Part two went way better than I had any right to expect to.
These are low performing 8th graders. Theoretically, they’ve been over exponent rules before. I had maybe 3 kids in all my classes who could even remember the word exponent two days ago.
So when I gave them this handout, some of the ones who peeked at the bottom gladly told me that you couldn’t have 0 or negative exponents.
It took more setup than yesterday’s did. The directions were that they could work ahead if they wanted, but if they got stuck they’d have to wait for me and the rest of the class to catch up.
The review was easy. The warmup exercise had been a repeat of representative problems from yesterdays worksheet, so they were keen on what went in the boxes, and what it meant. The struggle came in expressing the relationship between the decimal point and multiplying by powers of ten for the right side of the page> They knew how to do it, but had trouble with the language barrier. I never had to feed them the answer, though, the classes managed to get it on their own.
The setup for the second part was identifying the pattern before solving the problems, and having them identify what the continuation of the pattern would be.
They managed to quickly solve the middle box, and most kids moved on to the last box with no problem. Those that got hung up were trying to solve the problems in the last box, but quickly got it once prompted to just continue the pattern they’d established above.
Here’s the cool part:
I never told them that 10^0^ =1. I asked them (in simplified language) what the multiplicative identity was. They were more than happy to tell me that 10^0^ had to be one. Didn’t find it strange at all, thought it made perfect sense (since the 0 meant that you didn’t move the decimal at all, right?).
It was the first time in teaching exponents that I never had to correct someone who thought x^0^ was 0. Not once.
Negative exponents were just as easy: They remembered from yesterday that the decimal moved left when divided by 10, so then if the decimal moved left, a negative exponent must mean division.
It was a complete fringe benefit – I thought I’d have to explain the heck out of it, but they gladly explained it to me first.
The final part of the process was a talk on science with its big and small numbers, and writing down a tiny decimal, providing the mantissa, and letting them calculate the power of 10 to go with it.
Repeat for a large number.
Then have them guess at how I picked the mantissa. This part could have gone better (they’d worked their brains pretty hard, and were due for a rest) but it eventually made sense to them as well.
Once again, it could have used some reinforcement, but after the way they picked up where they left off from yesterday (usually unheard of) I think I can wrangle up something that’ll get them to dig it properly tomorrow.