Drummhill Well 2: Criteria, Constraints, and Filter Sizing

Hook (5 min): Project two photographs or descriptions: a white sink with an orange-brown stain around the drain, and the same fixture after treatment. Tell the class that the fictional Drummhill district has a new well with iron at 2.4 mg/L and manganese at 0.35 mg/L, and that no rule requires the district to treat for either one on health grounds. If students ask about health, note that manganese at 0.35 mg/L is slightly above EPA's 0.3 mg/L lifetime health advisory, which is guidance rather than an enforceable rule. Ask why a utility would spend money anyway, and collect answers on the board without ranking them.

Direct instruction (12 min): Define a criterion as a measurable statement of what the design must achieve and a constraint as a boundary the design may not cross. Write four statements about the Drummhill project on the board and sort them with the class: finished water at or below 0.3 mg/L iron, finished water at or below 0.05 mg/L manganese, the filter building must fit the existing 40-foot by 30-foot pad, and the project must be in service before the next summer peak. Then introduce loading rate as flow divided by filter surface area, and note that conventional filters typically run between 2 and 6 gallons per minute per square foot of surface. Model the formula on numbers that do not appear on the handout: a plant filtering 200 gpm through 50 square feet runs at 4.0 gpm per square foot.

Guided practice (12 min): Distribute the handout and work questions 1 and 2 together. Make the loading-rate rearrangement explicit on the board, showing that area equals flow divided by loading rate, and check that students write the units alongside each number. Ask the class to predict, before computing question 4, whether three vessels will be enough, then let the arithmetic settle it.

Independent practice (21 min): Students complete questions 3 through 10 in pairs. Circulate and press pairs on question 5 to explain why the actual loading rate came out lower than the design value rather than higher. For questions 6 and 7, check that pairs are dividing the amount removed by the raw-water concentration and not by the finished-water target.

Closure and formative check (5 min): Collect the handouts and read question 10 only. If fewer than three quarters of the class identified the pad size as the constraint, open the next session by listing five project statements and asking students to sort them with their thumbs before any discussion. Close by asking two pairs to read the criterion they would defend hardest if the budget were cut.