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Good Cop, Bad Cop (Updated!)

How should police departments address excessive use of force?

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Good Cop, Bad Cop (Updated!)

How should police departments address excessive use of force?

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Good Cop Bad Cop - Student Handout.pdf
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Good Cop Bad Cop - Teacher Guide.pdf
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2023-2024 Versions

In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.

You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.

How should police departments address excessive use of force? A number of high-profile cases have painted a disturbing picture of how police officers treat the people they’re supposed to keep safe.

In this lesson, students compare the distributions of excessive force of two police departments and explore how the shape of the distribution affects the effectiveness of different solution attempts.

REAL WORLD TAKEAWAYS

  • While some might assume that excessive use of force by police would be normally distributed, a 1991 study of the Los Angeles Police Department found that the department’s complaints more closely conformed to a power law distribution: the vast majority of officers received no complaints or very few, and a small number of officers were responsible for the vast majority of complaints.
  • The shape and distribution of data informs the appropriateness and effectiveness of a policy meant to change that data: In the case of excessive use of force in LAPD, we would expect a policy eliminating the worst offenders to have had a bigger impact than a policy aimed at modest improvements across the board.
  • Effective policy solutions won’t necessarily be palatable or feel fair to society.

MATH OBJECTIVES

  • Analyze and interpret graphical displays of univariate data to answer multi-step problems
  • Compare a normal vs. power law distribution, and understand how the shape of a distribution affects real-world policy
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.
Algebra 1
One-Variable Statistics
Algebra 1
One-Variable Statistics
Content Standards S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (a) Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. (b) Informally assess the fit of a function by plotting and analyzing residuals. (c) Fit a linear function for a scatter plot that suggests a linear association.
Mathematical Practices MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.

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Appropriate most times as students are developing conceptual understanding.

Wiibates (Updated!)

How much should Nintendo have charged for the Wii U console?

Algebra 1
Parabolas & Quadratics
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Billions & Billions (Updated!)

What are the consequences of human population growth?

Algebra 1
Exponential Functions (Beg.)
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Wage War (Updated!)

What are the pros and cons of increasing the minimum wage?

Algebra 1
Solving Linear Systems
Great anytime, including at the beginning of a unit before students have any formal introduction to the topic.

Prescripted (Updated!)

How much should medications cost?

Algebra 1
Parabolas & Quadratics
Appropriate most times as students are developing conceptual understanding.

Hereby Sentence (Updated!)

Is there evidence of racial bias in capital punishment?

Algebra 1
One-Variable Statistics
Appropriate most times as students are developing conceptual understanding.