Math problem set Grade 7 Engineering & Design

Stannock Bend Well Field: Pump Hours Under a Drawdown Limit

A grade 7 set on a fictional well field where students find a drawdown rate as a constant of proportionality and solve an inequality for safe pump hours.

Grade: Grade 7
Subject: Engineering & Design
Material: Math problem set
Time: 45 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 and 2 have students find three feet of drawdown per hour as the constant of proportionality in the Well 3 pump test and write the equation relating drawdown to pumping hours.

All materials for 7.RP.A.2 →

7.EE.B.4 Common Core Math

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

How this material aligns: Problem 4 asks students to construct and solve the inequality for pumping hours against the field's eighteen-foot drawdown limit, then read the solution as a greatest allowed run time.

All materials for 7.EE.B.4 →

MS-ETS1-1 NGSS

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

How this material aligns: Problem 10 asks students to classify the drawdown limit as a constraint rather than a criterion, distinguishing what bounds the design from what it must achieve.

All materials for MS-ETS1-1 →

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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 identify the constant of proportionality in a pump test and write it as an equation.
Students will construct and solve an inequality that keeps well drawdown within a stated design limit.
Students will convert a pumping rate and a time limit into a daily volume and compare it to a demand target.

Vocabulary

Drawdown: Drawdown is how far the water level in a well drops when a pump pulls water out. The harder and longer you pump, the bigger the drawdown gets.

Also: static water level, constant of proportionality, constraint

Teacher overview

Stannock Bend is a fictional village that draws its drinking water from two wells in a shallow sand aquifer. When a well pumps, the water level inside the well casing falls, and that drop is called drawdown. The village engineer has set a firm limit on how far the water level may fall, because pulling the level too low damages the pump and pulls in sand. This set has students turn a short pump test into a proportional relationship, write an inequality for the safe number of pumping hours, and check the resulting daily volume against the village's demand. A common error in this math is reading drawdown as the total depth from the ground surface down to the water, when drawdown is only the additional drop that pumping causes below the resting water level.

Stannock Bend Well Field: Pump Hours Under a Drawdown Limit — Grade 7 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Stannock Bend has two wells. In this fictional scenario, the village engineer will not allow the water level in either well to fall more than 18 feet below its resting level. That 18-foot figure is the drawdown limit. Use it for every problem below.

Well 3 was pump tested. Its water level fell 6 feet after 2 hours of steady pumping. The drop stayed steady the whole time. How many feet did the water level fall each hour?
Let d stand for the drawdown in feet and h stand for the hours of pumping. Using your rate from problem 1, write an equation that gives d for any number of hours h.
Using the same steady rate from problem 1, how far will the water level in Well 3 fall after 5 hours of pumping?
The drawdown limit for Well 3 is 18 feet. Write an inequality using the rate from problem 1, then solve it. What is the greatest number of hours Well 3 may pump?
Well 3 pumps 120 gallons every minute. If it runs for the greatest number of hours you found in problem 4, how many gallons does it deliver?
Stannock Bend wants 50,000 gallons a day from Well 3. How many gallons short of that target is your answer from problem 5?
Well 4 was tested the same way. Its water level fell 10 feet after 4 hours of steady pumping. How many feet did the water level fall each hour?
The drawdown limit for Well 4 is also 18 feet. Using your rate from problem 7, how many hours may Well 4 pump before it reaches that limit?
Well 4 pumps 95 gallons every minute. If it runs for the number of hours you found in problem 8, how many gallons does it deliver?
The village engineer set the 18-foot drawdown limit. Is that limit a criterion or a constraint? Explain your choice in one or two sentences.

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: 3 feet per hour.
The level fell 6 feet in 2 hours. 6 feet divided by 2 hours = 3 feet per hour. This is the constant of proportionality for Well 3.
Answer: d = 3h.
Drawdown is proportional to pumping time at 3 feet per hour, so multiplying the hours by the constant 3 gives the drawdown in feet.
Answer: 15 feet.
Substitute h = 5 into d = 3h. d = 3 x 5 = 15 feet of drawdown.
Answer: 6 hours.
The inequality is 3h is less than or equal to 18. Divide both sides by 3: h is less than or equal to 6. The greatest allowed pumping time is 6 hours.
Answer: 43,200 gallons.
6 hours x 60 minutes per hour = 360 minutes. 360 minutes x 120 gallons per minute = 43,200 gallons.
Answer: 6,800 gallons.
50,000 gallons wanted minus 43,200 gallons delivered = 6,800 gallons short of the target.
Answer: 2.5 feet per hour.
The level fell 10 feet in 4 hours. 10 feet divided by 4 hours = 2.5 feet per hour.
Answer: 7.2 hours.
18 feet divided by 2.5 feet per hour = 7.2 hours. Well 4 draws down more slowly, so it may run longer than Well 3.
Answer: 41,040 gallons.
7.2 hours x 60 minutes per hour = 432 minutes. 432 minutes x 95 gallons per minute = 41,040 gallons.
Answer: A constraint.
A constraint is a limit that bounds the design, while a criterion is a target the design must reach. The 18-foot drawdown limit does not describe what the well field must deliver; it sets a boundary the design may not cross. Accept any explanation that names the limit as a boundary on the design rather than a goal for it, and that contrasts it with a target such as the 50,000-gallon daily demand.

Differentiation

Support

Give these students problem 1 already set up as a division sentence with the numbers filled in, and provide a simple sketch of a well showing the resting water level, the pumping water level, and the drawdown measured between them. For problem 4, supply the inequality frame with only the rate missing. Allow a calculator on every problem.

Extension

Ask students to find the smallest pumping rate, in gallons per minute, that would let Well 3 deliver the full daily target while staying inside its six-hour limit. Then have them explain what a pump that fast would do to the drawdown rate, and why the answer is not simply a matter of buying a larger pump.

ELL supports

Pre-teach drawdown, resting level, and limit using a clear jar of water with a straw and a marked strip of tape showing the drop. Provide the sentence frame "The water level falls ___ feet in ___ hours, so it falls ___ feet each hour" for problems 1 and 7. Allow problem 10 to be answered with the frame "This is a ___ because it ___."

Extensions

Have students graph d = 3h for Well 3 and d = 2.5h for Well 4 on the same axes, with hours on the horizontal axis and drawdown on the vertical axis. Ask them to mark the point where each line crosses the 18-foot limit and to explain how the graph shows the same answers they found in problems 4 and 8. Students can then describe in writing what a steeper line tells an engineer about an aquifer.