Lesson plan Grade 6 Math

Fernbrook's Fountain Filter: Ratios in a Reverse-Osmosis System

A grade 6 lesson using ratio language and percent to describe how a fictional school's reverse-osmosis filter splits feed water into drinking and reject water.

Grade: Grade 6
Subject: Math
Material: Lesson plan
Time: 45 min
Prep: Low prep
Materials: Chart paper or whiteboard, Calculator (optional), Printed handout with the two independent practice questions, Index cards for the exit ticket

Standards

6.RP.A.1 Common Core Math

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, 'The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.'

How this material aligns: Students use the ratio language 'for every 4 gallons of feed water, 1 gallon becomes drinking water' throughout the Procedure, the exact for-every phrasing this standard models.

All materials for 6.RP.A.1 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Independent practice problems 1 and 2 require using the filter's 4-to-1 ratio to find missing feed or product amounts, the real-world ratio reasoning this standard covers.

All materials for 6.RP.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will use ratio language to describe the relationship between feed water, product water, and reject water in a reverse-osmosis filter.
Students will calculate product and reject water amounts from a stated ratio.
Students will calculate the percent of feed water recovered as drinking 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.

Also: feed water, product water, reject water, ratio

Teacher overview

Fernbrook Middle School (a fictional school used for this lesson) installs a small reverse-osmosis filter under its lobby drinking fountain. Not all of the water entering an RO filter becomes drinking water: some is pushed out as "reject" water carrying the removed dissolved minerals away. This lesson uses Fernbrook's filter ratio to give students practice with ratio language and percent in a single, concrete system.

A common misconception is assuming that a filter turns all of the water that enters it into drinking water. The direct instruction step is built to correct that directly, before students calculate any amounts.

Procedure

Hook (5 min): Ask students what they think happens to every gallon of water that goes into a filter. Does all of it come out as something you can drink? Collect a few predictions on the board.

Direct instruction (10 min): Introduce Fernbrook's fictional filter ratio: for every 4 gallons of feed water that enter the unit, it produces 1 gallon of drinking water (product water) and sends 3 gallons to the drain (reject water). Model the ratio language exactly: "for every 4 gallons of feed water, there is 1 gallon of product water and 3 gallons of reject water." Then calculate the percent of feed water recovered as drinking water: 1 ÷ 4 = 0.25, or 25 percent.

Guided practice (15 min): In pairs, students use the 4:1:3 ratio to find the product and reject amounts for 100 gallons of feed water, using a ratio table or a double number line to organize their work (25 gallons product, 75 gallons reject). Circulate and check that pairs are keeping the ratio consistent as they scale up.

Independent practice (10 min): Each student answers two questions on the handout:

How much product water and reject water result from 28 gallons of feed water?
How much feed water was needed to produce 18 gallons of product water?

Closure / exit ticket (5 min): Students answer one question on an index card: "For every 4 gallons of feed water, how many gallons become drinking water, and what percent is that?" Collect and scan for the correct ratio and percent before dismissal.

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

Answer Key

Answer: 7 gallons of product water and 21 gallons of reject water.
28 gallons of feed water ÷ 4 = 7 groups of the ratio, so product = 7 × 1 = 7 gallons and reject = 7 × 3 = 21 gallons.
Answer: 72 gallons of feed water.
Product water (18 gallons) represents 1 part of the 4-part ratio, so feed water = 18 × 4 = 72 gallons. Reject water would be 72 − 18 = 54 gallons.
Exit ticket answer: 1 gallon, which is 25 percent.
For every 4 gallons of feed water, 1 gallon becomes drinking water. 1 ÷ 4 = 0.25, or 25 percent.

Differentiation

Support (below grade level)

Provide a labeled diagram of the filter showing 4 gallons entering and splitting into 1 gallon of product water and 3 gallons of reject water, and let students count out physical counters (4 total, 1 of one color and 3 of another) to model the ratio before working with larger numbers.

Extension (above grade level)

Ask students to design a "better" filter that recovers 40 percent of its feed water as product instead of 25 percent, state the new ratio in for-every language, and calculate how many gallons of feed water that filter would need to produce the same 18 gallons of product water as problem 2.

ELL supports

Pre-teach "feed water," "product water," and "reject water" with a simple three-part diagram, labeled in English and, where possible, in students' home languages, showing the water flowing in one side and out two others. Allow the guided practice ratio table to be completed with numbers alone, without a written explanation.