Applying the Distributive Property to Algebraic Expressions

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SWBAT use the distributive property to simplify algebraic expressions.

Big Idea

How can we use the distributive property to simplify algebraic expressions?

Do Now

10 minutes

Students previously worked on identifying algebraic expressions and evaluating expressions.  The Do Now problems will focus on evaluating expressions.  Based on an exit ticket on this topic, students had difficulty with evaluating expressions that involved fractions and decimals.  I've chosen problems that will give students additional practice with this.

Do Now

Evaluate each expression.

1)    4a2 + 2 for a = ½

2)     3xy + 8x for x = 2.5 and y = 0.01

3)      12x2 + 3y3 + 8z for x = ¼ , y = 1/3 , z = 2/9

Students may have difficulty with problem #3, since it involves 3 variables with 3 different fractions.   For this problem students will need to use their prior knowledge of applying exponents to fractions and multiplying fractions.

After 10 minutes, I will model the steps to evaluating the expressions.  I will randomly call on students to explain a step to the class.


Mini Lesson

15 minutes

This lesson applies a previous topic (See Distributive Property) to algebra.

First, I will review the concept of the distributive property with the class.

What do you remember about the Distributive Property?

Students may remember that the distributive property is multiplication over addition.

Then, I will explain that the distributive property can be used in algebra.  We will work on simplifying expressions using the distributive property.

Ex. 1:  Simplify 4(x + 2)

What number is being distributed?  How can we multiply a number by a variable?

Many students may intuitively think to multiply to get 4x.  To support this, I will explain that we are multiplying 4 times the coefficient of x, which is 1, and we keep the variable. 4 should also be multiplied by the constant.  

What happens to the parentheses after we've used the distributive property?

Students should notice that the parentheses is no longer necessary.  This will be helpful in future lessons.

We will work through more examples together.

Ex. 2:  Simplify 2(x + 3)

Ex. 3:  Simplify 3(x + 6)

Ex. 4:  Simplify 5(8x + 7y)

For example 4, students should realize that 5 needs to be distributed to both terms in the parentheses.  However, each term has a variable.  I will have students discuss with their group how to simplify this expression.

Ex. 5:  Simplify (x + 7)3

In addition to simplifying expressions by using the distributive property, I will introduce students to factoring algebraic expressions.  As we work on a few examples together, students may realize that factoring is the distributive property in reverse.  The distributive property is multiplying a number to the terms in the parentheses, whereas factoring is dividing the terms by a common factor.

Ex. 6:  Factor 12x + 30

What is the GCF of 12 and 30?

Based on their prior knowledge of finding the GCF, students should be able to determine that the GCF is 6.  

If I factor out the GCF of 6, what would be the remaining factor in the parentheses?

It's important for students to realize that you have to divide both terms needed to be divided by the GCF to arrive at 6(2x + 5).

I will model a few more examples for the class, that present additional challenges like more than one variable.

Ex. 7:  Factor 24x - 16y

Ex. 8:  Factor 15x + 3y + 9z






Independent Practice

10 minutes

The Independent Practice is a continuation of the concepts learned in today's lesson.  Students will work on the problems independently and after 10 minutes they will discuss their answers with their group.  If there are any questions, I will discuss them with the class.

Students may have difficulty with problem 6, because if they are using mental math most will find the GCF to be 7 instead of 14.  Students may have difficulty with problem 8, because it contains two variables and an exponent.

Independent Practice

Rewrite each expression without parentheses.

1)6(2x + 4)

2)5(x + 5)

3)1(5m - 8)

4)9(3x - 6)

Factor out the GCF of each expression .

5)15x - 20

6)14r - 42x

7)8y + 12

8)24x2 - 18y



Lesson Summary

5 minutes

If students haven't realized that the distributive property and factoring algebraic expressions are related, I will pose the following questions:

How does the below equation show both the distributive property and factoring?

9(3x + 8) = 27x + 72

What is the relationship between the distributive property and factoring?