Conquering Two-Step Equations: A Visual Approach

Algebra 1 Grades High School 8:41 Video
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Lesson Description

Learn how to solve two-step linear equations using both abstract algebraic manipulation and concrete visual representations. This lesson builds on one-step equations and introduces the crucial concept of inverse operations.

Video Resource

Solving a more complicated equation | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 8:41
Watch on YouTube

Key Concepts

  • Inverse operations (addition/subtraction, multiplication/division)
  • Maintaining equality by performing the same operation on both sides of an equation
  • Simplifying equations to isolate the variable

Learning Objectives

  • Students will be able to identify the inverse operations needed to solve a two-step equation.
  • Students will be able to solve two-step linear equations algebraically.
  • Students will be able to explain the reasoning behind each step in solving a two-step equation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing one-step equations. Briefly discuss how the goal is to isolate the variable and how we use inverse operations to achieve this. Ask students to give examples of inverse operations.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Solving a more complicated equation | Linear equations | Algebra I | Khan Academy'. Encourage students to take notes on the steps involved in solving the equations presented.
  • Guided Practice (15 mins)
    Work through the examples from the video again, but this time, pause at each step and ask students why that particular operation is being performed. Emphasize the visual representation of subtracting objects from both sides to maintain equality. Work through the following example together as a class: 5x + 3 = 18. Then, solve for x.
  • Independent Practice (15 mins)
    Provide students with a set of two-step equations to solve independently. Circulate the room to provide assistance and answer questions. Examples: 2x - 7 = 3 -3x + 1 = -8 4x + 5 = 25 x/2 + 3 = 7
  • Wrap-up & Discussion (5 mins)
    Review the key steps in solving two-step equations. Answer any remaining questions. Preview the next lesson on more complex linear equations.

Interactive Exercises

  • Equation Balance
    Use an online equation balance scale (search for 'equation balance virtual manipulative') to visually demonstrate the effects of adding, subtracting, multiplying, and dividing both sides of an equation. Have students manipulate the scale to solve equations.

Discussion Questions

  • Why is it important to perform the same operation on both sides of an equation?
  • Can you solve a two-step equation in a different order? Does the order matter?
  • How does the visual representation help you understand the algebraic process?

Skills Developed

  • Problem-solving
  • Abstract reasoning
  • Algebraic manipulation
  • Critical thinking

Multiple Choice Questions

Question 1:

What is the first step in solving the equation 3x + 5 = 14?

Correct Answer: Subtract 5 from both sides

Question 2:

What is the inverse operation of addition?

Correct Answer: Subtraction

Question 3:

Solve for x: 2x - 4 = 6

Correct Answer: x = 5

Question 4:

Solve for y: 4y + 2 = 18

Correct Answer: y = 4

Question 5:

Solve for z: -2z + 5 = -1

Correct Answer: z = 3

Question 6:

What operation is used to undo multiplication?

Correct Answer: Division

Question 7:

Which value of 'a' satisfies the equation 5a - 10 = 0?

Correct Answer: a = 2

Question 8:

Solve for b: b/3 + 2 = 5

Correct Answer: b = 9

Question 9:

In the equation 7x - 3 = 11, which operation should be performed after adding 3 to both sides?

Correct Answer: Divide both sides by 7

Question 10:

Solve for c: -3c - 9 = 0

Correct Answer: c = -3

Fill in the Blank Questions

Question 1:

To solve for x in 4x - 2 = 10, first add 2 to both sides, then _______ both sides by 4.

Correct Answer: divide

Question 2:

The inverse operation of subtracting 7 is _______ 7.

Correct Answer: adding

Question 3:

To isolate the variable in an equation, use _______ operations.

Correct Answer: inverse

Question 4:

Solve for d: 5 + d/2 = 8, d = _______

Correct Answer: 6

Question 5:

To keep an equation balanced, perform the same _______ on both sides.

Correct Answer: operation

Question 6:

The solution to the equation 2y + 1 = 9 is y = _______

Correct Answer: 4

Question 7:

In 6z - 5 = 7, the first step after adding 5 to both sides is to ________ both sides by 6.

Correct Answer: divide

Question 8:

A way to solve a multi-step equation is to use ________ operations to reverse the expression.

Correct Answer: inverse

Question 9:

Solve for g: -3g + 4 = -5, g = _______

Correct Answer: 3

Question 10:

If 2x + 3 = 11, then x equals _______

Correct Answer: 4

Educational Standards

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. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties. A1.A.3.1:Solve equations involving several variables for one variable in terms of the others.

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