Maths Games for the Australian Curriculum - Book 3 by Teacher Superstore

BOOK 3

Year 3 and Year 4

RIC-6121

3.4/1203

Maths games for the Australian Curriculum (Book 3) Published by R.I.C. Publications® 2014 under licence from Didax Inc. Copyright© Gail Gerdemann with Kathleen Barta 2014 ISBN 978-1-922116-92-5 RIC–6121 Titles available in this series: Maths games for the Australian Curriculum (Book 1) Maths games for the Australian Curriculum (Book 2) Maths games for the Australian Curriculum (Book 3)

Copyright Notice A number of pages in this book are worksheets. The publisher licenses the individual teacher who purchased this book to photocopy these pages to hand out to students in their own classes. Except as allowed under the Copyright Act 1968, any other use (including digital and online uses and the creation of overhead transparencies or posters) or any use by or for other people (including by or for other teachers, students or institutions) is prohibited. If you want a licence to do anything outside the scope of the BLM licence above, please contact the Publisher. This information is provided to clarify the limits of this licence and its interaction with the Copyright Act. For your added protection in the case of copyright inspection, please complete the form below. Retain this form, the complete original document and the invoice or receipt as proof of purchase. Name of Purchaser:

All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2014. For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum. Elaborations: This may be a modified extract from the Australian Curriculum and may include the work of other authors. Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject. You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/ This material is reproduced with the permission of ACARA.

Date of Purchase: Supplier: School Order# (if applicable): Signature of Purchaser:

Internet websites In some cases, websites or specific URLs may be recommended. While these are checked and rechecked at the time of publication, the publisher has no control over any subsequent changes which may be made to webpages. It is strongly recommended that the class teacher checks all URLs before allowing students to access them.

View all pages online PO Box 332 Greenwood Western Australia 6924

Website: www.ricpublications.com.au Email: mail@ricgroup.com.au

Foreword Students are more engaged when they are having fun, and the collection of activities will improve student understanding and strengthen skills through lively, collaborative and interactive games. Games assist students with computational fluency and greater conceptual understanding as each in-depth unit includes warm-up activities, one or more games, ideas for differentiation and develops mathematical capabilities.

Contents

Teachers notes ................................... iv – vi Curriculum links ........................................ vii

Game 7 Factors and multiples Factors and multiples ........................ 22–24

Game 1 Guess my secret Rules and patterns ................................ 2–5

Game 8 Which is greater? Fraction equivalence and comparing ......................................... 25–28

Game 2 Make the most of it Place value comparisons ..................... 6–8 Game 3 What’s the difference? Fluency with addition and subtraction ........................................... 9–11 Game 4 Multiplication master One-digit by multi-digit multiplication ..................................... 12–15

Game 9 Feuding fractions Composing and decomposing fractions ............................................. 29–33 Game 10 Fraction salute Relating +/– of fractions and mixed numbers .......................... 34–36 Game 11 Fraction action Multiplying fractions .......................... 37–40

Game 5 Double digit doozies Two-digit by two-digit multiplication ..................................... 16–18

Game 12 Duelling decimals Comparing fraction decimals .......... 41–43

Game 6 Divide and conquer Division ............................................... 19–21

Reproducibles .................................. 45–61

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Teachers notes

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Teachers notes

Introduction Maths games for the Australian Curriculum series targets: • Operations and algebraic thinking • Number and operations in Base Ten • Number and operations—fractions These games are designed to help students understand key concepts and strengthen skills. Developing number sense can take time. We all know that students are more engaged when they are having fun, and these games are designed for both substance and fun. The games and activities program is also designed to be straightforward for teachers. Supplies include standard equipment like paperclips and coloured markers, as well as copies of blackline masters. All materials for the year may be duplicated and organised in about one hour. Basic manipulatives such as tiles and fraction pieces are recommended but not required. Each game provides: • Ideas for more support and some challenges • Discussion questions to help students make connections between the game and mathematical concepts • Straightforward directions • Blackline masters These games can also be used for home-school activities.

Materials Step 1: Duplicate blackline masters and place them in file folders. Step 2: Duplicate cards* (pages 60–61) on card stock; cut the cards. Step 3: Gather the recommended manipulatives. * Number cards (0–9): Regular playing cards may be substituted. Remove Kings, Jacks and 10s. Use the Ace as 1 and the Queens as zero. (‘Q’ looks similar to ‘O’). * Fraction cards: Only the eighths cards are required, but others are recommended. Student-created fraction cards may be substituted.

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Teachers notes

Bibliography T Carpenter, E Fennema, M L Franke, L Levi & S B Empson Children’s mathematics: Cognitively guided instruction. Heinemann, Portsmouth, NH (1999) R I Charles (Ed.) Developing essential understanding of rational numbers for teaching mathematics in Grades 3–5. NCTM, Reston, VA (2010) B J Dougherty (Ed.) Developing essential understanding of algebraic thinking for teaching mathematics in Grades 3–5. NCTM, Reston, VA (2011) C T Fosnot Models of intervention in mathematics: Reweaving the tapestry. Pearson (2010) C T Fosnot & M Dolk Young mathematicians at work: Constructing fractions, decimals and percents. Heinemann, Portsmouth, NH (2002) C Fosnot & M Dolk Young mathematicians at work: Constructing multiplication and division. Heinemann, Portsmouth, NH (2001) J Kilpatrick, J Swafford & B Findell (Eds.) Adding it up. National Academy Press, Washington DC (2001) R S Kitchen & E A Silver (Eds.) Assessing English language learners in mathematics, A Research Monograph of TODOS: Mathematics for all. National Education Association, Washington, DC (2010) E C Rathmell (Ed.) Developing essential understanding of multiplication and division for teaching mathematics in Grades 3–5. NCTM, Reston, VA (2011) J Van De Walle, K Karp & J Bay-Williams Elementary and middle school mathematics. Allyn & Bacon, New York (2010)

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Curriculum links Overview of games and activities Content descriptions

Games 5 6 7 8

–

9 10 11 12

Year 3 Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051) Recognise, model, represent and order numbers to at least 10 000

–

(ACMNA052)

Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (ACMNA053)

–

Recognise and explain the connection between addition and subtraction (ACMNA054)

–

Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

–

Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

–

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies

–

(ACMNA055)

(ACMNA057)

Model and represent unit fractions including 1⁄2, 1⁄4, 1⁄3, 1⁄5 and their multiples to a complete whole (ACMNA058)

–

EXTENSION

–

– –

–

Year 4 Investigate and use the properties of odd and even numbers (ACMNA071) Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

–

(ACMNA073)

Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9

(ACMNA074)

–

– –

Recall multiplication facts up to 10 × 10 and related division facts

–

Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

–

Investigate equivalent fractions used in contexts (ACMNA077)

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Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

–

EXTENSION

–

(ACMNA075)

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vii Math um s gam cu l es for the Australian Curri

Game 1

Guess my secret

Make number patterns that follow a given rule. Analyse the patterns.

Mathematical understanding and skills

Materials

Generate and analyse patterns.

For each student: • Game board for ‘Guess my secret’ (1 for each student)

Maths vocabulary • Constant amount of change

• 10 cubes or other markers, 2 cm or smaller

• Number sequence • Pattern • Sequence

For each pair of students:

• Term (of a sequence)

• Game cards (page 47) • Alternate game cards (page 48)

General vocabulary predict

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Game 1

Guess my secret

Explaining the game Number of players: 2 Object: Guess your partner’s secret number pattern and the rule with the least number of clues. How to play: Each player: 1. Writes a number pattern that follows a rule on the game board. Note: Game cards are provided with ideas for patterns. Use is optional. However, patterns should be limited to growing or shrinking patterns. Begin with patterns that use only one operation (addition or subtraction). 2. Covers each number of the pattern with a cube. Then Player A: 3. Uncovers two numbers on Player B’s game board. 4. Predicts what a third number will be and uncovers it. 5. If the number is correct, continues to guess and uncover numbers. 6. States the rule at any time. If the rule: • Is correct, Player A wins the round. • Is not correct, it is Player B’s turn. Player B repeats steps 1–4 with the pattern on Player A’s game board. Example with Player B’s pattern: (3, 8, 13, 18, 23, 28, 33, 38, 43) Player A uncovers:

Player A points to a covered number (see arrow) and predicts, ‘I think this is 18’. That is correct, so Player A gets to keep guessing covered numbers. At any time Player A can state the rule.

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Math um s gam cu l es for the Australian Curri

Game 1

Guess my secret

Differentiation Challenges

More support • Use alternate game cards for basic pattern ideas.

• Give students several numbers (parts of a pattern) that are multiples of a certain number, plus a decade number. For example: 37, 44 … 65 (multiples of 7, plus 30: 7 x 1 + 30, 7 x 2 + 30 … 7 x 5 + 30) or 66, 74 … 98 (multiples of 8, plus 50.) ~ Ask students to figure out a start number and a rule that would generate the numbers you give them, as well as other numbers. ~ The start number must be different than the first number given. • Have students choose a pattern with a constant amount of change. ~ Predict the 20th term, then check it. ~ Predict the 100th term. Try to find a way to check it without making a list of terms. • Have students create their own start number and rule. ~ Use multiplication or division. ~ Predict the 10th term, then check it.

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Game 1

Guess my secret

Deepening the understanding Ask the class

Mathematical capabilities

If four consecutive terms in a sequence are:

Understanding, fluency and reasoning.

…18, 25, 32, 39 …

Look for and make use of structure.

• What is the next number?

Look for and express regularity in repeated reasoning.

• What number comes before 18? • What is the constant amount of change? Use maths terms to explain how you know. For any sequence, if your rule or constant amount of change is ‘add 5’, what qualities or properties will the numbers in your sequence have? Why? Use maths terms to explain your ideas.

Reason abstractly and quantitatively. Understanding, fluency and reasoning.

(Note: The digit in the ones place will alternate between two digits, one even and one odd. There will be two numbers in each ‘decade’; for example, 23 and 28 are in one decade.) What are some other interesting qualities you found in other sequences you made/guessed today? What is an example of a rule that will generate only even numbers pattern in the pattern? Only odd numbers? Only numbers ending in 0? No numbers ending in 0? Only multiples of 3? No multiples of 3? etc.

Make sense of problems and persevere in solving them.

After a student shares an idea, ask the class if they agree or disagree and why.

Construct viable arguments and critique the reasoning of others.

Look for and make use of structure.

I agree because...

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Game 2

Make the most of it

Read and write multi-digit numbers based on meanings of digits in each place, and use >, = and < symbols to compare the numbers.

Mathematical understanding and skills

Materials

Generalise place value understanding for multi-digit whole numbers.

• A deck (four sets) of 0-9 digit cards for each pair of students (page 60) • Each student makes a simple placevalue mat. (Tip: Cut A4 paper in half lengthwise to create two mats. Fold mats in half widthwise and then into thirds to make 6 columns.)

Maths vocabulary • place value • ones place • tens place • hundreds place • thousands place • ten thousands place

Ten thousands

8 8 8

and Ten thous

Thousands

s Thousand

Hundreds

Tens

Ones

8 8 8 ®

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Make the most of it

Game 2

Explaining the game Number of players: 2 Object: Create the largest possible 5-digit number with the cards you draw. 1. Take turns drawing one card at a time. • Try to create the largest 5-digit number possible by placing the card in one of the place-value columns on your place-value mat. • Once a card is placed, it cannot be moved. 2. When the 6th card is drawn, you may: • Choose to replace one of the cards on the place-value mat with the 6th card, or • You may discard the 6th card. 3. The player with the largest 5-digit number wins a point and: • Writes the comparison sentence (e.g. 85 564 > 76 432). • Explains how he/she knows the winning number is larger. Ten thousands

Thousands

Hundreds

Tens

Ones

Differentiation More support • Start with a place-value mat that only goes to hundreds or thousands. Draw one more card than the number of place values on the mat. • Have students say the value after each placement. For example, if the first card placed is a 5 in the tens place the student says, ‘fifty’. If the second card played is a 6 in the hundreds place the student says ‘six hundred’.

Challenge • Create whole numbers that have more than five digits.

Advanced challenge • Create decimal numbers including tenths and hundredths. Whole numbers could be written in black and decimals in red.

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Math um s gam cu l es for the Australian Curri

Make the most of it

Game 2

Deepening the understanding Ask the class

Mathematical capabilities

What is a general strategy for making sure you have the largest possible number?

Reason abstractly and quantitatively.

Jenny has 76 901. Her sixth digit card is 5.

Reason abstractly and quantitatively.

What should she do? Explain why.

Understanding, fluency and reasoning.

Use mathematical terms. Jason has 85 340. His sixth digit card is 7.

Reason abstractly and quantitatively.

What should he do? Explain why.

Understanding, fluency and reasoning.

Use mathematical terms. What is a general strategy for placing (or discarding) the sixth card?

Reason abstractly and quantitatively.

Alice had the number 55 834. She said, ‘Oh look, both of the 5s are in the thousands place’. Is this true?

Make sense of problems and persevere in solving them.

Alice also said, ‘The number 55 834 has 558 hundreds’. Do you agree or disagree? Why? Use mathematical terms.

Reason abstractly and quantitatively.

Ask the class if they agree or disagree. Why? Why not?

Construct viable arguments and critique the reasoning of others. Understanding, fluency and reasoning.

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What’s the difference?

Game 3

Fluently add and subtract multi-digit whole numbers.

Mathematical understanding and skills

Materials

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

For each pair of students: • Game rules and spinner (page 49) for each pair of students

Maths vocabulary

• A deck (four sets) of 0-9 digit cards for each pair of students

• algorithm

• Each player makes a double placevalue mat. (Tip: Cut A4 paper lengthwise in half to create two mats. Fold mats in half widthwise, then into thirds, to make 6 columns. Use 5 of the columns.) Example of a double place-value mat: Ten thousands

Thousands

Hundreds

Tens

Ones

8 8 8 Ten thousands

5 9

1 8

7 est Larg m su

est Largrence diffe

llest Smaum s

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Math um s gam cu l es for the Australian Curri

Game 3

What’s the difference? Explaining the game Number of players: 2

Object: Create the sum or difference that best matches the target. The player with the answer closest to the target wins the round. Ten thousands

Thousands

Hundreds

Tens

Ones

1. Spin to determine the target of the game. 2. Take turns to draw and place five cards, one card at a time, to develop the first 5-digit number. • Place each card in a different place value position. • Once a card is placed, it cannot be moved. 3. Take turns to draw a sixth card. It may be used to replace one of the cards already played, or it may be discarded. 4. Repeat steps 2 and 3 to develop the second 5-digit number. 5. Finally, both players perform the operation according to the spinner target. When subtracting, subtract the smaller number from the larger number. • Clearly record your work. Use standard algorithms. • The player with the answer closest to the target wins the round.

Differentiation More support

Challenges

• Start with a place-value mat that only goes to hundreds or thousands.

• Create 6-digit numbers. • Draw one more card than the number of place values on the mat.

• Draw one more card than the number of place values on the mat.

Advanced challenge • Create decimal numbers including tenths and hundredths. Whole numbers could be written in black and decimals in red.

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What’s the difference?

Game 3

Deepening the understanding Ask the class

Mathematical capabilities

When the target is to form the largest sum, what is a general strategy for placing the digit cards?

Make sense of problems and persevere in solving them.

[Repeat for each of the four targets.]

Reason abstractly and quantitatively.

If you create two 5-digit numbers by using each of the 0–9 number cards only once, and do not use zero in the ten thousands place:

Make sense of problems and persevere in solving them.

• What is the largest possible sum?

Reason abstractly and quantitatively. Understanding, fluency and reasoning.

• What is the smallest possible sum? Explain how you know. Use mathematical terms. Note: After a student shares an idea, ask the class if they agree or disagree. Why? Why not?

Construct viable arguments and critique the reasoning of others.

3 17 x

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Game 4

Multiplication master

Create and solve multi-digit by one-digit multiplication problems using place value strategies.

Mathematical understanding and skills

Materials

Multiply a whole number of up to four digits by a one-digit whole number using strategies based on place value.

For each pair of students: • A deck of number cards 0–9 (page 60) • Game rules, if needed, after presentation

Maths vocabulary

• Coin to flip

• digit • product

3 9 0 3

5 0 1

2 3 8 8 8

2 ®

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Multiplication master

Game 4

Explaining the game Number of players: 2 Object: Use your cards to create a multiplication problem with the smallest or largest product. 1. Flip a coin to determine the object of the game. • Heads: Create the largest product. • Tails: Create the smallest product. 2. Draw four cards. (Each player does this.) • Create a 1-digit x 3-digit multiplication problem to match the object of the game. (Zero may not be used as the first or only digit.) • Find the product. Clearly record your work. 3. The winner of the round has the product that matches the goal. • Find the difference between the winning product and the partner’s product and win that many points.

Variations (Be sure to play both variations!) Three-card variation Create a 1-digit x 2-digit multiplication problem to match the object of the game. Find the product. Five-card variation Create a 1-digit x 4-digit multiplication problem to match the object of the game. Find the product.

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Game 4

Multiplication master Differentiation Challenge

More support • Modify the deck to include only the digits 0 to 5. • Begin by using the threecard variation. Create 1-digit x 2-digit problems with the largest product.

• Deal four cards each to two players. The goal is for each player to create a 1-digit by 3-digit multiplication problem with his/her cards so that the difference between the two products is as small as possible. One example: Player A has digits 2, 3, 4 and 8

Player B has digits 2, 4, 5 and 6

4 x 823 = 3292

6 x 542 = 3252

3292 – 3252 = 40

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Multiplication master

Game 4

Deepening the understanding Ask the class

Mathematical capabilities

Create a 1-digit by 4-digit multiplication problem with five different digits. (Do not use zero as the first digit.)

Make sense of problems and persevere in solving them.

• What is the largest possible product?

Reason abstractly and quantitatively.

~ How did you use place value? ~ Would your strategy work every time with other numbers? Explain why or why not. • What is the smallest possible product? ~ How did you use place value? ~ Will your strategy work every time with other numbers? Why/why not?

Look for and make use of structure. Look for and express regularity in repeated reasoning. Understanding, fluency and reasoning.

A student said, ‘I can figure out which player has the larger product and how much larger it is without figuring out the product of either player’s problem. I just compare the products for each place value separately’.

Make sense of problems and persevere in solving them.

Explain this students’ strategy: • Player A has 642 x 9 • Player B has 731 x 8 • Who won and by how much?

Model with mathematics.

A student could see the following: • Hundreds product Player A: 600 x 9 = 5400; Player B: 700 x 8 = 5600; Player B is up by 200

Look for and make use of structure.

Reason abstractly and quantitatively.

Use appropriate tools strategically.

• Tens product Player A: 40 x 9 = 360; Player B: 30 x 9 = 270; Player B is down by 120 • Ones product Player A: 2 x 9 = 18; Player B: 1 x 8 = 8; Player B is down by 10. • Overall Player B has 200 – 120 – 10 = 70 more than Player A. After a student shares an idea, ask the class if they agree or disagree and why.

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Construct viable arguments and critique the reasoning of others.

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Game 5

Double digit doozies

Create and solve two-digit by two-digit multiplication problems using place value strategies.

Mathematical understanding and skills

Materials

Multiply two two-digit numbers, using strategies based on place value.

For each pair of students: • A deck (four sets) of 0–9 cards (page 60)

Maths vocabulary

• Game rules, if needed, after presentation

• digit

• Paper for recording work

• product

• A coin to flip

5 9

3 0

8 8 8

3 0 X

9 95 x 30 0 ®

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Game 5

Double digit doozies

Explaining the game Number of players: 2 Object: Use your cards to create a multiplication problem with the smallest or largest product. 1. Flip a coin to determine the object of the game. • Heads: Create the largest product. • Tails: Create the smallest product. 2. Each player draws four cards. • Create a 2-digit by 2-digit multiplication problem to match the object of the game. Zero may not be used as the first digit in either number. • Find the product. Clearly record your work. 3. The winner of the round has the product that matches the goal. • Find the difference between the winning product and the partner’s product and win that many points.

Differentiation More support • Modify the deck to include only the digits 0 to 5. Then gradually add other digits to the deck.

Challenge • Play this game with a partner. Deal four cards to each player. The object of the game is for each player to create a 2-digit by 2-digit multiplication problem with his/her cards, so that the difference between the two products is as small as possible. Player A has digits 2, 5, 6 and 7

Player B has digits 0, 5, 6 and 9

52 x 67 = 3484

50 x 69 = 3450

3484 – 3450 = 34

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Game 5

Double digit doozies

Deepening the understanding Ask the class

Mathematical capabilities

Choose four different digits (as a class) to create a 2-digit by 2-digit multiplication problem. Zero may not be used as the first digit of either number.

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively.

~ What is the largest product you could create? How did you use place value to create it? Explain your thinking.

Model with mathematics.

~ What is the smallest product you could create with the same cards? ~ What relationship do you see between the problems that create the largest and smallest products with these four digits? ~ If you used the same four digits to create a 3-digit by 1-digit multiplication problem, how do the largest and smallest possible products compare to the smallest and largest products possible with the 2-digit by 2-digit products? Will this always be true?

Use appropriate tools strategically. Look for and make use of structure. Look for and express regularity in repeated reasoning. A solution using 6, 7, 8, 9: Largest: 96 x 87 = 8352

After a student shares an idea, ask the class if they agree or disagree and why.

Construct viable arguments and critique the reasoning of others.

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Divide and conquer

Game 6

Practice division strategies.

Mathematical understanding and skills

Materials

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division.

For each pair of students: • A deck of 0–9 number cards (page 60) • Game rules, if needed after presentation • A coin to flip

Maths vocabulary • dividend • divisor • quotient

0 5 1

8 8 8

0 1 ÷ 7 0 ÷ 5

4 2

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99 ÷ 11 9

50 ÷ 10 0 19

Math um s gam cu l es for the Australian Curri

Game 6

Divide and conquer

Explaining the game Number of players: 2 Object: Use the number cards to create and solve a division problem with the smallest or largest quotient. 1. Flip a coin to determine the object of the game. • Heads: Create the largest quotient. • Tails: Create the smallest quotient. 2. Each player draws 4 cards. • Arrange the cards to form a division problem with a 1-digit divisor and a 3-digit dividend. • Zeroes may only be placed in the dividend, in the tens or ones place. • After you place the cards, you cannot move them. 3. Divide. Use a strategy that works for you. 4. Partners check each other’s work. 5. The winner of the round earns 1 point.

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Game 6

Divide and conquer

Differentiation More support

Challenge

• Begin by simplifying the game—for example, use fewer cards. • Work with one dividend and divide by several different divisors to see a pattern. Next, work with one divisor and many different dividends. Look for a pattern/ generalisation. If needed, begin with easier divisors.

• Draw more than four cards for the dividend. • Make the divisor ten times more than the card drawn.

Deepening the understanding Ask the class

Mathematical capabilities

Jackson drew the cards 9, 5, 2 and 0. What division problem will make the largest quotient?

Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. Use appropriate tools strategically. Understanding, fluency and reasoning. Look for and make use of structure. Look for and express regularity in repeated reasoning.

What strategy did you use? Will your strategy work with other digits? How do you know?

If you could choose any four digits, how would you use them to make the problem with the largest possible quotient? Explain why your strategy works. If you could choose any four digits, how would you use them to make the problem with the smallest possible quotient? Explain why your strategy works.

Note: After a student shares an idea, ask the class if they agree or disagree. Why? Why not?

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21 Math um s gam cu l es for the Australian Curri

Game 7

Factors and multiples

Identify factors and multiples of whole numbers in the range of 1–100.

Mathematical understanding and skills

Materials

Gain familiarity with factors and multiples.

• One game board for each pair of students (page 50)

Maths vocabulary

• Game rules, if needed, after presentation

• composite • factor

8 X 9 10 X X

• prime

12 X

15 X

18 X

40 X

99 100

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Game 7

Factors and multiples Explaining the game Number of players: 2

Object: Work together to mark as many numbers as possible. 1. Player 1 marks numbers with an ‘O’, Player 2 marks numbers with an ‘X’. 2. Player 1 marks a multiple of 2. 3. Player 2 marks a factor or a multiple of the previous number. 4. Players take turns marking a factor or a multiple of the previous number. 5. Continue until no more moves are possible. 6. Count how many numbers are marked. 7. Start another game and try to end with more marked numbers.

11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 17 18 19 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Example • Player 1 circles 12. • Player 2 can mark either: ~ One of the factors of 12 (1, 2, 3, 4 or 6) ~ One of the multiples of 12 (24, 36, 48, 60, 72, 84 or 96).

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23 Math um s gam cu l es for the Australian Curri

Factors and multiples

Game 7

Differentiation More support

Challenge

• Use a 1–40 game board for a few games before using the 1–100 game board.

• Play the game competitively.

Deepening the understanding Ask the class

Mathematical capabilities

What advice would you give someone who was going to play this game and wants to mark as many numbers as possible before getting stuck?

Make sense of problems and persevere in solving them.

• What strategies do you recommend?

Understanding, fluency and reasoning.

• Which numbers should a player mark first? Why?

Look for and make use of structure.

Jen said that it is helpful to choose composite numbers in this game. Do you agree? Why or why not?

Reason abstractly and quantitatively.

Understanding, fluency and reasoning. Look for and make use of structure.

After a student shares an idea, ask the class if they agree or disagree and why.

Construct viable arguments and critique the reasoning of others.

Note: This game is based on a classic maths game called Juniper Green. The original Juniper Green game was developed by Richard Porteous, of Edinburgh, Scotland, to help his students learn multiplication and division.

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Game 8

Which is greater?

Compare fractions with different numerators and different denominators.

Mathematical understanding and skills

Materials

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1⁄2. Recognise that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, = or < and justify conclusions, e.g. by using a visual fraction model.

For each pair of students: • Game rules and spinner (page 51) • Recording sheet (for Warm-ups and for game) (page 52) • Number cards 1–9 for Differentiation challenge activity (page 60) • Fraction bars or fraction circles (for Warm-ups) (page 53)

Maths vocabulary • denominator • numerator

Warm-up A: Same denominator To play: • Spin only one denominator. Both players use that denominator. • Each player spins a numerator. • Each player writes his or her fraction on the recording sheet. Compare the fractions.

If the fractions are equivalent:

• The player with the greater fraction:

• Each player writes half of the equal sign (=).

~ Records the correct symbol (< or >) in the circle.

• Both players earn a point.

~ Explains why his/her fraction is larger with words and/or with diagrams, visuals or a number line. ~ Wins a point.

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25 Math um s gam cu l es for the Australian Curri

Game 8

Which is greater?

Warm-up B: Same numerator This game is similar to Warm-up A, but players spin only one numerator. Both players use that numerator. Each player spins a denominator.

Spinners

3 5

Numerator

100 6

Denominator

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Which is greater?

Game 8

Explaining the game Number of players: 2 Object: Spin and compare fractions with different numerators and different denominators.

1. Take turns to spin a numerator and a denominator. 2. Each player writes his or her fraction on the recording sheet. 3. Compare the fractions. (a)

(b)

If the fractions are equivalent: •

Players write the equal sign (=).

•

Both players earn a point.

If the fractions are not equivalent, the player with the greater fraction: • Records the correct symbol (< or >) in the circle. • Explains why his/her fraction is larger by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1⁄2. • Wins a point.

Differentiation More support • Allow more time to play the Warm-up games A and B before playing the ‘Which is greater?’ game.

Challenge • Play the ‘Smaller fraction’ game for two players with these rules: ~ Use number cards 1–9. ~ Each player draws two cards. ~ Create the smallest possible fraction with the two cards. ~ Record and compare the fractions. The smaller fraction wins.

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27 Math um s gam cu l es for the Australian Curri

Game 8

Which is greater?

Deepening the understanding Ask the class

Mathematical capabilities

If two fractions have the same denominator, how can you tell which is greater?

Reason abstractly and quantitatively.

A student said that 29 is greater than 27 because 9 is more than 7. Explain the flaw in this student’s logic. Use maths terms.

Reason abstractly and quantitatively.

Which is larger, 3⁄8 or 4⁄5?

Reason abstractly and quantitatively.

Explain using two methods.

Model with mathematics.

Understanding, fluency and reasoning.

Use appropriate tools strategically. Understanding, fluency and reasoning. Challenge:

Reason abstractly and quantitatively.

Which is larger, 7⁄12 or 75⁄100?

Use appropriate tools strategically.

Explain using three methods.

Understanding, fluency and reasoning.

Note: After a student shares an idea, ask the class if they agree or disagree. Why? Why not?

Construct viable arguments and critique the reasoning of others.

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Game 9

Feuding fractions

Compose and decompose fractions with like denominators.

Mathematical understanding and skills Understand addition of fractions as joining parts referring to the same whole.

Maths vocabulary • denominator

Materials • A deck (four sets) of 8ths (page 61) or 12ths (page 54) for each pair of students, but remove all cards with the numerator of zero. • A deck of 5ths (optional) (page 53)

• mixed number

• Game rules, if needed, after presentation

• numerator

• Fraction cards • Fraction bars or fraction circles (optional)

⁄8

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⁄8

29 Math um s gam cu l es for the Australian Curri

Game 9

Feuding fractions

Warm-up game: Make-a-whole solitaire Number of players: 2 Materials: One deck of fraction cards Object: Make pairs with fraction cards that equal one whole. 1. Deal five cards facing up. Place the remaining cards in a stack facedown. 2. Make pairs that equal one and collect them in a ‘win pile’. 3. Draw cards from the deck to replace any of the five cards that were used. 4. Continue making pairs that equal one. If you cannot make a pair, draw one more card at a time until you can. 5. Play stops when all cards have been used.

⁄

2 8

⁄

4 8

881⁄8

⁄

6 8

⁄

3 8

8 8 8

⁄

5 8

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Game 9

Feuding fractions

Explaining the game A: Fishing for fractions Number of players: 4 Materials: One deck of fraction cards (either eighths or fifths) Object: • Put (only) two cards together to make one whole. • Create as many pairs that make one whole as possible. The player with the most pairs is the winner. 1. Deal 5 cards to each player. Place the remaining cards facedown, spread out as ‘the pond’. The person to the left of the dealer is Player 1. 2. Player 1 puts all pairs of his/her cards that add up to one whole on the table. (The game is similar to ‘Go Fish’.) 3. Player 1 asks Player 2 for a fraction that, when added to a card in his/her hand, will make one whole. 4. If Player 2 has the fraction, he/she gives it to Player 1. Player 1 may put down that pair. Then it is the next player’s turn. 5. If Player 2 does not have the fraction, he/she says, ‘Go fishing’. Player 1 draws a card from the pond. If the card that is drawn completes a pair that adds up to one whole, Player 1 may put down that pair. Then it is the next player’s turn. 6. Take turns, repeating steps 1 and 2. If a player runs out of cards, he/she draws one from the pond. Then it is the next player’s turn. 7. After the pond is empty, players with cards continue taking turns until all cards that can make one whole are played.

Variations Put the fractions ⁄8 and higher in one deck to be used as the targets and put the cards with smaller fractions in a ‘draw pile’. Draw a card from the ‘target deck’. That fraction is the ‘target’ of the game. Draw playing cards from the ‘draw pile’ and follow the ‘Fishing for fractions’ rules. 5

~ Compose the target fraction by joining two ‘draw pile’ fraction cards. ~ As each player sets down the pair of cards, say the equation. For example, if the target is 7⁄8 and the cards are 2⁄8 and 5⁄8, the player says, ‘2⁄8 plus 5⁄8 equals 7⁄8’.

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31 Math um s gam cu l es for the Australian Curri

Game 9

Feuding fractions

Explaining the game B: Feuding fractions Number of players: 2 Materials: A deck of 8ths or a deck of 12ths for each pair of students (remove all cards with the numerator of zero.)

Object: Add fractions. • The player with the larger sum wins the cards of that round. • The player who captures most of the cards is the winner. 1. To start a turn, each player: • Draws 2 cards from the deck. • Adds the fractions. If the sum is less than one, player draws additional cards just until the sum is at least one whole. 2. Each player: • Reports the sum of all cards as a whole number or as a mixed number. • Checks and compares the sums of both players. 3. The player with the larger sum wins all the cards of that round. 4. If both players have the same sum, they return the cards to the bottom of the deck and again. 5. Play continues until one player wins by capturing most of the cards.

⁄8

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Game 9

Feuding fractions

Differentiation More support

Challenges

• Let students add pictorial representations of fractions to eighths cards or fourths cards. (Four sets in each deck.) Then play with those decks.

• Use a mixed deck of fourths and eighths, or a deck of halves, fourths and eighths. • Play with other targets (e.g. winner is the player whose sum is closest to 1⁄2 or 11⁄2).

Deepening the understanding Ask the class

Mathematical capabilities

What are all the ways you can write 5⁄8 as the sum of cards in the eighths deck?

Reason abstractly and quantitatively.

If you need to trade the seven cards below for two cards with the same value as the original seven cards, what are your options?

Reason abstractly and quantitatively.

⁄12, 1⁄12, 1⁄12, 1⁄12, 1⁄12, 1⁄12, 1⁄12

If you had 7⁄8 and 4⁄8, how could you easily add them in your head?

Reason abstractly and quantitatively.

(Note: An easy option is to decompose 4⁄8 into 1⁄8 + 3⁄8, and then add 7⁄8 + 1⁄8 = 1; 1 + 3⁄8 = 13⁄8) If you had 2⁄8, 5⁄8 and 6⁄8, how could you re-arrange the fractions to add them in your head?

Reason abstractly and quantitatively.

After a student shares an idea, ask the class if they agree or disagree and why.

Construct viable arguments and critique the reasoning of others.

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33 Math um s gam cu l es for the Australian Curri

Game 10

Fraction salute

Add and subtract fractions and mixed numbers with like denominators.

Mathematical understanding and skills

Materials

Add and subtract mixed numbers with like denominators, e.g. by using the relationship between addition and subtraction.

• Game rules (optional) • One deck of 8ths fraction cards for every 3 students (page 61) • Variation: other fraction cards (all same denominator)

Maths vocabulary • denominator • mixed number • numerator

1 /8 1

8 8 8

⁄ ⁄⁄

5 55888

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Game 10

Fraction salute

Explaining the game Number of players: 3—one captain and two players (roles may rotate) Materials: One deck of 8ths for every 3 students Object: • Find the missing addend to solve your own mystery card. • The first player to correctly solve his/her own number wins 1 point. 1. When the captain says ‘salute’, each player: • Draws a card • Does not look at the card • Puts the card on his/her forehead facing out so others can see it. 2. The captain: • Adds the numbers on the two cards • Reports and writes the sum as a fraction or as a mixed number if it is greater than one. 3. Each player: • Compares the fraction they see on the other player’s forehead to the sum • Figures out what card is on his/her own forehead • Play continues until both players figure out their card.

Captain says: ‘11⁄8’ ‘Remember, no peeking at your card!’

⁄8

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⁄8

35 Math um s gam cu l es for the Australian Curri

Game 10

Fraction salute

Differentiation More support

Challenge

• Use a deck of 4ths or 5ths instead of 8ths.

• Use a mixed deck of fractions, such as 4ths and 8ths.

Deepening the understanding Ask the class

Mathematical capabilities

As the captain, you need to add fractions. What strategies could you use to add 5⁄8 and 5⁄8?

Reason abstractly and quantitatively.

If you are one of the players …

Reason abstractly and quantitatively.

Explain two ways you could figure out your own fraction if the sum is 13⁄8 and you can see 5⁄8 on the other player’s forehead. In a special game the captain gave different clues. She said, ‘The sum is greater than 1 and the difference is less than 4⁄8.’

Make sense of problems and persevere in solving them.

• You can see that your partner has 7⁄8.

Reason abstractly and quantitatively.

• What are all the possible cards you could have? Note: After a student shares an idea, ask the class if they agree or disagree. Why? Why not?

Construct viable arguments and critique the reasoning of others.

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Game 11

Fraction action

Multiply a fraction by a whole number.

Mathematical understanding and skills

Materials

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

For each pair of students: • Fraction action recording sheet (page 55) • A deck (four sets) of number cards (2, 3, 4, 5, 6 and 8 only) (page 60) • Fraction bars or circles

Maths vocabulary • denominator

• Coin to flip

• mixed number • numerator

5 4

Player B Player A

Round 1

/4 1 /4 1 /4 1 /4

⁄4

Round 2

⁄8

Round 3

/8 1/ 8

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⁄5

Round 4 Round 4

⁄6

Round 5 Round 5

⁄10

37 Math um s gam cu l es for the Australian Curri

Game 11

Fraction action

Explaining the game Number of players: 2 Object: Make the largest (or smallest) product by multiplying a whole number by a fraction. Materials: For each pair of students: • Fraction action recording sheet • Coin to flip • A deck of number cards 1–9 for each pair of students • Fraction bars or circles and student-made number lines 1. Flip a coin (heads for largest product, tails for smallest product). 2. Each player: • Draws three cards and looks at the numbers. • Writes one number in each blank space on the recording sheet and discards the third number. • Cards are then placed back in the deck. • Finds the product and writes it on the recording sheet. (May use a visual fraction model.) 3. Play five rounds. The player with the most wins is the winner of the game.

Example of the Fraction action recording sheet. 3 cards drawn

Recording

⁄6

= /6

Note: Teachers may or may not decide to have students convert the product from an improper fraction to a mixed number.

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Game 11

Fraction action

Differentiation More support

Challenge

• Use a deck, four sets, of number cards 1–4 and this recording sheet.

• Ask students to generate a rule for multiplying fractions by whole numbers.

• Player A draws three cards, writes one number in each blank space on the recording sheet and discards the third. Uses visual models to find or verify the product. • Player B draws three cards and uses two of them to make a multiplication problem with a product that is as close as possible to Player A’s product. Uses visual models to find or verify the product. • Then flip the coin to determine the winner of the round (heads for largest product, tails for smallest product). If the fractions are equal, both players earn a point. Player A

Player B

Round 1

⁄4

Round 2

⁄4

Round 2

⁄4

Round 3

⁄4

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39 Math um s gam cu l es for the Australian Curri

Game 11

Fraction action

Deepening the understanding Ask the class:

Mathematical capabilities

Maria says: 2 x 5⁄6 = 10 x 1⁄6

Reason abstractly and quantitatively.

Do you agree or disagree?

Understanding, fluency and reasoning.

Show and/or explain your thinking in two or more ways.

Look for and make use of structure.

Use mathematical terms. A student wrote: 3 x 2⁄5 = 6⁄15

Reason abstractly and quantitatively.

He explained, ‘That’s what you get when you multiply the numerator and the denominator by 3’.

Understanding, fluency and reasoning. Look for and make use of structure.

Do you agree or disagree? Explain. Ali wrote: 2 x 4⁄5 = 4 x 2⁄5

Reason abstractly and quantitatively.

Do you agree or disagree? Why?

Look for and make use of structure.

Will this rearrangement of numerator and whole number always produce equal products? Justify your answer.

Look for and express regularity in repeated reasoning.

Write an equation with a whole number times a fraction on each side of the equal sign. Use the digits 3, 6 and 9 on each side of the equation.

Make sense of problems and persevere in solving them.

What pattern(s) do you notice?

Reason abstractly and quantitatively. Look for and make use of structure.

Why does the pattern work? After a student shares an idea, ask the class if they agree or disagree and why.

Construct viable arguments and critique the reasoning of others.

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Game 12

Duelling decimals

Use decimal notation for fractions and compare decimal fractions.

Mathematical understanding and skills

Maths vocabulary

• Use decimal notation for fractions with denominators of 10 and 100.

• denominator

• Compare two decimals to hundredths by reasoning about their size. Recognise that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, + and <, and justify the conclusions, e.g. by using a visual model.

• numerator

• mixed number

Materials For each pair of students: • ‘Duelling decimals’ game board (page 56) • Game rules • Two coloured markers • Choice of spinners: Spinners A and B (more support) or Spinner C (Challenge)

0.18 2

⁄100

⁄10

0.1

⁄100 0.2

⁄10

⁄100 ⁄10

0.17 1

⁄10

0.05 2

0.15 2

⁄10

0.08

⁄10

0.16 4

⁄100

0.14

⁄100

0.1

0.03

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To use the spinner, place a pencil tip through a paperclip.

41 Math um s gam cu l es for the Australian Curri

Game 12

Duelling decimals

Explaining the game Number of players: 2 Object: Colour the greatest total amount of the ‘whole.’ 1. Player 1 spins. • If a fraction is spun, uses the decimal notation for the fraction. • Colours a polygon (not necessarily a rectangle) in one of the four corners of the 10-by-10 grid that represents the decimal number. • Labels the polygon with the portion of the grid it represents. 2. Player 2 spins. • Starts another polygon in the opposite corner with a different colour. • Labels the polygon with the portion of the grid it represents. 3. The players record the results of this round in a table and circle the larger decimal fraction. See example below. 4. The players continue taking turns spinning and drawing polygons. Each added polygon: • Must share a side or part of a side of one of the player’s own polygons. (Only touching at one corner does not count.) • May only use squares that have not already been used. • May touch a side of the other player’s polygon(s). 5. Play stops when a player cannot fit a polygon on the board. 6. The winner is the player who wins the most rounds.

0.05

Recording table example

0.1

Player 1

Player 2

0.05

0.1

0.2

0.11

0.04

0.16

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Game 12

Duelling decimals

Differentiation More support

Challenge

• Focus first on decimals. Play the game with Spinner A.

• Use Spinner C, which includes some fractions in simplest form.

• Warm-up with fractions and decimals in hundredths (Spinner B).

Deepening the understanding Ask the class

Mathematical capabilities

What is the decimal fraction for 7⁄10?

Reason abstractly and quantitatively.

What is the decimal fraction for 7⁄100?

Model with mathematics.

Which is larger? Use a model to justify your answer (money, 100 grid, number line etc.). Which number is greater?

Reason abstractly and quantitatively.

0.4 or 0.04

Understanding, fluency and reasoning.

Explain how you know.

0.5 or 0.47 6

⁄10 or 0.58

After a student shares an idea, ask the class if they agree or disagree and why.

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Construct viable arguments and critique the reasoning of others.

43 Math um s gam cu l es for the Australian Curri

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Reproducibles ACTIVITY-SPECIFIC Game 1

REPRODUCIBLES

‘Guess my secret’ game board .................................................................... 46 ‘Guess my secret’ game cards ..................................................................... 47 ‘Guess my secret’ alternate game cards ..................................................... 48

Game 3

‘What’s the difference?’ spinner for the target ............................................. 49

Game 7

‘Factors and multiples’ game board ............................................................ 50

Game 8

‘Which is greater?’ spinners ........................................................................... 51 ‘Which is greater?’ recording sheet ............................................................... 52

Game 9

‘Feuding fractions’ 5ths fraction cards ......................................................... 53 ‘Feuding fractions’ 12ths fraction cards ....................................................... 54

Game 11

‘Fraction action’ recording sheet .................................................................. 55

Game 12

‘Duelling decimals’ game board .................................................................. 56 Spinners A, B and C .................................................................................. 57–59

REPRODUCIBLES

USED IN MORE THAN ONE ACTIVITY

0–9 number cards Used in games 2, 4, 5, 6 and 11 ........................................................................................... 60 8ths fraction cards Used in games 9 and 10 ...................................................................................................... 61

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45 Math um s gam cu l es for the Australian Curri

Game 1

Game 4

oard Game b

Game 3

Game 2

Game 1

Guess my secret

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Game 1

Guess my secret

ards Game c

(a) Start with 20. Then add 6 each time.

(b) Start with 30. Then add 9 each time.

(d) Start with 325. Then subtract 25 each time.

(e) Pick a start number larger than 25. Then add a constant amount.

(f)

Pick a start number larger than 500. Then subtract a constant amount.

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47 Math um s gam cu l es for the Australian Curri

Game 1

Guess my secret

s card Alternate game

(g) Start with 3. Then add 2 each time.

+2 +2 +2 3

(h) Start with 2. Then add 5 each time.

+5 +5 +5 2 (i)

Start with 17. Then add 2 each time.

+2 +2 +2 17 19 21 (j)

Start with 20. Then add 4 each time.

+4 +4 +4 20 24 28 (k) Start with 45. Then add 5 each time.

+5 +5 +5 45 50 55

速

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Whatâ&#x20AC;&#x2122;s the difference?

Game 3 t targe Spinner for the

To use the spinner, place a pencil tip through a paperclip.

Largest sum

Largest difference

Smallest sum

Smallest difference

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49 Math um s gam cu l es for the Australian Curri

Game 7

Factors and multiples

oard Game b

99 100

速

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Game 8

Which is greater?

er s Spinn

3 5

4 Numerator

100 6

Denominator tions.com.au R.I.C. Publications 速 cpublica www.ri

51 Math um s gam cu l es for the Australian Curri

Game 8

Which is greater?

Recording

she e

Round 1 Player 1

Player 2

Player 1

Player 2

Player 1

Player 2

Player 1

Player 2

Player 1

Player 2

Player 1

Player 2

Fractions: Round 2

Fractions: Round 3

Fractions: Round 4

Fractions: Round 5

Fractions: Round 6

Fractions:

速

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⁄5 ⁄5 3

⁄5 ⁄5

1 0

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s card

⁄5

5ths fraction

⁄5

Feuding fractions

Game 9

53 Math um s gam cu l es for the Australian Curri

Game 9

⁄12

s card

⁄12

8 7 6 5

⁄12 ⁄12

2 0

⁄12

12ths fraction

⁄12

Feuding fractions

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Game 11

Fraction action

Recording

Player A

t she e

Player B Round 1

Round 1

⁄4

Round 2

⁄4

⁄8

⁄5

⁄6

⁄10

Round 2

⁄8

Round 3

⁄5

Round 4

⁄6

Round 5

⁄10

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55 Math um s gam cu l es for the Australian Curri

Game 12

Duelling decimals

Player 1

oard Game b

Player 1

Player 2

Player 1

Player 2

速

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Game 12

Duelling decimals

0.19

rA Spinne

0.04 0.2

0.09 0.06

0.1

0.2

0.11

0.08

0.05

0.2

0.13 0.17

0.3 0.1

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0.14

57 Math um s gam cu l es for the Australian Curri

Game 12

Duelling decimals

⁄100

rB Spinne

0.17 0.07

0.04 2

⁄100

0.20

⁄100

0.09

⁄100

0.10 0.08

0.02

⁄100

0.05

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ublications.com.au

C R.I.

blic . Pu

ns atio

Game 12

Duelling decimals

1 16

0.18

⁄100

⁄10

rC Spinne

0.07

⁄100 0.2

⁄4

⁄100 ⁄100

0.17

⁄10

0.06

⁄10

0.15 1

0.08

⁄5 1

0.09

⁄100

0.14

⁄100

tions.com.au R.I.C. Publications ® cpublica www.ri

⁄100

0.2

⁄5

0.1

59 Math um s gam cu l es for the Australian Curri

Used in games 2, 4, 5, 6 and 11

5 6 7 8 9

0 1 2 3 4

0â&#x20AC;&#x201C;9 number cards

ÂŽ

Maths games for the Australian Curricu lu

www.r icp

ublications.com.au

C R.I.

blic . Pu

ns atio

⁄8 ⁄8

⁄8

7 6

tions.com.au R.I.C. Publications ® cpublica www.ri

⁄8 0

⁄8

Used in games 9 and 10

8ths fraction cards

61 Math um s gam cu l es for the Australian Curri