Worksheet Grade 6 Math

Kirkbride Plant's Backwash Water: Percent of a Day's Output

A grade 6 worksheet on filter cleaning at a small plant: students find what percent of a day's treated water washes the filters, and what recycling saves.

Grade: Grade 6
Subject: Math
Material: Worksheet
Time: 30 min
Prep: No prep
Materials: Printed worksheet, Calculators

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: Items 2 and 8 ask what percent one gallon total is of another, including a percent below one, using the plant's daily production as the whole, and item 6 finds 75 percent of the daily backwash volume.

All materials for 6.RP.A.3 →

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Item 3 converts one wash's volume and its duration into a rate in gallons per minute, the per-minute form an operator uses when sizing a backwash pump.

All materials for 6.RP.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 2026-09-03.

Objectives

Students will find what percent one quantity is of another, including a percent less than one.
Students will compute a rate in gallons per minute from a volume and a time.
Students will subtract a recycled amount to find the net water a process actually consumes.

Vocabulary

Backwash: Backwash is when a treatment plant reverses the flow of water through a filter to flush out the dirt and particles it has trapped. It is like rinsing out a dirty sponge so the filter can keep working well.

Also: filter, recycle, percent, rate

Teacher overview

A treatment plant's filters trap the particles that make water cloudy, and once a day the operator reverses the flow to wash those particles out. That wash uses finished water, so a plant spends some of its own product on cleaning. This worksheet follows one day at the fictional Kirkbride plant. Students frequently assume the wash water is wasted entirely, and items 6 through 8 show that a plant which recycles most of it consumes far less than the raw backwash figure suggests.

Kirkbride Plant's Backwash Water: Percent of a Day's Output — Grade 6 Math

Name: ____________________________ Date: ______________

Student Worksheet

The fictional Kirkbride plant treats 800,000 gallons of water a day. It has 4 filters. Each filter is washed once a day, and each wash uses 6,000 gallons and takes 10 minutes. Show your work.

How many gallons of backwash water does the plant use in one day, with all 4 filters washed once?
The plant treats 800,000 gallons a day and uses 24,000 gallons of it for backwash. What percent of the day's water is that?
One wash uses 6,000 gallons in 10 minutes. What is that rate in gallons per minute?
Start with the day's 800,000 gallons and subtract the 24,000 gallons used for backwash. How many gallons are left to send to town?
Suppose the plant uses 24,000 gallons of backwash water a day for 30 days. How many gallons is that in all?
The plant recycles 75 percent of its 24,000 gallons of daily backwash water. How many gallons does it recycle each day?
The plant uses 24,000 gallons of backwash water a day and recycles 18,000 gallons of it. How many gallons does the backwash actually consume each day?
The backwash consumes 6,000 gallons a day out of the 800,000 gallons treated. What percent of the day's water is that?
On a hot day each of the 4 filters is washed twice, and each wash still uses 6,000 gallons. How many gallons of backwash water is that for the day?
Four filters are washed one after another, and each wash takes 10 minutes. How many minutes does the whole round of washing take?

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: 24,000 gallons.
4 filters times 6,000 gallons each is 24,000 gallons.
Answer: 3 percent.
24,000 divided by 800,000 is 0.03, which is 3 percent.
Answer: 600 gpm.
6,000 gallons divided by 10 minutes is 600 gallons per minute.
Answer: 776,000 gallons.
800,000 minus 24,000 is 776,000 gallons.
Answer: 720,000 gallons.
24,000 gallons per day times 30 days is 720,000 gallons.
Answer: 18,000 gallons.
75 percent of 24,000 is 0.75 times 24,000, which is 18,000 gallons.
Answer: 6,000 gallons.
24,000 gallons used minus 18,000 gallons recycled leaves 6,000 gallons consumed.
Answer: 0.75 percent.
6,000 divided by 800,000 is 0.0075, which is 0.75 percent. This is one quarter of the 3 percent found in item 2, which matches recycling three quarters of the water.
Answer: 48,000 gallons.
4 filters times 2 washes is 8 washes, and 8 times 6,000 gallons is 48,000 gallons.
Answer: 40 minutes.
4 washes times 10 minutes each is 40 minutes.

Differentiation

Support

Give these students a filled-in first row for the fictional Kirkbride plant showing 4 filters times 6,000 gallons, and a reminder card that reads "percent = part divided by whole, then move the decimal two places." Assign items 1 through 5 first and add items 6 through 8 after the first group is checked.

Extension

Ask these students to find how many gallons the fictional Kirkbride plant would consume for backwash in a full year with recycling in place, and to compare that with a year without recycling. They should present both totals and the percent difference in a short written statement.

ELL supports

Pre-teach filter, backwash, and recycle with a two-arrow sketch of one filter, one arrow showing water going down through the sand and one showing wash water coming back up. Provide this sentence frame for item 7: "The plant uses ___ gallons and gets ___ gallons back, so it really uses ___ gallons."

Extensions

Have students compare the fictional Kirkbride figures with a real utility's published annual report, many of which list treated volume and backwash or process water separately. Computing the same percent from a real table shows students that the arithmetic they just practiced is the arithmetic in the report.