After a few weeks of mocks and many lessons of focussed revision, it was high time in my Yr11 class for a double lesson of open-ended problem solving. Enough time silently in rows, get rowdy at the whiteboards please.

We struggled with an excellent problem from Underground Maths, designed as a transition between GCSE and A level mathematics thinking.

What went well?

So much surprising maths covered here. The difference between proving an identity and solving an equation. The equation of a circle. The meaning of a variable. The properties of a quadrilateral. How and when to shift from using a compass to using algebraic variables. (The temptation to correct methods that I hadn’t thought of had to be quashed, to explore surprising links with other topics.)

Outstanding buzz in the room – stealing from other whiteboards, keen to solve the problem, naturally on-task. See video

The shift from constructing a circle given a triangle (very tangible) to finding a triangle given a circle (quite abstract) was effective – well done Underground Maths team!

I was surprised by who made the best insights into the problems. Not the same as those smashing out the top marks in the exams…

Extensions into special types of Pythagorean triples and beyond into Fermat’s Last Theorem (Numberphile video)

Some questions

Students flagging towards the end of the afternoon – how do I keep up the pace without providing too much structure?

This process took 100 minutes. How to teach students to do a miniature version of this when in an exam, and without any collaboration?

How could we have used technology better? A useful visualisation here, which we did not make much use of