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Worksheet Grade 12 Careers & CTE

Ashgate Springs Rebate Program: Conservation Specialist Math

Grade 12 worksheet comparing three water conservation rebates by cost per thousand gallons saved, then arguing which ones cost less than buying more water.

Objectives

  1. Students will calculate annual and lifetime water savings for three conservation rebates.
  2. Students will express each rebate's cost as dollars per thousand gallons saved and rank the three.
  3. Students will argue which rebates cost less than purchasing an additional block of water.

Vocabulary

Turf replacement
A program that pays people to take out thirsty lawn grass and plant water-wise gardens in its place.
Water efficiency
Doing the same jobs with less water, like a washing machine that cleans clothes using fewer gallons. Efficiency saves water without giving anything up.

Also: rebate, cost per thousand gallons, measure life, marginal cost

Teacher overview

A conservation specialist at a water utility decides which rebates to offer with a fixed program budget, and the decision rests on the cost of the water each rebate saves rather than on the size of the rebate itself. Three rebates that save very different amounts of water, over very different equipment lifetimes, become comparable only when each is expressed as a cost per thousand gallons saved. This worksheet takes students through that calculation for showerheads, leak repair, and turf replacement at the fictional Ashgate Springs Water District, then asks them to compare the results against what the district would pay to buy the same water. The error to watch for is comparing rebate amounts directly, since the largest rebate here saves the most water per household and is still the worst value the district can buy.

Ashgate Springs Rebate Program: Conservation Specialist Math — Grade 12 Careers & CTE
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Ashgate Springs Water District has $150,000 to spend on conservation rebates this program year and is weighing three options. Show your work and label every unit.

Rebate A pays $54 per household for three WaterSense showerheads. A standard showerhead flows at 2.5 gpm, while WaterSense-labeled models use 2.0 gpm or less. Assume a household of three people, each showering 8 minutes per day, and a ten-year measure life.

Rebate B pays $75 per household for a leak repair kit and inspection. EPA WaterSense reports that household leaks waste nearly 9,400 gallons per year, and the district assumes the kit cuts that waste in half over a five-year measure life.

Rebate C pays $1.50 per square foot to replace lawn with low-water landscaping, up to 600 square feet per household. The district assumes 22 gallons saved per square foot per year over a ten-year measure life.

  1. Under Rebate A, calculate the gallons a household saves per day, using the difference between the two showerhead flow rates and the household's total daily shower minutes.
  2. Calculate the gallons that household saves in one year, treating the year as 365 days.
  3. Calculate the household's savings over the ten-year measure life.
  4. Calculate Rebate A's cost to the district in dollars per thousand gallons saved. Round to the nearest cent.
  5. Under Rebate B, calculate the gallons a household saves per year.
  6. Calculate that household's savings over the five-year measure life.
  7. Calculate Rebate B's cost in dollars per thousand gallons saved. Round to the nearest cent.
  8. Under Rebate C, calculate the gallons a household saves per year at the full 600 square feet.
  9. Calculate Rebate C's cost in dollars per thousand gallons saved over its ten-year measure life. Round to the nearest cent.
  10. Rank the three rebates from lowest to highest cost per thousand gallons saved.
  11. If the district spent its entire budget on Rebate A, how many households could it fund? Give a whole number of households.
  12. Suppose the district's next block of purchased water costs $4.10 per thousand gallons. In two or three sentences, argue which rebates the district should fund, using your answers to items 4, 7, and 9 as evidence.

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: 12 gallons per day. The flow difference is 2.5 gpm minus 2.0 gpm = 0.5 gpm. Total shower time is 3 people x 8 minutes = 24 minutes per day. Savings = 0.5 gallons per minute x 24 minutes = 12 gallons per day.
  2. Answer: 4,380 gallons. Annual savings = 12 gallons per day x 365 days = 4,380 gallons.
  3. Answer: 43,800 gallons. Lifetime savings = 4,380 gallons per year x 10 years = 43,800 gallons.
  4. Answer: $1.23 per thousand gallons. The lifetime savings of 43,800 gallons is 43.8 thousand gallons. Cost = $54 / 43.8 = $1.2329, which rounds to $1.23 per thousand gallons.
  5. Answer: 4,700 gallons. Half of the 9,400 gallons wasted each year is 9,400 / 2 = 4,700 gallons saved per year.
  6. Answer: 23,500 gallons. Lifetime savings = 4,700 gallons per year x 5 years = 23,500 gallons.
  7. Answer: $3.19 per thousand gallons. The lifetime savings of 23,500 gallons is 23.5 thousand gallons. Cost = $75 / 23.5 = $3.1915, which rounds to $3.19 per thousand gallons.
  8. Answer: 13,200 gallons. Annual savings = 600 square feet x 22 gallons per square foot per year = 13,200 gallons per year.
  9. Answer: $6.82 per thousand gallons. Lifetime savings = 13,200 gallons per year x 10 years = 132,000 gallons, which is 132 thousand gallons. The rebate pays 600 square feet x $1.50 = $900. Cost = $900 / 132 = $6.818, which rounds to $6.82 per thousand gallons.
  10. Answer: Rebate A, then Rebate B, then Rebate C. Showerheads cost $1.23 per thousand gallons, leak repair kits $3.19, and turf replacement $6.82. Rebate C saves the most water per household in a year and is still the most expensive water the district can buy through this program.
  11. Answer: 2,777 households. Dividing, $150,000 / $54 per household = 2,777.8, and the district can only fund whole rebates, so 2,777 households.
  12. Answer: Fund Rebate A and Rebate B. Both cost the district less per thousand gallons saved than the $4.10 per thousand gallons it would pay for the next block of purchased water, at $1.23 and $3.19, so each dollar spent on them avoids more than a dollar of spending on purchased supply. Rebate C at $6.82 per thousand gallons costs more than buying the water outright, so on cost alone the district should not fund it, though a complete argument may note that turf replacement also cuts peak summer demand, which is when supply is scarcest.

Differentiation

Support

Give students a blank comparison table with columns for annual savings, measure life, lifetime savings, rebate amount, and cost per thousand gallons, so the structure of all three calculations is visible from the start. Work Rebate A through item 4 with the class, then let students complete Rebate B independently. Students who finish items 1 through 7 have met the first two objectives.

Extension

Ask students to recalculate Rebate C assuming a twenty-year measure life, since replanted landscaping often outlasts a showerhead, and describe how sensitive the ranking is to that single assumption. Students can also design a fourth rebate of their own, state its savings assumptions, and place it in the ranking.

ELL supports

Pre-teach rebate, measure life, savings, and ranking, and post the phrase "dollars per thousand gallons saved" with its calculation written underneath. Provide the three rebate descriptions as a labeled table rather than paragraphs, and give a sentence frame for item 12 that begins with the recommendation and then asks for two supporting figures.

Extensions

Have students find the rebate list their own water utility publishes, identify the assumptions behind one rebate, and estimate its cost per thousand gallons saved with the method used here. Students can also compare a rebate program with a rate structure as tools for reducing demand, and describe which customers each approach reaches.