'Learning Mathematics Through Games: 3. Creating Your Own Games'

From: http://nrich.maths.org/

          Question: How do find a game that fits the mathematical needs of my children exactly?

          Answer: Create the game yourself!

          Question: How do I do that?

          Answer: Read on...

Some games are worthy of playing in their own right - because they stimulate mathematical
thinking and strategy development. However, to take full advantage of the educational benefits of
playing games (and cope with a specified mathematics curriculum), we often need games that fit
particular mathematical objectives. As the teacher, you are the best person to design a game for
your class, or groups within your class. You know the children's mathematical abilities and needs.
You also know the content that needs to be covered, and other constraints such as time, resources
and space.

Not all of us a bursting with creative game ideas, but there are several ways to go about creating a
game that will assist even the busiest and most reluctant game designer.

1. Use the rules of an existing game, but use different materials or add extra materials.

Example 1: Tables Fish - use the rules of the old favourite "Go Fish", but make a pack of cards for
whichever multiplication facts need practising.

 

Bonus points can be given for collecting sets that the children might usually avoid, like 9 times 8.
It might be helpful to allow children to use a tables card to start with, then have them play without assistance as they become more confident.

Example 2: Maths Dominoes - Make a set of paper or card dominoes where the dots have been
replaced by equivalent values or matching concepts. Such as . . .

Equivalent Fractions

 

Basic Number Dominoes

 

Polygon Dominoes

2. Use the idea for a game and change the rules or the playing circumstances to fit whatever
classroom resources are available.

Example: Roll a Shape - This is based on games that involve rolling a die, or spinning a spinner, to
gradually build a beetle (or some other creature). The idea is to use some type of construction
material and a die or spinner to tell the players what pieces to pick up. For example, if 'Polydrons'
(click together polygons) are used, a die could be modified to show 3, 3, 3, 4, 5, 6 to indicate the
number of sides the piece must have. After 12 pieces (or some other specified amount) have been
collected, the aim is to try to use all the pieces to build one or more polyhedra (closed solid
shapes). Points are scored for the pieces used, points deducted for unused pieces.

Another version uses construction straws and an ordinary die. The numbers 1, 2, 3, 4 tell the
number of straws to pick up. The numbers 5 and 6 allow a connector to be picked up. Building
begins after 6 rolls. The aim is to make just one polyhedron using all the straws as edges.

3. Use a game board and add maths tasks to it. Most schools have board games with pieces
missing, like Ludo, Snakes and Ladders, Checkers, or racing games. Use the boards and make up
some new rules and put in some mathematics. Rather than write tasks directly onto the boards, just
place coloured stickers on certain spaces. Make up some colour-coded cards with quiz-type questions. A correct response - advance some spaces, incorrect - stay there. Include some fun
questions and chance cards.

Example: Operation Snakes and Ladders - use the board with two dice. On each turn the player has
the option of multiplying, dividing, adding or subtracting the two numbers, with a maximum
answer of twenty.

4. Ask the children to invent their own games. Put them into small groups. Give them some
possible topics, various resources and insist on an agreed plan before they start making anything.

Evaluating Your Game

Rate your game using these questions.

• Does the game match your mathematical objective?
• Does it cater for a range of abilities?
• Can the game be completed in a short time? (10 mins for infants, 15-20 for older)
• Is there an element of chance built in?
• Are there strategies to be developed to improve the likelihood of winning?
• Do the children enjoy playing it? (If not, ask them why and modify the game)

'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

'Learning Mathematics Through Games Series: 1. Why Games?'

We all know that children enjoy playing games. Experience tells us that games can be very
productive learning activities. But ..

• What should teachers say when asked to educationally justify the use of games in
  mathematics lessons?
• Are some games better than others?
• What educational benefits are there to be gained from games?

 

 This article supplies teachers with information that may be useful in better understanding the
nature of games and their role in teaching and learning mathematics.

What is a mathematical game?

When considering the use of games for teaching mathematics, educators should distinguish
between an 'activity' and a 'game'. Gough (1999) states that "A 'game' needs to have two or more
players, who take turns, each competing to achieve a 'winning' situation of some kind, each able to
exercise some choice about how to move at any time through the playing". The key idea in this
statement is that of 'choice'. In this sense, something like Snakes and Ladders is NOT a game
because winning relies totally on chance. The players make no decisions, nor do that have to think
further than counting. There is also no interaction between players - nothing that one player does
affects other players' turns in any way.

Oldfield (1991) says that mathematical games are 'activities' which:

• involve a challenge, usually against one or more opponents; 
• are governed by a set of rules and have a clear underlying structure;
• normally have a distinct finishing point;
• have specific mathematical cognitive objectives.

Benefits of Using Games

The advantages of using games in a mathematical programme have been summarised in an article
by Davies (1995) who researched the literature available at the time.

• Meaningful situations - for the application of mathematical skills are created by games
• Motivation - children freely choose to participate and enjoy playing
• Positive attitude - Games provide opportunities for building self-concept and developing
  positive attitudes towards mathematics, through reducing the fear of failure and error;
• Increased learning - in comparison to more formal activities, greater learning can occur
  through games due to the increased interaction between children, opportunities to test
  intuitive ideas and problem solving strategies
• Different levels - Games can allow children to operate at different levels of thinking and to
  learn from each other. In a group of children playing a game, one child might be
  encountering a concept for the first time, another may be developing his/her understanding
  of the concept, a third consolidating previously learned concepts
• Assessment - children's thinking often becomes apparent through the actions and decisions
  they make during a game, so the teacher has the opportunity to carry out diagnosis and
  assessment of learning in a non-threatening situation
• Home and school - Games provide 'hands-on' interactive tasks for both school and home
• Independence - Children can work independently of the teacher. The rules of the game and
  the children's motivation usually keep them on task.

Few language barriers - an additional benefit becomes evident when children from non-english speaking backgrounds are involved. The basic structures of some games are common to many
cultures, and the procedures of simple games can be quickly learned through observation. Children
who are reluctant to participate in other mathematical activities because of language barriers will
often join in a game, and so gain access to the mathematical learning as well as engage in
structured social interaction

Hints for Successful Classroom Games

These tips come from Alridge & Badham (1993):

• Make sure the game matches the mathematical objective
• Use games for specific purposes, not just time-fillers
• Keep the number of players from two to four, so that turns come around quickly
• The game should have enough of an element of chance so that it allows weaker students to
  feel that they a chance of winning
• Keep the game completion time short
• Use five or six 'basic' game structures so the children become familiar with the rules - vary
  the mathematics rather than the rules
• Send an established game home with a child for homework 
• Invite children to create their own board games or variations of known games.

Future articles in this series will cover types of games and creating your own games

References

Aldridge, S. & Badham, V. (1993). Beyond just a game. Pamphlet Number 21 . Primary
Mathematics Association.
Davies, B. (1995). The role of games in mathematics. Square One . Vol.5. No. 2
Gough, J. (1999). Playing mathematical games: When is a game not a game? Australian Primary
Mathematics Classroom. Vol 4. No.2
Oldfield, B. (1991). Games in the learning of mathematics. Mathematics in Schools. January

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