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Worksheet Grade 12 English Language Arts

Checking the Numbers in a Pell Junction Pump Station Letter

A grade 12 ELA worksheet where students test each numeric claim in a fictional letter to the editor against the water district's own pump station fact sheet.

Objectives

  1. Students will test each numeric claim in a persuasive text against a primary data source.
  2. Students will distinguish claims a source can verify from claims it cannot address at all.
  3. Students will write an evaluative claim about whether a text's evidence supports its conclusion.

Vocabulary

Key words: static pressure, boost, design flow, verifiable claim, evaluative claim

Teacher overview

Letters to the editor about public works often carry numbers, and readers rarely check them. This worksheet pairs a letter opposing a proposed booster pump station with the water district's own published fact sheet, so students can settle each numeric claim rather than argue about tone. The task is deliberately mixed: one of the writer's figures holds up, one is close but rounded in his favor, three are contradicted outright, and one cannot be tested with the source at hand. Students finish by writing an evaluative claim about whether the letter's evidence supports its conclusion.

Checking the Numbers in a Pell Junction Pump Station Letter — Grade 12 English Language Arts
Name: ____________________________ Date: ______________

Student Worksheet

Pell Junction, its water district, and the letter below are fictional, and all documents were written for this worksheet. Use the fact sheet and the conversion list to test the letter's numbers.

Letter to the editor, published in a village newspaper

I am writing to oppose the Tindall Booster Pump Station. The district wants to push over a thousand gallons a minute through a pipe under Tindall Street. Right now the tank alone gives Ridgeview homes barely 20 psi, the legal minimum, and once the booster runs, water will race through that twelve-inch main at highway speed and shake the pipe apart. The district admits our bills will climb by nearly a third. The whole project costs two and a half million dollars. The pumps will run around the clock and use more electricity than the village streetlights. Ridgeview has managed without a booster for sixty years, and it can manage for sixty more.

Fact sheet, Pell Junction Water District, Tindall Booster Pump Station

Item Value
Design flow 1.6 MGD
Discharge main inside diameter 12 inches, which is 1.0 foot
Pump boost at design flow 25 psi
Height of tank overflow above the highest Ridgeview homes 92 feet
Current average monthly residential bill $46.00
Projected average monthly residential bill $49.30
Project capital cost $2,400,000

Conversion list

  • One million gallons per day equals 694 gallons per minute.
  • One million gallons per day equals 1.547 cubic feet per second.
  • One foot of water column equals 0.433 psi.
  • Cross-sectional area of a round pipe, in square feet, equals 0.785 x diameter squared, with the diameter in feet.
  • Flow equals area times velocity.
  • Most states require a minimum of 20 psi in the distribution system.
  1. The fact sheet lists the tank overflow at 92 feet above the highest Ridgeview homes. Using 0.433 psi per foot, find the static pressure those homes see from the tank alone. Round to the nearest tenth.
  2. The fact sheet lists a design flow of 1.6 MGD. Using 694 gallons per minute per MGD, find the design flow in gallons per minute. Round to the nearest ten.
  3. The discharge main has an inside diameter of 1.0 foot. Using area equals 0.785 times diameter squared, find the cross-sectional area in square feet.
  4. Convert the design flow of 1.6 MGD to cubic feet per second, using 1.547 cubic feet per second per MGD. Round to the nearest hundredth.
  5. Take the pipe area as 0.785 square feet and the flow as 2.48 cubic feet per second. Using flow equals area times velocity, find the velocity in feet per second. Round to the nearest tenth.
  6. The static pressure at the highest Ridgeview homes is 39.8 psi, and the fact sheet lists a pump boost of 25 psi at design flow. Find the pressure those homes would see with the booster running.
  7. The current average monthly bill is $46.00 and the projected bill is $49.30. Find the percent increase. Round to the nearest tenth.
  8. The letter makes several numeric claims about what the station will do once it is built. Name the one such claim the fact sheet fully supports, and quote the sentence that carries it.
  9. Compare your answers to items 1 and 6 with the letter's claim about pressure at Ridgeview homes. State whether the claim is supported, and explain what the writer got wrong.
  10. A car on a highway moves at roughly 88 feet per second. Compare that with your answer to item 5, and explain what the phrase "highway speed" does to a reader who does not check it.
  11. The letter calls the project "two and a half million dollars." Compare that with the fact sheet, and judge whether the description is fair. Support the judgment in two sentences.
  12. Identify the one claim about how the station will operate that the fact sheet cannot test at all, name the specific data a reader would need to test it, then write a two-sentence evaluative claim about whether the letter's evidence supports its conclusion.

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: 39.8 psi. Multiply the 92 feet of head in the fictional fact sheet by 0.433 psi per foot: 92 x 0.433 = 39.836, which rounds to 39.8 psi.
  2. Answer: 1,110 gpm. Multiply 1.6 MGD by 694 gallons per minute per MGD: 1.6 x 694 = 1,110.4, which rounds to 1,110 gpm.
  3. Answer: 0.785 sq ft. Apply the area formula with a diameter of 1.0 foot: 0.785 x 1.0 x 1.0 = 0.785 square feet.
  4. Answer: 2.48 cfs. Multiply 1.6 MGD by 1.547 cubic feet per second per MGD: 1.6 x 1.547 = 2.4752, which rounds to 2.48 cfs.
  5. Answer: 3.2 ft/s. Rearrange flow equals area times velocity to get velocity equals flow divided by area: 2.48 / 0.785 = 3.159, which rounds to 3.2 feet per second.
  6. Answer: 64.8 psi. Add the boost to the static pressure: 39.8 + 25 = 64.8 psi, which is inside the 40 to 80 psi range distribution systems typically operate in.
  7. Answer: 7.2 percent. The increase is 49.30 - 46.00 = 3.30 dollars; divide by the starting bill and convert: 3.30 / 46.00 = 0.0717, or 7.2 percent.
  8. Answer: The claim that the station will push over a thousand gallons a minute. The sentence is "The district wants to push over a thousand gallons a minute through a pipe under Tindall Street," and item 2 puts the design flow at 1,110 gpm, which is above a thousand.
  9. Answer: The claim is not supported. Item 1 shows the tank alone already provides 39.8 psi, roughly double the 20 psi minimum rather than barely at it, and item 6 shows that adding the booster raises those homes to 64.8 psi. The writer treated the required minimum as though it were the current condition.
  10. Answer: Item 5 gives about 3.2 feet per second, which is roughly one twenty-seventh of highway speed and closer to a brisk walk. The phrase substitutes a vivid comparison for a measurement, so a reader who does not check it accepts a claim of danger that the fact sheet does not support.
  11. Answer: Accept either judgment if it is supported. The fact sheet lists $2,400,000, so "two and a half million" rounds up by about one hundred thousand dollars. A response calling it unfair should note that the writer rounds every figure in the direction that helps his case; a response calling it acceptable should note that a letter to the editor conventionally rounds and that the difference is under five percent of the total.
  12. Answer: The electricity claim cannot be tested, since the fact sheet reports no energy use for the pumps and nothing at all about village streetlights. A reader would need the pump motor horsepower or kilowatt rating, expected run hours, and the streetlight system's annual consumption. Accept any two-sentence evaluative claim that follows from the checks, for example: "The letter is accurate about how much water the station will move and about nothing else it quantifies. Because its two most alarming figures, the pressure claim and the bill increase, are contradicted by the district's own fact sheet, its evidence does not support the conclusion that the project should be stopped."

Differentiation

Support

Give these students a worked example that uses the same three formulas on a different fictional pressure zone, with each step labeled, before they begin item 1. Provide items 1 through 7 on a partially completed calculation grid that supplies the setup line for each one, so the work is arithmetic rather than translation.

Extension

Ask students to rewrite the letter so that every numeric claim it makes is accurate, keeping the writer's position that the station should not be built. They must then write a short note naming which of the original arguments could not survive the correction, and explain what that tells them about the letter's case.

ELL supports

Pre-teach "static pressure," "boost," "design flow," and "capital cost" with a labeled sketch of a tank, a pump, and a house at the top of a hill. Provide a formula card with each conversion written once as a sentence and once as a numeric example, and allow items 8 through 11 to be answered in three or four short sentences rather than a paragraph.