Diving In to Distributive Property

Diving In with

Distributive Property

Inv 1.4 Practice

Essential Question: ​How can you show that 2 expressions are equivalent?

Open Ended

In life, we can use different words to express the same thing. What words can you use to say that something is good?

(keep it school appropriate)

Multiple Choice

Alberto says the perimeter of the rectangle is P = 2(L + W). 

Mika says the perimeter is P = 2L + 2W.

Are both equations a correct way to calculate perimeter?

• Yes

• No

• Maybe

• What's perimeter?

You can use properties to prove that expressions are

equivalent.

Distributive Property

For any real numbers a,

b, and c:

a(b + c) = ab + ac

and

a(b - c) = ab - ac

Commutative Property
for any real numbers a

and b:

a + b = b + a

and

ab = ba

How does it work?

Multiple Choice

Which form is this expression in?

3(2x + 2)

• Factored

• Expanded

Multiple Choice

Which form is this expression in?

6x + 6

• Factored

• Expanded

Multiple Choice

Which form has parenthesis in the expression?

• Factored

• Expanded

For the next few problem we will connect Distributive Property to an area model.

Consider the pool below, divided into a swimming section & a diving section.
We find total area by multiplying the sides.

Think about swimming pools. Some pools are divided into sections that are used for different purposes.

​ab + ac
or
a (b + c)

Open Ended

Write an expression you can use to find the total area of the pool?

Open Ended

Write an expression you can use to find the total area of the pool?

Multiple Choice

Using the Distributive Property, which choice shows the expression below in expanded form.

         3(x + 5)

• x + 5 + 3

• 3x + 15

• x + 15

• 3x + 5

Draw

Write (or draw) the expression below in expanded form

2x(x + 5)

Multiple Choice

Using the Distributive Property, which choice shows the expression below in factored form.

        12+24x

• 12(2 + x)

• 12(2x)

• 12(1 + 2x)

Draw

Write (or draw) the expression below in factored form

3x + 15