Ben Orlin’s Fraction Problem

Earlier in the week I saw this tweet from Ben Orlin:

I looked like a pretty interesting problem and wanted to try it out with the boys. Today I finally got around to it. I won’t provide much of any commentary, but just leave the videos below as examples of kids working through this problem.

First up was my older son (6th grade). The problem was – as Ben predicted – difficult for him. After lots of thinking and a couple of false starts he did find a good approach to the problem:


After we finished up we checked the answer on Wolfram Alpha:


Next up was my younger son (4th grade). The problem was very difficult for him, but by the end of this video he’s found an approach he likes:


The process of finding a common denominator was challenging for him. I think this video is a good example of what a kid learning fractions can look like:


Finally, my younger son almost landed on a “common numerator” approach in the last video. That’s a nice approach to the problem, too, so I wanted to show both boys what that approach looked like:


So, a really productive morning talking about fractions. Thanks to Ben Orlin for posting this problem.