Even More Graphs of Functions

5 min

Narrative

The purpose of this Warm-up is for students to realize that different dependent variables can be used when making a model of a context. The choice of which variables we use affects how a graph representing the context looks. 

Students begin by comparing two graphs and determining what they think the creator of each graph chose as their dependent variable. During the partner discussion, students should listen to their partner’s argument and decide if they agree or disagree with what their partner is saying (MP3).

Launch

Arrange students in groups of 2. Give 1–2 minutes of quiet work time, then ask students to share their responses with their partner to see if they agree or disagree about which variables Diego and Lin graphed. If partners do not agree, encourage students to make sense of one another’s thinking and reach a consensus. Follow with a whole-class discussion.

Student Task

Here are five pictures of a dog taken at equal intervals of time.

<p>A series of five photos. The first two are identical, depicting the dog sitting far from the camera.  In the next three, the dog moves closer to the camera.</p>

Diego and Lin drew different graphs to represent this situation:

Diego's graph
Diego's graph, quadrant 1, starts a small bit above the origin, begins with zero slope, then increases.

Lin's graph
Lin's graph, quadrant 1, starts further above the origin, stays constant, and then decreases.

They both used time as the independent variable. What do you think each one used for the dependent variable? Explain your reasoning.

Sample Response

Sample response: Diego used the distance from the edge of the grass since it shows the value of something increasing, and Lin used the distance from the camera since it shows the value of something decreasing.

Synthesis

The goal of this discussion is for students to understand that the same situation can be represented in different ways depending on what variables are chosen.

Select students to share the different variables that they think Lin and Diego used in their graphs. If any partners disagreed at first, ask those groups to share how they decided on their final response for what variables Diego and Lin were using.

Standards
Addressing
  • 8.F.5·Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
  • 8.F.B.5·Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

10 min

20 min