Math problem set Grade 10 Math

Willowmere Aquifer Storage: Volume, Yield, and Overdraft

A grade 10 problem set on groundwater: students find aquifer storage in acre-feet and gallons, apply specific yield, and test pumping against a safe-yield limit.

Grade: Grade 10
Subject: Math
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Problems 3 and 4 convert acre-feet to gallons and gallons per day to gallons per year, carrying units through each step as this standard requires.

All materials for HSN-Q.A.1 →

HSG-MG.A.2 Common Core Math

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

How this material aligns: Problems 2 and 7 apply specific yield as a volume-based density fraction to find drainable water, the density-in-modeling reasoning this standard names.

All materials for HSG-MG.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 2026-07-23.

Objectives

Students will calculate aquifer storage volume and convert it to gallons.
Students will apply specific yield and compare pumping against a safe-yield limit.

Vocabulary

Aquifer: An aquifer is an underground layer of rock, sand, or gravel that holds water in the tiny spaces between its grains. Wells reach down into aquifers to bring water up to the surface.

Also: specific yield, safe yield, overdraft

Teacher overview

An aquifer holds water in the tiny spaces between grains of sand and gravel, but not all of that water will drain out to a well. Specific yield is the fraction of the total volume that actually drains, and it is smaller than the porosity because some water clings to the grains. This set uses the fictional town of Talmadge above the Willowmere aquifer. The misconception it corrects is assuming every gallon in the pores can be pumped: the drainable water is set by specific yield, not by porosity.

Willowmere Aquifer Storage: Volume, Yield, and Overdraft — Grade 10 Math

Name: ____________________________ Date: ______________

Problems

The town of Talmadge sits above the Willowmere aquifer. This scenario is fictional, and its numbers are set for this problem set.

Aquifer and town data:

Saturated area: 500 acres; saturated thickness: 40 feet
Specific yield: 0.20; total porosity: 0.30
1 acre-foot = 325,851 gallons
Current pumping: 1.5 MGD; safe yield (matched to recharge): 0.8 MGD

Find the bulk saturated volume of the aquifer, in acre-feet. Multiply area by thickness.
Find the drainable water, in acre-feet, by applying the specific yield of 0.20.
Convert the drainable water from item 2 to gallons.
Convert the current pumping of 1.5 MGD to gallons per year. Use 365 days.
With no recharge, how many years would the drainable water last at the current pumping rate?
Is the current pumping within the 0.8 MGD safe yield? By how much does it pass or exceed it?
Of the water in the pores, what percent stays behind and does not drain? Use porosity 0.30 and specific yield 0.20.
Explain why the drainable water is less than the total water held in the pores.

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: 20,000 acre-ft.
Bulk volume = 500 acres x 40 feet = 20,000 acre-feet.
Answer: 4,000 acre-ft.
Drainable water = 20,000 acre-feet x 0.20 = 4,000 acre-feet.
Answer: 1,303,404,000 gal.
4,000 acre-feet x 325,851 gallons per acre-foot = 1,303,404,000 gallons.
Answer: 547,500,000 gal/yr.
1.5 MGD is 1,500,000 gallons per day. Then 1,500,000 x 365 = 547,500,000 gallons per year.
Answer: 2.4 years.
1,303,404,000 gallons / 547,500,000 gallons per year = 2.38, or about 2.4 years.
Answer: No, it exceeds safe yield by 0.7 MGD.
Current pumping is 1.5 MGD, which is above the 0.8 MGD safe yield. The overdraft is 1.5 - 0.8 = 0.7 MGD.
Answer: 33 percent.
Water that stays behind is porosity minus specific yield: 0.30 - 0.20 = 0.10. As a share of porosity, 0.10 / 0.30 x 100 = 33.3, or about 33 percent.
Answer: Some pore water clings to the grains and will not drain to a well.
Porosity counts all the space holding water, but surface tension holds part of that water in place. Only the specific-yield fraction drains freely, so drainable water is always less than total pore water.

Differentiation

Support

Give students the storage steps as a labeled chain: area x thickness gives bulk acre-feet, times specific yield gives drainable acre-feet, times 325,851 gives gallons. Work problem 1 together before students continue.

Extension

Have students find how many years the drainable water would last if the town cut pumping to the fictional 0.8 MGD safe yield, then explain why matching pumping to recharge changes the answer from a countdown to a steady supply.

ELL supports

Pre-teach "aquifer," "porosity," and "specific yield" with a sponge demonstration: a full sponge holds water, but only some drips out when lifted. Provide a sentence frame for problem 8: "The drainable water is less because ___."