Algebra, Geometry, and STEM teacher
Ely Memorial Middle and High School
MCTM Region 8 Director
Does every picture tell a story?
Conversely, we might say that every story has a picture and in algebra that picture is usually a graph…. enter: Dan Meyer’s Graphing Stories.
Several years ago I ran across an excellent lesson on understanding graphs and rates of change in Dan Meyer’s blogsite (blog.mrmeyer.com.) I continue to use this lesson to nail home the meaning of slope at all levels of algebra and geometry. Most of my students can find slope given a graph, an equation, or two points. Understanding the meaning of slope is a different story (no pun intended).
Meyer’s created several short videos that students watched three times. Their task was to graph the movement in the video on a coordinate plane letting the x-axis represent time and the y-axis represent elevation, distance, speed, etc. Each student had a hand of pre-made coordinate planes, each one having a horizontal axis representing 15 seconds. The students watch the video and make a graph representing the motion in the story. The video is then shown a second time in slow motion allowing the students to adjust and refine their graphs. Finally, as the video is shown the third time, the image of the correct graph unfolds in the foreground of the video. Meaningful, in depth discussion follows as questions seem to explode out of interpreting these graphs. Mr. Meyer started out with graphs that were made up of relatively linear segments. Since then his videos have branched out into more advanced functions including piecewise, step, parabolic, etc.
My lesson starts after we have graphed several linear functions by plotting points. I introduce the lesson with a short clip from the movie Up. The trailer shows the house breaking free from the ground as the balloons carry it into the sky. I ask my students to pay particular attention to how the elevation changes as the time continues. The house rises out of the city; it sets sail, goes through a thunderstorm, and travels across an ocean before touching down in South America. Interpreting this short clip is a perfect way to talk about steepness of the graph as well as what a horizontal section on the graph means and why there are no vertical sections. My kids still love the Up trailer, but older students might be interested in more realistic action video clips such as the trailer from The Martian.
The first several videos are stories that are represented with graphs that seem to “look like” the story, but as we change the y-axis to represent quantities other than elevation, it becomes clear that the graph picture doesn’t always look like the story. We were able to do 8 graphs including discussion in a class period and the students left wanting more. More importantly, they left with a much deeper understanding of slope as a rate of change. One year several students returned to class the next day with a YouTube link to several graphing stories that they had created on a rather slippery day in the school court yard.
They say a picture is worth a thousand words, but sometime a graph tells more of the story.
Up trailer: https://www.youtube.com/watch?v=pkqzFUhGPJg
Graphing stories from Dan’s blog: http://graphingstories.com