Jack and Jill

Here is a short Geogebra example I put together as an example of how GeoGebra could be used to introduce young students to mathematics that they might never see unless they got into a precalculus class that included polar graphs.

Among the concepts used (but not named) are midpoint, rotation, rotational speed, and 3-leafed rose.
The only geometric term used is "circle".

Even so, the situation can be used as a springboard lots of questions.
 

Among those questions could be:

• What if they walked the same speed?
• What if Jill walked faster?
• What if they walked in the same direction around the circle?

Denying younger students the opportunity to ask these questions and explore their solutions is to do a disservice to those students.