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Lesson plan Grade 10 Math

Highgrove Plant Alum Dose: Feed Rate and Chemical Cost

A grade 10 math lesson using the pounds formula to find a fictional plant's alum feed rate in pounds per day, then its daily and yearly chemical cost.

Objectives

  1. Students will calculate a coagulant feed rate in pounds per day using the pounds formula.
  2. Students will find the daily and yearly chemical cost and the savings from a lower dose.

Vocabulary

Alum
Alum is the most common chemical that water plants add to make tiny dirt particles clump together. A pinch of alum can help a whole jar of muddy water turn clear.

Also: coagulant, dose, pounds formula

Teacher overview

Drinking-water plants add a coagulant such as alum to make small particles clump so they settle out. An operator runs a jar test to find the lowest dose that still works, because every extra milligram per liter is chemical the plant pays for. This lesson uses a fictional plant at Highgrove and the pounds formula, feed (lbs/day) = dose (mg/L) x flow (MGD) x 8.34, to price a dose. A common misconception this lesson addresses is that a higher dose is always safer; overdosing wastes money, lowers pH, and makes more sludge to handle.

Procedure

Hook (5 min): Show two jars that started with the same cloudy water, one that has settled clear and one still cloudy, and ask what an operator adds to make particles settle. Introduce alum and the idea that dose costs money.

Direct instruction (12 min): Write the pounds formula on the board: feed (lbs/day) = dose (mg/L) x flow (MGD) x 8.34. Explain that 8.34 is the weight of a gallon of water in pounds, and that daily cost is feed times the price per pound.

Guided modeling (13 min): Model with a fictional plant treating 3.0 MGD at a 30 mg/L alum dose. Together, find the feed of 30 x 3.0 x 8.34 = 750.6 pounds per day, labeling each unit. This worked example is for instruction only; students do not turn it in.

Independent practice (20 min): Students complete the Student Handout for the Highgrove plant. Circulate and check item 1's feed rate before students continue, since items 2 and 3 build on it.

Closure and formative check (5 min): On an index card, students write one sentence explaining why a lower dose that still clears the water saves money. Collect and scan for the idea that unused chemical is wasted cost.

Highgrove Plant Alum Dose: Feed Rate and Chemical Cost — Grade 10 Math
Name: ____________________________ Date: ______________

Student Handout

The Highgrove Water Treatment Plant is a fictional plant, and its numbers are set for this handout. Use feed (lbs/day) = dose (mg/L) x flow (MGD) x 8.34, and show your work.

Plant data:

  • Flow treated: 6.0 MGD
  • Alum dose from the jar test: 25 mg/L
  • Alum price: $0.30 per pound
  1. Find the alum feed rate in pounds per day at the 25 mg/L dose.
  2. Find the daily alum cost at $0.30 per pound.
  3. Find the yearly alum cost. Use 365 days.
  4. Flow rises to 8.0 MGD at the same 25 mg/L dose. Find the new feed rate in pounds per day.
  5. A second jar test finds 20 mg/L still works. At 6.0 MGD, find the feed rate at 20 mg/L.
  6. Find the pounds of alum saved per day by dropping from 25 mg/L to 20 mg/L at 6.0 MGD.
  7. Find the daily cost savings from that lower dose, at $0.30 per pound.
  8. Explain why finding the lowest effective dose matters, beyond just saving chemical money.

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: 1,251 lbs/day.
    25 mg/L x 6.0 MGD x 8.34 = 150 x 8.34 = 1,251 pounds per day.
  2. Answer: $375.30.
    1,251 pounds per day x $0.30 per pound = $375.30 per day.
  3. Answer: $136,985.
    $375.30 per day x 365 days = $136,984.50, which rounds to about $136,985 per year.
  4. Answer: 1,668 lbs/day.
    25 mg/L x 8.0 MGD x 8.34 = 200 x 8.34 = 1,668 pounds per day.
  5. Answer: 1,001 lbs/day.
    20 mg/L x 6.0 MGD x 8.34 = 120 x 8.34 = 1,000.8, which rounds to 1,001 pounds per day.
  6. Answer: 250 lbs/day.
    1,251 - 1,000.8 = 250.2, or about 250 pounds saved per day. This also equals 5 mg/L x 6.0 x 8.34 = 250.2.
  7. Answer: about $75 per day.
    250.2 pounds x $0.30 per pound = $75.06, or about $75 saved per day.
  8. Answer: Overdosing lowers pH and makes more sludge, so the lowest effective dose protects quality too.
    Extra alum beyond what the water needs drops the pH and increases the sludge the plant must remove and dispose of, so the right dose saves money and keeps the treated water in range.

Differentiation

Support

Provide the pounds formula and item 1 already set up as 25 x 6.0 x 8.34, so students focus on the arithmetic and the later comparisons. Allow calculators and a units checklist.

Extension

Have students find the yearly savings from the 20 mg/L dose at the plant's 6.0 MGD flow, then decide whether that saving would justify a fictional $2,000 upgrade to the jar-testing equipment, and explain their reasoning.

ELL supports

Pre-teach "coagulant," "dose," and "feed rate" with a picture of particles clumping and settling after alum is added. Provide a sentence frame for item 8: "The lowest effective dose matters because ___."