Interpreting and Creating Graphs

5 min

Narrative

This Warm-up prompts students to compare four graphs of functions relating time and temperature. 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 then time to share their thinking with their small group. In their small groups, tell each student 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

<p>A graph, origin O. Horizontal axis is labeled time. Vertical axis is labeled temperature. A horizontal line is drawn on the graph.</p>

B

<p>A graph, origin O. Horizontal axis is labeled time. Vertical axis is labeled temperature. The curve is shaped like a U and opens downward.</p>

C

<p>A graph. </p>
A graph, origin O. The horizontal axis is labeled time. The vertical axis is labeled temperature. A curve, shaped like a U, opens up. The curve has a minimum below the horizontal axis.

D

<p>A graph. </p>
A graph, origin O. Horizontal axis is labeled time. Vertical axis is labeled temperature. The curve begins on the vertical axis and trends up, then down, then up, then down forming U shapes, alternating opening up and down.

 

Sample Response

Sample responses:

A, B, and C go together because:
  • The temperature pattern shown does not repeat.
A, B, and D go together because:
  • The temperature is always positive.
  • They all have more than one minimum.
A, C, and D go together because:
  • They all have more than one maximum.
B, C, and D go together because:
  • The temperatures change.
  • The temperatures have a maximum and minimum (or they have points that are not a maximum and minimum).
  • The functions are nonlinear.
Activity Synthesis (Teacher Notes)

Invite each group to share one reason why a particular set of three goes 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, ask students to explain the meaning of any terminology they use, such as “intercepts,” “maximum,” or “linear functions.” Also, press students on unsubstantiated claims.

Standards
Addressing
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • F-IF.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
  • HSF-IF.B.4·For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. <span>Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.</span>

20 min

10 min