The freshman have been working on solving systems of equations by graphing. This has been done mainly in the context of word problems. They’ve gotten pretty good at finding equations to model the situations and at solving. They seem to understand the connection between an equation, the table of values, the graph, and the situation.
I wanted to make sure they really understood the concept of a variable. I wanted to give them an opportunity to create something. I wanted to stay on track with the other teachers and I was a day ahead of schedule. So I put two equations up and told each group that they had to create a situation which could be modeled by these equations, solve the system, and present the results to the class.
2x + 5y = 41
y = x + 4
I figured it would take about 10 minutes to create the situation, solve, and make a poster.
I was wrong.
After 5 minutes most were still arguing about the type of situation to create (I want to write about donuts – no I want to write about baseball – no I want to write about apples. I really didn’t understand the whole apple thing, but apparently he felt strongly about it as he seceded from his group for the day).
Finally I suggested that they divide up the tasks: someone create the situation, someone else start solving, someone else get the supplies for the poster… one student told me they couldn’t solve without knowing the situation (uh-oh). I sent them home with the task of each bringing back a situation to their group along with a solution to the system.
The next day they had five minutes to prepare their posters (no tech – sorry folks). It was interesting to see what they finally came up with. One group said that x represented the weight of a painted turtle and that y represented the weight of land turtle. A land turtle weights 4 pounds more than a painted turtle. There are 2 painted turtles and 5 land turtles and their combined weight is 41 pounds. The student was very happy she finally got to talk to us about turtles. She really likes turtles. Someone else pointed out that not all of the same types of turtles weigh the same. Turtle Girl thought he was being overly picky. He thought she wasn’t being precise. I was just amused by the whole conversation.
One group described a situation that involved the number of dates that two people had in a month (well, it could’ve been worse). One student was surprised that every group found that x = 3 and y = 7 even though the situations were all different (another uh-oh). One group in each class had a situation that didn’t match the equations given (we had a nice discussion about those and their classmates were able to suggest changes that made it work).
I said I was confused. I didn’t understand why everyone’s graphs looked different even though they started with the same equations. Their replies: Well Mrs. B, the graphs are really the same – see one has a positive slope, one has a negative. All of the graphs show the lines crossing at (3, 7). Everyone just scaled the graphs differently.
Yep, I think they’re getting it. I’ll see what happens during assessment week (portfolios are due Tuesday, in-class multiple choice on Tuesday, take-home exam due Wednesday, and in-class free-response on Wednesday. How do you English teachers do this? I’m dreading the stacks of paper already).