Simplifying Expressions: Combining Like Terms and the Distributive Property

Algebra 1 Grades High School 4:07 Video
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Lesson Description

Learn how to simplify algebraic expressions by combining like terms and applying the distributive property. This lesson builds upon order of operations and prepares students for more advanced algebraic concepts.

Video Resource

How to simplify an expression by combining like terms and the distributive property | Khan Academy

Khan Academy

Duration: 4:07
Watch on YouTube

Key Concepts

  • Like Terms
  • Distributive Property
  • Simplifying Expressions

Learning Objectives

  • Students will be able to identify like terms within an algebraic expression.
  • Students will be able to apply the distributive property to expand expressions.
  • Students will be able to simplify algebraic expressions by combining like terms after applying the distributive property.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concepts of 'order of operations' and 'like terms'. Ask students to provide examples of each. Briefly explain that this lesson will combine these concepts with the distributive property to simplify expressions.
  • Video Viewing (10 mins)
    Play the Khan Academy video: 'How to simplify an expression by combining like terms and the distributive property'. Instruct students to take notes on the key steps demonstrated in the video.
  • Guided Practice (15 mins)
    Work through example problems on the board, demonstrating the application of the distributive property and combining like terms. Start with simpler expressions and gradually increase the complexity. Encourage student participation by asking them to identify like terms and suggest the next steps.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of expressions to simplify. Encourage them to work independently but allow them to ask for assistance if needed. Circulate the classroom to provide support and address individual questions.
  • Wrap-up and Assessment (10 mins)
    Review the key concepts and steps for simplifying expressions. Administer the multiple-choice and fill-in-the-blank quizzes to assess student understanding.

Interactive Exercises

  • Whiteboard Challenge
    Divide students into small groups. Give each group a complex expression to simplify on a whiteboard. The first group to correctly simplify the expression wins.
  • Online Practice
    Direct students to the Khan Academy practice exercises related to combining like terms and the distributive property for additional practice and immediate feedback.

Discussion Questions

  • What are 'like terms', and how do we identify them?
  • How does the distributive property help us simplify expressions?
  • What are the common mistakes students make when simplifying expressions using these methods?

Skills Developed

  • Algebraic Manipulation
  • Problem Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

Which of the following terms is like 3x?

Correct Answer: -3x

Question 2:

What is the first step in simplifying 2(x + 5) - 3x?

Correct Answer: Distribute the 2

Question 3:

What is the simplified form of 4x + 2x - x?

Correct Answer: 5x

Question 4:

Simplify: 3(y - 2)

Correct Answer: 3y - 6

Question 5:

What is the simplified form of 5(x + 2) - 3?

Correct Answer: 5x + 7

Question 6:

Which expression is equivalent to 2x + 3(x - 1)?

Correct Answer: 5x - 3

Question 7:

Combine like terms: 7a + 3b - 2a + b

Correct Answer: 5a + 4b

Question 8:

Simplify: -4(x - 2)

Correct Answer: -4x + 8

Question 9:

What is the constant term in the expression 3x + 5 - 2x?

Correct Answer: 5

Question 10:

After distributing, which expression would you have if you started with 5(2x+3)?

Correct Answer: 10x+15

Fill in the Blank Questions

Question 1:

Terms that have the same variable raised to the same power are called ______ ______.

Correct Answer: like terms

Question 2:

The ________ property states that a(b + c) = ab + ac.

Correct Answer: distributive

Question 3:

To simplify an expression, you first apply the distributive property and then _______ like terms.

Correct Answer: combine

Question 4:

The simplified form of 2(x + 4) is ______.

Correct Answer: 2x+8

Question 5:

When simplifying 5x - 3x + 2, the like terms are 5x and ______.

Correct Answer: -3x

Question 6:

The constant term in the expression 4x + 7 is ______.

Correct Answer: 7

Question 7:

Distributing -2 to (x-5) gives you ______

Correct Answer: -2x+10

Question 8:

Combining 3x + 5x gives you _____.

Correct Answer: 8x

Question 9:

Simplifying 2(a+3) - a gives you ______

Correct Answer: a+6

Question 10:

The inverse operation of distribution is called ______

Correct Answer: factoring

Educational Standards

A1.A.3.2:Simplify polynomial expressions by adding, subtracting, or multiplying. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

Teaching Materials

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