## Sean Gourley: The Mathematics of War - Section 1: Opening

# Scatterplots and Non-Linear Data

Lesson 15 of 19

## Objective: SWBAT construct a scatter plot, determine a line of best fit, and recognize data that should be modeled by a non-linear function.

## Big Idea: In this lesson students discover that some bivariate data should not be modeled by linear functions. Other functions are considered.

*50 minutes*

#### Opening

*15 min*

I think that whenever possible, students should be exposed to mathematics that is actually being done in the real world. This TED Talk video, The Mathematics of War, provides my students with a vision of how algebra concepts that we are studying in class are being applied in a project undertaken by Physicist Sean Gourley and his team. The topic is very serious.

When showing this video I stop it periodically to allow students time to share what they have seen and process the information being presented. In particular, I like to pause this video each time he shows a scatter plot to simply ask about the correlation so that students can see a connection with what they are working on in class (around_2:20). Around 3:51 he mentions the equation for this particular data. While students may not fully understand the equation, I ask them to look at the screen and find vocabulary words that they recognize (slope, constant, probability). Around 5:51 he talks about the stable structure of war, I pause here so that students can really concentrate on what he is going to say about the findings of continuous wars. I also pause the video around 6:38 to have students make a hypothesis as to how to read that graph. I show them that the "small vertical lines" are actually versions of boxplots showing the range of troop force in each altercation.

While some of the content of this video is outside of the scope of this particular course, the students can draw some comparisons between their work and the work presented in the video.

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#### Closure

*10 min*

Today's ticket out the door (Scatter Plot_Day 3_TOD) is a pre-assessment to see how students currently think about residuals. The choice of the best fit line is fairly obvious, however, I want to see how students quantify the fit. I ask students to “use mathematics to support your answer.” This information will be valuable when students begin to informally analyze residuals and discuss correlation coefficients in the next lesson.

*expand content*

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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