Spot the Mistake: Mastering One-Step Equations

Mathematics Grades 7th Grade 4:04 Video
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Lesson Description

Learn how to identify errors in one-step equation solving, reinforcing your understanding of algebraic principles and critical thinking.

Video Resource

How to find mistakes in one step equations | 6th grade | Khan Academy

Khan Academy

Duration: 4:04
Watch on YouTube

Key Concepts

  • One-Step Equations
  • Inverse Operations
  • Maintaining Equality
  • Identifying Errors

Learning Objectives

  • Students will be able to identify errors in the steps taken to solve one-step equations.
  • Students will be able to explain why a particular step is incorrect based on algebraic principles.
  • Students will be able to solve one-step equations correctly.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic principles of solving one-step equations, emphasizing the importance of performing the same operation on both sides of the equation to maintain equality.
  • Video Viewing (10 mins)
    Watch the Khan Academy video 'How to find mistakes in one step equations' (https://www.youtube.com/watch?v=xKhU3iMKRiw). Instruct students to take notes on the types of errors demonstrated in the video.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video, pausing at each step to ask students to predict potential errors. Discuss why certain operations are valid or invalid.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing several solved one-step equations with intentional errors. Students must identify the error and correctly solve the equation.
  • Wrap-up and Assessment (5 mins)
    Administer the multiple-choice and fill-in-the-blank quizzes to assess student understanding of the concepts covered.

Interactive Exercises

  • Error Analysis Challenge
    Divide students into small groups and provide each group with a different incorrectly solved equation. Groups must identify the error, explain why it is incorrect, and then correctly solve the equation. Each group presents their analysis to the class.

Discussion Questions

  • Why is it important to perform the same operation on both sides of an equation?
  • What are some common mistakes people make when solving one-step equations?
  • How can you check your answer to make sure it is correct?

Skills Developed

  • Critical Thinking
  • Problem Solving
  • Algebraic Reasoning
  • Error Analysis

Multiple Choice Questions

Question 1:

What is the most important rule to remember when solving equations?

Correct Answer: Perform the same operation on both sides.

Question 2:

In the equation x + 5 = 12, what operation should you perform on both sides to solve for x?

Correct Answer: Subtraction

Question 3:

If someone divides only the left side of an equation by 3, what must they do to the right side to maintain equality?

Correct Answer: Divide by 3

Question 4:

Which of the following is an example of an inverse operation?

Correct Answer: Multiplying by 4 and dividing by 4

Question 5:

In the equation 3y = 15, what is the correct next step to solve for y?

Correct Answer: Divide both sides by 3

Question 6:

Carly tried to solve the equation 7a=28. She divided the left side by 'a' and the right side by 7. What was her mistake?

Correct Answer: She should have divided both sides by the same number.

Question 7:

Trent was solving g/3=4/3. He multiplied the left side by 3 and the right side by 1/3. What was his mistake?

Correct Answer: He should have multiplied the left and right side by the same number.

Question 8:

Ling tried to solve 12=p+6.2. She added 6.2 to the left side and subtracted 6.2 from the right side. What was her mistake?

Correct Answer: She should have done the opposite of what she did on both sides.

Question 9:

Alanna was solving 4c=12. She divided the left side by 4 and multiplied the right side by 4. What was her mistake?

Correct Answer: She should have divided both sides by 4.

Question 10:

Rico was solving n+12=18.3. He subtracted 12 from both sides and got n=7.3. What was his mistake?

Correct Answer: He made an arithmetic mistake. 18.3-12=6.3

Fill in the Blank Questions

Question 1:

To isolate a variable, use the ______ operation.

Correct Answer: inverse

Question 2:

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

Correct Answer: other

Question 3:

The goal of solving an equation is to get the variable by ______.

Correct Answer: itself

Question 4:

Addition and ______ are inverse operations.

Correct Answer: subtraction

Question 5:

Multiplication and ______ are inverse operations.

Correct Answer: division

Question 6:

If an equation says x + 7 = 10, you should ______ 7 from both sides to solve.

Correct Answer: subtract

Question 7:

To solve 4y = 20, you should ______ both sides by 4.

Correct Answer: divide

Question 8:

The basic principle of equation solving is maintaining ______.

Correct Answer: equality

Question 9:

In 7a=28, 'a' is called the ______.

Correct Answer: variable

Question 10:

When checking your answer, substitute your solution back into the ______ equation.

Correct Answer: original

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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