Cakes, clocks, dollars, and denominators

by Elizabeth Grumbach, fourth gradeGrumbachsmartboard_700

I sometimes wonder what the occasional adult visitor thinks when they walk into one of our lower school math classes. We had two nautical flags on the whiteboard and the class had to figure out what fraction of the two flags was red. Basically, the problem was to solve 1/5 + ½ =?  If you’re a grown-up who was paying attention in math class, seeing this math sentence is probably causing flashbacks like “least common multiple” or “common denominators.” So if you were sitting today with my 4th graders, you might have been surprised to watch the first volunteer go up to the whiteboard and start talking about money.

“Well, I know that 1/5 of a dollar is 20¢. And ½ of a dollar is 50¢. When I add those together that’s 70¢. Another way to say 70¢ is 70/100. So the answer is 70/100  or 7/10.” His classmates following his thinking nod in agreement and the next volunteer gets up to share a second strategy in another section of the whiteboard. She decides that creating a ‘cake’ made up of 1/10th will work. She knows that ½ of the cake would be 5/10ths, so she colors that in on her cake. She says, “I know that two tenths make up 1/5, so I’m going to color in 2/10 on my cake.” She’s left with 7/10 of her cake colored in and tells us that she agrees with Christian, that the answer is 7/10.

If that wasn’t good enough, there are lots more hands going up asking to share yet another strategy. Zoë is called on and she decides that using the model of a 60 minute clock face will work to find the answer. “Well, I know that on a clock, ½ of the clock face is from the 12 to the 6 (she colors that section of her clock face in.)” She looks at her work and you can tell that she’s trying to figure out how to color in 1/5 on the clock. To make a long story short, after some discussion with her classmates, they decide that 1/5 of the clock face is 12 minutes. So Zoë colors in another 12 minutes. She turns to her audience and says, “So the answer to this problem is 42 minutes on the clock face, or 42/60th.”

Fifteen minutes later we have a really messy whiteboard. It’s not like any chalkboard in any of my childhood classrooms. But it’s filled with examples of great problem-solving and critical thinking. Every step of each strategy was one that a student took toward understanding what they were doing and why.

So much for least common multiples.

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