Math problem set Grade 6 Careers & CTE

Undercliff Well Field Log: A Groundwater Technician's Math

A grade 6 careers problem set on a well field technician's daily log, covering drawdown, specific capacity as a unit rate, percent share, and a flow conversion.

Grade: Grade 6
Subject: Careers & CTE
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculators

Standards

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: Problems 3 and 4 find specific capacity in gallons per minute for each foot of drawdown, a unit rate drawn from the well log.

All materials for 6.RP.A.2 →

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: Problem 6 finds one well's percent share of the field total, and problem 8 uses a pumping rate in gallons per minute to find the gallons one well delivers over 12 hours.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Problems 1, 2, and 9 subtract multi-digit decimals taken from the technician's water level readings and specific capacity figures.

All materials for 6.NS.B.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 well drawdown from static and pumping water levels.
Students will express specific capacity as a gallons-per-minute-per-foot unit rate.
Students will find a percent share and convert a daily demand into gallons per minute.

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, pumping water level, specific capacity, well field

Teacher overview

Every problem in this set comes from one morning of readings at the fictional Undercliff well field, where a groundwater technician records water levels and pump rates as the wells start for the day. The set follows the order the technician actually works in, moving from raw readings to drawdown, then to a rate that lets three unequal wells be compared, and finally to the town's demand. One misconception runs through the whole topic and is worth naming before students begin: many students report the pumping water level as the drawdown. Drawdown is the difference between the pumping level and the static level, so the reading alone is never the answer.

Undercliff Well Field Log: A Groundwater Technician's Math — Grade 6 Careers & CTE

Name: ____________________________ Date: ______________

Problems

The Undercliff well field. You are a well field technician for the fictional Undercliff well field, which supplies the town of Wraysbury. Three wells draw from the same sand and gravel aquifer. Before the pumps start, you measure the static water level, which is the depth from the ground surface down to the water when the well is at rest. After the pump has run for an hour, you measure the pumping water level. The difference between the two is the drawdown. Most well field technicians start with a high school diploma and learn the field on the job, then earn a state operator license by exam, and many add a two-year college degree in water or environmental technology. The hydrogeologists who decide where a new well is drilled hold a four-year degree, and some continue to graduate study. Show every step of your work.

Morning log

Well	Static level (feet)	Pumping level (feet)	Pump rate (gallons per minute)
Well 1	44.0	58.0	350
Well 2	40.5	60.5	250
Well 3	38.5	54.5	400

Well 2 has a static level of 40.5 feet and a pumping level of 60.5 feet. What is the drawdown at Well 2?
Well 3 has a static level of 38.5 feet and a pumping level of 54.5 feet. What is the drawdown at Well 3?
Specific capacity tells you how many gallons per minute a well gives for each foot of drawdown. Well 1 pumps 350 gallons per minute with a drawdown of 14 feet. What is the specific capacity of Well 1?
Well 2 pumps 250 gallons per minute. Using your drawdown answer from problem 1, what is the specific capacity of Well 2?
Well 1 pumps 350 gallons per minute, Well 2 pumps 250 gallons per minute, and Well 3 pumps 400 gallons per minute. How many gallons per minute does the whole well field pump when all three run at once?
Well 3 pumps 400 gallons per minute out of the 1,000 gallons per minute the whole field pumps. What percent of the field total comes from Well 3?
On an average day the town of Wraysbury uses 1.0 million gallons. One million gallons per day equals 694 gallons per minute. How many gallons per minute is the town's average daily use?
Well 3 runs for 12 hours at 400 gallons per minute. There are 60 minutes in an hour. How many gallons does Well 3 pump in those 12 hours?
Last year the specific capacity of Well 2 was 20 gallons per minute for each foot of drawdown. Using your answer from problem 4, by how much has the specific capacity of Well 2 dropped?

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: 20 feet.
Drawdown equals the pumping level minus the static level. 60.5 feet minus 40.5 feet equals 20.0 feet of drawdown.
Answer: 16 feet.
54.5 feet minus 38.5 feet equals 16.0 feet of drawdown.
Answer: 25 gallons per minute per foot.
Specific capacity equals the pump rate divided by the drawdown. 350 gallons per minute divided by 14 feet equals 25 gallons per minute for each foot of drawdown.
Answer: 12.5 gallons per minute per foot.
The drawdown from problem 1 is 20 feet. 250 gallons per minute divided by 20 feet equals 12.5 gallons per minute for each foot of drawdown.
Answer: 1,000 gallons per minute.
350 plus 250 equals 600, and 600 plus 400 equals 1,000 gallons per minute for the whole field.
Answer: 40 percent.
400 divided by 1,000 equals 0.4, and 0.4 written as a percent is 40 percent.
Answer: 694 gallons per minute.
The town uses 1.0 million gallons per day, and each million gallons per day equals 694 gallons per minute. 1.0 times 694 equals 694 gallons per minute.
Answer: 288,000 gallons.
In one hour the well pumps 400 gallons per minute times 60 minutes, which equals 24,000 gallons. Over 12 hours, 24,000 gallons times 12 equals 288,000 gallons.
Answer: 7.5 gallons per minute per foot.
Last year Well 2 gave 20 gallons per minute for each foot of drawdown, and problem 4 shows it now gives 12.5. 20 minus 12.5 equals a drop of 7.5 gallons per minute for each foot.

Differentiation

Support

Give these students a vertical drawing of one well with the ground surface at the top, a line labeled static level, and a lower line labeled pumping level, and have them mark the drawdown as the gap between the two lines before starting problem 1. Provide problems 3 and 4 with the division already set up, and assign only problems 1 through 6.

Extension

Ask students to decide which well at the fictional Undercliff well field the technician should schedule for cleaning first, using the specific capacity figures from problems 3, 4, and 9. Students write a short paragraph naming the well, citing the numbers, and explaining why a falling specific capacity is a warning even while the pump still delivers water.

ELL supports

Pre-teach "static," "drawdown," and "specific capacity" with the well cross-section drawing and a card showing each term beside a one-sentence meaning. Provide the sentence frame "The drawdown at Well ____ is ____ feet because ____ minus ____ equals ____." Allow students to say answers aloud before writing them.

Extensions

Have students track how the specific capacity of a single well would change if the drawdown grew by one foot each year while the pump rate stayed the same, calculating the figure for three years and describing the trend in a sentence. Students then explain what the technician would recommend before the well reaches half its original specific capacity.