This lesson prompts students to find areas of figures—first on a grid and then without a grid. This work reiterates the two key principles about area: that two figures that match exactly when placed one on top of the other have the same area, and that the area of a figure is the sum of the areas of the non-overlapping pieces that compose it.

Students continue to use strategies from earlier explorations to find area, namely:

• Decompose a figure into shapes whose areas they can calculate.
• Decompose and rearrange it into shapes whose areas they can calculate.

The given figures in this lesson allow students to see that they can also:

• consider a figure as a familiar shape with one or more missing pieces, calculate the area of the shape, and then subtract the areas of the missing pieces 
• enclose a figure with a shape whose area they can calculate and subtract the area of extra pieces created by the enclosure

For now, rectangles are the only shapes whose areas students know how to calculate, but the strategies will become more powerful as students’ repertoires grow.

As students consider strategies for finding areas and use them, they practice looking for and making use of structure (MP7). In explaining their thinking, students practice constructing logical arguments (MP3).

A note about notation:

Starting in this lesson, consider using the “dot” notation instead of the “cross” notation when recording students’ solutions. Explain that the symbol and the symbol both represent multiplication. Doing so familiarizes students with the use of the notation before they see it in student-facing materials.