Unlocking Expressions: Mastering the Distributive Property

Mathematics Grades 7th Grade 6:28 Video
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Lesson Description

Learn how to use the distributive property with variables to simplify algebraic expressions. This lesson covers distributing numbers and factoring out common factors.

Video Resource

How to use the distributive property with variables | 6th grade | Khan Academy

Khan Academy

Duration: 6:28
Watch on YouTube

Key Concepts

  • Distributive Property
  • Factoring
  • Greatest Common Factor (GCF)

Learning Objectives

  • Students will be able to apply the distributive property to simplify algebraic expressions.
  • Students will be able to factor out the greatest common factor from algebraic expressions.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of the distributive property with numerical examples (e.g., 2(3+4) = 2*3 + 2*4). Explain that this property also applies to algebraic expressions with variables.
  • Video Viewing (10 mins)
    Watch the Khan Academy video 'How to use the distributive property with variables | 6th grade | Khan Academy'. Encourage students to take notes on the examples and steps shown in the video.
  • Guided Practice (15 mins)
    Work through additional examples of distributing with variables and factoring out the GCF as a class. Provide different levels of difficulty to address different learning paces. For example: Distribute 3(x + 2y - 1) and Factor 12a - 18.
  • Independent Practice (15 mins)
    Students work independently on a worksheet or online assignment with distributive property and factoring problems. Provide support as needed.
  • Wrap-up (5 mins)
    Review the key concepts and learning objectives. Answer any remaining questions. Preview the next lesson.

Interactive Exercises

  • Online Distributive Property Game
    Students can play an online game that provides instant feedback on their distributive property skills.
  • Factoring Challenge
    Present students with increasingly complex expressions to factor, challenging them to find the greatest common factor.

Discussion Questions

  • Why is the distributive property useful?
  • How can factoring help simplify expressions?
  • What are some common mistakes to avoid when using the distributive property?
  • How does knowing the greatest common factor make factoring easier?

Skills Developed

  • Algebraic manipulation
  • Problem-solving
  • Critical thinking

Multiple Choice Questions

Question 1:

What is the first step in applying the distributive property to the expression 4(2x - 3)?

Correct Answer: Multiply 4 by 2x

Question 2:

Simplify the expression 2(5a + 4b).

Correct Answer: 10a + 8b

Question 3:

What is the greatest common factor of 15x and 25?

Correct Answer: 5

Question 4:

Factor the expression 9y - 18.

Correct Answer: 9(y - 2)

Question 5:

Which expression is equivalent to 6(3m - 2n + 1)?

Correct Answer: 18m - 12n + 6

Question 6:

What does the distributive property allow you to do?

Correct Answer: Simplify expressions by multiplying a term across multiple terms inside parentheses

Question 7:

Which expression represents 5 times the sum of 'a' and 'b'?

Correct Answer: 5(a + b)

Question 8:

What is the factored form of 8x + 12?

Correct Answer: 4(2x + 3)

Question 9:

What is the expanded form of 3(2y - 5)?

Correct Answer: 6y - 15

Question 10:

What is the first step in applying the distributive property?

Correct Answer: Multiply the outside term by each term inside the parentheses

Fill in the Blank Questions

Question 1:

The distributive property states that a(b + c) = ab + ____.

Correct Answer: ac

Question 2:

To factor an expression, find the ______ ______ ______ of the terms.

Correct Answer: greatest common factor

Question 3:

When distributing, you _______ the term outside the parentheses by each term inside.

Correct Answer: multiply

Question 4:

The simplified form of 3(4x - 2) is 12x - ______.

Correct Answer: 6

Question 5:

The factored form of 20a + 10b is 10(2a + ____).

Correct Answer: b

Question 6:

Factoring is the ______ of distributing.

Correct Answer: opposite

Question 7:

The number that is multiplied by each term inside the parentheses is _______ outside.

Correct Answer: distributed

Question 8:

In the expression 4(x + 3), the number 4 is a ______.

Correct Answer: factor

Question 9:

When an expression is fully factored, the terms inside the parentheses share no common ______.

Correct Answer: factors

Question 10:

Applying the distributive property creates _______ expressions.

Correct Answer: equivalent

Educational Standards

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. 7.A.4.2:Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols. 7.A.3.1:Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers.

Teaching Materials

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