Line Designs
5 min
Narrative
This activity encourages students to think about the language they use to describe lines. The terms elicited here will be helpful later in the lesson when students attempt to describe lines and draw lines being described to them in a later activity. When describing similarity and differences between two lines, students need to be precise in their word choice and use of language (MP6).
Launch
Give students 2 minutes of quiet work time followed by a partner then whole-class discussion.
Student Task
Sample Response
Sample responses:
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Both lines pass through the point (2,1).
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Both lines show a linear relationship.
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Line m shows a proportional relationships and line ℓ does not.
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Line m has a positive slope and line ℓ has a negative slope.
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Line m has a vertical intercept of 0 and line ℓ has a vertical intercept of 7.
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Line ℓ does not go through the origin.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to hear how different terms can be used to describe two lines. Display the graph from the task for all to see.
Invite students to share similarities and differences between the two lines. When possible, record the observations on the graph. For example, if a student notices that the two lines have different horizontal intercepts, mark and label both of those points on the graph. Emphasize language about the slope of each line, intercepts, and coordinates of specific points.
If time allows, ask students to draw additional lines. For example, ask students to draw a line with the same vertical intercept as line ℓ but a different slope, or to draw a different line that also passes through the point (2,1).
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.
20 min
10 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Line Designs
5 min
Narrative
This activity encourages students to think about the language they use to describe lines. The terms elicited here will be helpful later in the lesson when students attempt to describe lines and draw lines being described to them in a later activity. When describing similarity and differences between two lines, students need to be precise in their word choice and use of language (MP6).
Launch
Give students 2 minutes of quiet work time followed by a partner then whole-class discussion.
Student Task
Sample Response
Sample responses:
-
Both lines pass through the point (2,1).
-
Both lines show a linear relationship.
-
Line m shows a proportional relationships and line ℓ does not.
-
Line m has a positive slope and line ℓ has a negative slope.
-
Line m has a vertical intercept of 0 and line ℓ has a vertical intercept of 7.
-
Line ℓ does not go through the origin.
Activity Synthesis (Teacher Notes)
The goal of this discussion is for students to hear how different terms can be used to describe two lines. Display the graph from the task for all to see.
Invite students to share similarities and differences between the two lines. When possible, record the observations on the graph. For example, if a student notices that the two lines have different horizontal intercepts, mark and label both of those points on the graph. Emphasize language about the slope of each line, intercepts, and coordinates of specific points.
If time allows, ask students to draw additional lines. For example, ask students to draw a line with the same vertical intercept as line ℓ but a different slope, or to draw a different line that also passes through the point (2,1).
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.