Representing the structure behind mathematics can help develop an understanding of arithmetic and/or algebra. This can also be linked with multiple representations of a concept as each of the illustrations below can be shown in alternative ways including number lines, sets & arrays of counters amongst others.
These are intended to provoke discussion amongst colleagues rather than to be used without thought or reflection with learners but SYMH would be happy to hear of colleagues' thoughts on these and if they have used any or similar models with learners to good effect.
You can also find here a series of resources that can be used with colleagues to discuss conceptual development and structures underlying some of the common techniques taught in number and algebra.
Click on each below link to download PDF