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Worksheet Grade 5 Math

Marrowvale Hatchery Tanks: A Grade 5 Unit Cube Volume Worksheet

A grade 5 worksheet in which students pack four fish-raising tanks at a fictional hatchery with unit cubes, then check the count against V = l x w x h.

Objectives

  1. Students will count unit cubes layer by layer to measure the volume of a rectangular tank.
  2. Students will apply the formula V = l x w x h to find volume in cubic feet.
  3. Students will add the volumes of two joined rectangular parts to find a total volume.

Vocabulary

Key words: volume, unit cube, cubic foot, layer, hatchery

Teacher overview

Marrowvale Hatchery is a fictional trout hatchery on Tarnwick Brook, downstream of a dam that releases cold water from deep in its reservoir, which keeps the brook cold enough for young fish. The crew there has to know how much water each raising tank holds before they can decide how many fish belong in it. This worksheet asks students to imagine each tank packed with cubes that measure one foot on every side, count those cubes layer by layer, and then check the count against the volume formula. The misconception it targets is the frequent student move of adding the three dimensions rather than multiplying them, which turns a tank measuring 6 feet by 3 feet by 2 feet into 11 cubic feet instead of 36.

Marrowvale Hatchery Tanks: A Grade 5 Unit Cube Volume Worksheet — Grade 5 Math
Name: ____________________________ Date: ______________

Student Worksheet

Marrowvale Hatchery raises trout in four tanks. Imagine each tank packed full of cubes. Each cube is 1 foot long, 1 foot wide, and 1 foot tall. One cube has a volume of 1 cubic foot.

  • Tank A is 6 feet long, 3 feet wide, and 2 feet deep.
  • Tank B is 5 feet long, 4 feet wide, and 3 feet deep.
  • Tank C has two parts. Part 1 is 4 feet long, 3 feet wide, and 2 feet deep. Part 2 is 4 feet long, 2 feet wide, and 2 feet deep.
  • The nursery box is 3 feet long, 2 feet wide, and 1 foot deep.
  1. Cubes cover the bottom of Tank A in one flat layer. How many cubes are in that layer?
  2. Tank A is 2 cubes deep. How many cubes fill the whole tank?
  3. Use V = l x w x h to find the volume of Tank A in cubic feet.
  4. Cubes cover the bottom of Tank B in one flat layer. How many cubes are in that layer?
  5. Use the formula to find the volume of Tank B in cubic feet.
  6. Which tank holds more water, Tank A or Tank B?
  7. How many more cubic feet does the larger of those two tanks hold?
  8. Find the volume of Part 1 of Tank C in cubic feet.
  9. Find the volume of Part 2 of Tank C in cubic feet.
  10. Add your last two answers to find the total volume of Tank C in cubic feet.
  11. Find the volume of the nursery box in cubic feet.
  12. Tank A holds 36 cubic feet. The nursery box holds 6 cubic feet. How many nursery boxes of water would fill Tank A?
  13. Explain why counting the cubes and using the formula give the same answer.

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 cubes. The bottom layer is 6 cubes long and 3 cubes wide, so 6 x 3 = 18 cubes.
  2. Answer: 36 cubes. There are two layers of 18 cubes, and 18 x 2 = 36 cubes.
  3. Answer: 36 cubic feet. 6 x 3 = 18, and 18 x 2 = 36 cubic feet, which matches the cube count in item 2.
  4. Answer: 20 cubes. The bottom layer is 5 cubes long and 4 cubes wide, so 5 x 4 = 20 cubes.
  5. Answer: 60 cubic feet. 5 x 4 = 20, and 20 x 3 = 60 cubic feet.
  6. Answer: Tank B. Tank B holds 60 cubic feet, while Tank A holds 36 cubic feet.
  7. Answer: 24 cubic feet. 60 - 36 = 24 cubic feet.
  8. Answer: 24 cubic feet. 4 x 3 = 12, and 12 x 2 = 24 cubic feet.
  9. Answer: 16 cubic feet. 4 x 2 = 8, and 8 x 2 = 16 cubic feet.
  10. Answer: 40 cubic feet. 24 + 16 = 40 cubic feet for the whole of Tank C.
  11. Answer: 6 cubic feet. 3 x 2 = 6, and 6 x 1 = 6 cubic feet.
  12. Answer: 6 boxes. 36 divided by 6 = 6 boxes of water.
  13. Answer: Both methods count the same cubes. The formula multiplies the number of cubes in one layer by the number of layers, so it is a faster way of doing the same count.

Differentiation

Support

Give students centimeter cubes or snap cubes and let them build Tank A at a scale of one cube per cubic foot before item 1. Once they have built and counted the two layers, ask them to write the multiplication that matches what they built, which makes the formula in item 3 a record of the count rather than a new rule.

Extension

Ask students to design a fifth tank for the hatchery that holds exactly 48 cubic feet, using whole-foot dimensions and a depth of no more than 3 feet, then show the multiplication that proves the design works. Have them find a second set of dimensions that also works and explain how the two designs differ.

ELL supports

Pre-teach "layer," "deep," "volume," and "cubic foot" with a physical stack of cubes labeled in English and, where possible, in students' home languages. Provide a sentence frame for item 13: "Counting cubes and using the formula match because ___."

Extensions

Have students measure a classroom bin or storage tub in inches, convert those measurements to feet, and find its volume in cubic feet. Ask them to compare that volume to the nursery box in item 11 and decide whether the bin could serve as a temporary holding container for young fish.