Quiz & test questions Grade 12 Math
Whitmarsh Basin Yield: A Watershed and Runoff Unit Test
A 45-minute, 40-point grade 12 test on a fictional basin: converting runoff depth to acre-feet and MGD, then reading average rates of change from a storage table.
Objectives
- Students will convert a basin's annual runoff depth into acre-feet, gallons, and million gallons per day.
- Students will compute average rate of change in reservoir storage across stated intervals.
- Students will explain why an average across months can conceal a faster decline within one month.
Vocabulary
- 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.
- 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: watershed divide, runoff coefficient, basin yield, average rate of change
Teacher overview
This 45-minute unit test is worth 40 points and covers watershed yield and reservoir drawdown for the fictional Whitmarsh Basin. It mixes two multiple-choice items, eight computation items, and two short-answer items, moving from basin area through annual yield in several units and then into a table of monthly reservoir storage. Students who can convert an inch of runoff over an area into gallons, and who can read an average rate of change from a table, should finish comfortably within the period.
Assessment
All values below describe the fictional Whitmarsh Basin, which drains through Whitmarsh Creek into the fictional Thrushmere Reservoir. Use 640 acres per square mile, 325,851 gallons per acre-foot, and 365 days per year.
Basin data: drainage area 96 square miles, average annual precipitation 38 inches, runoff coefficient 0.22.
Thrushmere Reservoir storage, read on the first of each month:
| Date | Storage (acre-feet) |
|---|---|
| April 1 | 24,600 |
| May 1 | 25,900 |
| June 1 | 24,100 |
| July 1 | 21,300 |
| August 1 | 18,200 |
| September 1 | 15,900 |
(2 points) A watershed divide is best described as:
- A) the highest peak inside a drainage basin
- B) the ridge line separating water that drains toward one stream from water that drains toward another
- C) the point where a river splits into two channels
- D) the boundary of a town's water service area
(2 points) A runoff coefficient of 0.22 for this basin means that:
- A) 22 percent of the basin's surface is covered by water
- B) about 22 percent of the precipitation falling on the basin leaves as streamflow
- C) the creek flows during about 22 percent of the year
- D) the basin receives 22 inches of precipitation per year
(4 points) Find the basin's drainage area in acres.
(4 points) Find the depth of runoff the basin produces in an average year, in inches.
(4 points) Convert your item 4 runoff depth over the full basin area into acre-feet per year. Round to the nearest acre-foot.
(4 points) Convert your item 5 answer to gallons, and report it in billions of gallons rounded to the nearest tenth.
(4 points) Find the basin's average yield in million gallons per day across a 365-day year. Round to the nearest tenth.
(4 points) Using the storage table, find the average rate of change in reservoir storage from June 1 to September 1, in acre-feet per month. Round to the nearest whole acre-foot per month.
(4 points) Which single one-month interval in the table shows the steepest decline, and what is that rate in acre-feet per month?
(4 points) The reservoir's intake sits at 9,000 acre-feet, below which the utility cannot draw. If storage keeps falling from the September 1 level at the August-to-September rate, how many months remain before storage reaches the intake level?
(2 points) Explain in two or three sentences why the average rate of change you found in item 8 understates the fastest drawdown the reservoir actually experienced.
(2 points) Give one specific reason the runoff coefficient for this basin might rise over the next twenty years, and state what that change would do to the yield you calculated in item 5.
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: B.
A divide is the high ground separating adjacent drainage areas. The highest peak may sit on a divide but does not define it, and a service area boundary is a political line rather than a topographic one.Answer: B.
The runoff coefficient is the fraction of precipitation that reaches the stream rather than being lost to evaporation, transpiration, and deep infiltration. It says nothing about surface water cover or how many days the creek flows.Answer: 61,440 acres.
96 square miles x 640 acres per square mile = 61,440 acres.Answer: 8.36 inches.
38 inches x 0.22 = 8.36 inches of runoff per year.Answer: 42,803 acre-ft.
Convert the depth to feet: 8.36 / 12 = 0.69667 feet. Yield = 61,440 acres x 0.69667 feet = 42,803 acre-feet per year.Answer: 13.9 billion gal.
42,803 acre-feet x 325,851 gallons per acre-foot = 13,947,400,353 gallons, or about 13.9 billion gallons per year.Answer: 38.2 MGD.
13,947,400,353 / 365 = 38,212,056 gallons per day, which is 38.2 million gallons per day. Award full credit for a correct chain from a slightly different rounding at item 6.Answer: -2,733 acre-ft per month.
Storage fell from 24,100 on June 1 to 15,900 on September 1, a change of -8,200 acre-feet across 3 months. Average rate of change = -8,200 / 3 = -2,733.3, or about -2,733 acre-feet per month.Answer: -3,100 acre-ft per month.
The monthly changes are +1,300, -1,800, -2,800, -3,100, and -2,300 acre-feet. The steepest decline is July 1 to August 1 at -3,100 acre-feet per month.Answer: 3.0 months.
The August-to-September rate is -2,300 acre-feet per month. Storage above the intake = 15,900 - 9,000 = 6,900 acre-feet. Months remaining = 6,900 / 2,300 = 3.0 months, which puts the reservoir at the intake level on December 1 if nothing changes.Answer: the average blends a slow month with a fast one.
Accept any answer making the averaging point. The three-month figure spreads the total decline evenly across June, July, and August, so the -2,800 and -3,100 months are pulled toward the milder -2,300 month. A supply planner watching only the three-month average would underestimate how quickly the reservoir can fall during the peak demand month.Answer: more impervious cover raises the coefficient.
Accept any specific, plausible cause with the correct effect: new subdivisions, roads, or parking lots replacing forest and field; loss of wetlands; or repeated wildfire hardening the soil surface. Each sends a larger share of precipitation to the stream rather than into the ground, which raises the runoff coefficient and therefore raises the calculated annual yield in item 5, while also making flows flashier and less reliable through a dry summer.
Differentiation
Support
Give students a conversion reference card for the fictional Whitmarsh items listing acres per square mile, inches to feet, and gallons per acre-foot, and provide item 5 partly set up with 8.36 / 12 already computed. Allow the monthly differences for item 9 to be supplied in a prepared column so the item tests interpretation rather than repeated subtraction.
Extension
Ask students to compute what annual runoff depth the fictional basin would need to refill Thrushmere Reservoir from the September 1 level back to the April 1 level, and to state whether that depth is plausible given the basin's 38-inch average precipitation.
ELL supports
Pre-teach "divide," "runoff coefficient," "yield," and "drawdown" with a labeled basin sketch showing the ridge line, the creek, and the reservoir. Provide a units column beside items 3 through 7 with the target unit for each answer already printed, and give sentence frames for items 11 and 12.
Extensions
Have students graph the fictional Thrushmere storage table on labeled and scaled axes, sketch the segment whose slope matches the item 8 average, and mark the single steepest segment from item 9. Ask them to extend the graph to the item 10 intake date and to write one sentence describing what a wet October would do to their extension. The graph turns three separate computations into one picture a utility board could read.