Some of the Iowa State “problems of the week” are great to share with kids

Saw a tweet about a really nice collection of problems yesterday:

Looking for good math problems? The mathematics dept at Iowa State University has been asking its students weekly math problems for years. Here they are with solutions. https://t.co/KnsEquEtTJ

— math prof (@mathematicsprof) April 2, 2018

As I clicked through a few of the problems last night, I thought that several (though definitely not all!) would be nice ones to share with kids. When my older son got home from school today I asked him about the problem from January 8th, 2018:

Here’s what he had to say – it is a really nice solution:

Next we moved on to the 2nd problem from January 2018:

He walked away before we could start solving this one . . . . 🙂

Update:

When my younger son got home from school I asked him the same question. His work shows what a kid thinking through a math problem can look like:

One that didn’t go so well – talking about knight’s tour problems with the boys

Saw a neat tweet from Joel David Hamkins at the end of last week:

A knight's tour of the infinite chess board! https://t.co/m9GDkg0KiQ

— Joel David Hamkins (@JDHamkins) March 30, 2018

I thought it would be fun to talk through the knight’s tour problems with the boys today and end by showing them the infinite problem. I ran into trouble almost immediately when we began to talk about the tours on the 3×3 and 4×4 boards. The difficulty they had explaining was a big surprise to me. We ended up talking about the 4×4 problem for almost 30 min.

Tonight I sat down with each of them and asked them to talk me through the problem and explain why the knight’s tour on the 4×4 board was impossible. You can see that my older son (in 8th grade) was able to explain the problem pretty well, but my younger son (in 6th grade) still really struggled.

Here’s what my older son had to say:

Here’s what my younger son had to say:

Definitely a much harder problem for kids than I thought. Hopefully will have some time during the week to explore this and maybe a few other tour problems with them.