6ACC Unit 5 Distributive Property Revisited

Which Expressions Represent Area?

Activating Strategy

Select all the expressions that represent the large rectangle's total area.

●3(5 + 4)

●5(4 +3)

●5(4)+ 15

●15+ 5(4)

●3(5)+ 3(4)

4

Partitioned Rectangles When

Lengths are Unknown

Mini-Lesson

1.

Here are two rectangles. The length and width of one rectangle are 8
and 5. The width of the other rectangle is 5, but its length is unknown so
we labeled it.

Write an expression for the sum of the areas of the two rectangles.

Partitioned Rectangles When

Lengths are Unknown

Mini-Lesson

2.

The two rectangles can be composed into one larger rectangle as
shown. What are the width and length of the new, large rectangle?

3.

Write an expression for the total area of the large rectangle as the
product of its width and its length.

Equivalent or Not?

Mini-Lesson

Determine if each of the following expressions are equivalent or not. If you
get stuck, consider drawing a rectangle.

a.

3(x + 4) and 3x + 4

b.

4(x + 3) and 4x + 12

c.

½(x + 6 + 10y) and ½x + 3 + 5y

Let’s Practice!

Small Group

Writing Equivalent Expressions

Summary

1.

Use the distributive property to write an expression that is
equivalent to 12 + 4x.

2.

Draw a diagram that shows the two expressions are equivalent.