Fraction Action: Solving One-Step Equations with Fractional Coefficients

Mathematics Grades 6th Grade 2:46 Video
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Lesson Description

Learn how to solve one-step equations when the variable is multiplied by a fraction. We'll use reciprocals and check our answers!

Video Resource

One-Step Equations with Fractional Coefficients (Part 2) | Expressions & Equations | Grade 6

Math is Simple!

Duration: 2:46
Watch on YouTube

Key Concepts

  • Reciprocal of a fraction
  • Inverse operations
  • Solving one-step equations
  • Checking solutions

Learning Objectives

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

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what a reciprocal is (flipping the numerator and denominator of a fraction). Ask students for examples of reciprocals (e.g., reciprocal of 2/3 is 3/2). Briefly discuss inverse operations.
  • Video Viewing (7 mins)
    Play the YouTube video "One-Step Equations with Fractional Coefficients (Part 2) | Expressions & Equations | Grade 6". Instruct students to pay attention to how the reciprocal is used to isolate the variable and how the solution is checked.
  • Guided Practice (10 mins)
    Work through the example from the video on the board, explaining each step clearly. Emphasize why multiplying by the reciprocal works to isolate the variable. Solve another similar problem together, soliciting input from students at each step.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing similar one-step equations with fractional coefficients. Have them solve the equations independently and check their answers. Circulate to provide assistance as needed.
  • Wrap-up (3 mins)
    Review the key concepts and learning objectives. Answer any remaining questions. Briefly introduce the concept of solving more complex equations with fractional coefficients.

Interactive Exercises

  • Reciprocal Relay Race
    Divide the class into teams. Write fractions on the board. The first student from each team runs to the board, writes the reciprocal of the fraction, and tags the next student. The team that correctly writes all the reciprocals first wins.
  • Equation Scavenger Hunt
    Hide equations with fractional coefficients around the classroom. Students must find the equations, solve them, and write the solution on a designated sheet. The first student to correctly solve all the equations wins.

Discussion Questions

  • What is the reciprocal of a fraction, and how do you find it?
  • Why does multiplying by the reciprocal isolate the variable in an equation with a fractional coefficient?
  • Why is it important to check your solution to an equation?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Applying mathematical concepts
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the reciprocal of 3/4?

Correct Answer: 4/3

Question 2:

What operation do you use to solve an equation?

Correct Answer: Opposite

Question 3:

To solve the equation (2/5)x = 6, what should you multiply both sides by?

Correct Answer: 5/2

Question 4:

What is the solution to the equation (1/3)x = 4?

Correct Answer: 12

Question 5:

Why do we multiply by the reciprocal when solving equations with fractional coefficients?

Correct Answer: To isolate the variable

Question 6:

What is the solution to the equation (-2/3)x = 8?

Correct Answer: -12

Question 7:

What should you do after solving an equation?

Correct Answer: Check your answer

Question 8:

Solve: (5/2)x = 10

Correct Answer: 4

Question 9:

What is the reciprocal of -1/5?

Correct Answer: -5

Question 10:

What should you do if you are stuck on a problem?

Correct Answer: Ask for help

Fill in the Blank Questions

Question 1:

The reciprocal of a fraction is found by _______ the numerator and denominator.

Correct Answer: flipping

Question 2:

To solve (3/7)x = 9, multiply both sides by the reciprocal, which is _______.

Correct Answer: 7/3

Question 3:

The solution to (1/4)x = 5 is x = _______.

Correct Answer: 20

Question 4:

Multiplying a fraction by its reciprocal always equals _______.

Correct Answer: 1

Question 5:

When solving an equation, you must do the same operation to _______ sides.

Correct Answer: both

Question 6:

Before solving, you should _______ the question.

Correct Answer: read

Question 7:

Solving (5/6)x = -10, multiply both sides by _______.

Correct Answer: 6/5

Question 8:

The solution to (2/9)x = 4 is x = _______.

Correct Answer: 18

Question 9:

Always _______ your work after solving for x.

Correct Answer: check

Question 10:

Another word for switching the numerator and denominator is _______.

Correct Answer: reciprocal

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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