Introduction

This is a 3 part lesson utilizing census data of the mean income of workers 18 years and older by education attainment levels. The data is also broken into gender and 3 ethnic groups - white, black, and Hispanic. Students will analyze census data to create graphs and take part in a simulation using this same data as a starting point to make financial decisions and budgets. Some familiarity with line and bar graphs is helpful.

In Part 1, students make a multiple line graph showing income levels for each education level for the past 8 years. In Part 2, the number of people for each ethnic group and gender is compared within each education level. Students create two bar graphs with this data one based on the number of people and the other based on the percent of the population. The two graphs are very different. Students analyze their graphs and describe situations in which they would use one graph instead of the other. Parts 1 and 2 make take several days depending on the students' ability level and the length of the class period.

Grade Level: 6-7

Part 1: Income vs. Education Level

Internet Link: http://www.census.gov/population/socdemo/education/tabA-3.pdf

1. Enter the data on to Student Worksheet 1 (HTML) / Student Worksheet 1 (PDF).
2. Create a line graph from the information in Student Worksheet 1.
3. Answer questions on Student Worksheet 1 page 2 (HTML) / Student Worksheet 1 page 2 (PDF).

Part 2: Education by Race and Gender

Internet Link: http://www.census.gov/population/socdemo/education/tabA-3.pdf

1. Enter the data on Student Worksheet 2a (HTML) / Student Worksheet 2a (PDF).
2. Create a bar graph from the information in Student Worksheet 2a.
3. Answer questions on Student Worksheet 2a page 2 (HTML) / Student Worksheet 2a page 2 (PDF).
4. Enter the data on Student Worksheet 2b (HTML) / Student Worksheet 2b (PDF).
5. Create a bar graph from the information in Student Worksheet 2b.
6. Answer questions on Student Worksheet 2b page 2 (HTML) / Student Worksheet 2b page 2 (PDF).

Part 3: Simulation

This can be done every day for a week or two or spread out over the course of the year. This works well with the Middle School Junior Achievement program (http://www.ja.org). This is also a wonderful vehicle in which to teach spreadsheet applications.

Internet Links:

• America's Job Bank: http://www.acinet.org/acinet/select_occupation.asp?stfips=&next=occ_rep
• Realfind/Newspaper Classified Ads: http://www.realfind.com
• Tax Rates: http://www.irs.gov/individuals/index.html
• Insurance Costs
  • Auto: http://www.insurance.ca.gov/docs/FS-Surveys.htm
  • Renter's: http://www.insurance.ca.gov/docs/FS-Surveys.htm
  • Health: Not convenient at this time.
• Spreadsheets 
• General Simulation Information - Health insurance costs, paycheck withholding amounts, transportation costs
• Event Cards
• Instruction for teachers

Procedure:

1. Assign each student an ethnic group, gender, and education attainment level. This can be based on their own ethnic group and gender or randomly. Each group should be in the same proportion as the data. For example, if 17% of the total population is white female at the advanced degree, then 17% of the students should be assigned to that group.The first task for the students is to find a job suitable for their education level and paying at a rate close to their assigned income level. The America's Job Bank site is an excellent resource. Not only are many different jobs described, but also the median income level and job outlook are given for the US as well as a particular state and the necessary skills and education needed for the job are described. Once students have found a job, they should print out the information obtained from America's Job Bank and add the information on the Simulation Information Sheet.Housing Students should look in the classified ads of a local newspaper or use the Realfind/Newspaper Classified Ads site for a place to rent. Once they have found a place to rent, they should add their housing information to the Simulation Information Sheet.Transportation Students will need to decide how they are going to get to and from work (car, public transportation, bicycling, walking, other). This information should also be added to the Simulation Information Sheet.After steps 2-4 are completed, students will complete a monthly budget planning sheet based on their assigned income. They may have to reconsider their housing and transportation choices in order to make a balanced budget.Now the simulation begins: There are class event cards and individual event cards. These have been designed to reflect what goes on in the "real world". Only one class event card per day should be chosen at random for the whole class to deal with, while individual event cards can be passed out at random for individual students to deal with. The class and individual event cards can be done simultaneously or on separate days. Class event cards should not be repeated during the simulation, while the individual event cards can be passed out again several times during the simulation. Students will be making decisions about the events based on their particular situation. Students will need to keep a "monthly budget" and write about how they dealt with the event and what affect it had on their budget. The writing should be part of a journal or log kept during the simulation. Ideally, the budget should be done using a spreadsheet program.Some of the events will be handled differently by different students. Some of them may have decided to pay for insurance which would deal with some of the problems, others may have benefits that come with the job, while some may not have any insurance at all. These situations will lead naturally to class discussions about what choice people have and how they choose to deal with events. If the simulation is done over a long period of time, local, national, or international events can be brought into the simulation.This simulation can be as involved and as long as you want to make it. It can be done every day for a week, part of every day for a month, or can be done once or twice a month during the course of the school year.
2. After the simulation has ended, students should discuss and record how they felt the simulation went. What things did they have control over? Were there any decisions they made about planning their budget at the beginning that they would like to change? What one thing was the underlying factor for how well they were able to be successful in the simulation? Hopefully, students will learn that their income was based on their education level and that ultimately, their future is dependent on their education.

AssessmentGraphs for Parts 1 and 2

• Part 1 line graph: Income by Education Level for the past 8 yearsPart 2 bar graph 1: Education by race based on number of people
• Part 2 bar graph 2: Education by race based on % of race total

Questions for parts 1 and 2Simulation assessment

• Completed Simulation Information Sheet (HTML) / (PDF)Completed budget "Monthly" record of income and expenditures (HTML) / (PDF) (spreadsheet or handmade)Graph of income and expenditures
• Log/journal of simulation experience

This lesson is still a work in progress, and I would welcome any suggestions and feedback. Please e-mail me at gmuller@marin.k12.ca.us or send it to Gretchen Muller, Del Mar Middle School, Tiburon, CA 94920

SCORE Mathematics | | SCORE Mathematics Lessons Index | |  SCORE Mathematics Search

California's Mathematics Academic Standards

6th Grade
Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages:

1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:

2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.
2.2 Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 divided 15/16 = 5/8 x 16/15 = 2/3).
2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

Algebra and Functions
1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results:

1.4 Solve problems manually by using correct order of operations or by using a scientific calculator.

2.0 Students analyze and use tables, graphs and rules to solve problems involving rates and proportions:

2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).
2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.
2.3 Solve problems involving rates, average speed, distance, and time.

Statistics, Data Analysis, and Probability
1.0 Students compute and analyze statistical measurement for data sets:

1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.
1.3 Understand how the inclusion or exclusion of outliers affect measures of central tendency.
1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context.

2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:

2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.
2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.7 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.

7th Grade
Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:

1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.
1.3 Convert fractions to decimals and percents and use these representations in estimation, computation, and applications.
1.6 Calculate the percentage of increases and decreases of a quantity.
1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

Algebra and Functions
1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs:

1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in terms of the situation represented by the graph.

Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:

1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based upon a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Make and test conjectures by using both inductive and deductive reasoning.
2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.6 Express the solution clearly and logically by using appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.8 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.

May 4, 1999
Revised July 27, 1999
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