options: Interpret linear models.

Calculate expected values and use them to solve problems.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Use random sampling to draw inferences about a population.

Develop understanding of statistical variability.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Summarize and describe distributions.

Investigate chance processes and develop, use, and evaluate probability models.

Draw informal comparative inferences about two populations.

Use probability to evaluate outcomes of decisions.

Understand independence and conditional probability and use them to interpret data.

Summarize, represent, and interpret data on a single count or measurement variable.

Investigate patterns of association in bivariate data.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Understand and evaluate random processes underlying statistical experiments.
problem_activity: Warm-up
The mathematical purpose of this activity is for students to describe the relationship between variables using mathematical terminology, such as strong or weak relationship and positive or negative relationship. These terms were defined in the previous lesson. Students must reason abstractly and quantitatively (MP2) to determine the type of relationship.
Launch
Arrange students in groups of 2. Tell students there are many possible answers for the questions. After quiet work time, ask students to compare their responses to their partner’s and decide if they are both correct, even if they are different. Follow with a whole-class discussion.
To help students understand some of the context, explain that, for many modern cars, it is recommended that the oil be changed every 5,000 miles driven or every 5 months.
Student Facing
Describe the strength and sign of the relationship you expect for each pair of variables. Explain your reasoning.
Used car price and original sale price of the car.
Used car price and number of cup holders in the car.
Used car price and number of oil changes the car has had.
Used car price and number of miles the car has been driven.
Student Response
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Activity Synthesis
The purpose of this discussion is for students to discuss the strength of relationships in preparation for having students distinguish between
causal relationships
and statistical relationships.
Encourage the use of the terms strong or weak relationship and positive or negative relationship in the discussion.
The discussion should focus on the reasoning for the last 2 problems and how they are similar and different. Here are some questions for discussion.
“How is the relationship between the car price and number of oil changes similar to the relationship between the car price and number of miles driven?” (They both have a strong, negative relationship.)
“How is the relationship between the car price and number of oil changes different from the relationship between the car price and number of miles driven?” (The number of miles the car has been driven seems more directly related to the price than the number of oil changes. It probably has a stronger negative relationship than the number of oil changes.)


correct_option_index: 2