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Friday, January 27, 2012

Crew News January 27, 2012

Math Exchanges

Every Friday during our Math time, we do something called Math Exchanges. Math Exchanges are meetings of small groups of students who work together and/or alone to solve a math problem. Ms. Dee and I each work with small groups and the rest of the students do other math activities like working on the computer, playing Everyday Math games and other math activities. We rotate through several sessions of small groups each Friday.

The best part for all of us is the discussions that we have when meeting in the small groups. The kids just jumped right in and were willing to tackle tough problems together right from the start. One of our most recent problems was:

Jill has 10 cookies to share with her friends Mary Beth and Dee. How many cookies will each friend get?

As the first group and I read the problem together, one student immediately started shaking his head saying this won't work. The other students ignored him at first and counted out 10 blocks to begin dividing up the cookies. It didn't take long before the conversation started. They couldn't figure out what to do with the "leftover" cookie. Each group that I met with had the same issue and then had such wonderful discussions to figure out what to do.

Some groups simply refused to cut the cookie into pieces. They just left that cookie out even when I questioned them and tried to get them to look for other solutions. One student said that cookies just crumble when you cut them so you should just leave that cookie out.

Another student used the fact that the names I used in the story were teachers from our school. She decided that I should just give the extra cookie to my daughter, Abby.
One student (the student who was shaking his head when we read the problem) counted out the blocks and saw the leftover cookie and immediately cut it into 3 pieces.

One group quickly decided that the leftover cookie had to be cut into 3 pieces but had lots of discussion about how to cut it in a "fair" way. They drew lots of variations that they decided weren't fair (or "fare" as they spelled it). Finally someone in the group thought of cutting the cookie like a "peace sign" and they were all satisfied that this would be fair.

The discussion in our small group times are very lively and the students learn so much. I, too, learn so much about them as mathematicians. Another great thing is that this type of thinking and sharing is spilling into the rest of our math time during other days of the week. Below are some examples of kids' thinking about a problem that was trying to determine which number is bigger, 23 or 15 and then they had to determine how much bigger. This student made each number in tally marks to compare them
and this student counted up from 15:
The exciting thing is that the students are much more willing to write and draw out their thinking as well as share their ideas with each other than they were before we started Math Exchanges. Ask your child what he/she thinks about Math Exchanges.

No homework for the weekend. Read a few good books with your child.

Our IA next week is Music.

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