PAYING FOR CRIME
Critical Analysis, Research, and Problem Solving
By Amy Lein, a Math and Special Education teacher at Newton North High School in Newton, Massachusetts.

Grades: High School

Time: Three 50-minute class periods

Background

The number of people in prison in America has been rising steadily, resulting in overcrowded prisons and a budget crisis. Contrary to popular belief, a rise in crime isn't the primary reason for the increase in prison populations. Studies have shown that changes in laws and policies regarding imprisonment seem to be the major cause.

Objective

In four linked activities, students will apply their knowledge of ratios, proportions, fractions, decimals, percents, scientific notation, mean, median, mode, range, and pie graphs to interpret data and statistics regarding the U.S. government's budget for prisons and correctional services. Then students will synthesize what they have learned and communicate it using diagrams and mathematical evidence.

Correlation to National Standards

ACTIVITIES

To introduce the activities, students should first read the Online NewsHour Extra Article: U.S. Prison Population Hits All-time High

Activity I: 30 minutes

Mathematical Focus: proportions, decimals, percents, pie graphs

Materials:
Excerpt #1: Criminal Justice Policies
Student Worksheet #1: Percents and Degrees of a Circle
Teacher Key to Worksheet #1
Template: Pie Graph
Protractors

Procedure

• A. Have students read Excerpt #1:Criminal Justice Policies.
  
  
• B. Discuss this data and use the students' suggestions and input to create a pie graph.

• On the board/overhead, model the skill of using proportions to calculate how many degrees of the circle there should be for each percent.
  
  
• Using the Teacher Key to Worksheet #1 as a guide, discuss the concepts, then work through the calculations. Students may use Student Worksheet #1 to calculate the numbers.
  
  
• Pass out Template: Pie Graph and a protractor so they can create their own pie graph.

Activity II: 20 minutes

Mathematical Focus: fractions, decimals, percents

Materials:
Excerpt #2: Prison Population
Student Worksheet #2: Percent of Prison Population
Teacher Key to Worksheet #2

Procedure:

• A. Have students read Excerpt #2: Prison Population, and discuss what the "correctional population" means as compared to those who are incarcerated.
  
  
• B. Using the Teacher Key to Worksheet #2 as a guide, discuss the concepts, then work through the calculations. Students may use Student Worksheet #2 to do the calculations.
  
  
• C. Discuss the importance of verifying sources by comparing them to information from other sources to check for consistency
  
  
• D. Then share the fact below from a different source (Measuring the Performance of Community Corrections. http://www.bja.evaluationwebsite.org/html/documents/measuring_the_performance_of_com.htm)

  1. Three out of four people in correctional services aren't in prison.

  2. Calculations:

  • ¾ = 75% not in prison, which is close to the calculation of 69% not in prison.

  3. Ask them if this second source verifies our data.

• E. Present students with this concept: while about only 30% of people in the correctional system are actually in prison, the numbers are rising. Plus, if we add in another piece of data, we can see how drastically prisons play into the correctional system's budget.

1. As of 1996, 80% of the government budget for correctional services was spent on prisons alone, leaving 20% for parole, probation and community corrections services. Source: http://www.ojp.usdoj.gov/bjs/pub/pdf/spe96.pdf

2. To rephrase this, 80% of the money is spent on 30% of the people, and 20% of the money is spent on 70% of the people.

Activity III: 50 minutes

Mathematical Focus: scientific notation, mean, median, mode, range

Materials:

Bureau of Justice Statistics State Prison Expenditures, 1996. The information you will need is from:
Page 2: Table 1. State prisons: Total, operating, and capital expenditures, and operating expenditures per inmate, fiscal year 1996 (http://www.ojp.usdoj.gov/bjs/pub/pdf/spe96.pdf)

Procedure:

• A. Pass out copies of Table 1. State prisons: Total, operating, and capital expenditures, and operating expenditures per inmate, fiscal year 1996.
  
  
• B. Tell the class that we are going to find the average amount spent by each state in the nation on prisons.
  
  
• C. Using the Key to Worksheet #3 as a guide, discuss the concepts, then work through the calculations. Students may use Student Worksheet #3 to do the calculations.
  
  
• D. Direct students to look at the table of all the states, and discuss if the average is the best measure for this set of data. If there is a very wide range, perhaps it would be beneficial to know the median and mode as well.
  
  
• E. Divide up into groups to calculate the range, median and mode of the data listed on page 2 (they may want to round off the numbers to make it more manageable)
  
  
• F. After calculating range, median, and mode, compare the median and mode to the average. Discuss similarities and differences and as a class decide on the most representative measure.

Activity IV: 50 Minutes

Mathematical Focus: fractions, decimals, percents, and pie graphs

Materials:

Bureau of Justice Statistics State Prison Expenditures, 1996:
http://www.ojp.usdoj.gov/bjs/pub/pdf/spe96.pdf

Worksheet #4: Prison Budgets
Activity 4 Table: Prison Budgets
Answer Key for Activity 4 Table: Prison Budgets
Template: Pie Graph
Protractors

Procedure:

• A. Tell students that they will be creating a pie graph to represent what prison budget money is spent on.
  
  
• B. Divide into groups and assign groups to certain pages (4-11) and ask them to highlight and pull out data about areas in which the money in prison budgets is spent. (Use Worksheet 4: Prison Budgets as a guide)
  
  
• C. Come back together as a whole class and pass out blank copies of Table: Prison Budgets.
  
  
• D. Ask groups to report on the data they found and how they can convert it first to percents, and then to degrees of the circle. (SEE ACTIVITY 1 for instructions on how to calculate degrees of circle)
  
  
• E. Pass out the pie graph templates and protractors and instruct each student to make a pie graph of the data in the table.
  
  
• Use the Prison Budgets Table Answer Key to check student answers.
  

Extension Activities:

1. Based on Activity IV, students can write up a quasi-scientific report explaining how and where the data came from, what calculations were done, the results of the calculations -- with work shown -- and what the findings mean.

2. Students can do research about the effectiveness of prisons and correctional programs, and consider how the budget is spent and if any cuts can be made while maintaining effectiveness.
Source: The Prison-Industrial complex http://www.theatlantic.com/issues/98dec/prisons.htm

3. Students can investigate statistics on racial breakdown of prison populations. Source: Comparative International Rates of Incarceration: An Examination of Causes and Trends June 20, 2003. page 3 http://www.sentencingproject.org/pdfs/pub9036.pdf and Source: "In the System" page 1 and page 6 http://www.pbs.org/newshour/bb/law/july-dec01/prison_8-28.html

4. Students can research alternatives to prison sentences. Source: "Debt to Society" http://www.motherjones.com/prisons/

Correlation to National Standards
NCTM Principles and Standards for School Mathematics
http://standards.nctm.org/document/chapter7/index.htm

Number and Operations Grades 9-12

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Compute fluently and make reasonable estimates
  

Data Analysis and Probability Grades 9-12

• Develop and evaluate inferences and predictions that are based on data
  

Problem Solving Grades 9-12:

• Build new mathematical knowledge through problem solving
• Solve problems that arise in mathematics and in other contexts
• Apply and adapt a variety of appropriate strategies to solve problems
• Monitor and reflect on the process of mathematical problem solving
  

Communication Grades 9-12:

• Organize and consolidate their mathematical thinking through communication
  
• Communicate their mathematical thinking coherently and clearly to peers, teachers, etc.
  
• Analyze and evaluate the mathematical thinking and strategies of others
• Use the language of mathematics to express mathematical ideas precisely
  

Connections Grades 9-12:

• Recognize and use connections among mathematical ideas
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
• Recognize and apply mathematics in contexts outside of mathematics
  

Author Amy Lein teaches Special Education and Math at Newton North High School in Newton, MA. She has a Master's Degree in Special Education from Lesley University, and a Bachelor's Degree in Psychology from Carleton College.

To find out more about opportunities to contribute to this site, contact Leah Clapman at extra@newshour.org.