Representation and Structure
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
Bank of support
Effective use of representation to support the understanding of mathematics is at the core of mathematics learning.
Recently we are focussing more on the mathematical structures as well as the representations we use in our classrooms.
Both the NCETM PD Materials and the Ready To Progress materials have a strong focus on developing representation and structure in tandem in order to secure a deep understanding that builds effectively on prior learning.
Stem sentences
 help pupils to develop and use precise and accurate language in mathematics
 provide suggested sentence structures for pupils to use to capture, connect and apply important mathematical ideas.
Once pupils have learnt to use a core sentence structure, they should be able to adapt and reason with it to apply their understanding in new contexts.
Enigma Maths Hub has collated sentence structures from the NCETM PD Materials for each of the spines. Download these documents below.
Thinking Boards
Think boards can help pupils to understand the structures linked to concepts.
See how the think boards help pupils to connect representations, symbols, pictories and stories.
Could this be useful for your pupils?