A Catriona Shearer puzzle that gave my son some troube

We did a fun series in the Spring using some Catriona Shearer puzzles to help my younger son review geometry. If you search for her name on the blog you’ll find those projects. The idea was to attempt to solve the puzzle and then to go through the twitter thread to find a neat solution to explain.

Today Shearer posted a great puzzle and I thought we’d try the old style of project today for fun. Here’s the puzzle:

The three green rectangles are congruent. What fraction of the square do they cover? pic.twitter.com/YV7pMHEKoM

— Catriona Shearer (@Cshearer41) July 23, 2020

My son was not able to solve this one, but here are his thoughts about the problem and some of the ideas that he tried:

This time we went to the twitter thread to find both interesting solutions and help on making progress. He liked two solutions – one from Vincent Pantaloni:

I knew I spotted a 3:4:5 triangle !
A mirror line to show that the central strip is congruent to the green rectangles and that therefore they have an aspect ratio of 1:3. The red triangle is there to prove that the yellow triangles are 3:4:5.
Answer : (9²-3×4)/9²=1-4/27=23/27 pic.twitter.com/HtSzJCuZQd

— Vincent Pantal🍩ni (@panlepan) July 23, 2020

And one from Misty Guthrie:

Using reasoning… drew perpendicular lines across near the middle at the points of intersection which gave me the rectangle which was one unit fraction of the middle third. I drew in the other units and figured it out from there. pic.twitter.com/c7nrrGvVnH

— Misty Guthrie (@TuckerCreekSTEM) July 23, 2020

Here’s his discussion of what he learned from those two solutions:

There are so many great ways to use Catriona Shearer’s puzzles with kids. When they can’t find a solution, the twitter threads are super helpful for seeing how to solve the problem. When they are able to solve them, the twitter threads are terrific for finding different solutions! It is always really fun going through these puzzles!