Lesson 8
Correlations
These materials, when encountered before Algebra 1, Unit 3, Lesson 8 support success in that lesson.
8.1: Notice and Wonder: Correlations (5 minutes)
Warm-up
The purpose of this warm-up is to elicit the idea that students can use scatter plots to interpret correlations between two variables. This is useful when students use scatter plots to describe relationships and think about the strength of relationships in a later activity. While students may notice and wonder many things about these scatter plots, correlation types are the important discussion points.
Launch
Display the scatter plots for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion.
Student Facing
What do you notice? What do you wonder?
Student Response
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Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the scatter plots. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information
If possible connections between the variables graphed on the \(x\) and \(y\) axes do not come up during the conversation, ask students to discuss this idea.
8.2: Variable Relationships (15 minutes)
Activity
The purpose of this activity is for students to understand relationships between variables and use data in a scatter plot to support their understanding. Students should be thinking about how the variables might be related and how trends visible in scatter plots can suggest a relationship. For this lesson, it is not important for students to use formal language or have definitive answers about the presence of a relationship. In the associated Algebra lesson, students will develop more formal language to describe the presence of relationships and categorize them as strong or weak as well as positive or negative. Students must reason abstractly and quantiatively (MP2) when they reason about the relationship between the variables.
Launch
Allow students to work independently to complete the activity. Tell students to work on the first question before analyzing the graphs in the second question.
Student Facing
- For each pair of variables, do you expect there to be a relationship? That is, do you think a change in one variable is accompanied by a change in the other variable? How do you expect the second variable to change if the first variable is increased?
- hours of sleep and energy level
- length of hair and energy level
- number of school events each week and time spent watching videos online each week
- temperature and watermelon sales
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Some data is collected for each pair of variables listed and represented by a scatter plot. For each pair of variables, how do the scatter plots support or contradict your answers from the previous question?
Student Response
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Activity Synthesis
The purpose of this discussion is for students to understand relationships between variables, and how data are used to support claims of a relationship. Here are sample questions to promote class discussion.
- “How did you think about whether there is a relationship based only on the variables?” (I thought about different situations like when the weather is cold or hot and whether I thought people would buy watermelons more often when it was cold or hot.)
- “Did you change your mind about any of the relationships after seeing the graphs?” (Yes, after seeing the graphs, I thought some of the relationships were more clear.)
- “What do you expect a scatter plot would look like for two variables that are very closely related?” (I expect the points would line up very tightly to a best fit line.)
8.3: Card Sort: Correlations (20 minutes)
Activity
A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).
Monitor for students who go beyond using the values on the axes to create the matches. Students should be able to recognize variables that have a positive or negative trend as well as whether the relationship should be fit well by a linear model.
Launch
Arrange students in groups of 2. Distribute one set of pre-cut slips. Give students time to work with their partner, followed by a whole-class discussion.
Student Facing
Your teacher will give you a set of cards. Match each scatter plot with a pair of variables. Be prepared to explain your reasoning.
Student Response
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Activity Synthesis
Select groups to share their answers and how they found their matches. Students may have different matches, but ensure that students’ reasoning to support their matches is aligned to what they have learned and practiced. Ask students how any trends in the data seen in the scatter plots might fit what they expect for the different pairs of variables as well as how closely the variables might be related can be seen in the scatter plots.