An introductory mathematical induction problem I learned thanks to Kelsey Houston-Edwards

Yesterday Annie Perkins asked about resources to help a student understand mathematical induction:

Looking for some resources I was reminded of this incredible video that Kelsey Houston-Edwards made in 2017 – the proof by induction example starts around 5:25:

Today I thought it would be fun to have the boys go back and work through that problem. I started by introducing the problem after we’d made some L shapes out of snap cubes. The boys were able to understand the problem and solve the 1×1 and 2×2 cases:

Now we moved to the 4×4 case. My older son started by looking at different cases – which was a good way to solve the specific 4×4 case. At first it was hard to see how to generalize this approach, though my younger son had some nice ideas about how to extend it:

The next step was a deep dive into the 4×4 case and looked carefully at the exact problem we were trying to solve. Here the boys did a great job of seeing how to extend the solution of the 2×2 case to the 4×4 case.

Finally, we looked at how to extend the 4×4 case to the 8×8 case, and then how to extend to all cases of the problem. We ended the project by discussing how / why mathematical induction works on problems like this one:

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s