Balancing Act: Solving One-Step Equations

Mathematics Grades 7th Grade 1:54 Video
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Lesson Description

Learn how to solve one-step equations using inverse operations. This lesson uses addition and subtraction to isolate variables and find their values.

Video Resource

Example of solving a one-step equation | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 1:54
Watch on YouTube

Key Concepts

  • Variables
  • Equations
  • Inverse Operations
  • Equality

Learning Objectives

  • Students will be able to identify the variable in a one-step equation.
  • Students will be able to use inverse operations to isolate the variable.
  • Students will be able to solve one-step equations involving addition and subtraction.
  • Students will be able to check their answers by substituting their answer back into the equation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of a variable and an equation. Ask students what they understand about solving for an unknown. Briefly introduce the idea of 'balancing' an equation.
  • Video Viewing (7 mins)
    Play the Khan Academy video "Example of solving a one-step equation | Linear equations | Algebra I | Khan Academy". Instruct students to pay close attention to how Sal solves the equation a + 5 = 54.
  • Guided Practice (10 mins)
    Work through the example problem from the video (a + 5 = 54) step-by-step on the board, explaining each step. Emphasize the importance of performing the same operation on both sides of the equation to maintain balance. Introduce additional examples like x - 3 = 10 and y + 7 = 25.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing various one-step equations involving addition and subtraction. Have them solve the equations independently and check their answers. Include a few more challenging problems with larger numbers.
  • Review and Wrap-up (3 mins)
    Review the key concepts of the lesson and answer any remaining questions. Briefly discuss the importance of one-step equations as a foundation for more complex algebraic equations.

Interactive Exercises

  • Equation Balance
    Use a virtual balance scale (online or physical) to demonstrate how performing the same operation on both sides of an equation keeps the scale balanced. Represent the equation with physical objects on the scale.
  • Group Problem Solving
    Divide students into small groups and provide each group with a set of one-step equations written on index cards. Have the groups work together to solve the equations, explaining their reasoning to each other.

Discussion Questions

  • What does it mean to 'solve' an equation?
  • Why is it important to perform the same operation on both sides of the equation?
  • What is an inverse operation, and how does it help us solve equations?

Skills Developed

  • Problem-solving
  • Algebraic thinking
  • Critical thinking
  • Attention to Detail

Multiple Choice Questions

Question 1:

What is the first step in solving the equation x + 8 = 12?

Correct Answer: Subtract 8 from both sides

Question 2:

What is the value of 'y' in the equation y - 5 = 15?

Correct Answer: 20

Question 3:

Which operation is the inverse of addition?

Correct Answer: Subtraction

Question 4:

If a + 3 = 7, what is the value of 'a'?

Correct Answer: 3

Question 5:

What does it mean to isolate the variable?

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

Question 6:

Which of the following is a one-step equation?

Correct Answer: x - 4 = 6

Question 7:

What should you do to both sides of the equation to solve z - 11 = 3?

Correct Answer: Add 11

Question 8:

What is the value of 'b' in the equation 10 + b = 18?

Correct Answer: 8

Question 9:

Which of the following expressions represents the solution to m + 6 = 14?

Correct Answer: m = 14 - 6

Question 10:

What is the value of 'p' if p - 9 = 1?

Correct Answer: 10

Fill in the Blank Questions

Question 1:

To solve an equation, you need to ________ the variable.

Correct Answer: isolate

Question 2:

The inverse operation of subtraction is ________.

Correct Answer: addition

Question 3:

If x + 2 = 9, then x = ________.

Correct Answer: 7

Question 4:

To keep an equation balanced, you must do the same thing to ________ sides.

Correct Answer: both

Question 5:

In the equation 'a - 4 = 12', 'a' is the ________.

Correct Answer: variable

Question 6:

The inverse operation of adding 7 is ________ 7.

Correct Answer: subtracting

Question 7:

If y - 10 = 20, then y = ________.

Correct Answer: 30

Question 8:

If 5 + z = 11, then z = _______.

Correct Answer: 6

Question 9:

The equation t + 3 = 8 can be solved by ________ 3 from both sides.

Correct Answer: subtracting

Question 10:

If q - 1 = 9, then q = _______.

Correct Answer: 10

Educational Standards

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. 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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