Using Math to solve problems

Friday’s Math lesson was an exercise in application. We had a problem in our class and we used Math to figure it out. It took a while. Students struggled, and argued, and, yes, whined a little. And then, we solved our problem.

It started with testing the week we returned from Christmas break. For two days in a row, the kids all had to take a mock standardized test so that we could collect some data and plan instruction. (No, we do not explicitly teach to the test, but I can explain that in a different post.) Then this past week we had three days of testing for our ELL students which meant that the majority of my class went to work in different classrooms for half of the day and other students filled the room to take the tests. What all of this meant was that every day our desks were moved into rows, then shifted back into groups or small clusters. To the kids it felt like they had to hunt for their seats every time they walked into Room 309. It was getting annoying. I didn’t want to just push they desks into a shape and call it done. The constant flux in the room had an impact and the kids needed to feel like they had a little control over the situation.

I paced out the center of the room to measure the area in the center that we use for desks. The edges of the room are filled with bookshelves, counters, worktables, and my desk and I didn’t think we should really tackle those messes at the same time. I marked off the space on grid paper, so they could clearly see the size and shape of the area we had to deal with. When I passed out the grids while describing the project, the kids surprised me with their exclamations. “This is gonna be so cool!” “Whoa, this sounds like fun Math.” Hooray for me – I planned a lesson they actually wanted to participate in!

We had 198 square feet of space to work with, conveniently marked for us by the square foot floor tiles, and figured out that each desk needed 8 square feet of space (which included room for the student to get in and out of her chair). When one student noted that our 20 desks only needed 160 square feet, the kids all said this challenge was going to be easier than they thought. But then they started drawing, and then erasing, and then begging for another piece of grid paper. “This can’t be done!” they wailed. I reminded them that our desks have always been in the center of the room so it must be possible. After about 15 minutes I stopped and shared a few design beginnings. We talked about what we liked about each one. Kids mentioned they liked that some desks got to be by themselves in one design since not everyone likes to be in a group. Others mentioned that one design left hardly any space for kids to move around, and how annoying it would be to be at a desk in the middle and have to maneuver through an obstacle course just to get a tissue. One design got them thinking of how I would need space to move around and help when they were working on Math.

Back to the drawing board, with this conversation in mind, they started using not only their understanding of area but also their understanding of the room. By the time we shared final designs, the kids had already debated the necessary characteristics of a good classroom design. Six students thought they had met the requirements of both space and use so we posted those, sorted them into groups with similar characteristics (horseshoe shapes, clustered rows, desk “islands”) and called kids up to vote. The “primary election” narrowed it down to two finalists. We discussed the merits of each and voted again. The clear winner had a few desk islands and four small rows of connected desks with a cross of aisles in between.

“OK guys, we have just enough time left in the day to put our design into practice. Let’s start moving the desks.”

“We get to make the design?” They all seemed surprised, which surprised me. Hmmm, I guess I didn’t introduce the purpose of the lesson well enough. I brought them back to the day’s objective, which I had read and talked about at the start of class. “We can use our understanding of area and perimeter to design our classroom and decide where desks will go.” I reminded them that people use Math every day to help them solve problems, just as they had just done. We moved the desks, then packed up to go home.

So, as I write this I have no proof that their design will work (other than that it is a pretty straightforward design that has been used in countless classrooms – don’t tell them). But I do know what did work: the struggle. I’ve been talking with my Math coach a lot lately about the value of struggle. We agree that kids need lots of opportunity to work out a problem that they’ve never seen before but that they can solve using the knowledge and skills they have learned. She had given me a few problem ideas that were fun in class. Though the content of this desk design problem was my own, my Math coach was really the inspiration. I felt safe leaving the Module for the day and knew she would support me. I can’t wait to tell her how it all worked out.

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