Unit Plan 21 (Grade 6 Math): Volume of Right Rectangular Prisms
6th graders use V = lwh and V = B·h to find the volume of right rectangular prisms with whole and fractional edge lengths. They solve real-world packing and capacity problems using cubic units, estimation, and clear reasoning.
Focus: Use V = lwh and V = B*h with whole and fractional edge lengths; packing and capacity problems.
Grade Level: 6
Subject Area: Mathematics (Geometry — Volume of Right Rectangular Prisms)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students build a deep, flexible understanding of volume by packing prisms with unit cubes (including fractional edge cubes), layering to see B*h, and calculating with V = lwh and V = B*h. They apply volume to packing (boxes, shipping) and capacity (containers, aquariums), communicate with correct cubic units, and check for reasonableness.
Essential Questions
- What does volume measure, and how does packing with unit cubes show what V = lwh means?
- How does B*h (area of base * height) connect to layers of cubes?
- How do I work accurately with fractional edge lengths and still communicate in cubic units?
- How do volume calculations support real-world decisions about packing and capacity?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Model volume by packing right rectangular prisms with unit cubes (including unit-fraction edges) and relate that count to V = lwh.
- Explain and use V = B*h where B is the area of the base; connect to layering.
- Compute volumes for prisms with whole and fractional edge lengths; label in correct cubic units (e.g., cubic centimeters).
- Solve packing (how many items fit) and capacity (how much a container holds) problems; interpret results with units.
- Check reasonableness via estimation, bounds, and unit sense.
Standards Alignment — CCSS Grade 6
- 6.G.2: Find the volume of a right rectangular prism with fractional edge lengths by packing with unit cubes and show that the volume equals the product of edge lengths (V = lwh). Apply V = lwh and V = B*h to real-world and mathematical problems.
- Mathematical Practices featured: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (use tools), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can show volume with unit cubes and explain how that matches V = lwh.
- I can use V = B*h by finding the area of the base and then multiplying by height.
- I can compute volume with fractional edges and give the answer in cubic units.
- I can solve packing/capacity problems and explain what my answer means.