We've been doing division in class lately. Perhaps other school districts start teaching division before third grade, for almost all of our kids, they are learning and practicing division for the first time.
It makes me very happy when one of my kids can actually explain to me what a division problem means. Most of my kids probably could NOT explain it, but one of my girls did today, so I was pleased.
I asked why we could not do 3 divided by 15. She explained it perfectly, saying that we could not start with three things and put them into 15 equal groups because there weren't enough things to start with.
On the other side of logic, I wrote this word problem on the board today:
Erin wants to share her cookies with her 2 sisters. She has 18 cookies. How many cookies will each sister get?
I let my kids work with a partner and gave them a few minutes to come up with a picture, a number sentence, and an answer.
Every one of them told me the answer was 9 cookies. Wait, I take that back. Every one of them told me that 18 divided by 2 was the way to solve the problem. One girl said that 18 divided by 2 equaled 7.
When I told them (much to their shock) that 9 cookies was NOT the answer to the problem, and that I would give them a couple more minutes to go back and very carefully read the problem again, they all saw the trick and came up with the right answer.
I'm just not sure how to teach the skill of carefulness and scrutiny. Especially when I have a group of kids that don't really want to read the words but would rather just grab the numbers and perform a random operation on them...