This page supports the Functions Dances activity from the Introducing Functions unit. You will compete in four different Function Dance categories.
Reflect Dances: Rotate Dances: Translate Dances: Dilate Dances:
For this function, the point on the polygon is the independent variable. Your job is to move the point at the arrowhead to keep it in the right location for the dependent variable. To get it in the right location, drag the point at the arrowhead so the cross-hairs are directly over the the independent variable (the point on the polygon). 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 point on the polygon.
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.
The GSP 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.
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Update History:20 May 2016: Added Dilate Dance #3 with a negative scale. Eliminated several ways to cheat.