##
* *Reflection: Discourse and Questioning
Box Plots and Interquartile Range - Section 6: Closure and Ticket to Go

During the closure, I also asked, “How many weeks are included in Sarah’s data set?” I called on students to share their observations. I wanted to make sure that students understood that just by looking at a box plot they cannot tell the number of values in the data set. This can be confusing to students when they are just learning about box plots, since you can determine the values in a data set from most other types of graphs.

*How many weeks are included in Sarah's data set?*

*Discourse and Questioning: How many weeks are included in Sarah's data set?*

# Box Plots and Interquartile Range

Lesson 15 of 22

## Objective: SWBAT: • Identify and label the minimum, maximum, lower quartile, upper quartile, and median of a data set and box plot. • Define and identify interquartile range. • Analyze and compare box plots.

#### Do Now

*7 min*

See my **Do Now** in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day. Today I want students to analyze a line graph in order to answer questions. Each edition of Scholastic DynaMath typically includes a graphs in each edition.

I ask for students to share their thinking. Students are engaging in **MP3: Construct viable arguments and critique the reasoning of others**.

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#### Problem

*5 min*

I introduce the problem to students. I want students to apply what they already know about box plots from the previous lesson. Students participate in a **Think Write Pair Share. ** I walk around and monitor student progress as they work.

I call on students to share out their ideas. I push students to support their idea with data from the set. I want students to notice that although Thaisha and Thaima have the same median about of money earned, their data sets are not identical. I also want students to notice that the size of the box is different for each box plot. If this comes up, I ask students what they think this tells us about the data sets. Students are engaging in **MP3: Construct viable arguments and critique the reasoning of others **and** MP2: Reason abstractly and quantitatively**.

#### Resources

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I call on students to read and fill in the definitions for the measures of center. I explain the difference between measures of center and measures of variability. I introduce the concept of interquartile range. We work together to calculate each measure for Thaisha and Thaima’s box plots. I want students to see that the box in Thaima’s box plot is longer, which means that the middle 50% of her earnings are spread between $84 and $94. Thaisha’s box is shorter, and her middle 50% of her earnings are spread between $85 and $90.

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#### Creating a Box Plot

*7 min*

We work together to use the data set to create a box plot. A common mistake is for students to immediately start to find the median of the data set without reordering the values from least to greatest. I start to make this mistake and ask students if they agree or disagree with my action and why.

For the last two questions, students participate in a **Think Write Pair Share. ** I want students to be able to explain that the IQR shows the range of the middle 50% of the data. Even though the range of the entire team is 9 inches, the range for the middle ½ of the players on the team is 3 inches.

#### Resources

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#### Practice

*13 min*

**Notes:**

- Before this lesson, I use the tickets to go from the previous lessons to
**Create Homogeneous Groups**of 3-4 students. - I also use the ticket to go data to determine which practice page each group should start on.
- I create and
**Post a Key**around the room. - I copy a
**Group Work Rubric**for each group.

I review expectations and students move into groups. I tell groups which practice page to start on. Different groups will work through the practice pages at a different pace. My goal is that I have grouped students so that they are working at a similar level for these practice problems. Students are engaging in **MP1: Make sense of problems and persevere, MP2: Reason abstractly and quantitatively, **and** MP3: Construct viable arguments and critique the reasoning of others.**

As students work, I walk around and monitor student progress and behavior. If a group of students complete a page, I quickly scan their work. If they are on track, I send them to check their work with the key. If students are struggling, I may ask them one of the following questions:

- What is the question asking?
- What does this point represent?
- What is does this part of the box plot tell us? How do you know?
- What is a quartile?

If students complete the questions they can work on the challenge problems.

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#### Closure and Ticket to Go

*10 min*

I ask students to flip to the closure problem. I ask students how the weekly hours compares between Sarah and DeShawn. I explain that they need to write 5 observations by analyzing the box plots. I also want them to think about the two other questions about IQR.

Students participate in a **Think Pair Share. **Students are engaging in MP2**: Reason abstractly and quantitatively** and **MP3: Construct a viable argument and critique the reasoning of others**.

I call on students to share out their observations. I push students to use accurate language and to use the box plot to support their observation. I want students to recognize that the IQR for DeShawn’s weekly hours is smaller than the IQR for Sarah’s hours. This means that the middle ½ of Shawn’s weekly hours have a range of 4 hours. Sarah’s IQR is larger because the middle ½ of her weekly hours have a range of 8 hours. I want students to see that Sarah’s data is symmetric and DeShawn’s data is skewed. Students are engaging in **MP6: Attend to precision**.

I pass out the **Ticket to Go **and the **Homework.**

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- UNIT 1: Intro to 6th Grade Math & Number Characteristics
- UNIT 2: The College Project - Working with Decimals
- UNIT 3: Integers and Rational Numbers
- UNIT 4: Fraction Operations
- UNIT 5: Proportional Reasoning: Ratios and Rates
- UNIT 6: Expressions, Equations, & Inequalities
- UNIT 7: Geometry
- UNIT 8: Geometry
- UNIT 9: Statistics
- UNIT 10: Review Unit

- LESSON 1: 100 Students Project: What If The World Were 100 People?
- LESSON 2: 100 Students Project: What do we want to know about our students?
- LESSON 3: 100 Students Project: Revising Questions & Planning the Survey
- LESSON 4: 100 Students Project: Conducting the Survey
- LESSON 5: 100 Students Project: Tallying Data and Brainstorming about Presentations
- LESSON 6: 100 Students Project: Analyzing Survey Results
- LESSON 7: 100 Students Project: Presenting Your Findings
- LESSON 8: 100 Students Project: Project Reflection
- LESSON 9: Median, Mode, and Range
- LESSON 10: Mean
- LESSON 11: Playing with Measures of Central Tendency
- LESSON 12: Choosing the Best Measure of Center
- LESSON 13: Show what you know
- LESSON 14: Introduction to Box Plots
- LESSON 15: Box Plots and Interquartile Range
- LESSON 16: Arm Span Day 1
- LESSON 17: Arm Span Day 2
- LESSON 18: Mean Absolute Deviation
- LESSON 19: Comparing Mean Absolute Deviation
- LESSON 20: Selecting Measures of Center and Variability
- LESSON 21: Statistics Jeopardy
- LESSON 22: Unit Test