Function Carnival by Desmos

Students watch a video and graph what they see to uncover (mis)conceptions about graphs.

What we had in mind

Algebra Students
One 60-minute class period
Students who have plotted points on a coordinate plane before

goals of this activity

Students will be able to...

Sketch accurate graphs to show how a variable changes over time.
Distinguish between a graph of a relationship between variables in a scenario and a picture of the scenario.

Supported Devices

About this activity

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?

How the activity works:

1. Watch

Students watch a 10 second video.

2. Graph

They graph what they see in the video.

3. Iterate

Students play back the video and see how their graphical model would be represented as an animation. They update their graphs based on that feedback.

4. Repeat

Students watch and graph two more scenarios.

The Student Experience

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.

Keep an eye out forstudents who find it difficult to start - invite them to “Draw anything and then press play.” If students are still stuck, show them how to draw single points to keep track of important events.

The Teacher Experience

While students are working, use the teacher view to identify students to talk with. For example:

Click to see an individual student’s work on each part of the activity.

Click to see and interact with the class’s graphs.

Track student progress through the activity. Look for students who are racing through the activity. Help them attend to precision.

Look for graphs with holes, multiple values and other interesting mistakes.

Make sure students answer the questions between activities. Encourage them to return to these questions if they have been skipped.

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.

Pro Tip!If you think of a graph that you would like students to see, but which no one has made, do this: In a new browser tab, sign in as a fictional student, and draw the graph you want them to see.

Tips from Teachers

Function Carnival

by Dylan Kane,@math8_teacher

"There are so many misconceptions here, and I think that these few minutes of graphing and sharing were the most important of the whole lesson."

Desmos Function Carnival: Tech & Teacher Take-Aways

by Cathy Yenca,@mathycathy

"Any time students try a new tool, we simply have to allow for some play time. Starting with the Cannon Man graphs, talk about what their scribbles mean. Showcase one or two gross graphs for the class to see."