Square the Shapes Puzzle

I’m very excited about the Square the Shapes Puzzle (this week’s puzzle table selection) because it’s got some hidden mathematics involved in solving it that aren’t obvious at first glance.

I find that my students are less likely to tackle the puzzle on the puzzle table when the math connection is blatantly obvious.

This week’s puzzle is called “Square the Shapes.” It is found in The Big, Big, Big Book of Brainteasers by The Grabarchuk Family. Sadly, the book is now out of print and the copies on Amazon at the moment are more than a bit pricey.

You can still access quite a few of the puzzles for free, though. Amazon’s Look Inside Feature lets you look at quite a few of the puzzles in The Big, Big, Big Book of Brainteasers for free. Just keep clicking “Surprise Me!” on the left pane to see a different page of puzzles. 

So, how does the square the shapes puzzle work? The puzzle board contains a grid of dots and one of each of the shapes involved in the puzzle: square, triangle, circle, and pentagon.

You are given three additional circles, pentagons, triangles, and squares to place on the grid.

Your task is to place the additional shapes on the grid so that a square is formed by each separate set of shapes. So, the four squares will form a square. The four triangles will form a different square.

The four pentagons will form a third square. And, the four circles will form a fourth square. To further complicate things, each square that is formed must be a DIFFERENT size.

This requirement for each square to be a different size has proved a challenge for my students who have tackled this puzzle so far this week.

I had to give one student a quick reminder lesson about finding the length of the hypotenuse of a 45-45-90 triangle, so this puzzle is definitely more geared towards older students.