

Draw pictures with horizontal and vertical line symmetry.

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

AF T

D R

Draw lines of symmetry on each shape. a

138

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

Describing polygons A regular polygon has equal sides and equal angles. An irregular polygon is a polygon which is not regular.

Regular polygon Equal sides are labelled with the same number of markings.

Deepen Complete the table. Sides (edges)

Angles (vertices)

Polygon type

Square

regular irregular

Picture

AF T

Shape

Octagon

regular irregular

D R

Irregular polygon

regular irregular

Hexagon

regular irregular

Draw the shapes.

regular pentagon

irregular hexagon

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

139

Match the quadrilaterals with their descriptions. • Regular shape • 4 Sides are the same length • 4 Angles are the same size

Rectangle

• Irregular shape • 1 Pair of parallel sides

Parallelogram

• Irregular shape • 2 Pairs of parallel sides Square

AF T

• Irregular shape • 4 Right angles • 2 Pairs of parallel sides

Complete the table. Image

140

D R

Trapezium

Shape name

Edges

Angles

Vertices

What do you notice about the number of edges, angles and vertices in each shape?

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

Complete the descriptions and name each shape.

a Regular:

Yes

Parallel lines:

Yes

Edges

Vertices

Angles

Regular:

Yes

Parallel lines:

Yes

Edges

Vertices

Angles

Regular:

Yes

Parallel lines:

Yes

Edges

Vertices

Angles

Regular:

Yes

Parallel lines:

Yes

Edges

Vertices

Angles

Regular:

Yes

Parallel lines:

Yes

Vertices

Angles

Name: b

Name:

D R

AF T

Name: e

Name:

Edges

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

141

Write 3 points to describe each shape, and then name it. Remember you can include descriptors such as number of edges, vertices, angle types, regular or irregular, lines of symmetry, etc.

Name: b

Name:

D R

AF T

Name: e

Name:

142

Do any of the shapes have a right angle?

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

Geometry | Spatial reasoning

Topic 4.2 3D shapes

Prism

Pyramid

Cone

• Perfectly round 3D shape

Circle all the pyramids.

D R

• Polygon as a base • All other faces are triangles

Prism

AF T

Match the 3D shapes with their descriptions.

Cylinder

Sphere

You can describe 3D shapes by their faces, edges and corners (vertices).

Learn 1

Cylinder

Sphere

• Shape with a circular base and a point at the tip

Pyramid

Cone

• 2 parallel bases of the same shape • All other faces are rectangles

• Shape with 2 circular ends and 1 curved face

What is the base shape of this prism?

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

143

On the following shapes, colour one face yellow, edges blue and vertices red. Then name the shape.

Write 1 similarity and 1 difference between these shapes.

144

Similarity:

D R

Similarity:

AF T

Difference:

Similarity:

Difference:

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

Make sure you circle 1 shape for every face of the 3D shapes.

Explore 1

Circle all the 2D shapes you need to make these 3D shapes.

AF T

D R

hen a 3D shape such as a box is flattened out, the 2D shape is called W a net.

Cube This is the net of a cube.

Match the nets to the 3D shape, and list the 2D shapes that make the net.

Rectangles, Squares

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

145

3 a

Draw a net for each of these 3D shapes. b

Triangular prism

Cube

Try drawing these shapes on your own. Then, list the 2D shapes that make up the 3D shape.

D R

AF T

a b

c d

146

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

Deepen 1

To see the front and side views, it helps to view the shape at eye level.

Label the top, front and side views of the shapes.

Shape 1

view

Shape 2

AF T

Complete the top views, front views and side views of the shapes.

D R

view

Top view

Front view

Side view

Front view Side view

Top view Front view

Side view

Top view Side view

Front view

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

147

Geometry | Spatial reasoning

Topic 4.3 Transformations Objects can be transformed by flipping, turning or sliding.

A reflection is when a shape is flipped over a line, creating a mirror image.

A rotation is when a shape is turned around a fixed point.

Can a shape go through two transformations?

A translation is when a shape is slid, without being turned or flipped.

Learn 1

Reflection, translation or rotation? b

Translation

D R

AF T

Rotation

Translation 2

Translation

Rotation

Translation

Reflection

Draw a line to match each image to the correct transformation.

Reflection 148

Reflection

Translation

Rotation

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

Draw a translation (slide) of each shape on the grids. b

Choose your own 2D shape to translate multiple times, to create a pattern. Colour it in to add impact.

D R

AF T

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

149

Remember - the mirror line doesn’t always touch the shape!

Explore 1

Draw the reflection of each shape on the grids. b

Label places where you can see examples of reflection or translation in this Fijian tapa cloth. Draw mirror lines and arrows to help explain. Discuss your findings with a classmate.

D R

AF T

150

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

Complete the table by drawing the shapes after they have been rotated. Rotate a 1 turn 2

Rotate a 1 turn to the right 4

Draw the next three shapes in these repeating patterns.

On the grid, select a simple shape that you can rotate around the central point to create a geometric design. For example, the design shown has been created by rotating a leaf.

D R

AF T

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

151

Deepen 1

Circle and label translations, rotations and reflections in these designs.

Translation, rotation or reflection? b

D R

AF T

152

Find 2 examples of reflection, translation or rotation patterns in your classroom.

Draw each pattern.

Label the transformations.

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

Geometry | Pathways

Topic 4.4 Grid references The tree is at B3.

The boy is at E1. The station is at E4.

To find what is at D2, put one finger on D and another on 2 and move them along the lines until they meet.

2 1 A

AF T

Learn 6

D R

5 4 3 2 1 A

What is at:

H4?

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

153

This is a bird’s-eye view of a park.

Write the grid reference for: 4

a tree

the picnic table

the slide

the ducks.

1 A

Write the letters in the correct squares.

AF T

D R

5 4 3 2 1 A

E in C4

K in E2

N in H4

L in D3

D in F4

W in B5

O in G3

E in I5

G in E4

Unscramble the message in question 3.

154

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

The four main compass directions are North, South, East and West. To remember their positions, some people use sayings such as W “Never Eat Soggy Weet-bix”.

N E S

Explore 1 Look at the map of a theme park. Use compass directions to describe the

position of different rides and stalls.

What would happen 1

Roller coaster

Hot dogs

Dodgem cars

Carousel

Pirate swing

Toilets

Start

AF T

Carousel

D R

if you did a 2 turn after leaving D1?

Ferris wheel

What is north of the toilets?

What is west of the Pirate swing?

What is east of the Dodgem cars?

There are two carousels. One is sitting at B3, what is the grid reference of the other carousel?

Give a grid reference for the following rides or stalls.

Hot dogs

If you enter at the “Start”, move 2 squares north, 2 squares east and 2

b Ferris wheel

c Pirate swing

squares north, where do you end up? Year 4 Student Workbook | Mathematics and Statistics for Aotearoa New Zealand (Second edition) Oxford University Press

155

The arrows show you which direction is north, south, east and west.

Hillcrest Showgrounds Through Road Animal nursery

Carnival rides

Main stage

Grand Arena

Car park

McKenzie Lane

Horse pavilion

Food stalls

Showbag hall Legend: Toilets First aid

ATM Information

Use the map to answer the following questions.

If you are in the horse pavilion, which direction would you have to walk to find an ATM?

In which direction is the Carnival rides from the Grand arena?

What is east of the food stalls?

If someone injured themselves on the Carnival rides, which direction should they go to get medical help?

If you were in the showbag hall, which directions could you go to get more information about the showground?

Write 2 questions about the map for your classmate to answer.

D R

AF T

Question 1: Question 2:

156

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

Deepen 1

In the empty grid, draw your school from a bird’s eye-view. It doesn’t have to be perfect–for example, just roughly place where buildings, playgrounds or courts are. Once you have completed your drawing, give grid references for the images in your map (e.g. Playground at B2). 7 6 5 4 3 2

D R

Grid references:

AF T

Describe your school map to a classmate. Listen to their description and draw it on the grid. Does it match your map? 7 6 5 4 3 2 1 A

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

J 157

Statistics | Developing knowledge from, visualisation of and interpretation of data

Topic 5.1 Dot plots Dot plots

A dot plot is a simple chart that shows data using dots! •

Each dot represents one person or one thing.

•

Dots stacked in a column show how many times something happens (this is called the frequency).

•

Number of siblings

It helps us see patterns quickly.

This example dot plot shows us that in the group surveyed, 5 people have no siblings, 1 person has 5 siblings and 4 people have 2 siblings.

Look at each dot plot and answer the questions.

Goals scored by team members

Number of track events entered per student

D R

158

AF T

Learn

What is the highest number of goals scored by a team member?

How many team members scored exactly 3 goals?

iii

What is the total number of goals scored by all team members combined?

Are there any team members who did not score any goals? If so, how many?

What is the most common number of events entered by students?

How many students entered only 1 track event?

iii

What is the total number of students who entered track events?

How many students entered 4 or more events?

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

How many students scored below 10?

iii

What is the total number of students who took the test?

What scores are the “middle group” of this data?

Number of days spent i at beach over summer

What is the most common number of days spent at the beach?

How many people spent 10 days at the beach?

iii

What is the total number of people surveyed?

How many spent fewer than 10 days at the beach?

Hours of sleep

What is the highest score achieved by a student?

AF T

What is the most common number of hours of sleep?

D R

Students scores on a test out of 20

How many peaks does this graph have?

iii

How many students were surveyed?

How many students sleep more than 9 hours?

Toroa class had a competition to see how many minutes they could skip without stopping.

Skipping minutes

The data: 3, 5, 5, 6, 7, 7, 7, 9. What is wrong with this dot plot? Explain.

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

159

Explore A community ran a “summer wellness program” aimed at encouraging outdoor activities. Participants were asked to report how many days they engaged in outdoor activities. The responses of the 50 participants were collected and are displayed in the table. 7

Frequency

Create a dot plot from this data. Remember to:

160

Title:

include a title

•

label the horizontal axis

•

write numbers on the axis

•

draw even circles and space them evenly.

D R

•

AF T

Number of days

Use information from your dot plot to answer the questions.

What is the most common number of days participants engaged in outdoor activities?

How many more participants spent 9 days compared to 13 days?

How many participants spent 10 days or more outdoors?

How many participants were outside fewer than 8 days?

What is the middle group of the data?

What is the total number of days spent outdoors by all participants combined?

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

45 students at Silver Oak school participated in a month-long reading challenge where they tracked the number of books they read. The results are shown. Number of books Frequency

0 3

1 5

2 7

3 10

4 8

5 6

6 4

7 2

Create a dot plot from this data. Remember to: include a title and label the horizontal axis

•

write numbers on the axis

•

draw even circles and space them evenly.

D R

Title:

AF T

•

Use information from your dot plot to answer the questions.

What is the most common number of books read by the students?

How many more students read 4 books compared to those who read 0 books?

What was the least common number of books read?

How many peaks does this graph have?

What is the total number of books read?

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

161

Deepen A group of daycare children were asked what their favourite fruit was. Their responses are shown (each piece of fruit represents one child’s response). Children’s responses

Sort the data into the table provided. Fruit Frequency Use the data from the table to create a dot plot. Key:

D R

Title:

AF T

162

= 2 children

Don’t forget about the key when answering questions!

Use the information from your dot plot to answer the questions.

Which fruit was the most popular among the children?

How many children chose apples as their favourite fruit?

How many children preferred pineapples compared to those who preferred bananas?

How many children were surveyed?

Which fruits were the least popular?

There were 20 children surveyed, why are there only 10 dots on the dot plot?

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

Statistics | Developing knowledge from, visualisation of and interpretation of data

Topic 5.2 Statistical investigations Collecting data When collecting data: •

have a clear question to ask

•

think about where you can find the data and how you can collect it

•

how you will record the data (e.g. tally charts, tables).

Learn 1

Match the data with the best source.

Observation

Survey

Number of cars driving past school

Students who know their times tables

Test results

Other sources (e.g. Census)

D R

AF T

Favourite foods in your class

Number of people who live in New Zealand

Circle the best question to ask if you want to find out the number of brothers and sisters your classmates have.

Do you have any brothers and sisters?

How many people are there in your family?

How many brothers and sisters do you have?

Ask 10 people the question you chose and record their answers in the tally chart. 0

4 or more

Number of brothers and sisters

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

163

Make a table with tally marks using the bar graph data.

Where I was born

Country

8 Number of people

7 6 5 4

Number of people

3 2 1 United Kingdom

New Zealand

China

India

Country

Nakeil checked the pencil cases of some of his friends and recorded how many pens they each had. 2, 0, 1, 2, 7, 3, 3, 2, 4, 1, 3, 2

Record the information in a table. 0

Tally

D R

Number of pens

AF T

Make a bar graph with the data.

Number of students

Number of pens

164

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

Data types Categorical Data

Numerical Data

Data that is sorted into groups or categories, not numbers. Examples: Favourite colour (red, blue), fruit (apple, banana) or day of the week (Monday, Tuesday).

Numerical data can be split into two groups: Discrete: Numbers you count (how many lollies you have) Continuous: Numbers you measure (how tall you are)

Explore 1

This table shows the favourite day of the week in 4S.

Day Number of students

Mon

Tues

Wed

Thurs

Fri

Sat

Sun

|||

||||

|||| |||| |

|||| ||

Is this data categorical or numerical? Explain why?

When this data is made into a bar graph, the bars will be touching.

D R

AF T

True False c

Use the data to complete the bar graph. Favourite day of the week in 4S 12 11 10 Number of students

9 8 7 6 5 4 3 2 1 0

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

Days of the week

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

165

Students in a class were each asked how long it takes them to get from home to school. This data is presented in the table.

40+ minutes | |

30-39 minutes | | | |

20-29 minutes

10-19 minutes

| | |

| | | |

| | |

0-9 minutes | | | |

| | | |

Create a dot plot of this data using the axes in the space. One student = one dot.

D R

AF T

10 9 8 7 6 5 4 3 2 1 0–9 minutes

10 - 19 minutes

20 - 29 minutes

30 – 39 minutes

40+ minutes

Look at the data in question 2.

How many students are in the class?

How many students take less than 10 minutes to get to school?

For continuous data, you sometimes need to round responses. If someone takes 19.5 minutes to get to school, which data interval would their response get recorded into?

166

In which data interval would you record someone who takes 9 minutes and 20 seconds to get to school?

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

Interpreting data visualisations Interpreting a graph means looking at it, figuring out what it is telling you, and explaining what you notice.

Explore 1

Favourite ice block flavours in 4P

What is the title of the graph?

What does the x-axis show?

What does the y-axis show?

Number of students

7 6 5 4 3 2 1 0

Lemon

Berry

Cola

Lime

AF T

Flavours

How many more students preferred Cola than Lemon?

What class were the students from?

D R

2 How I feel about school

10 9

Which response was most popular?

Least popular?

Is this data categorical or numerical?

Number of students

8 7 6 5 4 3 2 1 0

Boring

Fun

Challenging Interesting

Hard

Responses

How many students were surveyed?

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

167

Students in Kererū class were asked the survey question: What is your favourite afternoon snack?

Most popular afternoon snack in Kererū class 12 11 10

Number of students

9 8 7 6 5 4 3 2 1 0

Milkshake

Fruit

Sandwich

Biscuit

Popcorn

Other

Snacks

How many more students chose fruit than popcorn?

Did more students choose milkshakes or biscuits?

Tick the statement that best answers the survey question.

AF T

D R

Biscuits are Kererū class’s favourite afternoon snack. Kererū class likes a lot of different afternoon snacks. 4

Use the data in the dot plot to answer the questions. Number of pieces of fruit our group brought for brain break

a What is the most common number of pieces of fruit?

168

3 Pieces of fruit

Is this data categorical or numerical?

How many people were surveyed?

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

Deepen 1

Choose a categorical survey topic (such as favourite foods).

Write a question to ask your classmates. Topic:

Question:

Survey 12 students and record their responses.

Draw a graph of your results. Make sure you label the axes and give your graph a title.

Write 2 statements about your data.

D R

AF T

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

169

Choose a numerical survey topic (such as books read this month (discrete) or time to run 50m (continuous)).

Write a question to ask your classmates. Topic:

Question:

Survey 12 students and record their responses.

Draw a graph of your results. Make sure you label the axes and give your graph a title.

Write 2 statements about your data.

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170

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

Quick 10s / Tere Tekau Term 1 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

56 + 9 =

83 – 9 =

63 – 7 =

135 + 8 =

30 +

= 100

Smaller: 827 or 872?

32, 42, 52, 62,

12, 10, 8, 6,

Bigger: 254 or 245?

230, 330, 430,

600, 500, 400,

50 +

23 + 46 =

87, 77, 67, 57,

98 – 12 =

78 + 21 =

3, 6, 9, 12,

94 – 13 =

25, 20, 15, 10,

4, 8, 12, 16,

D 91 − 7 = 142 + 9 = Smaller: 765 or 756? 14, 12, 10, 8, 410, 510, 610, 60 +

= 100

93, 83, 73, 63, 49 + 28 = 86 − 14 =

AF T /10

/10

46 + 7 = 77 − 9 = 60 + = 100 11, 21, 31, 41, Bigger: 428 or 482? 720, 620, 520, 29 + 34 = 91 − 18 = 5, 10, 15, 20, 40, 38, 36, 34,

4, 8, 12, 16,

/10

74 + 8 = 59 − 6 = 40 + = 100 14, 24, 34, 44, Bigger: 312 or 319? 450, 350, 250, 38 + 27 = 85 − 14 = 2, 4, 6, 8, 30, 25, 20, 15,

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/10

= 100

82 − 5 = 165 + 8 = Smaller: 598 or 859? 12, 14, 16, 18, 620, 520, 420, 70 +

= 100

84, 94, 104, 114, 37 + 48 = 95 − 12 = 4, 8, 12, 16,

/10

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

/10 171

Quick 10s / Tere Tekau Term 1 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

64 + 9 = 65 − 8 = 72 + = 100 15, 25, 35, 45, Bigger: 651 or 618? 370, 470, 570 33 + 49 = 88 − 23 = 8, 16, 24, 32,

71 − 4 =

36, 33, 30, 27,

88 − 35 =

175 + 6 = Smaller: 482 or 428? 16, 20, 24, 28, 430, 530, 630, 35 +

= 100

74, 84, 94, 104,

AF T

45 + 38 =

I 58 + 6 = 72 − 9 = 37 + = 100 12, 22, 32, 42, Bigger: 704 or 740? 210, 310, 410, 41 + 36 = 95 − 29 = 6, 9, 12, 15, 45, 40, 35, 30,

2, 4, 6, 8,

J 62 − 3 = 182 + 9 = Smaller: 937 or 793? 20, 24, 28, 32, 640, 540, 440, 25 +

= 100

66, 76, 86, 96, 52 + 47 = 99 − 27 =

/10

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/10

53 + 6 = 84 − 8 = 65 + = 100 13, 23, 33, 43, Bigger: 549 or 593? 810, 710, 610, 47 + 28 = 76 − 34 = 4, 8, 12, 16, 42, 40, 38, 36,

10, 15, 20, 25,

/10 172

52 − 4 = 196 + 7 = Smaller: 864 or 846? 24, 28, 32, 36, 750, 650, 550, 57 +

= 100

58, 68, 78, 88, 63 + 38 = 94 − 18 = 27, 24, 21, 18,

/10

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

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

52 – 24 =

72 + 43 =

132 + 200 =

58 − 27 =

Smaller: 831 or 813?

46 +

44, 40, 36, 32,

108, 98, 88, 78,

843, 743, 643,

Bigger: 741 or 714?

24 +

325, 425, 525,

= 100

61, 71, 81, 91,

69 + 38 =

93 + 45 =

89 − 47 =

76 − 39 =

8, 16, 24, 32,

55, 60, 65, 70,

32, 28, 24, 20,

/10

AF T

/10

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67 + 21 = 64 − 18 = 87 + = 100 98, 88, 78, 68, Bigger: 892 or 882? 413, 513, 613, 87 + 24 = 92 − 44 = 16, 24, 32, 40, 24, 21, 18, 15,

49 − 23 =

75 + 39 =

56 − 29 =

82 + 37 =

264 − 100 =

109 + 300 =

Smaller: 927 or 792?

54 +

Smaller: 684 or 648?

40, 36, 32, 28,

118, 108, 98, 88,

48, 44, 40, 36,

912, 812, 712,

Bigger: 657 or 675?

831, 731, 631,

18 +

235, 335, 435,

22 +

54, 64, 74, 84,

58 + 47 =

62, 72, 82, 92,

101 − 46 =

96 − 52 =

114 − 30 =

197 + 53 =

6, 9, 12, 15,

183 + 47 =

65, 70, 75, 80,

30, 27, 24, 21,

/10

= 100

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

= 100

173

Quick 10s / Tere Tekau Term 2 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

45 + 78 =

86 – 43 = Round 57 to nearest 10 Round 123 to nearest 100 16, 24, 32, 40, Bigger: 345 or 364? + 67 = 100

AF T

359 + 80 = 564 – 200 =

D R

23, 33, 43, 53,

/10

37 + 52 = 103 − 48 = Round 49 to nearest 10 Round 631 to nearest 100 40, 32, 24, 16, Bigger: 578 or 587? + 23 = 100 298 + 70 = 812 − 300 = 92, 82, 72, 62,

/10

480, 380, 280, 42 + = 100 64 + 37 = 105 − 58 = Round 742 to nearest 100

79 + 28 = 144 − 72 = Round 47 to nearest 10 Round 915 to nearest 100

330, 430, 530, 37 + = 100 71 + 28 = 129 − 47 = Round 689 to nearest 100

391 + 600 = Smaller: 714 or 741? 412 − 70 = Round 34 to nearest 10 8, 12, 16, 20,

72, 62, 52, 42, Bigger: 847 or 874? + 36 = 100

478 + 500 = Smaller: 592 or 529? 645 − 90 = Round 57 to nearest 10 64, 56, 48, 40,

/10

174

340, 440, 540, 65 + = 100 78 + 43 = 98 – 67 = Round 916 to nearest 100 483 + 300 = Smaller: 829 or 819? 347 – 60 = Round 89 to nearest 10 12, 15, 18, 21,

389 + 60 = 1230 − 400 = 44, 48, 52, 56,

/10

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

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

81 + 19 = 167 − 59 = Round 26 to nearest 10 Round 534 to nearest 100 78, 68, 58, 48, Bigger: 758 or 785? + 29 = 100 523 + 70 = 900 − 250 = 8, 12, 16, 20,

360, 460, 560, 29 + = 100 58 + 46 = 137 − 62 = Round 254 to nearest 100 322 + 800 = Smaller: 481 or 418? 703 − 80 = Round 68 to nearest 10 75, 70, 65, 60,

38 + 59 = 92 − 47 = Round 63 to nearest 10 Round 287 to nearest 100 16, 24, 32, 40, Bigger: 429 or 492? + 74 = 100 412 + 90 = 745 − 200 = 86, 76, 66, 56,

D R

/10

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/10

290, 390, 490, 45 + = 100 82 + 37 = 146 − 59 = Round 811 to nearest 100 267 + 600 = Smaller: 736 or 673? 558 − 90 = Round 49 to nearest 10 15, 18, 21, 24,

84 + 57 = 118 − 59 = Round 52 to nearest 10 Round 749 to nearest 100 68, 58, 48, 38, Bigger: 713 or 731? + 52 = 100 364 + 90 = 905 − 400 = 12, 15, 18, 21,

520, 420, 320, 33 + = 100 69 + 25 = 153 − 77 = Round 678 to nearest 100 345 + 200 = Smaller: 847 or 784? 612 − 90 = Round 82 to nearest 10 32, 28, 24, 20,

/10

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

175

Quick 10s / Tere Tekau Term 2 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

61 + 39 = 135 − 67 = Round 58 to nearest 10 Round 842 to nearest 100 56, 46, 36, 26, Bigger: 659 or 695? + 48 = 100 277 + 40 = 1,062 − 500 = 15, 20, 25, 30,

540, 440, 340, 27 + = 100 63 + 48 = 182 − 59 = Round 989 to nearest 100 135 + 900 = Smaller: 758 or 785? 520 − 70 = Round 41 to nearest 10 44, 46, 48, 50,

53 + 29 = 156 − 78 = Round 33 to nearest 10 Round 678 to nearest 100 24, 27, 30, 33, Bigger: 924 or 942? + 14 = 100 461 + 90 = 1,590 − 700 = 84, 74, 64, 54,

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/10

260, 360, 460, 14 + = 100 97 + 26 = 201 − 88 = Round 715 to nearest 100 403 + 200 = Smaller: 694 or 649? 880 − 120 = Round 29 to nearest 10 5, 10, 15, 20,

57 + 38 = 153 − 71 = Round 21 to nearest 10 Round 409 to nearest 100 34, 44, 54, 64, Bigger: 836 or 863? + 55 = 100 346 + 80 = 1,100 − 450 = 98, 96, 94, 92,

470, 570, 670, 83 + = 100 44 + 99 = 240 − 95 = Round 536 to nearest 100 299 + 700 = Smaller: 821 or 812? 610 − 150 = Round 76 to nearest 10 33, 30, 27, 24,

/10

176

AF T

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

Quick 10s / Tere Tekau Term 3 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

3×4= 5×8= 32 ÷ 4 = 24 ÷ 3 = Round 409 to nearest 100 57 + 38 = 153 − 71 = 27, 24, 21, 18, 3 × 45 = 145 + 57 =

74 + 28 = 8, 12, 16, 20, 2×8= 40 ÷ 5 = 3×9= 56 ÷ 8 = Round 48 to nearest 10 5 × 14 = 6 × 23 = 193 − 86 =

3×7= 5×9= 80 ÷ 10 = 72 ÷ 8 = Round 521 to nearest 100 49 + 55 = 182 − 69 = 20, 30, 40, 50, 4 × 63 = 137 + 64 =

/10

82 + 37 = 10, 15, 20, 25, 4×7= 35 ÷ 5 = 4×8= 72 ÷ 8 = Round 63 to nearest 10 5 × 42 = 8 × 17 = 205 − 89 =

3×6= 5×4= 27 ÷ 3 = 40 ÷ 8 = Round 688 to nearest 100? 83 + 29 = 3, 6, 9, 12, 2 × 97 = 192 + 34 = 219 − 94 =

91 + 26 = 9, 12, 15, 18, 3×9= 40 ÷ 8 = 4×5= 56 ÷ 7 = Round 77 to nearest 10 4 × 36 = 8 × 24 = 214 − 97 =

/10

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

177

Quick 10s / Tere Tekau Term 3 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

4×9= 3×8= 35÷ 5 = 32 ÷ 4 = Round 631 to nearest 100 59 + 78 = 9, 12, 15, 18, 3 × 47 = 274 + 56 = 248 − 97 =

63 + 29 = 32, 40, 48, 56, 5×8= 32 ÷ 8 = 6×8= 42 ÷ 7 = Round 84 to nearest 10 5 × 67 = 4 × 39 = 236 − 58 =

3×7= 6×5= 36 ÷ 4 = 27 ÷ 3 = Round 647 to nearest 100 82 + 89 = 35, 40, 45, 50, 8 × 34 = 281 + 27 = 127 − 79 =

/10

76 + 38 = 32, 28, 24, 20, 3×9= 24 ÷ 6 = 5×8= 56 ÷ 8 = Round 35 to nearest 10 8 × 46 = 4 × 27 = 249 − 63 =

2×8= 3×9= 40 ÷ 5 = 56 ÷ 8 = Round 478 to nearest 100 74 + 29 = 193 − 86 = 8, 12, 16, 20, 5 × 14 = 139 + 82 =

82 + 39 = 20, 25, 30, 35, 6×8= 30 ÷ 5 = 7×4= 36 ÷ 6 = Round 97 to nearest 10 6 × 29 = 3 × 34 = 361 − 74 =

/10

D R

178

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

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

2×9= 4×8= 60 ÷ 10 = 48 ÷ 8 = Round 489 to nearest 100 53 + 46 = 195 − 78 = 5, 10, 15, 20, 5 × 27 = 142 + 58 =

93 + 18 = 27, 30, 33, 36, 8×7= 27 ÷ 3 = 8×6= 32 ÷ 4 = Round 169 to nearest 10 5 × 24 = 4 × 28 = 337 − 62 =

8×8= 6×5= 24 ÷ 4 = 45 ÷ 5 = Round 754 to nearest 100 47 + 66 = 18, 20, 22, 24, 4 × 53 = 158 + 81 = 225 − 83 =

/10

79 + 27 = 34, 36, 38, 40, 4×6= 35 ÷ 5 = 8×7= 48 ÷ 8 = Round 124 to nearest 10 8 × 23 = 3 × 31 = 412 − 86 =

2×9= 8×6= 21 ÷ 3 = 40 ÷ 5 = Round 589 to nearest 100 46 + 65 = 16, 24, 32, 40, 4 × 29 = 263 + 49 = 213 − 88 =

86 + 45 = 98, 96, 94, 92, 3×9= 25 ÷ 5 = 3×9 = 21 ÷ 3 = Round 172 to nearest 10 4 × 71 = 3 × 56 = 318 − 59 =

/10

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

179

Quick 10s / Tere Tekau Term 4 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

5×8= 32 ÷ 4 = Bigger: 1 or 1 ?

214 + 29 =

1 + 1 = 4 4

24 ÷ 4 =

3 × 27 =

72 +

= 100

24, 28, 32, 36,

Bigger: 1 or 1 ? 3

AF T

Round 56 to nearest 10

1 of 24? 2

346 + 27 = 212 – 89 = 64 ÷ 8 = 83 + = 100 4 × 38 =

/10

1 + 2 = 4 4

92 + 15 = 275 − 98 = Smaller: 4 or 2 ?

15, 20, 25, 30,

Bigger: 2 or 3 ?

Round 73 to nearest 10 Smaller: 906 or 960?

/10

4×9= 24 ÷ 3 = Bigger: 1 or 1 ?

1 of 20 = 4

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58 + 37 = 143 − 56 = Smaller: 2 or 3 ? 6 6 3 × 17 = 24 ÷ 8 =

Smaller: 758 or 785?

/10

5 × 82 = 64 ÷ 8 = 1 of 27 = 3

1 + 1 = 5 5

1 of 44? 2

Smaller: 2 or 3 ?

180

2×8= 40 ÷ 5 = Bigger: 1 or 1 ?

267 – 82 =

34 + 67 = 94 – 28 = 4 × 28 = 18 ÷ 3 =

/10

257 + 48 = 193 – 76 = 72 ÷ 8 = + 42 = 100 3 × 25 = 1 2

of 18 =

12, 16, 20, 24,

Bigger: 1 or 1 ? 3

Round 87 to nearest 10 Smaller: 674 or 746?

/10

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

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

7 1 + = 6

46 + 29 = 200 − 83 = Smaller: 3 or 4 ? 10 10 2 × 68 = 40 ÷ 8 = 1 of 25 = 5

/10

J 186 + 57 = 142 – 39 = 36 ÷ 4 = + 63 = 100 8 × 32 = 1 of 25 = 5

8, 12, 16, 20, Bigger: 1 or 2 ? 3

Round 54 to nearest 10 Smaller: 389 or 398?

/10

1 of 26 = 2

27, 24, 21, 18, Bigger: 1 or 1 ? 4

Round 85 to nearest 10 Smaller: 479 or 497?

AF T

1 6

93 + 68 = 158 – 47 = 24 ÷ 2 = + 36 = 100 5 × 48 =

D R

5×4= 32 ÷ 8 = Bigger: 1 or 1 ?

I 9

1 8

+ 3 = 8

67 + 24 = 181 − 74 = Smaller: 5 or 7 ? 12 12 5 × 14 = 40 ÷ 5 = 1 of 16 = 8

/10

4×7= 56 ÷ 8 =

Bigger: 1 or 1 ? 5

1 3

8×6= 30 ÷ 3 = Bigger: 1 or 1 ?

+ 1 = 3

48 + 39 = 112 − 47 = Smaller: 4 or 5 ? 9

5 × 34 = 27 ÷ 3 = 1 of 30 = 3

72 + 65 = 130 – 84 = 35 ÷ 5 = + 41 = 100 5 × 44 = 1 of 12 = 2

5, 10, 15, 20, Bigger: 4 or 2 ? 8

Round 29 to nearest 10 Smaller: 521 or 512?

/10

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

/10 181

Quick 10s / Tere Tekau Term 4 Your teacher will tell you when it’s time to refresh your skills using these Quick 10 quizzes!

3×8= 18 ÷ 3 = Bigger: 1 or 1 ? 5

145 + 38 = 187 – 69 = 32 ÷ 4 = + 55 = 100 3 × 48 =

4 + 1 = 6 6

1 of 16 = 4

39 + 56 = 167 − 49 =

16, 20, 24, 28,

Smaller: 2 or 4 ? 5 5

Bigger: 2 or 5 ?

4 × 28 = 32 ÷ 4 = 1 of 28 =

Round 75 to nearest 10: Smaller: 867 or 876?

P 199 + 87 = 190 – 76 = 40 ÷ 8 = + 37 = 100 4 × 31 = 1 of 27 =

1 + 3 = 9 9

71 + 22 = 189 − 75 = Smaller: 2 or 3 ? 11

R 2

54 + 37 = 220 − 64 = Smaller: 3 or 5 ?

Round 44 to nearest 10: Smaller: 233 or 323?

2 × 47 =

3 × 72 = 24 ÷ 3 = 1 of 24 =

Q 1 + 2 = 3 3

Bigger: 1 or 1 ?

/10

42, 36, 30, 24,

/10

5×8= 24 ÷ 4 = Bigger: 1 or 1 ?

6×5= 32 ÷ 8 = Bigger: 1 or 1 ?

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/10

182

AF T

40 ÷ 5 = 1 of 30 = 5

/10

274 + 59 = 200 – 46 = 40 ÷ 8 = + 62 = 100 4 × 21 = 1 5

of 10 =

15, 18, 21, 24,

Bigger: 1 or 2 ? 3

Round 91 to nearest 10: Smaller: 654 or 645?

/10

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

D R AF T

D R T