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Worksheet Grade 9 Social Studies & Civics

One Acre, One Vote in the Pennyfold Irrigation District

A grade 9 worksheet comparing acreage-weighted and per-owner voting in a fictional irrigation district, with vote shares, a majority inequality, and a vote cap.

Objectives

  1. Students will calculate vote shares under acreage-weighted and per-owner voting rules.
  2. Students will write and solve an inequality for the acreage needed to pass a district measure.
  3. Students will evaluate the argument that owners who pay by the acre should vote by the acre.

Vocabulary

Irrigation district
A local organization formed by farmers to bring water to their fields. It runs the canals, sets delivery schedules, and charges its members for the service.

Also: assessment, acreage-weighted vote, majority, vote cap

Teacher overview

Many irrigation districts do not run on one person, one vote. They weight each landowner's ballot by the acres that owner irrigates, on the reasoning that assessments are charged by the acre and the largest payers carry the largest risk. This worksheet uses the fictional Pennyfold Irrigation District on the Yarrowmede River to make that rule concrete by having students calculate the same district's decisions twice, once under each voting rule. The misconception worth correcting is that a landowner with a large share of the acreage automatically controls the district; a large owner in this scenario holds under a fifth of the votes and still needs partners, which is a more accurate picture of how these boards actually work.

One Acre, One Vote in the Pennyfold Irrigation District — Grade 9 Social Studies & Civics
Name: ____________________________ Date: ______________

Student Worksheet

The Pennyfold Irrigation District is fictional, invented for this worksheet, and so is every figure in it. The district was created in 1923 to divide water from the Yarrowmede River among the farms of one valley. It covers 28,000 irrigated acres held by 255 landowners, listed in the table below. Under the district's founding rule, each landowner casts one vote per acre owned, and a measure passes with more than half of the district's acre-votes.

Owner group Number of owners Total acres
Ridgeline Farms (one company) 1 5,400
Large family farms 6 7,200
Mid-size farms 22 6,600
Small farms 95 4,750
Orchard smallholders 130 2,600
Town of Pennyfold parcels 1 1,450
  1. Under the one acre, one vote rule, what percent of the district's 28,000 acre-votes does Ridgeline Farms hold with 5,400 acres? Round to the nearest tenth of a percent.
  2. Suppose the district switched to one owner, one vote. What percent of the district's 255 votes would Ridgeline Farms hold? Round to the nearest hundredth of a percent.
  3. Under the one acre, one vote rule, what percent of the 28,000 acre-votes do the 130 orchard smallholders hold together with 2,600 acres? Round to the nearest tenth of a percent.
  4. Under one owner, one vote, what percent of the 255 votes would those 130 orchard owners hold? Round to the nearest tenth of a percent.
  5. Ridgeline Farms and the six large family farms decide to vote together. How many acres do they control in total?
  6. Half of the district's acre-votes is 14,000. How many additional acre-votes would bring the group in item 5 to exactly half?
  7. Let a be the number of acres held by mid-size farm owners who join the group from item 5. Write an inequality stating that the combined acreage is more than half of 28,000, then solve the inequality for a.
  8. The 95 small farm owners and the 130 orchard smallholders oppose a measure together. How many acres do they control in total?
  9. Compare your answer in item 8 to the 14,000 acres that make up half the district. How many acres short of half are they?
  10. The small farm and orchard groups together contain 225 of the district's 255 landowners. What percent of the landowners is that? Round to the nearest tenth of a percent.
  11. Compare your answers to items 8 and 10. In two or three sentences, explain what the comparison shows about how much the choice of voting rule matters in the Pennyfold district.
  12. The founders chose the acreage rule in 1923 because assessments were charged by the acre. Give one argument that supports this reasoning and one argument against it.
  13. The district is considering a cap so that no single owner may cast more than 10 percent of the total acre-votes. How many acre-votes would Ridgeline Farms lose under that cap?

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: 19.3 percent.
    Divide 5,400 acres by the district's 28,000 acres to get 0.1929, which is 19.29 percent and rounds to 19.3 percent.
  2. Answer: 0.39 percent.
    Ridgeline Farms is one owner out of 255, so divide 1 by 255 to get 0.00392, which is 0.392 percent and rounds to 0.39 percent.
  3. Answer: 9.3 percent.
    Divide 2,600 acres by 28,000 acres to get 0.0929, which is 9.29 percent and rounds to 9.3 percent.
  4. Answer: 51.0 percent.
    Divide 130 owners by 255 owners to get 0.5098, which is 50.98 percent and rounds to 51.0 percent.
  5. Answer: 12,600 acres.
    Add Ridgeline Farms' 5,400 acres to the large family farms' 7,200 acres, which gives 12,600 acres of the fictional district.
  6. Answer: 1,400 acre-votes.
    Subtract the group's 12,600 acres from 14,000, which leaves 1,400. Reaching a majority requires more than that, because the rule says more than half.
  7. Answer: 12,600 + a > 14,000, so a > 1,400 acres.
    The inequality is 12,600 plus a is greater than 14,000. Subtracting 12,600 from both sides gives a greater than 1,400, so any acreage above 1,400 joining the group produces a majority, and the 22 mid-size farms hold 6,600 acres, which is far more than enough.
  8. Answer: 7,350 acres.
    Add the small farms' 4,750 acres to the orchard smallholders' 2,600 acres, which gives 7,350 acres.
  9. Answer: 6,650 acres.
    Subtract 7,350 from 14,000, which leaves the two groups 6,650 acres short of half the district.
  10. Answer: 88.2 percent.
    Divide 225 owners by 255 owners to get 0.8824, which is 88.24 percent and rounds to 88.2 percent.
  11. Answer: The rule decides the outcome. Under one acre, one vote the two groups hold 7,350 acres and cannot reach half, so they lose. Under one owner, one vote the same people are 88.2 percent of the landowners and would win easily, which means the district's founding choice, not the number of people who agree, settles most contested measures in the fictional Pennyfold district.
  12. Answer: In favor, the owners who pay the largest assessments carry the largest financial risk when the district borrows for a canal repair, so tying votes to acres ties control to who pays. Against, water in the fictional valley supports households and a town, not only acres, and a rule that gives 130 orchard families less weight than one company makes it hard for them to protect small holdings. Accept other reasonable arguments on each side.
  13. Answer: 2,600 acre-votes.
    Ten percent of 28,000 acre-votes is 2,800. Ridgeline Farms currently casts 5,400, so the cap would remove 5,400 minus 2,800, which is 2,600 acre-votes.

Differentiation

Support

Give students the table for the fictional Pennyfold district with two added percent columns partly filled, so items 1 through 4 become a matter of completing a pattern rather than setting up each division. Provide a number line marked at 14,000 acres for items 5 through 7, and allow calculators throughout.

Extension

Ask students to find the smallest number of the fictional district's 255 landowners who could pass a measure under the acreage rule, listing which groups they would come from. Then have them state the same number under one owner, one vote and explain why the two answers differ so sharply.

ELL supports

Pre-teach "acre," "assessment," "majority," and "cap" using a diagram of the fictional Pennyfold district drawn as a large rectangle divided into six blocks sized by acreage, with owner counts written inside. Provide sentence frames for items 11 and 12: "Under the acre rule the small owners hold ___, but they are ___ of the owners," and "The founders were right because ___, and wrong because ___."

Extensions

Students compare the fictional Pennyfold rule to the voting rule used by a real special district near them, such as a soil and water conservation district or a levee district, using only that district's published bylaws or state statute, and write one paragraph on which rule their own district uses and why. A second option is to redesign the Pennyfold ballot so that half the board seats are elected by acreage and half by landowner, then predict which measures would still pass.