5 Summary

This unit has focused on using visual representations to facilitate working with complex expressions. Once your students grasp the connections between area calculations and expanding brackets, they immediately have a way of working out identities rather than relying on their memories. These ideas allow students to give a meaning to what they are doing and therefore to feel that the ideas are their own.

It also suggests that the students play with these ideas, asking ‘What if I do it this way instead of that way, or make it more messy rather than less?’ This can relieve some of the anxieties from demanding memorisation and help students to remember what they learned more easily. This is important, because when students can reproduce identities from memory, they can solve mathematical problems more fluently. But often they are so worried about memorising, they cannot develop the fluency.

Pause for thought

Identify three ideas that you have used in this unit that would work when teaching other topics. Make a note of two topics you have to teach soon where those ideas can be used with some small adjustments.

4 Spotting patterns and adjusting algebraic identities