Every year, I keep trying a different way to review exponent rules. For my Algebra 2 students, I gave them a list of exponent rules.

We wrote a word summary of what type of problem each exponent rule would help us with. My marker choice was not good for photographing... Sorry!

They were really struggling with applying these to the problems we were simplifying. They kept claiming that they just didn't know where to start.

Eventually, I broke down and gave them an order of steps to follow. This helped them a lot. Though, I wish they could solve these problems without me writing out step by step directions.

We were working on simplifying expressions like this:

I guess where I struggle with this is that it *should* be review in Algebra 2. We don't have time to derive all of the rules from scratch. But, they act like they've never seen anything like this before. My main motivation for doing this as a skill is to prepare for dealing with negative and zero exponents when we work with rational exponents and logarithms.

I also drilled into their heads that (2xy)^2 = 4x^2y^2. For the past few years, most students have said 2x^2y^2 which was driving me bonkers. We did lots and lots of practice problems with that, and I don't think I've seen anyone make that mistake at all lately. Yay!

If anyone has ideas about how to review this without reteaching it from the beginning, I'd LOVE to hear it!

Exponent Rules file is here.

I don't have a better way to review, but I tell my students to always save getting rid of negative exponents for the last step. That way we only deal with negative exponents one time, not twice like you did in your example.

ReplyDeleteInteresting! I guess I usually just "fix" negative exponents at the end without thinking about it/writing it out, so I always fix them at the beginning.

DeleteI have to review from the start every time too. I usually tell them to look for zero exponents first. My students usually have issues with negative exp. in the denominator.

ReplyDeleteGlad I'm not alone!

DeleteWe try to develop the negative exponent rule first but even seeing a pattern doesn't seem to help them remember what to do with them. I tell them to think about it as "someone placed it in the wrong place. A negative exponent on the denominator means move it to the top, while a negative exponent on the numerator means move it to the bottom." They understand it for basic Algebra 1 problems, but not for more complex problems. And they also want to do it to negative numbers not negative exponents.

ReplyDeleteMy kids want to do the same thing and move negative numbers!!! I do like how you told them it means someone placed it in the wrong spot, though! Totally stealing this.

DeleteI always talk about living in an apartment. If you are unhappy (negative) upstairs (numerator) - hate carrying groceries up the stairs, then you need to move downstairs so you can be happy (positive). If you are unhappy downstairs (denominator) - hate hearing all those kids stomping around above you, then you better move upstairs so you can be happy. It works for some.

ReplyDeleteI haven't heard this one before!

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(parenthesis, means give them each and Exponent

Exponent to an exponent, Multiply exponents

Multiply with same bases, Add exponents

Divide with same bases, subtract exponents

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