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Lesson plan Grade 11 Math

Brackenford Water Bills: Is the Rate Affordable?

A 50-minute grade 11 math lesson where students compute water-bill burden as a percent of income, compare it to a common 4.5% threshold, and project a rate increase.

Objectives

  1. Students will calculate each household's water and sewer bill as a percent of income.
  2. Students will compare household burdens to a widely used high-burden threshold and find the median.
  3. Students will project a bill forward using a stated annual percent increase.

Vocabulary

Key words: affordability, burden, median, rate increase

Teacher overview

Water is often called cheap, yet a flat bill lands very differently on a high-income and a low-income household, and utilities increasingly track that gap. This lesson has grade 11 students measure affordability the way regulators do, as the water-and-sewer bill divided by household income, using data from Brackenford, a fictional city. Students then compare each household against a widely used high-burden threshold of 4.5 percent of income and project one more year of rising bills. A common student misconception is that the same dollar increase is equally affordable for every household; the percent-of-income calculation is designed to expose why that is false.

Procedure

Hook (5 min): Ask students whether a 60-dollar-a-year water increase would matter equally to every household, then point out that the same increase is minor for a higher-income Brackenford household but a real strain for a lower-income one. Tell students they will measure that difference with a single number.

Direct instruction (12 min): Define the affordability burden as annual water-and-sewer bill divided by annual household income, expressed as a percent. Work one fictional example on the board: a bill of 720 dollars on an income of 60,000 dollars is 720 divided by 60,000 = 0.012, or 1.2%. Introduce the widely used rule of thumb that a combined burden above about 4.5% of income counts as a high burden. Explain that the 4.5% comes from adding two EPA benchmarks, 2.5% for drinking water and 2% for wastewater, and that EPA has no single official cutoff; its 2024 affordability assessment used both 3% and 4.5%.

Guided practice (13 min): As a class, compute the burden for two more Brackenford households, Household 1 (a 600-dollar bill on an 80,000-dollar income) and Household 6 (a 780-dollar bill on a 30,000-dollar income), then sort a short list of burdens to find a median together. Emphasize that the median describes the typical household better than an average when incomes are uneven.

Independent practice (15 min): Students complete the Student Handout, computing burdens, identifying which households cross the 4.5% threshold, finding the median, and projecting bills forward using the 5.1% increase that combined bills saw in 2025.

Closure and exit ticket (5 min): On an index card, students answer: "A household pays 1,050 dollars on an income of 20,000 dollars. Is that above or below the 4.5% high-burden line, and by how much?" Collect the cards; a class is ready to move on when at least 80% correctly compute the 5.25% burden and compare it to 4.5%.

Brackenford Water Bills: Is the Rate Affordable? — Grade 11 Math
Name: ____________________________ Date: ______________

Student Handout

Brackenford is a fictional city. Answer each question and show your work.

  1. Household 2's yearly water-and-sewer bill is 840 dollars and its income is 24,000 dollars. What percent of income is the bill?
  2. Household 5's bill is 960 dollars and its income is 16,000 dollars. What percent of income is the bill?
  3. Household 3's bill is 900 dollars and its income is 18,000 dollars. What percent of income is the bill?
  4. A widely used rule of thumb treats a burden above about 4.5% of income as a high burden. Based on your answers to questions 1 through 3, which of Households 2, 3, and 5 are above the 4.5% threshold?
  5. The six Brackenford households have these burdens: 0.75%, 3.5%, 5.0%, 1.2%, 6.0%, and 2.6%. Find the median burden.
  6. Of those six households, how many are above the 4.5% high-burden threshold?
  7. Combined water and sewer bills rose about 5.1% in 2025. If Household 2's bill of 840 dollars rises 5.1%, what is the new bill?
  8. After that 5.1% increase, Household 2's income stays 24,000 dollars. What is the new burden percent? Round to the nearest tenth.
  9. Household 5's bill of 960 dollars also rises 5.1%. Does its burden stay above 4.5%? Show the new bill and the new burden.

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: 3.5%.
    840 dollars divided by 24,000 dollars = 0.035, or 3.5% of income.
  2. Answer: 6.0%.
    960 dollars divided by 16,000 dollars = 0.060, or 6.0% of income.
  3. Answer: 5.0%.
    900 dollars divided by 18,000 dollars = 0.050, or 5.0% of income.
  4. Answer: Households 3 and 5.
    Household 3 (5.0%) and Household 5 (6.0%) exceed 4.5%, while Household 2 (3.5%) does not.
  5. Answer: 3.05%.
    Ordered, the burdens are 0.75, 1.2, 2.6, 3.5, 5.0, 6.0. The two middle values are 2.6 and 3.5, so the median is (2.6 + 3.5) divided by 2 = 3.05%.
  6. Answer: 2 households.
    Only the 5.0% and 6.0% burdens exceed 4.5%, so two of the six households are above the threshold.
  7. Answer: 882.84 dollars.
    840 dollars x 1.051 = 882.84 dollars after the 5.1% increase.
  8. Answer: 3.7%.
    882.84 dollars divided by 24,000 dollars = 0.0368, which rounds to 3.7%.
  9. Answer: yes, still above 4.5%.
    960 dollars x 1.051 = 1,008.96 dollars; divided by 16,000 dollars = 0.0631, or 6.3%, which stays above the 4.5% threshold.

Differentiation

Support

Provide the division already set up for questions 1 through 3 (for example, 840 divided by 24,000 = ___) so students focus on interpreting the percent. Give a printed number line marked at 4.5% so students can place each burden visually.

Extension

Ask students to design a fixed dollar credit that the utility could give low-income households so that every one of the six Brackenford households falls below 4.5%, then explain what that credit would cost the utility per year across the six households.

ELL supports

Pre-teach "bill," "income," "burden," and "threshold" with a simple picture of a bill next to a paycheck. Provide a sentence frame for question 4: "Household ___ is above the threshold because its burden is ___."

Extensions

Have students find their own water utility's rate schedule online and estimate the annual bill for a household using about 300 gallons per day, then compute the burden at two different income levels and compare with the Brackenford results.