This lesson builds on students’ earlier work decomposing and rearranging regions to find area. It leads students to see that, in addition to using area-reasoning methods from previous lessons, they can use what they know to be true about parallelograms (i.e. that the area of a parallelogram is \(b \boldcdot h\)) to reason about the area of triangles.
Students begin to see that the area of a triangle is half of the area of the parallelogram of the same height, or that it is the same as the area of a parallelogram that is half its height. They build this intuition in several ways:
- by recalling that two copies of a triangle can be composed into a parallelogram;
- by recognizing that a triangle can be recomposed into a parallelogram that is half the triangle’s height; or
- by reasoning indirectly, using one or more rectangles with the same height as the triangle.
They apply this insight to find the area of triangles both on and off the grid.
- Draw a diagram to show that the area of a triangle is half the area of an associated parallelogram.
- Explain (orally and in writing) strategies for using the base and height of an associated parallelogram to determine the area of a triangle.
Let’s use what we know about parallelograms to find the area of triangles.
Students need access to tape or glue; it is not necessary to have both.
Each copy of the blackline master contains two copies of each of parallelograms A, B, C, and D. Prepare enough copies so that each student receives two copies of a parallelogram.
- I can use what I know about parallelograms to reason about the area of triangles.