Lesson 5

Students begin this lesson by comparing two strategies for finding the area of a parallelogram. This comparison sets the stage both for formally defining the terms base and height and for writing a general formula for the area of a parallelogram. Being able to correctly identify a base-height pair for a parallelogram requires looking for and making use of structure (MP7).

The terms base and height are potentially confusing because they are sometimes used to refer to particular line segments, and sometimes to the length of a line segment or the distance between parallel lines. Furthermore, there are always two base-height pairs for any parallelogram, so asking for the base and the height is not, technically, a well-posed question. Instead, asking for a base and its corresponding height is more appropriate. As students clarify their intended meaning when using these terms, they are attending to precision of language (MP6). In these materials, the words “base” and “height” mean the numbers unless it is clear from the context that it means a segment and that there is no potential confusion.

By the end of the lesson, students both look for a pattern they can generalize to the formula for the area of a rectangle (MP8) and make arguments that explain why this works for all parallelograms (MP3).