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# Negative powers, with numbers and exponents

I just dug this up. It’s what I handed back students after a “pre-quiz” (i.e. a quiz at the end of the unit, but before their quiz). I had forgotten that during that first year I handed back these things with class performance percentages on them.

Anyway, the way those percentages break down is interesting to me. Is it surprising that kids had so much trouble with negative exponents in numerical context, but had such less trouble with variables?

## 5 replies on “Negative powers, with numbers and exponents”

I think more options on the 3^{-2}. -6, 1/9, -1/9, -1/6… b^{-4} there’s less ways to go wrong.

Be interesting to sequence asking b^{-2} in one problem then a concrete evaluation after.

Krissays:

I’m curious if the most common incorrect answer to question #2 was 1/6? Meaning were the mistakes due to the basic understanding 3^2 or what the negative exponent implies? It appears that in #3 more students understood how to interpret a negative exponent.

I would certainly guess -9 for the most common wrong answer to #2. But maybe that’s my own mistake.

Lisa Csays:

I’m also curious about the most common incorrect answer to #2. Did many student simply ignore the negative sign?

AMooresays:

I agree with everything that’s been said so far. They probably knew to flip it but either put 1/6 or -1/9. It may also be that #3 shows a positive and a negative exponent next to each other so it may make students realize that something has to be different between the two. I imagine that the 25% who got #3 wrong probably lacked understanding of negative exponents and most likely got #2 wrong.

Would you give partial credit to a student who knew to flip it? They show understanding of the concept of negative exponents but made a computational error with 3^2. I find very little wiggle room for partial credit with the Common Core assessments, at least in NJ, which I feel is unfair to students who get the overall concept but may make errors along the way. Just my opinion.