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Beyond Heroes and Holidays: Math Lesson

Aggregate Income Simulation
By Jan Goodman

Explore Graph # 5 with students and discuss its implications. The graph shows how total income per household is unequally distributed in the United States. For example, almost three-fourths (75%) of the income is possessed by the top two-fifths (40%) of the country’s households. Less than 15% of the income is possessed by the lowest two-fifths of households. The top fifth of households have almost half of the total income, and within that fifth, the top 5% of households has 21.9% of the income.

To make the graph more concrete, use the cards on the following page to simulate actual income for thirty households. The cards are designed to align with income percentages and on the graph. Each group of six cards represents one-fifth of the U.S. population and their share of aggregate income. Each card represents one household.

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Cut out the cards and place each one in a separate envelope. Distribute one envelope per student or “family” in the classroom or group and ask them to remain silent after they open the envelope. Remind students that the money in the envelope represents their income for an entire year from the sources listed in the notes of the graph.

When the envelopes are distributed, have students line up, silently, by income, around the perimeter of the room, with the lowest incomes on one end of the room and the highest incomes on the other end. Do not use a circle for your line up. Be sure to create the line so that there is a significant amount of physical space between the lowest income and the top income.

Begin with the lowest income. Ask each student or “family” to reveal their household income and make a brief statement as to how they feel about the amount of money that they have for the entire year. Caution students to take the simulation seriously and avoid put-downs of groups or individuals as they announce the content of their envelope. Remind them that the class is a model of actual income distribution in the United States.

After each set of six envelopes are revealed, announce that these students represent one-fifth (20%) of the households in the room, and state the group’s average (mean) income, as shown below. Or, ask students to calculate the mean income in their fifth.

Fifth

% of Income

Average (Mean)

Lowest

3.6%

$9.017

Second

8.9%

$22,166

Third

14.8%

$36,783

Fourth

23.0%

$57,167

Highest

49.6%

$123,333

Total Money $1,490,800

$49,693

After all 30 envelopes are revealed, explain that if all the money were collected and redistributed equally, each household would have 49,693 (and all bars on the graph would be equal). Ask students if they are willing to trade in their money for the mean income. See who is willing to do so! Discuss the implications of these inequities.

© 2002 by Jan M. Goodman

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Income Cards For Graph # 5 Simulation

Household Income = $227,000

Household Income = $195,000

Household Income = $86,000

Household Income = $80,000

Household Income = $77,000

Household Income = $75,000

Household Income = $71,000

Household Income = $67,000

Household Income = $55,000

Household Income = $52,000

Household Income = $50,000

Household Income = $48,000

Household Income = $45,000

Household Income = $41,000

Household Income = $36,000

Household Income = $34,700

Household Income = $33,000

Household Income = $31,000

Household Income = $29,000

Household Income = $25,000

Household Income = $22,000

Household Income = $21,000

Household Income = $19,000

Household Income = $17,000

Household Income = $15,400

Household Income = $12,000

Household Income = $9,000

Household Income = $8,000

Household Income = $6,000

Household Income = $3,700

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Cards © 2002 by Jan M. Goodman

 

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