Key Messages:

The representation needs to clearly show the concept being taught, and in particular the key difficulty point. It exposes the structure.

In the end, the students need to be able to do the maths without the representation

A stem sentence describes the representation and helps the students move to working in the abstract (“ten tenths is equivalent to one whole”) and could be seen as a representation in itself

There will be some key representations which the students will meet time and again

Pattern and structure are related but different: Students may have seen a pattern without understanding the structure which causes that pattern