Unit Plan 21 (Grade 5 Math): Volume Problem Solving—Additive Volume
5th graders apply additive volume by decomposing composite right rectangular prisms into non-overlapping parts. Students calculate partial volumes using V = l × w × h or V = B × h, add them for total volume, and justify decompositions with labeled sketches, units, and reasonableness checks.
Focus: Solve real-world problems with composite right rectangular prisms by decomposing figures into non-overlapping prisms, finding each partial volume with V = l * w * h or V = B * h, and adding to get total volume.
Grade Level: 5
Subject Area: Mathematics (Measurement & Data)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students extend their understanding of volume to composite solids. They learn to see structure in 3D, partition a figure into simpler right rectangular prisms, compute partial volumes, and add them. They also tackle missing-dimension problems and compare different valid decompositions for efficiency and clarity.
Essential Questions
- How can I decompose a composite solid into right rectangular prisms I know how to measure?
- Why is volume additive, and how do I avoid double-counting or overlaps?
- When should I use V = l * w * h versus V = B * h, and how do units guide my choices?
- How can I communicate a clear plan: sketch, label, compute parts, and justify the total?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Identify non-overlapping right rectangular prisms within a composite figure and justify their decomposition.
- Compute partial volumes using V = l * w * h or V = B * h with correct cubic units.
- Explain and use additive volume to find a total volume and compare different decompositions for efficiency.
- Solve real-world and multi-step problems involving missing dimensions, consistent units, and reasonableness checks.
- Present solutions with sketches, labels, equations, and a short explanation of structure.
Standards Alignment — CCSS Grade 5
- 5.MD.5b: Apply V = l * w * h and V = B * h to find volumes of right rectangular prisms in context.
- 5.MD.5c: Recognize volume as additive; find volumes of composite solids by adding volumes of non-overlapping right rectangular prisms.
- Mathematical Practices emphasized: MP.1 (persevere), MP.2 (quantitative reasoning), MP.3 (justify/critique), MP.4 (model), MP.5 (tools), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can split a composite solid into non-overlapping rectangular prisms and explain my choice.
- I can find each partial volume with V = l * w * h or V = B * h and label cubic units.
- I can add partial volumes for a correct total and explain why my plan works.
- I can check reasonableness with quick estimates and unit sense.