The purpose of this lesson is for students to practice composing and decomposing irregular regions to calculate their area, in preparation for estimating the area of circles in the next lesson. In the first activity, the region is polygonal and students can calculate an exact answer for the area of the floorplan. In the second activity, students must approximate the area of the state.
Students use polygons to model regions on a map or floorplan (MP4). To complete each task, students need to identify relevant information, choose an appropriate strategy, and make simplifying assumptions. Students also have an opportunity to think about what factors affect the estimates. Students see that the nature of the information we have or could obtain, the assumptions we make, and the estimation methods we use affect how close our estimates are to the actual area measures. Adjust the length of lesson and the expectations on the depth of students’ investigations depending on the time available.
- Estimate the area of a complex, real-world region, e.g., a state or province, by approximating it with an irregular polygon, and indicate that it is an approximation when expressing the answer (orally and in writing).
- Explain (orally and in writing) how to calculate the area of an irregular polygon by decomposing it.
- Interpret floor plans and maps in order to identify the information needed to calculate area.
Let’s estimate the areas of weird shapes.
Provide access to geometry toolkits.
- I can calculate the area of a complicated shape by breaking it into shapes whose area I know how to calculate.