Fraction Action: Solving One-Step Equations!

Mathematics Grades 6th Grade 4:36 Video
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Lesson Description

Learn how to solve one-step equations where the variable is multiplied by a fraction! We'll use reciprocals to isolate the variable and find the solution.

Video Resource

Solving One-Step Equations with Fractions | Expressions & Equations | Grade 6

Math is Simple!

Duration: 4:36
Watch on YouTube

Key Concepts

  • Variable
  • Coefficient
  • Reciprocal
  • Multiplication Property of Equality

Learning Objectives

  • Students will be able to identify the coefficient and variable in a one-step equation.
  • Students will be able to determine the reciprocal of a fraction.
  • Students will be able to solve one-step equations involving fractional coefficients using the multiplication property of equality.
  • Students will be able to verify their solutions by substituting them back into the original equation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definitions of a variable, coefficient, and equation. Briefly discuss the goal of solving an equation: to isolate the variable.
  • Video Viewing (10 mins)
    Play the "Solving One-Step Equations with Fractions | Expressions & Equations | Grade 6" video by Math is Simple!. Encourage students to take notes on the steps involved in solving the equations.
  • Guided Practice (15 mins)
    Work through the examples from the video again, pausing to explain each step in more detail. Emphasize the concept of the reciprocal and how it helps to isolate the variable. Demonstrate both the standard multiplication method and the cross-canceling method.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing similar one-step equations with fractional coefficients. Have them solve the equations independently and check their answers. Provide assistance as needed.
  • Wrap-up (5 mins)
    Review the key concepts and steps involved in solving one-step equations with fractional coefficients. Answer any remaining questions and preview the next lesson.

Interactive Exercises

  • Reciprocal Relay Race
    Divide the class into teams. Give each team a set of fraction cards. Teams race to write the reciprocal of each fraction on a whiteboard or paper.
  • Equation Challenge
    Present the class with a series of one-step equations with fractional coefficients, increasing in difficulty. Students can work individually or in small groups to solve the equations. The first student or group to correctly solve each equation earns a point.

Discussion Questions

  • What is the reciprocal of a fraction, and why is it important for solving equations?
  • How does the multiplication property of equality help us solve equations?
  • Can you explain the steps involved in solving a one-step equation with a fractional coefficient?
  • Why do we need to isolate the variable?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Application of mathematical properties
  • Fraction manipulation

Multiple Choice Questions

Question 1:

What is the coefficient in the equation (2/3)x = 8?

Correct Answer: 2/3

Question 2:

What is the reciprocal of 5/7?

Correct Answer: 7/5

Question 3:

To solve (1/4)y = 3, you should multiply both sides by:

Correct Answer: 4

Question 4:

What is the value of 'w' in the equation (3/5)w = 6?

Correct Answer: 10

Question 5:

What property allows us to multiply both sides of an equation by the same number?

Correct Answer: Multiplication Property of Equality

Question 6:

In the equation (7/8)t = 14, what is the value of t?

Correct Answer: 16

Question 7:

If multiplying a fraction by its reciprocal results in 1, what is this called?

Correct Answer: Identity Property

Question 8:

Which of these operations can be used to solve a one-step equation with fractions?

Correct Answer: Multiplication

Question 9:

What does it mean to isolate the variable?

Correct Answer: Get the variable by itself on one side

Question 10:

To check your work, you should ________ the solution back into the original equation.

Correct Answer: Substitute

Fill in the Blank Questions

Question 1:

The number in front of the variable is called the ________.

Correct Answer: coefficient

Question 2:

The ________ of a fraction is found by switching the numerator and denominator.

Correct Answer: reciprocal

Question 3:

The letter that represents an unknown value is called a ________.

Correct Answer: variable

Question 4:

To solve (2/5)x = 4, multiply both sides by ________.

Correct Answer: 5/2

Question 5:

The ________ Property of Equality states that you can do the same operation to both sides of an equation.

Correct Answer: Multiplication

Question 6:

When you multiply a fraction by its reciprocal, the answer is always ________.

Correct Answer: 1

Question 7:

To ________ the variable means to get it alone on one side of the equation.

Correct Answer: isolate

Question 8:

Cross-________ is a way to simplify fractions before multiplying.

Correct Answer: canceling

Question 9:

In the equation (4/9)x = 8, x equals ________.

Correct Answer: 18

Question 10:

After solving for the variable, you should always ________ your answer to make sure it's correct.

Correct Answer: check

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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