Unit Plan 30 (Grade 3 Math): Area & Perimeter Design Challenge
Design a mini-park under area/perimeter constraints, calculate with A = l × w and decomposition, and justify layout choices using labeled diagrams, units, and clear math reasoning.
Focus: Plan a mini-park under area/perimeter constraints; justify design choices with clear mathematical models and explanations.
Grade Level: 3
Subject Area: Mathematics (Modeling with Area & Perimeter)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students apply prior learning about area and perimeter to design a “mini-park.” Working within constraints (e.g., fixed fencing length; target play-zone area), they create and iterate on layouts, compute area/perimeter, and defend choices (paths vs. garden beds vs. play zones) using labeled diagrams and numbers.
Essential Questions
- How do area and perimeter describe different features of the same design?
- How can I use rectangles, arrays, and decomposition to calculate area efficiently?
- How do I communicate and justify my design decisions with units, labels, and clear math?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Design a layout that meets stated area and/or perimeter constraints and real-world needs.
- Compute area of rectangles by tiling, by multiplication (A = l × w), and by adding parts of composite figures.
- Solve perimeter problems (find unknown side lengths, compare same area/different perimeter, and vice versa).
- Explain and defend design choices with labeled diagrams, correct units, and clear reasoning.
Standards Alignment — CCSS Grade 3
- 3.MD.7a–d: Relate area to multiplication and addition; multiply side lengths to find area; use the distributive property to decompose; recognize area as additive.
- 3.MD.8: Solve real-world and mathematical problems involving perimeter of polygons, including finding an unknown side length and designing rectangles with same perimeter and different areas (and vice versa).
- Mathematical Practices (threaded): MP.3 (Construct viable arguments & critique reasoning), MP.4 (Model with mathematics).
Success Criteria — Student Language
- I can draw and label a park plan that meets area/perimeter constraints.
- I can find area by tiling, by A = l × w, or by adding parts of a shape.
- I can find perimeter and explain how a shape can keep the same area but have a different perimeter (or the reverse).
- I can justify my design using units, labels, and clear math sentences.