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Lesson plan Grade 12 Math

Cresthaven Water Plant: CT Values and Disinfection Targets

A 55-minute grade 12 lesson where students compute CT values from contact time and chlorine residual at a fictional water plant.

Objectives

  1. Students will compute a CT value from a clearwell contact time and a chlorine residual.
  2. Students will decide whether a plant's CT meets a required disinfection target and stays under the chlorine MRDL.

Vocabulary

CT value
CT value is a way operators check that water has been disinfected long enough. It is found by multiplying how much disinfectant is in the water by how many minutes the water has been in contact with it.
Chlorine residual
Chlorine residual is the small amount of chlorine still left in the water after it leaves the treatment plant. It keeps protecting the water from germs all the way to your faucet.

Also: contact time, MRDL

Teacher overview

Cresthaven Water Plant is a fictional plant that disinfects with chlorine before sending water into distribution. Operators measure disinfection with a CT value, the product of the chlorine residual and the contact time the water spends in the clearwell. This lesson has students find contact time from flow and volume, multiply it by residual to get CT, and compare that CT to a required target while keeping the residual under the chlorine MRDL. A common misconception is that a steady chlorine residual guarantees steady disinfection; if flow rises and contact time falls, CT can drop even when the residual is unchanged, which the handout is built to reveal.

Procedure

Hook (5 min): Ask students how a plant can prove its water is disinfected before anyone drinks it. Collect ideas, then introduce the CT value as the number regulators actually use. Note that Cresthaven is a fictional plant used to make the math concrete.

Direct instruction (12 min): Define the two inputs. Contact time T is the clearwell volume divided by the flow, and residual C is the chlorine concentration leaving the clearwell. Write the relationship CT = C x T, with C in mg/L and T in minutes. Explain that a required CT target depends on temperature and the pathogen being controlled, and that the chlorine residual must stay under the MRDL of 4.0 mg/L.

Worked example (10 min): Model one full chain with numbers different from the handout so students see the method rather than copy answers. Use these teacher-modeled steps:

  • Convert a flow of 3.0 MGD to gpm: 3.0 x 694 = 2,082 gpm.
  • Divide a clearwell volume of 208,200 gallons by that flow: 208,200 / 2,082 = 100 minutes of contact time.
  • Multiply by a residual of 1.0 mg/L: CT = 1.0 x 100 = 100. Compare to a sample target of 90 and confirm it passes.

Student Handout practice (20 min): Students work the numbered handout questions in pairs, then check with another pair. Circulate and watch for the error of multiplying residual by flow instead of by contact time.

Closure and formative check (8 min): As an exit check, students answer aloud or on a card: "If flow rises and the residual stays the same, does CT go up or down, and why?" A correct response names that higher flow shortens contact time, so CT falls. Treat fewer than four out of five correct as a signal to reteach contact time before the next class.

Cresthaven Water Plant: CT Values and Disinfection Targets — Grade 12 Math
Name: ____________________________ Date: ______________

Student Handout

Cresthaven Water Plant is a fictional plant. Its clearwell holds an effective contact volume of 138,800 gallons. Use these relationships: 1 MGD = 694 gpm; contact time T (minutes) = volume (gallons) / flow (gpm); CT = residual (mg/L) x T (minutes); the chlorine MRDL is 4.0 mg/L.

  1. Convert the plant flow of 2.0 MGD to gallons per minute.
  2. Find the contact time in minutes, dividing the 138,800-gallon volume by your flow from question 1.
  3. The chlorine residual leaving the clearwell is 1.2 mg/L. Find the CT value.
  4. The required CT target at today's temperature is 104. Does the plant's CT meet it?
  5. The chlorine MRDL is 4.0 mg/L. By how much is the 1.2 mg/L residual below the MRDL?
  6. In cold weather the required CT rises to 150. At the same contact time from question 2, what residual, in mg/L, would reach that CT?
  7. Is the residual you found in question 6 still below the 4.0 mg/L MRDL?
  8. Demand rises and the flow increases to 2.5 MGD. Find the new contact time in minutes.
  9. At the higher flow and a 1.2 mg/L residual, find the new CT and state whether it still meets the target of 104.

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: 1,388 gpm.
    2.0 MGD x 694 gpm per MGD = 1,388 gallons per minute.

  2. Answer: 100 minutes.
    T = 138,800 gallons / 1,388 gpm = 100 minutes of contact time.

  3. Answer: 120 CT.
    CT = residual x contact time = 1.2 x 100 = 120.

  4. Answer: Yes.
    The plant's CT of 120 is at or above the required target of 104, so disinfection meets the requirement.

  5. Answer: 2.8 mg/L.
    The MRDL is 4.0 mg/L and the residual is 1.2 mg/L, so 4.0 - 1.2 = 2.8 mg/L below the limit.

  6. Answer: 1.5 mg/L.
    Solve C x 100 = 150, so C = 150 / 100 = 1.5 mg/L.

  7. Answer: Yes.
    The needed 1.5 mg/L residual is still below the 4.0 mg/L MRDL, so the plant can meet the higher target with room to spare.

  8. Answer: 80 minutes.
    At 2.5 MGD the flow is 2.5 x 694 = 1,735 gpm, so T = 138,800 / 1,735 = 80 minutes.

  9. Answer: 96 CT.
    CT = 1.2 x 80 = 96, which is below the target of 104, so the plant no longer meets it at the higher flow even though the residual is unchanged.

Differentiation

Support

Give students the contact-time and CT relationships on a labeled card, and pre-convert the flow in question 1 so they can begin from a known gpm value. Pair students so a stronger calculator user checks each step.

Extension

Ask students to find the flow, in MGD, at which the plant's CT would fall exactly to the 104 target while the residual stays unchanged, and to describe what an operator should do as flow approaches that point.

ELL supports

Provide a diagram of water moving through a clearwell with the residual measured at the outlet, glossing "contact time," "residual," "CT value," and "MRDL." Offer a sentence frame for the closure question: "When flow rises, contact time ___, so CT ___."

Extensions

Have students read the disinfection section of a local utility's annual water-quality report, identify the disinfectant and the reported residual, and discuss how the utility documents that it met its CT requirement.