Math problem set Grade 6 Math

Wexley's Water Plant: Cleaning Wastewater in Percents

A grade 6 problem set on the fictional Wexley plant, finding what percent of BOD and solids are removed from wastewater and a percent increase in daily flow.

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

Standards

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, 4, 6, and 8 have students find what percent of a starting amount is removed, and problem 5 finds a percent increase, the percent-of-a-quantity work 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 calculate the percent of BOD and solids a plant removes from wastewater.
Students will find a percent increase in a plant's daily flow of water.

Vocabulary

Key words: BOD, mg/L, percent removed, MGD

Teacher overview

A wastewater plant cleans the used water from homes before it returns to a river. One way to measure how dirty water is uses a number called BOD, in mg/L. The rule is that cleaned water leaving the plant must have a BOD at or below 30 mg/L. This problem set uses the fictional Wexley plant to practice percent removed and percent increase. A common misconception to watch for: students sometimes divide by the small cleaned value instead of the raw amount coming in, so the percent removed comes out far too high.

Wexley's Water Plant: Cleaning Wastewater in Percents — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

The fictional Wexley plant cleans the town's wastewater. Use these values:

Raw water coming in: BOD of 240 mg/L, solids (TSS) of 250 mg/L
Cleaned water leaving: BOD of 24 mg/L, solids of 25 mg/L
The plant cleans 2.0 MGD (million gallons a day)
The rule: cleaned water must be at or below 30 mg/L of BOD

The raw water has a BOD of 240 mg/L. The cleaned water is 24 mg/L. How many mg/L of BOD were removed?
What percent of the BOD was removed?
The cleaned water must be at or below 30 mg/L. Wexley's is 24 mg/L. Does it pass, and by how many mg/L?
The solids drop from 250 mg/L to 25 mg/L. What percent of the solids was removed?
The plant cleans 2.0 MGD. If the daily flow rises by 25 percent, what is the new flow?
On a rainy Monday the raw BOD is only 200 mg/L, and the cleaned water is 30 mg/L. What percent was removed that day?
Compare Monday's removal to the usual 90 percent. Is Monday better or worse, and by how many percentage points?
When the raw BOD is 300 mg/L, what percent must the plant remove to reach 30 mg/L?

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: 216 mg/L.
240 - 24 = 216 mg/L of BOD removed.
Answer: 90 percent.
216 ÷ 240 = 0.90, which is 90 percent. The amount removed is compared to the raw 240, the amount coming in.
Answer: 6 mg/L.
Yes, it passes. 30 - 24 = 6 mg/L below the limit.
Answer: 90 percent.
The solids removed are 250 - 25 = 225 mg/L. 225 ÷ 250 = 0.90, which is 90 percent.
Answer: 2.5 MGD.
A 25 percent rise means multiplying by 1.25. 2.0 × 1.25 = 2.5 MGD.
Answer: 85 percent.
Removed: 200 - 30 = 170 mg/L. 170 ÷ 200 = 0.85, which is 85 percent.
Answer: 5 percentage points.
Monday's 85 percent is worse than the usual 90 percent, by 90 - 85 = 5 percentage points.
Answer: 90 percent.
To go from 300 mg/L to 30 mg/L, the plant removes 300 - 30 = 270 mg/L. 270 ÷ 300 = 0.90, which is 90 percent.

Differentiation

Support

Give students the subtraction done for problem 1 and a note that percent removed equals the amount removed divided by the raw amount, then times 100. Let students use a calculator so the focus stays on which two numbers to divide.

Extension

Ask students to imagine a day when the raw BOD is 320 mg/L and the plant still must reach 30 mg/L. Have them find the percent that must be removed and compare it to the usual 90 percent.

ELL supports

Pair "raw," "cleaned," and "removed" with two labeled cups, one cloudy and one clear, and an arrow between them. Provide the frame: "The plant removed ___ percent of the BOD because ___."

Extensions

Have students explain in two sentences why heavy rain, which adds clean water to the pipes, can change the raw BOD the plant sees, using Monday's problem as their example.