1.1: Notice and Wonder: A Rocket Path (10 minutes)
The purpose of this warm-up is to elicit the idea that graphs can be interpreted to have meaning in situations, which will be useful when students interpret similar graphs in a later activity. While students may notice and wonder many things about these graphs, connections to the real situation are the important discussion points.
Display the graph for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner, followed by a whole-class discussion.
A rocket is shot into the air and some aspects of its flight are shown in the graph.
What do you notice? What do you wonder?
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the graph. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
If specific connections to height and time do not come up during the conversation, ask students to discuss these ideas.
1.2: Matching Descriptions and Graphs (15 minutes)
In this partner activity, students take turns matching descriptions of situations to graphs of those situations. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and critique the reasoning of others (MP3).
Arrange students in groups of 2. Tell students that for each description in column A, one partner finds a matching graph in column B and explains why they think it represents the situation. The partner's job is to listen and make sure they agree. If they don't agree, the partners discuss until they come to an agreement. For the next description in column A, the students swap roles. If necessary, demonstrate this protocol before students start working.
Match the graph to the description of the situation.
Match each description in column A with a graph from column B that represents the situation. Be prepared to explain your reasoning.
- Take turns with your partner to match a description with a graph.
- For each match that you find, explain to your partner how you know it’s a match.
For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
Mai begins at home and walks away from her home at a constant rate.
Jada begins at a neighbor’s house and walks away from home at a constant rate.
Clare begins her walk at school and walks home at a constant rate.
Elena begins at home and runs away from her home at a constant rate.
Lin begins at home and walks away from home for a while, then walks back home.
Priya begins at home and runs away from home, then walks for a while.
Much discussion takes place between partners. Invite students to share how they connected the description of a real situation to a graphical representation of the situation.
The goal of the synthesis is to connect parts of the graph with the actions of the students.
- “How are Mai’s and Elena’s trips similar and different? How did you recognize which graph goes with which description?” (They both started at home and went away from home at a constant rate. Mai walked and Elena ran. I could see the difference in the graph by looking at the slope of the line.)
- “Lin went away from home, then back toward her house. How far away from home did she get? How do you know?” (She got almost 200 meters away from home since that is the top of the graph shown.)
- “When Priya begins walking, does she turn around to go home? Explain how you know.” (No, she continues to move away from home. I know because the graph continues to get higher away from the \(x\)-axis, meaning that her distance from home is still growing.)
1.3: Say What You See (20 minutes)
In this activity, students practice interpreting graphs of situations by describing the graphs in their own words. The situations are very similar to the ones from the matching activity, so students can draw on that understanding to write their descriptions.
In your own words, describe these graphs.
The purpose of the discussion is to clarify language to connect graphs to the situations they represent. Select students to share their descriptions. After each description, ask if other students have different ways to describe the situation. Encourage students to be creative in their descriptions. For example, the last graph could be described as a rocket taking off from its “home planet.”