Water for Schools
Menu

Worksheet Grade 8 Social Studies & Civics

Flat Rate or Tiered Pricing: Water Billing in Pemberton Falls

A grade 8 worksheet in which students calculate water bills for four households under flat and tiered rate structures and evaluate affordability against a 4.5% guideline.

Objectives

  1. Students will calculate household water bills under flat-rate and tiered-rate pricing structures.
  2. Students will apply a widely used affordability guideline to evaluate the financial impact of a rate change on different households.

Vocabulary

Key words: flat rate, tiered rate, base charge, affordability threshold

Teacher overview

Water utilities decide how to charge customers, and that decision affects households differently depending on how much water they use and how much they earn. This worksheet compares two common rate designs: a flat rate, which charges every household the same amount regardless of use, and a tiered rate, which charges more per gallon as use increases. Students calculate bills for four households under each system, then apply a widely used affordability guideline, built from two EPA benchmarks, to judge whether a proposed rate change helps or hurts a low-income household. A common misconception is that a rate change described as encouraging conservation is automatically fairer to every household; the worksheet is built to test that assumption directly against a fixed-income household's numbers.

Flat Rate or Tiered Pricing: Water Billing in Pemberton Falls — Grade 8 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

The fictional town of Pemberton Falls currently bills every household a flat rate of $48.00 per month, no matter how much water it uses. The city council is considering switching to a tiered rate instead: a $15.00 base charge each month, plus $2.00 per 1,000 gallons for the first 5,000 gallons used, plus $4.00 per 1,000 gallons for any amount used above 5,000 gallons.

Use these numbers for every question below.

  1. Under the current flat rate, how much does every household in Pemberton Falls pay per month, regardless of how much water it uses?
  2. In one sentence, explain why a flat rate gives a household no financial reward for using less water.
  3. Household A, a two-person household, uses 3,000 gallons in a month. Calculate Household A's monthly bill under the proposed tiered rate. Show your work.
  4. Household C, the town's average household, uses 8,000 gallons in a month. Calculate Household C's monthly bill under the proposed tiered rate. Show your work.
  5. Household B, a five-person household with a lawn, uses 12,000 gallons in a month. Calculate Household B's monthly bill under the proposed tiered rate. Show your work.
  6. Compare each household's tiered-rate bill (items 3 through 5) to the flat rate of $48.00. Which households would pay less under the tiered rate, and which would pay more?
  7. A widely used rule of thumb, built by adding two EPA benchmarks (2.5% for drinking water and 2% for wastewater), treats combined water and sewer costs above roughly 4.5% of household income as a high financial burden. Suppose a household in Pemberton Falls earns a fictional $30,000 per year. What annual dollar amount equals 4.5% of that income?
  8. Household A's tiered-rate bill from item 3 applies every month. What is Household A's total annual water bill across 12 months? Is that annual total above or below the $1,350 threshold you found in item 7, assuming Household A also earns the fictional $30,000 per year?
  9. Household D is a fictional fixed-income household earning $14,000 per year. Household D uses 15,000 gallons per month because of an aging, leak-prone set of fixtures. Calculate Household D's monthly bill under the tiered rate, then find the annual total across 12 months.
  10. What percentage of Household D's $14,000 annual income does the annual bill from item 9 represent? Round to the nearest tenth of a percent. Based on the 4.5% guideline, is Pemberton Falls' proposed tiered rate more affordable or less affordable for Household D than the current $48.00 flat rate? Support your answer with numbers from items 6 and 9.

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: $48.00.
    The flat rate is the same for every household, so item 1's answer does not depend on usage: $48.00 per month.
  2. Answer: A flat rate does not change with usage.
    Because the monthly charge stays $48.00 whether a household uses 1,000 gallons or 15,000 gallons, using less water saves nothing on the bill.
  3. Answer: $21.00.
    Household A uses 3,000 gallons, all within the first tier. Base charge $15.00 + (3 × $2.00) = $15.00 + $6.00 = $21.00.
  4. Answer: $37.00.
    Household C uses 8,000 gallons. Base charge $15.00 + first 5,000 gallons (5 × $2.00 = $10.00) + remaining 3,000 gallons (3 × $4.00 = $12.00) = $15.00 + $10.00 + $12.00 = $37.00.
  5. Answer: $53.00.
    Household B uses 12,000 gallons. Base charge $15.00 + first 5,000 gallons (5 × $2.00 = $10.00) + remaining 7,000 gallons (7 × $4.00 = $28.00) = $15.00 + $10.00 + $28.00 = $53.00.
  6. Answer: Households A and C pay less; Household B pays more.
    Household A ($21.00) and Household C ($37.00) both fall below the $48.00 flat rate, while Household B ($53.00) rises above it, because Household B's higher usage crosses into the more expensive second tier.
  7. Answer: $1,350.
    4.5% of $30,000 = 0.045 × $30,000 = $1,350 per year.
  8. Answer: below.
    Household A's annual bill is $21.00 × 12 = $252.00, well below the $1,350 threshold calculated in item 7.
  9. Answer: $780.
    Household D uses 15,000 gallons. Base charge $15.00 + first 5,000 gallons (5 × $2.00 = $10.00) + remaining 10,000 gallons (10 × $4.00 = $40.00) = $65.00 per month. Annual total: $65.00 × 12 = $780.00 per year.
  10. Answer: less affordable.
    $780.00 ÷ $14,000 = 0.0557, or about 5.6% of Household D's income, above the 4.5% guideline. Under the current flat rate, Household D would pay $48.00 × 12 = $576.00 per year, about 4.1% of $14,000, below the guideline. The tiered rate lowers bills for smaller-usage households like A and C but raises Household D's bill above the affordability threshold, so the change is less affordable for this particular fixed-income, higher-usage household.

Differentiation

Support (below grade level)

Provide the tiered-rate formula as a filled-in worked example for a fifth household before students attempt items 3 through 5, and allow a calculator for all multiplication and division steps. Break item 10 into two smaller questions: first calculating the two annual totals, then comparing them to 4.5% of $14,000.

Extension (above grade level)

Ask students to find the exact usage level, in gallons, at which a household's tiered-rate bill under the fictional Pemberton Falls rate structure equals the flat-rate amount of $48.00, and to explain what that usage level means for the town's decision.

ELL supports

Pre-teach "flat rate," "tiered rate," "base charge," and "affordability threshold" with a simple two-column chart showing how each rate structure calculates a bill. Provide the multiplication and addition steps in item 9 as a labeled fill-in template so students can focus on the water-billing concept rather than organizing the arithmetic.