Water for Schools
Menu

Reading passage Grade 12 English Language Arts

Reconciling the Marrowby River's Three Water Ledgers

A grade 12 informational passage in which a fictional county analyst reconciles acre-feet, cubic feet per second, and gallons per day for one irrigation season.

Objectives

  1. Students will explain why three documents about one river report figures that look incompatible.
  2. Students will use conversion constants supplied by a text to compare quantities across units.
  3. Students will distinguish a disagreement about arithmetic from a disagreement about a definition.

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.
Diversion
Taking water out of a river or stream and sending it somewhere else, such as into a canal or pipeline, to be used by farms or cities.

Also: instream flow, seasonal mean, conversion constant, ledger

Teacher overview

Water is measured in whichever unit suits the job at hand, so a single river can be described in acre-feet by an irrigation district, in cubic feet per second by a stream gauge, and in million gallons per day by a town utility. Documents written in those three units look as though they contradict each other even when every figure is correct. This passage follows a fictional county analyst through that reconciliation, and then past it, to the definitional disagreement that the arithmetic cannot settle. It suits a grade 12 class that is ready to see how a technical dispute can hide inside a choice of units.

Reconciling the Marrowby River's Three Water Ledgers — Grade 12 English Language Arts
Name: ____________________________ Date: ______________

Passage

Perla Nadeau's first assignment as a water resources analyst for the fictional Kinnaird County was described to her as a filing problem. Three documents about the Marrowby River had come in for the same irrigation season, and the county attorney wanted to know which one was wrong.

The first was the annual report of the Marrowby Irrigation District. It stated that the district had diverted 12,000 acre-feet during the season. The second was the state gauge record, which reported a seasonal mean diversion of 33.6 cfs at the headgate. The third came from the town of Kinnaird's utility, which reported an average withdrawal of 2.0 MGD from the same reach for drinking water.

Nadeau's first observation was that none of the three was wrong, and that the attorney had asked the wrong question. The documents were not competing accounts. They were the same river measured by people with different jobs.

An acre-foot is a volume. It is the amount of water that would cover one acre to a depth of one foot, and it equals 325,851 gallons, or 43,560 cubic feet. Irrigation districts think in acre-feet because a water right is a quantity for a season, not a speed. A grower who is owed water wants to know how much, not how fast.

A cubic foot per second is a rate. A stream gauge cannot report a season's total, because it only knows what is passing the instrument at that moment. Over a season, a gauge produces a mean rate. That is the number a regulator wants when the question is whether enough water stayed in the channel on any given day.

Million gallons per day is also a rate, and it belongs to plants. A treatment plant is built to a daily capacity, its pumps are sized to a daily flow, and its operators think in the same unit their equipment is rated in. A household bill, meanwhile, arrives in gallons or in cubic feet, because those are the units a meter counts.

Converting among them took Nadeau twenty minutes. The district's 12,000 acre-feet is 522,720,000 cubic feet, since each acre-foot holds 43,560 of them. The district's season ran 180 days. Divided across those days, the diversion averages 2,904,000 cubic feet each day, and divided again across the 86,400 seconds in a day, it averages 33.6 cubic feet per second. The gauge record and the district report were the same quantity expressed two ways.

The town's figure fit the same frame. One million gallons per day equals 1.547 cubic feet per second, so 2.0 MGD is about 3.1 cfs. Across the same 180 days the town withdrew 360 million gallons, which is about 1,105 acre-feet. Set beside the district's 12,000, the town's share of the season's diversions is small, though Nadeau noted in her memo that the comparison is less simple than it looks: the town returns most of what it takes after treatment, and the district's water leaves the basin in crops and in vapor.

The reconciliation should have ended the assignment. It did not, because of a sentence in the county's own instream flow rule. The rule sets a minimum flow that must remain in the Marrowby during the irrigation season, and it defines that season as 150 days, running from the middle of May to the middle of October. The district's report defines the season as 180 days, from the middle of April.

The same 12,000 acre-feet, spread across a shorter season, is a larger rate. Whether the district exceeded the instream flow rule therefore depends on which definition of the season the county applies, and the two documents were never written to be compared. Ray Ottersby, who manages the district, told Nadeau that his April diversions fill the district's storage ponds before the growers need water, and that counting them inside a season that begins in May would misrepresent what the water is for. The county's rule was drafted a decade later, by staff whose concern was keeping enough flow in the channel for fish.

Nadeau's memo ran to two pages. The first page reconciled the units and showed that all three documents agreed. The second page said that the disagreement worth the attorney's time was not arithmetic at all, and recommended that the county and the district agree on a single definition of the season before either of them published another figure.

Document Figure as published Unit
Marrowby Irrigation District annual report 12,000 acre-feet per season
State gauge record, seasonal mean 33.6 cfs at the headgate
Town of Kinnaird utility report 2.0 MGD withdrawn

Questions

  1. Name the three units the three documents use, and state which job each unit suits, according to the passage.
  2. How many gallons are in one acre-foot, and how many cubic feet, according to the passage?
  3. Show how the district's seasonal total and the gauge's seasonal mean describe the same water. Use the season length the passage gives.
  4. The town's figure looks small beside the district's. Explain what the passage says makes that comparison less simple than it appears.
  5. State what the county and the district actually disagree about, and quote or paraphrase the detail in the passage that reveals it.
  6. Using context, explain what the passage means by a diversion, and why a stream gauge cannot report a seasonal total on its own.
  7. Suppose the county applies its own 150-day season to the district's same 12,000 acre-feet. Calculate the resulting average rate in cubic feet per second, and state whether the acre-foot figure would change.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: Acre-feet, cubic feet per second, and million gallons per day. Acre-feet suit an irrigation district because a water right is a seasonal quantity, cubic feet per second suit a stream gauge because an instrument can only measure what passes it at a moment, and million gallons per day suit a treatment plant because its equipment is rated in daily flow.
  2. Answer: 325,851 gallons, or 43,560 cubic feet. Both constants appear in the paragraph that defines an acre-foot.
  3. Answer: The district's 12,000 acre-feet equals 522,720,000 cubic feet, because each acre-foot holds 43,560 cubic feet. Spread across the district's 180-day season, that is 2,904,000 cubic feet per day, and dividing by the 86,400 seconds in a day gives 33.6 cubic feet per second, the same figure the gauge published.
  4. Answer: The passage notes that the town returns most of what it withdraws after treatment, while the district's water leaves the basin in crops and in evaporation. A comparison of the two withdrawal figures alone therefore says nothing about how much water each use actually removes from the river.
  5. Answer: They disagree about how long the irrigation season is. The county's instream flow rule defines the season as 150 days beginning in the middle of May, while the district's annual report uses 180 days beginning in the middle of April, so the same total volume converts to two different rates.
  6. Answer: A diversion is water taken out of the river at the headgate for use elsewhere, measured either as a volume or as a rate. A gauge cannot report a seasonal total by itself because it measures only what is passing the instrument at that instant, so a total has to be built from many readings over time.
  7. Answer: About 40.3 cubic feet per second, and the acre-foot figure would not change. Dividing 522,720,000 cubic feet by 150 days gives 3,484,800 cubic feet per day, and dividing by 86,400 seconds gives roughly 40.3 cubic feet per second. The volume diverted is the same either way, so only the rate moves.

Differentiation

Support

Give these students a conversion card listing the three constants from the passage with one worked example for each, and let them answer questions 3 and 7 by filling in a prepared chain of three boxes rather than setting up the division themselves. Assign questions 1, 2, 3, and 5, and read the paragraph about the instream flow rule aloud before they attempt question 5.

Extension

Ask students to write the one-paragraph note the fictional county attorney should send to both parties, stating what the documents agree on, what they do not, and what each side would have to give up to adopt a single season definition. Require the paragraph to name no unit more than once.

ELL supports

Pre-teach "acre-foot," "rate," "volume," and "seasonal mean," and post a two-column chart separating measures of volume from measures of rate, since the passage's whole argument rests on that distinction. Allow questions 2 and 7 to be answered with the numbers and the arithmetic alone, and permit oral answers for question 4.

Extensions

Have students find the unit used on their own household water bill, then write a short comparison explaining what that unit is good for and what it hides, using the passage's framework of matching a unit to a job. Ask them to propose one additional column the fictional county should require on every document about the Marrowby, and to justify the proposal in two sentences.