Unlocking Equivalent Expressions: Combining Like Terms and the Distributive Property

Mathematics Grades 7th Grade 1:57 Video
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Lesson Description

Learn how to simplify algebraic expressions by combining like terms and using the distributive property to find equivalent forms.

Video Resource

How to find equivalent expressions by combining like terms and using the distributive property

Khan Academy

Duration: 1:57
Watch on YouTube

Key Concepts

  • Like terms
  • Combining like terms
  • Distributive property
  • Factoring
  • Equivalent expressions

Learning Objectives

  • Students will be able to identify like terms in algebraic expressions.
  • Students will be able to combine like terms to simplify algebraic expressions.
  • Students will be able to apply the distributive property to expand or factor algebraic expressions.
  • Students will be able to determine if two or more algebraic expressions are equivalent.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definitions of variables, constants, terms, and expressions. Briefly discuss the concept of simplifying expressions.
  • Video Viewing (7 mins)
    Watch the Khan Academy video 'How to find equivalent expressions by combining like terms and using the distributive property'. Encourage students to take notes on key steps and vocabulary.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video, demonstrating how to combine like terms and apply the distributive property. Start with simpler examples and gradually increase complexity. Emphasize the importance of maintaining the order of operations.
  • Independent Practice (15 mins)
    Assign practice problems for students to work on individually or in pairs. Circulate to provide support and answer questions. Use varied problems, including those requiring factoring.
  • Wrap-up (3 mins)
    Review the key concepts and learning objectives. Answer any remaining questions. Preview the upcoming lesson or activity related to algebraic expressions.

Interactive Exercises

  • Term Sorting
    Provide a list of terms (e.g., 3x, 5, -2x, 7y, 9) and have students sort them into groups of like terms.
  • Distributive Property Matching
    Provide expressions like 2(x + 3) and have students match them to their expanded forms (e.g., 2x + 6).
  • Equivalent Expression Challenge
    Provide an expression and ask students to come up with at least two equivalent expressions using combining like terms or the distributive property.

Discussion Questions

  • What are like terms, and how do we identify them?
  • How does the distributive property help us simplify expressions?
  • Can you explain the difference between simplifying and solving an equation?
  • Why is it important to follow the order of operations when simplifying expressions?
  • How can factoring help us find equivalent expressions?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Critical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

Which of the following is equivalent to 3x + 2x - 5?

Correct Answer: 5x - 5

Question 2:

Simplify the expression: 4(y + 2)

Correct Answer: 4y + 8

Question 3:

Which terms are like terms in the expression: 7a + 3b - 2a + 5?

Correct Answer: 7a and -2a

Question 4:

What is the simplified form of 6x - 2x + 4?

Correct Answer: 4x + 4

Question 5:

Which expression is equivalent to 5(m - 1)?

Correct Answer: 5m - 5

Question 6:

What is the result of combining like terms in the expression: 9y + 2 - 4y?

Correct Answer: 5y + 2

Question 7:

Which expression is equivalent to 2x + 3y + 5x - y?

Correct Answer: 7x + 2y

Question 8:

Simplify: -3(z + 2)

Correct Answer: -3z - 6

Question 9:

What is a factor of 4x + 8?

Correct Answer: 4

Question 10:

Which of the following is equivalent to 2(x + y) + x?

Correct Answer: 3x + 2y

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:

Combining like terms simplifies an ____.

Correct Answer: expression

Question 4:

3x + 5x can be simplified to ____.

Correct Answer: 8x

Question 5:

To expand 4(x - 2), you multiply 4 by both ____ and ____.

Correct Answer: x and -2

Question 6:

Simplifying 7y - 3y + 1 results in ____.

Correct Answer: 4y + 1

Question 7:

____ means to rewrite an expression in a simpler form.

Correct Answer: Simplifying

Question 8:

Expressions that are the same, even though they may look different, are called ____ expressions.

Correct Answer: equivalent

Question 9:

The first step to simplifying 2(x + 3) + x is to use the ____ property.

Correct Answer: distributive

Question 10:

Factoring is the ____ of using the distributive property.

Correct Answer: opposite

Educational Standards

7.A.4:Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions. 7.A.4.1:Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents.

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