I use the acronym, G.E.T.S., to teach that a Graph, Equation, Table and Story are equivalent ways to represent a function. Some people would call this a “cheap trick” but let me assure you that it is only a memory device that I introduce after students have developed a rich understanding of functions.
I begin this unit by showing how a relationship between two quantities can be represented with an equation or table. We start by brainstorming relationships with stories: Jennifer is two years older than Joe, or Bob gets paid three times as much as Bill. I teach the students that a relationship between two quantities is called a “function.” To show how functions produce pairs of numbers, we use a “FUNction machine.”
One student gets in the function machine. Then another student puts numbers into the machine on a post-it. The student in the machine sends the post-it out with a second number. I haven’t taught this to my 5th graders yet so I redid the lesson with the 6th graders I used to teach. You can watch part of it here:
We record the pairs on this sheet with tables and fun robots.
After taking turns writing tables from equations, it is great to work backwards with the FUNction machine and represent the inverse of the function. Students can also guess the equation from the numbers they see in the table. If they do this with an actual student inside the FUNction machine, they will really experience how it is necessary to see several pairs before guessing the rule for the table.
I give an “exit slip” at the end of each class, which is a formative assessment of the day’s lesson. I am including the “exit slip” I made for this lesson here.
Later we graph the pairs of numbers. But that is for another day.