This activity gauges students’ ability to make meaningful inferences from graphs.
Students examine another situation in which the data are approximately linear. They make estimates and predictions based on graphs of the data and linear models informally fit to these graphs. Students will also consider the meaning of the starting point as well as the downward trend in the data with regard to the situation and the graph.
Students will work on this activity individually, with an opportunity to check understanding with group members, and then compare and discuss methods as a class.
5 minutes for introduction
20 minutes for activity (at home or in class)
20 minutes for discussion
Individuals, then groups, followed by whole-class discussion
The activity is similar to Sublette’s Cutoff and requires little introduction.
Students may not think about using the fact that all three families started 330 miles from the Green River. Use your judgment about whether to suggest that they include (0, 330) as one of their data points or to leave this idea for the follow-up discussion.
After students have had time to work individually, allow them to interact in their groups to first compare graphs and then to discuss answers and solution methods. You might select some groups to prepare transparencies for the discussion.
The discussion will likely follow similar lines as that for Sublette’s Cutoff. Use any opportunities that arise to emphasize important vocabulary and conventions. In particular, encourage the use of the term x-intercept when students discuss methods for Question 2 and constant rate when discussing Question 5.
At some point bring out, if no one else does, that all three groups started 330 miles from the Green River and that students can use this information to provide an additional data point. Ask, Where on the graph represents the starting point for each family? They can use this point as part of their work in making predictions and estimations.
Also ask students to consider the downward trend in the data for each family. How is the downward trend of the data evident in the graph?
Where on the graph represents the starting point for each family?
How is the downward trend of the data evident in the graph?