Math problem set Grade 7 Math

Tanager Flats PFAS Filters: A Complex-Fraction Rate Set

A grade 7 problem set on the fictional town of Tanager Flats, where students find gallons-per-hour rates from complex fractions to compare PFAS filter models.

Grade: Grade 7
Subject: Math
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator (optional)

Standards

7.RP.A.1 Common Core Math

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

How this material aligns: Problems 1, 2, 3, and 7 each divide a fractional number of gallons by a fractional number of hours to find a gallons-per-hour unit rate, the complex-fraction rate computation this standard defines.

All materials for 7.RP.A.1 →

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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 compute a unit rate in gallons per hour from a ratio of two fractions.
Students will use a computed unit rate to find gallons filtered or hours required.

Vocabulary

PFAS: A large family of human-made chemicals used in things like nonstick pans, waterproof fabric, and firefighting foam. They are called forever chemicals because they take a very long time to break down.

Also: unit rate, complex fraction

Teacher overview

PFAS are long-lasting chemicals that a home filter removes slowly, so the useful way to compare filter models is by how many gallons each one cleans per hour. The fictional town of Tanager Flats has PFOA and PFOS, two PFAS chemicals, above the 4.0 ppt federal limit set for each in 2024 (EPA has proposed giving some water systems more time to comply), and its residents are testing three filter models, each rated in a fraction of a gallon per a fraction of an hour. This set has students turn those complex fractions into plain gallons-per-hour rates and then use the rates to plan. The common misconception to correct here is inverting the division: a rate in gallons per hour is gallons divided by hours, so students must divide the gallon fraction by the hour fraction, not the other way around.

Tanager Flats PFAS Filters: A Complex-Fraction Rate Set — Grade 7 Math

Name: ____________________________ Date: ______________

Problems

Tanager Flats is a fictional town. Its well water has two PFAS chemicals, PFOA and PFOS, above the 4.0 ppt limit, so homes are testing filter models. Each model cleans a fraction of a gallon in a fraction of an hour. A rate in gallons per hour is gallons divided by hours.

Model A filters 1/2 gallon in 1/3 hour. Find its rate in gallons per hour.
Model B filters 3/4 gallon in 2/3 hour. Find its rate in gallons per hour.
Model C filters 2/5 gallon in 1/4 hour. Find its rate in gallons per hour.
Rank the three models from fastest to slowest, using your rates from problems 1, 2, and 3.
A family chooses Model A, at 1.5 gallons per hour. How many gallons can it filter in 8 hours?
Using Model A's rate of 1.5 gallons per hour, how many hours does it take to filter 6 gallons?
A whole-house unit filters 5/2 gallons in 5/4 hour. Find its rate in gallons per hour.
The whole-house unit must filter 30 gallons before morning. How many hours is that? If the family runs it for 12 hours overnight, will it finish in time?

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: 1.5 gallons per hour.
(1/2) ÷ (1/3) = (1/2) × (3/1) = 3/2 = 1.5 gallons per hour.
Answer: 1.125 gallons per hour.
(3/4) ÷ (2/3) = (3/4) × (3/2) = 9/8 = 1.125 gallons per hour.
Answer: 1.6 gallons per hour.
(2/5) ÷ (1/4) = (2/5) × (4/1) = 8/5 = 1.6 gallons per hour.
Answer: Model C, then Model A, then Model B.
Ordering the rates 1.6, 1.5, and 1.125 from largest to smallest gives Model C fastest, Model A next, and Model B slowest.
Answer: 12 gallons.
1.5 gallons per hour × 8 hours = 12 gallons.
Answer: 4 hours.
6 gallons ÷ 1.5 gallons per hour = 4 hours.
Answer: 2 gallons per hour.
(5/2) ÷ (5/4) = (5/2) × (4/5) = 20/10 = 2 gallons per hour.
Answer: 15 hours.
30 gallons ÷ 2 gallons per hour = 15 hours. Because 12 hours is less than 15 hours, the family would not finish in time.

Differentiation

Support

Give students the complex-fraction step already set up for problems 1 through 3, showing the "keep, change, flip" move written out once with a fourth example. Let them focus on carrying out the multiplication and simplifying, and allow a calculator for the decimal conversions.

Extension

Ask students to find a fraction of a gallon and a fraction of an hour that would give a filter a rate of exactly 2.5 gallons per hour, then prove their pair works by dividing. Challenge them to find a second pair different from the first.

ELL supports

Provide a labeled example that names each part of a rate: the gallons on top, the hours on the bottom, and the arrow to "gallons per hour." Pair each problem with the sentence frame "___ gallons in ___ hour is ___ gallons per hour" so students can read their answers aloud.

Extensions

Have students read the flow rate printed on a real pitcher filter or refrigerator filter box, usually given in gallons per minute, and convert it to gallons per hour. Comparing that real rate with the Tanager Flats models shows why a slow home filter still keeps up with a family's drinking water needs but not its whole-house use.