Yesterday's math lesson
Mar. 3rd, 2010 07:06 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
velvetpageThe grade five curriculum requires kids to develop a basic understanding of a variable for the first time: as an unknown number and as a series of values dependent on each other.
My kids already have the first definition. So yesterday we started on the second.
I put up on the board ___ + ___ = 17 and asked them to find all the ordered pairs that would fit in the blanks. I showed them how to write an ordered pair (0, 17) and then let them have at it in their groups. Meanwhile, on a piece of chart paper, I drew the upper right portion of a co-ordinate grid (because my kids haven't learned integers yet and I didn't have a lot of room, anyway.) When my kids were acting like they were done, I explained that a co-ordinate grid was a way of using math to draw things; it was just a format that everyone would use in much the same way, like a language, so that anyone who saw it would understand how it worked. I rewrote the equation on the board as x + y = 17, and asked one kid to come up and plot a point on the grid. She took (0, 17) and pointed to seventeen on each axis, saying that they were different points that were written the same way. She drew both points. I told the class that this was a problem; how could the same two numbers indicate two different points? How would that help anyone to figure anything out? I let them stew about it for a minute, and discuss how the points were different, until someone finally said, "But in the equation, x came first." I got that person up to the chart to explain what she meant, and we figured out that (0, 17) was a different point from (17, 0).
After that, we plotted each of their ordered pairs on the grid in turn, and I showed them how to label the points correctly. When we had about half the points up there, I got one of the girls who was complaining she didn't get it to come up. I handed her a metre stick and told her to play connect-the-dots.
I had expected the lesson to end there, but it didn't, because when my students notice something, I run with it. Half a dozen of my kids looked at the resulting triangle and said, "That's a right-angled triangle!" One more said, "It's a half-square triangle like in our quilt blocks!" We discussed the other two angles - both 45 degrees - and I asked the kids, "What do you think you'd have to do to get a triangle that wasn't a half-square triangle on this grid? What would the equation look like for that?"
Well, they tried x + y = 12, though my gifted kid told them right off the bat it was going to just make a smaller version of the same triangle. It did. When it seemed they were stumped, I took the metre stick and drew a line from (7,0) to (0,14). Then I asked them to figure out the relationship between seven and fourteen. They eventually got it, with a bit of help to get the form right: 2x=y, where x=7.
Every kid in the class understood the basics of the co-ordinate grid. Every kid as far as I could determine understood the ordered pairs and how they were graphed. A few kids couldn't wait to pull out the graph paper and try some equations on their own. They were tickled by the idea that I did this math in grade nine and it's currently in the curriculum in grade eight.
Today's lesson: Explain why x + y = a whole number is always going to produce a half-square triangle, no matter what the whole number is.
My kids already have the first definition. So yesterday we started on the second.
I put up on the board ___ + ___ = 17 and asked them to find all the ordered pairs that would fit in the blanks. I showed them how to write an ordered pair (0, 17) and then let them have at it in their groups. Meanwhile, on a piece of chart paper, I drew the upper right portion of a co-ordinate grid (because my kids haven't learned integers yet and I didn't have a lot of room, anyway.) When my kids were acting like they were done, I explained that a co-ordinate grid was a way of using math to draw things; it was just a format that everyone would use in much the same way, like a language, so that anyone who saw it would understand how it worked. I rewrote the equation on the board as x + y = 17, and asked one kid to come up and plot a point on the grid. She took (0, 17) and pointed to seventeen on each axis, saying that they were different points that were written the same way. She drew both points. I told the class that this was a problem; how could the same two numbers indicate two different points? How would that help anyone to figure anything out? I let them stew about it for a minute, and discuss how the points were different, until someone finally said, "But in the equation, x came first." I got that person up to the chart to explain what she meant, and we figured out that (0, 17) was a different point from (17, 0).
After that, we plotted each of their ordered pairs on the grid in turn, and I showed them how to label the points correctly. When we had about half the points up there, I got one of the girls who was complaining she didn't get it to come up. I handed her a metre stick and told her to play connect-the-dots.
I had expected the lesson to end there, but it didn't, because when my students notice something, I run with it. Half a dozen of my kids looked at the resulting triangle and said, "That's a right-angled triangle!" One more said, "It's a half-square triangle like in our quilt blocks!" We discussed the other two angles - both 45 degrees - and I asked the kids, "What do you think you'd have to do to get a triangle that wasn't a half-square triangle on this grid? What would the equation look like for that?"
Well, they tried x + y = 12, though my gifted kid told them right off the bat it was going to just make a smaller version of the same triangle. It did. When it seemed they were stumped, I took the metre stick and drew a line from (7,0) to (0,14). Then I asked them to figure out the relationship between seven and fourteen. They eventually got it, with a bit of help to get the form right: 2x=y, where x=7.
Every kid in the class understood the basics of the co-ordinate grid. Every kid as far as I could determine understood the ordered pairs and how they were graphed. A few kids couldn't wait to pull out the graph paper and try some equations on their own. They were tickled by the idea that I did this math in grade nine and it's currently in the curriculum in grade eight.
Today's lesson: Explain why x + y = a whole number is always going to produce a half-square triangle, no matter what the whole number is.
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(no subject)
Date: 2010-03-03 12:08 pm (UTC)(no subject)
Date: 2010-03-03 03:16 pm (UTC)It's interesting that you try to get the kids to be able to put every concept into words. I don't think I would be able to do that for a lot of the concepts you teach, partly due to lack of practice.
(no subject)
Date: 2010-03-03 10:20 pm (UTC)(no subject)
Date: 2010-03-04 02:02 am (UTC)(no subject)
Date: 2010-03-04 03:36 am (UTC)