I just love counting routines. I’ve learned a tremendous amount about counting routines from Jessica Shumway’s Number Sense Routines and the teachers featured in Elham Kazemi and Allison Hintz’s Intentional Talk. (Several of these teachers are featured in videos you can view online for free. This one is my favorite!)
Today I got to do a Count Around the Circle with a twist in a 3rd grade class launching its fraction unit. While 3rd graders have a good amount of experience with fractions, this group’s teacher was wondering about their understanding of the part/whole relationship and relationship among unit fractions. We decided to do this count to investigate these ideas!
After we gathered students in the counting circle, we told them that today we’d be counting around the circle in a different way. We’d be counting brownies today and each person would have one whole brownie. We explained that we’d be laying out the brownies (post-its!) on a big imaginary plate and we wondered how many brownies we’d have after we had each contributed one brownie to the plate. The students quickly sized up that we would have twenty brownies–one for each person in the circle. As students counted and placed their brownies in the middle of the circle, I helped them organize the brownies onto the plate in rows of five. I knew this would help them see some important relationships once we had counted by halves.
Next we got ready to count by half brownies. These students already had experience looking at different ways that two people could share one brownie equally, so they quickly suggested a way for cutting brownies into halves. Once each student had their half brownie in their hand we said, “We’re going to put these half brownies on another imaginary plate. Do you think we’ll have more or fewer brownies on the plate after we all count around the circle?” We first asked for a quick thumbs up or thumbs down to signify more or fewer brownies. The class was split! These were some of the ideas they shared after a quick turn and talk.
“It’s the same. There’s still twenty people and we still each have one piece to put in the circle.”
“More. This time we’ll have 40 because that’s double the twenty brownies.” (This one fascinated me! Playing around with doubling and halving, but still developing that fraction number sense!)
“Fewer. It will take two people to make a whole brownie.” (Some people had an idea of what number we’d land on. Others just knew fewer.)
As we counted, I again helped students place their brownies in rows of five. After the brownies were laid out we simply asked, “What do you notice? What do you wonder?”
There was a lot of clarifying talk about halving and doubling, two halves equally one whole, and twenty halves being equivalent to ten.
We moved on to our next task by saying, “Let’s save our plate of whole brownies and half brownies. I wonder what would happen if we counted by quarter/one-fourth of a brownie?” (Which we will do tomorrow! Can’t wait for the discussion of the relationship between the denominator and “size” of the pieces in unit fractions.)
Working with halves and wholes might seems overly simply for 3rd graders. But I’m reminded again that sometimes “simple” numbers offer an opportunity to explore big ideas and important relationships.
[Special thanks to 3rd grade teacher, Ellen Rogers, for planning, teaching, and reflecting on fraction counting circles with me.]