Math problem set Grade 6 Math

Harlow Home Reverse-Osmosis Recovery Ratio Problems

A grade 6 problem set on a fictional family's under-sink reverse-osmosis filter, using ratios and percent to compare clean water made with water sent to the drain.

Grade: Grade 6
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

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: Problems 1 and 9 have students write and describe the clean-water-to-drain ratio in simplest form using ratio language, the core skill this standard defines.

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: Problems 2 through 8 use ratio tables and finding a percent of the water entering the filter to compare two filters, the ratio-and-percent problem solving this standard names.

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 2026-07-23.

Objectives

Students will write the clean-to-drain ratio for a reverse-osmosis filter and find its recovery percent.
Students will use ratio tables to compare how much water two filters use to make the same clean amount.

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: ratio, percent, recovery

Teacher overview

A reverse-osmosis filter pushes tap water through a very fine membrane. Some water comes out clean, and the rest carries the trapped minerals to the drain. This problem set follows the Harlow family, a fictional family with an under-sink filter, and builds the idea of "recovery," the share of water that becomes clean. A common mistake to watch for is thinking recovery means all the water is saved; only the clean fraction is recovered, and the drain share is real water too. Watch also for students who mix up the clean amount with the drain amount in the ratio.

Harlow Home Reverse-Osmosis Recovery Ratio Problems — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Use these numbers for the whole set. In the Harlow family's fictional filter, for every 4 gallons of tap water that enter, 1 gallon comes out as clean drinking water and 3 gallons go down the drain.

Write the ratio of clean water to drain water in simplest form.
What percent of the water entering the filter becomes clean drinking water?
What percent of the water entering the filter goes down the drain?
The family makes 6 gallons of clean water for a party. How many gallons of tap water did the filter use to make it?
How many gallons went down the drain to make those 6 clean gallons?
The filter uses 4 gallons of tap water for each clean gallon. Complete this table.

Clean water (gallons) Tap water used (gallons)

2

5

10
A newer filter makes 1 clean gallon for every 2 gallons of tap water. What percent of the water becomes clean with the newer filter?
The family uses 10 gallons of clean water in a week. How many gallons of tap water is that with the old filter, how many with the newer filter, and how many gallons does the newer filter save?
Explain what "recovery" means for this filter, using the word ratio in your answer.
Suppose the family reused all the old filter's drain water in the garden. What percent of the water entering the filter would no longer be wasted?

Clean water (gallons)	Tap water used (gallons)
2
5
10

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: 1 : 3. For every 1 clean gallon there are 3 drain gallons, and 1 : 3 is already in simplest form.
Answer: 25 percent. 1 clean gallon out of 4 total gallons in is 1 ÷ 4 = 0.25, or 25 percent.
Answer: 75 percent. 3 drain gallons out of 4 total is 3 ÷ 4 = 0.75, or 75 percent.
Answer: 24 gallons. It takes 4 tap gallons for each clean gallon, so 6 × 4 = 24 gallons.
Answer: 18 gallons. Of the 24 gallons in, 6 came out clean, so 24 − 6 = 18 gallons to the drain (or 6 × 3 = 18).
Answer: 8; 20; 40. At 4 tap gallons for each clean gallon: 2 × 4 = 8, 5 × 4 = 20, 10 × 4 = 40 gallons.
Answer: 50 percent. 1 clean gallon out of 2 gallons in is 1 ÷ 2 = 0.5, or 50 percent.
Answer: 40 gallons old, 20 gallons new, saves 20 gallons. Old filter: 10 × 4 = 40; newer filter: 10 × 2 = 20; 40 − 20 = 20 gallons saved.
Answer: Recovery is the ratio of clean water to the total water that enters the filter; here 1 clean gallon for every 4 gallons in, so the recovery is 1 out of 4.
Answer: 75 percent. The drain share is 75 percent, so reusing all of it means that 75 percent is no longer wasted.

Differentiation

Support

Give students 4 counters to model each cycle: 1 marked "clean" and 3 marked "drain." Have them act out problems 4 and 5 by making stacks before they multiply. Provide the reminder "percent = part ÷ whole × 100" on a printed strip.

Extension

Ask students to find what recovery percent a filter would have if it made 2 clean gallons for every 5 gallons of tap water, and to compare that filter with the old and newer filters in this set. Have them rank the three filters from most to least wasteful.

ELL supports

Pre-teach "clean water," "drain," "ratio," and "recovery" with a simple diagram showing tap water splitting into a clean stream and a drain stream. Provide a sentence frame for problem 9: "Recovery is the ratio of ___ to ___." Allow counters or drawings as shown work.