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Math problem set Grade 6 Engineering & Design

Sedgewater Hatchery Aerator Selection Problems

Ten problems where students size an aerator set for a fictional trout hatchery raceway, then compare two models on purchase price, energy use, and years to pay back.

Objectives

  1. Students will convert a raceway exchange rate into gallons per minute and size an aerator set to that flow.
  2. Students will calculate purchase cost and daily energy use for two competing aerator models.
  3. Students will find how many years of energy savings repay the higher purchase price of the better model.

Vocabulary

Dissolved oxygen
Dissolved oxygen is the oxygen gas mixed into water that fish and other underwater animals breathe. Cold, moving water holds more oxygen than warm, still water.

Also: aerator, raceway, biofilter, payback

Teacher overview

Sedgewater Fish Hatchery is fictional, and its flows, prices, and energy figures were invented for this set. The hatchery raises trout in long concrete channels called raceways, and it recirculates the water through a biofilter, a bed of media where bacteria convert fish waste into less harmful forms. Most fish need dissolved oxygen above 5 milligrams per liter, and the bacteria in the biofilter consume oxygen as well, so aerators run day and night to keep the level up. Students size the aerator set to the raceway flow, then compare two models. The set is built to correct one common habit, which is treating the sticker price as the whole cost of a machine and choosing the cheaper unit without checking what it costs to run for a season.

Sedgewater Hatchery Aerator Selection Problems — Grade 6 Engineering & Design
Name: ____________________________ Date: ______________

Problems

All figures below belong to the fictional Sedgewater Hatchery.

  1. One raceway holds 9,000 gallons. The hatchery replaces all of that water 3 times each hour. How many gallons flow through the raceway in one hour?
  2. Using your answer from problem 1, how many gallons flow through the raceway each minute?
  3. One aerator can handle 150 gallons per minute. How many aerators does the raceway need?
  4. Model A aerators cost $640 each. What does a full set of Model A cost?
  5. Model B aerators cost $1,000 each. What does a full set of Model B cost?
  6. How much more does the Model B set cost than the Model A set?
  7. Each Model A aerator uses 12 kilowatt-hours of electricity a day. How many kilowatt-hours does the full Model A set use in one day?
  8. Each Model B aerator uses 8 kilowatt-hours a day. How many kilowatt-hours does the full Model B set use in one day?
  9. Electricity costs $0.15 for each kilowatt-hour, and the hatchery runs its aerators 300 days a year. How many dollars would the Model B set save in one year compared with the Model A set?
  10. Using your answers from problems 6 and 9, how many years of savings does the Model B set need to make up its higher purchase price?

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: 27,000 gallons. The raceway holds 9,000 gallons and the water is replaced 3 times an hour, so 9,000 x 3 = 27,000 gallons.
  2. Answer: 450 gallons per minute. One hour holds 60 minutes, so 27,000 / 60 = 450 gallons each minute.
  3. Answer: 3 aerators. Divide the flow by what one aerator handles: 450 / 150 = 3 aerators.
  4. Answer: $1,920. Three Model A aerators at 640 dollars each give 3 x 640 = 1,920 dollars.
  5. Answer: $3,000. Three Model B aerators at 1,000 dollars each give 3 x 1,000 = 3,000 dollars.
  6. Answer: $1,080. The Model B set costs 3,000 dollars and the Model A set costs 1,920 dollars, so 3,000 - 1,920 = 1,080 dollars more.
  7. Answer: 36 kilowatt-hours. Three Model A aerators use 12 kilowatt-hours each, so 3 x 12 = 36 kilowatt-hours a day.
  8. Answer: 24 kilowatt-hours. Three Model B aerators use 8 kilowatt-hours each, so 3 x 8 = 24 kilowatt-hours a day.
  9. Answer: $540. The Model B set uses 36 - 24 = 12 fewer kilowatt-hours a day. Over 300 days that is 12 x 300 = 3,600 kilowatt-hours, and 3,600 x 0.15 = 540 dollars saved.
  10. Answer: 2 years. The Model B set costs 1,080 dollars more and saves 540 dollars a year, so 1,080 / 540 = 2 years.

Differentiation

Support

Give students a supplier sheet for the fictional hatchery with the two models in a two-column chart, the price row and the energy row already labeled, and the reminder that one hour holds 60 minutes printed beside problem 2. Let them fill a ratio table of 1, 2, and 3 aerators against gallons per minute before answering problem 3.

Extension

Ask students to find, for this fictional hatchery, the electricity price per kilowatt-hour at which the Model B set would repay its higher purchase price in exactly one year, then to explain in a sentence why a higher electricity price shortens the payback.

ELL supports

Provide a picture of a raceway with an aerator drawn at one end and arrows showing water moving through, labeled with the words "flow," "aerator," and "oxygen." Allow students to record answers 4 through 8 in a prepared chart rather than in sentences.

Extensions

Have students list three other places where a machine that costs more to buy may cost less to run, such as a light bulb or a school bus, and write two sentences explaining what information a buyer would need in order to compare them fairly.