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Lesson plan Grade 12 Social Studies & Civics

Buying Phosphorus Credits on the Ainsdale River

A grade 12 lesson where students compute a fictional plant's phosphorus load and price a treatment upgrade against farm credits at a 2-to-1 trading ratio.

Objectives

  1. Students will calculate a wastewater plant's phosphorus load in pounds per day from concentration, flow, and the 8.34 pounds per gallon constant.
  2. Students will compare the annualized cost of a treatment upgrade with the cost of purchased credits under a stated trading ratio.
  3. Students will evaluate who gains and who carries the risk when a permit limit is met by trading rather than by treatment.

Vocabulary

Key words: nutrient credit, trading ratio, point source, nonpoint source, loading, annualized cost, permit limit

Teacher overview

A wastewater plant discharges through a pipe that can be sampled, so its pollution is easy to measure and easy to regulate. Fertilizer washing off cropland reaches the same river without passing any pipe, which makes it cheaper to reduce and much harder to verify. Water quality trading programs let a regulated plant pay farmers to make those cheaper reductions instead of building treatment it would otherwise need, usually at a ratio that requires more than one pound of farm reduction for each pound the plant keeps discharging. This lesson has students price both paths for the fictional town of Ledgeworth on the Ainsdale River and then judge the trade. Students commonly assume that a pound removed anywhere in the watershed helps the river equally, so the lesson keeps returning to the reach just below the outfall, where the plant's own discharge does not change.

Procedure

Framing the problem (8 min): Describe the fictional town of Ledgeworth, whose treatment plant discharges to the Ainsdale River, and the new watershed limit that cuts its allowed phosphorus concentration. Ask students to predict which is cheaper per pound removed, a plant upgrade or paying farmers upstream, and record the predictions.

Direct instruction (15 min): Teach the loading calculation, which converts a concentration and a flow into pounds per day by multiplying milligrams per liter by million gallons per day and by 8.34 pounds per gallon. Work one example at the board with numbers that do not appear on the handout, such as 2.0 mg/L at 1.5 MGD in a different fictional town, and have students name each unit as it cancels. Then introduce the trading ratio and explain that a ratio above one to one exists because a farm reduction is estimated from practices rather than measured at a pipe.

Guided practice (12 min): In pairs, students compute the town of Ledgeworth plant's current load and its permitted load from the handout figures, then compare answers with a neighboring pair before continuing.

Independent work (20 min): Students complete the remaining handout items on their own. Watch for the common error of applying the trading ratio to the plant's permitted load rather than to the required reduction.

Closure (5 min): Collect a one-sentence exit response naming one group that gains from the trade and one that carries new risk. Use the responses to open the next class if fewer than half of them name the river reach below the outfall or the downstream neighbors.

Buying Phosphorus Credits on the Ainsdale River — Grade 12 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Handout

The fictional town of Ledgeworth operates a wastewater treatment plant that discharges to the Ainsdale River. The plant treats 2.0 million gallons per day. Its effluent now contains 3.0 mg/L of phosphorus. A new watershed permit limits the effluent to 0.5 mg/L. Ledgeworth has two ways to comply. It can build a treatment upgrade that costs $9,000,000 and lasts 20 years, or it can buy phosphorus credits from the Harkstead farm district upstream, where cover crops and stream buffers cut runoff. Credits cost $12 per pound per year, and the state requires a trading ratio of 2 pounds of farm reduction for every 1 pound the plant does not remove. Use 8.34 pounds per gallon and 365 days per year for all items.

  1. Calculate the plant's current phosphorus load in pounds per day. Multiply 3.0 mg/L by 2.0 MGD by 8.34.
  2. Calculate the load the new permit allows, using 0.5 mg/L, 2.0 MGD, and 8.34.
  3. Subtract your answer to item 2 from your answer to item 1 to find the reduction the permit requires, in pounds per day.
  4. Convert that daily reduction to pounds per year using 365 days.
  5. The state requires 2 pounds of farm reduction for every 1 pound the plant leaves in place. How many pounds of farm reduction must Ledgeworth buy each year?
  6. At $12 per pound per year, what does Ledgeworth pay for credits each year?
  7. The upgrade costs $9,000,000 and lasts 20 years. What is its annualized cost, spreading the cost evenly across those years?
  8. Which option costs less each year, and by how much?
  9. Explain why the state requires 2 pounds of farm reduction rather than 1 for each pound the plant continues to discharge.
  10. Buying credits does not change what Ledgeworth's plant discharges into the stretch of the Ainsdale River just below its outfall, and farm reductions arrive mostly in wet weather rather than during low summer flows. Name one group that gains from the trade and one group that carries a new risk, and explain each.

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: 50.04 pounds per day. Using the loading formula for the fictional town of Ledgeworth, 3.0 mg/L times 2.0 MGD times 8.34 pounds per gallon equals 50.04 pounds per day.
  2. Answer: 8.34 pounds per day. 0.5 mg/L times 2.0 MGD times 8.34 equals 8.34 pounds per day.
  3. Answer: 41.7 pounds per day. 50.04 minus 8.34 equals 41.7 pounds per day of required reduction.
  4. Answer: 15,220.5 pounds per year. 41.7 pounds per day times 365 days equals 15,220.5 pounds per year.
  5. Answer: 30,441 pounds per year. The 2 to 1 ratio doubles the required reduction, so 15,220.5 times 2 equals 30,441 pounds of farm reduction.
  6. Answer: $365,292 per year. 30,441 pounds times $12 per pound equals $365,292.
  7. Answer: $450,000 per year. $9,000,000 divided by 20 years equals $450,000 per year.
  8. Answer: $84,708 per year less for credits. $450,000 minus $365,292 equals $84,708, so buying credits costs less each year than the upgrade.
  9. Answer: A farm reduction is estimated from the practices installed rather than measured in a pipe, so some of the promised pounds may never happen, may wash out in a wet year, or may stop when the contract ends. The extra pound builds a margin for that uncertainty and keeps the watershed from losing ground if the estimate is generous. Accept any answer that identifies measurement uncertainty or the risk that practices lapse.
  10. Answer: Answers vary. Farmers in the Harkstead district gain a payment for work that also holds soil on their fields, and Ledgeworth ratepayers gain a lower annual cost. Risk falls on residents and aquatic life along the reach below the outfall, where the discharge is unchanged, and on downstream neighbors who depend on reductions that no one meters. A strong answer names a specific group and ties it to a specific part of the calculation or the river.

Differentiation

Support

Provide a completed unit-cancellation strip for the loading formula, showing milligrams per liter times million gallons per day times pounds per gallon resolving to pounds per day, and pre-fill items 1 and 2 so students begin at the subtraction in item 3. Allow a calculator with the constants already entered.

Extension

Ask students to find the credit price per pound at which the fictional town of Ledgeworth would be indifferent between the two options, then explain what would happen to the trading program if the state raised the ratio to 3 to 1 at that price.

ELL supports

Pre-teach "load," "credit," "ratio," and "outfall" with a labeled sketch of a river showing farms upstream, a plant outfall, and a town downstream. Provide sentence frames for items 9 and 10: "The state requires two pounds because ." and " gains because ___, while ___ carries risk because ___."

Extensions

Have students write a one-page recommendation to the fictional Ledgeworth council that adopts one option and attaches two conditions, such as an inspection schedule for the Harkstead practices or a clause that ends the trade if monitoring shows the river below the outfall failing. Students should cite at least two of their computed figures and state which condition they would give up first if the farm district refused both.