design a board game - shell centre2. list and describe all the faults you notice with the board. 3....

NUMERACY ~ THROUGH ~ PROBLEM ~ SOLVING

Design aBoard Game

Shell Centre for Mathematical Education

Joint Matriculation Board

MASTERS FOR PHOTOCOPYING

Masters for PhotocopyingExcept where indicated, these Masters are designed to produce single-sided, reusable worksheets.Masters for consumable sheets are labelled (c). Masters for double-sided sheets are labelled *.

Contents

Chapter 1 Resource sheets

Stage 1 Isometric dotty paper (c) 18

'Comments' sheet (c) Isometric lined paper (c) 19

'Looking at other game~' sheet (c) 2 Squared dotty paper (c) 20

Assessment task 1: 'The Great Horse Race' 3 Squared lined paper (c) 21

Assessment task 1: Blank grids (c) 4 Chapter 2Assessmenttask 2: 'Snakes and Ladders' 5

'How to ... draw a spiral' 22Assessment task 2: Blank boards (c) 6

'Goal' problems 23

Stage 2 'Honeycomb' problems 24

'Brainstorming' sheet *(c) 7.8 'Making and playing board games' * 25,26

'Rough plan' sheet (c) 9 'Looking forwinning strategies' * 27,28

Assessment task 3: 'Deep Sea Diving' 10 'Games and probability' 29

Assessment task 4: 'Treasure' 11 Chapter 3Assessment task 4: Answer sheet (c) 12 Record sheet (c) 30

Stage 3Examination paper 1 task 1 31,32

Assessment task 2: 'Chasing Packs' 13,14Examination paper 1 task 2 33,34

Assessment task 3: 'Chuck-a-Luck'Examination paper 1 task 3 35

15Examination paper 2 task 1 36

Stage 4 Examination paper 2 task 2 37,38

'Evaluating your own game' sheets *(c) 16,17 Examination paper 2 task 3 39,40

LONGMAN GROUP UK LIMITED

Longman House, Burnt Mill, Harlow,Essex CM202JE, Englandand Associated Companies throughout the World

© Shell Centre for Mathematical Education/Joint Matriculation Board 1987

This work is copyright, but copies may be made without fee or prior permission provided that the work has been paid for and such copies are usedsolely within the institution for which the work is purchased. Works sent on approval or inspection and not yet paid for may not under anycircumstances be copied. For copying in any other circumstances (e.g. by an external resource centre) prior written permission must be obtainedfrom the Publishers and a fee may be payable.

First published 1987

Set in Neue Helvetica

Printed in Englandby Burgess & Son (Abingdon) Limited

~~~Longman::

STAGE 1 AND STAGE 4

CommentsName of the game _

Filled inby _

While you are playing, write down some good and bad features of it.

Bad pointsGood points

Play the game a few times.

Make a note of the result on the back of this sheet.

About how long did each game take? I -----.JI minutes

After you have played, say how you could improve the game.

DESIGN A BOARD GAME© Shell Centre for Mathematical Education/Joint Matriculation Board 1987

M1

STAGE 1

Looking at other gamesFilled inby _

Think of a board game that you like.

What is it called?

Why do you like it?

Is there anything you would change?

Think of a board game you don't like.

What is it called?

Why don't you like it?

What could you do to improve it?

DESIGN A BOARD GAME

© Shell Centre for Mathematical Education/Joint Matriculation Board 1987.

M2

STAGE 1 ASSESSMENT TASK 1

The Great Horse RaceTurn to pages 4 and 5 of you(Student's Booklet.

The 'Great Horse Race' is being played.

The scores on the first six throws of the dice are shown below:

[JQr;-;l~U~

IT] [S] IT] [8]Throw 2 • • Throw 3 • •• • • • • •

Throw 5 [8][8] Throw 6 [J[8]•• ••

Throw 1

Throw 4

1. On a copy of this grid, markthe positions of the horsesafter the six throws.

1-----1-------- --- ----- --1---+----+---+-+---+---+---1

I---+----+----t--+---+-------+---+---f--- -- -- f-

1----+---+------ ----1----+------+----- --+----+-+--+

'---- -- -- -------- --------------- ---- ------+----+--+----j

------ ----- ---- -------------- -------+------+---+

--- --------- --- -- ---- --r-----I-----1--t---+

-- ----- ---- - - -- --- --- - ----- -- --~-

T 2 ,I 4 S 6 T 8 9 TO TT T2I_ _ l_~ __ '--_ --' __ --'----'

START

2. Suppose you want to win the game.

(a) Which horse would you not choose?Explain your answer.

(b) Which horse would you choose?Explain your answer.

(c) Do you think the game is fair?Explain your answer.

DESIGN A BOARD GAME© Shell Centre for Mathematical Education/Joint Matr!culation Board 1987

M3


Blank grids for 'The Great Horse Race'

I 2 ,8 4 S 6 T 8 9 10 II 12

START

I 2 ,8 " S 6 T 8 9 10 II 12

START


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START

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START

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12,84S6T891DT112___...__ L.. -'----------'-_...1_-'--_-'----'--_'-_---"-----'

START

M4


Snakes and Ladders

Read the following description of a game, and answer the questions which follow.

This is a game for 2 players.You will need a coin and two counters.

Rules• Take it in turns to toss the coin.

If it is heads, move your counter 2 placesforward.If it is tails, move your counter1 place forward.

• If you reach the foot of a ladder, you must goup it.

If you reach the head of a snake, you mustgo down it.

• The winner is the first player to reach'FINISH'.

I

FINISH: 14II

13 12

81---7

11q5 I 4

I

2~--

1. Suppose you start by tossing a head, then a tail, then a head.Where is your counter now?

2. List and describe all the faults you notice with the board.

3. Using 3 snakes and 3 ladders, design a good game on a copy of this blank board.

I II I

FINISH: I I14 I 13 I 12I I II I ----- -I I

II I

8 I 9 I 10 I 11I I I

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START: 1 I 2 I 3I II I III I I


M5


Blank boards for 'Snakes and Ladders'

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M6

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STAGE 2 AND STAGE 3

Rough planNames ~

Our game is called ...

Who it's for ... What you need in order to play ...

What it's about ... Aims of the game ...

Rules

How to start ...

How to make a move ...

Other rules ...

DESIGN A BOARD GAME


M9


Deep Sea Diving

One group have been discussing their plans for a board game.

Here are some of the things they have decided:

Our game will be aboutdeep sea divers lookingfor treasure in a sunkenshipwreck.

Your task is to design a board for this game.

Try to make your design interesting and fair.

(You do not need to draw it accurately.)

You need to throw a diceto move around the board.

The game will befor 3 players.

The winner will be the firstto bring the treasure tothe surface.

\ I ~

~ ./ (/

There are sharks and other dangerswhich make the task more difficult.


M10


Treasure

The board drawn below was designed by a group of students, but they haven't written any rules.

2 I

18

34-3536

54- 53 41-7 31

5/ 522441 42 J4

27 zs

/ I /2


M11

STAGE 2 ASSESSMENT TASK 4 (CONTINUED)

Answer sheet for 'Treasure'

Fill in the 'Rough Plan' sheet shown below, so that a young child could understand how to play thisgame.

Rough plan

Names

Our game is called ...



Rules

How to start ...


Other rules ... Make sure you explain what happens if you land on a gun or a ship.


M12

STAGE 3 .ASSESSMENT TASK 2

Chasing PacksHere is part of a rough plan for a game called 'Chasing Packs'.

We wW..t ~ +he botAKJcf1Il, tl I~ s~ s kuJ-of CAA't1 b otVrri

( £o.4,of~~S"~SwrM b.e.

2~ t:J 2CM

DESIGN A BOARD GAME I __----------f~~=========~=~=~--r;Md13© Shell Centre for Mathematical Education/Joint Matriculation Board 1987

STAGE 3 ASSESSMENT TASK 2 (CONTINUED)

Chasing PacksTwo students are about to make this game.

1. How many counters will be needed altogether?

2. They are going to make a full-size version of the board. Work out how big the large cardboardbase should be, (use the measurements on the rough plan).

The students have found this scrap of black paper

3. They could cut out the black squares on the board from it and then paste them on.

How many 2 cm by 2 cm squares can be cut from this piece?

(Find the largest number you can make).

DESIGN A BOARD GAME


M14


Chuck-a-LuckA group of students have designed a board for a game called 'Chuck-a-Luck'.Draw the board full size, as accurately as you can.Make sure you follow the instructions in the bubbles.

DESIGN A BOARD GAME© Shell Centre for Mathematical Education/Joint Mcttriculation Board 1987

M15

STAGE 4

Evaluating your own gameName of the game _

Filled in by _

Read through the Comments sheets.

1. What did other people say about your game?

Tick the points you agree with.

2. These are the good points of the game:

3. These are weak points of the game:

Turn over

DESIGN A BOARD GAME


M16

STAGE 4

Evaluating your own game (continued)

4. I could improve it by changing the rules like this ....

5. I could improve it by changing the board like this ....

6. Next time I design a board game, I will ....

7. If a friend asked my advice about designing a board game, I'd say ....

8. Space for further points

DESIGN A BOARD GAME


M17

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Isometric lined paper

DESIGN A BOARD GAME


M19

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Squared lined paper

DESIGN A BOARD GAME


M21

How to ... draw a spiral

You will need: Pencil, ruler, compasses, scissors, glue, rubber.

1. Draw some concentric semi-circles, with diameters of 2, 4, 6, 8. .. units.

2. Now draw some more, with diameters of 3, 5, 7, 9 ... units .

.I-:~ .1.11------7

3. Now join the two halves together:

DESIGN A BOARD GAME


M22

'Goal' problems(See pages 8 and 9 in Stage 1)

1. In one particular game of Goal,

the red team put down: Ace, then 4, 6, 3 , 2, 10, 9, 7, 5, 8the black team put down: 8, then 3, 2, Ace, 10, 5, 4, 6, 9, 7

What was the final score?

2. Write down all the other possible final scores.

Describe one way in which the cards could be laid to give each of these final scores.

3. When you played 'Goal', you may have found it boring ... maybe no-one scored!

• Change the rules to make it more exciting• Write down your new rules• Play your new version.

4. Suppose you keep all the rules the same as on page 9, apart from the rule which says:

'If you have the higher value, move the ball one steptowards your opponent's goal.

• Change this rule to

'If your card is one higher than your opponent's,move the ball one step towards his/her goal;If your card is two higher, move the balltwo steps ... and so on'

• Play the game using this new rule.• What final scores are possible now?• Describe a game which ends in a score of 6-3.

5. Make up some similar questions of your own, which refer to your own rules for question 3.Give them to a friend to solve.

DESIGN A BOARD GAME

© Shell Centre for Mathematical Education/Joint Matriculation Board 19~7M23

IHoneycomb' problems(See pages 12 and 13 in Stage 1)

1. This diagram shows how the board looked after 8 moves in one game.

(a) Imagine that you are playing 'Drones' in this game. It is your turn.Where .would you put your next Drone counter?Explain why you would do this.

(b) Using the same board, now imagine that you are playing 'Workers'. It is your turn.Where would you put your next Worker counter?Explain why you would do this.

2. Do you think that the game of 'Honeycomb' is fair?Does it make any difference who goes first?Explain your answers as fully as you can.

3. If you start first, and you are playing 'Workers', where would be bad places to go? Explain why.If 'Drones' were to start first, where would be a bad move for them?

4. Can the game of 'Honeycomb' ever end in a draw?Either: show how the game can end in a drawor explain why the game can never end in a draw.

5. Try changing the rules to 'Honeycomb' and play your new version of the game.

DESIGN A BOARD GAME


M24

Making and playing board games

Choose a game from those described below.

Draw the board, full size, as accurately as you can.

Play the game with a friend and comment on it.

Now try changing the rules ...

Ashi.,...a game for 2 players from Ghana.

What you need: 8 counters, 4 of one colour, 4 of another.

Aim of the game: To get 3 counters of your colour ina straight line, before your opponent does.

How to playTake turns to put a counter on the board, like Noughtsand Crosses.

When all the counters are on the board, take turns tomove a counter to a neighbouring empty positionalong the lines.(You can only move a counter of your own colour).

Lau-Kati-Kata - a game for 2 players from Bengal.

What you need: 12 counters, 6 of one colour,6 of another.

Aim of the game: To 'take' all youropponent's counters.

How to start: Put your 6 counterson the dots to the left of the centre.Your opponent puts her counters onthe dots to the right. The centraldot is left empty.

How to playTake turns to move a counter to a neighbouringempty dot along a line.

You capture a counter by hopping over it to an emptyposition beyond. (This is a bit like 'Draughts').

As in 'Draughts', you can make more than one hop in a move.

If you can hop over one of your opponent's counters, then you must do so.

DESIGN A BOARD GAME


M25

Making and playing board games (continued)

Mu- Torere - a game for 2 players from New Zealand.

What you need: 4 black counters and 4 whitecounters.

Aim of the game: To block your opponent'scounters so that he cannot move.

How to start: Each player puts his pieces onfour neighbouring points of the star.

How to playBlack starts, and players take it in turns tomove their counters.

There are 3 kinds of move.(a) A counter may be moved to the centre circle if

one or both of the neighbouring points on thestar are occupied.

(b) A counter may move from one point to aneighbouring point if it is empty.

(c) A counter may move from the centre circle to apoint.

Only one piece is allowed on each point or in thecentre circle.Jumping is not allowed.

Drawing the boardDiameter of large circle = 16 cmDiameter of small circle = 2 cmThe points on the star are equallyspaced, 6 cm from the centre.

Sixteen Soldiers - a game for 2 players from Sri Lanka.-

What you need: 32 counters, 16 black and 16 white.

Aim of the game: To capture all youropponent's counters.

How to start: Put the counters on the board asshown below:

How to playTake turns to move a counter to a neighbouring emptydot along a line.You capture a counter by hopping over it to anempty position beyond. [[his is a bit like 'Draughts').As in Draughts, you can make more than one hop in a move.If you can hop over one of your opponent's countersthen you must do so.

DESIGN A BOARD GAME


M26

looking for winning strategies

Make one of the following games and play it.

In each game, one player can make sure that he or she always wins.

• Try to find this winning strategy• Try changing the rules, and see what happens

Now try playing a different game.

The Spiral Game

This is a game for 2 players.

Place a counter on the dot marked' t 5'.

Take it in turns to move the counter inwards,along tbe spiral.

On your turn you can only move the counter1,2,3,4,5 or 6 dots.

The first player to reach the dot marked ' ~ F' wins.

ts-

~ - - :1

~~F

~•L

WALLI

e e e e e

0 0 0 0 0WALL

Pin them down!

A game for 2 players.

Place the counters on the board as shown.

The players take it in turns to slide one of theircounters up or down the board any number ofspaces.

No jumping is allowed.

The aim is to stop your opponent from beingable to move, by pinning all her counters to the wall.


M27

Looking for winning strategies (continued)

First one home

This game is for 2 players.

Place the counter on any square of the grid.

Now take it in turns to slide the counter anynumber of squares due West, South orSouthwest (like the dotted arrows).

The winner is the player who moves the counterto "Finish".

...•~-- --- ~/

I// I

/

;I II

+

..----::-<'-

~Cj "'{s"

Domino square


You will need a supply of 8 dominoes or 8 paperrectangles.

Each player in turn, places a domino on thesquare grid, so that it covers two squares.

After a domino ha~ been placed, it cannot bemoved.

If you cannot place a domino on the grid,you lose the game.

For example:

This board shows the first five moves in onegame.

It is the second player1s turn.How can she win with her next move?

DESIGN A BOARD GAME


M28

Games and probabilityRead through the games described below.

Before you playa game, try to answer the following questions:• Is the game fair?• If the game is plaxed a lot of times, who would you expect to win most often?

Who do you expect to come second, third, ... last? Explain your reasoning.

Now play the game and see if your predictions are correct! Try to explain what you notice.

FINISHDouble-toss - a game for 3 players.

What you need: 3 counters, 2 coins and a large copyof the board.

0 1 2

Aim of the game: To be the first to get your counter pastthe finishing line.

How to start• Place the 3 counters on their starting

squares, labelled 0,1, and 2.• Each player chooses a different counter.

How to play• Toss the coins.• If you toss 0 heads, then move counter

number 0 one square forward

1 head, then move counternumber 1 one square forward

2 heads, then move counternumber 2 one square forward.

• Keep tossing until one counter wins.START

FINISHTake-away - a game for 2 or 3 players.

What you need: 5 counters, 2 dice and a large copy ofthe board.

0 1 2 3 4 5

Aim of the game: To be the first to get your counter pastthe finishing line.

How to start• Place the 6 counters on their starting squares, labelled

o to 5.

• Each player chooses 2 or 3 counters (depending on thenumber of players).

How to play

• Roll the dice.• Find the difference between the numbers you roll.

(e.g. ~ GJ gives a difference of 3)

• Move the counter which is labelled with this difference,one square forward.

(e.g. r;] GJ would mean that you move counter number 3one square forward)

START

DESIGN A BOARD GAME


M29

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Stage 1 Stage 2 Stage 3 Stage 4

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DESIGN A BOARD GAME


M30

PAPER 1 ASSESSMENT TASK 1

Overtaking

Here is the description of a game called 'Overtaking'.

Read it through and answer the questions which follow.


Green•• start andfinish

Yellowstart andfinish

11

Bluestart andfinish

Redstart and ..•finish

What it is aboutEach player has a counter.

Players take it in turn to throw a dice.

Each player moves his or her counter around the track the number of squares shown on thedice, in the direction of the arrows.

How to winThe first player to complete the circuit back to their 'home' square is the winner.

Rules1. Red starts first, then Yellow, then Green, then Blue.

2. If a counter lands on the same square as another, both counters are removed and thosetwo players are out of the game.The remaining players continue to play in the same order as before.

continued


M31

PAPER 1 ASSESSMENT TASK 1 (CONTINUED)

Overtaking

Using counters if you wish, become familiar with the game.

Then answer the questions.

The first 4 throws of the dice give these numbers:

Red Yellow

r;:-;l~

8 ~ Fl~ U ~

1. On a copy of the diagram, show the position of each counter after the matching moves.

The next three throws give r-;:In~~ ~ ~

2. Show the final positions of the counters after all the moves.

3. Which counter has moved the furthest round the track?

4. 'Now look what's happened! No-one can win this game!'

Explain how this situation could happen in the next move.

5. Change one of the rules so that there will always be a winner. Write down the changed rule.


M32


ArcadeThis is the rough plan of a board for the game of 'Arcade'.

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FINISHSf

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continued

DESIGN A BOARD GAME© Shell Centre for Mathematical Education/Joint Mat.-iculation Board 1987

M33


Arcade

Complete this rough plan for 'Arcade'

Rough planNames _

Our game is called. .. A r"'c.eu:le.

30~ round. aA,

~el)\ent ~~ de.

Aims of the game ...

Who it's for. . . What you need in order to play ...

a c..o~.e.r Ff" oQAdv

f>lj~Gt. olAce

What it's about ...

Rules

How to start ...


Other rules ... (make sure you explain what happens at the D and the ~ )

DESIGN A BOARD GAME


M34


Nsolo

Nsoro is a game for 2 players. Many versions of the game are found in parts of Africa and India withdifferent names.

A small picture of part of the board is shown here, with a row of 3 equal-sized circles inside arectangle.

TE()

'----_----J1lI I-scm :1!-10cm

All circles are equally spaced.The circle centres are 5 cm from thesides of the rectangle.All circles are 4 cm diameter.The rectangle is 10 cm by 20 cm.

1. Draw this part of the board accurately and full-size.

E()

oC\I

2. Using the same spacing as in question 1, how long would the rectangle be if the row had 5 circlesinstead of 3?(You do not need to draw this.)


M35


Star

The diagram below shows a small board design for playing a game called 'Star'.

these triangles areall equilateral

this hexagonis regular

The game will be played with circular counters, 2 cm in diameter.

The counters will be placed on the 18 black blobs (marked e) on the board.

The board must be large enough so that when the counters are placed on adjacent 'blobs',there is a 1 cm gap between them, and no counter is ever less than 1 cm from the edge of theboard.

This distance must be

Draw an accurate board which will satisfy these conditions.


M36


Build a PyramidThis· is a game for 2 players

AimThe first player to build a pyramid with 15 counters, wins the game.

EquipmentOne board for each player15 counters for each player2 dice, one black and one white.

PreparationEach player fills her board with numbers. A number from the set {1, 2, 3, 4, 5} must be written ineach square. A player can choose to place some or all of these numbers in any position. Forexample, here are three possible ways:

Rules• Decide which player will be 'BLACK' and which will be 'WHITE'.

• Throw the two dice.

• If the number on the black dice is greater than the number on the white dice, then BLACKcalculates the difference between the two numbers on the dice and covers any correspondinglynumbered square on her board with a counter.

• Similarly, if the number on the white dice is greater than the number on the black dice, thenWHITE calculates the difference and covers a corresponding square on her board.

• If both numbers on the dice are equal, neither player covers a number.

• The first player to cover all 15 squares and complete the pyramid wins the game.


M37


Build a Pyramid

Suppose that the two boards are filled in like this:

BLACK

1

5 I 5

3 3 3

2 21 2 2 I1 1 1 1 1

WHITE

1

3 3 3

5 5 5 55

1. The first four throws of the dice are:

~~. ~[S]. a~· tml;l, , ,tmL:JOn copies of the boards, show clearly which numbers have been covered.

2. Which player do you think is most likely to win?

(If you think that both players are equally likely to win, write 'You can't tell').

Give a reason to support your answer.

3. Now suppose that you were playing the game.

(a) Show how you would number your board to give the best chance of winning.

(b) Explain why you think this would give you the best chance of winning.

4. Suppose that the game is to be adapted for 3 players using 3 dice and 3 boards.Describe how you would adapt the rules, so that the game will still work.


M38


Underground

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continued


M39


Underground

A group is making up a game for 2 players. It is about travelling on the London Underground. Thegroup want to make up rules so that the winner is the first person to travel through or change trainsat every station on the map. Make up a complete workable set of instructions for their game. Youcan put extra details on the board if you wish.



Rules

How to start ...


Other rules ...


M40

design a board game - shell centre2. list and describe all the faults you notice with the board. 3....

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