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Worksheet Grade 9 Social Studies & Civics

Annexation or Wells: The Pikeworth Hollow Water Extension

A grade 9 worksheet costing out a fictional city water main extension and weighing the annexation condition the city attaches to the offer.

Objectives

  1. Students will calculate the per-household cost of a water main extension before and after grant funding.
  2. Students will compare an annual water cost to a household income threshold used in affordability policy.
  3. Students will explain why a city ties a service extension to annexation and who gains and loses from that condition.

Vocabulary

Key words: annexation, unincorporated, service extension, special assessment, affordability threshold

Teacher overview

When a settlement outside a city limit asks for water service, the answer is rarely a simple yes or no. Cities routinely attach a condition: the area must agree to be annexed, which changes who pays city taxes, who votes in city elections, and who the city council answers to. This worksheet uses the fictional city of Marlstead and the fictional settlement of Pikeworth Hollow to work through both halves of that decision, the construction arithmetic and the civic bargain. The misconception worth naming before students start is that the monthly bill is the whole cost of getting on a public water system; in practice a household on a newly extended main often repays a share of the construction for years, through a special assessment or connection charge, and that repayment adds to what the household pays each year.

Annexation or Wells: The Pikeworth Hollow Water Extension — Grade 9 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

Pikeworth Hollow, the city of Marlstead, Kirtling County, and every figure below are fictional, written for this worksheet.

Pikeworth Hollow is an unincorporated settlement of 168 households in Kirtling County, just outside the Marlstead city limit. Every household uses a private well. Thirty-four of those wells have gone dry or failed a test in the last three years. Marlstead has enough treatment and storage capacity to serve the Hollow, and the city council has made an offer: the city will extend a water main to the Hollow only if the Hollow agrees to be annexed into the city.

Project and household data:

  • Length of new water main required: 2.4 miles. One mile equals 5,280 feet.
  • Construction cost: $175 per foot of main.
  • Households in Pikeworth Hollow: 168.
  • A state drinking water fund would pay 60 percent of construction cost if Kirtling County applies on the Hollow's behalf.
  • Each household would repay its remaining share in equal yearly payments over 20 years, with no interest.
  • Marlstead water service for the median Hollow household: $61 per month.
  • Median household income in Pikeworth Hollow: $54,000 per year.
  • Annexation would add city property tax, city voting rights, city trash collection, and city police coverage. Septic systems would stay in place, so no sewer bill would be added.
  • A widely used rule of thumb, built by adding two EPA benchmarks (2.5 percent for drinking water and 2 percent for wastewater), treats combined water and sewer costs above roughly 4.5 percent of household income as a high burden. EPA itself has no single official cutoff.
  1. Convert the 2.4 miles of new main to feet, using 5,280 feet per mile.
  2. At $175 per foot, what is the total construction cost of the extension?
  3. Divide the total construction cost evenly among the 168 households. What is the cost per household before any grant?
  4. The state fund would pay 60 percent of the construction cost. How many dollars would the grant cover?
  5. How many dollars would remain to be paid locally after the grant?
  6. Divide the remaining local cost evenly among the 168 households. What is the cost per household after the grant?
  7. Each household repays its remaining share in equal yearly payments over 20 years with no interest. What is one yearly payment?
  8. Marlstead water service would cost the median Hollow household $61 per month. What is that cost for one year?
  9. Add the yearly repayment from item 7 to the yearly water bill from item 8. What would the median household pay for water in one year?
  10. Median household income in the Hollow is $54,000. Your answer to item 9 is what percent of that income? Round to the nearest tenth of a percent.
  11. Compare your answer to item 10 with the 4.5 percent burden threshold. Is the Hollow's water cost above or below that threshold?
  12. Annexation would place Pikeworth Hollow inside the Marlstead city limit. Name one benefit Hollow residents would gain and one obligation they would take on, then explain why the city ties the water extension to annexation instead of simply selling water to the Hollow.
  13. Kirtling County could pay for the extension itself and leave the Hollow unincorporated. Give one reason the county might prefer that arrangement, and one reason a Marlstead resident might object to it.

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: 12,672 feet.
    Multiply 2.4 miles by 5,280 feet per mile.
  2. Answer: $2,217,600.
    Multiply 12,672 feet by $175 per foot.
  3. Answer: $13,200 per household.
    Divide $2,217,600 by the 168 households in the fictional settlement.
  4. Answer: $1,330,560.
    Multiply $2,217,600 by 0.60.
  5. Answer: $887,040.
    Subtract $1,330,560 from $2,217,600. Students may also multiply $2,217,600 by 0.40.
  6. Answer: $5,280 per household.
    Divide $887,040 by 168 households.
  7. Answer: $264 per year.
    Divide $5,280 by 20 years.
  8. Answer: $732 per year.
    Multiply $61 per month by 12 months.
  9. Answer: $996 per year.
    Add the $264 yearly repayment to the $732 yearly bill.
  10. Answer: 1.8 percent.
    Divide $996 by $54,000 to get 0.018444, then multiply by 100, which rounds to 1.8 percent.
  11. Answer: Below the threshold.
    At about 1.8 percent of median income, the Hollow's water cost sits well under the 4.5 percent rule-of-thumb line for a high burden. Students should note that this holds for the median household and that a household near the bottom of the income range in the fictional settlement could still land above it.
  12. Answer: Residents would gain a reliable treated supply, a vote in Marlstead elections, and city services such as trash collection and police coverage; they would take on city property tax and city ordinances, including rules about wells, animals, and building. The city ties the extension to annexation because the city's ratepayers and taxpayers would be paying for capacity, staff, and future repairs, and annexation puts the Hollow on the same footing as everyone else who funds that system. Annexation also gives the council authority over the land the new main runs through, which matters when the city later has to control development along the line. Accept other well-supported pairs.
  13. Answer: The county might prefer to pay because it keeps land-use and service authority over the Hollow and any revenue tied to unincorporated areas, and because the county can act without waiting for a city vote. A Marlstead resident might object that city ratepayers would then be selling water at cost to people who pay nothing toward the city's storage, treatment, and debt, and who cannot be held to city water restrictions during a shortage. Accept other well-supported reasons on both sides.

Differentiation

Support

Give students a completed conversion ladder for item 1, with miles, feet, and dollars labeled at each rung, and work one parallel example on the board using a different fictional length such as 1.5 miles. Provide items 3, 6, and 7 on a separate half sheet with the division set up and only the numbers missing.

Extension

Ask students to find the largest per-foot construction cost the fictional project could carry and still keep the median household under 3.0 percent of income, holding the grant share and the 20-year repayment constant. Students must show the inequality they solved and state what the answer implies about how much cost a grant program has to absorb.

ELL supports

Pre-teach "annexation," "unincorporated," "special assessment," and "burden threshold" with a simple two-circle diagram showing the fictional city limit before and after annexation. Provide sentence frames for items 12 and 13: "Residents would gain ___, and they would have to ___," and "The county might prefer this because ___, but a city resident could object that ___."

Extensions

Students look up how their own state defines annexation and whether a city there may require it as a condition of utility service, using only the state municipal league's published explainer or the state code section itself, and compare that rule to the offer the fictional city of Marlstead made. A second option is to write the two-page recommendation the Kirtling County administrator would deliver to the county board, stating the calculated per-household cost, the affordability comparison, and a recommended position on annexation.