Causal Relationships

5 min

Narrative

The mathematical purpose of this activity is for students to describe the relationship between variables using mathematical terminology, such as ”strong relationship” or “weak relationship” and “positive relationship” 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 Task

Describe the strength and sign of the relationship you expect for each pair of variables. Be prepared to explain your reasoning.

  1. Used car price and original sale price of the car.
  2. Used car price and number of cup holders in the car.
  3. Used car price and number of oil changes the car has had.
  4. Used car price and number of miles the car has been driven.

Sample Response

Sample response:

  1. Strong, positive relationship. A car that cost a lot at first is probably still worth more later than a car that was less expensive when it was first bought.
  2. Weak to no relationship. Although it is useful to have some cup holders, very little of a car’s value is based on the number present in the car.
  3. Strong, negative relationship. Since cars usually have their oil changed every few thousand miles or months, a lot of oil changes indicates the car has either been driven very far or owned for a long time, so it is probably worth less than a car with fewer oil changes.
  4. Strong, negative relationship. Since the number of miles a car has been driven usually indicates more wear on the engine and other car parts, a car with a lot of miles is not worth as much as a car that has been driven less.
Activity Synthesis (Teacher Notes)

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 relationship” or “weak relationship” and “positive relationship” or “negative relationship” in the discussion.

The discussion should focus on the reasoning for the last two 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.)
Standards
Addressing
  • HSS-ID.B.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
  • S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
  • S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
  • S-ID.6·Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Building Toward
  • HSS-ID.C.9·Distinguish between correlation and causation.
  • S-ID.9·Distinguish between correlation and causation.
  • S-ID.9·Distinguish between correlation and causation.
  • S-ID.9·Distinguish between correlation and causation.

15 min

10 min