Should Cindermere and Nettlefold Share One Sewer Plant?

Hook (5 min): Ask students what a town does with the water that goes down its drains, and where that water goes after it leaves the house. Take three or four answers, then tell the class that both fictional towns in today's problem must rebuild the plant that handles it, and that neither town can afford the job comfortably on its own.

Framing the decision (10 min): Project the cost table from the handout and read it with the class. Explain the two options plainly. Under the first option each town builds its own plant and runs it alone. Under the second option the two towns form a joint authority, build one plant, and share both the cost and the control. Point out that the shared plant costs less than the two separate plants together because one set of buildings, pumps, and staff serves both towns.

Modeling a cost share (10 min): Work one example on the board that does not appear on the handout. Suppose two fictional villages build a $10 million plant together, one with 3,000 households and the other with 7,000. Show that the first village has 3,000 of the 10,000 households, or 30 percent, so it pays 0.30 times $10 million, which is $3 million. Show the second village's share the same way, and check that the two shares add back to $10 million. Ask students what would change if the villages split by gallons of wastewater instead of by households.

Independent work on the handout (20 min): Students complete the seven handout items, showing their work. Circulate and watch for two errors in particular: dividing by the wrong total when finding a percent, and forgetting to convert a percent to a decimal before multiplying. Encourage students to check each pair of shares by adding them back to the full cost.

Formative check (5 min): Ask every student to hold up one finger for the household split and two fingers for the flow split, then call on three students to name the measure their choice uses and one town it favors. Continue to the debrief only if at least three-quarters of the class can name the measure behind their vote; otherwise rework item 4 with the whole class first.

Debrief and process comparison (5 min): Close by asking students to compare the two ways this decision could be made. Draw out that two separate town meetings let each town decide alone but cannot produce a shared plant, while a joint authority board can act for both towns yet takes some control away from each. Note that a written intergovernmental agreement is what usually settles the split before construction starts.