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Students watch glasses filling with water 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 thought about relationships between stories and graphs 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

Students first draw the height of the water in a glass against time.play back their graph just like in  Function Carnival.

But then students create their own glasses. Once they successfully draw the graph of their own glass, it goes in the class cupboard. Now each student’s glass is right alongside glasses invented by their friends. These new glasses are graphable, too.

How the activity works:
1. Graph
Students watch a glass fill with water and graph the height of the water v. time. They play back the video to see how well they did.
2. Create
After graphing the third glass, students create their own glasses to graph.
3. Challenge
Once students successfully graph their own glasses, they add the glasses to the class cupboard to challenge their classmates!
The Student Experience
Students will press play on the faucet to watch the animation and then draw a graph of the water’s height v. time.

Help students focus their attention on the height of the water as time passes. You might do this by pouring from a pitcher of water into a wacky glass from the local thrift shop.

Challenge students to sketch graphs of the glasses that pop up on their screens, and to work at being accurate.

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 help them keep track of important events.
Students create their own glasses!
Students see the glasses they create in a cupboard alongside glasses invented by their friends. They can click on these new glasses and graph them.
The Teacher Experience

Use the teacher view to identify students to talk with. For example:

Click a student to expand her graphs and answers.
Click a tab at the top to view all of the answers for a prompt.
Look for struggling students. Help them focus on the relationship between the animation and the graph.
Students may attempt to sketch the outline of a glass as their graph. While the outline of the glass is an important consideration, the graph does not take the shape of the glass.
Look for students who are racing through the activity. Help them attend to precision.
Make sure students answer the questions between activities. Encourage them to return to these questions if they have been skipped.
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 your graph.

Some students will finish the activity quickly and need a challenge. This is where the class cupboard comes in. You could stock the cupboard with one or more challenging glasses by logging in as a student (either in advance or while students are working).

Take note of interesting graphs and glasses from the class cupboard that you’d like to discuss with the class at the end of the lesson, or for your own use after class has finished. You may choose graphs that are very accurate, graphs that have surprising errors, or graphs that show errors common among your students.

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.

Tips from Teachers