Kristen Fouss’s geometry problem with my younger son

Last night I saw this tweet from Kristen Fouss:

My older son is studying geometry right now and I thought the problem would be fun for him – his work from last night is here:

Our 3000th Math Video for Kids

My younger son and I also happen to be studying a bit of geometry right now in our Prealgebra book. In fact, just this morning we turned to the section on area. I thought it would be interesting to see how a kid who is seeing area for the first time would approach this problem.

Well . . . it was tough for him, but we were able to have a great conversation nonetheless. I definitely learned a lot about how kids see geometry from listening to him.

His first instinct is that the shape is a square with a side length of 4. His reasoning is below:

At the end of the last video he’s calculated that the area of the shape is 17. One difficulty, though, is that he’s assuming the shape is a square, but a proof of that fact is just a tiny bit out of reach (though he nearly walks into it, and looking back at the video now I wish I would have done a better job encouraging his ideas there.)

Eventually we end up looking at the larger square and subtracting off the areas of the four right triangles, just as my older son did last night:

So, as I said yesterday, I really like this problem. For my older son it turned out to be a nice review problem and a great chance to talk through several ideas in geoemetry. For my younger son it was also a great conversation, but rather than review it the conversation with him had lots of ideas that were brand new to him.

I love that this problem is able to lead to great math conversations with kids who are new to geometry and kids who have been studying geometry for a while. Really nice problem.

Our 3000th math video for kids

Well, I couldn’t be happier with how our 3000th video came to happen!

Tonight I saw an interesting thread on Twitter that started with this tweet from Kristen Fouss:

Seemed like a pretty interesting problem to have my son try out, and even though it was 10 minutes until bedtime I asked him to give it a shot. It turned out to be a great discussion.

A few things I like about the problem:

(1) There are multiple ways to solve it,

(2) Kids can wonder whether or not the shape is a square and also find a way to answer that question, and

(3) Drawing a larger 5×5 square around the picture could lead to a nice discussion
about the Pythagorean theorem

There’s probably many more things to talk about that I’ve overlooked, too.

In any case, we’ve spent the last 4 years playing around with neat problems – many of which we’ve found online (and on Twitter). One of the goals of sharing our projects and videos has been to show kids that math can be both fun and interesting. Another has been to show that working through math problems isn’t always a straight line from start to finish.

Hopefully the ideas my son shares in his solutions illustrate both of these ideas. How lucky to find such an awesome problem for our 3000th video 🙂