Tackling Equations: Mastering the Distributive Property

Algebra 1 Grades High School 6:04 Video
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Lesson Description

Learn how to solve linear equations using the distributive property. This lesson breaks down the steps, from simplifying expressions to isolating the variable, ensuring a solid understanding of this crucial algebraic skill.

Video Resource

Solving equations with the distributive property | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 6:04
Watch on YouTube

Key Concepts

  • Distributive Property
  • Combining Like Terms
  • Solving Linear Equations
  • Inverse Operations

Learning Objectives

  • Students will be able to apply the distributive property to simplify algebraic expressions.
  • Students will be able to solve linear equations involving the distributive property.
  • Students will be able to verify solutions to linear equations.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the distributive property: a(b + c) = ab + ac. Briefly discuss its importance in simplifying expressions and solving equations. Show a simple example like 2(x + 3) = 2x + 6.
  • Video Instruction (15 mins)
    Play the Khan Academy video 'Solving equations with the distributive property | Linear equations | Algebra I | Khan Academy'. Encourage students to follow along, taking notes on the steps involved in solving the example equation. Pause at key points to clarify any confusion.
  • Worked Example (10 mins)
    Work through the example from the video on the board, emphasizing each step: distributing, combining like terms, isolating the variable, and verifying the solution. Encourage student participation by asking questions about each step.
  • Practice Problems (15 mins)
    Provide students with practice problems to solve individually or in pairs. Start with simpler equations and gradually increase the complexity. Circulate the room to provide assistance and answer questions.
  • Review and Closure (5 mins)
    Review the key steps in solving equations with the distributive property. Address any remaining questions and highlight common mistakes. Assign homework for further practice.

Interactive Exercises

  • Whiteboard Challenge
    Divide students into groups. Write a linear equation with the distributive property on the board. Each group solves the equation on their whiteboard and shows their work. The first group to correctly solve the equation wins.
  • Error Analysis
    Present students with a worked-out equation that contains an error in applying the distributive property or solving for the variable. Have students identify the error and correct it.

Discussion Questions

  • Why is it important to apply the distributive property before combining like terms?
  • What are some common mistakes to avoid when solving equations with the distributive property?
  • How can you verify that your solution to an equation is correct?

Skills Developed

  • Applying the distributive property
  • Solving linear equations
  • Problem-solving
  • Critical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the first step in solving the equation 2(x + 3) = 10?

Correct Answer: Apply the distributive property

Question 2:

Which of the following is the correct application of the distributive property to the expression -3(2x - 5)?

Correct Answer: -6x + 15

Question 3:

Solve for x: 4(x - 2) = 12

Correct Answer: x = 5

Question 4:

What is the value of x in the equation -2(x + 1) = 8?

Correct Answer: -5

Question 5:

Simplify the expression: 5(2x + 3) - 4x

Correct Answer: 6x + 15

Question 6:

Solve for x: 3(x + 2) = 5x - 4

Correct Answer: x = 5

Question 7:

Simplify: -1(4x - 7)

Correct Answer: -4x + 7

Question 8:

What is the solution to -5(x - 3) = 10?

Correct Answer: x = 1

Question 9:

Evaluate the expression 2(3x + 1) if x = 2

Correct Answer: 14

Question 10:

Which operation do you preform first when solving equations with parenthesis?

Correct Answer: Distribution

Fill in the Blank Questions

Question 1:

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

Correct Answer: distributive

Question 2:

To solve an equation with the distributive property, first __________ the expression inside the parentheses.

Correct Answer: distribute

Question 3:

After distributing, you should __________ like terms on each side of the equation.

Correct Answer: combine

Question 4:

The goal when solving any equation is to __________ the variable.

Correct Answer: isolate

Question 5:

To check your solution, __________ the value of the variable back into the original equation.

Correct Answer: substitute

Question 6:

When multiplying a negative number by a quantity in parenthesis, be careful with the __________ of each term.

Correct Answer: sign

Question 7:

To isolate a variable, use __________ operations to undo addition, subtraction, multiplication and division.

Correct Answer: inverse

Question 8:

Parenthesis are usually removed by __________ the term directly outside of it to the terms inside.

Correct Answer: multiplying

Question 9:

If two equations are equivalent, they have the same __________.

Correct Answer: solution

Question 10:

Expressions on either side of the equals sign must have the same __________ to be equivalent.

Correct Answer: value

Educational Standards

A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties. A1.A.1:Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context.

Teaching Materials

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