One and a Half

Today we ventured into fractionland.

I usually do random pairings, but today I paired my students up into teams and gave them some Play Dough. Then I gave them 5 minutes to mess around with it.

I then them to make five balls with their allotment. The balls were their dango, a kind of Japanese snack. And I told them to share the five dango evenly between them. I got this problem from a book recommended to me, Teaching Student Centered Mathematics: Grades K-3.

The first question from my students was whether they could tear them apart to which I said they could do whatever they wanted. One bright girl asked for the plastic knife I was holding onto for a later demonstration. Thinking that her observation was worth a reward, I gave her the knife.

I wish I had found enough knives for each group before hand, I had tried but there weren't any in the kitchen, because after each group had ripped their dango into two, their instinct was to roll the small part they had just torn off into a ball as well. Using paper would have eliminated that problem, but the students enjoyed playing with the Play Dough, and that was worth it this time. Next time though, I will prepare some paper so they have to cut it.

After the first problem, I continued by giving them a few more problems where they had to share different numbers of dango between different numbers of people.

While working out the problems, the vocabulary I want them to learn naturally became a part of the conversations so I was able to write them on the board. I have an idea in my head about how I want to do vocabulary this unit, but right now we/I am just collecting the vocabulary that arises from our conversations.

Towards the end of the lesson, I asked one student to come up and tell me how he got an answer. I drew the five circles on the board for him and he proceeded to show me how he divided one of them into fours. I thought this was good thinking, so I started talking to the class about the different names of the pieces that were drawn on the whiteboard. I was hoping to dispel a misconception they had about how when you divide something into two, you get two, rather than two halves.

While we were talking about wholes, halves, and quarters, a new misconception came up. One girl kept saying "one and a half" for "one-half". Fortunately, the other students helped me quickly corrected that mistake before it could spread.