I actually enjoy the puzzle-like aspect of exponent rules, and simplifying radicals. For me, there is something satisfying about learning ways to manipulate numbers and letters – probably why I love algebra so much. But I am tuned-in enough to my students to know that many of them don’t find the same satisfaction from doing this work just for the sake of intellectual exercise. And since calculators came into vogue, it’s been harder to justify the need for rationalizing the denominator or expressing the square root of 50 as 5 times the square root of 2. But we are tasked to follow standards that often include these kinds of skills and it has been helpful for me to turn this into exploration or game learning as much as possible.
I did some mining of the MTBoS for ideas to teach rules of exponent arithmetic and came across this post, which includes a nice exploratory worksheet from Andrew Stadel. He describes a similar issue with contextualizing exponent rules for middle schoolers – one of the really great things about our online community are these moments where we are reminded that we are not alone. He asks his students to find the mistakes in the equations, to explain where the author went wrong, and to find the correct solutions. He used a bunch of the common misconceptions found on mathmistakes.org to help students to catch themselves in the common errors. Very nicely done. This would have been a good lesson as is.
Then I remembered the Bucket O Lies protocol from Nora Oswald at Simplify With Me. Nora manages to gamify math like no one else that I’ve seen. She manages to add entertainment even to potentially dry topics like this one. I combined Andrew’s worksheet with Nora’s idea to make a bucket-o-exponent lies. I printed the 3 worksheets, cut them out into individual problems, folded them up, and put them into buckets (or baskets). Voila! Drama and Motivation. In pairs or threes, learning happened.
Of course, I hammed it up with the students. There’s nothing like telling teenagers that someone is trying to get one over on them to motivate them. This has worked well for me in the past, especially when it came from advertisements. I riled them up by acting outraged that someone had created this whole set of math material, which was full of mistakes! (Actually, I blamed Andrew :) ) …Lies I tell you… these baskets are FULL OF LIES! Let’s find the mistakes so we can write a self-righteous set of corrections back to this author who was deliberately spreading bad math.
They quickly saw through my act, but it was enough. They were already motivated in spite of themselves. Andrew’s worksheet was just enough for everyone. I started by coaching the groups who needed help getting started and moved to pairs who were making mistakes with fractional exponents. For my honors group, I added a few more examples with rational exponents.
Thanks Andrew! Thanks Nora! Our generous community is the Best!