What we had in mind
goals of this activity
Students will be able to...
We know it’s important for students to connect different representations of relationships together. Representing and interpreting relationships between variables is an important skill even for students who do not study math beyond high school.
When a student draws a graph with pencil and paper, she also has to imagine what that graph says about the world, and her imagination may be riddled with misconceptions. Function Carnival changes that. Students watch a video. They try to graph what they see. Then they play back the video and see how their graphical model would be represented as an animation. Does what they meant to graph about the world actually match the world?
Tell your students, “I need you to watch this short video. It’s quick so pay attention.” Play the video of Cannon Man. Play it again. Then ask them to tell their friends everything they saw. “No detail is too small.”
Tell them the day’s challenge is to take the things you can see and say and turn them into graphs that computers and mathematicians can understand. Show them the blank Cannon Man graph and tell them their task is to draw what happened to his height over time.
While students are working, use the teacher view to identify students to talk with. For example:
Take note of interesting graphs to discuss with the class at the end of the lesson, or for your own use after class has finished. You might choose graphs that are very accurate, graphs that have surprising errors, or graphs that show errors that are common among your students.
Some students will finish the activity quickly and need a challenge. We’ve added one bonus question at the end that students can try on a separate piece of paper. For an additional challenge, you could ask the students to try to graph speed v. time for each of the 3 scenarios.
When students finish the activity, have a class discussion to highlight the important ideas behind the activity. Call up the interesting graphs you selected earlier, one at a time, and ask questions to get students to state these ideas. For example, the graph to the left has certain broad features of Cannon Man’s motion but not the specifics.