Materials & Prep
Prepare one handout or projected slide containing the 4-by-5 voter grid and the two district plans described below. Students need paper for an evidence-based claim and a brief closing response. No special materials are needed beyond the usual classroom setup.
Opening
Display this voter grid. A represents a vote for Candidate A and B represents a vote for Candidate B.
A A A B B
A A B B B
A B A B B
A B B B B
Ask“Without changing any votes, which candidate receives more votes overall? How many?” Students count and predict. The result is 8 votes for A and 12 for B. Then say that voters do not cast ballots for individual candidates directly in one at-large election. They are grouped into four equal-population districts, and the candidate with more votes in each district wins that district’s seat. Students should notice that the same 20 votes can produce a different number of seats depending on how the grid is grouped. Do not introduce the terms yet. This succeeds using counting and the familiar idea that the plurality winner wins a contest.
Direct instruction
ConnectExplain that district boundaries determine which voters are counted together. A computer can calculate population, display maps, and enforce boundaries, but people choose the criteria and constraints that the computer applies. The shape matters because it changes the composition of each district, not because shape itself has political power.
Worked exampleFirst show Plan 1, with each horizontal row as one district. The district results are 3–2 for A, 2–3 for B, 2–3 for B, and 1–4 for B. A wins 1 of 4 seats; B wins 3 of 4. Then show Plan 2:
D1 D1 D1 D3 D3
D1 D1 D2 D3 D3
D2 D2 D2 D2 D3
D2 D4 D4 D4 D4
Count aloud: D1 gives A 5 votes and B 0, so A wins. D2 gives A 3 and B 2, so A wins. D3 gives A 0 and B 5, and D4 gives A 0 and B 5, so B wins both. The votes are still 8 for A and 12 for B, but A now wins 2 seats and B wins 2. Emphasize the common error: students may compare the statewide totals and conclude that B must win three or four seats. The relevant comparison is the vote total inside each district.
DefineRedistricting is changing district boundaries. Packing concentrates a group’s voters into a small number of districts. Cracking spreads them across several districts so they are outvoted. A fair analysis must also consider equal population, contiguity, geographic communities, legal requirements, and whose interests shaped the map.
Check for understandingStudents answer on paper, “What changed between Plan 1 and Plan 2, and what did not?” Require the terms boundaries, district composition, and votes. Sample response: “The boundaries and district composition changed; the voters and their votes did not.”
Guided practice
Have students work in pairs with the two plans. They complete a four-row table listing each district, A votes, B votes, and the winner for both plans. Circulate and ask, “Which exact voters are now counted together?” and “Why does the statewide total not determine the seat total?”
ConfrontAsk students to commit to this claim before discussion: “If the same voters cast the same ballots, the election outcome cannot change.” Pairs must use Plan 1 and Plan 2 to accept, reject, or revise the claim. Discuss why a computer-generated map is not automatically neutral. The computer may optimize compactness or population equality, but the choice of data, constraints, and objective remains consequential.
ScaffoldProvide the sentence frame, “Plan produces seats for A because Districts and each contain more votes than votes.” Students who need access may first circle A and B in each district before recording totals.
Independent work or discussion
Students write a short evidence-based response: “Explain how boundary placement can change election outcomes even when no votes change. Use both plans, include the seat totals, and distinguish vote share from seat share.” Require one paragraph of at least five sentences and two specific numerical references.
ExtensionStudents add a third plan or propose a rule for drawing districts that would make the outcome more representative. They must state the rule, show how it would affect the given grid, and address one tradeoff, such as compactness versus preserving a community or proportional representation versus single-member districts.
DiscussInvite two students with different proposed rules to defend them. Ask, “Should a map be judged only by its result, or also by the process and criteria used to produce it?” Require students to identify evidence and acknowledge a competing consideration.
Closing
Exit ticket“Using the 20-voter example, explain in two or three sentences how the same votes produced different seat outcomes. State the result under both plans and identify the mechanism that caused the change.” Look for the complete chain: boundaries changed which voters were grouped together, district winners changed, and therefore the number of seats changed despite identical votes.