Slopes Don't Have to Be Positive
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four lines. 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 lines 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 lines 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:
Lines a, b, and c go together because:
-
they are all going up from left to right.
Lines a, b, and d go together because:
-
slope triangles for these lines are all similar.
Lines a, c, and d go together because:
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none of these lines are parallel.
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they are all the same color.
Lines b, c, and d go together because:
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they all go through the same point.
-
none of these lines are parallel.
Activity Synthesis (Teacher Notes)
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 “parallel,” “intersect,” and “slope triangle,” 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?”
Standards
- 8.EE.B·Understand the connections between proportional relationships, lines, and linear equations.
- 8.EE.B·Understand the connections between proportional relationships, lines, and linear equations.
15 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Slopes Don't Have to Be Positive
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four lines. 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 lines 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 lines 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:
Lines a, b, and c go together because:
-
they are all going up from left to right.
Lines a, b, and d go together because:
-
slope triangles for these lines are all similar.
Lines a, c, and d go together because:
-
none of these lines are parallel.
-
they are all the same color.
Lines b, c, and d go together because:
-
they all go through the same point.
-
none of these lines are parallel.
Activity Synthesis (Teacher Notes)
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 “parallel,” “intersect,” and “slope triangle,” 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?”
Standards
- 8.EE.B·Understand the connections between proportional relationships, lines, and linear equations.
- 8.EE.B·Understand the connections between proportional relationships, lines, and linear equations.