Possible or Not: Thinking About Functions

I first saw this a few years ago at Shodor Interactivate. I think it is a good way to start thinking about functions. My favorite part is having students make up stories for each graph.

This is the first time I’ve put it into a Google Doc presentation. Feel free to copy and improve. (Right now it is just an introduction. When I have more time I’ll actually put in the brief notes on functions.)

See update below…

I’m not sure if you can make a copy from the embedded version but you should be able to make a copy from this.


I should probably elaborate on how I use this. I show the class a graph and ask 3 questions:

1) Is the graph possible or not?
2) If it is not possible, how could you change it to make it possible?
3) Make up a story that goes with the graph.

I give students time to discuss the questions with their partner and then I call on random students to answer each question. Since some graphs have multiple interpretations, I can ask different students the same questions.

It leads to some interesting discussions. The first graph seems to imply time travel. And I can ask how fast the person in going back in time. Is it a jump back or is it just moving back at the same rate we’re moving forward? Another graph seems to show teleportation.

At the end I show all of the graphs, I remind students which ones were possible and I ask them to come up with 3 things that all of the possible graphs have in common. This, sometimes, leads into the idea that a single x can’t have more than one y. If it doesn’t come up I remind them of the “vertical line test” and we talk about functions.

I do point out that “Is it possible?” and “Is it a function?” are NOT the same question. After all not all functions are possible. And impossible graphs still might be functions. (Is that saying the same thing?)

Anyway, my favorite part is when students make up stories to go with each graph. This year the stories seemed to mostly involve the death of a character… or food…

Thanks for the mention Dan.

About Damon

I teach everyone's favorite subject to Juniors.

Posted on October 1, 2012, in Lessons and tagged , . Bookmark the permalink. 5 Comments.

  1. I used this for part of class today. Only made it through 3 graphs (bad time management on a wacky schedule day). It was a good way to get them thinking creatively/flexibly, which they struggle with during math class. Thanks for putting it together!

  2. I’ve given questions like this is tests and exams where a graph is given and students need to make a up a story. Over the years, I’ve had some very interesting stories. Your blog post made me realise that it would be great to use this as a classroom activity and post some of the better stories on classroom walls.

  1. Pingback: dy/dan » Blog Archive » Great Classroom Action

  2. Pingback: Possible and Impossible Graphs | Algebra One Blog

  3. Pingback: Graphing Stories | Differentiated Mathematics

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