More Relationships

5 min

Narrative

This Warm-up prompts students to compare four graphs of points on a coordinate grid. 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 find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

A
Coordinate plane with the origin labeled "O." Nine points are graphed and the trend of the data points move linearly upward and to the right, where the first point begins at the origin.<br>  
Coordinate plane with the origin labeled "O." Nine points are graphed and the trend of the data points move linearly upward and to the right, where the first point begins at the origin.  

B
Coordinate plane with the origin labeled "O." 11 points are graphed and the trend of the data points move linearly downward and to the right, where the first point begins on the vertical axis, high above the origin.<br>  
Coordinate plane with the origin labeled "O." 11 points are graphed and the trend of the data points move linearly downward and to the right, where the first point begins on the vertical axis, high above the origin.  

C
Coordinate plane with the origin labeled "O." 11 points are graphed and the trend of the data points move in a curve that moves upward and to the right, where the first point begins on the vertical axis, slightly above the origin.
Coordinate plane with the origin labeled "O." 11 points are graphed and the trend of the data points move in a curve that moves upward and to the right, where the first point begins on the vertical axis, slightly above the origin.

D
Coordinate plane with the origin labeled "O." 11 points are graphed and the trend of the data points move horizontally and to the right, where the first point begins on the vertical axis and slightly above the origin.<br>  
Coordinate plane with the origin labeled "O." 11 points are graphed and the trend of the data points move horizontally and to the right, where the first point begins on the vertical axis and slightly above the origin.  

Sample Response

Sample responses:

  • A, B, and C go together because the vertical values change,  either increase or decrease, as the graph goes from the left to the right.
  • A, B, and D go together because the points look like they are in a straight line.
  • A, C, and D go together because they all have a point at (2,2)(2, 2).
  • B, C, and D go together because the first point on the left is above the origin (0,0)(0, 0). 

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. 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 “points,” “coordinate,” “increasing,” , 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
Building Toward
  • 6.EE.9·Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. <em>For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.</em>
  • 6.EE.C.9·Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. <span>For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation <span class="math">\(d = 65t\)</span> to represent the relationship between distance and time.</span>

15 min

15 min

10 min