Circle Tracer Challenges

Geometry tends not to receive much love in  elementary curricula, and that’s a shame. In this post, I’ll describe some of my new ideas for using Web Sketchpad to introduce young learners to fundamental properties of circles.

On page 1 of the websketch below (and here), begin by asking students to drag point P and describe what they notice. Students will likely observe that point C does not move as they drag point P, and that the length of the segment seems to stay the same regardless of point P‘s location. Continue by asking students asking students to visualize and describe point P‘s path as they drag it.

To test students’ conjectures, ask them to press the Spin P button. Point P will leave behind a trace of its circular path.  This is a good opportunity to introduce the term radius and discuss the distance definition of a circle: the collection of all points that are the same distance from another point—the center of the circle.

On page 2 of the websketch, there is a circle already in place. The challenge is to position the segment so that when you press Spin P, the trace of point P‘s path exactly matches the circle. Pressing New Puzzle generates new  problems.

Page 3 of the websketch is similar to  page 2, but now, we see the circumference of the circle spin. When students have completed several puzzles on both pages, ask them which of the two puzzle varieties they found easier, the spinning radius or the spinning circumference, and why.

For all the puzzles above, the length of the segment matches  the radius or circumference of the circle. As an added challenge, in the websketch below (and here), the  length of the spinning segment does not match the radius or circumference of the given circle. Students must drag point P to adjust the length of the segment as well as position the segment so that point P traces the circle.

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