Thanks for your question, Alison. In that problem, the pool is 3×3. The tiles that surround the pool are 5×5. Does that make sense?

For estimate #3, they had trouble getting the size of the pole within the tolerance using the bar. To be honest, I think this is a feature of the activity, as long as the teacher/guide knows to push through. This experience underscored the value of using numbers to specify measurements and expressions for calculating those values.

If you felt a need to address this specific issue, one alternative would be to provide an input box where the students could type in a numerical value for the radius of the pole.

Third, it was very hard to use the scrollbar to get the right diameter for the pole. This was frustrating, almost enough to put them off the activity.

Can you expand on this? What were they frustrated about? What do you think would help?

I’d note that these are urban kids with almost no experience of lawnmowing. While that context didn’t connect with their personal experience, the video introduction made sense to them why someone might use this mowing strategy and why missed patches would be a problem. They were less clear why it would matter if the loops overlapped, but that was easy to address with wasted fuel.

Second, the animations are compelling. This was really the key hook that interested them in the activity.

Third, it was very hard to use the scrollbar to get the right diameter for the pole. This was frustrating, almost enough to put them off the activity. When they got the chance to enter an expression, it was a relief. When they got to see the animation apply their expression several times, it was a delight.

I think the power of these examples is less about the applicability to a life situation, and more about allowing students to create something meaningful from mathematics. That is I want to say it is more about the ability for students to guide mathematics rather than the mathematics guiding them.

Hi Joe, thanks for the comment. I’m afraid I don’t understand how a goat on a rope is more (or less) real than a lawnmower on a pin. Maybe it would help you to know that people actually do this to mow their lawns.

Me, I don’t find “real” to be precise enough of a term to be a useful critique in these situations. My view is that “real” is a matter of what students do with a context in their minds as much as where that context exists in the physical world.