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# Combining Like Terms with the Distributive Property

Lesson 8 of 16

## Objective: SWBAT apply the distributive property to combining like terms.

*50 minutes*

#### Do Now

*10 min*

In a previous lesson, Combining Like Terms, students identified like terms and developed steps for simplifying algebraic expressions. The Do Now is an assessment of their understanding of like terms. Problems 2 and 3 display common mistakes made by students. It is important for students to be able to explain why these are not correct equations.

**Do Now**

True or False. If false, explain why.

1. 8x + 3x = 11x

2. 7x + 7y = 14xy

3. 4x + 4x = 8x^{2}

Simplify

4. 8a + 2 + 3b + 9 + a + 6b + 1

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#### Mini Lesson

*15 min*

This lesson is a continuation of Combining Like Terms, but I will introduce students to how the distributive property can be used to simplify expressions and combine like terms.

We will work through several problems together

**Ex. 1 - Simplify 7x + 3(x+ 4)**

*What property of math do you see in this expression?*

Students should recognize that the distributive property can be applied.

*How can we simplify this expression using the distributive property?*

Students have prior knowledge of the distributive property, but I will review how 3 should be multiplied by both terms in the parentheses.

*Can we simplify this expression further? Are there like terms in this expression?*

Students should identify 7x and 3x as like terms.

**Ex. 2 - Simplify 8 + 5(3x + 4y + 2) + 6y**

*What should we do first?*

Students should suggest that we apply the distributive property. For students who think that we can combine like terms first, I will bring to their attention that, similar to order of operations, we need to clear the parentheses first.

*How many terms are inside the parentheses? What is the 5 distributed to?*

Students should know that there are 3 terms that the 5 should be distributed to.

*Can we simplify this expression? Are there like terms?*

Students should recognize that they can combine the y variables and the constants.

**Ex. 3 - Write an expression for the perimeter of a rectangle with a length of 2x + 4 and a width of x + 9**

I will have students draw a rectangle and label it, so it is easier to visualize the problem.

*There are two different ways to find the perimeter of a rectangle. What is one strategy?*

Most students will suggest adding all the sides, which will give us the expression 2x + 4 + x + 9 + 2x + 4 + x + 9.

*Can we simplify this expression?*

Students should recognize the like terms. I will remind students to be aware of the "invisible" ones, which changes x to 1x.

*What is another strategy for finding perimeter of a rectangle?*

Some students may know of the formula P = 2l + 2w. This will give us the expression 2(2x+4) + 2(x+9). We will simplify this expression using the distributive property and combining like terms. It is important for students to see that either method gives us the same simplified expression.

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#### Independent Practice

*20 min*

For the Independent Practice, students will be given problems where they will have to apply the distributive property and combining like terms.

**Independent Practice**

1) Simplify 4 + (x + 3)6

2) Simplify 3x^{2} + 7x + 5(x + 3) + x^{2}

3) Simplify 9x^{3} + 2x^{2} + 3(x^{2} + x) + 5x

4) Find the perimeter of a triangle with sides 2x + 3, 5x + 8 + x, and 7x - 2.

5) Simplify 2(a + 5) - a + 6

6) Simplify 6y + 4m + 3(3y + m)

7) Simplify 15 + 2(x + 4) + 10

After 10 minutes, I will assign each group a problem and give them a white board to show their work on. They will have about 5 minutes to agree on their work and answer with their group, before they present the problem to the class. Students should be able to explain their work using math vocabulary such as expressions, distributive property, combining like terms, coefficient, constant, and variable.

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#### Exit Ticket

*5 min*

To assess students understanding of combining like terms using the distributive property, I will give them an exit ticket. The exit ticket will be a problem that will challenge students and force them to carefully organize their work.

**Exit Ticket**

Simplify the expression.

4(x + 5 + 2y) + 4(5y + 6) + (3 + 2x + 8) - 1 + 2(3x + y + 1)

I will use the results of the exit ticket to group students for the following lesson.

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- UNIT 1: First Week of School
- UNIT 2: Properties of Math
- UNIT 3: Divisibility Rules
- UNIT 4: Factors and Multiples
- UNIT 5: Introduction to Fractions
- UNIT 6: Adding and Subtracting Fractions
- UNIT 7: Multiplying and Dividing Fractions
- UNIT 8: Algorithms and Decimal Operations
- UNIT 9: Multi-Unit Summative Assessments
- UNIT 10: Rational Numbers
- UNIT 11: Equivalent Ratios
- UNIT 12: Unit Rate
- UNIT 13: Fractions, Decimals, and Percents
- UNIT 14: Algebra
- UNIT 15: Geometry

- LESSON 1: Exponents
- LESSON 2: Order of Operations
- LESSON 3: Identifying Algebraic Expressions
- LESSON 4: Translating Expressions
- LESSON 5: Evaluating Algebraic Expressions
- LESSON 6: Applying the Distributive Property to Algebraic Expressions
- LESSON 7: Combining Like Terms
- LESSON 8: Combining Like Terms with the Distributive Property
- LESSON 9: Algebraic Expressions Quiz
- LESSON 10: Solving 1 Step Algebraic Equations
- LESSON 11: Solving 2 Step Algebraic Equations
- LESSON 12: Writing Algebraic Inequalities
- LESSON 13: Graphing Inequalities on a Number Line
- LESSON 14: Using Inequalities to Solve Problems
- LESSON 15: Algebra Review Stations
- LESSON 16: Algebra Unit Exam