Lesson plan Grade 9 Math

Ravensford Chlorine Dosing: The Pounds Formula in Action

A 45-minute grade 9 lesson at the fictional Ravensford plant, using the pounds formula and demand-plus-residual to find a chlorine dose and daily feed rate.

Objectives

  1. Students will calculate chlorine feed in pounds per day using the pounds formula.
  2. Students will find chlorine demand as the dose minus the measured residual.
  3. Students will solve for the dose that leaves a target residual in the water.

Vocabulary

Disinfection
Disinfection is the step that kills or disables germs in water so it is safe to drink. Water plants usually disinfect with chlorine, ultraviolet light, or ozone.

Also: chlorine demand, dose, residual, pounds formula, MRDL

Teacher overview

The fictional Ravensford plant adds chlorine to kill germs, but part of the chlorine is used up reacting with material in the water before any is left to protect the water downstream. Operators plan for this with two ideas: the pounds formula for how much chlorine to feed, and chlorine demand, the part the dose loses before a residual remains. This lesson builds both. A common misconception is treating the residual as the whole dose; the dose must cover the demand first and still leave the residual behind.

Procedure

Hook (5 min): Ask students why adding "just enough" chlorine to kill germs at the plant might leave none at the far end of town. Take a few ideas, then introduce chlorine demand as the chlorine used up along the way.

Direct instruction (12 min): State the two tools for the fictional plant: feed in pounds per day = dose in mg/L, times flow in MGD, times 8.34, and chlorine demand = dose minus residual. Model one worked example on the board: at a 4 MGD flow and a 2.5 mg/L dose, feed = 2.5 times 4 times 8.34 = 83.4 pounds per day. This example is teacher-modeled only; students solve different numbers on the handout.

Guided practice (11 min): With a partner, students work handout items 1 through 3, computing a feed, finding a demand, and solving for a dose that leaves a target residual. Circulate and confirm they add demand and residual to get the dose.

Independent practice (12 min): Students complete handout items 4 through 7 on their own: recomputing feed at the new dose, scaling feed to a higher flow, checking the residual against the chlorine MRDL, and explaining why a residual is kept.

Closure and formative check (5 min): As an exit ticket, each student answers on a card: if demand is 1.0 mg/L and the operator wants a 0.5 mg/L residual, what dose is needed? Collect and scan for 1.0 plus 0.5 = 1.5 mg/L. If more than a third miss it, reteach demand plus residual before the next class.

Answer Key

  1. Answer: 50.04 lb/day. 2.0 mg/L times 3 MGD times 8.34 = 50.04 pounds per day.
  2. Answer: 1.2 mg/L. Demand = dose minus residual = 2.0 minus 0.8 = 1.2 mg/L.
  3. Answer: 2.7 mg/L. Dose = demand plus residual = 1.2 plus 1.5 = 2.7 mg/L.
  4. Answer: 67.55 lb/day. 2.7 mg/L times 3 MGD times 8.34 = 67.554, about 67.55 pounds per day.
  5. Answer: 112.59 lb/day. 2.7 mg/L times 5 MGD times 8.34 = 112.59 pounds per day.
  6. Answer: Yes. The 1.5 mg/L residual is below the 4.0 mg/L MRDL, which limits the chlorine remaining in the water rather than the dose.
  7. Answer: The demand is chlorine used up in the water, so a dose that only meets demand leaves nothing behind. A residual keeps protecting the water as it travels through the distribution system to the last home.

Differentiation

Support

Give students the two rules on a reference card with the 8.34 constant and the flow already filled in for item 1, so they multiply one step at a time. Provide the demand-plus-residual sum set up for item 3.

Extension

Ask students to find the dose that would leave a 2.0 mg/L residual at the item-2 demand, then the feed that dose needs at 4 MGD, and to check whether that residual still stays within the MRDL.

ELL supports

Pre-teach "dose," "demand," and "residual" with a bar picture: a full bar for the dose, a used-up piece for demand, and the leftover piece for residual. Provide a sentence frame for item 7: "A residual keeps the water safe as it ___ to homes."