6th Grade Math Lesson

Reasoning to Find Area: Composition and Decomposition

Shared by Jennifer Schwartz

Advanced 6th Grade MathBTC Style / Thinking Classrooms6.G.3Measurement: Students identify geometric attributes that create two- and three-dimensional shapes in order to perform measurements and apply formulas to find area and volume. 6.G.3.aDetermine the area of quadrilaterals and triangles by composition and decomposition of these shapes, as well as applications of properties and formulas. Quadrilaterals include parallelograms and trapezoids.40 min

Learning Objective

Students will determine the area of triangles, parallelograms, and trapezoids by composing and decomposing these shapes into simpler figures, justifying their reasoning.

Lesson Overview

Students progress from counting unit squares on a grid to decomposing complex polygons into triangles and rectangles, using composition and decomposition strategies to find area of quadrilaterals and triangles without formulas first, then connecting to formulas.

Materials

Vertical whiteboards or chart paper
Dry-erase markers and erasers
Pencils and blank paper for notes

Scaffolded Task Progression

1Task 1

The rectangle below has been drawn on a grid. Each small square has side length

1

cm. Find the area of the rectangle.

[ Interactive graph / diagram, available in the full lesson ]

2Task 2

The right triangle below sits on the same grid. Each square is

1

cm. Find the area of the triangle.

[ Interactive graph / diagram, available in the full lesson ]

Hint: Draw the rectangle that surrounds the triangle. What fraction of the rectangle is the triangle?

3Task 3

This triangle is NOT a right triangle. Each grid square is

1

cm. Find its area.

[ Interactive graph / diagram, available in the full lesson ]

Can you still use the rectangle strategy? Explain your reasoning.

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