Worksheet Grade 10 Math

Verdant Hollow Recovery Facility: Nutrient Load and Removal

A grade 10 worksheet using the pounds formula to find nitrogen and phosphorus loads, removal efficiency, and permit compliance at a fictional treatment plant.

Grade: Grade 10
Subject: Math
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

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: Items 1, 2, 4, and 5 carry mg/L, MGD, and the 8.34 constant through the pounds formula, the consistent multi-step unit reasoning this standard targets.

All materials for HSN-Q.A.1 →

HSN-Q.A.2 Common Core Math

Define appropriate quantities for the purpose of descriptive modeling.

How this material aligns: Item 8 asks students to decide whether a load in pounds per day or a concentration in mg/L is the better quantity for comparing plants of different sizes.

All materials for HSN-Q.A.2 →

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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 nitrogen and phosphorus mass loads in pounds per day using the pounds formula.
Students will find removal efficiency and compare treated effluent against a permit limit.

Vocabulary

Effluent: Effluent is the cleaned water that leaves a treatment plant at the end of the process. It is tested carefully before being released to a river, lake, or the ocean.

Also: nutrient load, pounds formula, removal efficiency

Teacher overview

Nitrogen and phosphorus are nutrients that plants need, yet in a river they feed algae and lower dissolved oxygen. A treatment plant reports how much of each nutrient it removes as a mass, in pounds per day, not just as a concentration. This worksheet uses the fictional town of Verdant Hollow and the pounds formula, load (lbs/day) = concentration (mg/L) x flow (MGD) x 8.34. Teaching note: before students start, work one load out loud so they see that flow, not concentration alone, sets how many pounds reach the river each day.

Verdant Hollow Recovery Facility: Nutrient Load and Removal — Grade 10 Math

Name: ____________________________ Date: ______________

Student Worksheet

The town of Verdant Hollow runs a water resource recovery facility. This plant is fictional, and its numbers are set for this worksheet. Use the pounds formula for every load: load (lbs/day) = concentration (mg/L) x flow (MGD) x 8.34.

Plant data:

Flow treated: 3.2 MGD
Total nitrogen: 35 mg/L coming in, 8 mg/L going out
Total phosphorus: 6 mg/L coming in, 1 mg/L going out
Permit limit for total nitrogen leaving the plant: 10 mg/L

Find the nitrogen load coming into the plant, in pounds per day.
Find the nitrogen load leaving the plant, in pounds per day.
Find the nitrogen removal efficiency as a percent. Use removal efficiency (%) = (in - out) / in x 100.
Find the phosphorus load coming into the plant, in pounds per day.
Find the pounds of phosphorus the plant removes each day.
The plant's nitrogen leaves at 8 mg/L. Does that meet the 10 mg/L permit limit? By how many mg/L does it pass or miss?
Find the phosphorus removal efficiency as a percent.
A smaller plant treats less flow but reports a higher nitrogen concentration than Verdant Hollow. Explain why comparing pounds per day, rather than mg/L alone, tells you which plant sends more nitrogen to the river.

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: 934 lbs/day.
35 mg/L x 3.2 MGD x 8.34 = 112 x 8.34 = 934.08, which rounds to 934 pounds per day.
Answer: 214 lbs/day.
8 mg/L x 3.2 MGD x 8.34 = 25.6 x 8.34 = 213.5, which rounds to 214 pounds per day.
Answer: 77 percent.
(35 - 8) / 35 x 100 = 27 / 35 x 100 = 77.1, or about 77 percent. Students who use the loads get the same result: (934 - 214) / 934 x 100 is about 77 percent.
Answer: 160 lbs/day.
6 mg/L x 3.2 MGD x 8.34 = 19.2 x 8.34 = 160.1, which rounds to 160 pounds per day.
Answer: 133 lbs/day.
Phosphorus removed is (6 - 1) = 5 mg/L. Then 5 x 3.2 x 8.34 = 16 x 8.34 = 133.4, which rounds to 133 pounds per day.
Answer: Yes, by 2 mg/L.
The nitrogen leaves at 8 mg/L, which is below the 10 mg/L limit, so it passes with a margin of 10 - 8 = 2 mg/L.
Answer: 83 percent.
(6 - 1) / 6 x 100 = 5 / 6 x 100 = 83.3, or about 83 percent.
Answer: Pounds per day account for flow, so they show the true amount reaching the river.
A high concentration at a low flow can still be fewer pounds than a lower concentration at a high flow. The river responds to total mass, so pounds per day is the fair comparison between plants of different sizes.

Differentiation

Support

Give students a printed formula strip with load (lbs/day) = concentration x flow x 8.34 and the removal-efficiency formula already written out. Work item 1 together, labeling each number with its unit, before students continue on their own.

Extension

Have students find the pounds of nitrogen the river would receive in a full 30-day month at the current effluent load, and explain how a wetter month with higher flow would change that monthly total even if the concentration held steady.

ELL supports

Pre-teach "nutrient," "load," "influent," and "effluent" with a simple labeled diagram showing water entering and leaving a plant. Provide a sentence frame for item 8: "Pounds per day is a better comparison because ___."