Unit Plan 34 (Grade 5 Math): Volume Design Project
5th graders apply volume formulas to design and compare rectangular prisms under real constraints. They compute, optimize, and justify choices using V = l × w × h and V = B × h, defending their designs with math, units, and reasoning.
Focus: Plan and compare rectangular prisms by volume; optimize designs under constraints; defend final choices with math and context.
Grade Level: 5
Subject Area: Mathematics (Measurement & Data—Volume)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students become volume designers. They use unit cubes, V = l × w × h, and V = B × h to plan containers/crates/storage boxes that meet real constraints (space limits, cube budgets, target capacities). They compare options, choose the best-fit design, and justify the pick with clear math, units, and trade-offs.
Essential Questions
- How do models (arrays, nets with layers, unit cubes) connect to formulas for volume?
- How can I optimize a rectangular prism’s volume under constraints?
- What evidence (calculations, units, and context) makes a design defensible?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Describe volume using unit cubes and cubic units; connect layers of cubes to V = l × w × h and V = B × h.
- Compute volumes of rectangular prisms and composite prisms via addition of volumes.
- Interpret and apply constraints (e.g., height limit, footprint limit, fixed number of cubes) to generate feasible designs.
- Compare candidate designs and choose an optimal one for the context, explaining trade-offs.
- Present a design defense with labeled drawings, calculations, units, and a reasonableness check.
Standards Alignment — CCSS Grade 5
- 5.MD.3: Recognize volume as an attribute of solid figures; understand unit cubes and cubic units.
- 5.MD.4: Measure volume by counting unit cubes, using cubic cm/in/ft, and improvised units.
- 5.MD.5: Relate volume to multiplication and addition and solve real-world/math problems:
- 5.MD.5a: Find volume of a right rectangular prism by packing/using the formula V = l × w × h.
- 5.MD.5b: Find volume using the additive property (sum of non-overlapping right rectangular prisms).
- 5.MD.5c: Recognize volume as additive; apply formulas to solve problems.
Success Criteria — Student Language
- I can explain volume with unit cubes and use V = l × w × h and V = B × h correctly.
- I can add volumes for composite prisms.
- I can design within constraints and choose the best option for the situation.
- I can defend my choice with labeled drawings, units, and a check that the answer makes sense.