We did some multiplication number talks this week. I suppose it should not come as a surprise that a few students did the algorithm in their heads.
The problem was 13 times 12.
"I put the 13 above the 12. Then I multiplied 2 times the 3 and got 6. Then I multiplied the 2 times the 1 and got 2. I put it next to the 6. (Note: I put the 2 to the right of the 6, since she said 'next to the 6') . In FRONT of the 6, I mean. Next I put a 0 under the six."
"Can you help us understand why you put the 0 here?"
"I put it there because you are supposed to.....um,....., as a place holder."
"Ok, thank you."
"After that I did 1 times 3 to get 3 and put it in front of the 0, and last I multiplied 1 times 1 to get 1 and put it in front of the 3. When I was done with multiplying I added up and got 156."
First of all, I was impressed that anyone could keep all that in her head.
Second, I asked if anyone wanted to share another strategy.
Thankfully, the very next strategy perfectly mirrored what the algorithm girl was trying to do.
After the students were done sharing, we went back and noticed how the two strategies were related. I wanted them to see that the 0 isn't just something that you put there as a place holder. I wanted them to notice what they were really multiplying by. I didn't do any of the talking. Other kids pointed out how the one related to the other.
All in all, a good talk.
For the next one, I want to pick a problem that will work nicely with the halving and doubling strategy.