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Math problem set Grade 5 Math

Sizing Granite Bluff Elementary's Flood-Control Detention Basin

A grade 5 math problem set that finds the volume of a rectangular detention basin in cubic feet, converts to gallons, and checks its storage capacity.

Objectives

  1. Students will calculate the volume of a rectangular detention basin using V = l x w x h.
  2. Students will convert a volume in cubic feet to gallons and use that value to solve a real-world problem.

Vocabulary

Detention basin
A detention basin is a dug-out area that fills with stormwater during a storm and then slowly drains empty over hours or days. It holds the water back so streets and streams downstream do not flood.

Also: volume, rectangular prism, cubic feet

Teacher overview

Granite Bluff Elementary, a fictional school used for this problem set, built a rectangular detention basin behind its building after heavy storms flooded the parking lot. The basin is a rectangular prism designed to hold stormwater temporarily before releasing it slowly into a nearby creek. This problem set walks students through finding the basin's volume, converting that volume to gallons, and checking how the basin's capacity compares to a smaller version being planned nearby. A common misconception in this math is assuming that cutting every dimension of a rectangular prism in half cuts the volume in half, when it actually leaves one eighth; problem 8 has students check what happens when only one dimension is halved.

Sizing Granite Bluff Elementary's Flood-Control Detention Basin — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

  1. The basin is 25 feet long, 10 feet wide, and 4 feet deep. Find its volume in cubic feet. Use Volume = length × width × height.
  2. One cubic foot holds 7.48 gallons. Convert your answer from problem 1 to gallons.
  3. After one storm, the basin held water only 2.5 feet deep. The length and width stayed the same. Find the volume of water in the basin at that depth.
  4. Convert your answer from problem 3 to gallons.
  5. The basin's pipe lets out 935 gallons of water each day. Using your answer from problem 4, how many days will the basin take to drain completely?
  6. A second, smaller basin is planned nearby. It will be half as long as the original, 12.5 feet, but the same width and depth. Find its full volume in cubic feet.
  7. Convert the smaller basin's volume from problem 6 to gallons.
  8. Challenge. Compare the smaller basin (problem 6) to the original basin (problem 1). Is the smaller basin's volume exactly half of the original? Explain why or why not, using the three dimensions.

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: 1000 cubic feet.
    Volume = 25 ft × 10 ft × 4 ft = 1,000 cu ft.
  2. Answer: 7480 gallons.
    1,000 cu ft × 7.48 gal/cu ft = 7,480 gallons.
  3. Answer: 625 cubic feet.
    Volume = 25 ft × 10 ft × 2.5 ft = 625 cu ft.
  4. Answer: 4675 gallons.
    625 cu ft × 7.48 gal/cu ft = 4,675 gallons.
  5. Answer: 5 days.
    4,675 gallons ÷ 935 gallons per day = 5 days.
  6. Answer: 500 cubic feet.
    Volume = 12.5 ft × 10 ft × 4 ft = 500 cu ft.
  7. Answer: 3740 gallons.
    500 cu ft × 7.48 gal/cu ft = 3,740 gallons.
  8. Answer: Yes, exactly half.
    Only the length was cut in half (25 ft to 12.5 ft) while the width and depth stayed the same, so the volume, which is length times width times height, is also cut exactly in half: 500 cu ft is half of 1,000 cu ft. Cutting only one of the three dimensions in half always cuts the total volume in half, but cutting two or three dimensions in half would cut the volume by more than half.

Differentiation

Support (below grade level)

Provide the volume formula written as a fill-in-the-blank ("Volume = ___ ft × ___ ft × ___ ft") for problems 1, 3, and 6, and allow a calculator for every multiplication and division step.

Extension (above grade level)

Ask students to find what basin depth (keeping the original 25-foot length and 10-foot width) would be needed to hold exactly 10,000 gallons, working backward from the target gallon amount to cubic feet and then to depth.

ELL supports

Provide a labeled diagram of the rectangular basin showing length, width, and depth as three separate arrows before problem 1. Allow students to show their work using the diagram and numbers rather than full sentences for problems 1 through 7.

Extensions

Measure a rectangular space at your own school, such as a garden bed or a section of hallway, and calculate how many gallons of water it could hold if it were built into a basin one foot deep, then discuss whether that would be enough to handle a heavy storm.