Equations of All Kinds of Lines
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four images. 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 images for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three pairs of 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:
A, B, and C go together because:
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they all have one line that goes through the point (0,10).
-
they all have one line with a vertical intercept of 10.
A, B, and D go together because:
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they all have lines that are slanted upward or downward.
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they all have lines with a non-zero slope.
A, C, and D go together because:
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they all have a pair of parallel lines.
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they all have lines with non-negative y-intercepts.
B, C, and D go together because:
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they all have lines with a non-negative slope.
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,” “origin,” “coordinate,” “ordered pair,” “quadrant,” or “slope,” 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
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Equations of All Kinds of Lines
5 min
Teacher Prep
Setup
Narrative
This Warm-up prompts students to compare four images. 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 images for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed three pairs of 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:
A, B, and C go together because:
-
they all have one line that goes through the point (0,10).
-
they all have one line with a vertical intercept of 10.
A, B, and D go together because:
-
they all have lines that are slanted upward or downward.
-
they all have lines with a non-zero slope.
A, C, and D go together because:
-
they all have a pair of parallel lines.
-
they all have lines with non-negative y-intercepts.
B, C, and D go together because:
-
they all have lines with a non-negative slope.
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,” “origin,” “coordinate,” “ordered pair,” “quadrant,” or “slope,” 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
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.