For this function, the red point is the independent variable. Your job is to move the blue point to keep it in the right location for the dependent variable. (To get it in the right location, drag the blue point so the cross-hairs are directly over the red point. When you have it right, the polygon turns green.)

Once you have the blue point in the right starting place, press Ready...Set...Go and prepare to dance. After a short countdown, the independent variable will begin moving along its restricted domain. Your job is to dance along with the independent variable, always keeping the cross-hairs over the red point.

When the independent variable stops dancing, press Check Result to see how you did. If you're not satisfied with your dance, try it again; you will get better with practice. When you are satisfied, increase the level of difficulty, or try a different dance.

To improve your dancing, be aware of the relative rate of change of the two variables: what are their relative speeds and directions? To dance well, your behavior as a dancer must be the same as the mathematical behavior of the function.

Translation Dances:             Reflection Dances:             Rotation Dances:             Dilation Dances:

The full version of this activity — including student worksheet, notes for the teacher, and two sketches (one for Sketchpad and one for Sketchpad Explorer) — is available here on the Dynamic Number site.