Class Opener – Day 2 – Wild Cube Sums

Many days, I just like to have something interesting on the projector as kids walk in, hoping to see what conversation is generated. This one comes courtesy of Derek Orr.

As students walked in, many immediately became interested in the equations, and found them “neat”.  For others, it took a few minutes until the “ohhhh” moment hit them.  Some highlights from the discussion?

ME: Who do you think figured these out?

Somebody lonely with a lot of time on their hands

STUDENT: Does it matter if we switch the numbers around?

This led to a review of the commutative property, and we quickly realized that switching the numbers was futile here.

My last period of the day became focused on whether there may be other trios with this unique property. I don’t see any real rhyme or reason to the numbers here, and while the kids thought I might be playing “dumb” I really have no clue if there may be many more examples, or if this is all there is.  But then came the magic words kids of this generation hug like blue blankies:

Let’s Google It!

I was pretty skeptical that anything would come from a Google search.  What would you google anyway? How do you phrase it? But sure enough, after a few minutes one of my students found references and some more interesting examples:

Cubes

How cool is that!  More on these intersting number facts can be found in a paper called “A Curious Cubic Identity and Self-Similar Sums of Squares” .  Check it out and the associated research!

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