Archive for February, 2011
The essential, enduring understanding of algebra in middle school is that a graph, table and equation are different ways to describe the same function. That is why I have dedicated 3 posts to it, and that is why I’m going to explain the graph part of it here.
But first, let me entice you by saying that when you teach this lesson, you get to wear a costume:
This costume obviously took me about 2 minutes to put together. That’s so I could spend the rest of time making photocopies.
Before you get to graphing, students must already understand what a function is and how it can be represented using an equation and story (I discuss this in a previous post). They should also know how to graph coordinates. Then it is quite easy to take the points generated by the “FUNction machine” and graph those.
Students do not seem to struggle going from number pairs to a graph. They seem to struggle going from a graph to number pairs. This is where the acronym, G.E.T.S., is important.
I want to be able to say: “You see a graph of a function, what do you need to do?”
Students should say: “Find the equation by making a table.”
Of course, it’s really important for students to look at graphs on a bigger level before they do this or they won’t really understand why we bother with graphs at all. Here’s the plan I use:
Day 1: Students write functions as equations and tables. (Again, I wrote about this in a previous post.)
Day 2: Students make observations of graphs without numbers to see how graphs describe global behavior in a way that points on a table do not. This is a great way to informally introduce the idea of slope and y-intercept.
Day 3: Students use points to make a graph. They use a graph to find points. They say “G.E.T.S” over and over so many times it becomes drilled into their brains.
From here students can begin to use G.E.T.S in problem solving. I have created twelve pages of practice because we did one worksheet a week for the rest of the year after this unit. When students really understand functions, they can do this sweet enrichment activity that brings it all together through geometry. That is when your heart will really get racing.