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Lesson plan Grade 10 Health & Consumer Science

Carbon Pitcher or Reverse Osmosis? A Home Filter Cost Decision

A grade 10 consumer lesson comparing a fictional home's carbon pitcher and reverse-osmosis costs, the break-even point against bottled water, and a filtered PFAS result.

Objectives

  1. Students will compare two point-of-use treatment options on first-year cost and annual cost.
  2. Students will write and solve an equation for the break-even point between a filter and bottled water.

Vocabulary

Reverse osmosis
Reverse osmosis cleans water by pushing it through a membrane with holes so tiny that salt and most other dissolved things cannot fit through. It can even turn seawater into fresh water.
Activated carbon
Activated carbon is a special charcoal full of microscopic holes that grab and hold chemicals as water flows past. It is the same material used in many home water filter pitchers.
Parts per trillion
A unit for measuring extremely small amounts of a chemical in water. PFAS limits are set in parts per trillion because these chemicals matter even in tiny doses.

Also: point-of-use treatment, break-even

Teacher overview

Families worried about contaminants at the tap often weigh a countertop carbon pitcher against an under-sink reverse-osmosis system, and both compete with the habit of simply buying bottled water. This lesson has students compare two fictional certified options on upfront cost and yearly replacement cost, check whether a certified filter brings a PFAS reading under the limit, then write an equation to find when the reverse-osmosis system pays for itself against bottled water. A common misconception this lesson addresses is that the cheaper sticker price is always the cheaper choice; the replacement and per-gallon costs, and the break-even point, tell a fuller story.

Procedure

Hook (5 min): Ask students to guess how much a family that drinks and cooks with bottled water spends in a year. Record a few guesses, then reveal that they will calculate it exactly for a fictional household.

Direct instruction (12 min): Introduce point-of-use treatment: activated carbon reduces many contaminants, and some carbon filters are certified to reduce lead or PFAS, while reverse osmosis pushes water through a membrane that removes a wider range of dissolved substances, including PFAS and lead. Model how a first-year cost combines an upfront price with one year of replacements, using an instructor example distinct from the handout numbers. Then preview the break-even idea, where two running costs meet at the month when cumulative spending is equal.

Guided practice (13 min): With the class, set up a break-even equation for a sample system and a sample bottled cost, solving for the number of months. Emphasize labeling each term with its unit and checking that the answer is a sensible number of months.

Independent practice (20 min): Students complete the Student Handout, comparing the fictional Whitfield household's carbon pitcher and reverse-osmosis options, computing annual bottled cost, solving the break-even equation, and checking a PFAS result against the 4.0 ppt limit.

Closure and exit ticket (5 min): Students answer on a card: "Which option would you recommend to the Whitfield household? Name the single number from your work that most supports your choice." Collect and scan for a justified answer.

Carbon Pitcher or Reverse Osmosis? A Home Filter Cost Decision — Grade 10 Health & Consumer Science
Name: ____________________________ Date: ______________

Student Handout

All prices and readings below are invented for this fictional scenario. The maximum contaminant level for PFOA is 4.0 ppt.

The fictional Whitfield household is choosing how to treat its drinking and cooking water. Use these figures:

  • Carbon pitcher: $45 upfront, plus $48 per year in replacement cartridges.
  • Reverse-osmosis system: $220 upfront, plus $60 per year in replacement filters.
  • Bottled water currently costs $1.20 per gallon.
  • The household uses 3 gallons of drinking and cooking water per day. Use 365 days per year.
  • A recent tap sample measured PFOA at 12 ppt.
  1. What is the first-year total cost of the carbon pitcher option, upfront plus one year of cartridges?
  2. What is the first-year total cost of the reverse-osmosis option, upfront plus one year of filters?
  3. How many gallons of drinking and cooking water does the household use in one year at 3 gallons per day?
  4. What is the bottled-water cost for one year, at $1.20 per gallon for that many gallons?
  5. In the first year, how much less does the reverse-osmosis option cost than buying bottled water?
  6. The reverse-osmosis cost after m months is (220 + 5m) dollars, and the bottled-water cost after m months is (109.5m) dollars. Write the equation setting them equal and solve for m, the break-even month.
  7. A certified filter removes at least 90 percent of PFOA. Applied to the 12 ppt reading, what is the highest level that could remain?
  8. After that reduction, is the treated water at or below the 4.0 ppt MCL, and by how much?

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

All values below refer to the fictional Whitfield household scenario.

  1. Answer: $93.
    Carbon pitcher first-year cost is $45 upfront + $48 in cartridges = $93.
  2. Answer: $280.
    Reverse-osmosis first-year cost is $220 upfront + $60 in filters = $280.
  3. Answer: 1,095 gallons.
    At 3 gallons per day for 365 days: 3 x 365 = 1,095 gallons per year.
  4. Answer: $1,314.
    Bottled water for 1,095 gallons at $1.20 per gallon: 1,095 x 1.20 = $1,314.
  5. Answer: $1,034.
    The reverse-osmosis first-year cost is $280, so it costs $1,314 - $280 = $1,034 less than bottled water in year one.
  6. Answer: about 2.1 months.
    Set 220 + 5m = 109.5m. Then 220 = 104.5m, so m = 220 / 104.5, or about 2.1 months, the point where the reverse-osmosis system has cost the same as bottled water.
  7. Answer: 1.2 ppt.
    Removing at least 90 percent leaves at most 10 percent: 12 x 0.10 = 1.2 ppt remaining.
  8. Answer: 2.8 ppt below.
    The 1.2 ppt treated level is at or below the 4.0 ppt MCL, clearing it by 4.0 - 1.2 = 2.8 ppt.

Differentiation

Support

Give students a two-column table already labeled with upfront cost, yearly replacement, and first-year total, so they organize the two options before comparing. Pre-solve the guided break-even example on the handout as a reference for question 6.

Extension

Ask students to decide whether the carbon pitcher (45 + 4m dollars) and the reverse-osmosis system (220 + 5m dollars) ever reach the same cumulative cost after m months, to show the algebra, and to explain what the result means for a family choosing between them.

ELL supports

Pre-teach "upfront," "replacement," "break-even," and "membrane" with simple visuals. Allow the exit ticket to be completed with a short phrase, and provide a sentence frame: "I would choose ___ because ___."

Extensions

Have students look up two real certified pitchers or systems using published manufacturer specifications, list their upfront and replacement costs without endorsing a brand, and redo the break-even calculation with those figures to test whether the fictional example held up.