This article discusses a small group of activities taken from the Mathematical Games Archive on the NRICH site. They all have a related structure that can be used to develop the skills of strategic thinking and reasoning as well as ideas of analogy and isomorphisms. Students at all levels of ability and age can access them. At the most basic level, they offer opportunities for practising
arithmetical skills. At a higher level, they can be used to promote mathematical discussion by demanding detailed and reasoned explanations for a winning strategy, or an explanation of the mathematics that links the games.
These games can be tackled in any order, but we suggest the order given below:
Several of the games link into one another. One suggestion is given below. Can you describe the similarities between all of these games?
Links with the UK Framework
The following objectives are to be found in the Frameworks for teaching mathematics for Key Stages 1, 2 and 3, and apply to the activities in this theme.
Solve mathematical problems or puzzles, recognise simple patterns and relationships, generalise and predict.
Discuss the chance or likelihood of particular events.
Use the language associated with probability to discuss events.
Understand addition and subtraction mental calculation strategies.
Represent problems mathematically.
Explain and justify methods and conclusions.
Recognise and visualise the transformation and symmetry of a 2-D shape.
Use logical argument to establish the truth of a statement.
Solve increasingly demanding problems and evaluate solutions.
Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory text.
Suggest extensions to problems, conjecture and generalise.
Noughts and Crosses
Play the game on line. If you start, is it possible to guarantee that you will win the game? Try to explain the strategy. You might find diagrams helpful.
Play the game on line. If you start, is it possible to guarantee that you will win the game? Try to explain the strategy using diagrams as appropriate.