James Tanton’s penny and dime exercise

I saw a neat tweet from James Tanton yesterday:

"Notice & wonder" in K-8 world helps Ss develop the life skill of developing & refining natural next qus. In HS world let's not quelch NNQs! A curiosity like attached leads to: Change nmbr of pennies? Asymmetrical leapfrogging? 3D? Right-angled leaps? etc. And teaches curriculum. pic.twitter.com/1mpghA5KZc

— James Tanton (@jamestanton) December 30, 2017

After seeing the tweet, I couldn’t wait to do the project today. It turned out to be much more difficult than I was expecting, though. One of the difficulties that really caught me off guard was the time it took to make accurate measurements of the positions. The difficulty there turned what I mistakenly thought was going to be a really quick part of the project into maybe 90% of the project’s time.

Maybe a nice surprise with this project is that it could be a good introductory project for introducing kids to measurement.

So, although I’ll publish all 6 videos from today’s project, the main ideas are in the first and last videos.

Here’s the introduction to the project:

The boys weren’t totally sure what happened the first time around, so we tried again:

After two tries, they still weren’t sure what was going on, so we tried one more time:

After this third try, they had some interesting observations:

One idea they had in the last video was to see what would happen if the 3 points were on a line.

To wrap up, the boys wondered about a few other set ups. I was happy to hear that they were starting to think about new ideas.

I think Tanton’s problem is an absolutely great exercise for kids. I’m sorry that I misjudged the difficulty coming from the measurements, though.