The purpose of this activity is for students to find the areas of figures that are composed of rectangles but are not fully gridded with squares. Partially gridded figures help prepare students to find the areas of figures with only side length measurements. Students should be encouraged to find side lengths and multiply, rather than rely on counting, as the grids disappear. If students continue to draw in the squares, ask them if there is another way to find the area.

• “What was your strategy for finding the area of the second figure?”
• “What helps you find the areas of figures like these when the shape is not fully covered with squares?” (Imagining where the squares would be so I can count them or find the side lengths. Finding the side lengths and multiplying to find the areas of rectangles in the figure.)

The purpose of this activity is for students to find the area of a figure composed of rectangles, given only the side lengths of the rectangles. The context of paving a patio provides students a link to their experience with squares of various sizes and should help them imagine how the diagram of the patio could be covered with squares. Students decompose the patio into rectangles and can multiply to find the area of the patio, but they should make the connection that the number of pavers needed to cover the patio is the same as the area of the patio. When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2).

• “Tell me how you found the area of the figure.”
• “How would overlapping the rectangles affect the number of squares it would take to cover the figure?”

• “How did you figure out how many pavers Noah would need?”
• Select students to share a variety of strategies. Display any expressions students used in their explanations.
• During each explanation, ask the class which measurements were and were not used and why.
• “How does each expression represent a way of finding the area of the figure?” (The expression shows the figure decomposed into a large rectangle across the top and a small rectangle below. Each expression in parentheses represents one of the smaller rectangles in the figure. The equations , , and show how the figure was decomposed into a 6-foot-by-3-foot rectangle on the left and a 4-foot-by-6-foot rectangle on the right, and then the areas were added.)