Math problem set Grade 7 Math

Dellmoor Booster Pumps: A Grade 7 Proportional-Rate Problem Set

A grade 7 set where students test proportionality, find a pump's flow rate as a constant of proportionality, and compute complex-fraction rates for a fictional station.

Grade: Grade 7
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

7.RP.A.2 Common Core Math

Recognize and represent proportional relationships between quantities, including identifying the constant of proportionality and representing proportional relationships by equations.

How this material aligns: Problems 1 through 5 have students test whether gallons are proportional to minutes, name the flow rate as the constant of proportionality, and write and use its equation, exactly what this standard names.

All materials for 7.RP.A.2 →

7.RP.A.1 Common Core Math

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

How this material aligns: Problems 6 and 7 have students compute a flow rate from a fractional number of gallons over a fractional number of minutes, the complex-fraction unit rate this standard requires.

All materials for 7.RP.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 test a table of values for proportionality and name the constant of proportionality.
Students will write and use an equation for a proportional pumping relationship.
Students will compute a unit rate from a ratio of two fractions.

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: proportional, constant of proportionality, unit rate

Teacher overview

A booster pump station pushes water to homes on higher ground, and each pump moves a steady number of gallons every minute. This set uses a fictional station to build proportional reasoning from a table, to an equation, and finally to two pumps whose rates come as a fraction of a gallon over a fraction of a minute. A common misconception is that any table showing "more time, more water" must be proportional; problem 1 asks students to check the ratios first rather than assume it, because a real pump only pumps proportionally once it is running at steady speed.

Dellmoor Booster Pumps: A Grade 7 Proportional-Rate Problem Set — Grade 7 Math

Name: ____________________________ Date: ______________

Problems

The Dellmoor booster station is a fictional pump station used for this set. Pump A runs at a steady speed. A crew records how much water it moves.

Minutes running	Gallons pumped
5	900
10	1,800
15	2,700

Are the gallons pumped proportional to the minutes running? Check the ratio of gallons to minutes for all three rows and explain.
Find Pump A's flow rate as the constant of proportionality, in gallons per minute.
Write an equation that gives the gallons pumped, g, after m minutes.
Use your equation to find how many gallons Pump A moves in 25 minutes.
How many minutes does Pump A need to move 5,400 gallons?
Pump B is tested at a trickle. It moves 2 and 1/2 gallons in 1/3 of a minute. Find its flow rate in gallons per minute.
Pump C moves 3/4 of a gallon in 1/6 of a minute. Find its flow rate in gallons per minute.
Compare Pump B and Pump C. Which one is faster, and by how many gallons per minute?
The crew runs Pump A and Pump B together. Their rates add. How many minutes will the two pumps need to fill a 5,625-gallon tank?

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: Yes, the rate is proportional.
900 ÷ 5 = 180; 1,800 ÷ 10 = 180; 2,700 ÷ 15 = 180. Every row gives the same ratio of 180 gallons per minute, so gallons are proportional to minutes.
Answer: 180 gpm.
The constant of proportionality is the shared ratio from problem 1, 180 gallons per minute.
Answer: g = 180m.
Gallons pumped equals the flow rate times the minutes, so g = 180 × m.
Answer: 4,500 gallons. g = 180 × 25 = 4,500 gallons.
Answer: 30 minutes.
5,400 ÷ 180 = 30 minutes.
Answer: 7.5 gpm.
2 and 1/2 gallons is 2.5 gallons. 2.5 ÷ (1/3) = 2.5 × 3 = 7.5 gallons per minute.
Answer: 4.5 gpm.
3/4 of a gallon is 0.75 gallons. 0.75 ÷ (1/6) = 0.75 × 6 = 4.5 gallons per minute.
Answer: Pump B, by 3 gpm.
Pump B runs at 7.5 and Pump C at 4.5. 7.5 − 4.5 = 3 gallons per minute, so Pump B is faster by 3 gallons per minute.
Answer: 30 minutes.
Together the pumps move 180 + 7.5 = 187.5 gallons per minute. 5,625 ÷ 187.5 = 30 minutes.

Differentiation

Support

Give students the ratio setup for problem 1 already written as 900 ÷ 5, 1,800 ÷ 10, and 2,700 ÷ 15 so they only compute and compare. For problems 6 and 7, remind them on the page that dividing by a fraction is the same as multiplying by its reciprocal.

Extension

Ask students to find the flow rate of a fourth pump that would fill the 5,625-gallon tank from problem 9 in exactly 25 minutes on its own, and to write the equation relating its gallons and minutes.

ELL supports

Provide a labeled example of a complex-fraction rate before problem 6, showing "gallons over minutes" as a stacked fraction that becomes a division problem. Offer the sentence frame: "Pump ___ is faster because it moves ___ gallons per minute."