Description/Aim

The aim of this activity is to introduce students to the idea of connected rates of change in a practical manner. Increasing blots of ink, shrinking balloons,... Aren't these activities crying out for an experiment?

This activity gets students to consider how the height of water in a cone changes using a video of the experiment. If you have access to taps in your classroom you can even get the students to carry out the experiment for themselves.

Why we like this activity ….

This is a fantastic activity for getting to grips with this topic. The practical element generates discussion and helps students get the ideas clear in their minds.

How this activity be used ….

I introduce the ideas of connected rates of change by posing the problem of a ladder slipping away from a wall, "The foot of a ladder is slipping away from a wall at a constant rate. Does the top of the ladder slip down the wall at a constant rate?" This can be visualised with this. Then it is time to get those party balloons out! "Air is escaping at a constant rate from the balloon. Discuss how the radius changes with respect to time."

Then to the main activity. If students have access to computers they can view the videos for themselves otherwise show them on a screen at the front of the class.

What to expect when using this activity – from our experience

Lots of discussion. "What would happen if the cone were infinitely tall?"

Extra Notes