In this activity, students examine a scatter plot showing weight and fuel efficiency of cars. Students can show their understanding of what data graphed as points means and become familiar with the context of fuel efficiency.

Invite several partners to share one question with the class and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as finding individual cars in the scatter plot or noticing a pattern in the data.

If necessary, explain a bit about fuel efficiency so that students understand this measurement. Fuel efficiency is a measure of the average distance a car will travel using a certain amount of gas. Commonly this is measured in miles per gallon. For example, a car that has a fuel efficiency of 25 miles per gallon (mpg) should be able to drive approximately 25 miles while using up a gallon of gas. Many factors can influence fuel efficiency, including the way an engine is engineered (to produce more power, an engine may use more gasoline), driving conditions (more frequent stopping and starting or driving up and down hills will use fuel less efficiently), and what accessories are being used (air conditioning requires energy from burning fuel that is not used for actually driving the car).

The analysis of scatter plots continues with data about the weight of automobiles and their fuel efficiency. Again, students connect points in the scatter plot with rows of data in a table, but now there is a third column that gives a name to each pair.

After picking out information about points in the scatter plot and table, students begin to think about how scatter plots can help them make predictions. Specifically, when looking at two particular points in the scatter plot, students are asked if the results are surprising given the overall trend of the data. In later lessons, students develop more sophisticated tools for answering questions like this (specifically, by fitting lines to the data), so a heuristic discussion is all that is expected at this point.

In the digital version of the activity, students use an applet to create the scatter plot and drag a point to answer a question. The applet allows students to enter data in a table and let the computer create the visualization. Use the digital version if available to allow students to focus on analyzing the scatter plot without worrying about construction.

In this activity, students continue to identify points on a scatter plot as representatives of a single month when two variables are measured. Students are also asked to explain the meaning of some abstract points in the context of the problem and identify when it does not make sense to extrapolate information from the graph based on the context (MP2).

Monitor for students who understand that 60 degrees Celsius is unreasonable for an average monthly temperature in most parts of the world, as well as those who identify the trend to predict negative sales, which does not make sense in this context either.