IM 6.6.11 Lesson: The Distributive Property, Part 3
A rectangle with dimensions 6 cm and cm is partitioned into two smaller rectangles.
Explain why each of these expressions represents the area, in cm2, of the shaded region.
Draw lines to match each expression in column 1 to an equivalent expression in column 2. If you get stuck, consider drawing a diagram in the other applet.
The distributive property can be used to write equivalent expressions. In each row, use the distributive property to write an equivalent expression. If you get stuck, consider drawing a diagram in the applet below the table.
This rectangle has been cut up into squares of varying sizes. Both small squares have side length 1 unit. The square in the middle has side length x units.
Suppose that is 3. Find the area of each square in the diagram. Then find the area of the large rectangle.
Find the side lengths of the large rectangle assuming that is 3. Find the area of the large rectangle by multiplying the length times the width. Check that this is the same area you found before.
Now suppose that we do not know the value of . Write an expression for the side lengths of the large rectangle that involves .