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Worksheet Grade 6 Careers & CTE

Harmon Falls Water Rates: A Rate Analyst Worksheet

A grade 6 careers worksheet where students work as a utility rate analyst, finding percent rate increases and checking a bill against an affordability guideline.

Objectives

  1. Students will calculate the percent increase of a water rate and of a full monthly bill.
  2. Students will check a monthly bill against an income-based affordability guideline.

Vocabulary

Key words: rate analyst, usage rate, percent increase, affordability

Teacher overview

A rate analyst studies what a utility charges, how much a proposed change would cost customers, and whether bills stay affordable. This worksheet puts students in that role for a fictional utility that is proposing a rate increase. Students find percent increases and then use an income-based guideline to judge affordability. A useful teaching point appears in the numbers: because the fixed charge does not change, the full bill rises by a smaller percent than the usage rate does. The math is grade 6 ratio and percent work.

Harmon Falls Water Rates: A Rate Analyst Worksheet — Grade 6 Careers & CTE
Name: ____________________________ Date: ______________

Student Worksheet

You are a rate analyst for the town of Harmon Falls, studying a proposal from Harmon Falls Municipal Water. The current usage rate is $3.20 per 1,000 gallons, and the utility proposes raising it to $3.68 per 1,000 gallons. The fixed monthly charge is $12.00 and would not change. An average home uses 5,000 gallons per month. Show your work.

  1. At the current rate of $3.20 per 1,000 gallons, find the usage charge for a home that uses 5,000 gallons.
  2. The proposed rate is $3.68 per 1,000 gallons. By what percent would the usage rate increase from $3.20?
  3. Find the usage charge for the same 5,000 gallons at the proposed $3.68 rate.
  4. Add the $12.00 fixed charge to your answer from question 3 to find the full monthly bill at the new rate.
  5. At the old rate, the full monthly bill for this home was $28.00. By how many dollars does the full bill rise under the new rate?
  6. The full bill rises from $28.00 to your answer in question 4. By what percent did the full monthly bill rise? Round to the nearest tenth of a percent.
  7. A widely used guideline, built by adding two EPA benchmarks, treats a combined water-and-sewer bill above 4.5 percent of a household's income as a high burden. For a household earning $2,000 per month, what dollar amount is 4.5 percent of that income?
  8. This household's combined water-and-sewer bill is $76.00 per month. Is that above or below the high-burden line you found in question 7?
  9. Explain why the full monthly bill rose by a smaller percent than the usage rate did.

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: $16.00.
    5 thousands of gallons x $3.20 per thousand = $16.00.
  2. Answer: 15 percent.
    The rate rose by $3.68 - $3.20 = $0.48. $0.48 / $3.20 = 0.15, a 15 percent increase.
  3. Answer: $18.40.
    5 thousands of gallons x $3.68 per thousand = $18.40.
  4. Answer: $30.40.
    $12.00 fixed charge + $18.40 usage charge = $30.40.
  5. Answer: $2.40.
    $30.40 - $28.00 = $2.40.
  6. Answer: 8.6 percent.
    The bill rose $2.40 from $28.00. $2.40 / $28.00 = 0.0857, which rounds to 8.6 percent.
  7. Answer: $90.00.
    4.5 percent of $2,000 = 0.045 x $2,000 = $90.00.
  8. Answer: Below.
    The $76.00 bill is less than the $90.00 high-burden line, so it is below the guideline.
  9. Answer: The fixed charge did not change.
    Only the usage part of the bill went up 15 percent, while the $12.00 fixed charge stayed the same, so that unchanged part pulls the whole bill's percent increase down to about 8.6 percent.

Differentiation

Support

Give these students the divisions in questions 2 and 6 already set up (the rate change over the old rate, and the bill change over the old bill) so they focus on the division and on converting a decimal to a percent. Allow a calculator throughout.

Extension

Ask students to find the largest whole-dollar monthly bill the household in question 7 could have and still stay at or below the 4.5 percent high-burden line, and to explain how they used question 7 to decide.

ELL supports

Pre-teach "rate analyst," "usage rate," "percent increase," and "affordability" with a labeled before-and-after bill. Provide a sentence frame for question 9: "The full bill rose less because the ___ charge did not change."