## Fluency, Flexibility and Originality

As you probably wrote in Patch 5, Japanese lessons often revolve around one particular problem. Japanese pupils are then encouraged to think of multiple ways of tackling the problem. These different approaches are then shared through discussion as the students try to decide which is the most effective method.

In advance of the lesson, the teacher prepares a list of expected responses, which are classified and arranged in order, item by item, according to their mathematical features.

The pupil’s indivudual achievement is evaluated against three criteria.

- Fluency – how many solutions did the pupil produce?
- Flexibility – how many different mathematical ideas are discovered by the pupil?
- Originality – to what degree are pupil’s ideas original?

It is now your turn to do some maths.

In each case 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.

For the moment restrict yourself to tasks 1, 2 and 3. Take your time and enjoy doing some maths – there is no need to rush through them.