Worksheet Grade 10 Math

Greywillow Reclamation Facility: BOD Removal and Loading Worksheet

A grade 10 worksheet using the pounds formula and removal-efficiency formula on a fictional city's wastewater plant, comparing BOD and TSS to secondary limits.

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 4 through 7 carry concentration in milligrams per liter and flow in million gallons per day through the pounds formula to a mass load in pounds per day, using units to guide each step.

All materials for HSN-Q.A.1 →

HSA-CED.A.1 Common Core Math

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

How this material aligns: Item 8 asks students to create and solve a one-variable equation for the effluent concentration that meets a stated ninety-percent removal target, the equation-from-a-relationship skill this standard requires.

All materials for HSA-CED.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 calculate BOD and TSS removal efficiency from influent and effluent concentrations.
Students will use the pounds formula to find pollutant mass loads in pounds per day.
Students will write and solve an equation for the effluent concentration that meets a removal target.

Vocabulary

Influent: Influent is the incoming dirty water that arrives at a treatment plant, ready to be cleaned. Operators test it to see how much work the plant has to do.
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.
Biochemical oxygen demand (BOD): Biochemical oxygen demand, or BOD, measures how much oxygen tiny microbes will use up as they eat the waste in water. Dirtier water has a higher BOD.
Total suspended solids (TSS): Total suspended solids is the amount of solid material floating or suspended in water, measured by filtering a sample and weighing what gets left behind. High TSS makes water look cloudy and can smother fish habitat and clog treatment equipment.

Also: removal efficiency

Teacher overview

The city of Greywillow, a fictional city used for this worksheet, runs a water reclamation facility that must meet the federal secondary treatment standard of 30 milligrams per liter for both BOD and TSS in its monthly-average effluent. Students calculate how well the plant removes each pollutant, then use the pounds formula to convert concentrations into the actual mass of pollutant the process handles each day. The worksheet closes by asking students to solve for the effluent concentration a stricter removal target would require, connecting a percentage to a concrete equation.

Greywillow Reclamation Facility: BOD Removal and Loading Worksheet — Grade 10 Math

Name: ____________________________ Date: ______________

Student Worksheet

The city of Greywillow's water reclamation facility treats 2.5 million gallons per day (MGD). Over one month of monitoring, the plant recorded these average concentrations.

Influent BOD (entering the plant): 220 milligrams per liter (mg/L).
Effluent BOD (leaving the plant): 24 mg/L.
Influent TSS: 240 mg/L.
Effluent TSS: 18 mg/L.

Use these facts for all problems:

Removal efficiency (%) = (influent − effluent) ÷ influent × 100.
Loading (pounds per day) = concentration (mg/L) × flow (MGD) × 8.34.
The secondary treatment standard is 30 mg/L for both BOD and TSS.

Find the plant's BOD removal efficiency as a percentage. Round to the nearest tenth.
Find the plant's TSS removal efficiency as a percentage. Round to the nearest tenth.
Does the effluent meet the 30 mg/L secondary standard for both BOD and TSS? Answer for each pollutant.
Find the BOD mass load entering the plant, in pounds per day, using the pounds formula.
Find the BOD mass load leaving the plant in the effluent, in pounds per day.
Find the pounds of BOD removed per day. Confirm that it equals the removed concentration (influent − effluent) run through the pounds formula.
Find the pounds of TSS removed per day.
Suppose the plant must reach 90 percent BOD removal or better. With the influent BOD held at 220 mg/L, write and solve an equation for the highest effluent BOD concentration that still meets a 90 percent removal target.
Compare the plant's current effluent BOD of 24 mg/L with your answer to item 8. Does the plant currently meet a 90 percent removal target? Explain using your numbers.
Explain why an operator reports the pounds of BOD removed each day in addition to the removal percentage, and what the pounds figure tells the operator that the percentage does not.

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: 89.1 %.
(220 − 24) ÷ 220 × 100 = 196 ÷ 220 × 100 = 89.09, which rounds to 89.1 percent.
Answer: 92.5 %.
(240 − 18) ÷ 240 × 100 = 222 ÷ 240 × 100 = 92.5 percent.
Answer: Yes for both.
BOD effluent is 24 mg/L, which is at or below the 30 mg/L limit, and TSS effluent is 18 mg/L, also below 30 mg/L, so the plant meets the secondary standard for both.
Answer: 4,587 lb/day.
Loading = 220 mg/L × 2.5 MGD × 8.34 = 550 × 8.34 = 4,587 pounds per day.
Answer: 500.4 lb/day.
Loading = 24 mg/L × 2.5 MGD × 8.34 = 60 × 8.34 = 500.4 pounds per day.
Answer: 4,086.6 lb/day.
Pounds removed = entering − leaving = 4,587 − 500.4 = 4,086.6 pounds per day. Using removed concentration: (220 − 24) × 2.5 × 8.34 = 196 × 2.5 × 8.34 = 490 × 8.34 = 4,086.6 pounds per day, which matches.
Answer: 4,628.7 lb/day.
Removed TSS concentration = 240 − 18 = 222 mg/L. Loading = 222 × 2.5 × 8.34 = 555 × 8.34 = 4,628.7 pounds per day.
Answer: 22 mg/L.
Let E be the effluent BOD. Removal target: (220 − E) ÷ 220 = 0.90. Then 220 − E = 198, so E = 22 mg/L. Any effluent at or below 22 mg/L meets the 90 percent target.
Answer: No, it falls just short.
The plant's effluent BOD of 24 mg/L is higher than the 22 mg/L ceiling from item 8, and its removal of 89.1 percent (item 1) is below 90 percent. The plant is close but does not currently meet a 90 percent removal target.
Answer: Pounds show the actual mass the process must handle.
The percentage describes how efficient the plant is, but two plants with the same removal percentage can handle very different masses depending on their flow. The pounds-per-day figure tells the operator the real load on the biological process and on sludge handling, which is what sizing and staffing decisions depend on.

Differentiation

Support

Provide the two formulas on a printed reference card and work item 1 and item 4 through together as a class so students see one removal-efficiency calculation and one pounds-formula calculation before working independently. Allow a calculator for every item.

Extension

Ask students to find the flow, in million gallons per day, at which the plant's current BOD load entering the plant would double, and to explain why doubling the flow at the same influent concentration doubles the pounds per day.

ELL supports

Provide a simple process diagram labeling "influent" at the inlet and "effluent" at the outlet, with an arrow showing water flowing through the plant. Pre-teach "removal efficiency," "load," and "concentration" with the diagram, and give a sentence frame for item 10: "The pounds figure tells the operator ___, which the percentage does not show."