Volume with Fractional Edges — Worksheet

Volume with Fractional Edges

Worksheet

Open the Volume with Fractional Edges module. Set the length, width, and height as described in each question, then answer below. Use Add layer to count the cubes, and drag the box to spin it around.

Name: Date:

Part A: Counting the cubes

1. Set length = 2.5, width = 1.5, and height = 3. The prism is packed with unit cubes. What is the edge length of each cube? 1 pt
  • 1
  • 1/2
  • 1/5
  • 2
2. For the 2.5 by 1.5 by 3 prism, how many cubes fit in one layer? 1 pt
Answer:
3. How many layers tall is the 2.5 by 1.5 by 3 prism? 1 pt
Answer:
4. What is the total number of cubes in the 2.5 by 1.5 by 3 prism? 1 pt
Answer:

Part B: Fractional edge lengths

5. Each cube has an edge of 1/2, so its volume is 1/2 × 1/2 × 1/2. Use the cube count to find the volume by counting. Round to two places if needed. 1 pt
Answer:
6. Now find the volume by multiplying the edges: V = 2.5 × 1.5 × 3. Round to two places if needed. 1 pt
Answer:
7. Compare your answer to the counting method with your answer to V = l × w × h. What does this show? 2 pts
  • Counting cubes gives a different volume than the formula.
  • The formula only works when all the edges are whole numbers.
  • Counting cubes and the formula give the same volume, even with fractional edges.
  • The cube edge should have been 1, not 1/2.

Part C: Reasoning

8. Set length = 3, width = 2, and height = 1.5. What fraction does the module use for the cube edge? Write it as a fraction or a decimal. 1 pt
9. For the 3 by 2 by 1.5 prism, how many cubes fit in one layer? 1 pt
Answer:
10. Explain why a prism with fractional edge lengths can still be packed with cubes, and why V = l × w × h gives the same volume as counting those cubes. 2 pts