Balancing Act: Mastering Two-Step Equations

Algebra 1 Grades High School 5:12 Video
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Lesson Description

Learn to solve two-step equations using the concept of equality, applying inverse operations to isolate the variable. This lesson connects abstract algebra to a visual representation using balanced scales.

Video Resource

Solving two-step equations | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 5:12
Watch on YouTube

Key Concepts

  • Equality: Maintaining balance by performing the same operation on both sides of an equation.
  • Inverse Operations: Using opposite operations (addition/subtraction, multiplication/division) to isolate the variable.
  • Two-Step Equations: Equations that require two operations to solve for the unknown variable.

Learning Objectives

  • Students will be able to translate a real-world scenario (balanced scale) into a two-step algebraic equation.
  • Students will be able to solve two-step equations using inverse operations while maintaining equality.
  • Students will be able to verify the solution by substituting it back into the original equation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of equality and how it relates to a balanced scale. Show a simple balanced scale with equal weights on both sides. Pose the question: 'What happens if we add or remove weight from only one side?' Briefly discuss how equations are like balanced scales.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Solving two-step equations'. Instruct students to pay close attention to how the balanced scale is represented mathematically and how operations are performed on both sides.
  • Guided Practice (15 mins)
    Work through two or three similar examples on the board, explaining each step clearly. Use the balanced scale analogy to demonstrate why each operation is valid. For example: 2x + 3 = 7. Subtract 3 from both sides, divide both sides by 2.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of two-step equations to solve. Circulate the room to provide assistance and answer questions.
  • Wrap-up (5 mins)
    Review the key concepts of equality and inverse operations. Ask students to summarize the steps involved in solving a two-step equation.

Interactive Exercises

  • Online Equation Solver
    Use an online equation solver (like Wolfram Alpha) to check the answers to the independent practice problems. Discuss any discrepancies and why they might occur (e.g., rounding errors).
  • Balance Scale Simulation
    If possible, use an online balance scale simulation where students can visually manipulate weights on both sides of the scale to solve equations. This reinforces the concept of equality.

Discussion Questions

  • Why is it important to perform the same operation on both sides of an equation?
  • What is the purpose of using inverse operations when solving equations?
  • Can you think of real-world situations where solving equations might be useful?

Skills Developed

  • Problem-solving: Applying mathematical concepts to solve equations.
  • Abstract Reasoning: Translating real-world scenarios into algebraic representations.
  • Procedural Fluency: Executing the steps involved in solving two-step equations accurately.

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:

To isolate the variable in the equation 2x - 7 = 1, you should:

Correct Answer: Add 7 to both sides, then divide by 2

Question 3:

What operation is the inverse of multiplication?

Correct Answer: Division

Question 4:

If a balanced scale has 2x + 4 on one side and 10 on the other, what is the value of x?

Correct Answer: 14

Question 5:

Which of the following equations is a two-step equation?

Correct Answer: 2x - 1 = 9

Question 6:

When solving for x in the equation (x/4) + 2 = 5, which operation do you perform first?

Correct Answer: Subtract 2

Question 7:

In the equation 5x - 3 = 12, what is the value of x?

Correct Answer: 3

Question 8:

What does it mean to 'isolate the variable'?

Correct Answer: To get the variable alone on one side of the equation

Question 9:

Which property justifies adding the same number to both sides of an equation?

Correct Answer: Addition Property of Equality

Question 10:

Which operation is the inverse of subtraction?

Correct Answer: Addition

Fill in the Blank Questions

Question 1:

To solve for a variable, you must ________ it.

Correct Answer: isolate

Question 2:

The inverse operation of adding 7 is ________ 7.

Correct Answer: subtracting

Question 3:

The equation 4x + 2 = 10 requires ________ steps to solve.

Correct Answer: two

Question 4:

The addition property of ________ allows you to add the same value to both sides of an equation.

Correct Answer: equality

Question 5:

When solving an equation, you perform operations to both ________ of the equation.

Correct Answer: sides

Question 6:

If 2x - 5 = 9, then x = ________.

Correct Answer: 7

Question 7:

To undo multiplication, you use ________.

Correct Answer: division

Question 8:

In the equation (x/3) + 1 = 4, the value of x is ________.

Correct Answer: 9

Question 9:

Using the balanced scale analogy, performing the same operation on both sides maintains the ________.

Correct Answer: balance

Question 10:

The opposite operation of dividing by 5 is ________ by 5.

Correct Answer: multiplying

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.

Teaching Materials

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