Math problem set Grade 12 Science

Pinehaven Watershed Water Budget: Precipitation to Supply

A grade 12 problem set turning a fictional watershed's rainfall into acre-feet and gallons, then splitting it into evapotranspiration, runoff, and recharge.

Grade: Grade 12
Subject: Science
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: Students carry units through the inches-to-feet, feet-to-acre-feet, acre-feet-to-gallons, and gallons-to-MGD chain in problems 1 through 8, the multi-step dimensional analysis this standard names.

All materials for HSN-Q.A.1 →

HSN-Q.A.2 Common Core Math

Define appropriate quantities for the purpose of descriptive modeling.

How this material aligns: Problems 7 and 9 ask students to choose whether acre-feet, MGD, or gpm best answers a supply question, the modeling-quantity decision this standard requires.

All materials for HSN-Q.A.2 →

HS-ESS3-3 NGSS

Create a computational simulation to illustrate the relationships among the management of natural resources, the sustainability of human populations, and biodiversity.

How this material aligns: Problems 4 through 6 build a simplified water-budget model splitting the watershed's precipitation among evapotranspiration, runoff, and recharge, and problem 9 compares the wells' annual withdrawal against that recharge to judge whether the pumping is sustainable.

All materials for HS-ESS3-3 →

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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 convert an annual precipitation depth over a watershed area into a volume in acre-feet and gallons.
Students will partition precipitation into evapotranspiration, runoff, and recharge using given percentages.
Students will compare annual groundwater recharge with well withdrawals to judge sustainability.

Vocabulary

Watershed: A watershed is all the land where rain that falls will drain to the same stream, river, or lake. Everyone lives in a watershed, no matter how far from the water they live.
Evapotranspiration: Evapotranspiration is the total amount of water that leaves the land and goes into the air, both from wet surfaces and from plants. Scientists combine evaporation and transpiration into one word.
Recharge: Recharge is water soaking down through the ground to refill an aquifer, the way rain refills an underground sponge. Aquifers stay healthy only if recharge keeps up with pumping.
Acre-foot: The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.
Water budget: A water budget is a way of tracking all the water coming into an area, like rain and snowmelt, against all the water leaving it, like evaporation and streamflow. Scientists use water budgets to see whether a watershed or aquifer is gaining or losing water over time.

Teacher overview

The fictional Pinehaven watershed drains 12,000 acres of forest and farmland, and this problem set follows a year's precipitation from the rain gauge to the water supply. Students convert a rainfall depth into a volume, split that volume into the three paths water takes, and then compare recharge against the wells that draw on the aquifer. A common error is treating inches of rain as if they were feet. Depth must be converted from inches to feet before it is multiplied by the area in acres, or the acre-foot total comes out twelve times too large.

Pinehaven Watershed Water Budget: Precipitation to Supply — Grade 12 Science

Name: ____________________________ Date: ______________

Problems

Use these values and conversions for the fictional Pinehaven watershed:

Watershed area: 12,000 acres
Average annual precipitation: 40 inches
Of the precipitation, 55 percent returns to the air as evapotranspiration, 30 percent becomes surface runoff, and 15 percent recharges groundwater.
Conversions: 1 acre-foot = 325,851 gallons; depth in feet = inches / 12; 1 MGD = 694 gpm.

Convert the 40 inches of annual precipitation to a depth in feet.
Calculate the total volume of precipitation on the watershed in acre-feet, by multiplying the area in acres by the depth in feet.
Convert the total precipitation from problem 2 to gallons.
Calculate the evapotranspiration volume in acre-feet (55 percent of the total precipitation).
Calculate the surface runoff volume in acre-feet (30 percent of the total precipitation).
Calculate the groundwater recharge volume in acre-feet (15 percent of the total precipitation).
Convert the annual surface runoff from problem 5 to an average daily flow in MGD, by converting to gallons and dividing across 365 days. Round to the nearest hundredth.
Express the average runoff flow from problem 7 in gallons per minute, using 1 MGD = 694 gpm. Round to the nearest whole gpm.
Pinehaven's wells pump a steady 2.0 MGD year-round from the aquifer. Convert that annual withdrawal to acre-feet per year and state whether it is less than the recharge from problem 6.
Explain why the three percentages for evapotranspiration, runoff, and recharge must add to 100 percent in this simple budget, and name one real process the model leaves out.

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: 3.33 feet.
40 inches / 12 inches per foot = 3.333, which rounds to 3.33 feet.
Answer: 40,000 acre-feet.
12,000 acres x 3.3333 feet = 40,000 acre-feet.
Answer: 13,034,040,000 gallons.
40,000 acre-feet x 325,851 gallons per acre-foot = 13,034,040,000 gallons, about 13.0 billion gallons.
Answer: 22,000 acre-feet.
0.55 x 40,000 acre-feet = 22,000 acre-feet of evapotranspiration.
Answer: 12,000 acre-feet.
0.30 x 40,000 acre-feet = 12,000 acre-feet of surface runoff.
Answer: 6,000 acre-feet.
0.15 x 40,000 acre-feet = 6,000 acre-feet of groundwater recharge.
Answer: 10.71 MGD.
12,000 acre-feet x 325,851 = 3,910,212,000 gallons per year. Divided by 365 days = 10,712,910 gallons per day, which is 10.71 MGD.
Answer: 7,433 gpm.
10.71 MGD x 694 gpm per MGD = 7,432.7, which rounds to 7,433 gpm.
Answer: 2,240 acre-feet per year, which is less than recharge.
2.0 MGD x 365 days = 730 million gallons per year. 730,000,000 / 325,851 = 2,240.3, about 2,240 acre-feet per year. That is well below the 6,000 acre-feet of recharge, so pumping is within the annual recharge.
Answer: The three paths account for all the precipitation, so they sum to 100 percent.
Every inch of precipitation either evaporates and transpires, runs off, or recharges the ground, so in this closed budget the shares must total 100 percent. The model leaves out year-to-year storage changes, such as soil moisture and snowpack carried over, and it treats the percentages as fixed when they actually shift with weather and land cover.

Differentiation

Support

Provide problems 4 through 6 with the multiplication set up (0.55 x 40,000 = ___) so students complete only the arithmetic, and give the conversion factors on a printed card. Work problem 1 and problem 2 together first so the inches-to-feet step is clear.

Extension

Ask students to find how much of the watershed's runoff a downstream city could rely on if it could capture only 40 percent of the annual runoff, expressed in both acre-feet and MGD, and to state one reason the full runoff cannot be captured.

ELL supports

Pre-teach "watershed," "evapotranspiration," and "recharge" with a labeled diagram showing rain splitting into three arrows. Provide a sentence frame for problem 10 and allow the three-path idea to be shown as a labeled diagram.

Extensions

Have students look up the drainage area of their own local watershed and its average annual rainfall, then repeat problems 1 through 3 with those real figures to estimate how much water falls on their watershed in a year.