The first article in this series discussed what is meant by 'mathematical games', and the possible

benefits of using them as part of a teaching programme. This article looks at some different types

of games and the sort of mathematical thinking they can develop.

One way of classifying games is by their format, that is; the equipment used and the sort of actions

the players are involved in. Some of the following classification has been drawn from two articles

by Gough (1999). Examples have been provided by referring to well-known games, 'hotlinks' to

games that have been published on the Primary Website, or a brief description of a game. Some

thoughts on the nature of mathematics involved are also given.

**Game Formats**

**Races**

These games involve racing pieces around or across a board to a finishing point, like Ludo. Other

games might be a race against time.

Some race games depend on rote learnt skills, like basic counting or reciting number facts, and

therefore have limited mathematical value. Such games also tend to have little interaction between

players, or interdependence between 'turns' and therefore require little or no strategy development.

However, race games can be deliberately designed to focus on particular mathematical skills, such

as the probability game and the arithmetic game given below.

*Tricky Track*Place counters on the squares numbered 2 to 12. Roll two dice and add to decide which

player moves forward one square. The game should be played several times and discussion

about the fairness of the game encouraged.

**Fast Figuring**
Using the number cards from an ordinary pack, deal out five cards to each player. Turn up

one more card to reveal the 'target number'. Players race to use their five cards and any of

the four operations (+, -, x, / ) to form a statement that results in the target number. The first

player to do so wins a point. If, after 3 minutes, no one can find a solution, the players show

their hands for checking, then cards are shuffled and play continues.

one more card to reveal the 'target number'. Players race to use their five cards and any of

the four operations (+, -, x, / ) to form a statement that results in the target number. The first

player to do so wins a point. If, after 3 minutes, no one can find a solution, the players show

their hands for checking, then cards are shuffled and play continues.

**Board Games**

Moving round a board to build to build towards a goal, like Monopoly. Whilst there is some

mathematical value in these games, they are perhaps most useful in the classroom when adapted to

include problems and puzzles, which when solved, give some advantage to the player (or players).

mathematical value in these games, they are perhaps most useful in the classroom when adapted to

include problems and puzzles, which when solved, give some advantage to the player (or players).

**Spatial Strategy Games**

*Spatial Strategy:*This might involve moving pieces around a board strategically, usually to capture

or block an opponent, like Chess and Draughts (see Mini Draughts below).

*Mini Draughts*

Draughts can be difficult for young children to learn. A reduction in the size of the game

grid and the number of pieces can provide the challenge and interest of 'real' draughts

without the overwhelming number of possibilities for moves.

Spatial strategy games involve placing pieces to make a pattern or seize territory, like Noughts and

Crosses or Connect Four

Crosses or Connect Four

**Numerical Strategy Games**

This usually involves removing pieces to achieve a goal, like Nim or Mancala

*Magic 15*

This is a game for two players. Begin with the numbers 1 to 9. Players take turns to select a

number, with each number used only once. The winner is the first player to have exactly

three numbers that total 15. (There's a link to magic squares).

number, with each number used only once. The winner is the first player to have exactly

three numbers that total 15. (There's a link to magic squares).

As suggested in the title, to be successful at strategy games, players need to analyse the 'moves'

and patterns of moves that lead to winning. This is where the underlying mathematics is

discovered! Once the patterns have been found and practised, the games lose their appeal, but can

be revived through variations and extensions.

and patterns of moves that lead to winning. This is where the underlying mathematics is

discovered! Once the patterns have been found and practised, the games lose their appeal, but can

be revived through variations and extensions.

**Card Games**

Using a pack of cards: taking tricks, building sets, emptying one's hand, like Rummy, Fish or Old

Maid. These can be further adapted to create more mathematical games (see January's article).

Maid. These can be further adapted to create more mathematical games (see January's article).

**Arithmetical Games**

These games might use cards (like ONO'99), dice (like Number Boggle) or targets (like Darts) to

deliver the numbers that are then calculated in some way according to a set of rules. The games

usually involve an element of chance, which adds more interest.

deliver the numbers that are then calculated in some way according to a set of rules. The games

usually involve an element of chance, which adds more interest.

*Roll Six*

Players roll six dice and use five of the numbers together with any of the four operations to

make the sixth number. Points are scored for successful equations.

**Matching Games**

Using a set of tiles, matching ends or making patterns, like Dominoes and the less known number

game Triominoes. Memory (under its many other names) involves turning a set of pairs of cards

face down and trying to locate the pairs turning only two cards face-up at a time.

game Triominoes. Memory (under its many other names) involves turning a set of pairs of cards

face down and trying to locate the pairs turning only two cards face-up at a time.

This type of game is very useful for practise and consolidation of basic number skills, particularly

with very young children, but usually involves little strategy or player interaction.

**Mystery Games**

Guess My Number and Twenty Questions type games can stimulate quite a lot of mathematical

thinking and strategy development.

thinking and strategy development.

Teachers, take advantage of the fact that children will happily play and enjoy mathematical games

that they wouldn't normally choose to play at home!

References

Car, J. (1999) Primary Mathematics Masterclasses.

Gough, J. (1999). Arithmetics Games: Very equable?

Vol.4 No. 3

Gough, J. (1999). Strategy Board Games and Spatial Thinking.

Classroom . Vol 4. No.4

*Mathematics in School*, January 1999.Gough, J. (1999). Arithmetics Games: Very equable?

*Australian Primary Mathematics Classroom*.Vol.4 No. 3

Gough, J. (1999). Strategy Board Games and Spatial Thinking.

*Australian Primary Mathematics*Classroom . Vol 4. No.4

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