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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 di erent. Here are some question 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 di erent 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.)
9.2 Cause or E ect?
15 minutes
The mathematical purpose of this activity is for students to describe how two variables are related, and to determine whether or not there is a causal relationship.
Instructional Routines
• Think pair share
What: Students have quiet time to think about a problem and work on it individually, and then time to share their response or their progress with a partner. Once these partner conversations have taken place, some students are selected to share their thoughts with the class.
Why: This is a teaching routine useful in many contexts whose purpose is to give all students enough time to think about a prompt and form a response before they are expected to try to verbalize their thinking. First they have an opportunity to share their thinking in a low-stakes way with one partner, so that when they share with the class they can feel calm and con dent, as well as say something meaningful that might advance everyone’s understanding. Additionally, the teacher has an opportunity to eavesdrop on the partner conversations so that she can purposefully select students to share with the class.
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 di erent. Follow with whole-class discussion.
Unit 3 Lesson 9: Causal Relationships 141