## Animated Situations

These are animations of situations which invite working on expressing relationships between things that are changing.

Overflow

Bottema's Theorem

Overflow

Bottema's Theorem

## OverFlow

An empty open topped can is gradually immersed (open top upwards) in a bucket containing some water.

What might happen as the can is immersed?

What can be predicted?

Applet Folder

What might happen as the can is immersed?

What can be predicted?

Applet Folder

The animation depicts only one possibility. The graph on the right shows what happens to different quantities.

Initial work could consist of making sense of the graphs in relation to the animation.

The applet enables adjustments to be made to various quantities.

Initial work could consist of making sense of the graphs in relation to the animation.

The applet enables adjustments to be made to various quantities.

## Bottema's Theorem

What is the locus of H as the point C (and hence the attached squares) varies?
An animation of Bottema's Theorem, with an applet to enable the user to make variations. A second animation shows a generalisation. The applet also enables exploration of two generalisations of the theorem Bottema Applet and Animations |