# Rekindling Beauty

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