Lesson plan Grade 9 Health & Consumer Science

Should the Sattlers Buy a Reverse-Osmosis System? A Cost Lesson

Grade 9 consumer-science lesson comparing the per-gallon cost of a pitcher filter, an under-sink reverse-osmosis system, and bottled water for a family.

Grade: Grade 9
Subject: Health & Consumer Science
Material: Lesson plan
Time: 45 min
Prep: No prep
Materials: Printed Student Handout, Calculators

Standards

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Students carry dollars and gallons through a multistep cost-per-gallon calculation for each filtration option, keeping the units consistent so the three prices can be compared fairly.

All materials for HSN-Q.A.1 →

D2.Eco.2.9-12 C3 Framework

Use marginal benefits and marginal costs to construct an argument for or against an approach or solution to an economic issue.

How this material aligns: Students use marginal cost and benefit reasoning to argue whether the Sattlers should buy the reverse-osmosis system, since it costs more up front but less for each additional year of use.

All materials for D2.Eco.2.9-12 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate the cost per gallon of treated water for a pitcher filter and a reverse-osmosis system.
Students will build a cost argument for or against a household purchase using marginal reasoning over several years.

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.

Also: membrane, cost per gallon, cartridge

Teacher overview

Home water filters are a consumer purchase, and the sticker price is only part of the decision. A pitcher filter is cheap to buy but the cartridges add up, while a reverse-osmosis system costs more at the start yet treats water for less over time. Reverse osmosis pushes water through a membrane that blocks very small contaminants, including many that a basic pitcher does not, which matters for families concerned about substances such as PFAS, where the maximum contaminant level for PFOA and PFOS is 4.0 ppt each. This lesson has students compute the cost per gallon of each option for the fictional Sattler family and then argue which purchase makes sense. A common misconception is that the cheapest device to buy is always the cheapest to own, which the per-gallon math corrects.

Procedure

Hook (5 min): Describe three items: a filter pitcher, an under-sink system, and a case of bottled water. Ask students which they think gives the cheapest treated water per gallon, and record the show of hands.

Direct instruction (12 min): Using fictional Sattler figures, model cost per gallon for the pitcher: a cartridge that costs a set amount and treats a set number of gallons gives dollars divided by gallons. Show the units canceling so the result reads as dollars per gallon. Stress that the one-time pitcher cost is separate from the per-gallon cartridge cost.

Guided practice (10 min): Work the reverse-osmosis first-year cost with the class, adding the install cost to the yearly filter cost and dividing by the family's yearly gallons. Then compute the second-year cost per gallon, when only the filters must be replaced, so students see the number drop.

Independent practice (13 min): Students finish the Student Handout, comparing all three options over one and two years and finding the year in which the reverse-osmosis system becomes the cheaper choice. Circulate and check that students track the up-front cost separately from the yearly cost.

Formative check and closure (5 min): Exit ticket: "Give one reason the reverse-osmosis system could be worth its higher up-front cost for the Sattlers." Collect and scan for answers that reference either the falling per-gallon cost over time or the wider range of contaminants removed.

Should the Sattlers Buy a Reverse-Osmosis System? A Cost Lesson — Grade 9 Health & Consumer Science

Name: ____________________________ Date: ______________

Student Handout

Suppose the Sattler family uses 0.75 gallons of drinking and cooking water per day and is choosing how to treat it. All prices below are fictional figures for this scenario. A pitcher cartridge costs $18 and treats 40 gallons; the pitcher itself costs $34 once. An under-sink reverse-osmosis system costs $260 to install and $70 per year for replacement filters. Bottled water costs $1.20 per gallon. Show your steps.

The family uses 0.75 gallons per day. How many gallons is that in a 365-day year? Round to the nearest gallon.
A pitcher cartridge costs $18 and treats 40 gallons. What is the cartridge cost per gallon?
About how many cartridges would the family need to treat one year of water from item 1? Round up to a whole cartridge.
What is the family's yearly cartridge cost for the pitcher filter, using the number of cartridges from item 3?
The reverse-osmosis system costs $260 to install plus $70 in filters the first year. What is its total first-year cost?
What is the reverse-osmosis cost per gallon in the first year, treating the yearly gallons from item 1? Round to the nearest cent.
In the second year the reverse-osmosis system costs only the $70 in filters. What is its cost per gallon that year? Round to the nearest cent.
Bottled water costs $1.20 per gallon. What would one year of bottled water cost for the gallons in item 1? Round to the nearest dollar.
Over two full years, the cumulative pitcher cost is modeled by 34 + 126y dollars and the reverse-osmosis cost by 260 + 70y dollars, where y is the number of years. Which option costs less at y = 2?
Using the two equations in item 9, find the number of years at which the reverse-osmosis total first drops below the pitcher total, and explain what that means for the Sattlers' decision.

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 Sattler prices below are fictional figures built into the scenario.

Answer: 274 gallons. 0.75 gallons per day times 365 days is 273.75, which rounds to 274 gallons.
Answer: $0.45 per gallon. $18 divided by 40 gallons is $0.45 per gallon.
Answer: 7 cartridges. 274 gallons divided by 40 gallons per cartridge is 6.85, which rounds up to 7 cartridges.
Answer: $126.00. 7 cartridges times $18 each is $126 for the year.
Answer: $330.00. The $260 install plus $70 in first-year filters is $330.
Answer: $1.20 per gallon. $330 divided by 274 gallons is $1.204, about $1.20 per gallon.
Answer: $0.26 per gallon. $70 divided by 274 gallons is $0.255, about $0.26 per gallon.
Answer: $329.00. 274 gallons times $1.20 per gallon is $328.80, about $329.
Answer: The pitcher. At y = 2, pitcher = 34 + 126 times 2 = $286, while reverse osmosis = 260 + 70 times 2 = $400, so the pitcher costs less after two years.
Answer: About 4 years. Setting 34 + 126y equal to 260 + 70y gives 56y = 226, so y is about 4.04 years. At exactly four years the pitcher total is still $2 lower ($538 against $540), so the reverse-osmosis system first becomes the cheaper option just after the four-year mark; counted in whole years, it is cheaper from the fifth year on. If the Sattlers expect to keep it longer than four years, its higher up-front cost pays off.

Differentiation

Support

Provide a cost table with the price labels already filled in and only the per-gallon and yearly-cost cells blank. Let students use a calculator and a worked example of one cost-per-gallon computation before starting item 2.

Extension

Ask students to add the reverse-osmosis system's reject water, assuming it sends 3 gallons to the drain for every 1 gallon it treats, and recompute how many total gallons the household draws to still get its 274 treated gallons.

ELL supports

Pre-teach "cartridge," "membrane," and "per gallon" with a labeled diagram of each device. Provide a sentence frame for item 10: "Reverse osmosis becomes cheaper after about ___ years because its yearly cost is only $___ while the pitcher keeps costing $___ each year."