For the warm up today I decided to get groups of three at the whiteboards explaining and justifying the rules for multiplying and dividing integers. They all knew the rules for multiplying integers but few could explain why they worked. I asked different groups what it means to multiply two positive numbers. They explained. I then asked what it means to multiply a positive by a negative and let them sort that out. Overall, groups did quite well until they got to a negative by a negative. One group described this as being the opposite of a positive times a negative. This would have been a good time to get into the distributive property but I didn't. I was worried about losing too many students. We'll come back to that idea later. We looked at the patterns in the left column on the board below, then the one on the right. It seemed to make sense to them and the idea of looking for patterns will come in handy later.
We wrote a quick note about multiplying and dividing integers then got back to the work we started yesterday.
All groups were quick to start. Many groups were asking for details about the Pythagorean Theorem. I gave them enough to get started and let them work. Some made mistakes like forgetting to take the square root when finding the hypotenuse but realized that their answer didn't make sense. We talked about the step they missed. It didn't take long for every group to come up with an answer.
There were some great discussions, lots of reasoning and a sense of accomplishment at the end. We ran out of time for me to show the answer but most groups felt confident in their work. I'll show Act 3 tomorrow.
I gave them a page of multiplying and dividing integers as homework.
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