##
* *Reflection: Relevance
Stepping into Box Plots - Section 1: Entry Event – Shoe Sizes!

I made a mistake on this one and didn't follow my own plan!

As the students entered the room, I mistakingly had written for them to record shoe SIZES on the board, to shoe measurements (in cm) as is detailed in the lesson plan. As we began analyzing the data, one student spoke up by raising his hand and saying "Aren't boys and girls shoe sizes different?" I was taken back at first, because YES, they are! It was a great discussion with the class and the student made an excellent conclusion about our data set. The fact that boys and girls shoe sizes are different skewed out data.

I feel as though my honest mistake still taught the students something mathematically. It turned out to be a really neat addition to the lesson that I had not originally anticipated. I actually made the most out of an honest mistake, and the students learn a lot from seeing how a teacher responds in moments like these.

*Oooops! Use cm measures for feet, not sizes!*

*Relevance: Oooops! Use cm measures for feet, not sizes!*

# Stepping into Box Plots

Lesson 4 of 21

## Objective: Students will be able to participate in the data collection of a whole class observational study. They will learn about the benefits and pitfalls of displaying data in a box plot and set the stage for motivating future lessons.

As the students enter the classroom, I greet them at the door and ask them to place their back heels against the wall. On the floor, I have taped cm increments. Every student who enters my classroom has his/her feet measured and recorded. To get everyone involved in the data collection, I measure the first person, then have that person measure and record the second person, and so on. This ensures that everyone participates in the data collection. It is really helpful to use an easel to record the data so that you can carry it to the front of the classroom when the students are done!

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In this portion of the lesson, I display the data where all students can see it. I ask them what they notice about the data, how it was collected, and what conclusions we may be looking to draw. I also ask them what types of questions they might be interested in investigating about the foot sizes. For example:

1. What is the mean (representative) foot size of the class? What is the median (typical) foot size of the class? What is the shortest foot size in the class? What is the longest foot size in the class?

2. Are there differences in foot sizes for boys and girls? If so, what are the differences?

3. Are foot sizes related to any other variables?

This discussion is usually a really good one! Additional follow up questions: Did any students forget to take off their shoes? What were the pro’s and con’s of having multiple people involved in measuring the data? ** **

I also begin talking to the students about the difference between an observational study and an experimental study. Since nothing was deliberately done to the students, (other than ask them to take off their shoes), this is an observational study. I ask the students for examples of other observational and experimental studies, and we create a list on the board.

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#### Exit Slip

*8 min*

In this exit slip, the students will be required to think critically about the benefits and shortcomings of a box plot. They are asked questions that prompt them to view statistics with a well-informed eye! For example, the exit slip figure shows data from two different data sets, each one containing 18 values that vary from 1 to 6 (they are actually histograms, which we will learn about in a later lesson). Data set A has an equal number of values in each group, while Data set B has two peaks at 2 and 5. In other words, the data is symmetric, but their shapes are clearly different. This box plots both look the same! This is because the data sets both have the same five-number summaries — they're both symmetric with the same amount of distance between Q1, the median, and Q3. The students are asked to think critically about his scenario in the exit slip!

*expand content*

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Statistics - Opening Activities and Discussion
- LESSON 2: Role Play PLUS Flaws and Fallacies in Statistical Thinking
- LESSON 3: Flaws and Fallacies (cont.) AND Types of Data
- LESSON 4: Stepping into Box Plots
- LESSON 5: An Introduction to Histograms
- LESSON 6: Using Excel to Create a Histogram
- LESSON 7: A-Mazing Inferential and Descriptive Statistics!
- LESSON 8: What does the Bell Curve SOUND like?
- LESSON 9: The HOW and WHY Behind Standard Deviation
- LESSON 10: A Second Dose of Standard Deviation
- LESSON 11: Straight Walkin' With Statistics - Day #1
- LESSON 12: Straight Walkin' With Statistics - Day #2
- LESSON 13: Straight Walkin' With Statistics - Day #3
- LESSON 14: Review and Extensions
- LESSON 15: Student Motivated Workshop
- LESSON 16: Let's Help the 6th Graders!
- LESSON 17: Let’s Help the 6th Graders: Problem Work Time
- LESSON 18: Let’s Help the 6th Graders: Final Day
- LESSON 19: Let's Help the 6th Graders: Debrief
- LESSON 20: Teaching Numbers and Excel
- LESSON 21: Muddying the Waters: Formative Assessment Lesson