##
* *Reflection: Student Ownership
Describing Data - Day 2 of 2 - Section 2: Investigation

One of the things I like about this lesson is that it allows students to become the "experts" of some content. I like how they use technology to learn something new and then have to think about a way to share it and teach other students. I think this is a good way to shift the mathematical authority in the room away from the teacher and on to the students.

*Students become the experts*

*Student Ownership: Students become the experts*

# Describing Data - Day 2 of 2

Lesson 2 of 14

## Objective: SWBAT create dot plots, histograms, and box plots to describe data. SWBAT articulate the advantages and disadvantages of the three representations.

#### Opening

*5 min*

I remind students that yesterday they collected some group data - 10 pulse readings for each member of their group. At the end of the class, they did their best to describe their group's data without just listing the numbers. I let students know that today, they will learn three different ways to represent data and discuss the advantages and disadvantages of each method.

*expand content*

#### Investigation

*30 min*

Students will now work in their small groups learning about either dot plots, histograms, or box plots. Students will watch short videos in groups, so I make sure I have technology available (computers, laptops, or ipads) and perhaps a small amount of quiet space for some groups outside of the classroom (if possible).

I explain to the class that their group will be assigned to learn about a method for representing their data and they will need to learn about the method, graph their pulse data in this method on a poster board, and then share what they learned with the class. For more information about my plan for today, see my video narrative.

I assign groups of students to:

- dot plots
- histograms
- box plots.

Next, the small groups watch these short videos and then make the appropriate representations on poster board.

**How to make a Dot Plots**

**Source**: YouTube (Accessed August 19, 2014)

**How to make a Histogram**

**Source: **YouTube (Accessed August 19, 2014)

**How to make a Box Plot**

**Source:** YouTube (Accessed August 19, 2014)

As students work, I circulate and clarify and questions. A few points that I focus on when I interact with students during this lesson are:

- I make sure to be clear with students working on the dot plot that the data does not have to start at zero. They can start with their lowest pulse value.
- I talk to students working on the histogram about the possibility of representing their values in buckets for the range of data, though for this particular data using consecutive numbers is probably best.
- The box plot group may need a lot more time than the other groups (the dot plot group will probably be done first). I take this into consideration when I assign the group, and/or have some follow up work for the groups that finish first.

I remind students that after they have created their own representation of the data, they will be teaching the other groups who learned about a different method. I encourage groups to really think through their presentations, especially those who finish early.

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#### Discussion + Closing

*25 min*

After students work for a sufficient amount of time, I will choose three different groups to share out their methods. As they do, I check for understanding with the other groups, especially on the box plots. I may choose to jump in with further explanations or more detailed instructions, depending on how thorough my students are. I usually choose this lesson to ask the histogram group to make a distinction between a histogram and a bar graph, since many students decide that these are interchangeable terms.

Today's lesson is really to give students a refresher on how to create the three types of graphs; I will be going into greater detail in future lessons. I always leave time at the end to discuss what students think are the advantages and disadvantages of each plot. I like to let students lead this conversation here. When I intervene it might be to ask a question like, "Do you have ideas about when a box plot would be more useful than a dot plot?" I want to make sure that my students do not attach their way of thinking to a particular ("the simplest representation") because they feel most comfortable with it. I want them to know how to use different representations, depending on the data and the story that they want to tell using the data.

I close class by distributing a homework assignment that gives my students the opportunity to practice some of what they have learned. I assign a task like the following:

**The following data set shows the number of songs downloaded in one week by each student in Mrs. Jones class: **

**10, 20, 12, 14, 12, 27, 88, 2, 7, 30, 16, 16, 32, 25, 15, 4, 0, 15, 6**

**Choose and create a plot to represent the data.**

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Resources used:

High School Flip Book Common Core State Standards for Mathematics from the Kansas Association of Teachers of Mathematics website (www.KATM.org, accessed September 16, 2013).

Source: http://katm.org/wp/wp-content/uploads/flipbooks/High-School-CCSS-Flip-Book-USD-259-2012.pdf

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- UNIT 1: Introduction to Algebra: Focus on Problem Solving
- UNIT 2: Multiple Representations: Situations, Tables, Graphs, and Equations
- UNIT 3: Systems of Equations and Inequalities
- UNIT 4: Quadratics!
- UNIT 5: Data and Statistics
- UNIT 6: Arithmetic & Geometric Sequences
- UNIT 7: Functions

- LESSON 1: Describing Data - Day 1 of 2
- LESSON 2: Describing Data - Day 2 of 2
- LESSON 3: Speeding Data: Creating and Comparing Box Plots
- LESSON 4: Group Comparisons: Student Project
- LESSON 5: Sending Text Messages
- LESSON 6: Five Seconds
- LESSON 7: Introducing Normal Distribution
- LESSON 8: Spread Out
- LESSON 9: Standard Deviation
- LESSON 10: Exploring Standard Deviation
- LESSON 11: How Much for a Used Car?
- LESSON 12: Understanding the Correlation Coefficient
- LESSON 13: Are Women Paid Less Than Men?
- LESSON 14: Working with Residuals