36 Maths Games

RIC-2370 6/1038

36 maths games of chance and strategy

Copyright Notice Published by R.I.C. Publications® 2012 Copyright© Catherine Connolly 2012 ISBN 978-1-84654-347-0 PR– 2370

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.

Titles available in this series: 30 maths games for lower primary (Ages 5–7) 36 maths games of chance and strategy for lower primary (Ages 5–8)

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.

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Foreword 36 maths games of chance and strategy for lower primary (Ages 5–8) is a teacher resource book of fun, hands-on board games which provide opportunities for students to acquire and practise mathematical skills in number, number operations, measurement, shape and space, and strategy. The variety of photocopiable games in the book provides tactile opportunities to use knowledge in a relaxed ‘play’ situation without memorising or tedious rote learning.

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Another R.I.C. Publications® title you might want to check is: 30 maths games for lower primary

The Racetrack Money game .................... 38–41 Tens and Units game .............................. 42–43 Stepping Stones game ............................ 44–46 Pay the Difference game ................................ 47 Snakes and Ladders game ...................... 48–49 The 100-Square game ............................ 50–51 Combinations game ................................ 52–53 The Tallest Giraffe game ......................... 54–57 The Longest Toothbrush game ................ 58–59 Shape and Direction game (2-D) ............. 60–61 Shape and Direction game (3-D) ............. 62–63

Book format ............................................... iv – v Introduction ..............................................vi – vii Basic game-playing rules ............................... viii Using the games ......................................viii – ix Making the games ..................................... ix – x Suggestions for organising the games ....... x – xi How it works ................................................... xi Parent Paired Maths Record .....................xii – xiii Loan sheet for borrowed games ..................... xiv Language cards .................................... xv – xvii Letter to parents ...........................................xviii Throwing the dice and rules of play ............... xix Thank you cards for parents ........................... xx Congratulations cards for students.................. xxi Checklist for parents ..................................... xxii Spinners and arrows ...........................xxiii – xxvi

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Section 2 – Games of strategy ........... 64–93 Strategy games ...................................... 64–65 Noughts and Crosses game .................... 66–67 Three Men’s Morris game ....................... 68–69 Nine-Point Star game .............................. 70–71 Six Men’s Morris game ........................... 72–73 Nine Men’s Morris game ......................... 74–75 Twelve Men’s Morris game ..................... 76–77 Four in a Row game ................................ 78–79 Five in a Row game ................................ 80–81 Cat and Mice game ................................. 82–83 Fox and Geese game .............................. 84–85 Draughts and Checkers game ................. 86–87 Chinese Checkers game ......................... 88–89 Pathway game ........................................ 90–91 Mancala game ........................................ 92–93 References .................................................... 94

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Section 1 – Games of chance ............... 1–63 Large Lollipop game ................................... 2–3 Hen game ................................................... 4–5 Snail game ................................................. 6–7 Space Invaders® game ............................... 8–9 Pairs to Make 10 game ........................... 10–11 Pairs to Make 20 game ........................... 12–15 Number Dominoes game ........................ 16–29 Odd and Even game ................................ 30–32 Build a Ladybird game ................................... 33 Halves game ........................................... 34–35 Hen game (Doubles) ............................... 36–37

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36 maths games of chance and strategy

Book format – 1 Pairs to Make 10 game Aim To aid recall of pairs of numbers which make 10 What you need: A set of 20 cards (enlarged) Number of players Two How to play The cards are shuffled and placed facedown on the playing surface. Players take turns to turn over two cards at a time. They add the dots on both cards. If the dots add to 10, these cards are removed from the board and kept next to the player.

That player has made a ‘trick’.

If the cards do not make 10, they are returned to the playing surface and placed facedown in their original position. Play continues until no more pairs can be made. The player with more pairs is the winner.

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Most games include: • full instructions • a baseboard.

Each instruction page provides information about: • the aim of the game • what you need – details of the equipment needed to play the game • the number of players needed to play the game • how to play – instructions for playing the game.

Some games are accompanied by variations, notes or extension activities.

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36 maths games of chance and strategy

Stepping Stones game baseboard (blank)

The Racetrack Money game Aims 1. To practise moving from one space to the next using a counter 2. To practise counting on and addition skills 3. To provide practice with recognising, exchanging and using coins to the value of 20c/30c/40c/50c 4. To provide practice tendering and receiving amounts of money to the value of 20c/30c/40c/50c What you need: t Four to six side racetrack baseboards and four corner racetrack baseboards arranged as shown, with smiley and sad face symbols dotted randomly along the track. t One or two six-sided dice featuring numerals or dots from 1 to 6. If practising addition skills, use one dice with numerals and the other with dots. Start with the numeral and count on using the dots. t A pack of ‘smiley face’ bonus cards* t A pack of ‘sad face’ penalty cards* t A variety of ‘coins’ for each player to the value of 20c/30c/40c/50c t A place marker such as a counter for each player

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C.Publ i cat i ons •f orr evi ew pur posesonl y• Number of players Two to four (One will be the banker.)

How to play Players take turns to throw the dice and move their marker around the track, according to the number thrown. If a player lands on a smiley face symbol, he or she draws a card from the ‘smiley face’ pack and receives a bonus (collects money from the bank). If, however, a player lands on a ‘sad face’ symbol, he or she draws a card from the appropriate pack and incurs a penalty (pays money to the bank). Drawn cards are returned to the bottom of the pile or placed in a discard pile. The discard pile can be shuffled and used as play continues. The player who has accumulated the most money at the end of the game is the winner.

Variation Players can play with half a racetrack initially. As players’ skill with exchanging and using coins increases, the bonus/penalty cards can be made more complex.

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Note* Teachers will need to make the cards and glue a ‘smiley face’ on the back of the ‘Collect from bank’ cards and a ‘sad face’ on the back of the ‘Pay to bank’ cards.

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Build a Ladybird game Aims 1. To reinforce addition skills up to 20 (Level 1) 2. To reinforce understanding and use of addition skills, with carrying up to 50 (Level 2) What you need: t A card shared between players showing scoring points. These points also correspond to the throw of the dice.

Body Head Legs (all six) Feelers/Antennae (both) Spots (up to any number)

(6 (5 (4 (3 +(2 20

points) points) points) points) points) points in total

t A blank sheet of paper for each player to draw on and a pencil. Alternatively, use a board and chalk. t A six-sided dice featuring numerals 1 to 6. (‘One’ can be a bonus symbol that allows the player to draw the ladybird part of his/her own choice.)

Number of players Two players and one recorder. (Alternatively, players can do their own recording.)

How to play Level 1 The object of this game is for each player to progressively draw a picture of a ladybird. They do this by throwing the dice and drawing the part of the ladybird to which the number on the dice corresponds. (Refer to the scoring points table above.)

Before the players commence the game, show them how to draw a simplified ladybird shape: a circle for the body, semicircle for head, two antennae, six legs, and any number of spots. Players take alternate turns and must throw a 6 to begin. They then draw the body of the ladybird. Players cannot draw antennae until the head has been drawn. Spots and legs can be drawn in any order. The first player to complete his or her drawing shouts ‘ladybird’ and is the winner, signifying the end of the game. Both players total their scores.

Level 2 After the first game has ended, play can continue for two more games with players recording their finishing score each time. At the end of three games, the player with the higher overall score is the winner.

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Variation This game can be adapted to drawing parts of a bird. Use a simplified picture, making use of circles and triangles.

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36 maths games of chance and strategy

Each baseboard is simply illustrated and can be easily photocopied, coloured and laminated for use. All can be enlarged for ease of use.

Each is clearly labelled so teachers can match the baseboard to the corresponding game instructions.

Some games, such as the ‘Stepping Stones game’, include a blank format so that teachers can include the numbers of their choice and make them more appropriate for the ability level of the children in their class.

Others, such as the ‘Build a Ladybird game’, do not have a baseboard but have full instructions and examples to assist the teacher.

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36 maths games of chance and strategy

Introduction Board games have long held the public’s interest.

Not only are they fun, they play an important role in harnessing the impulse for play in young children to develop and consolidate mathematical concepts.

Mathematics is about the acquisition, understanding and application of skills. As, the Cockcroft report (1982) states:

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‘All pupils need opportunities to practise skills and routines which they have recently acquired and to consolidate those which they already possess so they may be available for use in problem solving.’

(Paragraph 248).

However, the report further urges that mathematics be presented as a subject for use and for enjoyment. To provide meaningful and interesting mathematical experiences for all learners, teachers need to be flexible in their selection of teaching strategies, materials and reinforcement methods. Mathematical board games, used in the classroom or in the home, provide an opportunity through play for the acquisition and practice of basic skills by students from a wide spectrum of ability, learning readiness and interests.

Due to the shorter attention span of most young learners, a lot of repetition of basic concepts is required both to anchor and retain those concepts. Repetitive memorising is tedious, with the onus of responsibility on the teacher to provide this constant consolidation. The variety of games within this book provides the less able child with much-needed repetition. Games can make repetitive memorising interesting, while helping to reinforce lightly held knowledge. While playing the games, children are relaxed and have a good learning disposition. Crucially, the element of chance inherent in the games allows equalisation of opportunity, so that a less able child can succeed. Combining dice allows the games to be played at varying levels of difficulty so that more able children are constantly being challenged. The visually appealing, exciting and tactile aspects of the games ‘respect’ the brain’s learning patterns by providing sensory, emotional and physical involvement in learning. Hannaford (1995) calls this ‘the elaborate interplay of brain and body in learning’.

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Mathematical board games simultaneously satisfy many of the pedagogical, psychological, sociological and emotional needs of young learners by:

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• aiding the development of visual, motor and memory skills • promoting a desire for competence.

They also provide:

• learning opportunities for the visual, auditory and kinaesthetic learner through the use of artwork, social interaction and movement • excitement and challenge at varying levels of difficulty • a happy, purposeful and intrinsically motivating activity taken at a child’s own pace and an activity in which children are actively involved • ownership of the learning process and reduced dependence on the teacher • instantaneous and self-evident feedback (because the child will either win or lose).

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Board games also: • • • • • • •

cultivate a positive attitude towards mathematics encourage persistence, perseverance and a ‘try again’ mindset … all attributes of the self-regulated learner promote acceptance of victory, defeat and reversals of fortune; e.g. unexpectedly getting a zero stimulate mathematical discussion often after the event provide a face-saving device for the losing player through the use of dice promote mental computations; for example: ‘I need three more to reach the end’ focus a player’s process skills, such as implementation, application, communication and expression, integration and connection, understanding and recall • provide numerous counting opportunities • have enough structure and rules to satisfy the learner’s security needs … yet are open-ended.

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From a school perspective, they:

promote parental involvement through paired maths games activities allow the teacher, through observation, to identify gaps in learning and rectify them link with existing mathematical structures as well as having cross-curricular links ensure high participation levels as the competitive element inherent in the games ensures the undivided attention of most players • allow older school students and ‘buddy class’ members to work with younger children on a fun activity.

For photocopiable resources and more information on the theory and practice underlying paired maths, and for an international perspective on this approach, read Topping and Bamford (1998) and Topping, Bamford et al (1998).

Refer to the references on page 94 at the end of the book.

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Basic game-playing rules It is important to establish basic ground rules for playing games. These rules are best learnt initially with two-player games as there is less confusion about turn taking. Praise children who play by the rules and treat others fairly.

Play depends on whatever symbol of the dice lands uppermost.

Wait for your turn and when it comes, do not take several turns at once.

Play does not resume until the previous player has completed his or her turn.

If a numeral or space is already covered, play passes to the next player.

When each individual play is completed, place the dice back in the shaker and pass it to the next player.

Accept that things will not always go your way.

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Using the Games

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In the classroom Where there is more than one game dealing with the same teaching point, start with a game you think the children will like, and over a period of time add to your collection. As your collection increases, rotate the games to retain children’s interest. Games can be slotted into the timetable as one of your play activities in the afternoon or morning.

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It is important that games are easily accessible so that children can collect and return them with as little help as possible. Praise children who put games away in an orderly manner. Games could be stored in individual plastic wallets on a designated maths table.

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Games are pictorial representations of the ‘real thing’, and it is presumed that a lot of concrete work will precede the use of these games; for example, talking about food, healthy eating, colours, items of clothing or showing real items of food.

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You might decide to keep the dice in a special container on your desk. Ensure that children return the dice to that container while you oversee the return.

This reduces the number of dice going astray.

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In relation to number work, nothing can replace children working with concrete materials as a foundation for the important mathematical concepts of counting and numeration, number operations, spatial awareness, algebra (recognising patterns in numbers), fractions, comparing and ordering, place value, length and classifying objects by shape. The purpose of the games in this book is to consolidate such work in an exciting and pleasurable way.

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For paired maths Paired maths follows the same format as shared reading. It is a system for parents, or sometimes older students, which allows them to interact with children using structured mathematical material. It is a gamebased approach with a focus on:

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• parental involvement by harnessing the interest, energy and enthusiasm of parents in their child’s development • developing a positive attitude to mathematics in all parties involved through the use of stimulating activities or materials • learning in a social context through human support, interaction and feedback—something that is difficult to replicate on a computer • equality of opportunity among players, with the element of chance introduced through the use of dice • equality of access for all children and their families, including special needs children • discussion, often after the event, and the promotion of mathematical vocabulary. Each game has a list of keywords.

Over the course of the use of this book, it is hoped that children will be cumulatively exposed to a range of appropriate mathematical language • self-selection of games by participants to maximise relevance and individuality of learning.

Any or all of these points can form the basis of evaluation of a six-week program with a group of 10 children at a time.

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C.Publ i cat i ons Making the games •f or r evi ew pu r pos esonl y•

The games in this book are easy to create by using a photocopier, coloured card and paper.

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1. Photocopy the chosen game onto brightly-coloured cardboard, such as yellow, to create a good background, enlarging them if required.

2. Photocopy the game again onto another colour cardboard of your choice—fluorescent pink, green or orange.

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3. Cut out and paste items from the second copy onto the outlined background cardboard. Introduce as many or few colours as you like. For some games, such as the ‘Space Invaders® game’ and the shrubbery surrounding the ‘Racetrack Money game’, it is best to add colour with markers or poster paint. This reduces unnecessary consumption of paper.

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4. From this ‘master copy’ of the game make as many duplicates as required using a colour photocopier.

5. Photocopy the instructions for play and insert into wallet as a separate sheet.

6. Laminate the game for durability, or cover it with clear adhesive plastic.

7. Store the game with two baseboards, game pieces, counters, language cards, dice and a shaker in a large zipped plastic bag or wallet, or similar container. (Shakers can be made from the recycled tops of bottles, such as fabric conditioner, shampoo, or roll-on deodorant. Counters can be sourced from recycled lids of milk, fruit juice bottles or similar.)

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Notes • Lost game pieces can easily be replaced by photocopying replacements from the game in this book. It is advisable to have extra game pieces and dice set aside to speed up replacement.

• Specialised 10-, 12- and 20-sided dice are available from many educational catalogues. Instead of using 10- or 12-sided dice, you may wish to combine two 0-to-5, or 1-to-6 dice. It is helpful if one of those dice has numerals and the other has dots. Ask the children to start with the numeral and count on using the dots. Instead of a 20-sided dice, you can combine two 10-sided dice. Spinners are an option, but should only be used as a last resort as they do not generate the same levels of excitement and anticipation as dice.

• If you intend to use additional commercially-purchased games and want to be sure of their value, a good game has the following criteria: ~ visually attractive ~ enjoyable ~ age-appropriate ~ brief (lasts about 5 minutes) ~ robust ~ allows for extension work ~ inexpensive to replace ~ not like schoolwork ~ easy to follow the rules ~ well packaged ~ easily handled ~ a task with a clear mathematical objective ~ compact in size (preferably A4 for ease of transport and storage).

• You may find it easier if you can share the workload or create resources with a colleague in your own or another school.

Suggestions for organising © R. I .

C.P ubl i cat i ons the games •f orr evi ew pur posesonl y• • Divide your games into categories; for example: Number (counting and numeration), Number Operations,

• • •

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Measurement, Shape and Space, and Strategy. (See chart on facing page for suggested categories.)

Allocate a colour (such as red, blue and green) for each category.

Grade each game according to difficulty within each category, using the numbers 1 to 3 and so on.

Place a sticker or coloured dot on each plastic wallet according to the category and level of difficulty; for example: Red 1, Red 2, Red 3.

Collate the games wallets. Each wallet could contain: ~ two game baseboards ~ game pieces or counters ~ dice and shaker ~ language cards (Refer to pages xv to xvii.) ~ a parent checklist of items to return. (Refer to page xxii.) ~ throwing the dice and rules of play ~ instructions for play Store the games in matching coloured containers, available from discount stores.

Photocopy the ‘Parent Paired Record’ booklet (see pages xii – xiii.) and give copies to parents. Parents sign the ‘Paired Maths Record’ when a child borrows a game, and when the game is returned to school.

Photocopy the letter to parents on page xviii to give to each parent before any games are taken home.

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Suggested game categories Measurement and shape

• Large Lollipop game • Hen game • Snail game • Space Invaders® game • Pairs to Make Ten game • Halves game • Pairs to Make Twenty game • Hen game (Doubles) • Number Dominoes game • Ten and Units game • Stepping Stones game • Build a Ladybird game • Pay the Difference game • Combinations game • The Racetrack Money game (Money/Number) • The One Hundred Square game • Odd and Even game (Algebra) • Snakes and Ladders game

• The Tallest Giraffe game • The Longest Toothbrush game • Shape and Direction (2-D) game (includes Data) • Shape and Direction (3-D) game

Strategy • Noughts and Crosses game • Three Men’s Morris game • Nine-Point Star game • Six Men’s Morris game • Nine Men’s Morris game • Twelve Men’s Morris game • Four in a Row • Five in a Row • Cat and Mice game • Fox and Geese game • Draughts/Checkers game • Chinese Checkers game • Pathway game • Mancala game

r o e t s Bo r e p ok u S How it works

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Number

The children choose a game once each week (or more often if the need arises). They should keep the game for up to a week, but if it is boring or unsuitable it should be changed as soon as possible.

• Decide what time of day games will be chosen and checked in or out—mornings or afternoons.

• Oversee returns, check for missing pieces, answer questions, listen to experiences, and troubleshoot as required.

• Use the loan sheet provided to track who has what.

• Have a ‘no blame’ policy with regard to missing pieces and dice, but stress the need to take care of games and ask to be notified if things go missing.

• Parents sign ‘Paired Maths Record’ when the child is finished with the game, the game is returned to school, and a new one chosen.

• You may decide to have a formal launch or explain the Paired Maths Program to parents in a letter. (Refer to page xviii.)

• You could start in the middle of the year or at the beginning of the final term to revise or consolidate maths concepts. Present certificates and ‘Thank you’ cards at the end of the six-week program, if desired.

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36 maths games of chance and strategy

Possible student w e i comments: ev Pr

Enjoyable

Interesting

Too easy

Too difficult

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Parent Paired Maths Record – front and back covers

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Student picture

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Parent Paired Maths Record

Name ww

Class

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Parent Paired Maths Record – inside pages

Comments Name of game

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Parent’s signature

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Comments

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Date

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Parent’s signature

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Date

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36 maths games of chance and strategy

Loan sheet for maths games borrowed and returned Category Colour

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Put in number of game taken. Tick on return.

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Name of child

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beside next to right left horizontal vertical up down beginning end top bottom altogether makes do the same as matches

Number Dominoes game

How many more do you need?

How many altogether?

How many left?

bottom

match check correct Do you have a match? next time What do you think?

Count the spots on the domino cards to find out.

Is it a match?

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top

take away

count

empty

full

large

Lollipop game

Hen game

Snail game

o c . che e r o t r s super body head antennae legs spots points total highest score add plus altogether makes next

half halves is half of check two equal shares almost there spaces to cover difficult easy

Halves game

Earth planet space circles round pointed curved corners rows across down left above beside closest right next to furthest away under/over

What is the double of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10?

Can you think of the number that, when doubled, gives the answer 2?

Hen game (doubles)

track corners bends start finish collect moving forward pay extra turn How many more spaces to the next smiley/sad face? bonus penalty

The Racetrack Money game

count pair count Is it enough? pair/two How many altogether?

How many more do you need to get a match? rectangle enough almost enough almost enough face downwards How many altogether?

How many pairs have you got?

How many pairs have you got?

How many have I? Which of us has the most?

What shape are the cards?

Pairs to Make Pairs to Make Ten game Twenty game

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Build a Ladybird game

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odd even skip counting by 2s starting at 2 (2, 4, 6, 8, 10, 12, 14, 16, 18, 20) skip counting by 2s starting at 1 (1, 3, 5, 7, 9, 11, 13, 15, 17, 19) How many more do I/you need to finish?

Odd and Even game

one two three four five six seven eight nine ten space covered already covered Do you have a match? next time How many more do you need to win?

Space Invaders® game

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Large

Language cards – 1

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target total tally add on take away score How much more do I need to reach target? subtract minus compare difference between hexagon

tens units place bundles groups rename swap exchange equals as many as enough to make ten abacus

36 maths games of chance and strategy

tall taller tallest short shorter shortest same equal By how much?

Which is the tallest giraffe?

Are they the same height?

How many more do you need?

Pay the Difference game

o c . che e r o t r s super square below circle border rectangle in/on near corner edge straight curved flat next to opposite away triangle oval behind between from twist turn more start semicircle horizontal left/right top/bottom up/down under/over back/front in front of forwards/backwards sideways point round side

Shape and Direction game (2-D)

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long short longer shorter longest shortest How many pieces in the longest/shortest toothbrush?

Which is the longest?

By how much?

Are they equal?

Are they the same?

The Longest Toothbrush game cube cuboid cylinder sphere cone solid roll slide sides edges left/right below border behind next to near corner edge straight curved flat in/on away from more top/bottom up/down under/over back/front between in front of opposite sideways horizontal vertical twist/turn higher/lower forwards/backwards

Shape and Direction game (3-D)

shape row down left horizontal go back above before odd even ten more ten less

square column across pattern right vertical forward below after

The 100-Square game

Teac he r

snakes ladders heads tails up down across above below under start finish ahead behind odd even How many more spaces to reach snake’s tail?

Snakes and Ladders game

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Who has the least?

Who has the most?

Are the rows equal?

Are the rows the same?

How much money have I left?

What is the difference and between ?

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The Tallest Giraffe game

Stepping Stones game

Block your opponent.

left/right corner

middle

three in a row

next to

across

up/down

row

diagonally

vertical

horizontal

Noughts and Crosses game

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Tens and Units game

up/down middle corner left/right horizontal vertical diagonally across square opposite outer middle inner square three in a row block your opponent points/corners straight lines

Three Men’s Morris game

number cards 1 to 12

total

split between

share

not enough spaces

enough spaces

even

odd

fit together

combine

Combinations game

Language cards – 2

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middle

left/right

up/down

corner

vacant up/down middle corner left/right horizontal vertical diagonally slide across square opposite inner outer middle points/corners straight line three in a row Block your opponent. vertical

across

middle

diagonally

outer

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squares rows columns chain jump capture horizontal vertical diagonal trap

empty vacant line space cat mice trap jump over capture triangle Can you see the pentagon shape in the middle?

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Fox and Geese game

right

left

Draughts and Checkers game/Chinese Checkers game

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Cat and Mice game

straight lines

opposite

points/corners

Block your opponent.

three in a row

square

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inner

horizontal vertical diagonal baseline spaces rows Block your opponent.

up/down middle corner left/right horizontal vertical across outer square opposite diagonally middle inner square three in a row Block your opponent. points/corners straight lines

up/down middle corner left/right horizontal vertical diagonal across square opposite outer middle inner square three in a row Block your opponent. points/corners straight lines

Teac he r Four in a Row game

Twelve Men’s Morris game

Nine Men’s Morris game

circles pathway touching opposite side right left up down across Block your opponent. dark/light vertical

horizontal

diagonal

jump

toward

forward

Pathway game

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Six Men’s Morris game

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Nine-Point Star game

right

left

extra turn

anticlockwise

clockwise

full

empty

store

bowls

Mancala game

horizontal vertical diagonal baseline spaces rows Block your opponent.

Five in a Row game

Language cards – 3

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36 maths games of chance and strategy

Letter to parents Dear parents You are invited to participate with your child in a Paired Maths Program. This program is hugely beneficial to children if parents become involved in, and support, their child’s learning at school.

Paired maths involves the parent spending five to 10 minutes each day playing a mathematical game with their child. The emphasis is on having fun while learning.

The program will run for approximately six weeks, with a group of 10 children at a time.

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How the program works On

day of week/time

, your child selects a mathematical game from a selection at school.

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Each game is stored in a plastic wallet or storage bag which includes the game itself with playing instructions on the back, dice and a shaker; a Paired Maths Record for you to sign when you have finished the game; and a language card which provides a set of mathematical words you might use during and after the game. (Many of the words will occur naturally during the course of play.)

The game may be kept for up to one week, but if it proves unsuitable it can be changed the next day.

The games are categorised, and it is advisable that, over the course of the six-week period, your child chooses at least one game from each category.

How to make the experience more enjoyable:

• Choose a time and place when you and your child are relaxed, comfortable and without distractions.

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• Spend five to 10 minutes playing the game, but if the game is enjoyable, continue for a longer time.

• If the game is uninteresting or too difficult, you don’t need to continue.

• Show your child how to use the shaker properly and follow the rules of play. (Refer to notes.)

• Make the experience as enjoyable as possible and discuss the game after play is finished.

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• Sign the record booklet, replace the game with all the game pieces in the storage bag or wallet, and return it to your child’s school bag.

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• Report any missing pieces or dice to the teacher so the items can be replaced and the game is ready for the next player.

How to take care of the games

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Encourage your child to take care of the games by:

• making sure his or her hands are clean before starting to play • not eating or drinking while playing the game

• keeping the game, dice, shaker and language card in the plastic bag or wallet when not in use • trying not to lose the dice, or placing it in his or her mouth.

Yours sincerely

Class teacher

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Throwing the dice and Rules of play Throwing the dice Cover the shaker (tops of deodorant, hairspray or other aerosol cans) with your hand.

Shake and turn shaker upside down onto desk or floor. Lift shaker and read the number on the uppermost side of the dice.

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If noise is a problem, place some cotton wool or tissue inside the bottom of the shaker.

• Your move depends on the symbol which lands uppermost on the dice.

• Wait for your turn to come and then take one turn only.

• You must finish placing your piece or counter before the next player throws the dice.

• If a number or space is already covered, skip your turn and give the dice to the next player.

• When you have taken your turn, place the dice inside the shaker and hand it to the next player.

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C.Publ i cat i ons •f orr evi ew pur posesonl y• Throwing the dice

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Cover the shaker (tops of deodorant, hairspray or other aerosol cans) with your hand.

Shake and turn shaker upside down onto desk or floor. Lift shaker and read the number on the uppermost side of the dice.

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If noise is a problem, place some cotton wool or tissue inside the bottom of the shaker.

o c . c e • Your move depends onh thee symbol which lands uppermost onr the dice. o t r s s r uonee • Wait for your turn to come and then takep turn only.

Rules of play

• You must finish placing your piece or counter before the next player throws the dice.

• If a number or space is already covered, skip your turn and give the dice to the next player.

• When you have taken your turn, place the dice inside the shaker and hand it to the next player.

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Thank you cards for parents

Thank you Teac he r

Class teacher

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r o e t s Bo r e p ok u S for your help with the Paired Maths Program.

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o c . che e r o t r s Program. su for your help with the Paired Maths per Class teacher

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Congratulations cards for students

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r o e t s Bo r e p ok u S participated in Paired Maths and You have games.

successfully completed Well done!

Class teacher

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o c . e You havec participated in Paired Maths and her r o st games. super successfully completed Well done!

Class teacher

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Checklist for parents Checklist for parents

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Checklist for parents

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When returning the plastic bag or wallet containing the game, ensure the following items are included: • game baseboard • game pieces, such as cards • dice and shaker • language card • play instruction card (if not already glued to the back of the game) • throwing the dice and rules of play.

When returning the plastic bag or wallet containing the game, ensure the following items are included: • game baseboard • game pieces, such as cards • dice and shaker • language card • play instruction card (if not already glued to the back of the game) • throwing the dice and rules of play.

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Checklist for parents . te o When returning the plastic bag or wallet containing the game, ensure c . ch e the following items are included: r e o r st super • game baseboard • • • • •

game pieces, such as cards dice and shaker language card play instruction card (if not already glued to the back of the game) throwing the dice and rules of play. xxii

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Spinner – 1 to 10

2

3

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Use a split pin to attach arrows to centre of spinner.

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Spinner – Even numbers 2 to 20

14 2

8 8 www 1

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Use a split pin to attach arrows to centre of spinner.

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Spinner – 1 to 20

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3 1

2 4 1

6 20 5

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Use a split pin to attach arrows to centre of spinner.

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Arrows for spinners

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36 maths games of chance and strategy

Large Lollipop game Aim To reinforce the cardinal aspects of the numbers 1 to 20 What you need: • Two lollipop baseboards (one per player) • A dice featuring the numerals 0 to 5, or 1 to 6.

• Twenty lids per player (These can be recycled lids from two-litre plastic bottles of milk or fruit juice bottles.)

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Number of players Two

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How to play Players take turns to throw the dice, putting ‘lollipops’ in their jar according to the number thrown on the dice. The first player to fill all the lollipop spaces in his or her jar is the winner.

Variation The game can be extended by playing it in reverse. Each player uses lids to cover all the circular sections of the lollipops on his or her baseboard. In this version, the winner is the first player to empty his or her jar. This is useful for reinforcing the concept of subtraction as deduction.

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Teac he r

Large Lollipop game baseboard

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36 maths games of chance and strategy

Hen game Aim To consolidate understanding and recall of number bonds 1 to 10 What you need: • A Hen game baseboard for each player • Twenty counters (10 per player) • A sheet of domino-type cards (see below) showing the relevant number bonds for each number. This is to be shared between both players.

• A 10-sided dice, featuring numerals 1 to 10; or alternatively, two six-sided dice featuring numerals 0 to 5

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Teac he r

Number of players Two

How to play Players take turns to throw the dice. They compare the number(s) thrown to the number bonds on their baseboard. If they find a number bond that matches or equals the number thrown, they place a counter on that number bond. Players who are unsure can check the domino sheet to find the answer. Play continues until one player has covered all of his or her eggs. The first to do this is the winner.

As players’ skill develops, the domino sheet with the answers can be removed from the game.

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Extension activity Players work out and recall the corresponding subtraction facts for counters on the baseboard; e.g. 5 + 2 = 7 7–2=5 7–5=2

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0+1=1

5+1=6

o c . che e r 2+0=2 r 3+0=3 3 +t 1o =4 4+1=5 s super

5+2=7

4+4=8

6+3=9

5 + 5 = 10

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Hen game baseboard

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Snail game Aims Level 1 – To reinforce recognition of numerals 1 to 10 Level 2 – To reinforce addition skills to 10 Level 3 – To reinforce subtractions skills within 10

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Teac he r

What you need: • Two Snail game baseboards • A 10-sided dice featuring numerals 1 to 10 (Level 1) • Twenty plastic bottle tops • Two dice featuring numerals 0 to 5, or 1 to 6. One dice is marked with dots, the other with numerals. (Level 2) • Two 10-sided dice featuring numerals 1 to 10. (Level 3) Number of players Two

How to play Level 1 Players take turns to throw the dice. They cover the numeral on their ‘snail’s shell’ with a bottle top, according to the numeral thrown. The first player to cover all of his or her numerals is the winner.

Level 2 Players throw two dice. They combine the two top numbers on the dice and cover the number corresponding to this total on the snail baseboard. If players get a total of 11 or 12, these are regarded as bonus numbers and a player can cover any numeral of his/her choice on the baseboard. To assist with counting, players should start with the numeral and ‘count on’ using the dots to find the total.

Level 3 Players play with two 10-sided dice. Players throw both dice. They take the smaller number from the bigger number and cover the numeral on the shell corresponding to the answer. Players may need to check their answers using a number line.

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Note* If 10- and 20-sided dice are not available, use spinners instead.

0

1

2

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Snail game baseboard

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Space Invaders ® game Aims Level 1 – To reinforce recognition of numerals 1 to 10 Level 2 – To reinforce addition skills to 10 Level 3 – To reinforce subtractions skills within 10

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What you need: • Two Space Invaders® game baseboards • A 10-sided dice featuring numerals 1 to 10 (Level 1) • Twenty plastic bottle tops • Two dice featuring numerals 0 to 5, or 1 to 6. One dice is marked with dots, the other with numerals. (Level 2) • Two 10-sided dice featuring numerals 1 to 10. (Level 3) Number of players Two

How to play Level 1 Players take turns to throw the dice. They cover the numeral on the Space Invaders® baseboard with a plastic bottle top, according to the numeral thrown.

The first player to cover all of his or her numerals is the winner.

Level 2 Players throw two dice. They combine the two top numbers on the dice and cover the number corresponding to this total on the Space Invaders® baseboard.

If players get a total of 11 or 12, these are regarded as bonus numbers and a player can cover any numeral of their choice on the baseboard. To assist with counting, players should start with the numeral and ‘count on’ using the dots to find the total.

Level 3 Players play with two 10-sided dice. Players throw both dice. They take the smaller number from the bigger number and cover the numeral on the baseboard corresponding to the answer. Players could check their answers using a number line.

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Note* If 10- and 20-sided dice are not available, spinners could be used instead.

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Pairs to Make 10 game Aim To aid recall of pairs of numbers which make 10 What you need: A set of 20 cards (enlarged) Number of players Two

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How to play The cards are shuffled and placed facedown on the playing surface. Players take turns to turn over two cards at a time. They add the dots on both cards. If the dots add to 10, these cards are removed from the board and kept next to the player.

That player has made a ‘trick’.

If the cards do not make 10, they are returned to the playing surface and placed facedown in their original position. Play continues until no more pairs can be made. The player with more pairs is the winner.

Variations 1. Addition and Subtraction turnover Each player is given 11 cards numbered 0–10. These are placed face up in front of the players. Players then take alternate turns to throw two 0–5 dice and may add or subtract the two top numbers thrown on the dice. If the sum or difference matches one of the number cards the player can turn that card facedown. Play continues in this way until one of the players has turned over all of his/her cards. The first player to do this is the winner.

2. Players use cards to play Snap

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Pairs to Make 20 game Aim To aid recall of number pairs within 20

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What you need: • A set of cards 0 to 10 (with stars) • A set of cards 10 to 20 (with pictures) Number of players Two

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How to play The cards are shuffled and placed facedown on the playing surface. Players take it in turns to turn over two cards at a time. They add the components of both cards and if this adds to 20, these cards are removed from the board and kept by the player. That player has made a ‘trick’.

If the cards do not make 20, they are returned to the playing surface and placed face downwards in their original position. Play continues until no more pairs can be made. The player with most pairs wins.

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Note* When players are checking their cards to see if they have made a 20, get them to start with the larger number and count on with the smaller number.

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Variation Addition and Subtraction turnover Each player is given a set of cards 0–20. These are placed face up in front of the players. Players then take alternate turns to throw two 0–10 dice, and may add or subtract the two top numbers thrown on the dice. If the sum or difference matches one of the number cards the player can turn that card facedown. Play continues in this way until one of the players has turned over all of his/her cards. The first player to do this is the winner.

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Number Dominoes game Aims 1. To reinforce recognition of numerals 1 to 10 and the cardinal aspects of those numerals 2. To reinforce recognition of numeral words one to ten 3. To reinforce recognition of some of the addition and subtraction facts within 10 4. To reinforce the understanding and use of positional words: left, right, beginning, end, top, bottom, up, down, next to, beside

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What you need: A set of Number Domino cards (laminated)

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Number of players One to five

How to play The dealer shuffles the cards and hands out five cards in random order to each player, leaving any remaining cards facedown in a pile on the table or floor. The top card from this pile is placed face up in the centre of the playing area and this becomes the starting card. (The order of play can be clockwise or anticlockwise, depending on how the players are seated.)

The players hold their cards in front of them and can only play with one card for each turn of play. The opening player scrutinises his or her cards and if he or she can find a card to match either end of the starting card that card is placed in the correct position.

Play continues in this way for all the other players. If a player cannot match his or her card to either end of a previously played card, that player misses a turn. Lines of cards must be single and can extend to the right, left, upwards or downwards from a previously played card. A new line cannot be formed parallel to an existing one. Play continues in this way until one of the players has disposed of all of his or her cards. The first player to do this is the winner.

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Variations The inclusion of addition or subtraction fact cards can be delayed until player confidence and skill develops.

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Odd and Even game Aim To reinforce recognition of odd and even numerals from 1 to 20 What you need: • A ‘mushroom house’ baseboard marked with even numerals from 1 to 20 for Player 1 • A ‘mushroom house’ baseboard marked with odd numerals from 1 to 20 for Player 2 • Twenty counters (10 for each player) • A 20-sided dice featuring the numerals 1 to 20

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Number of players Two

How to play Players take turns to throw the dice. Player 1 covers all the even numbers on his or her baseboard as they occur, according to the throw of the dice. Player 2 covers all the odd numbers as they occur. The first player to cover all of his or her selected numbers with counters is the winner.

Notes* • To speed up the game, two 20-sided dice can be used together.

• Two 10-sided dice can be used as an alternative to one 20-sided dice. Players throw the dice and combine the two numbers to see if the total is odd or even. They can check their answer on a number line.

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Build a Ladybird game Aims 1. To reinforce addition skills up to 20 (Level 1) 2. To reinforce understanding and use of addition skills, with carrying up to 50 (Level 2)

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What you need: • A card shared between players showing scoring points. These points also correspond to the throw of the dice.

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(6 (5 (4 (3 +(2 20

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Body Head Legs (all six) Feelers/Antennae (both) Spots (up to any number)

• A blank sheet of paper for each player to draw on and a pencil. Alternatively, use a board and chalk.

• A six-sided dice featuring numerals 1 to 6. (‘One’ can be a bonus symbol that allows the player to draw the ladybird part of his/her own choice.)

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C.Publ i cat i ons •f rr evi ew pur posesonl y• How too play

Number of players Two players and one recorder. (Alternatively, players can do their own recording.)

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Level 1 The object of this game is for each player to progressively draw a picture of a ladybird. They do this by throwing the dice and drawing the part of the ladybird to which the number on the dice corresponds. (Refer to the scoring points table above.)

Before the players commence the game, show them how to draw a simplified ladybird shape: a circle for the body, semicircle for head, two antennae, six legs, and any number of spots. Players take alternate turns and must throw a 6 to begin. They then draw the body of the ladybird. Players cannot draw antennae until the head has been drawn. Spots and legs can be drawn in any order. The first player to complete his or her drawing shouts ‘ladybird’ and is the winner, signifying the end of the game. Both players total their scores.

Level 2 After the first game has ended, play can continue for two more games with players recording their finishing score each time. At the end of three games, the player with the higher overall score is the winner.

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Variation This game can be adapted to drawing parts of a bird. Use a simplified picture, making use of circles and triangles.

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Halves game Aim To reinforce the understanding and recall of halves from 2 to 20

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What you need: • A ‘teddy bear’ baseboard for each player • Ten counters for Player A • Ten counters for Player B • A set of domino cards showing halves of numbers 2 to 20, placed face upwards for both players to share • A 20-sided dice with odd numbers blotted out. (Use nail varnish to do this.)

Alternatively, use a spinner showing numbers 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20.

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Number of players Two

How to play Players take turns to throw the dice or twist the spinner. For whatever number lands uppermost on the dice, the players must locate the half of that number on their teddy bear baseboard and cover it with a counter. Players who are unsure of the answer can check the domino cards to find the half of the number thrown.

The first player to cover all the spaces on his/her teddy bear wins.

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Half of 2 = 1

Half of 4 = 2

Half of 6 = 3

Half of 8 = 4

Half of 10 = 5

Half of 12 = 6

Half of 14 = 7

Half of 16 = 8

Half of 18 = 9

Half of 20 = 10

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Halves games baseboard

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Hen game (Doubles) Aim To reinforce the understanding and recalling of doubles from 1 to 20

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What you need: • A Hen game (Doubles) baseboard for each player, marked with 10 even numbers from 2 to 20.

• Twenty counters or cubes (10 per player) • A 10-sided dice featuring numerals 1 to 10 or alternatively two six-sided dice featuring numerals 0 to 5. If dice are not available, use a spinner instead.

• A set of domino cards showing doubles 1 to 10, shared between both players for reference Number of players Two How to play Players take turns to throw dice. Whatever number lands uppermost on the dice e.g. a 7, the players must locate the double of that number on their baseboard and cover it with a counter. If using two dice, they combine the two numbers and double the total. Players who are unsure can check the domino cards to find the double of the number thrown. These cards are spread face up between the players.

The first player to cover all of his or her doubles with a counter is the winner.

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Double 2 = 4

Double 3 = 6

Double 4 = 8

Double 5 = 10

Double 6 = 12 Double 7 = 14 Double 8 = 16 Double 9 = 18 Double 10 = 20

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The Racetrack Money game Aims 1. To practise moving from one space to the next using a counter 2. To practise counting on and addition skills 3. To provide practice with recognising, exchanging and using coins to the value of 20c/30c/40c/50c 4. To provide practice tendering and receiving amounts of money to the value of 20c/30c/40c/50c

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What you need: • Four to six side racetrack baseboards and four corner racetrack baseboards arranged as shown, with smiley and sad face symbols dotted randomly along the track.

• One or two six-sided dice featuring numerals or dots from 1 to 6. If practising addition skills, use one dice with numerals and the other with dots. Start with the numeral and count on using the dots.

• A pack of ‘smiley face’ bonus cards* • A pack of ‘sad face’ penalty cards* • A variety of ‘coins’ for each player to the value of 20c/30c/40c/50c • A place marker such as a counter for each player

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according to the number thrown. If a player lands on a smiley face symbol, he or she draws a card from the ‘smiley face’ pack and receives a bonus (collects money from the bank). If, however, a player lands on a ‘sad face’ symbol, he or she draws a card from the appropriate pack and incurs a penalty (pays money to the bank). Drawn cards are returned to the bottom of the pile or placed in a discard pile. The discard pile can be shuffled and used as play continues. The game ends when time is called, and the player who has accumulated the most money at this point is the winner.

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Variation Players can play with half a racetrack initially. As players’ skill with exchanging and using coins increases, the bonus/penalty cards can be made more complex.

Note* Teachers will need to glue a ‘smiley face’ on the back of the ‘Collect bank’ cards and a ‘sad face’ on the back of the ‘Pay to bank’ cards.

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The Racetrack Money game – corner baseboard

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The Racetrack Money game – side baseboards

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The Racetrack Money game – smiley/sad face card backs

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Tens and Units game Aim To record tens and units within 100, using concrete materials on an abacus

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What you need: • A Tens and Units baseboard for each player • Bundles of ten craft sticks glued together, one on top of the other‚ or held together with elastic bands to represent tens • Spare sticks to represent units • A six-sided dice featuring numerals 0 to 5, or 1 to 6 Number of players Two

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Note* Players must not exceed the target number. If they do, they are out.

As player skill increases the target number can be raised.

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How to play Players select a target number from 0 to 20 and write it down. They then take turns to throw the dice and place the corresponding amount of sticks on the units side of the abacus. Whenever a player has collected 10 sticks, this is exchanged for a bundle of 10. Any spare sticks in excess of 10 are kept on the units line and go towards forming the next bundle of 10. Play continues until one player reaches his/her target number and becomes the winner.

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Tens and Units game

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Stepping Stones game Aims 1. To reinforce addition and/or subtraction skills 2. To develop the strategy skill of forward planning

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What you need: • A Stepping Stones game board shared between two players • A quantity of counters or lids of one colour for Player 1 to place on the game board • A quantity of counters or lids of a different colour for Player 2 to place on the game board • A number line or quantity of counters for both players to keep a running total Number of players Two players and one recorder

How to play For addition skills Between them the players select a target number, initially from 10 to 20; then‚ as player skill develops, from 20 to 30. They take turns to place counters on any stepping stone of their choice, including zero, on the game board. However, a player cannot place his or her counter on a stepping stone already occupied by the opposing player. They select and add numbers progressively to the first number chosen. The first player to reach the target number exactly is the winner.

Any player who exceeds the target number is out. Each player can record his or her own numbers and keep a running total, or a third child can act as a recorder for both players.

For subtractions skills Players subtract each number chosen from the target number until exactly zero is reached.

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Variations 1. Use addition and subtraction skills as required within the same game.

2. Use the blank template on page 46 to add numbers of your own choice.

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Stepping Stones game baseboard

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Stepping Stones game baseboard (blank)

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Pay the Difference game Aims 1. To reinforce understanding of the concepts of ‘more than’, ‘less than’, ‘most’ and ‘least’ 2. To compare equivalent and non-equivalent sets 0 to 10 and describe the difference between them 3. To understand subtraction as difference

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What you need: • A flat surface, such as a desk or the floor, to play on • Ten counters of a particular colour for Player A • Ten counters of a different colour for Player B (Counters for both players should be a similar size. Recycled plastic bottle tops could be used.)

• A 10-sided dice featuring numerals 0 to 10; or two six-sided dice from 0 to 5, one with numbers and one with dots • A ‘purse’ with 20 cubes (coins) for Player A • A ‘purse’ with 20 cubes (coins) for Player B Number of players Two

How to play Player A throws the dice and places counters corresponding to the number thrown in a straight line in front of him or her. Player B then throws the dice and places his or her counters exactly under those of Player A. Any difference is noted. The player with the least amount of counters pays the difference in ‘coins’ from his/ her ‘purse’ to the player with the most. They both withdraw their counters and throw again. Play continues in this way, with the player scoring the least having to pay the difference each time. The game is over when one of the players is left without any ‘money’. The player who has collected the most amount of money during play is the winner.

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Variations 1. The game can also be played by reversing the rules. This time, the player with the most amount after each throw of the dice has to pay the difference.

2. Individual play coins labelled with ‘one’ can be used instead of cubes for paying the difference.

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Snakes and Ladders game Aims 1. To reinforce recognition of numerals 1 to 100 2. To reinforce addition skills within 10 or 20 (if combining two or three dice) 3. To examine number patterns on the game board as an extension activity

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What you need: • A Snakes and Ladders game baseboard shared among players • A marker, such as a counter, for each player • A dice featuring the numerals 0 to 5 or 1 to 6 Number of players Two to four

How to play Each player moves across the grid according to the throw of the dice and following the directional arrows. If playing with two or more dice, players combine the numbers thrown and move according to this total. Landing at the bottom of a ladder allows a player to move his or her marker immediately to the top of it.

Landing on a snake’s head means that a player’s marker has to slide immediately to the bottom of its body. The first player to reach 100 exactly wins.

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1. If using two dice, players move according to the total or the difference of the two numbers thrown.

2. If using two dice, players can only move if the score is odd or even using the game board from 1 to 50.

3. A throw of 6 allows an extra turn.

4. Play the game in reverse; go up the snakes and down the ladders.

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The 100-square game Aims 1. To reinforce recognition of numerals 1 to 100 2. To give practice in adding on and subtracting 10 What you need: • A 100-square game board shared between two players • A marker for each player • A dice featuring the numerals 0 to 5 or 1 to 6 Number of players Two

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How to play Players take turns to move across the 100 squares, going from left to right down the baseboard according to the number thrown on the dice. If they land on a square with a smiley face, they immediately move forward 10 more spaces (or to the square immediately below them). If they land on a square with a sad face, they must go back 10 spaces (or to the square immediately above them). The first player to reach 100 is the winner.

Note* For ease of recognition, colour the smiley faces green and the sad faces red. Alternatively, colour the spaces of the following numbers green: 12, 20, 37, 41, 51, 56, 58, 74, 76, 80 and 87. Colour the spaces of the following numbers red: 17, 23, 27, 39, 50, 55, 73, 78, 91 and 96.

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100- game Square

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Combinations game Aims 1. To find combinations for addition of numbers from 1 to 12 2. To reinforce recognition of odd and even numbers from 1 to 12 through colour coding

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What you need: • A baseboard for each player marked with even numbers in one colour and odd numbers in another colour.

• Two dice featuring the numerals 0 to 5 or 1 to 6 • Twelve counters each for Player 1 and Player 2 Number of players Two How to play Players take turns to throw both dice and add the numbers thrown. They then use their counters to cover that number on their board or any combination of numbers that add up exactly to that number. For example, if a player throws a 3 or a 4, adding up to 7, that player could cover the 7 space on the board, or the 5 and the 2, 4 and 3, or 6 and 1 spaces if they were available. Players are allowed to cover more than two spaces; for example, if a 12 is thrown, players may cover the 1, 2, 3 and 6 spaces if available. If players cannot cover enough spaces according to the number thrown, they miss a turn.

Play continues in this way until all the spaces are filled. The first player to do this is the winner.

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Note* If players have not had enough time to complete the game, they add the numbers that have not been covered and the player with the lowest score wins.

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The Tallest Giraffe game Aims 1. To reinforce the concept of tall, taller, tallest, or short, shorter, shortest 2. To reinforce the cardinal aspects of numerals 1, 2 and 3 3. To introduce the comparison of totals with appropriate mathematical vocabulary; for example: Who has the most? Least? By how much? How many do you have?

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What you need: • A giraffe head and legs with 10 to 12 ‘neck’ pieces per player • A six-sided dice featuring the numerals 1 to 3 (twice) Number of players Two to three

How to play Players position the leg cards so that they are level. If playing the game on the floor, draw a starting line with chalk. ‘Neck’ cards are placed face up in a pile adjacent to players. Players take turns to throw the dice, adding neck pieces according to the number thrown. Cards must be placed end to end without gaps.

Play continues until all the neck pieces have been used up. The winner is the player with the tallest giraffe.

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Note* For older children, use a six-sided dice featuring numerals from 0 to 5 and allow 15 to 20 neck pieces per player.

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The Tallest Giraffe game – head

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The Tallest Giraffe game – body

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The Tallest Giraffe game – neck pieces

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The Longest Toothbrush game Aims 1. To reinforce the concept of long, longer, longest, or short, shorter and shortest 2. To reinforce the cardinal aspects of numerals 1, 2 and 3 3. To introduce the comparison of totals with appropriate mathematical vocabulary; for example: Who has most? Least? How many pieces do you have?

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What you need: • A toothbrush head and end with 10 to 12 handle lengths per player • A six-sided dice featuring the numerals 1 to 3 (twice) Number of players Two to three

How to play Players place their toothbrush heads one below the other at the far-left side of the play area. They take turns to throw the dice, adding handle pieces according to the number thrown. Play continues until all the handle pieces have been used up. To complete the toothbrush, players place end pieces on each of their toothbrushes.

The winner is the player who has the longest toothbrush.

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C.Publ i cat i ons Note* • f orr evi ew pur posesonl y• This game can be introduced when dealing with self-care issues in the social, personal

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and health education learning areas.

For older children use a 6-sided dice featuring numerals 0–5, or 1–6 and allow 15 to 20 handle pieces per player.

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The longest toothbrush

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Shape and Direction game (2-D shape)

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What you need: • Two Shape and Direction baseboards (one per player) • A six-sided dice featuring the numerals 1 to 3 (twice) • A six-sided dice featuring the following symbols and labels: up

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Aims 1. To reinforce recognition of two-dimensional (2-D) shapes: square, rectangle, triangle, circle, semicircle and oval 2. To reinforce recognition of those 2-D shapes even when oriented in a different position 3. To reinforce understanding and use of positional terms; for example: left, right, top, bottom, up, down, under, over, below, beside, between, behind, back, front, in front of, next to, opposite, sideways, near, side, edge, corner, direction, in, on, away from, in front, forwards, backwards, twist, turn, move

bonus symbol

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• Six counters per player

Number of players Two

How to play Players take turns to throw both the symbol and number dice. From the starting

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3 position, they follow the directions given by both dice. For example, means turn right and move three spaces. Each time a player lands on a shape, he or she places a counter on the corresponding shape on the strip at the top of the baseboard. Whenever the bonus symbol appears on the dice, a player can travel in any direction of his or her choice. If a player does not have enough room to move, he or she misses a turn. The first player to cover all of his or her shapes on the strip at the top of their baseboard is the winner.

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Note* 1. The direction dice can be made from a cube or blank dice with the arrows, zero and bonus symbol glued in place. A net to create a cube with cardboard is provided.

2. This game could be used to introduce new shapes, such as the hexagon, rhombus, pentagon etc.

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Shape and Direction 2-D Shape

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Shape and Direction game (3-D shape)

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Aims 1. To reinforce recognition of three-dimensional (3-D) shapes: cube, cuboid, cylinder, sphere and cone 2. To reinforce recognition of those 3-D shapes even when oriented in a different position 3. To reinforce understanding and use of positional terms; for example; left, right, top, bottom, up, down, under, over, below, beside, between, behind, back, front, in front of, next to, opposite, sideways, near, side, edge, corner, direction, in, on, away from, in front, forwards, backwards, twist, turn, move What you need: • A Shape and Direction baseboard for each player • A six-sided dice featuring the numerals 1 to 3 (twice) • A six-sided dice featuring the following symbols and labels: up

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C.Publ i cat i ons • f orr evi ew pur posesonl y• How to play • Six counters per player Number of players Two

Players take turns to throw both the symbol and number dice. From the starting

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3 means position, they follow the directions given by both dice; for example, turn right and move three spaces. Each time a player lands on a shape, he or she places a counter on the corresponding shape on the strip at the top of the baseboard. Whenever the bonus symbol appears on the dice, a player can travel in any direction of his or her choice. If a player does not have enough room to move, he or she misses a turn. The first player to cover all of his or her shapes on the strip at the top of their baseboard is the winner.

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Note* The direction dice can be made from a cube or blank dice with the arrows, zero and bonus symbol glued in place. A net to create a cube with cardboard is provided.

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Strategy games The games are broadly presented in order of complexity. However, it is worth noting that competent strategy use (for example, as is required with the game of ‘mancala’) evolves in stages over a long time and not all children will progress through these stages at the same time and speed. Nevertheless, even children as young as seven or eight can, with support, benefit from the rich intellectual experience provided by many strategy games, and in so doing engage in generative rather than passive learning.

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Strategy games broadly fit into the area of problem solving, and require a player to plan, evaluate, monitor, take risks and learn from trial and error.

They require flexibility on the part of the players to provide an adaptive response to the shifting circumstances of the game as it evolves. This puts children in a decision-making role, with costs and benefits attached to the quality of the decisions made. They further require the development of good spatial visualisation and reasoning skills and, for some of the games, the adept use of memorised strategies.

Note*

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Board games have a universal appeal and have been in use from as far back as the early civilisations in the Nile, Tigris and Euphrates river valleys. From these centres of civilisation they were spread throughout Africa, then to Europe, India and, later, the New World, by traders, travellers, armies and slaves. They reflected the interests/occupations of their time: the hunt, the siege, the race, and the alignment of equal or unequal forces. The strategy games presented in this section of the book have origins spanning several cultures and centuries. The game of ‘mancala’, for example, may have originated in Asia in the third millennium BC, although others place it in Egypt circa 1580–1150 BC. These games have stood the test of time and still resonate with the 21st-century mind. For further information on these games, see Bell (1960/1979) and Murray (1951).

The strategies in this book also fit into the categories of number, measurement and geometry. They include aspects relating to counting and numeration, developing spatial visualisation, reasoning and awareness skills.

They also help to promote and develop the mathematical skills of: • application and problem solving • communication and expression • integration and connection • reasoning • implementation • understanding and recollection.

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Fox and Geese

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Noughts and Crosses game (tic-tac-toe) Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To reinforce understanding and use of positional words; for example: up, down, right, left, top, bottom, diagonal, vertical and horizontal

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What you need: • A baseboard shared between two players. (This can be drawn on a child’s blackboard, a sheet of paper, or with chalk on the playground.)

• Three plastic bottle tops of one colour or marked with an ‘X’ (cross), or counters, for Player 1 • Three plastic bottle tops of a different colour or marked with an ‘O’ (nought), or counters, for Player 2 Number of players Two How to play Players take alternate turns. The opening player places his or her ‘X’ (cross) in any position and the opposing player then places his/her ‘O’ (nought). The aim is to be the first player to get three ‘X’ or three ‘O’ symbols in a row, vertically, horizontally or diagonally, while simultaneously trying to block their opponent’s attempts to do likewise.

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Variation If after all the plastic bottle tops have been placed without either player forming a line of three, play continues with players taking turns to slide any one of their lids or counters into an adjacent empty space in an attempt to form a line of three.

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Three Men’s Morris game Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

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What you need: • A baseboard shared between two players • Three plastic bottle tops (‘men’) of one colour, or counters, for Player 1 • Three plastic bottle tops (‘men’) of a different colour, or counters, for Player 2 Number of players Two

How to play Players take turns to place a ‘man’ on any vacant black spot on the board. When all the pieces have been placed, play continues with players taking turns to move a piece along a line to an adjacent vacant point. The first player to place three pieces in a row (to form a ‘mill’) horizontally, vertically or diagonally is the winner.

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Note* The Chinese played a game similar to this around the time of Confucius (circa 500 BC).

This game reached Britain only after the Norman Conquest, but was well established by 1300.

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Three Men’s Morris game baseboard

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Nine-point Star game

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What you need: • A baseboard shared between two players • Four counters of one colour for Player 1 • Four counters of a different colour for Player 2 Number of players Two

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Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

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How to play Players take turns to place a counter on any vacant black spot on the baseboard.

The aim is to place one’s counters in a straight line of three, with the first player to do this being the winner.

If all the counters have been placed without either player forming a line of three, play continues with each player picking up (not sliding along a line) any one of his or her counters and placing it on a vacant spot.

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Nine-point Star game baseboard

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Six Men’s Morris game

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Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

What you need: • A baseboard shared between two players • Six plastic bottle tops or counters (‘men’) of one colour for Player 1 • Six plastic bottle tops or counters (‘men’) of a different colour for Player 2 Number of players Two

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How to play Players take turns to place a counter at points of intersection of the lines. Each player tries to form a line of three along one of the sides of either the large outer square, or the smaller inner square. This is known as forming a mill. A player who succeeds in forming a mill captures any one of his or her opponent’s pieces and removes it from the board. A mill can be made or broken several times.

When all the pieces have been placed, play continues with players taking turns to move a piece along a line to an adjacent empty point. Each time a mill is formed, a piece is captured from the opposing player and removed from the board. A player loses when reduced to two counters.

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Nine Men’s Morris game

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Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

What you need: • A baseboard shared between two players • Nine plastic bottle tops or counters (‘men’) of one colour for Player 1 • Nine plastic bottle tops or counters (‘men’) of a different colour for Player 2 Number of players Two

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How to play The rules are the same as for the Six Men’s Morris game. Players place pieces (‘men’) alternately on the game board until all the pieces are used. Play continues with players taking turns to move a piece along a line to an adjacent empty spot.

When a ‘mill’ (three pieces in a row), is formed, a piece is captured from the opposing player but it cannot be taken from the opposing player’s mill unless there is no other alternative. A player loses when reduced to two counters.

Note* This is the best known of the ‘Morris’ games. A varient of it was played 3500 years ago in Egypt and also in Troy and in Ireland (during the Bronze Age). A game board was also found in the Gokstad Viking ship in Norway, dating from 900 AD.

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Twelve Men’s Morris game

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Aims 1. To develop and promote the strategy skills of forward planning, estimation, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

What you need: • A baseboard shared between two players • Twelve plastic bottle tops or counters (‘men’) of one colour for Player 1 • Twelve plastic bottle tops or counters (‘men’) of a different colour for Player 2 Number of players Two

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The rules are the same as for the Nine Men’s Morris game. The baseboard has the addition of diagonal lines, linking each set of four corner points and an extra outer grid.

Note* Encourage players to observe that certain points on the baseboard allow for four directions of movement, while others allow only two. Ask which points control movement from one circuit to another. The diagonal lines in this version of the game first appeared around 1400 AD. The game itself is much older and versions of the playing board have been found carved into the roofing of the Temple of Seti I in Abydos, Egypt circa 1400 BC.

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Twelve Men’s Morris game baseboard

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Four in a Row game

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Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

What you need: • A baseboard shared between two players • A supply of counters or plastic bottle tops of one colour for Player 1 • A supply of counters or plastic bottle tops of a different colour for Player 2 Number of players Two

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How to play Players take turns to place a piece on the board. Pieces must be placed either on the baseline or on the line above a piece which is already on the board. The first player to make a line of four counters diagonally, vertically or horizontally is the winner.

The pieces can be placed anywhere in the baseboard to make a line of four.

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Five in a Row game Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

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What you need: • A baseboard shared between two players • Eighteen counters or plastic bottle tops of one colour for Player 1 • Eighteen counters or plastic bottle tops of a different colour for Player 2 Number of players Two

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How to play Players take turns to place a plastic bottle top or counter on the board. Pieces must be placed either on the baseline or on the line above a piece which is already on board. The first player to place five of his or her markers in a row horizontally, vertically or diagonally is the winner.

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Variation When all the counters have been placed, play continues by moving a piece one space at a time horizontally, diagonally or vertically. Jumping over an opponent’s counter (without capturing) is also allowed. The first player to form a line of five with his or her counters is the winner.

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Note* This game is loosely based on the Japanese game of hasami shogi, which was introduced into Europe in the late 1800s.

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Cat and mice game

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Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

What you need: • A baseboard shared between two players • Seven plastic bottle tops or counters (‘mice’) of one colour for Player 1 • One plastic bottle top or counter (‘cat’) of a different colour for Player 2 Number of players Two

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How to play The first player places the ‘cat’ marker on any vacant point on the board. The second player places a ‘mouse’ marker on any other vacant point. The cat is now free to move along a line in any direction to an adjacent empty point. Mice can only move when all seven have been placed. Mice are also free to move along a line in any direction. If the cat jumps over a mouse to a vacant point beyond, the mouse is removed from the board. Two or more mice can be removed during a series of chain jumps. The mice cannot jump over the cat. The cat wins if he or she captures three mice. The mice win if they ‘trap’ the cat, preventing further movement.

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Note* This game makes an easy introduction to ‘Fox and Geese’.

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Fox and Geese game Aims 1. To develop and promote the strategy skills of forward planning, estimation and self-monitoring 2. To develop and promote spatial visualisation and reasoning skills

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x = fox • = geese

What you need: • A baseboard shared between two players • Thirteen plastic bottle tops or counters of one colour for Player 1 (Geese) • One plastic bottle top or counter of a different colour for Player 2 (Fox) Number of players Two

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How to play Arrange the fox and geese markers as shown above. Players take turns to play.

Both players can move horizontally or vertically (but not diagonally) in any direction to an adjacent vacant point. If the fox jumps over a goose, the goose is removed from the board. Two or more geese can be removed by chain jumping. The geese cannot jump over the fox.

The geese win if he or she can trap the fox and make movement impossible.

The fox wins if he or she can remove the geese so the fox cannot be trapped.

Note* If the ‘geese’ role is played correctly, it should always win.

This game originated in Northern Europe, possibly around 1300 AD. It may have Asiatic origins. It is thought that it evolved by joining together five of the Three Men’s Morris game boards to form a cross. Hunting-style games, such as Fox and Geese, were popular in France and Britain during the Middle Ages.

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Draughts and Checkers game Aims 1. To develop and promote the strategy skills of forward planning, evaluation and selfmonitoring 2. To develop and promote spatial visualisation and reasoning skills

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What you need: • A baseboard with 64 squares, alternating between 32 dark and 32 light squares. The board is positioned so there is a light square in the righthand corner closest to each player • Twelve black plastic bottle tops or counters or interlocking cubes for Player 1 • Twelve red plastic bottle tops or counters or interlocking cubes for Player 2 Number of players Two

How to play Players set up their counters on the 12 dark squares closest to them. The player with the black counters has the first move, after which players move in turns. Moves are allowed only on the dark squares, so pieces move diagonally, one square at a time, in a forward direction towards the opposing player. A piece may jump over an opponent’s piece to an empty space beyond and capture it. Jumped or captured pieces are removed from the board. Only one piece may be captured in a single jump but chain or multiple jumps are allowed in a single turn. A piece may shift direction diagonally (either left or right) during a chain jump, but must always jump towards the opposing player.

If a player is able to make a capture, he/she has no option and must complete that move.

A player who fails to make a capturing move (through lack of awareness, for example) has one of his/her pieces confiscated by the opposing player. If there is more than one option to capture a piece during a move, the player is free to choose whichever capture is preferred.

When a piece reaches the back row of the opposing player it is ‘crowned’ by one of the pieces previously captured and becomes a ‘king’. The ‘king’ is then twice as big as a single piece. Kings are still limited to moving diagonally but can move forwards or backwards. Kings are allowed to jump and may combine jumps in several directions forwards and backwards in the same turn.

A player wins the game when the opposing player cannot make a move because: (i) all of his/her pieces have been captured (ii) all of his/her pieces are blocked from moving.

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Note* Plastic bottle tops, cubes or counters can be stuck together to make a king.

Draughts is a game of European origin, played on a chessboard. It was invented in the 12th century, probably in the south of France.

Chess, itself an elaborate battle game, had many precedents, the earliest being from India in the second half of the 6th century AD.

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Draughts and Checkers game baseboard

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Chinese Checkers game Aims 1. To develop and promote the strategy skills of forward planning, evaluation and self-monitoring.

2. To develop and promote spatial visualisation and reasoning skills

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What you need: • A baseboard shared between two players with starting positions as illustrated • Six plastic bottle tops or counters of one colour for Player 1 • Six plastic bottle tops or counters of a different colour for Player 2

Number of players Two

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How to play Players take turns to move their plastic bottle tops or counters one space at a time, in any direction. Counters jump over other counters to an adjacent empty space beyond. Chain jumping is allowed. ‘Jumped’ pieces are not captured, but remain on the board. The aim for each player is to move his or her counters or bottle tops to a position on the board opposite his or her starting position. The first player to do this is the winner.

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Chinese Checkers game baseboard

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Pathway game Aim To develop and promote the strategy skills of forward planning, evaluation and self-monitoring

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What you need: • A baseboard shared between two players • Twelve counters of one colour for Player 1 • Twelve counters of a different colour for Player 2 Number of players Two

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How to play Players take turns to put one counter on any empty circle. Each player tries to make a path of his or her own counters, which joins any side of the board to the opposite side. The first player to do this is the winner. The pathway need not be a straight line, but must be made of the player’s own colours in circles which touch each other.

If, after all the counters have been placed on the board, a pathway is not formed, play continues by players taking turns to slide any one of their counters into an adjacent empty circle.

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Pathway game baseboard

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Mancala game Aims 1. To develop and promote the skills of evaluation, forward planning, selfmonitoring and the recall of strategies 2. To develop and promote spatial visualisation and reasoning skills 3. To reinforce counting skills

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What you need: • Six cereal bowls for Player 1 (with a seventh larger bowl to his or her right) • Six cereal bowls for Player 2 (with a seventh larger bowl to his or her right) • Twenty-four pebbles, seeds, shells, cubes etc. for Player 1 (four to a bowl) • Twenty-four pebbles, seeds, shells, cubes etc. for Player 2 (four to a bowl) Number of players Two

How to play Each player has one row of six bowls arranged in a straight line in front of him or her, with a larger bowl or container (known as the ‘Mancala’) for storage to his or her right. Each bowl contains four pebbles, seeds, shells, cubes etc. at the start of play and the storage bowls are empty.

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A turn of play is made up of one or more moves in an anticlockwise direction.

The opening player may start from any one of his or her bowls by lifting all the ‘seeds’ out of it and dropping them one at a time into each of the consecutive bowls in an anticlockwise direction. When this player reaches the end of his or her own row, he or she then drops a seed into his or her store. If the player still has enough seeds left, he or she then crosses to the opponent’s row, ‘sowing’ a seed in each bowl in turn and continuing in an anticlockwise direction until there are no more seeds left. The opposing player then takes a turn.

During the course of play, if seeds are lifted from a heavily loaded bowl, there may be enough for that player to do a complete circuit of the board. Players never put seeds into their opponent’s store if they have occasion to pass. Play continues in this way until one of the players is left without any seeds in his or her bowls to move. Play then stops regardless of whether the opposing player has any seeds left or not. Any leftover seeds are not counted in the final total. The winner is the player with the most seeds in his or her store at the end of play.

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Mancala game continued An ‘extra turn’ can be obtained whenever a player’s last seed falls into his or her own store. There are several ways of engineering this.

A player could try to collect six seeds in the bowl farthest from his or her own store and use these to obtain an extra turn. Extra turns can also be gained by collecting seeds in each of the consecutive bowls thus:

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The strategic placing of seeds in an opponent’s bowls prevents him or her from obtaining an extra turn and thereby an extra opportunity to collect seeds in his or her store. Alternatively, the haphazard placing of ‘seeds’ in opponent’s bowls can benefit the opposing player if he or she is vigilant enough to notice the opportunity.

Players try to maximise their own opportunity for gaining an extra turn, while at the same time spoiling the opposing player’s attempt to do so.

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As player skill increases, extra rules can be added: • Players may not play from a bowl with one seed unless there is no alternative.

• A player must drop a seed into the opponent’s storage bowl when passing it.

• If a player quits the game before it is over, the opposing player is allowed to put all the remaining seeds from his or her side of the board into his or her own storage. Strategy sets in when the players decide whether it is wiser to quit or play longer, depending on how many seeds are in the opposing player’s bowls.

• To integrate with number work in other areas, pick a target number (e.g. 5, 6 or 7) and then have a rule that if a player drops a seed into a bowl, giving that bowl the target number of seeds, the player who owns the bowl is allowed to place those seeds into his or her own storage bowl. The skill comes in manoeuvring the play to achieve this bonus for oneself, and denying the opposing player a similar bonus.

• If a player’s last seed falls into his/her own empty bowl that player is allowed to capture the seeds in the opposing player’s bowl which is directly opposite and place them in his/her own store.

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Note* This is based on an ancient game still played widely throughout Africa and Asia.

It is sometimes called ‘The Sowing Game’ or ‘Count and Capture’.

• The game can be made more accessible to children by suggesting that each player is a squirrel, gathering nuts for its winter store of food.

• Many children find this game deeply absorbing. This encourages them to persevere at the game, which in turn leads to competence.

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references Bell, RC (1979), Board and table games from many civilizations New York, Dover Publications Inc. The Cockcroft report (1982), Mathematics counts London: H.M.S.O

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Hannaford, C (1995), Smart moves: Why learning is not all in your head Arlington: Great Ocean Publishers Murray, HJR (1951), A History of board games other than chess Oxford University Press

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Primary school mathematics curriculum (Ireland, revised 1999), Dept of Education and Skills Stationery Office, Dublin

Taskmaster Ltd., Morris Road, Leicester LE2 6BR, England, (<www.taskmasteronline. co.uk> for online catalogue), for 10-, 20-sided and other novelty dice.

Topping K and Bamford, J. (1998) The paired maths handbook David Fulton Publishers Ltd., London

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Topping K and Bamford, J, Arora, T, Mallinson, A, and Shanahan, K (1998), Parent involvement and peer tutoring in mathematics and science David Fulton Publisher Ltd., London

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