Worksheet Grade 7 Engineering & Design

Pike Hollow PFAS Filter: Sizing Carbon and Flow

Students design a fictional town's carbon filter for PFAS, using percent removal to check each well against the 4.0 ppt limit and sizing the daily flow.

Grade: Grade 7
Subject: Engineering & Design
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Items 1, 3, and 7 use percent removal and a percent of the carbon's capacity, the multistep percent reasoning applied to real numbers this standard asks students to carry out.

All materials for 7.RP.A.3 →

MS-ETS1-1 NGSS

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

How this material aligns: Items 2, 4, and 5 check each treated well against the 4.0 parts per trillion limit, defining the design's water-quality constraint with the precision this standard expects.

All materials for MS-ETS1-1 →

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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 use a percent removal rate to find a treated well's PFAS level after one or more passes through a carbon filter.
Students will check treated water against the PFAS limit and size the filter's daily flow.

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.
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: carbon filter, constraint

Teacher overview

PFAS are human-made chemicals that do not break down easily and can build up in drinking water. The federal limit for two of them, PFOA and PFOS, is 4.0 parts per trillion (ppt) each. That rule is still in motion: water systems must comply by April 2029, and in May 2026 EPA proposed letting eligible systems apply for a two-year exemption, to April 2031. That proposal was not final as of September 2026. This worksheet uses the fictional town of Pike Hollow, which found PFAS in its wells. Students design a carbon filter to bring each well under the limit. A common misconception is that a "percent removed" leaves that same percent behind; if a filter removes 85 percent, then 15 percent stays, and that leftover share is what students must compare to the limit.

Pike Hollow PFAS Filter: Sizing Carbon and Flow — Grade 7 Engineering & Design

Name: ____________________________ Date: ______________

Student Worksheet

Use these values for the fictional Pike Hollow design. The 4.0 ppt limit is real; the well levels and filter details below are made up for this scenario.

Well A tests at 20 ppt of PFOA.
The carbon filter removes 85 percent of the PFOA in each pass. So 15 percent stays after each pass.
The treated water must be at or below the 4.0 ppt limit.

Well A starts at 20 ppt. After one pass through the filter, 15 percent stays. Find the PFOA level in the treated water.
Does the treated Well A water meet the 4.0 ppt limit? By how many ppt is it below the limit?
Find the removal efficiency for Well A as a percent, using the start of 20 ppt and your treated level from item 1. Removal efficiency (%) = (start − end) ÷ start × 100.
Well B tests higher, at 40 ppt. After one pass (15 percent stays), find its treated level. Does one pass meet the 4.0 ppt limit?
Well B is run through the filter a second time. Take your item 4 answer and keep 15 percent again. Find the new level. Does it meet the 4.0 ppt limit now?
The filter vessel treats 50 gpm (gallons per minute). One day it runs for 8 hours, which is 480 minutes. How many gallons does it treat in that day?
The carbon must be replaced after treating 3,000,000 gallons. After one day of 24,000 gallons, what percent of the carbon's capacity has been used? Round to the nearest tenth of a percent.
PFAS rules are still changing, and some towns may be allowed more time to meet the limit. Explain one reason Pike Hollow might install this filter now instead of waiting.

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: 3.0 ppt.
15 percent of 20 stays: 20 × 0.15 = 3.0 ppt.
Answer: 1.0 ppt below the limit.
Yes, it meets the limit. 4.0 − 3.0 = 1.0 ppt below the 4.0 ppt limit.
Answer: 85%.
(20 − 3.0) ÷ 20 × 100 = 17 ÷ 20 × 100 = 0.85 × 100 = 85%.
Answer: 6.0 ppt.
40 × 0.15 = 6.0 ppt. No, one pass does not meet the limit, because 6.0 ppt is above 4.0 ppt.
Answer: 0.9 ppt.
6.0 × 0.15 = 0.9 ppt. Yes, it now meets the limit, because 0.9 ppt is below 4.0 ppt.
Answer: 24,000 gallons.
50 gpm × 480 minutes = 24,000 gallons treated in the day.
Answer: 0.8%.
24,000 ÷ 3,000,000 = 0.008, which is 0.8 percent of the carbon's capacity.
Answer: Installing now protects people sooner.
Accept any answer explaining that treating the water now lowers PFAS exposure right away, meets the health-based limit regardless of the exact deadline, and avoids a last-minute rush if Pike Hollow does not get extra time.

Differentiation

Support

Give students a printed reminder that "removes 85 percent" means "15 percent stays," with item 1 worked as a model (20 × 0.15 = 3.0). Allow a calculator throughout, and provide the removal-efficiency formula already set up for item 3.

Extension

Ask students to find how many passes a very high well of 100 ppt would need to reach the 4.0 ppt limit, keeping 15 percent each pass, and to show the level after each pass.

ELL supports

Provide a picture of water flowing through a carbon filter with "85 percent removed" and "15 percent stays" labeled. Pre-teach "PFAS," "carbon filter," and "limit." Allow item 8 to be answered with a sentence frame: "Pike Hollow should install the filter now because ___."