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Quiz & test questions Grade 12 Math

Cranmoor Water District Finance and Infrastructure Test

A grade 12 unit test on water infrastructure and utility finance, mixing recall of real US figures with cost math for a fictional water district.

Objectives

  1. Students will identify key facts about US water infrastructure condition and investment needs.
  2. Students will calculate a per-household water charge from a utility's revenue requirement.
  3. Students will compare a household's water charge with an affordability threshold.

Vocabulary

Revenue requirement
The total amount of money a utility must collect from customers each year to run the water system safely. Rates are set so that all the bills together add up to this amount.
Water main
A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: affordability, infrastructure, rate

Teacher overview

This 30-minute unit test (30 points total) checks whether students can recall key facts about the condition of US water infrastructure and apply cost math to a utility's budget. It mixes two multiple-choice items, two short-answer items, and six computation items built around the fictional Cranmoor Regional Water District. Real national figures are used for the recall items, while all district-specific dollar amounts are stated hypotheticals.

Cranmoor Water District Finance and Infrastructure Test — Grade 12 Math
Name: ____________________________ Date: ______________

Assessment

  1. (2 points) The ASCE 2025 Infrastructure Report Card graded US drinking water infrastructure at what level?

    • A) A
    • B) B+
    • C) C-
    • D) F

  2. (2 points) About how often does a water main break somewhere in the US?

    • A) Every 2 minutes
    • B) Every 2 hours
    • C) Every 2 days
    • D) Every 2 weeks

  3. (2 points) EPA estimates about $625 billion in drinking-water investment is needed over 20 years. About what share of that need is for distribution pipes?

  4. (4 points) Suppose the fictional Cranmoor Regional Water District serves 8,000 households and has an annual revenue requirement (its total yearly cost to run the system) of $9,600,000. What even annual charge per household would cover that cost?

  5. (3 points) Convert the annual charge from item 4 to an average monthly bill.

  6. (4 points) 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 4.5% of household income as a high burden. For a Cranmoor household earning $30,000 per year, what dollar amount is the 4.5% threshold?

  7. (3 points) Is the district's annual water charge from item 4 above or below your threshold from item 6, and by how much? Note that the charge does not include sewer.

  8. (4 points) Combined US water and sewer bills rose about 24% from 2019 to 2024. Suppose a Cranmoor household's combined bill was $1,000 in 2019 and rose 24%. What was the 2024 bill?

  9. (4 points) The district has 120 miles of water main and replaces 1.5 miles per year. At that rate, how many years would it take to replace all 120 miles?

  10. (2 points) Explain why the replacement cycle you found in item 9 can be a problem when many pipes have a shorter useful life, and name one consequence.

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: Choice C, a C-minus grade.
    The ASCE 2025 Report Card gave US drinking water a C-, so choice C is correct; the other grades do not match the report.

  2. Answer: Choice A, about every 2 minutes.
    ASCE talking points state a water main breaks roughly every two minutes, making choice A correct and the longer intervals wrong.

  3. Answer: About two-thirds.
    EPA's needs assessment attributes about two-thirds of the $625 billion need to distribution pipes, the largest single category.

  4. Answer: $1,200 per household per year.
    Charge = revenue requirement / households = $9,600,000 / 8,000 = $1,200 per household per year.

  5. Answer: $100 per month.
    $1,200 per year / 12 months = $100 per month.

  6. Answer: $1,350 per year.
    Threshold = 0.045 x $30,000 = $1,350 per year, the point at which cost reaches 4.5 percent of income.

  7. Answer: Below, by $150.
    The $1,200 charge is below the $1,350 threshold by $1,350 - $1,200 = $150, though adding a sewer charge could push the household closer to or past the threshold.

  8. Answer: $1,240.
    A 24 percent increase: $1,000 x 1.24 = $1,240 for the 2024 combined bill.

  9. Answer: 80 years.
    120 miles / 1.5 miles per year = 80 years to replace all the pipe at that rate.

  10. Answer: Pipe wears out faster than an 80-year cycle replaces it.
    If much of the 120 miles has a useful life shorter than 80 years, pipe is failing faster than it is being replaced, so the backlog grows. One consequence is more frequent water main breaks and emergency repairs.

Differentiation

Support

Provide a formula reference for items 4 through 6 (charge = cost / households; threshold = rate x income) and allow a calculator on every computation item. Let students answer item 10 as a short bulleted list.

Extension

Ask students to find what annual revenue requirement would push the per-household charge to exactly the affordability threshold from item 6 for 8,000 households, and discuss what a district could do if costs rose above that point.

ELL supports

Pre-teach "revenue requirement," "affordability," and "water main" with short definitions and an example bill. Provide sentence frames for items 7 and 10, such as "The charge is ___ the threshold by ___."

Extensions

Have students look up their own water utility's yearly report or rate schedule and compare a real household charge with the Cranmoor figures. A short written comparison connects the test's math to the bills their families actually pay.