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# Interpreting Stories and Graphs

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Interactive

Size: 1.2 MB

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Source: Teaching Math Grades 6-8: "Interpreting Stories and 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 helps students gain a better understanding of the meaning of a line graph and how line graphs can be used to represent realistic mathematical data contained in a story. Addressing three different rate problems, students complete a story using information that can be interpreted from a line graph, sketch a graph based on mathematical data contained in a story, and write a thematic story consistent with data points plotted on a line graph.

Background Essay

Each type of graph used in mathematics has characteristics that make it useful in certain situations. Line graphs excel in clearly showing trends in data. They reveal how one variable affects another as the line increases or decreases.

Before starting this activity, students should understand that the graphs they’ll be working with represent information about change that occurs over time. Time, whether it’s hours in a day, days in a week, or some other unit, is reflected along the x-axis in these scenarios. By contrast, the y-axis shows a range of variables for which data might be collected. Units might include speed, altitude, money, or temperature—essentially, any measure that might be expected to change over time.

As information is plotted on the graph and a line is drawn connecting the points, students should be able to interpret what’s happening. This is the story the data tell: a flat or horizontal line segment between points suggests no change over time; a slope running “up” from left to right records an increase in the unit of measure; and a slope running “down” from left to right shows a decrease in the unit of measure. If the unit being measured is speed over time, then positive acceleration produces a line with an upward, or positive, slope. Negative acceleration (i.e., slowing down) produces line with a downward, or negative, slope.

Once students understand what is represented on line graphs, they can start interpreting stories from them or sketch their own graphs from short narratives. These problems are the first two presented in this activity. For the final problem, students write a story to describe a situation displayed on a graph with no information provided other than a line.

Connections

Connections to the Common Core State Standards

Expressions and Equations

• Understand the connections between proportional relationships, lines, and linear equations.
• 8.EE.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance–time graph to a distance–time equation to determine which of two moving objects has greater speed.

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
This activity requires some prerequisite knowledge of graphs and graphing. Using the Model Line Graph (PDF) as an overhead or handout, review the model graph. Highlight the important elements, including the x-axis, the y-axis, and their respective labels; and the origin, data points, and certain characteristics of the line. To measure students’ understanding, ask guiding questions, such as, What is happening on the first horizontal line, and What does the slope of the line indicate?

(Note: You may wish to address a potential student misconception by mentioning that slope on a graph does not typically represent movement uphill or downhill.)

During the activity
As the students complete the activity, you may use the following questions and prompts to gauge their learning:

• What does the steepness of the slope on a graph tell you?
• What does a flat section on a graph tell you?
• "Write Your Own Story"—have students read their stories aloud and indicate on the graph what is happening from start to finish.
• "Write Your Own Story"—depending on which scenario they choose to write about, have students identify where on the graph they had the most customers at their bake sale, observed the greatest temperature increase, or saved the most money.

Standards

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