Organise a day-long masterclass for primary and secondary pupils and get them working together on the mathematics of classic shapes in co-ordinate geometry.

We invited six Year 6s from a local primary to spend a day studying conic sections with six of our Year 10 pupils through Buckinghamshire County Council’s mathematics masterclasses.

The day was split into three sessions, starting with discovering the sections. We cut four plastic foam flower-arranging cones (one each for a pair of Year 6 students and one with which to demonstrate) using my favourite kitchen knife.

Pupils painted their sections different colours and we discussed how the various shapes had appeared.

Then they painted a parabola, an ellipse and a hyperbola using foci and directrices and compared them with shapes obtained with the cones.

In the final session, we used equations to produce more parabolae on co-ordinate axes, plotting the graphs on large sheets of graph paper.

The excited Year 6 pupils went home clutching “goodies” having experienced some quite advanced mathematics but, for me, the pinnacle of the day came from one of my Year 10 pupils who said: “We have learnt so much mathematics today.”

Useful literaturePlane Geometry for Advanced Students (Part II) by C. V.

Durrell, MacMillan (1910), Elementary Analytical Conics by J. H. Shackleton Bailey, Oxford University Press (1936), or appropriate parts of AS and A-level texts for pure mathematics and further pure mathematics.

John Pryor, formerly head of faculty of mathematics at Chesham Park Community College, Chesham, Bucks