This Warm-up prompts students to carefully analyze and compare four rates. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terms that students know and how students talk about rates. During the discussion, listen for the terms "unit rate," “speed,“ and “pace“ (which at this point students may use informally as a synonym for speed), and ways in which students reason about whether two rates indicate the same speed.
Arrange students in groups of 2–4. Display the four statements for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three statements that go together and can explain why. Next, tell students to share their response with their group and then together to find as many sets of three as they can.
Which three go together? Why do they go together?
Sample responses:
A, B, and C go together because:
A, B, and D go together because:
A, C, and D go together because:
B, C, and D go together because:
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 that the reasons given are correct.
During the discussion, ask students to explain the meaning of any terms that they use, such as “unit rate,” “speed,” or “pace,” and to clarify their reasoning as needed. Consider asking: