The beginnings of division

I recently read The Doorbell Rang to my class and it introduced the concept of dividing a fixed amount by various numbers of people so that each person can have the same number of cookies. During small groups this week, the students worked with paper cookies and bananas and needed to share them with the hungry monkeys. I reminded the students that each monkey needed to have the same number of treats, that they needed to do a "fair share". All 11 of the students were able to divide an even number of cookies or bananas between the two monkeys. Some needed me to hold the cookies while they passed out on at a time, but all were able to do it. When I asked how they knew it was a "fair share", many of them counted the cookies that were distributed to each monkey and commented that each one had the same number. Some of the less verbal children lined up the cookies that each monkey had and pointed to each line, saying "they same size".

Wanting to push them further and challenge their thinking, I gave some children an odd number of cookies to divide between the same two monkeys. I wanted to know what they would do with the remainder. I had modeled sharing one thing between two people by cutting the paper in half earlier in the week and was curious to see if they would apply that strategy or what other ideas they might generate. The students divided the cookies evenly until they got to the remainder.

One student gave the cookie to one of the monkeys, thus creating unequal piles. When I asked her about, she said she was going to eat the extra.

Another student said that he needed to go to the store to buy another cookie.

One student moved the remainder cookie back and forth between the two monkeys several times and then put it in the middle.

The final student in the group suggested breaking it so each monkey could have a piece. We talked about the concept of half and how we would break the cookie so it was fair.

Then on Friday, we acted out the book with real cookies and a real bell. After shopping in the wee hours of the morning, I found the package of cookies at the store with the closest number of cookies to the number of students in my class. There was one cookie left over after everyone had one. The students noticed and asked what they were going to do with. I was just thinking I would put it back in the package and nibble it after school, but since they had noticed, I had to do something. So I asked them what I should do with it. Almost instantly, they told me "cut it to same size pieces". It take them a while to determine how many "same size" pieces I needed to cut it into, but they got it and i successfully cut the cookie into twelve approximately equal pieces to share with each of them.

Overall, they got the basic concept that when you divide something, you breaking it into equal parts. I was impressed by and proud of them. Some of them struggled with the vocabulary but they were still were able to express a fairly complex idea for their age. Go K1