'Learning Mathematics Through Games Series: 2. types of Games'

http://nrich.maths.org/  The article is from this site.

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.

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).

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

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).

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.

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).

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.

          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.

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.

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. 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