Monday, September 25, 2017

Fun for All the Family

I'm always on the look out for math problems that can be used with people of any age. These puzzles are usually easy to explain but not so easy (or obvious) to solve. Here is one that I recently created and posted on our board's Math Twitter account (@DCDSBMath) that has proved popular with kids and adults alike.
To clarify: you can use any number of pieces to make a rectangle so right from the get go it has multiple entry points.
I gave this task to our principals and Math Lead teachers this week and as they worked through it, I was struck by the energy in the room. First two pieces were put together to make rectangles

then three:

and then the question was asked, "Is it possible to use all six pieces?" I put on my best enigmatic smile and said, "Perhaps!" With no immediate solution obvious, these adults had to persist at trying different arrangements.  Snippets of conversations from each table showed some common ground to the thinking going on:
"Are we allowed to flip the shapes?"
"How big must the rectangle be?"
"Either 6 by 4 or 3 by 8."
Then, around the room, shouts of delight went up and high fives abounded as different solutions were found.

When I made this puzzle, I did so knowing that this solution could yield a second solution.

As we moved from table to table airplaying the solutions, I was pleasantly surprised to see some I had not thought about. These two are a nice variation of each other:

As are these two:

But this one really toasted my crumpet:

Which of course begs the question: Can we find all the solutions? I'll leave that up to the reader to figure out.
A question arose during the session as to how to make this task more accessible to students who might have a visual-processing LD. One possible accommodation might be to colour-code the pieces and provide a template for them like this:

What I like about this problem is that not only is it great for developing spatial reasoning, it is one that can be attempted by adults and children alike: it is a problem that would be great for families to do together! And if you like problems such as this, then you will also love games such as Blokus and Kanoodle.
Or for those of you of a certain age, Tetris!

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