The purpose of this discussion is for students to consider the type of relationship between variables in a real situation. Select students to share their answers to the questions.

Here are some questions for discussion:

• “Are the number of cows and the number of chickens correlated? Explain how you know.” (Yes. They are correlated because there is a trend in the data that is reasonably fit by a linear model.)
• “Do you think a scatter plot for the number of farms and the number of chickens would also be correlated? Explain your reasoning.” (Both cases should be correlated. It makes sense in terms of the situation that more farms should likely mean more chickens. It also makes sense in terms of the correlation since farms are correlated with cows, and cows are correlated with chickens.)

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.

The purpose of this discussion is for students to share their reasoning about correlation and causal relationships. Although students may not use the term causal relationship at this point, highlight any differences that arise when students discuss their answers to each question.

Direct students’ attention to the reference created using Collect and Display. Ask students to share their reasoning about the relationship between a pair of variables. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Select students to share their responses. Here are sample questions to promote class discussion:

• "Why is it important to consider variables that might be related to a situation?" (Some variables may be related, but it might be a third thing that causes the changes.)
• "What are some ways that variables A and B could be related?" (A could cause B to change, B could cause A to change, or another variable, C, could cause both A and B to change.)
• "Why might it be important to think about the variables to determine the relationship rather than just looking at a scatter plot of data?" (Some pairs of variables may be more directly related or even have one variable cause the other to change, while others may be indirectly related.)
• "If two variables are correlated, will changing one of the variables change the other?" (Not necessarily. For example, from the last activity, having more cows will not make a farm get more chickens even though the variables are correlated.)