I stumbled upon this wonderful activity when I was looking through the resources uploaded by one of my favourite contributors to TES, and as soon as I saw it I was blown away. It contained a piece of mathematics that I was not familiar with – the ability to estimate square roots using a ruler and a pair of compasses. I was looking for an enrichment activity to give to my lovely Year 11 class, and this fit the bill perfectly.

As the accompanying PowerPoint explains, the method of geometrical square rooting comes from Rene Descartes. The technique is very simple to learn and provides excellent practise of students’ ability to measure and construct arcs using compasses. This makes it suitable for all ages and abilities. What I particularly love about this activity, however, is that it begs the question why – why on earth would this technique give you the square root of any number? And you will be pleased to know that there is a beautiful algebraic explanation that provided perfect A/A* practise for my Year 11s, who were completely enthralled at this point.

Thank you for sharing!

Craig Barton

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