## Functional Drawing at C&!

Last week I taught at the first (year 0) of C&!, the Camp for Algorithmic Math Play. It was a lot of fun working on mathematical play and games with a group of 8 to 12 year olds, who both love math and are incredibly good at it. One of my courses was to use Desmos to help develop thinking on functions and start to get to some of the ideas of calculus (without the need for the algebra). Here are the example calculators that I set up for the course. Click on each one to go to Desmos, animate and adjust to play for yourself! Each calculator/graph also includes additional information about what is happening.

We begin with a list of curvesKeeping the idea of a list we can create circles traveling along another curve you are free to define, varying radius as you go.

The next one does not look so interesting perhaps, as it is just a frame from an animation, click to see the whole thing. It is a version of the dots from the previous image traveling along a track, but now using differentiation to make sure they stay touching. A second animation, uses the direction of the curve at each point.

### Bonus Material

Some more calculators doing interesting things, for example distorting a grid of circles:Or showing a vector fieldor showing the first family of cubic equations to have their directions analysed by calculus, from Newton’s tract of 1666: