Handshakes, Cards, Roses and Triangles

If everyone in the room clinked glasses at a Christmas party with everyone else, how many clinks would there be?

Give them that question, divide them into teams and you will have a very vibrant lesson!

There are upteen different ways of tackling this one, and the beauty of it will be that, with luck and a bit of eucouragement, your teams will all take a different angle on it. So there will be lots of opportunity for debate and discussion.

Some may just multiply some numbers together and think they have solved the problem, others may try acting it out, others may start drawing diagrams.

Once they have all had a crack at it and are coming up with different answers, guide them to the idea of trying a simpler case and then building a pattern.

What would happen if there was only one person at the party. What about 2? What about 3? Do these numbers fit with the answer they got earlier?

This is a great problem for the end of the December term. There are four related challenges, all on a Christmas/New Year theme, which all produce numbers and patterns linked to the triangular number sequence: 1, 3, 6, 10 etc.

Lots of numbers, pretty patterns and lots of fun.

Ages 10-13    Printable materials (pdf) - 7 pages of teacher's notes and 10 pupil copymasters.