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What is it?
The simplest ideas often make for the best resources, and that is certainly true with this little beauty. It is a starter activity where students get to practise their substitution skills, followed by a single slide that challenges them to decide which of four expressions give the biggest answer. But from this humble beginning comes untold richness! Because, of course, the expression that gives the biggest value depends very much on which values of x you substitute in. Hence, very quickly we move from simple substitution to trial and error, equation solving, graph sketching, proof, and more.

How can it be used?
This lesson could conceivably be used with any year group who are comfortable with the process of algebraic substitution. Trying out different values of x is a systematic way will certainly get the students a long way into this task. Depending on the group, it may be down to the teacher to suggest the idea of plotting the expressions on a graph to see how this helps us. The author suggests using Autograph from this, but as I demonstrate in the video, Desmos is an equally suitable, free alternative. And if you needed any more reason to try out this lovely activity, one of the expressions is an exponential one, which makes it perfectly suited to the new GCSE Maths specification. Ideal!

Thanks for sharing!
Craig Barton

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