Math problem set Grade 6 Math

Grantham Plant Daily Flow: Ratios, Percent, and Tanks

A grade 6 math problem set at a fictional treatment plant, covering percent of a daily limit, a single-step flow conversion, and two-tank ratios.

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 1, 2, and 5 have students find a percent of a quantity, and problem 3 converts a flow of one million gallons a day to gallons per minute, the percent and unit-conversion work this standard targets.

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: Problem 6 has students use a fixed fill rate in gallons per minute to find a fill time, the unit-rate reasoning this standard requires.

All materials for 6.RP.A.2 →

Download Word file

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 what percent of a plant's daily limit a given day's flow represents.
Students will convert a daily flow to gallons per minute and use a fill rate and tank ratio to solve related problems.

Vocabulary

Flow rate: Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: percent, ratio, unit rate

Teacher overview

A treatment plant has a daily limit, which is the most water it is built to clean in one day. Comparing each day's flow to that limit is a natural percent problem, and it is the kind of check an operator runs every shift. This set also uses one standard conversion, that one million gallons a day equals 694 gallons per minute, kept to a single step so it fits grade 6. Grantham is a fictional plant created for this problem set. A common misconception is comparing today's flow to yesterday's flow instead of to the fixed daily limit; percent of capacity always uses the limit as the whole.

Grantham Plant Daily Flow: Ratios, Percent, and Tanks — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Suppose the fictional Grantham plant cleans water drawn from Otter Creek. On the busiest day it can treat 6 million gallons. Use the numbers in each problem.

On Tuesday the plant treated 4.5 million gallons. What percent of its 6-million-gallon limit is that?
On Wednesday it treated 3 million gallons. What percent of the 6-million-gallon limit is that?
One million gallons a day equals 694 gallons per minute. On a 2-million-gallon day, how many gallons per minute is that?
The plant has two holding tanks. Tank A holds 20,000 gallons and Tank B holds 30,000 gallons. Write the ratio of A to B in simplest form.
What percent of the two tanks' combined volume does Tank A hold?
Water flows into Tank A at 500 gallons per minute. How many minutes does it take to fill Tank A?
The plant adds 3 gallons of treatment liquid for every 10,000 gallons of water. How many gallons of treatment liquid does 6 million gallons need?
Explain why percent of capacity uses the 6-million-gallon limit and not yesterday's flow.

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: 75%. 4.5 ÷ 6 = 0.75, and 0.75 × 100 = 75 percent of the limit.
Answer: 50%. 3 ÷ 6 = 0.5, and 0.5 × 100 = 50 percent of the limit.
Answer: 1,388 gallons per minute. Two million gallons a day is 2 × 694 = 1,388 gallons per minute.
Answer: 2; the ratio of A to B is 2 to 3. Both 20,000 and 30,000 divide by 10,000, giving 2:3.
Answer: 40%. The tanks hold 20,000 + 30,000 = 50,000 gallons; Tank A is 20,000 ÷ 50,000 = 0.40, or 40 percent.
Answer: 40 minutes. 20,000 gallons ÷ 500 gallons per minute = 40 minutes.
Answer: 1,800 gallons. 6,000,000 ÷ 10,000 = 600 units, and 600 × 3 = 1,800 gallons of treatment liquid.
Answer: The limit is the fixed whole. Percent of capacity compares the day's flow to the most the plant can ever treat, which stays the same, while yesterday's flow changes.

Differentiation

Support

Rewrite the million-gallon figures as plain numbers first (6 million as 6) so students can see problems 1 and 2 as simple part-over-whole fractions. Provide the conversion 1 million gallons a day equals 694 gallons per minute on a card for problem 3, and allow a calculator throughout.

Extension

Ask students to find the plant's percent of capacity on a day when it treats 5.4 million gallons, and then find how many more million gallons it could still treat that day before reaching the limit. Have them show both answers with the same whole.

ELL supports

Pre-teach limit, flow, tank, and ratio with a simple labeled drawing of the plant and its two tanks. Provide a sentence frame for problem 8: "Percent of capacity uses the limit because ___." Allow labeled number sentences instead of full sentences.