## Variables

Wheel size:  what difference does it make?  What if both wheels are small? What if both wheels are large? What if the wheels are different sizes?  What if the difference in size is great?  What if the difference in size  is small?  Try these ideas out, then give us some feedback on the following ideas for curriculum development.

At present our Fantastic Elastic lessons do not systematically explore the effect of different variables.  For example, there could be a lesson that would lead students to explore the effect of a wind up having two small wheels, two middle size wheels, or two large wheels. They would find that some go further but are harder to get started. Others start easily but expend their energy quickly.

Another lesson could experiment with windups having two wheels of different sizes.  Although all such wind-ups go in circles, the circles are of different sizes.  And there is a relationship between the radii of the two wheels, how far apart the wheels are set, and the radius of the circle the wind-up traces. This relationship can be explored on a qualitative level, but it can also be explored by collecting data on the wheel sizes, their distance apart, and the diameter of the circle the wind-up makes. This becomes a good experience in geometry.

There are other variables to be explored more systematically, with data collected on them. Three of these are
• the number of turns we put into the wind-up and how this effects wind-up performance;
• the difference made by different thicknesses of rubber bands on the wind-up performance;
• the difference made by different lengths of rubber band (of the same thickness) on performance.

This does not exhaust the variables effecting wind-up performance.  There are differences in sticks, surface over which the wind-up is running, and the nature of the wind-up wheels, and still more things to explore.  Our questions to you are:

Should we develop activities that would structure a more systematic exploration of variables and if so, what are your favorite variables?