## Thursday, 7 December 2017

### Rate of Change Graphs

In grade 12 advanced functions (pre-calculus) we look at rates of change of functions. Our students have been working with rates of change since grade 9, but we now look at instantaneous rates of change, or slopes of tangents to a graph, along with rates of change of slopes of tangents. This can all be rather confusing to students so I decided to make a game to help my students build up their skills and vocabulary.

I started by placing all the desks in pairs, facing each other. Each pair had 2 small whiteboards and markers. I randomly assigned the pairs and had them decide who would be person A and person B.

Here was their challenge -

They jumped right in and were asking each other good questions. I paused them at one point and we talked about the fact that, as they couldn't ask about the actual graph, the person drawing should be able to come up with the shape of the graph but there could be horizontal and vertical translations.

They soon discovered that the orange piles had more challenging graphs and actually chose those ones! Once they had each gone through a number of graphs, I suggested they could make their own. And, boy, did they! Here are some samples:

Along the way there were great conversations and many misconceptions came to light.

My colleague suggested having students create velocity-time and acceleration-time graphs based on the green and orange graphs (assuming they were position-time graphs). That produced even more misconceptions.

It was great to see them engaged and challenging each other in a really positive way.

Here are the graphs that I used - the first 6 were the green graphs and the last 6 were the orange graphs.