Maths Plus NSW Student Book 3 Full Digital Sample

Harry O’Brien

Greg Purcell

The Maths Plus NSW Syllabus/Australian Curriculum series, Year K to Year 6, is based on the NSW Education Standards Authority 2023 Mathematics K–6 Syllabus for the Australian Curriculum Mathematics (ACARA). Each book after Year K builds upon prior knowledge and works towards an understanding of the achievement standards for the relevant year level and beyond. Maths Plus provides students with opportunities to sequentially develop their skills and knowledge in the strands of the Australian Curriculum Mathematics: Number, Algebra, Measurement, Space, Statistics and Probability

Series components

Student Books

Work towards achieving the relevant outcomes by developing skills and competency in understanding mathematical structures, fluency, reasoning and problem solving.

Mentals and Homework Books

Provide concise, essential revision and consolidation activities that correspond with the concepts and units of work presented in the Student Books.

Assessment Books

Include short post-tests with a simple marking system to assess students’ skills and understanding of the concepts in the Student Books.

Student Book features

• All pages are colour coded.

• Australian Curriculum Mathematics content descriptions, proficiency strand references and general capabilities appear on each page.

• The Dictionary (Years 2 to 6) features clear and simple explanations of mathematical terms and language.

Diagnostic term reviews

• Diagnostic term reviews (Years 1 to 6) assist in pinpointing students’ strengths and weaknesses, allowing intervention and re-teaching opportunities where required.

• The Find a topic page allows teachers the freedom to address particular topics and student needs as appropriate, providing essential revision and consolidation opportunities.

Teacher Book and Teacher Dashboard

Provide access to a wealth of resources and support material:

• curricula and planning documents

• interactive teaching tools

• potential difficulties videos

• learning activities

• support and extension activities

• reflection

• blackline masters and investigation pages

www.oxfordowl.com.au

is the home for Oxford

Primary professional resources.

• links to Advanced Primary Maths (Years 3 to 6)

• assessment tests

• answers for student resources

NSW Syllabus Outcomes

MA2-RN-01 Representing numbers using place value

Applies an understanding of place value and the role of zero to represent numbers to at least tens of thousands

MA2-RN-02

Represents and compares decimals up to 2 decimal places using place value

MA2-AR-01 Additive relations

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers

MA2-AR-02

Completes number sentences involving addition and subtraction by finding missing values

MA2-MR-01 Multiplicative relations

Represents and uses the structure of multiplicative relations to 10 × 10 to solve problems

MA2-MR-02

Completes number sentences involving multiplication and division by finding missing values

MA2-PF-01 Partitioned fractions

Represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

MEASUREMENT AND SPACE

MA2-GM-01

Geometric measure

Uses grid maps and directional language to locate positions and follow routes

MA2-GM-02

Measures and estimates lengths in metres, centimetres and millimetres

MA2-GM-03

Identifies angles and classifies them by comparing to a right angle

MA2-2DS-01

Two-dimensional spatial structure

Compares two-dimensional shapes and describes their features

MA2-2DS-02

Performs transformations by combining and splitting two-dimensional shapes

MA2-2DS-03

Estimates, measures and compares areas using square centimetres and square metres

MA2-3DS-01

Three-dimensional spatial structure

Makes and sketches models and nets of three-dimensional objects including prisms and pyramids

MA2-3DS-02

Estimates, measures and compares capacities (internal volumes) using litres, millilitres and volumes using cubic centimetres

MA2-NSM-01

Non-spatial measure

Estimates, measures and compares the masses of objects using kilograms and grams

MA2-NSM-02

Represents and interprets analog and digital time in hours, minutes and seconds

MA2-DATA-01 Data

Collects discrete data and constructs graphs using a given scale

MA2-DATA-02

Interprets data in tables, dot plots and column graphs

MA2-CHAN-01 Chance

Records and compares the results of chance experiments

MAO-WM-01 Working mathematically

STATISTICS AND PROBABILITY

Develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly

MA2-RN-01 Representing numbers using place value

MA2-RN-02

MA2-AR-01 Additive relations

MA2-AR-02

MA2-MR-01 Multiplicative relations

MA2-MR-02

MA2-PF-01 Partitioned fractions

MA2-GM-01 Geometric measure

MA2-GM-02

MA2-GM-03

MA2-2DS-01

MA2-2DS-02

MA2-2DS-03

MA2-3DS-01

MA2-3DS-02

MA2-NSM-01

MA2-NSM-02

Two-dimensional spatial structure

MEASUREMENT AND SPACE

Three-dimensional spatial structure

Non-spatial measure

MA2-DATA-01 Data

MA3-DATA-02

MA2-CHAN-01 Chance

MAO-WM-01 Working mathematically

STATISTICS AND PROBABILITY

What

Skip counting

Use skip counting to find the total number in each group. The first one has been started for you.

Use skip counting to find the total amount in each group, even though some are hidden.

Three-dimensional objects

Colour all the prisms blue and tick all the cylinders to identify them from the rest of the objects.

MATCHES

Find and list some things in your classroom that are prisms and cylinders.

Draw a line matching each 3D object with its correct name.

DRAFT

Which objects above have curved surfaces?

Makes and sketches models and nets of three-dimensional objects including prisms and pyramids

sphere cylinder prism cone pyramid

Baked Beans

and record the lengths of five pencils in your classroom.

Use the 1 cm dot paper to draw the following lines.

Length can be measured in centimetres. The short way of writing centimetres is cm. There are 100 centimetres in 1 metre. A Base 10 one is about 1 centimetre long.

Subtraction facts 2

Writing and ordering numbers

Write the number represented by the Base 10 materials.

Hundreds Tens Ones Number

Use Base 10 materials to make more numbers, then record them.

Write each number in words. You may need to use some of the words in the box to help you with the spelling.

one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety, hundred, thousand

a 321

b 737

c 295

d 574

Order the following numbers from smallest to largest.

a 256, 307, 291

b 999, 807, 364

c 259, 952, 529

d 742, 247, 472, 274

e 507, 607, 705, 605

A line of symmetry is a line that divides something exactly in half.

DRAFT

Jamal laid a plastic grid over the shapes. Use the grid to answer the questions.

a Which shape has the largest area?

b Which shape has the smallest area?

c Which two shapes have the same area?

d Which shape has an area of 16 square units?

Liam said that there was only one rectangle you could make with an area of 18 squares. He drew it below. Zoe thought that there was more than one.

See if you can draw more rectangles with an area of 18 squares to see who is correct.

Liam’s rectangle

18 squares

Emily covered her desk with round plates.

a Do you think these are good measuring units for area?

b Explain why or why not to a friend and then listen to what they have to say.

c Were their ideas the same as yours?

3 Changing addends to make 10

Look for pairs of numbers that make 10 when adding, e.g. 4 + 8 + 6 = 18. Add the 4 and 6 first.

By looking for numbers that add to make 10, the addition sum becomes easier for you to do.

How much did he save in the 3 months?

farm. How many animals did she see?

Mack and Myer Department Store

Calculate the cost of buying the following items.

a A baseball bat and a soccer ball $

b A teddy bear, a book and a car $

c A pen, a teddy and a car $

d A baseball bat, a teddy and a soccer ball $

On a piece of paper, write some of your own additions that have a 10 combination.

Write number sentences to describe the groups.

2 groups of equals .

groups of equals .

groups of equals .

Draw groups to illustrate this number sentence: 3 groups of 6 equals 18

3 Describing position

Use the tray cupboard to answer the questions.

a Whose tray is on the top shelf on the right?

b Whose tray is in the middle of the shelf third from the bottom?

c Describe the position of Sienna’s tray.

d Write Harry’s name on his tray, second shelf from the top, on the left.

e Write Lauren’s name on her tray, second shelf from the bottom, in the middle.

f Write Zoe’s name on her tray, which is directly to the right of Brooke’s.

g Write Ethan’s name on his tray, which is in the bottom right corner.

h Describe the position of the tray with no name on it.

Find the secret message by placing letters on the shelves.

a Put a Y in the top left shelf.

b Put an I in the box in the 2nd top row and 2nd from the right.

c Put an S in the box in the 3rd bottom row, on the right.

d Put a V in the 2nd bottom row, on the left.

e Put a T in the 3rd row from the top and on the left.

f Put a D in the 2nd row from the top, on the right.

g Put an R in the 2nd row from the bottom and 2nd from the right.

Tally marks and column graphs

Tally the vehicles that are parked in or near your school.

Cars parked at my school

Manufacturer Tally

Ford

Holden

Toyota

Mitsubishi

Volkswagen

BMW

Subaru

Honda

Mazda

Hyundai

Other

a What was the most popular make of vehicle around your school?

b What was the least popular?

c Were any equally popular?

d What is your favourite make of car?

Mr Lee’s class did a survey and graphed the four most popular cars.

a Which was the most popular car?

b Which was the least popular car?

c Which car had a total of 6?

d Which car had a total of 5?

e How many more Holdens were there than Toyotas?

4 Inverse operations of addition and subtraction

Two subtraction number sentences can be written from 18 + 12 = 30. They are 30 – 12 = 18 and 30 – 18 = 12.

DRAFT

I had $12 but spent $7. Now I have $5. 12 – 7 = 5 7 + 5 = 12

On the board, the teacher wrote a number sentence that had an answer of 36. Write some addition number sentences that have a total of 36, then check your additions using subtraction.

Use the arrays to solve the multiplication facts.

Use the arrays to complete the table of twos.

Solve the problems.

a Mrs Jones bought 7 books at $2 each. How much did she spend?

b Harry had 8 bags of 2 cakes. How many cakes did he have?

c Linh had 5 boxes with 2 books in each. How many books did she have?

d Austin bought 6 books at the shop for $2 each. How much change did he get from $20?

e Milla had 9 pairs of shoes. How many shoes did Milla have altogether?

Is there a relationship between the two times table and even numbers?

Learn your two times table over the next two weeks.

4 Prisms and cylinders

Study each set of faces and surfaces. Match each object to its set of faces or surfaces. Then, colour each 3D object and its set of matching faces or surfaces the same colour. The first one is done for you.

A vertex is where two or more lines meet to form an angle.

An edge is where two surfaces meet or intersect. Edges can be straight or curved.

Estimate and then measure the length of these leaves in centimetres.

What is the difference in length between the longest and the shortest leaf? cm

Find these real-life objects and measure the length of each in centimetres.

Use the letters a, b,

to place the objects above in order of length from shortest to longest.

5 Odd and even numbers

Colour the circles to model the numbers. Then tick the column to record if they are odd or even. The first one is done for you.

Odd Even a 12 ✔

b 13 c 18

d 25

e 28 f 31

Numbers that pair equally are even.

6

DRAFT

Shade all even numbers blue and odd numbers yellow.

All numbers that end in the digits 0, 2, 4, 6 and 8 are .

All numbers that end in the digits 1, 3, 5, 7 and 9 are .

Continue the skip counting patterns with odd and even numbers.

Connecting addition and subtraction

Use each addition fact to make two subtraction facts. The first one is done for you.

a 8 + 4 = 12 12 4 = 8 12 8 = 4

b 7 + 5 = 12 = =

c 6 + 9 = 15 = =

d 8 + 7 = 15 = =

e 9 + 8 = 17 = =

f 12 + 8 = 20 = =

g 13 + 6 = 19 = =

7

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

Problem

Number sentence

a Sally has 17 toys in a box. If she took 8 out, how many toys would be left in the box? =

b Kim needs $16 to buy a new game. If she has already saved $8, how much more does Kim need to save? =

c Harry had $20 in his bank account. He spent $14. How much money is left in the bank? =

=

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Triangles

A triangle is made up of 3 straight sides and has 3 angles.

There are many different shaped triangles.

Cut straws to the lengths that are shown to see if they make triangles. Sketch the ones that do.

Is it possible for a triangle to contain a right angle?

Compares two-dimensional shapes and describes their features

13

Time in minutes 5

A watch has:

a minute hand that shows minutes past the hour or minutes to the hour

an hour hand that shows the hour

a second hand that measures 60 seconds in each minute.

The minute hand counts off 60 minutes every hour. Each number on the clock represents a span of 5 minutes.

How many minutes does it take for the minute hand to move from:

a 12 to 1?

b 12 to 2?

c 12 to 3?

d 12 to 4?

e 12 to 6?

DRAFT

f 2 to 3?

g 4 to 6?

h 5 to 8?

i 6 to 9?

j 8 to 12?

The minute hand has fallen off Ben’s watch. Draw the minute hand on the watches below to show the times.

How many minutes does it take the hour hand to move from one number to the next?

Expanding 3-digit numbers 6

Use these number expanders to expand the numbers.

a 285 hundreds tens ones

b 743 hundreds tens ones

c 854 hundreds tens ones

d 999 hundreds tens ones

e 870 hundreds tens ones

f 809 hundreds tens ones

Expand each number. The first one has been done for you.

a 527 = 500 + 20 + 7

b 363 = + +

The symbols > (greater than) and < (less than) are used to compare numbers.

Use the greater than or less than symbol to make these number sentences true.

Forty-five is less than sixty-three. We write it like this:

45 < 63

Write a multiplication fact to describe each array.

Use the arrays to complete the table of fives and other facts.

Revise your multiplication facts by solving the problems.

a Peyton saved $4 per week for 5 weeks. How much did she save?

b Stephen trains 5 days a week, running 5 km each day. How far does he run each week?

c Jarrah bought a ticket for $9 but Yindi’s ticket cost 5 times as much. How much did Yindi pay for her ticket?

Multiply by 10 then halve to solve these questions.

What happens when you multiply these numbers by zero in your calculator? 8

Learn your five times table over the next two weeks. 9

Grid maps

Grids help you locate places on maps. A grid uses lines to make rows and columns on a map. The rows go from side to side. The columns go from top to bottom. Letters are used to label the columns, and numbers label the rows.

DRAFT

What can be found in these grid references? a A1

F2

Are the shops north of Spin City School?

Is Lake Spin south of Jack’s house?

Give all the grid references for the shops.

Give all the grid references for Forest Park.

Tall Tales River passes through the following grid references. Answer true or false.

Is Tom’s house west of Forest Park?

18 19

Dot plots

A dot plot is a number line that uses dots to record the frequency of events. For example, in this survey six people selected C.

on the picture graph?

The owners of the ten-pin bowling alley did a survey to find out who used their bowling alley on a Thursday afternoon. They recorded their data using tally marks.

DRAFT

Bowlers Tally Men

Women

Bowlers Tally Girls Boys

Create a dot plot to record the number of tenpin bowlers. Use one dot to represent each person. The faint grid might help you.

Answer the questions.

a How many men were at the bowling alley?

b How many girls were there?

c How many boys were there?

Bike Car

How we get to school Bus Walk

Thursday afternoon bowling

Men Women Girls Boys

The division symbol 7

Division can be expressed using the division symbol (÷) in number sentences.

The division symbol (÷) means: in groups of shared between divided by

Use the balls to help solve the divisions.

a 20 divided by 5 20 ÷

b 20 divided by 4 20 =

c 20 divided by 2 20 =

d 20 divided by 10 20 =

e 20 divided by 1 20 =

Use some counting materials to answer the questions, then check your answers with a calculator.

Represents and uses the structure of multiplicative relations to 10 × 10 to solve problems Completes number sentences involving multiplication and division by finding missing

Jump strategy for addition 7

Use jump strategies to solve the additions. The first one is done for you.

Use the jump strategy to add the numbers.

a 35 + 23 becomes 20 35 + + 3 =

b 42 + 25 becomes + + =

c 33 + 34 becomes + + =

d 46 + 24 becomes + + =

e 52 + 26 becomes + + =

32 + 25 becomes 32 + 20 + 5 = 57

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Two or more lines that are exactly the same distance apart are called parallel lines. They do not have to be the same length and can be in any direction.

Shade all boxes that contain sets of parallel lines.

Some shapes have parallel sides.

a Is the broom parallel to the side of the door?

b Is the top of the door parallel to the leg of the table?

c Is the curtain rod parallel to the top of the window?

d Is the side of the door parallel to the leg of the table?

e Tick all horizontal lines that are found on the table.

Tick the shapes below that have parallel sides.

Using three small containers like a mug, a tea cup and a glass, tally how many are needed to fill a 1 L bowl or container.

Tally

Informal capacity/litres

Containers needed

Use the grid to graph the results.

Draw lines to match the most suitable container to measure the capacity of the kettle, bath, medicine bottle and fruit-juice box.

Find three containers that have their capacity labelled and record them.

a Fruit juice 4 L c

8

Subtraction patterns/equal differences

We know that 7 4 = 3, so 70 40 must equal 30. Complete these examples to extend the basic number facts. The first one has been done for you.

You can add or subtract numbers from number sentences to make equal differences. Equal differences can make calculations easier for everyone.

If you add 2 to both sides of 66 – 28 you get 68 – 30.

72 – 39 becomes 73 – 40 Much easier!

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Halves, quarters and eighths

Fractions can be written using a numerator and a denominator

1 4

The numerator shows us how many parts out of the whole (the fractional part).

g h

DRAFT

out of out of out of

Three children folded strips of paper.

Ravi Alisha Sam

Who folded their paper into quarters?

Who folded their paper into halves?

Who folded their paper into eighths?

8 Pyramids

Identify the faces, edges and vertices of the pyramids.

a Draw a coloured circle on all the vertices.

b Trace over all the edges with a coloured pencil.

edge face vertex

Draw a set of faces for each pyramid.

DRAFT

c Shade the three faces you can see in different colours.

What is the difference between a square pyramid and a cube?

Pyramids have only 1 base and all other faces are triangular.

Makes and sketches models and nets of three-dimensional objects including prisms and pyramids

Calculating area 8

Callum is setting the table for dinner. He has laid out a new tablecloth and some placemats. He has decided to measure the area of the tablecloth using the placemats. Placemat

It’s just like an array.

Tablecloth

Use the diagram to solve the problems.

a How many placemats has he used so far?

b How many placemats fit across the length of the table?

c How many placemats fit down the width of the table?

12

Explain the strategy you would use to work out how many placemats would fit on the table.

DRAFT

Jon and Ky were each given identical L shapes which they covered with square and rectangular grid overlays. Jon said his shape was bigger because he used more squares than Ky’s rectangles.

13

Explain why you agree or disagree with Jon.

Split strategy for addition 9

Add the following numbers by adding the tens part, then adding the ones part, then combining them. The first one has been done for you.

a 23 + 44 becomes 60 + 7 = 67

b 33 + 52 becomes + =

c 43 + 44 becomes + =

d 38 + 23 becomes +

e 27 + 45 becomes +

f 66 + 18 becomes +

g 49 + 44 becomes +

h 36 + 56 becomes + =

i 45 + 47 becomes + =

j 56 + 28 becomes + =

k 29 + 47 becomes + =

l 48 + 36 becomes +

Calculate the distance travelled to make the following journeys.

a Capital Hill to North Point via Light House.

b North Point to Cheetah Town via Leopard Hill.

c Cheetah Town to Capital Hill via Kangaroo Valley.

d Capital Hill to North Point via Possum Place.

e Light House to Leopard Hill via North Point and Possum Place.

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Use your head. 57 + 26 becomes 50 + 20 = 70 plus 7 + 6 = 13, so 70 + 13 = 83.

Related multiplication facts (4s)

Complete the tables. The arrays will help you. a

Use the grid to answer the questions.

a Circle the table of 2s.

b Colour the table of 4s.

c What did you notice?

Use the “double then double again” strategy to multiply these numbers by 4.

Think double 6 = 12. Then double 12 = 24.

Learn your four times tables over the next two weeks.

9 Computer graph making

Mrs Tam’s class did a survey and made a tally of some very popular cars used by students’ parents to take them to school.

The class then made a dot plot of the data they collected.

How we get to school

Computer graph making

On a computer, make a column graph and a pie graph of the data presented in the dot plot above.

You may need to fill in a data grid that looks like this.

Examples of what the graphs may look like are supplied below.

Collects discrete data and constructs graphs using a given scale Interprets

Ford Holden Toyota Mitsubishi

Ford Holden Toyota Mitsubishi

Ford Holden Toyota Mitsubishi

Brands

Column graph

Pie graph

Series 1

DRAFT

Digital time is always read as minutes past the hour.

E.g. 12:35 is read as 35 minutes past 12 or twelve thirty-five. :

I eat lunch at

DRAFT

f Eleven twenty-six

Write digital times for the times given in words.

a 25 minutes past 3 : e six thirty-two :

b 35 minutes past 4 : f seven forty-three :

c 13 minutes past 12 : g nine forty-one :

d 56 minutes past 10 : h 39 minutes past 1 :

9 10

Mrs Wilson has four appointments today which she has listed in alphabetical order. Put them in the order that she will see her visitors throughout the morning.

Notes

Alana 11:45

Bree 10:30

Fran 9:45

Hilda 11:10

Name Time

My appointment is at 9:45.

d 3 + 8 + 7 = g 5 + 8 + 5 = e 6 + 8 + 4 = h 30 + 30 =

f 6 + 9 + 4 = i 40 + 50 =

Use the split strategy to add these numbers.

j 23 + 35 50 + =

k 37 + 52 + =

l 26 + 33 + =

m 23 + 76 + =

Answer the subtractions.

a – 6 18 20 12 24 16 4

b 8 5 = f 90 7 =

c 12 7 = g 80 50 =

d 15 6 = h 120 40 =

e 25 4 = i 130 60 =

Use skip counting to find the total number in each group.

multiplications.

divisions.

a Write 267 in the numeral expander. hundreds tens ones

Expand these numbers.

b 569 + +

c 267 + +

d 853 + +

4

Label the cube’s parts with the words ‘face’, ‘edge’ and ‘vertex’.

a Who read the most books?

b Who read four books?

c Who read only two books?

Mary

10 Using addition to solve subtraction

Use known addition facts to answer the subtractions. The first one is done for you.

a 12 7 think 7 + 5 = 12

b 14 7 think + =

c 13 7 think + =

d 19 12 think + =

e 20 13 think + =

f 17 11 think + =

Demonstrate how addition can be used to solve subtractions. The first one is done for you.

a 38 32 think 32 + 6 = 38

b 47 42 think + =

c 58 51 think + =

d 69 61 think + =

e 22 18 think + =

f 33 27 think + =

g 142 138 think + =

h 154 148 think + =

Explain how you would solve 67 62 = . 3

13 minus 5? Think 5 + 8 = 13. The answer is 8. 39

Comparing and ordering fractions

Shade the fractions.

Order the fractions above from smallest to largest. 8 , 8 , 8 , 8

5 Order the fractions below from smallest to largest.

a 7 8 6 8 4 8 2 8

b 2 8 5 8 1 8 6 8

c 1 8 7 8 2 8 4 8

d 3 8 5 8 6 8 2 8

What other fraction could 4 8 be equal to?

Compare the fractions in the table above to find out whether the statements are true or false.

greater than < less than = equal to

Tell a friend what you noticed about fractions that have the same number for the denominator and numerator, e.g. 2

and 8 8

An angle is the amount of opening between two arms. Angles can be measured and named according to the size of their opening.

This common angle is called a right angle.

It is equal to a 1 4 turn of the hands on a clock face.

than a right angle?

e How many angles are larger than a right angle?

f How many right angles are there?

10 11

Name five angles larger than a right angle found in your classroom.

Construct some angles on geoboards, then draw them below.

Right angles

Angles smaller than a right angle

Angles larger than a right angle

Length can be measured in metres. The short way of writing metres is m. There are 100 centimetres in 1 metre.

Cut a streamer that is one metre long and use it to measure the objects to complete

Measure the length of these objects to the nearest metre using a metre rule or tape measure.

How many centimetres are there in:

Counting by tens 11

Count forward by tens to complete each sequence.

Count backwards by tens to complete each sequence.

Use your counting by ten skills to quickly count the pencils.

Adil folded three strips of paper then sketched dotted lines on their folds.

a Put a tick on the paper he folded into thirds.

b Draw a face on the paper he folded into halves.

c Draw a square on the paper he folded into quarters. Shade the shapes to match the thirds.

netball court is divided into thirds.

Continue the number patterns modelled by the shapes, then write a rule for each one. a

3 6 9

4 8 12

6 12 18

5 10 15

8 16 24

Represents and uses the structure of multiplicative relations to 10 × 10 to solve problems Completes number sentences involving multiplication and division by finding missing values

Use a pan balance to see how many Base 10 longs, marbles and pencils are needed to balance a calculator.

Why were the results different?

Which unit was the best for measuring the mass of the calculator?

Explain why.

Use Base 10 longs as a measuring unit to estimate and measure the mass of these objects. Lift each item to help with your estimates. Then measure and record the mass of each object.

Remember to do estimates and measure one item at a time.

Finding numbers on a number line

Put a cross to describe the position of each number on the number lines.

Put a cross on the number lines to estimate the numbers.

Use the array to complete the tables.

The two machines magically multiply the amounts put in by 2 and by 10. Calculate the answers after the amounts have been through the machines.

What if …?

a If 4 friends each ate 10 cakes, they would have eaten cakes.

b If 10 friends each bought a pair of socks, there would be socks.

c If 6 friends each paid $10, they would have spent $ .

d If 4 friends each scored 10 points, they would have a total of points.

e If 7 friends each wrote 10 pages, they would have written pages. Learn your 10 times table over the next two weeks.

Discover the facts about these shapes.

a Trace over the following shapes, then cut them out.

b Carefully fold the shapes to discover the number of lines of symmetry for each shape.

c Draw the lines of symmetry on the shapes below.

d Does each line of symmetry break the shape into two identical shapes?

e Record the number of sides, angles and lines of symmetry for each shape.

DRAFT

Do these two quadrilaterals have lines of symmetry?

Compares two-dimensional shapes and describes their features

Heads or tails?

a What are the two possible outcomes for flipping a coin?

b What do you think the result will be if a coin is tossed 30 times?

c In a group, toss a coin 30 times to discover which side comes up most. Use the table to tally your results. ( )

d Which side came up most in your experiment, heads or tails?

e Did the result of your experiment turn out as you thought it would, or was it different? Discuss this with your group and record your findings.

Colour the coins to create a picture graph of your result.

There are four possible ways that two coins can land when tossed into the air.

Subtraction jump strategy 13

Use jump strategies to solve the subtractions. The first one is done for you.

Use the jump strategy to answer the questions.

a 40 16 think 40 10 6

b 50 24 think 50

c 60 33 think 60

d 34 13 think 34

e 35 21 think 35

f 46 23 think 46

g 57 32 think 57

Think! 57 – 20 = 37. Now take away 3, equals 34.

Write fractions to represent the shaded part of each shape.

Shade the shapes to match the fractions.

Write the fractions in ascending order.

Represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

Sometimes an angle is formed when only one arm of the angle is visible, such as a door opening or a car driving up a hill. In these cases you have to visualise where the other arm would be.

DRAFT

Answer the questions.

a Which door formed the smallest angle?

b Which door formed the largest angle?

c Is the angle formed by door 1 larger than the angle formed by door 3?

d Which door formed the closest to a right angle?

9 10

In your school, find two examples of angles with hidden arms.

The paint cupboard door forms an angle.

Capacity can be measured in litres.

The symbol for litre is a capital L. The most common example of a litre in everyday use is the milk carton.

Many everyday products such as milk, cordial, ice cream, soft drink and detergent are sold in containers measured in litres. Collect five containers that are marked in litres and list them below, along with the number of litres they each hold.

Container

Number of litres

DRAFT

Use a 1 L milk carton to estimate and measure the capacity of these containers.

Bridging the decades/equality 14

Add these numbers by breaking up the second number and adding to a ten first.

a 9 + 6 becomes 9 + 1 + 5 = 15

b 8 + 7 becomes + + =

c 17 + 5 becomes + + =

d 16 + 5 becomes + + =

e 28 + 4 becomes + + =

f 47 + 5 becomes + + =

g 38 + 5 becomes + + =

h 54 + 17 becomes 10 + 6 + 1 = 54 +

i 39 + 13 becomes + + = +

j 46 + 26 becomes + + = +

k 67 + 27 becomes + + = +

Write the missing numbers to make the number sentences equivalent.

Write true or false. a 31 + 23 = 42 + 12

b 80 25 = 38 + 19

Use the counters to solve the problems.

a Ten marbles were shared between two girls. How many did each girl receive? marbles

b Fifteen toys were shared among three children. How many did each child receive? toys

c Fourteen pencils were shared between two boys. How many did each boy receive? pencils

d Twelve stickers were shared among four children. How many did each child receive? stickers

Modelling objects/nets 14

Construct the prisms below using centicubes or similar building cubes. After you have correctly modelled each prism, pull it apart and record how many blocks were used in its construction.

Use polydrons or paper nets copied onto 2 cm grid paper to discover which nets fold to form a cube. Put a cross on the ones that form a cube.

Describe to a friend how you folded one of the nets to form a cube.

Mr Riley’s class searched the playground for insects and recorded their findings in a table.

Ants Flies Butterflies Cicadas Cockroaches Bees

50 24 4 0 8 11

Interpret the table.

a Which was the most common insect?

b Which insect did they fail to find and why do you think this was so?

c What can you say about the number of ants found compared to the number of butterflies?

d Of which insect were there 6 times more than butterflies?

e Create your own table by recording the number of children with each hair colour in your class.

Blonde Brown Black Fair Red Other

Complete the table using tally marks ( ) and the information about the children’s favourite winter sports.

DRAFT

Soccer Rugby Netball Touch football

Mark Nadine Luca Lauren

Jenni Mohammed Sofia Trent

Sally Tom Lola Xavier

Bill Jack Maria Anita

John Emma Amber

Con Harry

12

Answer the questions.

Sport Boys Girls

Soccer Rugby Netball Touch football

a Which sport was the most popular for the boys?

b Which was the most popular sport for the girls?

c How many more boys played soccer than played rugby?

d How many more girls played netball than played touch football?

e If there were 25 children surveyed, how many didn’t have a favourite sport?

Draw a line to round each number to the nearest 10.

Use the pink number line below to assist you with the next question.

Round each number to the nearest 10. Numbers that end with a 5 are rounded up. a 19 to

to

to

Round these larger numbers to the nearest 10.

a 129 to c 637 to e

to d 251 to f 372 to

Round each number in the addition number sentences to estimate an answer.

a 8 + 21 is about

b 17 + 22 is about

c 36 + 23 is about

Write some numbers and round them to the nearest 10. 5

4-digit numbers

How many of each piece of Base 10 material would be needed to make the number? Use tally marks to model your answer, e.g. ( = 5).

3746 equals 3 thousands + 7 hundreds + 4 tens + 6 ones.

Thousands Hundreds Tens Ones

a 3764

b 7569

c 3570

d 6964

e 8507

f 2643

Write the number before and after the numbers given.

Expand these numbers on the number expanders. The first one is done for you.

a 3724 thousands hundreds tens ones 3 7 2 4

b 5694 thousands hundreds tens ones

c 8763 thousands hundreds tens ones

d 1144 thousands hundreds tens ones

e 1067 thousands hundreds tens ones

Write the largest number you can using the digits supplied.

Continue the doubling patterns (multiplying by 2). Shoes Tricycles Horses

Bowling pins Continue the halving patterns (dividing by 2). You may need a calculator.

pins Complete the function machines.

Quarter to and quarter past

15

When the minute hand reaches 3 it is a quarter of the way around the clock face. We call this quarter past (15 minutes past) the hour.

When the minute hand reaches 9 it only has one quarter of the way to go. We call this quarter to (15 minutes to) the hour.

Use the large clock face to help you write the times.

to Quarter past Quarter to past

Draw the times on the clock faces.

10

Each number the hour hand counts is equal to 1 hour (60 minutes).

How many minutes does it take for the hour hand to:

a move from one number to the next?

b move from 12 to 1?

c move from 12 to 2?

How many minutes would it take for the hour hand to move halfway between 12 and 1?

Addition patterns

Adding the same single-digit numbers results in the same digit in the ones position. You can use this knowledge to add larger numbers, e.g.

Revising multiplication facts

Study the arrays, then complete the number sentences.

Draw arrays of your own to model the number sentences, then answer them.

Use the arrays to complete the tables.

Represents and uses the structure of multiplicative relations to 10 × 10 to solve problems Completes number sentences involving multiplication and division by finding missing values

Collecting data

School snacks

Sai said that chocolate is the most popular school snack for children under 10.

Predict whether you think this is correct or incorrect.

Survey your class using tally marks to find out the most popular snacks for your class. Each student may have two choices.

a Which snack was most popular?

b Which snack was least popular?

c What is the difference in total between the most popular snack and the least popular snack?

d Were chips more popular than bananas?

e Were sultanas more popular than cupcakes?

Favourite cereals of our class

a What is your favourite cereal?

b What is the favourite cereal of the person sitting closest to you?

c How might you go about finding out the favourite cereal of the whole class?

d Discuss in a group how you might find out your class’s favourite cereal.

e What is your class’s favourite cereal?

The base unit for measuring mass is the kilogram. The symbol for kilogram is kg.

Many grocery items, such as sugar, are packaged in kilograms. Draw three items that you could buy that are packaged or purchased in kilograms.

Hold a 1 kg mass in one hand and the object, shown in the table below, in the other hand. Estimate whether each object has a mass of less than 1 kg, about 1 kg or more than 1 kg. Shade the appropriate box to record your answer.

Object Less than 1 kg About 1 kg More than 1 kg

Use a balance scale to check if your estimates above were correct.

Solve these problems based on kilograms.

a Jack had a mass of 34 kg but Joe’s mass was 14 kg more. What was Joe’s mass? kg

b Sanjay had a sack of potatoes that had a mass of 60 kg. If he took 25 kg out of the bag, how many kilograms of potatoes were left? kg

c Sally had 6 bags of potatoes. Each bag had a mass of 5 kg. How many kilograms of potatoes did she have? kg

17 Empty number lines

Rory had to solve this number sentence using an empty number line. This is what he did.

Solve the number sentences by completing the empty number lines. Some help has been given.

had 22 marbles in one bag and 31 in another. How many marbles did she have in total? 22

had 192 pop sticks but gave 33 away. How many did he have left?

Explain another strategy you could use to solve 86 23 =

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

4 rows of 3 = 12

3 columns of 4 = 12

12 shared into 4 rows = 3

12 shared into 3 columns = 4

4 × 3 = 12

3 × 4 = 12

12 ÷ 3 = 4

12 ÷ 4 = 3

DRAFT

4

Use the pictures to help you write a number sentence to solve each problem.

a There are 16 fish in the rock pool. How many groups of 4 fish can be made?

b James has 12 marbles. If he shares them among himself and three other friends, how many would they each receive?

c 15 girls are shared among five teams. How many girls are in each team?

Use the map to answer the questions.

a Start at George’s house and go down Shane St to the corner of South St. Turn left into South St and follow it until it reaches the intersection of Batman Ave. Turn right into Batman Ave and follow it until you are halfway between North Rd and Second Ave.

Whose house did you find?

b Colour the shortest route from the primary school to the swimming pool.

c Whose house is on the corner of Ship Rd and Batman Ave?

d What two streets form part of the boundary of the park?

e Colour a route from the swimming pool to George’s house.

Imagination Island

Interpret the map.

a Can you get to Happy City by road?

b Which town can only be reached by train?

c Which town can only be reached by boat and rail?

d List all the ways you can reach The Palms.

e Is Ban Bay south of Princeville?

Measuring and recording perimeter

Perimeter is the total distance around the edge of a two-dimensional shape. Shapes with straight sides can be measured with a ruler or tape measure.

Measure the dimensions of each shape in centimetres then calculate the perimeter of each one. The first one has been done for you.

Find two shapes in your classroom that could have their perimeters measured in centimetres. Sketch each shape, then record its perimeter.

I found a small book to measure.

Learning to trade in an addition sum.

Complete the additions, then check them by doing them again.

Add these numbers. Look for combinations that make it easier.

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers

3

Complete each pattern.

a 0 2 4 6

b 0 3 6 9

c 0 5 10 15

4

Number patterns 18

d 0 4 8 12

e 0 6 12 18

f 0 7 14 21

Complete each pattern, then write a rule for it.

a 8 12 16 20

b 7 10 13 16

c 18 22 26 30

d 30 35 40 45

5

Make up your own number pattern, then ask a friend to guess its rule.

Use the + function on your calculator to make counting patterns.

a 7 + 4 = = = = = = =

b 8 + 6 = = = = = = =

c 12 + 5 = = = = = = = =

d 6 + 7 = = = = = = = =

e 3 + 9 = = = = = = = =

f 9 + 8 = = = = = = = =

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Hexagonal prism

Prisms have two parallel faces that are congruent. All other faces on a prism are rectangular if the faces are square to the ends.

Prisms are named by these congruent faces.

DRAFT

A vertex is where two or more lines meet to form an angle.

six other rectangular faces.

I am a prism that has two octagonal faces and eight other rectangular faces.

An edge is where two faces meet or intersect.

Small areas are measured using square centimetres. The symbol for square centimetre is cm².

Calculate the area of each shape below by counting the square centimetres.

Draw as many shapes as you can that cover an area of 9 cm2.

Tanya said that there is only one rectangle with an area of 24 cm². Can you prove her wrong by drawing more? They may overlap.

Count forwards by ten.

a 50 60 70

b 32 42 52

Count backwards by ten.

c 80 70 60

d 97 87 77

Solve these subtractions.

a 12 6 = f 14 7 =

b 11 5 = g 47 43 =

c 14 6 = h 38 22 =

d 18 13 = i 57 43 =

e 20 8 = j 38 28 =

Use bridging to 10 to solve the additions.

a 9 + 5 becomes 9 + 1 + =

b 17 + 4 becomes + + =

c 26 + 7 becomes + + =

d 77 + 8 becomes + + =

Write a fraction for the shaded section of each shape.

a b c

Complete the multiplication facts.

a 8 × 3 = d 7 × 5 =

b 6 × 10 = e 6 × 4 =

c 8 × 4 = f 9 × 5 =

Complete the division facts. a

16 ÷ 4 = 18 ÷ 3 =

c Twenty cakes were shared among 5 children. How many did each receive?

Round these numbers to the nearest 10.

a 38 b 21

c 69 d 141

Round these numbers to the nearest 100.

e 396 f 301

g 417 h 579

19

Counting by tens or hundreds

Count forward by tens or hundreds to complete the sequences.

Supply the missing numbers to complete the sequences.

Count backwards by tens or hundreds to complete the sequences.

Write the largest and smallest number you can using the supplied digits.

Think of a number between 1 and 30, then count on by 100 each time.

Solve the problems.

a Mrs Jones bought 7 books at $3 each. How much did she spend?

b Harry had 8 bags of 3 cakes. How many cakes did he have?

c Charlotte had 5 boxes with 3 books in each. How many books did she have?

d Arjun bought 6 books at the shop for $3 each. How much change did he get from $20?

What is the highest number before 50 you can reach if you skip count by 3s?

Draw a line to match each label with a place on the scale from ‘Never’ to ‘Certain’.

The school swimming carnival will be on a Monday.

We will have homework tonight.

A tossed coin lands on heads.

I’ll get to school before my teacher.

A red bead is picked out of a bag of five different colours.

A baby is born a boy.

16

Throwing a double with two dice

a Predict how many times it will take you to throw a double.

b Roll two dice to find out how many times it does take.

c Did everyone get the same result?

Certain Likely

Equally likely

Unlikely

Never

d Colour the label that best describes the chance of throwing a double at first go.

CERTAIN NEVER UNLIKELY PROBABLE

17

The football team is about to get a new uniform. They have a choice of a blue top or a yellow top, and blue, red or yellow shorts.

Sketch how many different combinations of uniforms the team could have.

Blue Yellow

Blue Yellow Red

Trading in subtraction

Learning to trade in subtraction.

5 ones from 3 ones can’t be done. Trade 1 ten from the tens column to the ones column to make 13 ones. 5 ones from 13 ones equals 8 ones.

Subtract 1 ten from 3 tens to give 2 tens.

Complete

Trade 1 ten for 10 ones.

Tens Ones

Jack’s little sister spilt paint all over his homework. Help Jack to fix his homework.

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Division from multiplication

Write a division fact from each multiplication fact. The first one has been done for you.

a 6 × 2 = 12 12 ÷ 2 = 6

b 9 × 2 = 18

c 5 × 4 = 20

d 4 × 4 = 16

e 5 × 3 = 15

f 7 × 5 = 35

g 6 × 4 = 24

6 × 5 = 30

=

Division and multiplication are related!

Use a calculator to write some harder multiplication number sentences. Then write a division fact for each, e.g. 9 × 7 = 63 and 63 ÷ 7 = 9.

=

Circle the winning bingo card. a 3 × 4 = i 32 ÷ 4 = b 5 × 4 = j 45 ÷ 5 = c 8 × 2 = k 12 ÷ 6 = d 8 × 4 =

Represents and uses the structure of multiplicative relations to 10 × 10 to solve problems Completes number sentences involving multiplication and division by finding missing values

An angle is the amount of opening between two arms.

Make an angle tester out of the right-angled corner of a piece of paper. Compare it to the angles above and answer the questions.

a Which angles are right angles?

b Which angles are smaller than right angles?

c Which angles are larger than right angles?

Use the angle tester to find and classify some more angles in your school environment.

Where the angle was found

Draw copies of these angles on the dot paper below. The bottom arm of each angle has been drawn for you.

Angle tester

Length can be measured in millimetres. The short way of writing millimetres is mm. There are 10 millimetres in each centimetre.

Use the rulers to measure the length of the objects in millimetres. Remember that 1 centimetre is equal to 10 millimetres.

Draw lines of these lengths. a 50 mm b 80 mm c 120 mm

How many millimetres in:

How many centimetres in:

3-digit addition

Complete these 3-digit additions without trading.

Complete these 3-digit additions with trading in the ones.

Create different addends for each sum.

Write a problem to suit each number sentence.

237 + 123 =

209

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Salespeople often use ‘counting on’ when giving a customer their change. EXAMPLE What change did I get if I bought a pencil for 65 cents and I paid with one dollar?

Pencil 65c + = 70c + = 80c + = $1.00. I received 35c change.

Five people each handed $5 to the salesperson to buy things. Show how you would count out the change by drawing tally marks under each coin you would give the customer.

Total change

a Pencil $3.50 $ .

b Scissors $4.20 $ .

c Eraser $1.40 $ .

d Ruler $2.80 $ .

e Tape $1.75 $ .

DRAFT

Calculate the change that each person would receive.

a Aki handed over $5 when he bought a tin of baked beans costing $3.60.

b Kirsty handed over $4 when she bought a juice box costing $1.80.

c Max handed over $5 when he bought a carton of milk costing $2.70.

d Zeedan handed over $20 when he bought a book costing $18.50.

e Tara handed over $5 when she bought an apple for $0.80.

Strategy

Evaluating strategies

There are many strategies that you can use to solve addition problems, such as levelling, compensation, bridging to decades and the split strategy.

g a guitar and a skateboard

h two guitars and a set of headphones

i two skateboards and two tennis racquets 125 + 24

A teacher wrote the sum 125 + 24 on the board and asked the children to solve it mentally.

a Write the mental strategy you used to solve it.

b Find another person in the class who solved it in a different way to you and describe their method.

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Use a 1 L measuring jug or 1 L milk carton to measure the capacity of these items.

a A kettle

b A large bowl

c A tote tray litres litres litres

Solve the problems.

a Mum put 45 L of petrol in her car and 38 L of petrol in Dad’s car. How many litres was that in total?

b Some campers took an 80 L water container camping.

If they drank 62 L, how much water was left?

How many of each container could be filled from the 40 L oil drum?

DRAFT

Litre containers can be various shapes. Two litre containers have been supplied. Find and sketch some more.

Trading in 3-digit subtraction

Solve the problems.

a What is the difference in price between Mall Madness and Crazy Car Chase?

c What is the difference in price between Create-a-Word and Amazing Art Drawing Software?

e How much would I pay for two copies of Amazing Art Drawing Software?

b What is the difference in price between Amazing Art Drawing Software and Sonic Penguin?

d How much would I pay for Mall Madness and Sonic Penguin?

f What change would I get from $150 if I bought Crazy Car Chase and Sonic Penguin?

Fractions of a quantity

Find the fraction of each quantity.

a 1 2 of 8 carrots =

b d 1 2 of 12 apples = 1 5 of 10 squares =

Melinda baked eight cakes.

c 1 4 of 8 triangles =

a Her daughter Alisha ate half of all the cakes. How many was that?

b Her son Zak ate one-quarter of all the cakes. How many was that?

c How many were left for Melinda?

Use division facts to solve the problems.

a How many students went on the music camp if 1 5 of the 30 children in our class went?

Fractions can show part of a quantity. 1 3 of 6 boys = 2 boys 1 5 of 25?

Think 25 ÷ 5 = 5.

b How many points did Ashleigh score if she scored 1 4 of our team’s total of 24?

c When we did our traffic survey we found out that 1 2 of the children walk to school. How many walk if there were 40 children in our survey?

d How old is Elizabeth if she is 1 5 the age of her sister Rachael, who is 15 years old?

Answer the questions.

Represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

Turns

A turn is the amount of rotation around a centre point. Some common turns are 1 4 turns, 1 2 turns, 3 4 turns and a full rotation of the compass (clockwise). This shape has been rotated around a full turn.

Write the amount of turn for each shape: 1 4

Start Turns

1 (full rotation).

Start Turns

Performs transformations by combining and splitting two-dimensional shapes Represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

Time intervals

The hands on a clock tell us a lot of information.

The hour markers on the clock tell us the hour, but also count off lots of 5 minutes or 5 seconds. This clock shows: 3 the hour shown by the hour hand

5 minutes past the hour, shown by the minute hand

25 seconds counted off by the second hand The time on the clock is 5 minutes past 3. We do not usually include the seconds unless an extremely accurate time is needed.

On the watches below, draw a minute hand to complete the time.

DRAFT

On the watches below, add a second hand to show the seconds.

Twelve ten and twenty seconds

Twelve twenty-five and five seconds

Twelve twenty and fifteen seconds

Ten twenty and thirty-five seconds

Estimate a length of time for each activity (for example, 20 minutes).

Activity

a Play half a game of football

b Sneeze

c Lunchtime at school

d Read a small book

e Wash the car

f Brush my teeth

Time units

Do you know your tables? Your teacher will give you 35 seconds to complete each table.

What happens when you multiply a number by 10?

a 5 books = $

b 6 pens = $

c 10 glue sticks = $

d 3 calculators = $

e 4 staplers = $

4 books and a stapler = $

6 glue sticks and a calculator = $

8 pens and a book = $

6 calculators and a stapler = $

2 books and 7 pens = $

Can you say your 2, 3, 4, 5 or 10 times tables in less than 30 seconds? Work with a partner to find out.

Sometimes it’s easier to solve additions if you do levelling. In other words, you balance both numbers to more manageable numbers. For example, 38 + 36 can be viewed as 40 + 34 = 74.

Add 2 Subtract 2

Solve these additions using levelling.

a 68 + 25 becomes 70 + 23 =

b 37 + 46 becomes + =

c 49 + 38 becomes + =

d 66 + 34 becomes + =

e 78 + 36 becomes + =

f 86 + 23 becomes + =

g 117 + 26 becomes + =

h 128 + 42 becomes + =

i 139 + 36 becomes + =

j 148 + 37 becomes + =

A subtraction method is to apply the constant difference strategy. Again, you need to balance both numbers.

For example, 84 – 27 can be viewed as 87 – 30 = 57

Add 3 Add 3

Solve the subtractions using the constant difference strategy.

a 83 – 28 becomes 85 – 30 =

b 76 – 37 becomes – =

c 93 – 47 becomes – =

d 146 – 38 becomes – =

e 173 – 57 becomes – =

f 127 – 38 becomes – =

136 + 38 becomes 140 + 34 = 174

Much easier!

184 – 26 becomes 188 – 30

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

I found block 2 at grid reference E3. 2

Sam put all his letter, number and shape blocks into a stack. He then labelled them across from A to G and up from 1 to 5.

Find the blocks from the grid references. Remember to read ACROSS before UP. The first one is done for you.

Give grid references for these blocks.

Draw on the blocks on the grid at the top of the page.

a Draw a hand on the block with a grid reference of B4.

b Draw a face on the block G1.

c Put a cross on the block C5.

d Colour the block D4.

Find the secret word by writing the letters found at each grid reference.

Favourite T-shirt colours

Every student in Mrs Cook’s class drew a picture of their favourite coloured T-shirt. They drew the first letter of the colour on the drawing of their T-shirt before pinning their drawings up on the wall.

Represent each coloured T-shirt using tally marks. Red White Blue Pink

Answer the questions.

a Which was the most popular coloured T-shirt?

b Which T-shirt colour had a tally of 4?

c Which was the least popular colour of T-shirt?

d How many more children like blue than like pink?

e What coloured T-shirt do you like the most?

f Carrie said that all girls like blue T-shirts the best. If there are 15 girls in Mrs Cook’s class, do you think she was correct?

Use your tally to make a column graph of the T-shirt colours. Colour one square on the graph for each T-shirt.

Favourite T-shirts

Yellow Orange

Compensation strategy

The compensation strategy involves rounding one of the numbers so that you can work out the answer in your head. Later you have to take off the amount you rounded, e.g. 54 + 38 =

Think 54 + 40 = 94, then take off the 2 that was rounded up. The answer is 92.

Use this strategy to complete these additions. The first one has been done for you.

a 26 + 38 becomes 26 + 40 2 = 64

b 34 + 27 becomes + =

c 28 + 39 becomes + =

d 46 + 28 becomes +

e 27 + 49 becomes +

f 35 + 48 becomes +

g 56 + 27 becomes +

h 63 + 28 becomes +

i 47 + 49 becomes +

j 76 + 37 becomes +

Mario has completed these operations on a calculator but has made some mistakes. Use your estimation skills to decide which ones he should do again.

Question Good Do again

Question Good

a 38 + 43 = 81 h 71 + 28 = 80

b 27 + 61 = 88 i 52 − 27 = 35

c 74 − 37 = 57 j 68 + 24 = 92

d 49 + 33 = 62

e 92 − 56 = 13

f 62 + 27 = 89

g 39 − 22 = 37

k 96 − 38 = 48

l 82 − 39 = 43

m 48 − 33 = 15

n 93 − 37 = 76

When adding 56 + 39, think 56 + 40 – 1 = 95.

Division facts and strategies

Use known facts or the arrays to answer the questions.

Use known facts to solve the problems.

a 10 marbles shared among 5 boys.

b 15 football cards shared among 3 girls.

c $40 shared among 10 sisters.

d 9 cows shared among 3 paddocks.

e $24 shared among 4 children.

f 32 eggs shared among 4 people.

g 40 chickens shared among 4 families.

Solve the secret code by exchanging numerals for letters.

Testing predictions

Predict answers to the following questions.

Prediction

What will the colour of the next car to pass our school be?

What will the most popular colour car to pass our school be?

Survey

With your teacher, conduct a survey of the colours of cars passing, or parked in or around, your school. Complete the survey details on the grid. Fifty cars will be enough. Use tally marks to record your survey information on this grid.

Silver Black White

Construct a dot plot to record your results. The vertical axis shows how many cars. The horizontal axis shows what colour car.

Silver Black White Other

What colour was the next car to pass the school?

What was the most popular colour car to pass the school?

I think red is the most popular.

Fruit and vegetables are often sold in kilogram lots. Record the mass of each purchase.

Look carefully at the scales in the picture. What can be learnt from them?

Solve the problems.

a Julia travelled from The Ship to Roller Coaster. If she passed through Bumper Cars, how far did she travel?

b Marco travelled from The Ship to Ferris Wheel. If he passed through Gravitron, Carousel and The Tower, how far did he travel?

c Write another problem based on this map.

Use any strategy you wish to solve the problems. Problem

a Our hens laid 80 eggs on Saturday and 65 on Sunday. How many eggs did they lay over the weekend?

b Farmer Green sheared 43 sheep on Monday, 44 on Tuesday and 42 on Wednesday. How many sheep has he shorn?

c If 75 cows were milked this morning and 75 will be milked this afternoon, how many will be milked today?

d The water tank has 123 L of water. If a further 47 L of water are added, how much water will there be in the tank?

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Fractions on a number line

Draw lines to place the fractions in the correct positions on the number line.

James and Jacinta were told to fold their paper strips into fifths.

a Explain why James has done it incorrectly.

b Jacinta said that 1 5 is a bigger fraction than 1 10 . Explain why.

Shade the fractions of each bar.

Represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)

Polygons – trapeziums, rhombuses and kites

Polygons are two-dimensional shapes with three or more straight sides. Examples include triangles, quadrilaterals, pentagons and hexagons. A few trickier polygons are mentioned below.

A trapezium is a four-sided polygon with one set of parallel sides.

A rhombus is a polygon that has four equal sides with the opposite angles being equal.

A kite is a four-sided polygon that has two pairs of equal sides. None of the sides are parallel to other sides.

Classify the shapes below by writing R for rhombus, T for trapezium, or K for kite on them.

Compares two-dimensional shapes and describes their features

Square centimetres are not suitable for measuring large areas.

Large areas such as the area of a room are measured using square metres.

The symbol for square metre is m²

Make your own square metre.

Using newspaper, stick pieces together to make a square that is one metre wide and one metre long.

Use your square metre to measure the area of these places. Make an estimate first. Place Estimate Area

a The area of a large table square metres square metres

b The area of a handball court square metres square metres

c The area of a small room square metres square metres

d The area of a square drawn on the playground with 4 m sides square metres square metres

8 9 10

Look carefully at the shape above. It is 2 m long and 1 2 m wide. Does it take up a square metre of space?

Explain why.

3-digit subtraction (trading)

Complete the 3-digit subtraction algorithms with trading in the tens.

Find the missing digits in each subtraction.

DRAFT

Four children have each been saving to buy the Racer.

Special $469

Racer

Calculate how much more each person needs to save before they can buy the car.

Reuben has saved $137.

has saved $318.

has saved $267.

Erin has saved $375.

4-digit numbers

The 4 in 4527 is worth a lot more than the 4 in 5436.

d 6740 = + + + e 8407 = + + +

f 9936 = + + +

6 7

Place each set of numbers in descending order (highest to lowest).

a 8507, 7503, 5073, 3057

b 2645, 3658, 1999, 2500

c 2907, 8436, 3541, 2657

d 3524, 5234, 2453, 4532

e 837, 238, 1438, 2745

Octa means eight. An octagon is a shape with eight sides.

A regular octagon has all its sides equal in length and all its angles equal. Regular octagon Irregular octagon

Carefully count and then record the number of sides and angles on each shape. Write the name of each shape on the shape.

Join the dots to form the shapes, then write their names on them.

Answer the questions.

a How many sides on two pentagons and three octagons?

b How many sides on two hexagons and five triangles?

c How many sides on five squares and two octagons?

Cubic centimetres

Jack cut the front off two identical boxes then filled one with centicubes and the other with marbles.

a Which unit do you think was better for measuring the volume of the boxes?

b Explain why.

A standard unit for measuring volume is the cubic centimetre The abbreviation for cubic centimetre is cm³. A cubic centimetre is a cube that has 1 cm sides.

Make these models from centicubes or Base 10 ones, then record their volumes by counting the number of cubes used in their construction.

Ava made this object with a volume of 8 cubic centimetres. Make another object with a volume of 8 cubic centimetres.

Multiplication mental strategies

When multiplying a one-digit number by a multiple of ten, we can use the strategy of repeated addition.

Use repeated addition to multiply the numbers. The number line above may assist you.

We can also use place value strategies to multiply by a multiple of 10. E.g. 4 × 20 becomes 4 × 2 tens = 8 tens = 80.

Use this strategy to multiply the numbers below.

Write as many multiplication number sentences as you can to create 120. 3

a How many groups of 5?

b How many groups of 3?

a How many groups of 4?

b How many groups of 5?

c How many groups of 10?

d How many groups of 2?

Another method of solving division is to use known table facts, e.g. 20 ÷ 5. Think 4 × 5 = 20, so the answer is 4.

7

At the start of the year Mrs Miller put 32 children into 4 sports teams. How many children in each team?

When giving grid references, always read the horizontal axis first (A to I) then the vertical axis (1 to 3). Arun’s house can be found at E1.

The closest bus stop to Jill’s house is on the intersection of Hope St and Collins St.

Use compass points to answer the questions.

a Is the school to the west of Green Park?

b What direction would Ben travel along Brown St to go to Sam’s house?

c What direction would Jill travel along Green St to go to Green Park?

Jimmy has a bag of 20 marbles.

a How many of the marbles are red?

b How many of the marbles are blue?

c How many of the marbles are pink?

d How many of the marbles are green?

e How many of the marbles are yellow?

Use the data you have collected above to answer the questions.

a Is it more likely that a red marble will be pulled out of the bag than a green one?

b Is it less likely that a green marble will be pulled out of the bag than a yellow one?

c Is it more likely that a green marble will be pulled out of the bag than a pink one?

Mr Brown placed 12 coloured marbles in a bag. He asked each child to select one marble at a time and then to put it back into the bag. Colour the label which best describes the chance of pulling out each colour.

There are 10 counters in a box. They are made up of three different colours. The counter that is most likely to be drawn out of the box is green, the least likely colour is red and the colour which has a slightly better chance than red is blue.

Colour the counters to display these chances.

Solve the following.

Solve the additions using the compensation strategy or any other strategy.

e 46 + 28 =

f 34 + 39 =

g 27 + 49 =

h 54 + 29 =

i 27 + 37 =

Answer the multiplications.

k I bought 6 packets of nails. If there are 5 nails in each packet, how many nails did I buy?

Check Kuljit’s subtractions by repeating them yourself.

2

What did Kuljit forget to do in question 1b above?

Amelia did four calculations on her calculator and has given us her answers. Use a calculator to check, then mark her work by giving her a tick or a cross in each box.

a 6 books cost $46

b A watch and a skateboard cost $60

c 7 calculators cost $105

d 5 watches cost $150

Jarrah has done five subtractions. His teacher asked him to check them by doing additions. He has done the first one, can you do the rest?

5

When numbers are added it doesn’t matter in which order they are added, e.g. 4 + 5 = 9, 5 + 4 = 9.

Add the following numbers to see if this is true.

a 6 + 4 = 4 + 6 =

b 7 + 6 = 6 + 7 =

c 9 + 7 = 7 + 9 =

d 10 + 12 = 12 + 10 =

e 16 + 4 = 4 + 16 =

f 18 + 5 = 5 + 18 =

g 16 + 8 = 8 + 16 =

6

Enter some large numbers on your calculator to see if the order they are added in makes a difference.

7 8 9

For each fact given, write another multiplication fact using the same numbers. The first one is done for you.

Can numbers be multiplied in any order?

What did you notice?

Solve the problem.

Mitchell hit six fours and then was bowled out. Georgia hit four sixes and then was caught out. Who scored more runs: Mitchell or Georgia?

Drawing objects 28

Sketch each 3D object. Try to show how long it is, how wide it is and how tall it is.

Below are two drawings of a square pyramid from different views. Sketch the pyramids with the help that has been given, then draw them by yourself.

Model object

With some help

My drawing

Makes and sketches models and nets of three-dimensional objects including prisms and pyramids

Baked Beans

Perfume

Kilograms

Many items are packaged in half-kilogram packages. Half a kilogram is 500 grams.

Fruit and veg. Estimate Amount

Apples

Oranges

Bananas

Tomatoes

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

3-digit addition (trading) 29

Complete these additions with trading in the tens. The first one is done for you.

Complete these additions with trading in the tens and ones.

Calculate the cost of the following items.

A farmer has 24 sheep that will need to be separated into equal groups for shearing.

Write a number sentence to solve each problem.

Problem

a Farmer Bindi wants to put the sheep into three paddocks. How many will be in each paddock?

b Farmer Mills wants to put the sheep into six paddocks. How many sheep will he have in each paddock?

c Farmer Hassan wants to put the sheep into two paddocks only. How many sheep will he have in each paddock?

d Farmer Julie wants to put the sheep into four paddocks. How many sheep will she have in each paddock?

Solve these problems.

a Divide 18 people into 3 groups.

b Share 20 marbles among 5 children.

c Divide 24 plants into 4 groups.

d Share 25 cakes among 5 people.

e Share 30 teddies among 5 girls.

f Break 20 lollies into 4 groups.

g Share 30 marbles among 6 children.

h Share 30 fish into 5 fish bowls.

i Share 40 chocolates among 5 boys.

Number sentence

This parallelogram’s opposite sides are of equal length and are parallel to each other.

A rectangle is a parallelogram because its opposite sides are of equal length and are parallel to each other.

Colour the shapes below that are parallelograms.

DRAFT

A square is also a parallelogram because its opposite sides are equal and parallel to each other.

A rhombus is a parallelogram because its opposite sides are equal and parallel.

Use the dot paper to complete these models of three parallelograms.

Answer the questions.

a Which shapes above are parallelograms?

b Which shapes have parallel sides but are not parallelograms?

c Which shapes have no parallel sides?

Parallelograms are four-sided shapes (quadrilaterals) where each pair of opposite sides are parallel and of equal length. Identifies angles and classifies them by comparing to a right angle

d Do all parallelograms contain at least one right angle?

Answer true or false.

a Blue is the most likely colour to be spun.

b The spinner is more likely to spin yellow than green.

c Red is the least likely colour to be spun.

d The spinner is more likely to spin yellow than blue.

e The spinner is less likely to spin red than blue.

f There is no chance of spinning purple.

g Green is more likely to be spun than all the other colours combined.

Mr Borg gave his class a spinning wheel divided into 10 sections. He asked his class to colour the sections to reflect the chances of the colours being spun, shown on the labels below.

a

Green has only one chance of being spun.

b

Red is twice as likely to be spun than green.

c

Pink has twice the chance that red has.

d

Yellow has more chance than red but less than pink.

11

Answer the questions.

a What are the possible outcomes when drawing a lolly out of this box?

LolliesSuper

b Are you more likely to pick out a black lolly than a blue lolly?

Yellow Blue

Green Red

Trading Cards ALBUM

Angelo had 3133 trading cards in one album and 2119 in another. How many did he have altogether?

Add 3 thousands plus 2 thousands equals 5 thousands.

3 ones plus 9 ones equals 12 ones. Trade 10 ones for 1 ten. Record 2 in the ones column. Add 1 hundred plus 1 hundred equals 2 hundreds.

Add 1 ten plus 3 tens plus 1 ten equals 5 tens.

Jack worked out a way to add 500 + 650 easily. He added 500 + 500 to make 1000 and then added 150 more to make 1150.

Use any mental strategy you wish to add these numbers mentally.

300 + 425 =

500 + 617 =

600 + 780 =

800 + 965 =

600 + 837 = b 600 + 725 =

Complementary fractional parts

The complement of a fraction is the number of parts that haven’t been counted. For example, if you look at 3 5 , then 2 5 is the complement because it takes both 3 5 and 2 5 to make the whole ( 5 5 ).

Write the shaded fraction and the complementary fractional part for each.

Write the complementary fraction of each strip below.

Extend each strip to one whole.

8

30 Constant difference in subtraction/estimation

Sometimes it’s easier to solve subtraction if you balance both numbers to more manageable numbers. For example, 83 – 36 can be viewed as 87 – 40 = 47.

Add 4 Add 4

74 – 39 becomes

75 – 40 = 35 Much easier!

DRAFT

i 163 – 38 becomes – =

j 262 – 47 becomes – =

Example

Round up to 50 Round down to 30

48 – 33 is about 20

a 79 – 31 is about

b 63 – 22 is about

f 88 – 34 is about

g 99 – 51 is about

c 87 – 24 is about h 73 – 47 is about

d 83 – 58 is about i 172 – 37 is about

e 92 – 47 is about

j 264 – 46 is about

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

Quadrilaterals are shapes that have 4 straight sides. There are many types of quadrilaterals and some have special names.

A B C

A square is a quadrilateral that has 4 equal sides and 4 right angles.

A rectangle is a quadrilateral that has 2 pairs of equal sides and 4 right angles.

A rhombus is a quadrilateral that has 4 equal sides and the opposite angles are equal.

D E F

A trapezium is a quadrilateral with one set of parallel sides.

A parallelogram is any quadrilateral with 2 sets of parallel sides.

Draw an example of each quadrilateral listed above.

A kite is a quadrilateral that has two pairs of equal sides. None of the sides are parallel to other sides.

Answer the questions.

a Do all quadrilaterals have parallel sides?

b Which quadrilaterals (A to F above) have all sides of equal length?

Write the numbers on the place value chart. The first one has been done for you.

Write the place value of each bold digit.

Expand each number. The first one has been done for you.

The 4 in 4679 is worth a lot more than the 4 in 8046.

Order the numbers from least to greatest.

Patterns on hundreds charts

5

Counting by 3 and 6

31

a Start at 3 and circle all numbers as you count by 3 to 100.

b Start at 6 and colour all numbers blue as you count by 6 to 100.

c What patterns do you see?

6

More patterns

a Start at 9 and circle all numbers as you count by 9 to 100.

b Put a cross on all numbers that are 5 less than any number ending in 9.

c What patterns do you see?

Can you see any other patterns on the hundreds chart? What are they? 7

Continuing a pattern

a What is the next number in this pattern?

b Continue the pattern.

c If the pattern was extended past 100, what would the next four numbers be?

Nets 31

Find a small cardboard box, such as a thumbtack box, sultana packet or staples box, and carefully tear along the edges until you can lay it out flat.

Study its net and sketch it in the space opposite.

Find a larger box, such as a cardboard fruit box, and pull it apart to reveal its net.

Study its net, then sketch it below.

Makes and sketches models and nets of three-dimensional objects including prisms and pyramids

Grams are used to measure objects that are not very heavy. 1 kilogram = 1000 grams.

The packet of oats is 400 g.

Use a pan balance to see how many of these standard masses are needed to balance 1 kg.

What is the total mass of these masses?

Number patterns 32

Complete the pattern up to eight numbers, then state what the tenth number would be. a 40 36 32 28 24

8 16 24 32 40

What would the tenth number be? What would the tenth number be?

7 14 21 28 35

18 27 36 45

What would the tenth number be? What would the tenth number be? Complete the fraction patterns.

What did you learn?

Subtract 6 from this group of numbers.

What did you learn?

Make up a number pattern that adds 7 to a sequence of numbers.

Subtraction bar models

Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers Completes number sentences involving addition and subtraction by finding missing values

I am a shape that has 4 right angles and 4 sides the same length. I am drawn with my base on a different orientation.

I am a shape that has 4 right angles. I have 2 shorter sides the same length and 2 longer sides the same length.

I am a 3-sided shape. I have 3 angles the same size and 3 sides the same length.

I am an irregular shape that has 5 sides. My angles and side lengths are not always the same size.

I am a regular shape with 6 sides. All my angles are the same size. All my sides are the same length.

I am a 3-sided shape. I have 2 angles the same size and 2 sides the same length.

I am a regular shape that has 5 sides. All my angles are the same size. All my sides are the same length.

I am a regular shape with 8 sides. All my angles are the same size. All my sides are the same length.

I am a quadrilateral. I have one pair of parallel sides only.

I am a quadrilateral. None of my angles are the same size, all my side lengths are different. None of my sides are parallel.

I am an irregular shape that has 8 sides. My angles and side lengths are not always the same size.

Cubic centimetres

Find a small box, such as a sultana packet or small chalk box, and fill it with cubic centimetre blocks, e.g. centicubes or Base 10 ones.

What was the volume of the box? cm3

Make these models from centicubes or Base 10 ones, then record their volumes by counting the number of cubes used in their construction.

Which model has the smallest volume?

Which model has the largest volume?

Which four models have the same volume?

SULTANAS SULTANAS

Samantha had $3476 in her bank account but spent $2232 on a new TV. How much did she have left?

Solve the problems. 2

a How much more expensive is the watch than the ring?

b How much more expensive is the ring than the bracelet?

When numbers are added, it doesn’t matter in which order they are added, e.g. 2 + 7 + 8 = 17 8 + 7 + 2 = 17 7 + 8 + 2 = 17

When numbers are multiplied, it doesn’t matter in which order they are multiplied,

Complete the sets of number sentences to see if the rule above is true.

a 6 + 5 + 4 =

b 7 + 5 + 6 =

d

e

f

=

Write your own multiplication number sentences.

Rewrite each number sentence to make it easier to solve.

a 6 + 8 + 4 = becomes + + =

b 17 + 9 + 3 = becomes + + =

c 18 + 7 + 2 = becomes + + =

d 9 + 15 + 5 = becomes + + =

e 17 + 4 + 6 = becomes + + =

f 5 × 7 × 2 = becomes × × =

Who baked the most cakes?

Dad baked enough cakes to fill 2 trays with 5 rows of 4 cakes on each tray. Grandma baked enough cakes to fill 4 plates with 2 rows of 5 cakes on each plate.

Non-standard partitioning

Complete the numeral expanders to show how the numbers can be partitioned in different ways.

How many tens in each number?

a 374

b 563

c 727

d 805

e 297

8 9

How many hundreds in each number?

a 3546

b 2780

c 3676

d 8504

e 3874

f 5679

What number is 354 tens and 6 ones? 3446, 3546, or 6453?

Millilitres are used to measure small quantities of liquid. The symbol for millilitres is  mL. There are 1000 mL in one litre (1 L).

Use a 1 millilitre eye dropper to measure the capacity of a teaspoon. You may have to balance the teaspoon with a pencil.

Use a 50 mL medicine glass to measure the capacity of four caps that you can find around the school. For example, the cap from a bottle of water, or a glue stick.

4

Fractions can be written as decimals.

E.g. 25 out of 100 can be written in the decimal form as 0.25

The decimal point separates the fractional part from the whole number.

Order the decimals you marked on the metre ruler above from smallest to largest. Smallest Largest

Double and double again to multiply by four.

a 2 × 4 = f 7 × 4 =

b 3 × 4 = g 9 × 4 =

c 5 × 4 = h 8 × 4 =

d 4 × 4 = i 10 × 4 =

e 6 × 4 = j 1 × 4 =

Double a smaller times table to find the answer.

a 3 × 6 = e 10 × 6 =

b 5 × 6 = f 9 × 6 =

c 2 × 6 = g 7 × 6 =

d 4 × 6 = h 6 × 6 =

the skip counting patterns for 6, 7, 8 and 9.

Use the skip counting patterns above to complete the multiplication number sentences.

Combining and splitting shapes

Reflect, rotate and translate the tangram shapes to construct the designs shown on the right. Use tangram sets, or trace over the tangram below and cut it out to complete the activity.

DRAFT

Use tangrams to construct these shapes. Help has been given by shading some tangram shapes.

Length using decimal notation

Length can be measured in metres.

Write m for metre or cm for centimetre to show which unit you would use to measure these lengths.

a Length of a matchbox

b Length of a car

c Length of a book

d Length of a glue stick

e Length of a soccer field

f Length of the playground

Decimal notation can be used to record lengths or distances, e.g. 1 metre 35 centimetres can be recorded as 1.35 m.

Convert each measurement from metres and centimetres to metres using decimal notation.

a 1 m 65 cm = 1.65 m

b 2 m 75 cm =

c 3 m 45 cm =

Problem solving

Find the difference in cost between the:

a watch and calculator $ d scooter and calculator $

b watch and kettle $ e scooter and kettle $

c kettle and calculator $ f laptop and scooter $

Solve the problems, then check them using a calculator.

a How much would a watch and scooter cost? $

b How much would a kettle and watch cost? $

c How much for a calculator, laptop and watch? $

d How much for 5 calculators? $

e How much for 10 watches? $

f If John bought 2 kettles, how much change would he receive from $100? $

g If Anna bought a calculator and a watch, how much change would she receive from $50? $

h If Kelly bought a scooter and a calculator, how much change would she receive from $200? $

i How much more does a scooter cost than a watch? $

j Jamal bought a watch and a scooter. If he paid for them with four $50 notes, how much change did he receive? $

Missing numbers 35

Ms Wu wrote a number sentence and an answer on the board. Her head blocked out the sentence but we could see the answer was 24. What could the number sentence have been? Write some solutions. The first one has been done for you.

Use + , and × symbols in the number sentences below to make them true.

Penta means five. A pentagon is a shape with five sides. A regular pentagon has all its sides equal in length and all its angles equal.

Which of the shapes above are: a triangles? b pentagons? c hexagons?

Use the dot paper to draw two pentagons of your own.

b

35 Square centimetres

Calculate the area of each of the shapes below by counting the square centimetres. The short way of writing square centimetres is cm2.

Which shape’s area was the hardest to measure? Why?

Can you find a better way to count the square centimetres on squares and rectangles? What is it?

Solve the problems.

a Mr Bean saved $136 in May and $138 in April. What are his savings for the two months?

b Juanita had 28 marbles to share among 4 people. How many did each receive?

c Aki had a bag of 252 pegs but used 124. How many pegs were left?

5

a Start at X and travel north 4 spaces.

b Turn east and travel 3 spaces.

c Turn south and travel 3 spaces.

d Head east 4 spaces then north 3 spaces.

e Head west 2 spaces.

f What shape did you find?

abacus

An instrument used for calculating.

ascending order

An arrangement of numbers from smallest to largest.

256, 291, 307, 452

associative property

Thou Hund Tens Ones

acute angle

An angle less than 90°

acute angle

addition (+)

The operation that finds the sum or total. am ( ante meridiem )

The morning. Any time from midnight to noon, e.g. 7:30 am is 7:30 in the morning.

analog clock

A clock face with numbers 1 to 12, and two hands.

A series of numbers can be added in any order without changing the result.

5 + 4 + 6 = 15

4 + 6 + 5 = 15

6 + 5 + 4 = 15

A series of numbers can be multiplied in any order without changing the result.

5 × 4 × 3 = 60

4 × 3 × 5 = 60

3 × 5 × 4 = 60

axis of symmetry

An imaginary line that divides a shape exactly in half. If a shape is folded along this line, both sides will match.

angle

The amount of turn between two arms around a common endpoint (the vertex).

arm area

amount of turn vertex arm

The surface covered by any 2D shape. Area can be measured in cm2, m2, hectares and km2.

3 cm

Area = 6 cm2

array

2 cm

An arrangement of objects or symbols into rows and columns.

base

The bottom line of a 2D shape.

base

The bottom face of a 3D object.

base

• pyramids have one base base

For example:

• prisms have two bases. base base

capacity

The amount a container can hold. Capacity can be measured in millilitres (mL), litres (L) and kilolitres (kL).

centimetre (cm)

A unit for measuring length. 100 cm = 1 metre 0 1 2 3

circle

A plane shape bounded by a continual curve that is always the same distance from the centre point.

column graph (bar graph or bar chart)

A column graph generally uses vertical columns to represent data. In a bar graph or bar chart the bars can be either vertical or horizontal.

coordinate points

Coordinates or grid references locate points or positions on a grid. The horizontal position is given before the vertical position, e.g. the circle is located at (C,3).

corner (vertex)

The point where two or more lines meet to form an angle.

cross-section

The face that is left when a solid (3D) object is cut through, parallel with its base.

cube

commutative property

Two numbers can be added in any order to give the same total.

15 + 13 = 28 13 + 15 = 28

Two numbers can be multiplied in any order to give the same product.

5 × 4 = 20 4 × 5 = 20

compass points

The cardinal compass points are north, south, east and west.

(north)

(east) (west) E W N S

(south)

A 3D object with six square faces, eight corners and twelve edges.

cubic centimetre

A unit of volume. A centimetre cube has a volume equal to one cubic centimetre.

cylinder

An object with two circular faces and one curved surface.

data

Information gathered together, such as a set of numbers or facts.

cone

A 3D object with a circular base, tapering to a point (the apex).

decade

Ten years, e.g. 2013–2023. Also, a group of tens.

decimal

A fraction can be written as a decimal, e.g. 75 out of 100 can be written as 0.75 in decimal form.

Blue Orange Red Yellow Green

decimal point

A point used to separate the fraction part from the whole number.

whole number part

decimal point

denominator

4.75

edge

The intersection of two faces on a 3D object.

fraction part

The bottom number of a fraction that tells how many equal parts there are in the whole.

1 4 numerator denominator

descending order

An arrangement of numbers from largest to smallest, e.g. 108, 99, 76, 54

diagonal

A straight line which joins two non-adjacent corners of a polygon. diagonal

digital clock

A clock which displays only numbers. It has no hands.

dimension

A measurement of length, width (breadth) or height.

height width (breadth) length

division ( ÷ )

The operation that breaks groups or numbers into equal parts. 15 ÷ 3 = 5

double

Multiply by two.

edge

equivalent fractions

Fractions having the same value.

1 2 2 4 even number

A number that can be divided equally by two, e.g. 2, 4, 6, 8, 10, 12. faces

The surfaces of a 3D object. face face face flip (reflect)

To turn a shape over.

fraction

Any part of a whole or group.

front view

The view we see when we look at an object from the front.

3D object

front view

gram

A unit for measuring mass.

1000 grams = 1 kilogram

greater than (>)

The ‘greater than’ symbol shows the relationship between two unequal numbers, e.g.

8 > 5

grid references

Grid references locate positions on a map or grid. The horizontal position is given before the vertical position, e.g. the circle is located at C3.

length

The longer of the two dimensions of a shape.

length

less than ( < )

width (or breadth)

The ‘less than’ symbol shows the relationship between two unequal numbers.

5 < 8

grouping

A way of dividing an amount into equal-sized groups, e.g.

hexagon

2

A 2D shape with six straight sides.

line of symmetry

A line which divides a shape in half exactly. Shapes can have more than one line of symmetry.

line of symmetry

regular hexagon irregular hexagon

horizontal

At right angles to the vertical.

vertical line

horizontal line

hundredth

One part of a whole that has 100 parts altogether.

kilogram (kg)

The base unit for measuring mass.

Flour

1 kg

1 kg = 1000 grams

kilometre (km)

A unit of length.

1 km = 1000 metres

litre (L)

A unit of capacity.

1 L = 1000 millilitres

mass

DRAFT

The amount of substance in an object.

1000 grams = 1 kg

1000 kg = 1 tonne

metre (m)

A unit of length.

1 metre = 100 cm

millilitre (mL)

A unit of capacity. An object with a volume of 1 cm3 displaces 1 mL of water.

millimetre (mm)

A unit of length.

multiple

1 cm 1 cm

1000 mL = 1 litre 1 cm

10 mm = 1 centimetre

The result of multiplying a given number by any other number is a multiple of that given number.

Multiples of 4 are: 4, 8, 12, 16, 20, etc.

Multiples of 5 are: 5, 10, 15, 20, 25, etc.

groups of 4 in 8

multiplication (×)

The operation which finds the product of two or more numbers. Multiplication can be seen as repeated addition.

2 + 2 + 2 + 2 + 2 = 10 5 × 2 = 10

parallelogram

A four-sided 2D shape which has two pairs of opposite sides that are parallel and of equal length.

pattern

net

A flat shape that can be folded to make a 3D object.

number line

A line on which numbers are marked. Number lines can be used to represent calculations.

3 + 5 = 8

0 1 2 3 4 5 6 7 8 9 10

number pattern

Any set of numbers that follow a pattern or sequence.

1, 3, 5, 7, ___ , ___ , (The pattern is + 2)

3, 9, 27, ___ , ___ , (The pattern is × 3)

numeral

Any figure used to represent a number, e.g.

0, 1, 2, 3, 4, 5

A series of shapes, letters, numbers or objects arranged in a recurring sequence, e.g.

4, 14, 24, 34 … or

pentagon

A 2D shape with five straight sides. irregular pentagon

regular pentagon

perimeter

The distance around the edges of a shape.

Perimeter = 3 m + 4 m + 5 m

3 m 5m

4 m

numerator

The top number of a fraction, telling us how many equal parts there are out of the whole.

octagon

Perimeter = 12 m

perpendicular lines

Lines that intersect at right angles.

3

4 numerator denominator

A 2D shape with eight straight sides.

regular octagon

odd number

irregular octagon

A number that is not divisible by two, e.g.

1, 3, 5, 7, 9, 11

parallel lines

Two or more lines that never meet and are exactly the same distance apart along their entire length.

picture graph

A graph that uses symbols to represent quantities.

Favourite animals sheep

horse cat hen cow

place value

The value of a digit determined by its place in the number.

plan

A diagram from above, showing the position of objects.

quarter

One-fourth of a whole or a group.

= 1 4

1 4 are girls

rectangle

plane shape

A 2D shape.

Example: octagon

pm ( post meridiem )

After midday. Any time between noon and midnight, e.g. 7:30 pm is 7:30 in the evening.

polygon

A 2D shape with three or more angles and straight sides.

prism

Example: octagon

A 3D object that has a pair of congruent parallel bases that are polygons, and rectangular side faces.

product

The answer achieved by multiplication.

9 × 3 = 27

product

A four-sided 2D shape with four right angles and two pairs of parallel sides that are also equal.

square oblong

reflect (flip)

To turn a shape over. rhombus

A four-sided, 2D shape with all four sides equal. A rhombus has two pairs of parallel sides and its opposite angles are equal.

right angle

An angle of 90° .

pyramid

A 3D object that has only one base and all the other faces are triangular, meeting at a point (the apex).

quadrilateral

A 2D shape with four sides, e.g. a square, a rectangle, a rhombus and a parallelogram. rhombus

rigid

A fixed shape that cannot be pulled out of shape.

rotate (turn)

To turn an object around a fixed point.

rigid non-rigid

point

rounding

Changing an exact value to an estimated value of a more convenient size.

69 70 (rounded to the nearest 10)

785 800 (rounded to the nearest 100)

side view

The view we see when we look at an object from the side.

3D object side view

skip counting

To count by adding the same number each time.

4… 8… 12… 16… 20…

Skip counting by 4

slide (translate)

To move a shape to a new position without turning it.

square kilometre (km2)

A unit for measuring area.

1 km

1 km

1 km × 1 km = 1 km2

square metre (m2)

A unit for measuring area.

1 m

1 m

1 m × 1 m = 1 m2

subtraction (−)

The operation which removes part of a group, and finds the difference.

sphere

A perfectly round 3D object, e.g. a ball.

square

A 2D shape with four equal straight sides and four right angles. A square is also a rectangle.

square centimetre (cm2)

A unit for measuring area.

1 cm 1 cm

1 cm × 1 cm = 1 cm2

DRAFT

9 5 = 4 difference

sum

The answer of addition. The total.

symmetry

A shape has line symmetry if both parts match when it is folded along a line.

tally

To keep count by placing a stroke to represent each item. The fifth stroke crosses the four preceding strokes each time.

= 22

tessellation

A pattern formed by the repetition of shapes so that they fit together without gaps.

three-dimensional (3D)

A description of solid objects having three dimensions: length, width (breadth) and height. length

time

twelve-hour time

Time shown by traditional clocks and watches, divided into 12 hours.

twenty-four-hour time

width

height (breadth)

60 seconds = 1 minute

60 minutes = 1 hour

24 hours = 1 day

365 days = 1 year

366 days = a leap year

timeline

A line representing a span of time.

Born School High school Work Married

1998 2003 2008 2013 2018 2023

tonne

A unit of mass.

top view

1000 kg = 1 tonne

The view we see when we look at an object from the top.

3D object

translate (slide)

To move a shape to a new position without turning it.

trapezium

A four-sided, 2D shape with only one pair of parallel sides.

triangle

A 2D shape with three sides and three angles.

turn (rotate)

To move an object around a fixed point.

Time divided into 24-hour time intervals numbered from 1 to 24, so as to distinguish between times in the morning and times in the afternoon.

two-dimensional (2D)

Plane shapes have only two dimensions: length and width (breadth).

vertex

DRAFT

The point where two or more lines meet to form an angle.

vertical

vertex

At right angles to the horizontal. horizontal line vertical line

top view

volume

The amount of space a 3D object occupies.

volume = 2 × 3 × 2 = 12 m3

whole numbers

The counting numbers from one to infinity. 1, 2, 3, 4,

width (breadth)

The shorter of the two dimensions of a shape.

width (breadth)

length

b 3 groups of 3 equals 9

c 3 groups of 5 equals 15

d 2 groups of 6 equals 12

e 4 groups of 6 equals 24

f 5 groups of 6 equals 30

g 4 groups of 4 equals 16 h 5 groups of 4 equals 20

groups of 5 equals 20

groups of 5 equals 25

15 60

UNIT

1 hundreds tens ones 2 8 5

a 285 hundreds tens ones 7 4 3

b 743 hundreds tens ones 8 5 4

c 854 hundreds tens ones 9 9 9

d 999 hundreds tens ones 8 7 0

e 870 hundreds tens ones 8 0 9

f 809

2

a 500 + 20 + 7 g 300 + 40 + 7

b 300 + 60 + 3 h 200 + 90 + 6

c 700 + 20 + 5 i 300 + 90 + 0

d 600 + 90 + 4 j 400 + 70 + 0

e 800 + 50 + 6 k 500 + 0 + 8

f 700 + 90 + 7 l 600 + 0 + 9

3

a 45 < 63 h 153 < 298 o 864 > 67

b 72 > 51 i 504 > 376 p 67 < 325

c 86 > 49 j 900 > 899 q 63 > 9

d 37 < 80 k 401 < 921 r 504 > 405

e 8 < 81 l 569 > 385 s 327 < 723

f 21 < 45 m 216 < 621 t 528 > 347

g 89 > 53 n 308 < 925 u 999 > 100

4 a 2 × 5 = 10 or 5 × 2 = 10

b 3 × 5 = 15 or 5 × 3 = 15

c 5 × 5 = 25

d 4 × 5 = 20 or 5 × 4 = 20

5 a 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

b 6, 10, 14, 12, 16, 4, 2, 0, 20, 8

6 a $20 b 25 km c $45

7 a 30 c 50 e 60

b 25 d 45 f 80

8 All answers will be zero.

9 Hands on.

10

a Lake Spin e Forest Park

b Police f Shops

c Tom’s house g Gina’s house

d Town Hall 11 Yes 12 Yes

Thursday afternoon bowling

Men Women Girls Boys

12

(Multiply L × W or count all placemats needed to cover table.) 13

DIAGNOSTIC REVIEW

g 18 h 60 i 90

j 50 + 8 = 58 k 80 + 9 = 89

l 50 + 9 = 59 m 90 + 9 = 99 Part 2

a 6 18 20 12 24 16

b 3 d 9 f 83 h 80

c 5 e 21 g 30 i 70

Part 3

a 20 b 35 c 24

d 4, 10, 6, 8, 12

e 10, 25, 15, 30, 40

f 10 g 4

Part 4

a hundreds tens ones 2 6 7

b 569 500 + 60 + 9

c 267 200 + 60 + 7

d 853 800 + 50 + 3

Part 5

a Vertex b Face c Edge d

Part 6

b, d, f are parallel

Part 7

11–13 Hands on. (It is less likely that two heads will be flipped because there is only one combination of two heads but two combinations for heads and tails.)

3

0, 2, 4, 6, 8, 10, 12 b 0, 3, 6, 9, 12, 15, 18 c 0, 5, 10, 15, 20, 25, 30 d 0, 4, 8, 12, 16, 20, 24 e

6, 12, 18, 24, 30, 36 f 0, 7, 14, 21, 28, 35, 42

4 Rule and missing numbers:

a 24 28 32 36 Add 4

b 19 22 25 28 Add 3

c 34 38 42 46 Add 4

d 50 55 60 65 Add 5

5 Hands on.

b

am a prism that has two triangles as faces and three other rectangular faces. am a prism that has six rectangular faces. am a special kind of prism because all my faces are squares.

e

I am a prism that has two hexagonal faces and six other rectangular faces. am a prism that has two octagonal faces and eight other rectangular faces.

8 Hands on – some examples below.

a A cube has 6 square faces, 8 vertices and 12 edges.

b A rectangular prism has 6 faces, 8 vertices and 12 edges.

c A triangular prism has 2 triangular faces, 3 rectangular faces, 9 edges and 6 vertices.

d A hexagonal prism has 2 hexagonal faces, 6 rectangular faces, 12 vertices and 18 edges.

9 a 40 cm2 b 36 cm2

10 Hands on.

11 Possible solutions:

3 cm × 8 cm, 4 cm × 6 cm

DIAGNOSTIC REVIEW

1 The missing numbers are:

2 a $20 d $15 g $11 j $22

b $12 e $40 h $20

c $10 f $26 i $40

3 Hands on.

4 a 70 + 23 = 93

b 40 + 43 = 83

c 50 + 37 = 87

d 70 + 30 = 100

e 80 + 34 = 114

f 90 + 19 = 109

g 120 + 23 = 143

h 130 + 40 = 170

i 140 + 35 = 175

j 150 + 35 = 185

5 a 85 – 30 = 55

b 79 – 40 = 39

c 96 – 50 = 46

d 148 – 40 = 108

e 176 – 60 = 116

f 129 – 40 = 89

6 a B3 = e E2 = i A5 =

b B2 = f F1 = j D2 =

c C3 = g G4 =

d E5 = h A3 =

7 a = C4 c = D3 e = B5

b = G3 d = F4

Favourite T-shirts

4 a Hands on – James has not folded his paper into 5 equal parts. b Hands on – 1 5 is larger than 1 10 because the whole has only been divided into 5 pieces not 10.

d 46 + 30 2 = 74

e 27 + 50 1 = 76

f 35 + 50 2 = 83

g 56 + 30 3 = 83

h 63 + 30 2 = 91

j

5 Each pair of sentences has the same total. They are:

8

on. (It doesn’t matter in which order they are multiplied.)

9 Mitchell and Georgia both scored 24. 10

2 a hundreds b ones

c thousands d hundreds

e ones f ten thousands

g hundreds h thousands

3 a 2000 + 300 + 40 + 7

b 3000 + 500 + 70 + 8

c 6000 + 300 + 50 + 4

d 30000 + 5000 + 600 + 70 + 2

e 70000 + 4000 + 200 + 60 + 3 4

2 Missing fractions:

a 5 8, 6 8, 7 8 c 5 4, 6 4, 7 4

b 5 10 , 6 10 , 7 10 d 5 5, 6 5, 7 5

3 12 22 32 42 52 62 72 82 92

What did you learn? Hands on.

4 13 23 33 43 53 63 73 83 93

What did you learn? Hands on.

5 Hands on.

6 a 55 – 32 = 23

55 – 23 = 32

b 64 – 42 = 22

64 – 22 = 42

c 77 – 62 = 15

77 – 15 = 62

d 67 – 44 = 23

67 – 23 = 44

e 52 – 39 = 13

52 – 13 = 39

f 72 – 44 = 28

72 – 28 = 44

g 65 – 39 = 26

65 – 26 = 39

h 60 – 45 = 15

60 – 15 = 45

i 199 – 106 = 93 199 – 93 = 106

j 192 – 103 = 89 192 – 89 = 103

7 a b c d e f g h i j k

8 Hands on.

9 a 8 cm3

b 12 cm3

c 16 cm3

10 a 11

I am a shape that has 4 right angles and 4 sides the same length. am drawn with my base on a different orientation.

I am a shape that has 4 right angles.

I have 2 shorter sides the same length and 2 longer sides the same length.

I am a 3-sided shape. have 3 angles the same size and 3 sides the same length.

I am an irregular shape that has 5 sides. My angles and side lengths are not always the same size.

I am a regular shape with 6 sides. All my angles are the same size. All my sides are the same length.

I am a 3-sided shape. have 2 angles the same size and 2 sides the same length.

I am a regular shape that has 5 sides. All my angles are the same size. All my sides are the same length.

I am a regular shape with 8 sides. All my angles are the same size. All my sides are the same length.

I am a quadrilateral. have one pair of parallel sides only.

I am a quadrilateral. None of my angles are the same size, all my side lengths are different. None of my sides are parallel.

I am an irregular shape that has 8 sides. My angles and side lengths are not always the same size.

d 10 cm3

g 12 cm3

e 12 cm3 h 10 cm3

f 12 cm3

c 12 b, e, f, g