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# Location Graphs

Media Type:
Interactive

Size: 1.7 MB

or

Source: Teaching Math Grades 6-8: "Location Graphs"

This asset is adapted from an activity from Annenberg Learner's Teaching Math Grades 6-8, a professional development course for teachers.

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This interactive activity adapted from Annenberg Learner’s Teaching Math Grades 6–8 challenges students to identify two undisclosed locations by interpreting data contained on corresponding line graphs. These graphs contain plotted data that represent the number of people present at each location over the course of a day. After reviewing a sample location graph that highlights distinctive features, students view two new line graphs. Students use the features of the graph and some additional hints to determine what each location might be from a list of options.

Background Essay

Data can be collected in many ways. The simplest way is direct observation. For example, if you want to find how many cars pass by a certain point on a road in a 10-minute interval, you can simply stand there and count the cars for 10 minutes. A line graph is a useful tool for representing data or information that changes continuously over time. The points that are plotted on a line graph are connected by a line. Interpreting data on a graph can be easy, especially when you understand from the graph’s title what it is you are meant to interpret. However, in this activity, the title—an undisclosed location—is unknown. By interpreting the information that appears on the graph, students should still be able to determine the location.

As students begin the activity, they’ll examine each graph and reflect on the hints provided. Using all the information they have, they will try to infer which type of real-world location each graph could represent: a bank, train station, school, library, movie theater, or gas station. At each of these locations, you can expect different numbers of people to come and go at different times during the day and on different days of the week. These are the variables that will influence what each graph looks like. What may appear as peaks, valleys, and plateaus on a graph, then, reflect the changes in volume of people over time. An increase in volume appears as a positive slope. The faster the increase occurs, the steeper the slope. In contrast, a decrease in volume appears as a negative slope. The faster the drop-off, the steeper the negative slope. If there is no change in volume over time—this might mean the number of people remains at 0 for a given time period or holds steady at 100—the line remains flat until there is a change.

Students should be familiar with the locations selected for this activity. The hints are there to get them to think about what might be happening at a given time. Using this information, they should be able to eliminate all but one of the choices and determine the mystery location.

Connections

Connections to the Common Core State Standards

Functions

• Use functions to model relationships between quantities.
• 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.

Teaching Tips

Before the activity
You may wish to have students complete this activity in pairs or small groups. This way, they will be encouraged to ask questions of one another and defend their interpretations.

During the activity
Make sure students can justify their selections. You can use the following questions and suggestions to assess their understanding:

• What does the steepness of the slope on a line graph tell you about the rate of change? What does a change in slope tell you? Give specific examples from one of the locations featured in this activity.
• What other relevant questions could you have asked about each graph besides those answered by the hints and explanations?
• What was your argument for choosing the location you did when identifying each graph?
• How did you justify your selection?

After the activity
Ask students to create their own line graph that represents activity during a day at a commonly known location. (If time and logistics permit, you can also include data gathering as part of this activity.) Be sure they provide appropriate elements on the graph, including labels for the axes, hints, and explanations. The explanations should demonstrate their reasoning for choosing the number of people present at each hour.

Standards

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