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# 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