# A picture speaks a thousand words

- Cambridge Mathematics
- Mathematical salad
- A picture speaks a thousand words

### 27 October 2017

#### A picture speaks a thousand words

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?

**KS1 **

Even and odd

**KS2 **

Factors of 12

Equivalent fractions

http://www.bbc.co.uk/skillswise/factsheet/ma17frac-l1-f-fraction-wall

**KS3**

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

Pythagoras’ theorem

**KS4**

(a+b)^{2} – 4ab = (a-b)^{2}

**KS5 **

References

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.

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