# Lesson 4

The Shape of Data Distributions

These materials, when encountered before Algebra 1, Unit 1, Lesson 4 support success in that lesson.

## 4.1: Math Talk: Number Line Distance (5 minutes)

### Warm-up

The purpose of this Math Talk is to elicit strategies and understandings students have for finding distances on a number line. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to compute mean absolute deviation (MAD).

### Launch

Display one problem at a time. Give students quiet think time for each problem and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.

### Student Facing

Mentally, find the distance between the two values on a number line.

• 70 and 62
• 70 and 70
• 70 and 79
• 70 and 97

### Activity Synthesis

Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:

• “Who can restate $$\underline{\hspace{.5in}}$$’s reasoning in a different way?”
• “Did anyone have the same strategy but would explain it differently?”
• “Did anyone solve the problem in a different way?”
• “Does anyone want to add on to $$\underline{\hspace{.5in}}$$’s strategy?”
• “Do you agree or disagree? Why?”

## 4.2: Suspicious Descriptions (20 minutes)

### Activity

Students look at different examples of distribution shapes and their descriptions and determine whether or not they are accurate descriptions of the given distribution shapes. Whether the students agree or disagree with the descriptions, they will explain why. Explaining their answers allows students to engage in MP3 by focusing on and critiquing the explanations provided. This prepares students for a later lesson when they have to determine which data displays depict the same data set. In order to be successful with that task, students will have to remember the importance of distribution shapes. This activity also prepares students to create statistical questions or scenarios based solely on a distribution shape, because they will understand what the shape means about the data set and what types of data sets make sense for a given distribution shape.

### Launch

Display for all to see one of the dot plots created as a class from a previous lesson. Ask students to come up with at least one piece of information they can see in the dot plot. Invite a few students to share. For example, they may say that each dot represents one person, or that the number of dots tells you how many people responded with a certain value. The purpose of this launch is just to quickly refamiliarize students with how dot plots represent a data set.

Allow students to work with a partner or as individuals. Each student should write their own explanation for each question.

### Student Facing

For each picture and description:

• Do you agree or disagree with the description?
• If you agree, explain how you know it is correct.
• If you disagree, explain the error and write the correct description. Explain how you know it is correct.

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### Anticipated Misconceptions

Students may think that “symmetric” is equivalent to “bell-shaped”. Ensure that students understand that distributions can be symmetric, but still not bell-shaped as in the question that is labeled accurately as "symmetric," but is also bimodal. Compare this question to the question that is symmetric and bell-shaped.

### Activity Synthesis

The goal of this activity is for students to be able to explain why a distribution shape is labeled as its respective shape. Review correct answers as a whole group, if time permits.

## 4.3: Whipping Data into Shape (15 minutes)

### Activity

In this activity, students practice using mathematical language to describe the shape of distributions. Students engage in MP6 as they attend to the precision of their language, including using the term approximately as needed.

### Launch

If desired, ask students to close their books or devices. Designate an area of the classroom for each distribution shape: symmetric, skewed, uniform, bimodal, and bell-shaped. Tell students that you will show them a diagram, and they will move to the area that corresponds to their answer.

Display each diagram one at a time, and give students a minute to move to the area of the room that they choose. After each diagram, ask a student who moved to the correct area to explain why they chose that area. If more than one answer is true for any problem, students can move to either area. Ensure that the explanations are addressed and students understand why it has two descriptions.

### Student Facing

Describe the shape of each distribution using the terms approximately, symmetric, bell-shaped, skewed left, skewed right, uniform, or bimodal. Estimate the center of each distribution.

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