On or Off the Line?

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 to find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

A
<p>A graph in the x y plane.</p>
<p>A graph in the x y plane. Three lines that do not intersect. One line crosses the x axis to the left of the origin and the y axis below the origin. Another line crosses the y axis above the origin and the x axis to the right of the origin. The third line crosses the y axis above the origin and the x axis to the right of the origin. </p>  

B
&lt;p&gt;A graph in the x y plane. &lt;/p&gt;
<p>A graph in the x y plane. Two intersecting lines. One line crosses the x axis to the left of the origin and the y axis below the origin. Another line crosses the y axis above the origin. </p>  

C
&lt;p&gt;A graph in the x y plane.&lt;/p&gt;
<p>A graph in the x y plane. Three lines that intersect at a single point. One line crosses the y axis above the origin. Another line crosses the x axis to the right of the origin and the y axis below the origin. The third line crosses the x axis to the right of the origin.</p>  

D
&lt;p&gt;A graph in the x y plane.&lt;/p&gt;
<p>A graph in the x y plane. Three lines. There are 3 points of intersection between two lines each. One line crosses the y axis above the origin. Another line crosses the x axis to the left of the origin and the y axis above the origin. The third line crosses the x axis to the right of the origin.</p>  

 

Sample Response

Sample responses:

A, B, and C go together because:

  • They have 0 or 1 intersection points.
  • At least one of the lines has a negative vertical intercept.

A, B, and D go together because:

  • The blue line has a negative slope.

A, C, and D go together because:

  • They have 3 lines.

B, C, and D go together because:

  • there are no parallel lines.

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. Because 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, prompt students to explain the meaning of any terminology they use, such as “intersection” or “parallel,” 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
Addressing
  • 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
  • 8.EE.C·Analyze and solve linear equations and pairs of simultaneous linear equations.
Building Toward
  • 8.EE.8·Analyze and solve pairs of simultaneous linear equations.
  • 8.EE.C.8·Analyze and solve pairs of simultaneous linear equations.

15 min

15 min