Unit Plan 19 (Grade 6 Math): Area by Composition & Decomposition
6th graders find the area of triangles, quadrilaterals, and polygons by composing and decomposing shapes. They apply base–height reasoning, justify methods, and solve real-world geometry problems with precise units and clear explanations.
Focus: Find area of triangles, special quadrilaterals, and polygons by building/breaking shapes; apply in real contexts.
Grade Level: 6
Subject Area: Mathematics (Geometry — Area via Composition/Decomposition)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students develop flexible strategies for finding area by composing shapes (fitting pieces together) or decomposing shapes (cutting into simpler parts). They connect these strategies to formulas for rectangles, triangles, and special quadrilaterals (parallelograms, trapezoids, rhombi, kites) and apply them to composite and irregular polygons. Emphasis: units, base–height as a perpendicular pair, and clearly justifying methods.
Essential Questions
- How can I build or break a figure to make its area easier to find?
- What do base and height mean, and why must they be perpendicular?
- How do area formulas arise from composition/decomposition?
- How do I communicate my method and units so another person can follow my work?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Use composition and decomposition to find the area of triangles, special quadrilaterals, and polygons.
- Explain and use area relationships:
- Rectangle: A = length × width
- Parallelogram: A = base × height (height is perpendicular to base)
- Triangle: A = (1/2) × base × height (as half of a parallelogram/rectangle)
- Trapezoid: Area by composing/decomposing into a rectangle + triangles (or two congruent trapezoids to form a parallelogram).
- Solve real-world and mathematical area problems for composite figures; label calculations with correct square units.
- Choose and defend a strategy (add pieces, subtract holes, or rearrange) with clear diagrams and reasoning.
- Check reasonableness using estimation, bounds, and unit sense.
Standards Alignment — CCSS Grade 6
- 6.G.1: Find areas of triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply to real-world and mathematical problems.
- Mathematical Practices emphasized: 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 choose a decomposition (or composition) and show it on a diagram.
- I can identify a base–height pair that is perpendicular and use it correctly.
- I can find the area of a triangle using A = (1/2)baseheight and a parallelogram using A = base*height.
- I can find the area of a trapezoid and composite shapes by adding and/or subtracting parts.
- I label units (square units) and explain my steps so someone else can follow.