Stephen ARNOLD
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Half a Glass Please!

At a restaurant recently, the waiter offered to fill my glass.

Since I was driving, I asked for just half a glass.

To what height should the glass be filled?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)

Drag the point marked "a" to explore this problem.

Try and find an algebraic model for the volume of drink in the glass. (Double-click anywhere on the graph screen to bring up a full working version of the GeoGebra software and enter your own algebraic functions for graphing!)

Now use the other drag points to try different glasses!

Steve Arnold, 11/12/06, Created with GeoGebra


This problem may also be modelled using CabriJr on the TI-83/84 series calculator. Click on the graphic below to download the file and try it yourself!

Try having students work in pairs: one generating data points using the CabriJr model and the partner entering these into lists to plot and then to help build their algebraic model!


And just wait until you try this with TI-nspire CAS!

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