Balancing Act: Solving One-Step Equations!

Mathematics Grades 7th Grade 2:09 Video
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Lesson Description

Learn how to solve one-step equations using addition and subtraction. Discover the importance of keeping both sides of the equation balanced!

Video Resource

How to solve one-step equations | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 2:09
Watch on YouTube

Key Concepts

  • Variable
  • Equation
  • Inverse Operations
  • Balancing Equations

Learning Objectives

  • Students will be able to identify the variable in a one-step equation.
  • Students will be able to solve one-step equations using addition.
  • Students will be able to solve one-step equations using subtraction.
  • Students will be able to explain the concept of balancing equations.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what an equation is and the meaning of a variable. Briefly discuss why solving equations is important in mathematics and real-world applications. Ask students if they've ever had to 'undo' something to get back to the original state (e.g., putting away toys, returning a book).
  • Video Viewing (7 mins)
    Play the Khan Academy video: 'How to solve one-step equations | Linear equations | Algebra I | Khan Academy'. Instruct students to take notes on the methods used to solve the equations.
  • Guided Practice (10 mins)
    Work through the examples from the video on the board. Emphasize the importance of performing the same operation on both sides of the equation. Model solving additional one-step equations, varying the numbers and using both addition and subtraction. Explain how to verify solutions.
  • Independent Practice (10 mins)
    Distribute a worksheet with one-step equations for students to solve independently. Circulate to provide assistance and answer questions.
  • Wrap-up & Discussion (8 mins)
    Review the solutions to the independent practice problems. Facilitate a class discussion about the strategies used to solve the equations and the importance of balancing equations. Preview the next steps: solving one-step equations with multiplication and division.

Interactive Exercises

  • Equation Balance
    Use a virtual balance scale to visually represent equations. Students can add or subtract quantities from both sides of the scale to maintain balance and solve for the unknown variable. Examples: https://www.geogebra.org/m/wwXcEq3H
  • Equation Scavenger Hunt
    Hide index cards with one-step equations around the classroom. Students find a card, solve the equation, and then find another card with the solution printed on it. They continue until they have solved all the equations.

Discussion Questions

  • Why is it important to perform the same operation on both sides of an equation?
  • How can you check if your solution to an equation is correct?
  • Can you think of any real-world scenarios where you might need to solve a one-step equation?
  • What are inverse operations?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Algebraic reasoning
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the first step in solving the equation x + 5 = 9?

Correct Answer: Subtract 5 from both sides

Question 2:

Which operation is the inverse of addition?

Correct Answer: Subtraction

Question 3:

What does it mean to 'balance' an equation?

Correct Answer: To make both sides equal

Question 4:

Solve for y: y - 3 = 7

Correct Answer: y = 10

Question 5:

Solve for z: z + 2 = -5

Correct Answer: z = -7

Question 6:

What is a variable?

Correct Answer: A letter that represents an unknown value

Question 7:

In the equation 'a + 8 = 12', what is the value of 'a'?

Correct Answer: 4

Question 8:

Which of the following equations is solved correctly?

Correct Answer: z - 2 = 10; z = 12

Question 9:

What operation would you use to isolate 'x' in the equation 'x + (-3) = 5'?

Correct Answer: Add 3 to both sides

Question 10:

Which of the following demonstrates the correct balancing method for x - 5 = 10?

Correct Answer: x - 5 + 5 = 10 + 5

Fill in the Blank Questions

Question 1:

In the equation x + 3 = 8, the _______ is 'x'.

Correct Answer: variable

Question 2:

To solve for x in x - 5 = 2, you must ______ 5 to both sides of the equation.

Correct Answer: add

Question 3:

An equation is like a balanced ______.

Correct Answer: scale

Question 4:

The inverse operation of subtracting 4 is _______ 4.

Correct Answer: adding

Question 5:

If y + 6 = 11, then y = _______.

Correct Answer: 5

Question 6:

Whatever you do to one side of an equation, you must do to the ______ side.

Correct Answer: other

Question 7:

The goal when solving for a variable is to ______ it on one side of the equation.

Correct Answer: isolate

Question 8:

In the equation a - 9 = -2, the value of a is ____.

Correct Answer: 7

Question 9:

To solve the one-step equation n + 7 = 12, you should _______ 7 from both sides.

Correct Answer: subtract

Question 10:

When solving for a variable, always remember to use _______ operations.

Correct Answer: inverse

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:Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions.

Teaching Materials

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