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Math problem set Grade 7 Careers & CTE

Sundrell's Booster Station: An Operator Trainee's Pump Log

A grade 7 problem set built on one fictional booster station log, moving from a complex-fraction unit rate to proportional equations and license-hour percents.

Objectives

  1. Students will compute a unit rate from a quantity measured over a fractional hour.
  2. Students will identify a constant of proportionality and write its equation.
  3. Students will solve multistep percent problems about pumping totals and training hours.

Vocabulary

Key words: booster station, unit rate, constant of proportionality, operator trainee, percent increase

Teacher overview

Every problem in this set comes from one week of the pump log kept by an operator trainee at the fictional Sundrell Water District. A booster station is a small building with a pump that pushes water uphill to a higher part of town, and the trainee records how long the pump runs and how much it delivers. The set also tracks the hours the trainee logs toward a state operator license, since licenses are earned by exam after documented time on the job. The misconception this set corrects is the belief that dividing by three quarters of an hour must make an answer smaller. Dividing by a number less than one makes the result larger, which is why a pump that moved 13,500 gallons in three quarters of an hour is running at a higher rate than 13,500 gallons per hour.

Sundrell's Booster Station: An Operator Trainee's Pump Log — Grade 7 Careers & CTE
Name: ____________________________ Date: ______________

Problems

The fictional Sundrell Water District serves a town of about 11,000 people. One booster station lifts water to the neighborhoods on the ridge. Every figure below was invented for this problem set.

  1. On Monday the booster pump ran for three quarters of an hour and delivered 13,500 gallons. What was the pump's rate in gallons per hour?
  2. The trainee recorded three more runs: 10 minutes delivered 3,000 gallons, 25 minutes delivered 7,500 gallons, and 40 minutes delivered 12,000 gallons. Do these three pairs show a proportional relationship between minutes and gallons?
  3. Using the same three runs from problem 2, what is the constant of proportionality, in gallons per minute?
  4. Write an equation for the gallons delivered, g, when the pump runs for m minutes.
  5. On Tuesday the pump ran for two and a half hours at the Monday rate of 18,000 gallons per hour. How many gallons did it deliver?
  6. On Thursday the ridge needs 27,000 gallons. At 18,000 gallons per hour, how many hours must the pump run?
  7. The station delivered 45,000 gallons on Tuesday and 54,000 gallons on Wednesday. What was the percent increase from Tuesday to Wednesday?
  8. On Wednesday the whole fictional Sundrell district delivered 300,000 gallons to customers. The booster station handled 54,000 of those gallons. What percent of the district total is that?
  9. In our scenario, the trainee's state requires 1,800 hours of documented plant experience before the operator exam. The trainee has logged 1,260 hours. What percent of the requirement is complete?
  10. The trainee logs 36 hours each week. Using the requirement and the total from problem 9, how many more weeks of logging are needed to reach 1,800 hours?

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: 18,000 gallons per hour.
    Three quarters of an hour is the fraction 3/4. Divide the gallons by that fraction: 13,500 divided by 3/4 is the same as 13,500 times 4/3. That gives 54,000 divided by 3, which is 18,000 gallons per hour. A student who multiplies instead of dividing gets 10,125 gallons, which is the error this set is built to catch.
  2. Answer: Yes.
    Divide gallons by minutes for each pair. The first pair gives 3,000 divided by 10, which is 300. The second gives 7,500 divided by 25, which is 300. The third gives 12,000 divided by 40, which is 300. All three ratios are equal, so the relationship is proportional.
  3. Answer: 300 gallons per minute.
    Every pair in problem 2 reduces to the same quotient of 300, so the constant of proportionality is 300 gallons per minute. This matches problem 1, because 300 gallons per minute times 60 minutes is 18,000 gallons per hour.
  4. Answer: g = 300m.
    The constant of proportionality multiplies the number of minutes. With g in gallons and m in minutes, the equation is g equals 300 times m.
  5. Answer: 45,000 gallons.
    Two and a half hours times 18,000 gallons per hour equals 45,000 gallons. Checking with the other unit works too: two and a half hours is 150 minutes, and 150 times 300 gallons per minute is 45,000 gallons.
  6. Answer: 1.5 hours.
    Divide the gallons needed by the hourly rate: 27,000 divided by 18,000 equals 1.5 hours. That is one hour and thirty minutes of run time.
  7. Answer: 20 percent.
    The increase is 54,000 minus 45,000, which is 9,000 gallons. Divide by the starting amount: 9,000 divided by 45,000 equals 0.2, which is 20 percent. Dividing by 54,000 instead gives about 16.7 percent, which answers a different question.
  8. Answer: 18 percent.
    Divide the station's gallons by the district total: 54,000 divided by 300,000 equals 0.18. As a percent that is 18 percent of what the fictional district delivered that day.
  9. Answer: 70 percent.
    Divide the hours logged by the hours required: 1,260 divided by 1,800 equals 0.7, which is 70 percent of the requirement.
  10. Answer: 15 weeks.
    The hours still needed are 1,800 minus 1,260, which is 540 hours. Divide by the weekly hours: 540 divided by 36 equals 15 weeks. Checked the other way, 15 times 36 is 540, and 1,260 plus 540 is 1,800.

Differentiation

Support

Give these students problem 1 worked as a model, with the division by 3/4 rewritten as multiplication by 4/3 on a separate line. For problems 2 and 3, supply a three-row table with a blank column headed "gallons divided by minutes" so the equal ratios become visible before the question is asked. Allow a calculator throughout, and let problem 4 be answered by circling the correct equation from three choices.

Extension

Ask these students to find how long the fictional Sundrell pump would need to run to deliver a full day's ridge demand of 90,000 gallons, then to write an inequality describing the run times that would keep the pump under 6 hours a day. They can also explain in writing why the trainee's log matters to a licensing board.

ELL supports

Pre-teach booster station, run time, rate, and constant of proportionality with a labeled sketch showing a pump, a pipe, and a tank uphill. Provide the phrase frame "___ gallons in ___ minutes is ___ gallons each minute" for problems 2 and 3, and let students say each answer aloud with its unit before writing it.

Extensions

Ask students to look up the water operator certification page for their own state and to find what the first license class requires in experience and education. A short comparison with the 1,800-hour figure invented for the fictional Sundrell scenario shows how much these requirements vary from state to state.