Unit 3, Lesson 9
What’s the Correlation?
Extra Support Materials for Algebra 1
9.1
Warm-up
Standards Alignment
Building On
Addressing
HSS-ID.B
Summarize, represent, and interpret data on two categorical and quantitative variables
Building Toward
Instructional Routines
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This Warm-up prompts students to compare three pairs of variables. Students construct viable arguments when they explain why each pair of variables has or does not have a causal relationship (MP3). It gives the teacher an opportunity to hear how students, in comparison to one another, use terminology and talk about characteristics of the variables.
Launch
Arrange students in groups of 2.
Activity
NoneFor each pair of variables, decide if one variable causes the other to change. Explain your reasoning to your partner.
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the number of pictures painted and the amount of paint left in the paint can
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the number of visits to the pool the summer before and the number of visits to the pool this summer
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the distance run and the number of water breaks during the run
Student Response
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Building on Student Thinking
Activity Synthesis
The goal of this discussion is to differentiate between variables having a relationship and variables in which a change in one variable causes the other to change. Here are some questions for discussion:
- “Which pairs of variables did you say have a causal relationship? Why did you feel they were causal?” (A and C have a causal relationship because it seems like pictures painted would affect the amount of paint, and the more someone runs the more water that person would need.)
- “Why isn’t B a causal relationship?” (The number of times I visit a pool one summer doesn’t cause me to visit more or less the next summer.)
- “Could the amount of visits to a pool one summer to the next still be related even though it's not causal?” (Yes. If I really like the pool I might visit a lot both summers.) “What is another pair of variables that you can think of that would have a causal relationship?” (A child’s age and height. Generally as people get older they also get taller, at least through childhood.)
- “What is another pair of variables that you can think of that are related but do not have a causal relationship?” (The number of people at the pool and the number of people at an amusement park. Both would increase in the summer, but they do not cause each other to change.)
9.2
Activity
Instructional Routines
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NoneActivity Narrative
The purpose of this activity is for students to begin to recognize that correlated variables can have different relationships. Students examine two pairs of variables that are similarly correlated, but with only one of the pairs having a causal relationship. As students discuss the possible causal relationship, they construct arguments and critique the reasoning of others (MP3). This activity prepares students to recognize, in the associated Algebra 1 lesson, the difference between correlation and causal relationships.
Launch
Arrange students in groups of 2.
Action and Expression: Develop Expression and Communication. Invite students to talk about their ideas with a partner before writing them down. To support students when they explain their ideas, display sentence frames such as
- “I noticed , so I .”
- “I agree/disagree because .”
9.3
Activity
Instructional Routines
MLR2: Collect and DisplayMaterials
NoneActivity Narrative
The mathematical purpose of this activity is for students to extend their thinking about relationships between variables to understand that they are not unique to causal relationships. Students identify variables that may be involved in a situation, and they then determine whether those variables are related and whether one causes the other to change. This activity prepares for the supported Algebra 1 lessons when students compare relationships and create their own situations to represent correlations and causal relationships. Students attend to precision (MP6) as they use precise language to describe the difference between correlations and causal relationships.
This activity uses the Collect and Display math language routine to advance conversing and reading as students clarify, build on, or make connections to mathematical language.
Launch
Arrange students in groups of 2. Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language that students use to describe how variables are related. Display words and phrases, such as “decreasing,” “increasing,” “causes,” “related,” and “influence.”