Unit Plan 20 (Grade 7 Math): Area of Circles & Composite Figures
7th graders derive and apply A = πr² to find areas of circles and composite shapes with circular parts. They decompose figures, use precise units, justify rounding, and solve real-world design and measurement problems.
Focus: Compute area of circles and composite shapes involving circular regions; apply to real-world contexts.
Grade Level: 7
Subject Area: Mathematics (Geometry • Measurement & Modeling)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students develop and use the circle area formula and apply it to composite figures that include circular pieces (semicircles, quarter circles, rings/annuli). They connect circumference ideas to area through a wedge rearrangement argument, practice precise unit work and rounding, and solve practical problems (materials, cost, coverage, paving).
Essential Questions
- How does the structure of a circle lead to the formula A = πr^2?
- How do I decompose or compose shapes with circular parts to find total area?
- Where do units, precision, and reasonableness checks matter most in area problems?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Define and relate radius (r) and diameter (d = 2r); compute area of a circle with A = πr^2.
- Explain an informal derivation of A = πr^2 (wedge rearrangement or “area ≈ (1/2) × C × r”).
- Compute areas of semicircles, quarter circles, and rings (annuli); carry correct square units.
- Solve composite area problems by adding/subtracting parts; justify decomposition choices and rounding.
- Apply area to real contexts (materials, coverage, cost) with clear unit conversions and concluding statements.
Standards Alignment — CCSS Grade 7
- 7.G.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the area of a circle.
- 7.G.6 (connection): Solve real-world and mathematical problems involving area of two-dimensional objects composed of triangles, quadrilaterals, and other polygons—extended here to composite figures including circular regions.
- Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (use tools), MP.6 (precision).
Success Criteria — Student Language
- I can choose and use A = πr^2 with the correct square units.
- I can explain the wedge or (1/2) × C × r idea that leads to A = πr^2.
- I can break a composite figure into simple parts (add/subtract) and show the calculations.
- I can state a clear conclusion with units and reasonable rounding.
- I can check whether my answer makes sense using estimates/bounds.