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.

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

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.

The Teacher Experience

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

Describing Relationships - Active Learning "This is one of the most engaging tasks on this topic I’ve seen. The predictions of height of water vs. time and the ability to self correct is amazing!"

Desmos Waterline Activityvideo "I saw frustration, surprise, amusement, and confusion. . . . It seems that this task really helps students have a deeper, more dynamic understanding of the mathematics involved."

Modeling and Graphing Real-World Situationsvideo “The most important thing is to have an activity or a task that everybody has access to.” Krista McAtee teaches Water Line with a computer, a projector, and old-fashioned paper-and-pencil.