Students form perceptions about mathematics by the kinds of tasks you ask them to do (Hiebert et al.,1997). If you simply ask your students to perform routine exercises based on the topic that you just taught the, they think maths is all about following procedures. If you want your students to think maths is more about solving problems for which they have no prescribed method to employ (Van de Walle, 2013) then they need to spend most of their time solving problems. The same applies to you!
In our examples, you will be given a task to think about. You should now answer the task on your own and then think about how your pupils might try to approach the task themselves. The more ways you can think of the better. It is an important lesson to learn, there are usually many ways of solving a problem and it is important to encourage your pupils to think for themselves!
We suggest that you use your problem solving notebook for these tasks.
For each task, include the task, your own solution strategies and any ideas you had so that you can refer to them later in group discussion. Also include a section on possible methods your pupils might use – the more the better.
Finally think about where this question might fit in your scheme of work. Remember it is meant to introduce new learning, so make it clear what you think this might be.
Task 1 – This is shape 3 (Year 7+)
Task 2 – And the winner is … (Year 6+)
Task 3 – The marble problem (Year 9+)
Task 4 – A square problem (Year 7+)
Task 5 – One up one down (Year 5+)
Task 6 – Making a difference (Year 2+)
Task 7 – Equal teams (Year 5+)
Task 8 – Missing fractions (Year 6+)
Task 9 – Odd one out (Year 5+)
Task 10 – Hot shot (KS4/5)
Task 11 – Lots! (Ks4/5)