Instructional Activity# Decomposing to Find Area

Lesson 1. Unit 8. Grade 8 Open Up Resources

Open Up Resources15 min(s)

This Instructional Activity is a part of the Lesson 1, Unit 8, Grade 8. The purpose of this task is for students to find the areas of squares whose side lengths are not easy to determine by inspection. The squares are represented in an increasingly abstract way: the first square shows all of the square units explicitly, making it easy to see that putting two "leftover" triangles together will make a rectangle with the same dimensions, or even piecing individual square units together that can be counted. The next only shows the grid units along the edges, providing a bridge to the third, which only provides labels for side lengths. The numbers are chosen to encourage the decomposing, rearranging, and subtracting strategy for finding the area, although decomposing and using the formulas for the area of a square and a triangle is also perfectly appropriate. This sequence of tasks also provides practice for students in using the area and finding strategies they will need to understand and explain a proof of the Pythagorean Theorem in a later lesson.