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# Modeling with Box Plots and Histograms

Lesson 8 of 19

## Objective: SWBAT organize a set of data using box plots and histograms. They will be able to analyze the graphs and tables to extract pertinent information

#### Opening

*15 min*

For today's investigation I will group students with others of like ability. All students who are working on Histogram Day2 Form A should be paired with another students who are working on Form A. The same applies for Histogram Day2 Form B. I will determine the groupings based on the students' work on the Exit Ticket from yesterday's lesson.

**My students often struggle when asked to extract information from cumulative frequency tables or histograms. Today's opening activity is meant to give students a better understanding of how to interpret these graphical models (MP4). As they work I will circulate and observe carefully. I want to get a clear sense of who understands these models and who does not. In order to facilitate observation, each student gets a small dry erase board to work of for the opener.**

**Teaching Note**: When using whiteboards I keep a roster with me so that I can put marks next to students names either for needing to be extended or needing help or scaffolding. This way during the practice or investigation portion of the lesson, I know who I need to work with. This also becomes useful after several days have past and you can check back in with students to see their progress.

Slide 2 of stats_histograms_box_plot gives students an opportunity to practice interpreting a Histogram. I let students get to work and after a minute or two I will ask the class, "How do you know that this histogram does not represent cumulative frequency?" I expect my students will make observations like, "the bars don't keep getting taller" and "the intervals all have a different starting point." I use this line of questioning to make sure that they are thinking about the difference between frequency and cumulative frequency.

As mentioned above, I plan to have students answer the question from the opening presentation on whiteboards. At regular intervals, I will ask students to hold up the boards to show their answers. As I read the boards, I usually call on a student to explain their thinking. Rather than ask for multiple explanations, I ask other students to follow up adding pertinent information to the current explanation.

When students begin working on the runner's age data on Slide 3, I encourage students to begin by looking at the table and considering how many runners are actually in each age group. In order to make sure that students are interpreting the data correctly, I have students complete a short **Think-Pair-Share**. Then, I ask the question, "How many runners are in their 40s?"

**Teaching Notes: **If many students in the class are having difficulty. It is worth the time to have them make a list of how many runners are in their 20's, 30's, 40's, etc. This way they can practice pulling the information out of the table and putting it into more understandable terms.

The series of questions on Slide 4 (view as animation) is designed to informally assess whether my students understand how to interpret a cumulative frequency histogram. The second question oftne elicits interesting responses because no students were added in the "50-199" interval. This means that students either stopped after 149 yards or swam for 249 yards or more.

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#### Independent Practice

*30 min*

The Independent Practice portion of this lesson has two versions. In Version A, there are less data points, the data points are given in order, and the intervals have been provided for the students. Often, underachieving students struggle with organization. While the basic outcomes of the task are the same, students do not need to get bogged down with having disorganized data. Histogram Day2 Version B is a more independent version of the activity, which I will give to all students if they are up to the task.

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#### Closure

*5 min*

Using Slide 5 of Histograms & Box_Plot, I want to get an idea of how students can bridge the gap between box plot vocabulary/understanding and frequency histograms. This Ticket out the Door assesses students understanding of how the data is distributed and helps me to prepare for the next lesson, Connecting Box Plots and Histograms.

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- LESSON 1: Asking a Statistical Question
- LESSON 2: Measures of Center
- LESSON 3: Practice with Measures of Central Tendency
- LESSON 4: Organizing Data with a Box Plot
- LESSON 5: Understanding Box Plots (with Assessment)
- LESSON 6: Analyzing a Box Plot
- LESSON 7: Constructing a Histogram
- LESSON 8: Modeling with Box Plots and Histograms
- LESSON 9: Connecting Box Plots and Histograms
- LESSON 10: What's this table saying?
- LESSON 11: Creating Two-Way Tables
- LESSON 12: More with Conditional, Joint, and Marginal Frequencies
- LESSON 13: Using a Scatterplot to Model Data
- LESSON 14: A Bivariate Relationship
- LESSON 15: Scatterplots and Non-Linear Data
- LESSON 16: Modeling with Non-Linear Data
- LESSON 17: Analyzing Residuals
- LESSON 18: Creating a Residual Plot
- LESSON 19: Got Ups? A Statistics Unit Task