- Encourage fluency in key mathematical skills to build a toolkit for thinking
- Find a counterexample e.g. to n^2+ n + 41 is always prime
- Generalise e.g. from 1, 1+3, 1+3+5,… to the general formulae
- Conjecture e.g. all quadrilaterals tessellate
- Give an example of… another…and another e.g. a shape with area 9
- Define e.g. a square is a shape with…is this necessary and sufficient?
- Compare and contrast e.g. x^2+y^2 = 4 and x^2+y^2 =4x
- Consider impossible things e.g. construct a 4, 5, 10 triangle
- Odd one out e.g. 15, 16, 17 – the only triangle number, square, prime.
- Is it always, sometimes or never true e.g. ‘division makes things smaller’
- Ordering e.g. 60% of £ 18, 20% of £ 58 and 30% of £38 increasing
- Use puzzles to engage in non-routine mathematics
- Justify or prove e.g. that the product of two odd numbers is odd
- Create your own question
- Explain your solution to another and compare solutions
- Draw a diagram that helps to illustrate the problem or solution
- How is this linked to another area of mathematics?
- Devise your own notation e.g. for describing a polygon
- How might your method of solution be used elsewhere?
- Can you revisit your solution and make it more efficient?
Further details on many of these can be found in ‘Thinkers’ by Chris Bills et al, ATM (2004)