Fraction Action: Solving One-Step Equations with Fractional Coefficients

Mathematics Grades 6th Grade 3:18 Video
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Lesson Description

Learn how to solve one-step equations when the variable is multiplied by a fraction! This lesson focuses on using reciprocals to isolate the variable and check your work.

Video Resource

One-Step Equations with Fractional Coefficients (Part 1) | Expressions & Equations | Grade 6

Math is Simple!

Duration: 3:18
Watch on YouTube

Key Concepts

  • Reciprocal of a fraction
  • Inverse operations (multiplication and division)
  • Solving one-step equations
  • Checking solutions

Learning Objectives

  • Students will be able to identify the reciprocal of a fraction.
  • Students will be able to solve one-step equations with fractional coefficients using the reciprocal.
  • Students will be able to check their solutions to ensure accuracy.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of a reciprocal. Ask students what a reciprocal is and how to find it. Provide examples of fractions and their reciprocals (e.g., 2/3 and 3/2, 1/4 and 4/1).
  • Video Viewing (7 mins)
    Play the YouTube video "One-Step Equations with Fractional Coefficients (Part 1)". Instruct students to pay attention to how the reciprocal is used to solve the equation and the importance of checking the solution.
  • Guided Practice (10 mins)
    Work through example problems similar to the video on the board. Emphasize the steps: Identify the coefficient, find its reciprocal, multiply both sides of the equation by the reciprocal, simplify, and check the answer. For example: (2/5)x = 8. (Answer: x = 20)
  • Independent Practice (10 mins)
    Provide students with practice problems to solve independently. Circulate to provide support and answer questions. Example problems: (3/4)y = 9, (-1/2)z = 5, (5/3)a = 10. (Answers: y = 12, z = -10, a = 6)
  • Review and Wrap-up (3 mins)
    Review the key concepts and steps for solving one-step equations with fractional coefficients. Answer any remaining questions.

Interactive Exercises

  • Reciprocal Matching Game
    Create a set of cards with fractions on some cards and their reciprocals on other cards. Students match the fraction cards to their corresponding reciprocal cards.
  • Equation Relay Race
    Divide the class into teams. Each team receives a set of one-step equations with fractional coefficients. Team members take turns solving an equation and passing it to the next team member to check the solution. The first team to correctly solve and check all equations wins.

Discussion Questions

  • What is a reciprocal and why is it important when solving equations with fractional coefficients?
  • Why is it important to check your solution after solving an equation?
  • Can you think of a real-world example where you might need to solve an equation with a fractional coefficient?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Procedural fluency
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the reciprocal of 2/5?

Correct Answer: 5/2

Question 2:

To solve the equation (3/4)x = 6, what should you multiply both sides by?

Correct Answer: 4/3

Question 3:

What is the value of x in the equation (1/3)x = 4?

Correct Answer: 12

Question 4:

What is the first step in solving an equation with a fractional coefficient?

Correct Answer: Find the reciprocal of the fraction

Question 5:

What is the reciprocal of -4/7?

Correct Answer: -7/4

Question 6:

Solve for m: (5/8)m = 10

Correct Answer: m = 16

Question 7:

Which of these equations shows the correct first step to solve (2/3)x = 8?

Correct Answer: (2/3)x * (3/2) = 8 * (3/2)

Question 8:

What does it mean to 'check your work' when solving an equation?

Correct Answer: Substitute the answer back into the equation

Question 9:

Solve for x: (-1/4)x = -3

Correct Answer: x = 12

Question 10:

The equation (4/5)y = 1 represents what problem?

Correct Answer: 4/5 of a number equals 1

Fill in the Blank Questions

Question 1:

The reciprocal of a fraction is found by flipping the numerator and the _________.

Correct Answer: denominator

Question 2:

To solve an equation like (1/2)x = 5, you multiply both sides by the _________ of 1/2, which is 2/1.

Correct Answer: reciprocal

Question 3:

The solution to the equation (2/3)x = 4 is x = _________.

Correct Answer: 6

Question 4:

When checking your solution, you _________ the value you found for the variable back into the original equation.

Correct Answer: substitute

Question 5:

Multiplying a number by its reciprocal always equals _________

Correct Answer: 1

Question 6:

To isolate the variable 'x' in the equation (3/5)x = 9, you would multiply both sides by _________

Correct Answer: 5/3

Question 7:

If (1/6)y = 2, then y = _________

Correct Answer: 12

Question 8:

The opposite operation of multiplying by a fraction is multiplying by its _________

Correct Answer: reciprocal

Question 9:

Solving for z: (7/2)z = 14, z = _________

Correct Answer: 4

Question 10:

If your answer doesn't make the original equation true when you check, you know your answer is _________

Correct Answer: incorrect

Educational Standards

6.A.3.2:Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution. 6.N.4.3:Multiply and divide fractions and decimals using efficient and generalizable procedures.

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