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Worksheet Grade 11 Social Studies & Civics

The Trenholm Bottoms Levee: A Grade 11 Benefit-Cost Worksheet

Students apply the benefit-cost test federal flood control has used since 1936 to two options for a fictional river district, a levee or an upstream detention basin.

Objectives

  1. Students will compute total cost, total benefit, benefit-cost ratio, and net benefit over a fixed study period.
  2. Students will compare two flood protection options using more than one decision measure.
  3. Students will explain why a favorable benefit-cost ratio does not by itself decide a public works question.

Vocabulary

Floodplain
A floodplain is the flat land next to a river that the river spills onto when it floods. Floodplains are natural storage areas that give floodwater a safe place to spread out.
Detention basin
A detention basin is a dug-out area that fills with stormwater during a storm and then slowly drains empty over hours or days. It holds the water back so streets and streams downstream do not flood.
Levee
A long earthen wall built along a river to keep floodwater out of the nearby land. Levees protect many towns, but they can fail if water rises too high.

Also: benefit-cost ratio, net benefit, study period, residual risk, annual maintenance

Teacher overview

The Flood Control Act of 1936 committed the federal government to building flood works across the country, and it attached a condition that has shaped public works ever since: a project qualifies only if its benefits exceed its costs. That single sentence turned engineering choices into arithmetic a citizen can check. This worksheet applies the same test to a fictional river district weighing a levee against a basin built upstream, and then asks students where the arithmetic stops being enough.

The Trenholm Bottoms Levee: A Grade 11 Benefit-Cost Worksheet — Grade 11 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

The city of Havenrock, the Mowbray River, and the Trenholm Bottoms are fictional, and every figure below was invented for this worksheet.

The Trenholm Bottoms is a low district of Havenrock along the Mowbray River. It holds 250 households. The river has flooded the district four times since 1970. The city is weighing two options, and both are evaluated over a study period of 50 years.

Option A is an earthen levee along the river side of the district. It holds the river out of the neighborhood, and the channel beside the levee carries the same water in a narrower space.

Option B is a detention basin at Elstow Flats, eleven miles upstream on county farmland. The basin holds back part of the peak flow during a storm and releases it slowly afterward.

Item Option A, levee Option B, upstream basin
Construction or land cost $24,000,000 $31,000,000
Annual maintenance cost $300,000 $120,000
Average yearly flood damage avoided $1,900,000 $2,400,000
Study period 50 years 50 years
  1. Option A costs $24,000,000 to build and $300,000 each year to maintain. Calculate its total cost over the 50-year study period.
  2. Option A avoids an average of $1,900,000 in flood damage each year. Calculate its total benefit over the 50-year study period.
  3. Divide Option A's total benefit by its total cost to find its benefit-cost ratio. Round to two decimal places.
  4. Option B costs $31,000,000 to build and $120,000 each year to maintain. Calculate its total cost over the 50-year study period.
  5. Option B avoids an average of $2,400,000 in flood damage each year. Calculate its total benefit over the 50-year study period.
  6. Divide Option B's total benefit by its total cost to find its benefit-cost ratio. Round to two decimal places.
  7. Net benefit is total benefit minus total cost. Using Option A's benefit of $95,000,000 and cost of $39,000,000, calculate Option A's net benefit.
  8. Using Option B's benefit of $120,000,000 and cost of $37,000,000, calculate Option B's net benefit.
  9. Subtract Option A's net benefit of $56,000,000 from Option B's net benefit of $83,000,000 to find how much larger Option B's net benefit is.
  10. Option A costs $24,000,000 and protects the 250 households of the Trenholm Bottoms. Calculate its construction cost per household protected.
  11. Both options have a benefit-cost ratio well above 1.00. In three or four sentences, explain why that result does not by itself tell Havenrock which option to choose. Name at least one effect on the river or on people outside the district that the ratio does not capture.
  12. Engineers describe Option A as protecting the district against the 100-year flood. In two or three sentences, explain what that term means and what it does not promise.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: $39,000,000. Maintenance is $300,000 times 50 years, or $15,000,000, added to the $24,000,000 construction cost.
  2. Answer: $95,000,000. Multiply $1,900,000 per year by 50 years.
  3. Answer: 2.44. Divide $95,000,000 by $39,000,000 to get 2.4359, which rounds to 2.44.
  4. Answer: $37,000,000. Maintenance is $120,000 times 50 years, or $6,000,000, added to the $31,000,000 land and construction cost.
  5. Answer: $120,000,000. Multiply $2,400,000 per year by 50 years.
  6. Answer: 3.24. Divide $120,000,000 by $37,000,000 to get 3.2432, which rounds to 3.24.
  7. Answer: $56,000,000. Subtract the $39,000,000 cost from the $95,000,000 benefit.
  8. Answer: $83,000,000. Subtract the $37,000,000 cost from the $120,000,000 benefit.
  9. Answer: $27,000,000. Subtract $56,000,000 from $83,000,000.
  10. Answer: $96,000 per household. Divide $24,000,000 by 250 households.
  11. Answer: A ratio compares two totals and hides everything the totals leave out. A levee narrows the channel, so it raises flood levels for neighbors upstream and across the river, and it leaves residual risk if the water ever tops it. The upstream basin moves the burden onto county landowners at Elstow Flats, whose fields hold the water that the city no longer receives. Accept any answer that names a group outside the district, a physical effect on the river, or a risk that remains after the project is built.
  12. Answer: The term means a flood with a one percent chance of being equaled or exceeded in any single year, estimated from past records. It does not promise one flood per century, it does not mean the district is safe once a flood has occurred, and it gives no protection against a larger flood. Accept any answer that gives the annual probability and rejects the once-a-century reading.

Differentiation

Support

Give these students the fictional table with the 50-year maintenance totals already computed for both options, so items 1 and 4 reduce to a single addition. Provide the benefit-cost ratio as a labeled fraction with the benefit on top before they attempt item 3, and allow item 11 to be answered in two sentences.

Extension

Ask these students to recompute both benefit-cost ratios for a 25-year study period instead of 50 years, explain in a paragraph why the ranking of the two fictional options does not change, and name the kind of cost that would have to differ for a shorter study period to reverse the result.

ELL supports

Pre-teach levee, detention basin, benefit, cost, and ratio with a simple cross-section sketch showing a river, a wall of earth beside it, and a shallow bowl of land upstream. Provide sentence frames for items 11 and 12: "The ratio does not show ___," and "A 100-year flood means ___, but it does not mean ___." Allow calculations to be shown as labeled arithmetic.

Extensions

Have students locate their own address or their school on the public flood hazard map their state or county provides, note which flood zone it falls in, and write a paragraph explaining what that zone designation does and does not tell a homeowner about risk.