This Warm-up prompts students to compare four representations of data. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students, in comparison to one another, use terminology and talk about characteristics of the items.

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure that the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, such as “association,“ “correlation,“ “linear model,“ “strong relationship,“ and “weak relationship,“ and to clarify their reasoning as needed. Consider asking:

• “How do you know ?”
• “What do you mean by ?”
• “Can you say that in another way?”

The mathematical purpose of this activity is for students to practice synthesizing the component skills needed to interpret data. Students are presented with a scatter plot, a table, and some concluding statements about the data. In this partner activity, students take turns sharing their initial ideas and first drafts. As students trade roles explaining their thinking and listening, they have opportunities to explain their reasoning and to critique the reasoning of others (MP3).

The purpose of this discussion is to highlight students’ reasoning about synthesizing the various components.

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their responses to Elena’s conclusions. In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help clarify and strengthen their partner’s ideas and writing.

If time allows, display these prompts for feedback:

• “ makes sense, but what do you mean when you say ?”
• “Can you describe that another way?”
• “How do you know ? What else do you know is true?”

Close the partner conversations, and give students 3–5 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer. If time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.

After Stronger and Clearer Each Time, here are sample questions to promote class discussion:

• “Why does a positive relationship make sense for the two variables in the question?” (This type of relationship makes sense for the variables because the utility bill is higher the more energy that is consumed.)
• “Could you critique Elena’s claim of a weak, positive relationship without the value?” (Yes, the scatter plot and linear model provide information about the type of relationship that the two variables have. Since the points appear to lay really close to a straight line, I can conclude that there is a strong relationship, not a weak one.)
• “How can you tell that Elena’s prediction using the linear model is incorrect?” (In order to use the linear model to predict an outcome, you have to find the coordinates for a specific point on the linear model. I see that when is 1,200 kWh, the -value is \$270, not \$260.)

The mathematical purpose of this activity is for students to practice synthesizing the component skills needed to interpret data. Students are given a data set presented in a table, and they practice creating a scatter plot, calculating the correlation coefficient with technology, and drawing conclusions about the data. 

The purpose of this discussion is for students to share their reasoning about interpreting data. Here are sample questions to promote class discussion:

• “Can you determine what type of relationship two variables have, using a table only?” (You could determine if there is a negative or positive relationship, but the strength of the relationship is harder to determine using only a table. For both the type and strength of the relationship, it is easier to use a scatter plot.)
• “What are other ways to ask about the relationship between players’ confidence and the number of points they score?” (The question can ask about a correlation between the two. The question can also be worded using “variables” instead of explicitly asking about the specific variables in the problem. Another way to ask this question is to ask whether a variable increases or decreases in relation to the other.)
• “How can you determine if players performed worse or better than what the model predicts?” (Look at the linear model and where the points lie in relation to the line. If points are above the line, I know they scored more points than predicted and that is better than the prediction. If points are below the line, I know the player scored fewer points than predicted and that is worse than the prediction.)