A great day in trig

My trig students are reviewing some algebra concepts before we jump into trigonometry, and the most recent thing was composition of functions. So today, I put this picture up on the screen:

And I asked them to find a set of functions, the composition of which would show how much fabric I need to buy of each color. I told them to work with one another, and that I would answer any questions they have about quilting or fabric.

At first, they were just sitting there at their desks, making uncertain pencil marks on their papers. I said, “Work together. Talk to someone near you. Get up and talk to someone far away from you. Use one another to figure it out.”

Within a couple of minutes, they were all sitting on the floor at the front of the room “so we can powwow.” One girl didn’t want to sit on the floor, so she started writing on the board. Most of them ended up getting up and crowding around the board (or the pull-down graph, or the other board); a few of them continued to huddle on the floor and work on paper. But they were all engaged and trying to figure this thing out.

They first asked me how many blocks there are in the quilt, and I pointed to the image and counted. They asked me how big the blocks were. I said that for the one I made in the picture, I used blocks that were 6″ squares, but that the block size was what needed to vary. I did have to point out to them that quilting uses 1/4″ seam allowances, but one student who does some sewing knew what I meant and explained once I said the phrase, catching on immediately to why that was important.

They asked if they could just write a function of how much it would cost to buy a quilt from Wal-Mart instead. I denied that request.

There was a lot of argument over whether the size of the block or the size of the strips within a block was the most important. Once they remembered that they were looking at how much fabric per color to buy, they focused in on the strips instead of the block.

Then they pretty much all got hung up on the area of the block.

“If it’s gonna be six inches finished,” they told me, “then the strips will be six-and-a-half by two-and-a-half inches –”

Wait, I said. Where’d you get two and a half?

“We added the quarter inch seam allowance four times, once for each side.”

Didn’t you already give it a seam allowance on the top and bottom? Why are you using those quarter inches again? (This part actually caused more confusion than this summary indicates.)

“Oh! Right, so they’re six-and-a-half by two inches.”

Okay, got it.

“So then, 6.5 times 2 is…thirteen, and then we need 48 of those, so we need 624 inches.”

So…you multiplied a length times a width times a count, and you ended up with a length?

“Ugh! I knew there was something about that that didn’t quite work! (to friend) Come on, let’s try again.”

At one point a group asked me how long a bolt of fabric was. Hiding my surprise that a 16-year-old boy knew that fabric comes on bolts, I clarified, “Do you want to know how long or how wide?” He changed the question to how wide, and I told him, normally 40 to 44 inches, and I usually use 40 when I’m calculating how much to get. A girl drew on the board to show a classmate how the fabric is wrapped around the bolt and where the 40 would be. A boy asked if I would want to buy any extra fabric; I said that normally, yes, I would, but for the sake of our problem they could assume that I was buying exactly what I needed. (The amount of extra I get varies, so it’s not like a constant they could add.)

They weren’t done at the end of class. I told them their homework is to continue to struggle with it – it’s okay if they don’t come up with an answer, but I want them to work on it some more. One girl said, “But my work is on the board!” So I let her use her phone to take pictures of her work, and the rest of the class asked her to send the pictures to them.

All of them were engaged. All of them were thinking and working to figure out what information was important and what wasn’t. It was awesome, and I hope I can come up with more problems like it. :)

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Comments

  • Sarah Cannon  On August 31, 2010 at 12:49 pm

    I was dubious when @k8nowak was asking about a quilt-themed math lesson on Twitter the other week. (Much as I would have loved it wasn’t sure the kids would be sold.) Sounds like you sold it to be an awesome problem.

  • Dermawand Reviews  On August 3, 2013 at 1:24 am

    Hi, after reading this amazing paragraph i am also glad to share my experience here with
    colleagues.

Trackbacks

  • […] This post was mentioned on Twitter by Museum of Math, Jason Buell. Jason Buell said: Good stuff by @praxisofreflect on trig and umm.. quilting. http://bit.ly/aR47lT […]

  • By Quilt problem: My solution « Praxis of Reflection on September 1, 2010 at 5:11 pm

    […] I just realized that I’m going to be late for our church supper tonight if I don’t get out of here, but I think that was pretty much what I wanted to say. Oh, and after letting them share, I walked them through my solution, asking them questions to get them to come up with the functions I had. I don’t know if any of them drew out the fabric with rectangles cut out of it…importance of drawing a picture to help you solve something! By Amanda, on September 1, 2010 at 5:11 pm, under Lessons. Tags:lessons, posing problems, student thinking, trig/ag. No Comments Post a comment or leave a trackback: Trackback URL. « A great day in trig […]

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