Quilt problem: My solution

I finally got my solution for yesterday’s quilt problem typed up and published as a pdf. It’s here. I used both composition and multiplication of functions. Would you do it differently?

I had to go and ask another teacher a question right before that class came in today, so they were already in the room when I got back. And they were at the board, putting up what they’d done on the problem last night, or looking over each other’s work. I hadn’t instructed them to do that; they just did. YAY! :)

I think they probably could have continued working on it all period today, but I did have other things to teach them as well. So first I let them share their thoughts, but I gave more telling feedback. “Hmm…I think I’d run out of fabric if I only got that much. Can you figure out why?” (That kid was very close; he just didn’t think about how I need to cut rectangles of a particular size, so I can’t just divide the area of all the rectangles by the width of the fabric – in other words, the necessity of the greatest integer function for this problem.) “So for a quilt that’ll only be 48 by 64 inches–” (she was giving me an example of a specific block size rather than a function for any block size) “–you want me to get thirty-four YARDS of fabric? It’ll probably cost $3.99 a yard…do I need to spend THAT much money?” (I think she was trying to make me cut one super-long strip of fabric, leaving about 37.5 inches of the 40-inch fabric width untouched.)

So I took a few of their ideas, and really, most of them were focusing on figuring it out for a particular size block. One pair of girls who tried to make it a function didn’t recognize that the width and the length of a fabric strip in a block can both be expressed in terms of the same variable, so they were working with x and y. But you know what? When I was organizing my thinking to start off, *I* was going through a specific example in my mind. So I don’t think there’s a problem with using a specific example to help orient yourself to a problem.

I think the key is that in my mind, I always knew that I’d identified x and was working to figure out what I wanted to do to it by rehearsing what I do when x=6. I’m not sure whether they did that or not; in fact, I’d be willing to bet that most of them were just planning to figure out what x should be after they’d solved the problem with their particular example, or else that they forgot they were supposed to be looking for a function and would just consider themselves done when they reached the solution for their example. So the next time I use this activity, I need to make that point more clear at the outset, and I need to emphasize it over and over while they’re working as well.

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!

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Comments

  • Elizabeth S  On October 5, 2010 at 7:00 pm

    Your PDF of the write-up comes up blank at Google docs. Would you please check and re-post? I’m dying to see how you did this.

    • Amanda Dean  On October 5, 2010 at 8:36 pm

      Thanks for letting me know! I must have put in the wrong link by mistake and not realized because it works for me. I changed it, so hopefully it will work now – just tell me if it doesn’t!

  • Elizabeth S  On October 5, 2010 at 8:41 pm

    Thank you for fixing this link so quickly. The suspense was getting to me! ;-)

    Plus I like how you laid out your solution. And I’m glad to see a real-world application of the greatest/least integer function (that is to say, real-world applicability to MY world).

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