OzzieMaths Series - Year 2

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Title: OzzieMaths Series Maths: Year 2 © 2017 Ready-Ed Publications Printed in Australia Author: Anita Green Illustrator: Alison Mutton

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Reproduction and Communication by others

Contents Teachers’ Notes Curriculum Links

4 5-6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Section 2: Fractions, Decimals and Money Two for one coins Making a dollar How much?

Adding up Bouncy balls Halves or quarters?

Cutting shapes Sharing cookies

25 26 27 28 29 30 31 32

Section 3: Patterns and Algebra Predicting patterns Number sentences Word problems - addition Word problems - subtraction Making patterns

34 35 36 37 38

40 41 42 43 44 45 46 47 48 49

Section 5: Location and Transformation Mapping 1 Mapping 2 Flip, slide and turn 1 Flip, slide and turn 2 Turns Bird’s eye view

51 52 53 54 55 56

Section 6: Chance and Data Tally marks Transport data Collecting data Playing games Graphing 1 Graphing 2 Comparing data What’s the chance?

58 59 60 61 62 63 64 65

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Section 1: Number and Algebra Stone collection How many numbers?

What’s the pattern? 1 Adding strategies Sharing Doubles!

Near doubles Footy scores Times three Division Arrays 1 Arrays 2 Addition Subtraction Using an abacus Empty number lines

Section 4: Shapes and Units of Measurement Balance scales Telling time 1 Telling time 2 Months of the year Calendars Fun with shapes What’s my shape?

Measuring 1 Measuring 2 Capacity

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Teachers’ Notes This book is part of a series containing a range of maths activities linked to the Australian Curriculum. Each activity is linked to a content description and elaboration.

Many of the questions and activities in the book are designed to be open-ended, however where appropriate answers or suggested answers are provided. The idea of keeping the questions and activities open-ended is to focus on processes and strategies and allow for greater differentiation. The activities enable all students of different abilities to be working on the same problem but allow students to tackle the problem at different levels. They can approach the task from their level and feel confident in being able to complete it.

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To get the most out of these activities reflection time needs to be incorporated into each lesson. This doesn’t need to be just at the end of the lesson but can be at various times throughout the lesson too. This gives the students time to share their strategies with the class and see how other students are solving the same problem.

It’s important for students to see that they all might have the right answer but there are many ways to get to that answer. Offering students this time means they can learn from each other and provides assistance to those students who might be struggling by giving them a strategy to try.

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The book is divided into six sections: Section 1: Number and Place Value Section 2: Fractions, Decimals and Money Section 3: Patterns and Algebra Section 4: Shapes and units and Measurement Section 5: Location and Transformation Section 6: Chance and Data

As teachers, the questions we ask can help the students delve deeper and think more critically about their learning. Try using some of these questions in your lessons: 1. Is there another way you could work that out?

2. Have you found every possible answer?

3. What would happen if … ?

4. Is there a pattern?

5. You and … have different answers… who is right?

6. You and … have the same answer but different working out. Share with each other what you did.

7. Can you prove it?

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With the help of this book you can ensure you are covering each area of the curriculum and make maths fun and engaging for your students.

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Curriculum Links

Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and tens from any starting point, then moving to other sequences (ACMNA026) Elaborations • developing fluency and confidence with numbers and calculations by saying number sequences • recognising patterns in number sequences, such as adding 10 always results in the same final digit

visualising a group of objects as a unit and using this to calculate the number of objects in several identical groups

Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Elaborations • dividing the class or a collection of objects into equal sizes groups • identifying the differece between dividing a set of objects into 3 equal groups and dividing the same set of objects into groups of three

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Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) Elaborations • using an abacus to model and represent numbers • understanding three-digit numbers as comprised of hundreds, tens and ones/units

Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Elaborations • recognising that sets of objects can be partitioned in different ways to demonstrate fractions • relating the number of parts to the size of a fraction

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Recognise, model, represent and order numbers to at least 1000 (ACMNA027) Elaboration • developing fluency with writing numbers in meaningful contexts

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© ReadyEdPu bl i cat i ons Count and order small collections of Australian coins and notes according to their • f o r r e v i e w p u r po sesonl y• value (ACMNA034) Explore the connection between addition and

Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Elaborations • becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10 • modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines

Describe patterns with numbers and identify missing elements (ACMNA035) Elaborations • describing a pattern created by skip counting and representing the pattern on a number line • investigating features of number patterns resulting from adding twos, fives or 10s

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Elaborations • identifying equivalent values in collections of coins or notes, such as two five-cent coins having the same value as one 10-cent coin • counting collections of coins or notes to make up a particular value, such as that shown on a price tag

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subtraction (ACMNA029) Elaborations • becoming fluent with partitioning numbers to understand the connection between addition and subtraction • using counting on to identify the missing element in an additive problem

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Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Elaborations • representing array problems with available materials and explaining reasoning

Solve problems by using number sentences for addition or subtraction (ACMNA036) Elaborations • representing a word problem as a number sentence • writing a word problem to represent a number sentence

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Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Elaborations • comparing areas using the palm of the hand or a stone • comparing capacities using a range of containers

Investigate the effect of onestep slides and flips with and without digital technologies (ACMMG045) Elaboration: • understanding that objects can be moved but changing position does not alter an object’s size or features Investigate the effect of onestep slides and flips with and without digital technologies (ACMMG045) Elaboration • understanding that objects can be moved but changing position does not alter an object’s size or features

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Tell time to the quarter-hour, using the language of ‘past’ and ‘to’ (ACMMG039) Elaboration • describing the characteristics of quarter-past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three

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Compare masses of objects using balance scales (ACMMG038) Elaboration • using balance scales to determine whether the mass of different objects is more, less or about the same, or to find out how many marbles are needed to balance a tub of margarine or a carton of milk

on maps, to allow us to receive and give directions and to describe place

Identify and describe half and quarter turns (ACMMG046) Elaboration • predicting and reproducing a pattern based around half and quarter turns of a shape and sketching the next element in the pattern

Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) Elaboration: • classifying a list of everyday events according to how likely they are to happen, using the language of chance, and explaining reasoning

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Describe and draw two dimensional shapes with or without technologies (ACMMG042) Elaboration • identifying key features of squares, rectangles, triangles, kites, rhombuses and circles, such as straight lines or curved lines, and counting the edges and corners

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Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048) Elaboration • determining the variety of birdlife in the playground and using a prepared table to record observations

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Describe the features of three dimensional objects (ACMMG043) Elaboration • Identifying geometric features such as the number of faces, corners or edges

Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) Elaboration • understanding that we use representations of objects and their positions, such as 6

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Name and order months and seasons (ACMMG040) Elaborations • investigating the seasons used by Aboriginal people, comparing them to those used in Western society and recognising the connection to weather patterns

Collect, check and classify data (ACMSP049) Elaboration • recognising the usefulness of tally marks Create displays of data using lists, table and picture graphs and interpret them (ACMSP050) Elaboration • creating picture graphs to represent data using one to one correspondence

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Number and Algebra

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Stone collection My Dad and I take a walk after dinner every night. I collect stones that I find on our walks. On Monday I collected 3 stones and then I collected 1 more stone every day for the rest of the week.

Can you work out how many stones I have collected by Sunday?

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Day

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How many stones do I have at the end of the week?

Extension: How many stones will I have at the end of 2 weeks?

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Curriculum Link: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028)

How many numbers?

Sam and his sister have just finished playing cards. Sam notices after they have packed up that there are still four cards lying on the floor under the table. They are:

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9

5

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1. How many different numbers can you make using these digits?

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2. Now come up with your own four numbers. (You could come up with these numbers using playing cards or dice.)

3. Using your four digits, how many different numbers can you make? Complete your working out on the back of this sheet.

Curriculum Link: Recognise, model, represent and order numbers to at least 1000 (ACMNA027) Elaboration: developing fluency with writing numbers in meaningful contexts

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What’s the pattern? 1 Complete the patterns.

1. 75

65

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Explain the pattern:_ ________________________________________

r o e st Bo r 38 36 34o e p u k S Explain the pattern:_ ________________________________________

2.

3. 140

110 100

80

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46 44

Explain the pattern:_ ________________________________________

© ReadyEdPubl i cat i ons Choose a number of your own and then create three different patterns •f or r ev i enumber. w pur posesonl y• going backwards using your

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My number: ___________

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Curriculum Link: Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences (ACMNA026) Elaboration: developing fluency and confidence with numbers and calculations by saying number sequences

Adding strategies 1.

In class the teacher gave us this problem:

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Show how you would solve it:

© ReadyEdPubl i cat i ons 2. I noticed that my friend wrote in her book: •f orr evi ew pur posesonl y•

19 – 12 = __

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Why did she write it like this? Will it get her the right answer? How? ________________________________________________________

. te o ________________________________________________________ c . che e r o r ________________________________________________________ st super 3. How could we use the strategy in question 2 to solve other problems? Give an example.

Curriculum Link: Explore the connection between addition and subtraction (ACMNA029) Elaboration: becoming fluent with partitioning numbers to understand the connection between addition and subtraction, using counting on to identify the missing element in an additive problem

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Sharing I have 12 lollies. How many people can I share them with evenly?

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What if I have 24 lollies? How many people can I share them with evenly?

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Extension What if I have 36 lollies? Show your working out on the back of this sheet.

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Curriculum Link: Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Elaboration: dividing the class or a collection of objects into equal sized groups

Doubles!

My friend Jake has a lot of footy cards. He received so many for his birthday that he now has double the amount that he had before his birthday. How many cards do you think he had before his birthday and how many cards do you think he has now?

Show your working out.

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I only have half as many cards as Jake. How many cards do you think I have? Show your working out.

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Curriculum Link: Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Elaboration: becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10

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Near doubles 1.

The teacher wrote this problem on the board:

8 + 9 = __

This sum is easy because it is a near double!

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___________________________ ___________________________

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or eBo st r e p ok u S ___________________________ Sarah said it was easy because it was a near double. What does she mean by near double?

© ReadyEdPubl i cat i ons ___________________________

2. Write some of your own near double equations.

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Curriculum Link: Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Elaboration: becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10

Footy scores Mum took my brother and I to the AFL footy on Wednesday. At half time we got a hot dog each. While we were trying to make our way back to our seats after half time our team scored 10 points! What might have been the score at half time and what might the score be now?

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What if our team had scored 20 points while• we were making our back to s f o rr evi e wway pu r po esonl y• our seats at half time? What might have been the score at half time and what might the score be now?

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Extension What if the team had scored 30, 40 or 50 points? Try some of these on the back of the sheet.

Curriculum Link: Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Elaboration: becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10

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Times three Look at each set of shapes below. If I have three times as many of each set of shapes, how many do I have? Write the numbers in the table below.

Shape sets

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b.

Three times as many

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Create a collection of objects on your desk using items from around the classroom. Ask your friend how many objects would be on your desk if there were three times as many.

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a. How many objects are in your collection? ______________

_____________________________________________

Extension Look at the sets of shapes in the table above again. On the back of this sheet work out how many shapes there would be in each set if there were four times as many. Show your working out.

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Curriculum Link: Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Elaboration: visualising a group of objects as a unit and using this to calculate the number of objects in several identical groups

Division 1.

Draw lines to match the word problems to the pictures that show the working out. Write a number sentence for each.

a. I shared my 15 lollies between my 3 friends. How many lollies did they each receive?

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he gets $5 pocket money a week, how many weeks will it take him to save it all?

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xx r o e t s B r xx e o p ok u S b. Tom wants to buy a game for $20. If

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xx xxx

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xx xxx

© ReadyEdPubl i cat i ons xx xxx •f orr evi ew pur posesxo l y• x xn xx

c. My mum gives me 20 new books packed into 5 small boxes. How many books are in each box?

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d. The man at the fruit shop is putting apples into bags of 3. If he has 15 apples, how many bags does he need?

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Write your own word problem that involves sharing.

Then draw a picture that you could use to help solve it.

Curriculum Link: Recognise and represent division as grouping into equal sets and solve simple problems using these representations (ACMNA032) Elaboration: dividing the class or a collection of objects into equal sized groups, identifying the difference between dividing a set of objects into three equal groups and dividing the same set of objects into groups of three

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Arrays 1 1.

Draw an array for each problem.

a. Jack has 3 times as many cars as Max. If Max has 6 cars, how many does Jack have?

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c. In the classroom there are cups that each have 4 dice in. If there are 7 cups, how many dice are there altogether?

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b. When the teacher asks a question in the classroom 5 hands go up. How many fingers can the teacher see?

Write your own word problem for the array below.

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d. Zoe’s cousin ise twice age. ©R adher yEdPubl i cat i ons If Zoe is 12, how old is her •f orr evi ew pur posesonl y• cousin?

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Extension Make your own array using objects from your classroom, e.g. counters, blocks, etc. Take a photo of your array and write a problem to go with it on the back of this sheet.

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Curriculum Link: Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Elaboration: representing array problems with available materials and explaining reasoning

Arrays 2 There are 24 jelly cups on a tray ready to go into the fridge. How could they be arranged on the tray? Draw the possibilities below.

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How many different ways did you find to arrange them?

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_______________________________________________________ _______________________________________________________

Extension What if there are 48 jelly cups waiting to go in the fridge? What might the tray look like?

How might the cups be arranged? Use the back of this sheet to work this out.

Curriculum Link: Recognise and represent multiplication as repeated addition, groups and arrays (ACMNA031) Elaboration: representing array problems with available materials and explaining reasoning

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Addition My friend Lucy is trying to teach me her way of solving addition problems. She said she just uses partitioning and her knowledge of “tens mates”.

Easy!

This is what she said to me about the sum :

16 + 7 =

or eBo st r e p ok u S 16 + 4 = 20 20 + 3 = 23

Use Lucy’s strategy to solve the equations below.

Equation

Working out

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“I know 6 and 4 is 10, so I know 16 and 4 will make 20. So I partition the 7 into 4 and 3. Easy!” On her page I saw this:

Answer

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15 + 17 =

39 + 12 = .

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Extension

Can you come up with two equations of your own that can be worked out using the same strategy? Write them on the back of this sheet and give them to a friend to solve.

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Curriculum Link: Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Elaboration: becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10, modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines

Subtraction Partitioning and knowledge of “tens mates” can be used to help you to solve subtraction problems as well as addition problems. For example:

23 – 8 =

or eBo st r e p ok u 23 – 3 = 20S 20 – 5 = 15

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We know that we can just take away 3 to get 20, so we can partition the 8 into 3 and 5:

Use this strategy to solve the equations in the table below.

Equation

Working out

Answer

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38 – 9 =

23 – 15 =. t 34 – 17 = 42 – 24 =

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Extension

Come up with two equations of your own that can be worked out using the same strategy. Write the equations on the back of this sheet and give them to a friend to solve.

Curriculum Link: Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Elaboration: becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10, modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines

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Using an abacus An abacus can be used to represent a number and show how many hundreds, tens and ones make up the number. For example, the abacus (right) represents the number 217. In this number, there are 2 hundreds, 1 ten and 7 ones.

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Hundreds

Tens

Ones

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What numbers are represented on these abacuses?

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Tens

Ones

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b.e d. n ©R adyEdc.Publ i cat i o s •make f or r e vi ewonpthe ur posesonl y• Draw to the numbers abacuses. a.

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Hundreds

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Hundreds

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Extension 1. Draw an abacus on the back of this sheet with a number represented on it and see if someone can work out what number it is. Give a friend a number and see if they can represent it on an abacus.

2. My friend Tom has drawn an abacus with 2 beads on the hundreds, 11 on the tens and 5 on the ones. My teacher said he has actually represented 315. How? What has he done wrong? Can you fix it?

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Curriculum Link: Group, partition and rearrange collections up to 1000 in hundreds, tens and ones to facilitate more efficient counting (ACMNA028) Elaboration: using an abacus to model and represent numbers, understanding three digit numbers as comprised of hundreds, tens and ones/units

Empty number lines There are many ways to use empty number lines to help you to solve problems. In class we have been given a problem: 36 + 25.

There are several different ways that we can solve it. Here are two ways: +20

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+4

+1

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36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

Would you have solved this problem using one of the above methods or do you have another way? Show your method on a number line below.

© Rea yEd Pub l i cat i ons Solve the problems byd drawing number lines.

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2. 33 + 24 =

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Extension

Find someone who has solved one of the problems above differently to you. Did you both get the same answer? Share your strategies.

Discuss and decide who used the most efficient strategy. Which strategy did you decide on and why?

Curriculum Link: Solve simple addition and subtraction problems using a range of efficient mental and written strategies (ACMNA030) Elaboration: becoming fluent with a range of mental strategies for addition and subtraction problems, such as commutativity for addition, building to 10, doubles, 10 facts and adding 10, modelling and representing simple additive situations using materials such as 10 frames, 20 frames and empty number lines

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Section 2: r o e t s B r e oo p u k S Fractions, Decimals and Money

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Two for one coins I have 2 coins in my right hand and 1 coin in my left hand. The coins in my right hand equal the same value as the coin in my left hand. What coins might I have in each hand? Draw the possibilities in the table below.

Left hand: 1 coin

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Right hand: 2 coins

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Could you do this with notes? Are there 2 notes that you can think of that added together to equal the value of another note?

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Extension Are there 3 coins that you can add together to equal the value of 1 coin? Or 4 coins? Or 5 coins?

Explore possibilities on the back of this sheet.

Curriculum Link: Count and order small collections of Australian coins and notes according to their value (ACMNA034) Elaboration: identifying equivalent values in collections of coins or notes, such as two five cent coins having the same value as one 10 cent coin

25

Making a dollar

or eBo st r e p ok u S

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Teac he r

1. Draw as many ways as you can to make a dollar using more than 3 coins.

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 2. What is the least amount of coins I could use to make $1?

3. What is the greatest amount of coins I could use to make $1?

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o c . che e r 4. I made $2 using exactly 5 r coins.

What coins might o st they be? super Extension

On the back of this sheet draw two ways that you could make $2 using more than 5 coins.

26

Curriculum Link: Count and order small collections of Australian coins and notes according to their value (ACMNA034) Elaboration: identifying equivalent values in collections of coins or notes, such as two five cent coins having the same value as one 10 cent coin

How much?

1.

How quickly can you count up the coins in each box below? b.

or eBo st r e p ok u Total: _____ S Total: _____

c.

d.

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Teac he r

a.

© Re ady EdPubl i cat i on s_____ Total: _____ Total: •f orr evi ew pur posesonl y•

Draw coins for the prices shown below.

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a. $1.25

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c. $5.30

b. $3.85

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2.

o c . che e r o r st super d. $6.60

Curriculum Link: Count and order small collections of Australian coins and notes according to their value (ACMNA034) Elaboration: counting collections of coins or notes to make up a particular value, such as that shown on a price tag

27

Adding up Hint: We each have more than enough money!

or eBo st r e p ok u S

Lina’s pile of money:

ew i ev Pr

Teac he r

My friend Lina and I want to buy a bead set each to make some jewellery. The sets are $7.95 each. We are trying to work out if we have enough money to buy ourselves a bead set each. When we look at our money it turns out we both have the same amount of money but each pile looks completely different.

How much might we each have and what might each pile look like?

My pile of money:

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Total: _____

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Total: _____

Which amount do you think is easier to count and why?

. t e o ___________________________________________________________ c . che e r o r st super ___________________________________________________________

Extension

Can you work out how much we each have left over once we have bought a bead set? Me: ________________ Lina: ________________ We notice that the shop sells a book of instructions to help us to make the jewellery for $2.95. Do we have enough money to buy an instruction book each? _______________________ What if we combine our money? ______________________ 28

Curriculum Link: Count and order small collections of Australian coins and notes according to their value (ACMNA034) Elaboration: counting collections of coins or notes to make up a particular value, such as that shown on a price tag

Bouncy balls 1.

Marko the magician has a magic hat full of red and blue bouncy balls. Half the bouncy balls in his hat are red and half are blue.

How many bouncy balls might there be and how many are red?

Show four possibilities. b.

c.

or eBo st r e p ok u S

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Teac he r

a.

d.

© ReadyEdPubl i cat i ons f o rr ev i ew p ur pose sontol y • and trick his audience, the magician decides change 2. To try•

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a.

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c.

Extension

b.

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the bouncy balls. Now only one quarter are red. What might this look like? Show four possibilities.

o c . che e r o r st supd. er

What if only one eighth are red? Show the possibilities on the back of this sheet.

Curriculum Link: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Elaboration: recognising that sets of objects can be partitioned in different ways to demonstrate fractions

29

Halves or quarters?

I walked into the kitchen to find my Mum making a sandwich for my school lunch. She asked me, “Would you like it cut into halves or quarters?”

ew i ev Pr

Today, I decided I would like my sandwich quarters.

HowP ©cutRinto ea dyEd ubl i cat i ons many ways could my Mum cut •f orinto r ev i ew p posesonl y• the sandwich quarters?

Inu ar different colour, draw each way of cutting the sandwich.

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Could you cut a sandwich into eighths? Draw what this might look like on the back of this sheet.

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m . u

2.

or eBo st r e p ok u S

How many ways could my mum cut my sandwich into halves?

Draw the possibilities.

Teac he r

1.

Halves or quarters?

o c . ch ecan you cut a you are cutting a cake? How 3. What about when r e o r stfractions equally? s cake into halves, quarters, eighths orr other upe Draw your answers below.

30

Curriculum Link: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Elaboration: recognising that sets of objects can be partitioned in different ways to demonstrate fractions

Cutting shapes Draw 6 different shapes below. Using a ruler rule a line to cut each one in half. Look at the example to help you.

or eBo st r e p ok u S

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Teac he r

1.

ea dyEd ubl i cat i ons youR know each one is inP half?

2. How do© •f orr evi ew pur posesonl y• _________________________________________________________

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m . u

_________________________________________________________

draw any of the shapes above and cut them into quarters 3. Can you.

te

o c . che e r o r st super

or eighths? Look at the example to help you.

Curriculum Link: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Elaboration: recognising that sets of objects can be partitioned in different ways to demonstrate fractions, relating the number of parts to the size of a fraction

31

Sharing cookies My Dad and I baked a tray of cookies so I could share them with my friends that afternoon.

We baked 12 delicious, chocolate chip cookies!

Teac he r

ew i ev Pr

or eBo t s r e 1. When my friends p arrived Judd said he was really hungry so I o decided to giveu Shim half of the cookies. How manykdid he get?

2. Then, I gave Alex one quarter of the cookies. How many did he get?

© ReadyEdPubl i cat i ons 3. How many cookies are now left?

•f orr evi ew pur posesonl y•

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m . u

w ww

4. If there are just the three of us, how many cookies would we each receive if we shared them out evenly?

o c .

5. What fraction ofc the cookies do we each receive? e her r o st super

6. If there were 4 of us, how many cookies would we each receive?

7. What fraction of the cookies is that?

32

Curriculum Link: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections (ACMNA033) Elaboration: recognising that sets of objects can be partitioned in different ways to demonstrate fractions

or eBo st r e p ok Section 3: u S

Teac he r

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Patterns and Algebra

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super

33

Predicting patterns Work out what the 10th number in each patterns is.

1. 22, 24, 26, 28, 30, 32, Explain the pattern:_ _______________________ 10th number:_______

ew i ev Pr

Teac he r

2. 45,

or eBo st r e p60, 65, 70, ok 50, u 55, S

Explain the pattern:_ _______________________ 10th number:_______

3. 30, 40, 50, 60, 70, 80,

tho Re_______________________ adyEdPubl i ca t i ns ______ Explain the © pattern:_ 10 number:_

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•f orr evi ew pur posesonl y• 4. 65, 70, 75, 80, 85, 90,

Explain the pattern:_ _______________________ 10th number:_______

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o c .

Extension che e r o What would the 15th number in each r t r s s u e p pattern above be? What about the 20th number? Show your working out and answers on the back of this sheet.

Create a pattern of your own in your work book and see if a friend can predict the 10th, 15th and 20th numbers in your patterns.

34

Curriculum Link: Describe patterns with numbers and identify missing elements (ACMNA035) Elaboration: investigating features of number patterns resulting from adding twos, fives or 10s, describing a pattern created by skip counting and representing the pattern on a number line

Number sentences 1.

There are 14 books on a bookshelf and the librarian places 12 more books on the bookshelf. How many books are on the shelf now?

_________________ Write the number sentence for this word problem:

or eBo st r e p ok Maths u Show your S working out: Maths, Maths, Maths!

All About

Maths

I Love Maths!

In Space

One Million Maths Problems

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Teac he r

_______________________________

© ReadyEdPubl i cat i ons orproblem r evi e wyour pu r p othis se sonl y• af word of own for number sentence: 2. Write•

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___________________________________

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15 + 18 =

o c . che e r ___________________________________ o r st super ___________________________________

___________________________________

Extension Write some more of your own word problems on the back of this sheet and see if a friend can solve them.

Curriculum Link: Solve problems by using number sentences for addition or subtraction (ACMNA036) Elaboration: representing a word problem as a number sentence, writing a word problem to represent a number sentence

35

Word problems - addition 1.

I have 2 boxes of Smarties. One box contains 24 Smarties and the other box contains 22 Smarties. How many Smarties altogether?

or eBo st r e p ok u S

ew i ev Pr

Teac he r

Number sentence and answer:

2. Ask a friend to write a word problem for you to solve here:

________________________________________________________

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• ________________________________________________________ ________________________________________________________

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Number sentence and answer:

o c . che e r o t r s s r u e p 3. Did you write a word problem for a friend? What was the

number sentence for the word problem that you wrote for him/her? Did your friend solve it?

36

Curriculum Link: Solve problems by using number sentences for addition or subtraction (ACMNA036) Elaboration: representing a word problem as a number sentence, writing a word problem to represent a number sentence

Word problems - subtraction On the weekend Jed and his mum made cupcakes for his birthday. They made 56 cupcakes in total and Jed took 24 cupcakes to school for his classmates. How many cupcakes were left at home? Show your working out.

or eBo st r e p ok u S

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Teac he r

1.

2. Ask a friend to write a word problem for you to solve:

________________________________________________________ ________________________________________________________

© ReadyEdPubl i cat i ons ________________________________________________________ •f orr evi ew pur posesonl y•

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m . u

Number sentence and answer:

o c . che e r o t r s s r u e p 3. Did you write a word problem for a friend to solve? What was

the number sentence for the word problem that you wrote for him/her? Did your friend solve it?

Curriculum Link: Solve problems by using number sentences for addition or subtraction (ACMNA036) Elaboration: representing a word problem as a number sentence, writing a word problem to represent a number sentence

37

Making patterns 1.

Create patterns using the numbers below.

a. 65, 75, 50, 40, 70, 35, 55, 45, 60

or eBo st r e p ok u 23, 17,S 31, 29, 19, 25, 21, 27, 33

Pattern:________________________________________________

Teac he r

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b.

Pattern:________________________________________________

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2.

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c. 83, 123, 43, 103, 53, 113, 93, 73, 63 © ReadyEdPubl i cat i ons Pattern:________________________________________________ •f orr evi ew pur posesonl y•

Create a pattern of your own. Jumble the numbers. Can your friend work out the original pattern?

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o c . che e Jumbled numbers:_______________________________________ r o r st super

My friend’s solution:

Pattern:________________________________________________ Make sure you try one that someone else has created too!

38

Curriculum Link: Describe patterns with numbers and identify missing elements (ACMNA035) Elaboration: investigating features of number patterns resulting from adding twos, fives or 10s, describing a pattern created by skip counting and representing the pattern on a number line

Teac he r

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Section 4: r o e t s B r e oo p u k S Shapes and Units of Measurement

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m . u

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super

39

Balance scales 1.

Colour which is heavier.

b.

feather

2.

or eBo st r e p ok u S grapes pencil

milk

ew i ev Pr

Teac he r

a.

Using objects from around the room use balance scales to compare items weighs. ©how Rmuch ead yE dPubl i cat i ons

w ww

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•f o rr evi ew pur p oses nl y• Items Which iso heavier?

o c . che e r o r st super

Extension

If one book weighs the equivalent of 14 marbles. How many marbles do 2 books weigh? What about 5 books? Show your answers on the back of this sheet.

40

Curriculum Link: Compare masses of objects using balance scales (ACMMG038) Elaboration: using balance scales to determine whether the mass of different objects is more, less or about the same, or to find out how many marbles are needed to balance a tub of margarine or a carton of milk

Telling time 1 1.

What time is it on these clocks?

b.

or eBo st r e p ok u S

c.

d.

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Teac he r

a.

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2.

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o t r s su r e p ________________________________

Draw a ‘quarter past’ time on the clock below. What do you usually do at this time of the day?

________________________________ ________________________________ ________________________________ Curriculum Link: Tell time to the quarter hour, using the language of ‘past’ and ‘to’ (ACMMG039) Elaboration: describing the characteristics of quarter past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three.

41

Telling time 2 1.

What time is it on these clocks?

b.

or eBo st r e p ok u S

c.

d.

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Teac he r

a.

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2.

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o t r s su r e p ________________________________

Draw a ‘quarter to’ time on the clock below. What do you usually do at this time of the day?

________________________________ ________________________________ ________________________________

42

Curriculum Link: Tell time to the quarter hour, using the language of ‘past’ and ‘to’ (ACMMG039) Elaboration: describing the characteristics of quarter past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three

Months of the year 1.

How many months of the year do you know?

ew i ev Pr

Teac he r

or eBo st r e p ok u What is your favourite S month and why?

____________________________________________________________

Match the pictures to the months.

© ReadyEdPubl i cat i ons April •f orr evi ew pur poseso nl y•

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September

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2.

February co .

che e r o r st super

July December Curriculum Link: Name and order months and seasons (ACMMG040)

43

Calendars

M

5

T

I love changing the page on our calendar on the 1st day of the month!

Decemb W

Th

1

er

F

2

S

3

Su

or eBo st r e p ok u S

6

7

4

Teac he r

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8 9 10 1 1 12 13 1 4 15 16 17 18 19 20 2 1 22 23 24 25 26 27 2 8 29 30 31

Use the calendar and what you already know to complete the questions.

©isR ea EdPubl i cat i ons 1. What day the 1std ofy December?

•f orr evi ew pur posesonl y•

w ww

3. What day is the last day of December?

4. What day is Christmas Day?

m . u

2. What month comes before December?

. tof the week will the 1st of o 5. What daye c . che January fall on? e r o st su 6. What day will it be 12 r days from the r pe 5th?

Extension How many days are in January?

Look at the calendar. What day of the week will it be on the 17th of January?

44

Curriculum Link: Name and order months and seasons (ACMMG040)

Fun with shapes The teacher draws a square on the board and asks the class if anyone knows what shape it is and how they know. I put my hand up and say: “It’s a square. It has 4 equal sides.”

The teacher then asks what other shapes students know.

or eBo st r e p ok u S

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Teac he r

How many shapes do you know? What features are special to these shapes?

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m . u

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super Shape pictures!

On a separate piece of paper draw a picture using just 2D shapes.

Try to use as many 2D shapes as you can. Describe your picture to a friend to see if he/she can draw it. How did your friend go? Ask your friend to describe his/her picture to you and you have a go at trying to draw it. Does it look the same as your friend’s picture?

Curriculum Link: Describe and draw two dimensional shapes, with and without digital technologies (ACMMG042) Elaboration: identifying key features of squares, rectangles, triangles, kites, rhombuses and circles, such as straight lines or curved lines, and counting the edges and corners

45

What’s my shape?

What shapes are these and how do you know?

Name of shape

Description

or eBo st r e p ok u S

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Teac he r

Shape

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super

Extra With a friend play Guess My Shape. Find an object to represent one of the shapes above (e.g. a dice for a cube) and have your partner ask you questions about the shape to try and work out which one it is.

46

Curriculum Link: Describe the features of three dimensional objects (ACMMG043) Elaboration: identifying geometric features such as the number of faces, corners or edges

Measuring 1 1.

We can use lots of different things to measure objects. Can you find objects around your classroom that are longer than, shorter than and equal to the length of your foot?

Equal to..

Longer than..

or eBo st r e p ok u S

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Teac he r

Shorter than..

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Use your feet to do some more measuring. Write what you measured and how many foot lengths it was.

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Item

table

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m . u

2.

How many foot lengths?

o c . che e r o r st super

Extra If you and your friend both measured the width of the classroom in foot lengths, would your answers be the same? Explain your answer on the back of this sheet.

Curriculum Link: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Elaboration: comparing lengths using finger length, hand span or a piece of string

47

Measuring 2 The area of a shape or object is the amount of space its surface takes up. Have a look around your classroom and see if you can find things that have a surface area bigger than, smaller than and about the same as your hand.

2.

About the same...

Bigger than...

or eBo st r e p ok u S

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Teac he r

Smaller than...

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Use your hand to do some more measuring.

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Surface area of...

Maths book Table

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How many hands?

m . u

1.

o c . che e r o r st super

Extra Did your friend get the same surface area in hands length of the table as you? Explain the result.

48

Curriculum Link: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Elaboration: comparing areas using the palm of the hand or a stone

Capacity 1.

Which container do you think holds more and why? ________________________________________________________ ________________________________________________________

or eBo st r e p ok u S

a.

b.

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Teac he r

________________________________________________________

© ReadyEdPubl i cat i ons o rr ev i ewcontainers pur po es onl y• twof different shaped ins your classroom.

2. Find •

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Draw your containers here:

o c . che e r o r st super

Which one I think holds more and why:______________________ ________________________________________________________ What I did to find out if I was correct: __________________________ ________________________________________________________ Curriculum Link: Compare and order several shapes and objects based on length, area, volume and capacity using appropriate uniform informal units (ACMMG037) Elaboration: comparing capacities using a range of containers

49

Teac he r

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Section 5: r o e t s B r e oo p u k S Location and Transformation

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super

Mapping 1 Below is a map of the streets around Franco’s house.

Bank

CHIP STREET

Police Station

Michael’s house

Nick’s house

Amy’s house

Cafe

Supermarket

LONG STREET

Jake’s

house

house

house

house

house

POP STREET

Jill’s

Cinema

Library

Leanne’s

FRANCO’S

house

house

Lisa’s

Pam’s

house

house

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Bob;s

BELL STREET

Hannah’s

Teac he r

house

or e st Bo r Bell Street e p o u Primary k GLASS STREET S School Kevin’s

HIGH STREET

Michelle’s

Stuart’s

Allies’s

house

house

PARK STREET Swimming

John’s

Vicky’s

Pool

house

house

PArk/Playground

© ReadyEdPubl i cat i ons Read about Franco’s movements below.

•f o rr ev i ew pu r posesonl y•

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m . u

w ww

Franco leaves the cinema in the direction of the library and takes his first left. He turns right at the end of that street then his first left. He takes the next left and then the first right and his destination will be on the left.

o c . che e r o r Where did Franco end up? st super Extension Using the map above write your own set of directions to a place on the map. Have a friend follow them and see if he/she ends up in the right place.

Curriculum Link: Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) Elaboration: understanding that we use representations of objects and their positions, such as on maps, to allow us to receive and give directions and to describe place

51

Mapping 2 1.

Write a set of directions to get from your classroom to the toilets. ________________________________________________________ ________________________________________________________

or eBo st r e p ok u ________________________________________________________ S

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Teac he r

________________________________________________________

Compare your directions with a friend’s directions. Are they the same? What is different about them?

________________________________________________________

© ReadyEdPubl i cat i ons f oofrdirections r evi ew pu r p os esonl y • a set to get from your classroom to another 2. Write•

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place in the school.

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________________________________________________________

. te o ________________________________________________________ c . che e r o r st super ________________________________________________________ ________________________________________________________

Give them to a group of friends to see if they can follow them. Did they end up at the right spot? Why/why not? ________________________________________________________ ________________________________________________________ 52

Curriculum Link: Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) Elaboration: understanding that we use representations of objects and their positions, such as on maps, to allow us to receive and give directions and to describe place

Flip, slide and turn 1 1.

Match the arrows to the words.

or eBo st r e slide p ok u S turn

ew i ev Pr

Teac he r

flip

2.

©R ea y EdofPflips, ubl i ca t i o ns What come next in d the pattern slides and turns?

3.

Create your own patterns using the flip, slide and turn icons and see if anyone can work out what comes next.

w ww

a.

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m . u

•f orr evi ew pur posesonl y•

o c . che e r o r st super

b.

Curriculum Link: Investigate the effect of onestep slides and flips with and without digital technologies (ACMMG045) Elaboration: understanding that objects can be moved but changing position does not alter an object’s size or features

53

Flip, slide and turn 2 1.

Cut out the L shape in the bottom right hand corner of this sheet.

Trace around it, to complete the table below.

2.

Flip

Turn

or eBo st r e p ok u S

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Teac he r

Original

Use the same shape and copy it below to create a turn, flip, turn pattern. Use the original above as your starting position.

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Extension Create your own shape on a separate piece of paper to cut out. Now experiment flipping, sliding and turning it. Which action do you find the most difficult?

54

m . u

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Curriculum Link: Investigate the effect of onestep slides and flips with and without digital technologies (ACMMG045) Elaboration: understanding that objects can be moved but changing position does not alter an object’s size or features

Turns There are many different types of turns. Look at the four different ways that Robbie Robot has been turned.

original

Teac he r

1.

Draw this shape in each box below after it has been turned from its original position.

ew i ev Pr

or eBo st r e half turn antiwhole (full) turn p o quarter turn three-quarter turn k u clockwise/ clockwise or anticlockwise S anti-clockwise clockwise clockwise original position

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• half turn clockwise

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three-quarter turn anti-clockwise

o c . che e r o r st super

Create your own shape and use it to show the different turns.

quarter turn

clockwise or whole (full) turn

m . u

2.

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quarter turn clockwise

half turn

My shape:

three-quarter turn

whole (full) turn

Extra: Create a pattern with your shape on a separate piece of paper by using the different turns.

Curriculum Link: Identify and describe half and quarter turns (ACMMG046) Elaboration: predicting and reproducing a pattern based around half and quarter turns of a shape and sketching the next element in the pattern

55

Bird’s eye view 1.

Some maps are drawn from a ‘bird’s eye view’. Can you explain what a ‘bird’s eye view’ is? ______________________________________________

or eBo st r e ______________________________________________ p ok u S

2.

Draw a bird’s eye view of your classroom.

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Teac he r

______________________________________________

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m . u

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super

Extra: Compare your drawing with a friend’s drawing. Are they the same? Talk about similarities and/or differences.

Extension Draw a bird’s eye view of your bedroom on a separate piece of paper.

56

Curriculum Link: Interpret simple maps of familiar locations and identify the relative positions of key features (ACMMG044) Elaboration: understanding that we use representations of objects and their positions, such as on maps, to allow us to receive and give directions and to describe place

or eBo st r e Section 6: p ok u S

Teac he r

ew i ev Pr

Chance and Data

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super

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Tally marks The teacher asks students in the class to choose a favourite animal. They can choose from: a dog, a cat or a fish. She records the data like this:

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Why did she record the data like this?

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1.

© ReadyEdPubl i cat i ons ____________________________________________________________ •f orr evi ew pur posesonl y• ____________________________________________________________

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Complete the table above by writing the number of people who chose each animal.

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Curriculum Link: Collect, check and classify data (ACMSP049) Elaboration: recognising the usefulness of tally marks

Transport data

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1. There are many different types of cars and they all come in many different colours. Spend some time observing the cars that drive past your street. Note the colours of the cars that drive past. Record your data in the table below. What headings do you need?

2. Could you useR your data above toP create al graph to share your © e a d y E d u b i c a t i o n s findings? Choose a type of graph and create it on a separate piece of f orr evi ew pur posesonl y• graph• paper.

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Comment 1:

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3. Once you have completed your graph write two comments about what your graph shows.

____________________________________________________________

Comment 2:

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____________________________________________________________

4. Write one question that someone else could answer using your graph. __________________________________________________________ Curriculum Link: Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048) Elaboration: determining the variety of birdlife in the playground and using a prepared table to record observations

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Collecting data 1. Create a question to ask the students in your class, e.g. What is your favourite sport? You are going to survey your classmates.

My question: ____________________________________________________________

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Responses

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____________________________________________________________

Tally marks (

)

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3. What have you learnt from your data? ____________________________________________________________ ____________________________________________________________

Extra: Can you show your data in graph form on the back of this page?

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Curriculum Link: Identify a question of interest based on one categorical variable. Gather data relevant to the question (ACMSP048) Elaboration: determining the variety of birdlife in the playground and using a prepared table to record observations Curriculum Link: Collect, check and classify data (ACMSP049) Elaboration: recognising the usefulness of tally marks

Playing games 1. Patrick and Liam are playing a game. Each need to roll a 6 to start.

Patrick rolls a 6 straight away. But Liam has had 5 rolls and still hasn’t rolled a 6. Patrick says, “This is your 6th turn so it has to be a 6 this time.” Is he right? Why/why not?

or eBo t s r e ____________________________________________________________ p ok u S ____________________________________________________________

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____________________________________________________________

____________________________________________________________

2. Roll a dice and see how many rolls it takes to roll a 6. Try this 3 times ©theRresults. eadyEdPubl i cat i ons and record

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2nd attempt

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1st attempt

o c . che e r o Answer these questions. r st super

3. How many rolls do you think it will take you to roll a 2?_ __________ 4. Which number do you think has the greatest chance of being rolled and why? __________________________________________________________ Curriculum Link: Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) Elaboration: classifying a list of everyday events according to how likely they are to happen, using the language of chance, and explaining reasoning

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Graphing 1

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Have a look at the graph below. It’s not quite finished.

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1. What do you think this graph could be about?

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o c . che e r o 3. Write two interesting facts based on this graph. r st super

2. Once you have decided what you think the graph could be about, complete it by adding headings, labels and numbers.

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Fact 1:

Fact 2:

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

Curriculum Link: Create displays of data using lists, table and picture graphs and interpret them (ACMSP050) Elaboration: creating picture graphs to represent data using one to one correspondence

Graphing 2 Below is some data collected by a Year 2 class on the times they go to bed.

6.30

7.00

7.30

8.00

8.30

9.00

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Number of students

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or eBo t s r e Create a graph below using the data above. o p k Su

o c . che e r o Bed Timer r s up est

Extra Compare your graph with a friend’s graph.

Discuss similarities and differences.

Swap your graphs and write two interesting facts or questions on each other’s graph.

Curriculum Link: Create displays of data using lists, table and picture graphs and interpret them (ACMSP050) Elaboration: creating picture graphs to represent data using one to one correspondence

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Comparing data Mrs. Bunting’s Year 2 class collected data on favourite colours.

Below are two different ways the data was represented by two different students. Each shows the same information.

Method 1 Favourite colour

Students

or eBo st r e p ok u SElliot, Jack, Ruby, Liam,

red

John, Minnie, Ava

green

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blue

Max, Jacob, Riley, Reece

yellow

Chase

pink

Lucy, Ciara, Scarlett, Gemma, Sophie, Maddison

purple

Tayla, Hayden

eadJane, yE dPubl i cat i ons orange© R Aidan, Alex,

•f orTyler, r ev i ew pur posesonl y• other Daniel blue

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green

yellow

pink

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Method 2 orange

other

. te o c Which method of collating and representing the data. do you think is che e r the best? o r st super

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Curriculum Link: Create displays of data using lists, table and picture graphs and interpret them (ACMSP050) Elaboration: comparing the usefulness of different data displays

What’s the chance?

When we talk about chance we talk about the likelihood of something happening. We can use words like ‘possible’, ‘impossible’ and ‘certain’.

Write something that is certain to happen today.

or eBo st r e p ok Write somethingu that can not possibly happen today.

S

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Use the bolded words to describe the chance of the events below happening.

certain, impossible, likely, possible, unlikely ©R eadyEd Pub l i cat i o ns

1. It is going to r rain today. _ ______________ •f o r e vi ew pur poseso nl y• 2. Your favourite footy team will win on the weekend. _________________

4. If you flip a coin it will land on heads.

_ ______________

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3. You will get to visit space one day.

o c . cwill e 6. A giant beanstalk grow in your backyard. r _ ______________ he o t r s s r u e p 7. If you roll a dice it will land on 6. _ ______________ 5. You will have dinner tonight.

_ ______________

8. You will go to school tomorrow.

_ ______________

Extra Make up some chance events of your own on the back of this sheet and use words to describe the likelihood of each event happening.

Chance Events

Curriculum Link: Identify practical activities and everyday events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and identify some events as ‘certain’ or ‘impossible’ (ACMSP047) Elaboration: classifying a list of everyday events according to how likely they are to happen, using the language of chance, and explaining reasoning

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Answers Page 8 – Stone collection Monday Tuesday Wednesday Thursday Friday Saturday Sunday

3 4 5 6 7 8 9

Page 13 – Doubles!

1. Answers will vary. Some of the possibilities are shown below:

3 7 12 18 25 33 42

Cards before his birthday 6 5 10 15 9 20 50 11

End of one week: 42 stones.

End of two weeks: 479 stones.

2. Answers will vary. Some possibilities are:

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Page 9 – How many numbers?

1. 1, 3, 5, 9, 13, 31, 15, 19, 91, 93, 95, 139, 195, 519, 539, 1359, 9135, 3519

Page 11 – Adding strategies 1.12 + 7 = 19 2.19 – 12 = 17 (To solve this problem the student used his/her knowledge of the relationship between addition and subtraction. For example, if you know 6 + 7 = 13, then you also know: 7 + 6 = 13; 13 - 6 = 7; 13 - 7 = 6.)

Jake’s cards 14 20 24 8 32 80 60 44

My cards 7 10 12 4 16 40 30 22

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Page 10 – What’s the pattern? 1 1. Goes down in 5s - 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25 2. Goes down in 2s – 48, 46, 44, 42, 40, 38, 36, 34, 32, 30, 28 3. Goes down in10s – 140, 130, 120, 110, 100, 90, 80, 70, 60

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Cards after his birthday 12 10 20 30 18 40 100 22

Page 14 – Near doubles 1. 8 + 9 = 17 (8 + 8 = 16 or 9 + 9 = 18) 2. 6 + 7 =, 10 + 11 =, 19 + 20 =, 29 + 30 =

© ReadyEdPubl i cat i ons Page 12 – Sharing •f orr evi ew pur posesonl y• 1. There are five ways that 12 lollies can be shared

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evenly.

2 people = 6 lollies each; 3 people = 4 lollies each; 4 people = lollies each; 6 people = lollies each; 12 people = 1 lolly each.

2. There are 7 ways that 24 lollies can be shared evenly.

2 people = 12 lollies each; 3 people = 8 lollies each; 4 people = 6 lollies each; 6 people = 4 lollies each; 8 people = 3 lollies each; 12 people = 2 lollies each.

24 people = 1 lolly each.

Extension 1 person = 36 lollies each; 2 people = 18 lollies each; 3 people = 12 lollies each; 4 people = 9 lollies each; 6 people = 6 lollies each; 9 people = 4 lollies each.

12 people = 3 lollies each.

18 people = 2 lollies each.

36 people = 1 lolly each.

Page 15 – Footy scores 1. Answers will vary. Some possibilities are: 26 – 36, 45 – 55, 31 – 41, 7 – 17, 19 – 29 2. Answers will vary. Some possibilities are: 7 – 27, 16 – 36, 25 – 45, 31 – 51, 59 – 79 Extension Possibilities for 30 points: 5 - 35; 26 - 56; 12 - 42 Possibilities for 40 points: 9 - 49; 17 - 57; 35 - 75 Possibilities for 50 points: 7 - 57; 31 - 81; 14 - 64 Page 16 – Times three 1. a.18 b.27 c.21 d.45 e.30 Extension a.24 b.36 c.28 d.60 e.40

o c . che e r o r st super Page 17 – Division 1. a.5 b.4 c.4 d.5 Page 18 – Array 1 Possibility: a.

xxxxxx Jack x x x x x x xxxxxx

Max xx xx xx

b. x x x x x x x x x x xxx xxx xxx xxx xxx c. xx xx d.

Zoe

xx xx xxxx xxxx xxxx

xx xx

xx xx

xx xx

xx xx

xx xx

Zoe’s xx xx xx xx xx xx xx xx cousin x x x x x x x x

Page 19 – Arrays 2 1)24 jellycups can be arranged in the following arrays: 8 x 3 3 x 8 2 x 12 12 x 2 4 x 6 6 x 4 Extension 48 - 6 x 8; 4 x 12; 2 x 24; 8 x 6; 12 x 4; 24 x 2 Page 20 – Addition 18 + 8 - 18 + 2 = 20 + 6 = 26 24 + 7 - 24 + 6 = 30 + 1 = 31 15 + 17 - 17 + 10 = 27 + 3 = 30 + 2 = 32 39 + 12 - 39 + 10 = 49 + 1 = 50 + 1 = 51 27 + 16 - 27 + 10 = 37 + 3 = 40 + 3 = 43 33 + 19 - 33 + 10 = 43 + 7 = 50 + 2 = 52

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Page 29 – Bouncy balls 1. Possibilities: 6 red and 6 blue; 5 red and 5 blue; 12 red and 12 blue 2. Possibilities: 4 red and 12 blue; 2 red and 6 blue; 5 red and 15 blue Extension Possibilities: 2 red and 14 blue; 4 red and 28 blue; 5 red and 35 blue

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• f.

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g. H T O h. H T O Extension Tom needs to trade 10 tens for one 100 on his abacus.

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1. 28 + 14 = 42 2. 33 + 24 = 57 3. 41 + 19 = 60 4. 27 + 35 = 62 Page 25 – Two for one coins 1.

Right hand: 2 coins $1, $1 50c, 50c 10c, 10c 5c, 5c

Page 28 – Adding up Lina’s: $2, $2, $2, $2, $1, 20c, 5c Mine: $2, $1, $1, $1, $1, 50c, 50c, 50c, 50c, 50c, 50, 10c, 10c, 5c Extension Each would have $1.30 left. If the money was combined, they would still be 35c short.

Left hand: 1 coin

Page 30 – Halves or quarters

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1.a.$1.25, b.$4.20, c.$7, d.$2.60 2.Teacher to check.

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Page 22 – Using an abacus a.354 b.167 c.490 d.227

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Page 26 – Make a dollar 1.Teacher to check. Students could draw the following possibilities: 20c + 20c + 20c + 20c + 20c 50c + 50c 50c + 20c + 20c + 10c 20c + 20c + 20c + 10c + 10c + 5c + 5c + 5c + 5c 2.50c and 50c 3.20 x 5c 4.$1, 50c, 20c, 20c and 10c

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Page 21 – Subtraction 15 – 9 - 15 - 5 = 10 - 4 = 6 21 – 6 - 21 - 1 = 20 - 5 = 15 38 – 9 - 38 - 8 = 30 - 1 = 29 23 – 15 - 23 - 10 = 13 - 3 = 10 - 2 = 8 34 – 17 - 34 - 10 = 24 - 4 = 20 - 3 = 17 42 – 24 - 42 - 20 = 22 - 2 = 20 - 2 = 18

e.

Possibilities for 3 coins = none Possibilities for 4 coins = 4 x 5c = 20c Possibilities for 5 coins = 5 x 10c = 50c; 5 x 20c = $1; 5 x $1 = $5

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$2 $1 20c 10c

2. $5 and $5 = $10, $10 + $10 = $20, $50 + $50 = $100 Extension

Page 31 – Cutting shapes Teacher to check.

Page 32 – Sharing cookies 1.6 2.3 3.3 4.4 5.1/3 6.3 7.¼ Page 34 – Predicting patterns 1.Goes up in 2s. 10th number = 40 2. Goes up in 5s. 10th number = 90 67

Page 55 – Turns

3. Goes up in10s. 10th number = 120 4. Goes up in 5s. 10th number = 110 Page 35 – Number sentences 1.14 + 12 = 26 2.15 + 18 = 33

quarter turn clockwise

Page 36 – Word problems addition 1.24 + 22 = 46

three-quarter turn anti-clockwise

clockwise or whole (full) turn

Page 58 – Tally marks 1. 13, 4, 8

Page 37 – Word problem subtraction 1.56 – 24 = 32

Page 61 – Playing games 1. No. Each number has an equal chance of being rolled. A one in six chance.

Page 38 – Making patterns 1.a.35, 40, 45, 50, 55, 60, 65, 70, 75, b.17, 19, 21, 23, 25, 27, 29, 31, 33 c.43, 53, 63, 73, 83, 93, 103, 113, 123

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Page 41 – Telling time 1 1)a.10.15 b.7.30 c.2.15 d.3.30 Page 42 – Telling time 2 1.a.6.15 b.10.45 c.12.30 d.4.45

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Page 62 – Graphing 1 1. The graph looks to be about transport. It could be about different types of transport in a carpark, or observing transport that drives past, or perhaps surveying a class on its favourite transport.

Page 40 – Balance scales 1)a. grapes b.milk Extension 2 books = 28 marbles; 5 books = 70 marbles

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half turn clockwise

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Page 45 Examples: a circle = no edges or corners; a triangle = 3 sides; a rectangle = 4 sides, 2 short and 2 long

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Page 46 – What’s my shape? cone, cube, cylinder, sphere, pyramid Page 51 – Mapping 1 Franco ended up at the bank Page 53 – Flip, slide, turn 1.

= turn;

2.

(turn)

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Page 44 – Calendars 1.Thursday 2.November 3.Saturday 4.Sunday 5.Sunday 6.Saturday Extension a. January has 31 days b. The 17th January will be a Tuesday

= slide;

= flip