Adding up perfect squares with snap cubes

We did a really fun project based on this tweet the day before Christmas.

After posting the project (whose link is embedded in the tweets below), James Key pointed out two videos that he thought my kids would like, and he was right!

and

 

This morning my older son and I had a great time working through the ideas in the two videos. Here’s how it went:

(1) First we reviewed the three pyramids that inspired the first project and discussed a little bit about how the project related to adding up squares:

 

(2) Next we moved on to a slightly bigger example: a geometric interpretation of the sum of the first 5 squares. We show how you the shape we get by combining these three large pyramids is starting to look more like a cube:

 

(3) The final piece of this project was moving on to the algebra. We come up with a counting formula for the number of snap cubes in our three pyramids and compare it with the formula for the sum of squares that I mentioned in our previous project (well, technically 3x that formula). We don’t work through the algebra – that’s an exercise for the reader! – but we do check that the two formulas give the same answer for the first 5 squares.

 

So, a nice follow up project, and also a fun little project for the morning after Christmas. Thanks to James Key for pointing out the additional videos!

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