Source: Teaching Math Grades 6-8: "Interpreting Stories and Graphs"
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.
Download and ShareEach 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 to the Common Core State Standards
Expressions and Equations
Functions
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:
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