Intent

Students identify variables that might affect the outcome of an experiment.

Mathematics

To determine whether there is a relationship between two aspects of some situation—such as the number of crimes on a city block and that block’s distance from the nearest police station—one would conduct a controlled experiment. That is, one would hold all (or almost all) other aspects of the situation constant so as to isolate the effect of one of the two aspects in question on the other. One would then change one aspect and try to observe a change in the other, and then repeat this process. The resulting data would be analyzed to see whether they support the hypothesis that a relationship exists. This activity helps students refine their understanding of this process.

Progression

Students will work on the activity individually and then share their results in a class discussion.

Approximate Time

15 minutes for activity (at home or in class)

15 minutes for discussion

Classroom Organization

Individuals, followed by whole-class discussion

Doing the Activity

This activity will require little or no introduction.

Discussing and Debriefing the Activity

Have volunteers share their ideas about the activity. Some students might think that the data support the position that having more police stations would reduce crime, as, according to the chart, the number of crimes does rise as the distance from the police station increases. Others may be skeptical about this conclusion. Use their skepticism to explore why—given the fact that the number of crimes does increase with the distance—one might not conclude that building more police stations will decrease crime.

One relevant issue is whether the differences shown in the table are great enough to justify any conclusions. This question will be important later in the unit, so look for opportunities to discuss it. If it doesn’t come up on its own, you might ask something like, What if the numbers in the table were 1.3, 1.31, and 1.32? Would you reach the same conclusion?

This discussion may blend into the discussion of Question 2. Other explanations for differences in crime rate might include lack of streetlights, presence of activities that attract crime, and a higher concentration of people.

Building on this idea, ask, How could we determine whether the increase in crime is actually caused by increased distance from the police station? Students might suggest, for example, comparing blocks that are essentially the same in other ways that might affect crime or the need to gather data over a longer period of time.

Introduce the term controlled study or controlled experiment to refer to what students are describing, and see if they can put this general idea into words. They might describe it as a study or an experiment in which everything is the same except for the variable being tested.

Key Question

How might you test whether distance from the police station is the reason for the increase in crimes per block?

Supplemental Activity

Octane Variation (reinforcement) is similar to this activity, asking students to assess the validity of potential conclusions based on a small data set and to propose improvements to the experiment.