So, here’s something cool that Johnny Ball showed me that I hadn’t seen before. I love it when this happens although I fear that as the years roll on and I become a wizened old maths teacher it may happen less and less…

Anyway, here’s a picture to explain, click on it to move the points:

Multiply the moduli of the x-coordinates of the two points where the line intersects the curve and you get the y coordinate where the line intersects the y-axis. (Or another way of looking at it, multiply the x co-ordinates and you get the negative of the y-axis intersect.)

Neat.

The proof for this is very satisfying and would make a nice extension exercise for Year 12 C1 class. Here are my scribbles. Enjoy!

Here is a simple, but effective idea that I used with my M2 class. Using bits of card to create shapes and trying to balance them on a ruler to find the centre of mass

They don’t get to do much of this stuff at A level, but it was a really effective way of getting them to appreciate what a centre of mass is before developing a method of calculating it for different shapes. Full details in these files:

OnaKnifeEdge

OnaKnifeEdge

## Ideas for better maths teaching