A picture speaks a thousand words by @CambridgeMaths

I love patterns, diagrams and pictures. Ask me to record information and it gets plastered over a page in bubbles, a mind map or random boxes. I’m not particularly artistic but I find I like to store information in this way. Even with telephone numbers – I remember the pattern the digits make, not the number itself.

The power of geometry is that it can represent abstract ideas and concepts in a completely different way. Often giving students something concrete (a diagram, model or representation) can help them understand what’s going on, increase transfer (Richland et al., 2007, p. 1129), help retention and foster connections between seemingly unrelated ideas: “By using representation students can begin to recognise that the underlying mathematical concept extends into unexpected domains” (Watson et. al, 2013 p.8).

Here’s a selection of the visual representations or demonstrations I’ve come across recently. No doubt you will recognise some of them but I hope others will be new to you. Can you explain how they represent the mathematics? Can you use them in your lessons?


Even and odd


Factors of 12

Equivalent fractions



(a+b)(c+d) = ac + ad + bc + bd

Pythagoras’ theorem


(a+b)2 – 4ab = (a-b)2



Richland, L.E., Zur, O. and Holyoak, K.J., 2007. Cognitive supports for analogies in the mathematics classroom. Science – New York then Washington, 316(5828), p.1128.

Watson, A., Jones, K., Pratt, D., 2013. Key Ideas in Teaching Mathematics. Oxford University Press, Oxford, UK.

The article was originally posted here.

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