For this standard, students will be modeling area formulas. The use of modeling is most crucial here as they are NOT expected to just memorize a formula and use it. Instead, they will be using hands-on shapes and materials (it’s easiest to use paper shapes) to physically decompose them (break them into smaller, familiar shapes) and manipulate them to form a well-known shape. In this case, students will be rearranging parts of parallelograms, trapezoids, and triangles to form rectangles. This is because the rectangle is the easiest and most familiar shape they can use for finding area, as it is simply length x width.
How can the following parallelogram be decomposed into a rectangle to find the area? Justify your thinking.
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6.8 Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to represent relationships and solve problems. The student is expected to:
(B) model area formulas for parallelograms, trapezoids, and triangles by decomposing and rearranging parts of these shapes