Decimal Division: Solving One-Step Equations

Mathematics Grades 6th Grade 5:00 Video
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Lesson Description

Learn how to solve one-step equations with decimals using the division property of equality. This lesson covers inverse operations and decimal division techniques.

Video Resource

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

Math is Simple!

Duration: 5:00
Watch on YouTube

Key Concepts

  • One-step equations
  • Division property of equality
  • Inverse operations
  • Decimal division

Learning Objectives

  • Students will be able to identify the operation in a one-step equation with decimals.
  • Students will be able to use the division property of equality to isolate the variable.
  • Students will be able to solve one-step equations involving decimals using division.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concepts of variables, coefficients, and equations. Briefly discuss inverse operations (multiplication and division). Show a simple example of a one-step equation with whole numbers to refresh prior knowledge.
  • Video Viewing (10 mins)
    Play the "Solving One-Step Equations with Decimals | Expressions & Equations | Grade 6" video by Math is Simple! (https://www.youtube.com/watch?v=9b_SxjkBZng). Instruct 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 at each step to explain the reasoning and answer any questions. Emphasize the importance of aligning decimal points during division and using the division property of equality. Present additional examples, gradually increasing the complexity, and work through them together as a class. Encourage active participation from students.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of one-step equations with decimals to solve independently. Circulate the classroom to provide assistance and answer questions. Have students check their answers with a partner or using a provided answer key.
  • Wrap-up (5 mins)
    Review the key concepts and learning objectives of the lesson. Answer any remaining questions and provide a preview of the next lesson on solving multi-step equations.

Interactive Exercises

  • Think-Pair-Share
    Present a one-step equation with decimals. Have students individually think about the steps required to solve it. Then, pair students up to discuss their approaches. Finally, have a few pairs share their solutions with the whole class.
  • Whiteboard Practice
    Divide the class into groups and provide each group with a whiteboard. Present a one-step equation with decimals. The first group to correctly solve the equation on their whiteboard wins a point. Repeat with different equations.

Discussion Questions

  • What is the division property of equality and why is it important?
  • How does solving one-step equations with decimals compare to solving one-step equations with whole numbers?
  • What are some real-world scenarios where you might need to solve equations with decimals?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Decimal division
  • Algebraic reasoning

Multiple Choice Questions

Question 1:

What is the first step in solving the equation 2.5x = 10?

Correct Answer: Divide both sides by 2.5

Question 2:

What is the inverse operation of multiplication?

Correct Answer: Division

Question 3:

Solve for x: 1.2x = 3.6

Correct Answer: x = 3

Question 4:

When dividing decimals, what do you need to do with the decimal point in the divisor?

Correct Answer: Move it to the right until it is a whole number

Question 5:

Solve for y: 0.5y = 2.0

Correct Answer: y = 4.0

Question 6:

What does 'coefficient' mean in the expression 3.2x?

Correct Answer: The number being multiplied by the variable

Question 7:

Solve for z: 4.0z = 16.0

Correct Answer: z = 4.0

Question 8:

Which property states that what you do to one side of an equation, you must do to the other?

Correct Answer: Division Property of Equality

Question 9:

Solve for a: 0.25a = 1

Correct Answer: a = 4

Question 10:

What is the purpose of isolating the variable in an equation?

Correct Answer: To find the value of the variable

Fill in the Blank Questions

Question 1:

The opposite of multiplication is ___________.

Correct Answer: division

Question 2:

In the equation 3.5x = 7, the number 3.5 is the ___________.

Correct Answer: coefficient

Question 3:

To solve 2.0x = 8, you should ___________ both sides by 2.0.

Correct Answer: divide

Question 4:

If you divide one side of the equation by a number, you must ___________ the other side by the same number.

Correct Answer: divide

Question 5:

The division property of ___________ helps us to solve equations.

Correct Answer: equality

Question 6:

Isolating the ___________ means getting it alone on one side of the equation.

Correct Answer: variable

Question 7:

Before dividing decimals, sometimes you need to move the ___________ point.

Correct Answer: decimal

Question 8:

In the equation 0.75x = 3, x equals ___________.

Correct Answer: 4

Question 9:

A letter that represents a number is called a ___________.

Correct Answer: variable

Question 10:

When we move a decimal in the divisor, we have to do the _________ thing in the dividend.

Correct Answer: same

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.

Teaching Materials

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