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Classroom activity Grade 7 Math

Setting Tidemill's Water Rate: A Grade 7 Budget Station Activity

Four rotating stations have each group act as a water district board, computing the percent increase, the revenue it raises, and the burden on a household.

Objectives

  1. Students will calculate a percent increase on a monthly water bill and its annual effect.
  2. Students will scale a per-household increase to a utility's total annual revenue.
  3. Students will write and solve an inequality for a revenue target.

Vocabulary

Key words: rate, revenue, percent increase, affordability

Teacher overview

This is a four-station rotation for groups of four, in which each group acts as the board of the fictional Tidemill Water District and every figure on the station cards was written for this activity. Tidemill has aging cast-iron mains to replace and must decide how large a rate increase to adopt, so the stations walk a group through the same sequence a real board follows: what the increase does to one household's bill, what it raises across the whole system and buys in replaced pipe, whether it meets the board's target, and whether households can carry it. Each station holds one link in that chain, and the handout restates the figure a group needs to carry forward, so groups can begin at different stations and still follow the sequence.

Activity Directions

  1. Before class (10 min of prep): Print the four station cards for the fictional Tidemill Water District and place one at each of four tables. Station 1 carries the household bill of $42.00 a month and the board's proposed 6 percent increase. Station 2 carries the district size of 4,000 households and the main replacement cost of $900,000 a mile. Station 3 carries the board's revenue target of $150,000 a year. Station 4 carries a household income of $2,400 a month and a monthly sewer bill of $38.00. Print one Student Handout for each student.

  2. Assign roles (5 min): Put students in groups of four and assign one role each. The rate analyst reads the station card aloud, the operations lead records the calculation, the customer advocate checks whether the result is reasonable for a household, and the recorder writes the group's answer on the handout. Tell students that real utilities employ people in each of these roles, reached through paths that range from a state operator license earned by exam to a finance or engineering degree.

  3. Explain the rotation (part of the same 5 minutes): Groups start at different stations and move clockwise on your signal. Every group visits all four stations. Each station has 8 minutes, for 32 minutes of rotation in all.

  4. Run station 1, the household bill (8 min): Groups complete handout items 1 through 3, finding the dollar increase, the new monthly bill, and the extra amount a household pays over twelve months.

  5. Run station 2, the system revenue (8 min): Groups complete handout items 4 and 5, scaling one household's yearly increase to 4,000 households and then finding how long that revenue takes to pay for one mile of replaced main.

  6. Run station 3, the revenue target (8 min): Groups complete handout items 6 and 7, finding the district's current annual revenue and writing an inequality for the percent increase that reaches the board's target.

  7. Run station 4, the household burden (8 min): Groups complete handout items 8 and 9, finding the combined water and sewer bill as a percent of monthly income and comparing it with the high-burden threshold.

  8. Close with the board vote and debrief (8 min): The activity ends once every group has finished all four stations. Each group announces the percent increase it would adopt and gives one number from the handout as its reason. Then ask the class two questions: why does a 6 percent increase fall short of the board's revenue target, and what does item 9 tell the board about raising the rate further? Record the class's answers beside the station chain on the board.

Setting Tidemill's Water Rate: A Grade 7 Budget Station Activity — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

Tidemill Water District is fictional, and all of these numbers were written for this activity. Answer each item using the numbers it gives you. Round money to the nearest cent and percents to the nearest tenth unless the item says otherwise.

  1. A Tidemill household pays $42.00 a month for water. The board proposes a 6 percent increase. How many dollars is the increase?
  2. Use item 1. What is the new monthly bill?
  3. Use item 1. How much more does a household pay over 12 months?
  4. Tidemill serves 4,000 households. Using the $30.24 a year from item 3, how much new revenue does the increase raise each year?
  5. Replacing one mile of water main costs $900,000. At $120,960 of new revenue a year, how many years does one mile take to fund? Round to the nearest tenth of a year.
  6. Tidemill's 4,000 households each pay $42.00 a month now. What is the district's current annual revenue?
  7. The board wants at least $150,000 in new revenue each year. Let p stand for the percent increase. Using the $2,016,000 of current revenue, write an inequality for p and solve it. Round to the nearest hundredth of a percent.
  8. A Tidemill household earns $2,400 a month. Its new water bill is $44.52 and its sewer bill is $38.00. What percent of the household's monthly income is the combined bill?
  9. A widely used rule of thumb, built from two EPA benchmarks, treats combined water and sewer costs above roughly 4.5 percent of household income as a high burden. Compare your answer to item 8 with that figure, and explain what it tells the board about room to raise the rate further.

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: $2.52.
    Multiply the bill by the rate of increase: 42.00 x 0.06 = 2.52.
  2. Answer: $44.52.
    Add the increase to the old bill: 42.00 + 2.52 = 44.52 a month.
  3. Answer: $30.24.
    Multiply the monthly increase by twelve months: 2.52 x 12 = 30.24 a year.
  4. Answer: $120,960.
    Multiply the yearly increase for one household by the number of households: 30.24 x 4,000 = 120,960.
  5. Answer: 7.4 years.
    Divide the cost of a mile by the new yearly revenue: 900,000 / 120,960 = 7.4405, which rounds to 7.4 years.
  6. Answer: $2,016,000.
    One household pays 42.00 x 12 = 504.00 a year. Multiply by the households: 504.00 x 4,000 = 2,016,000.
  7. Answer: 7.44 percent.
    One percent of current revenue is 2,016,000 / 100 = 20,160. Write 20,160p at least 150,000, then divide both sides by 20,160 to get p at least 7.4404. Rounded, the board needs an increase of at least 7.44 percent, so a 6 percent increase does not reach the target.
  8. Answer: 3.4 percent.
    Add the two bills: 44.52 + 38.00 = 82.52. Divide by monthly income: 82.52 / 2,400 = 0.034383, which is about 3.4 percent.
  9. Answer: The combined bill sits below the high-burden figure, so the board has some room.
    At about 3.4 percent, the household is under the 4.5 percent rule-of-thumb figure by roughly 1.1 percentage points. That leaves room for the larger increase item 7 calls for, though the board would also need to consider households earning less than $2,400 a month, for whom the same bill takes a larger share.

Differentiation

Support

Give these groups a station card for the fictional Tidemill district with the first calculation of each station already set up, such as 42.00 x 0.06 written under item 1. Pair the percent work with a hundredths grid so students can see 6 percent as six squares out of one hundred before they multiply.

Extension

Ask groups to find how many miles of main the fictional district could fund in ten years at the 7.44 percent increase from item 7, and to write a short recommendation to the board that names both the miles gained and the effect on the household percent in item 8.

ELL supports

Provide each station card for the fictional Tidemill district with a small labeled diagram, such as a bill for station 1 and a length of pipe for station 2, and gloss "revenue," "rate," and "burden" in student-friendly language. Offer role cards with one sentence each so the rate analyst, operations lead, customer advocate, and recorder know what to say when their turn comes.

Extensions

Students can find their own utility's published rate schedule and repeat the item 1 through 4 chain with the real monthly charge, keeping the fictional Tidemill household count for comparison. A second follow-on asks groups to design a two-step increase, such as 4 percent this year and 4 percent next year, and to determine whether the compounded result reaches the board's $150,000 target sooner than a single increase would.