Two Graphs for Each Relationship
5 min
Narrative
This Warm-up prompts students to compare four graphs. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
Launch
Arrange students in groups of 2–4. Display the graphs for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three graphs that go together and can explain why. Next, tell students to share their response with their group, and then together find as many sets of three as they can.
Student Task
Which three go together? Why do they go together?
Sample Response
Sample responses:
A, B, and C go together because:
- The axes are counting by 1s.
- They are steep. They go up faster than they go over.
A, B, and D go together because:
- They pass through the origin (0, 0).
A, C, and D go together because:
- They are straight lines or lie on a straight line.
B, C, and D go together because:
- They are solid (not dotted).
Synthesis
Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, prompt students to explain the meaning of any terminology they use, such as “straight line,” “solid line,” “steep,” “shallow,” and “origin,” and to clarify their reasoning as needed. Consider asking:
- “How do you know . . . ?”
- “What do you mean by . . . ?”
- “Can you say that in another way?”
If time allows, invite 2–3 students to briefly share what they notice all of the figures have in common (for example, they are all graphs in the first quadrant, they all go up from left to right, the axes are labeled with numbers but not with quantities). The purpose of this concluding share out is to provide more opportunities for students to use terminology to describe aspects of graphs.
Standards
- 7.RP.2.d·Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
- 7.RP.A.2.d·Explain what a point <span class="math">\((x, y)\)</span> on the graph of a proportional relationship means in terms of the situation, with special attention to the points <span class="math">\((0, 0)\)</span> and <span class="math">\((1, r)\)</span> where <span class="math">\(r\)</span> is the unit rate.