Substitution Solutions: Cracking the Code of Equations

Algebra 1 Grades High School 3:44 Video
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Lesson Description

Learn how to verify if a given value is a solution to an equation by using substitution. This lesson reinforces algebraic thinking and problem-solving skills.

Video Resource

How to test solutions to equations using substitution | 6th grade | Khan Academy

Khan Academy

Duration: 3:44
Watch on YouTube

Key Concepts

  • Equation
  • Variable
  • Solution
  • Substitution
  • Order of Operations

Learning Objectives

  • Students will be able to define what it means for a value to be a solution to an equation.
  • Students will be able to test whether a given value is a solution to an equation by using substitution.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definitions of equation, variable, and solution. Ask students to provide examples of each. Explain that the lesson will focus on how to check if a specific number is a solution to an equation.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'How to test solutions to equations using substitution | 6th grade | Khan Academy'. Encourage students to take notes on the steps the video demonstrates.
  • Guided Practice (10 mins)
    Work through the examples from the video on the board, emphasizing each step of the substitution process. Reinforce the importance of following the order of operations (PEMDAS/BODMAS). Discuss why some values satisfy the equation while others do not.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing equations and potential solutions. Have them work individually to determine which values are solutions by using substitution.
  • Review and Wrap-up (8 mins)
    Review the answers to the independent practice problems. Address any remaining questions or misconceptions. Summarize the key concepts of the lesson and preview the next steps in solving equations.

Interactive Exercises

  • Think-Pair-Share
    Present an equation and a potential solution. Have students individually determine if the value is a solution. Then, have them pair with a partner to discuss their findings and justify their reasoning. Finally, share their conclusions with the class.
  • Online Equation Solver (Verification)
    Introduce students to online equation solvers. After manually testing a solution via substitution, they can use the solver to confirm their answer.

Discussion Questions

  • What does it mean for a number to be a 'solution' to an equation?
  • Why is it important to follow the order of operations when substituting values into an equation?
  • Can an equation have more than one solution? Are there equations that have no solutions?

Skills Developed

  • Algebraic Thinking
  • Problem-Solving
  • Attention to Detail
  • Order of Operations

Multiple Choice Questions

Question 1:

What does it mean for a value to be a solution to an equation?

Correct Answer: It makes the equation true when substituted for the variable.

Question 2:

In the equation 3x + 5 = 14, is x = 2 a solution?

Correct Answer: No

Question 3:

In the equation 2y - 7 = 3, is y = 5 a solution?

Correct Answer: Yes

Question 4:

Which of the following is the first step when testing a solution to an equation using substitution?

Correct Answer: Substitute the given value for the variable.

Question 5:

In the equation x/2 + 1 = 4, is x = 6 a solution?

Correct Answer: Yes

Question 6:

Given the equation 4a - 2 = 10, which value of 'a' is a solution?

Correct Answer: 3

Question 7:

What is the role of the order of operations (PEMDAS/BODMAS) in substitution?

Correct Answer: It dictates the sequence of calculations for accurate evaluation.

Question 8:

If substituting a value for a variable results in a false statement, what does this indicate?

Correct Answer: The value is not a solution to the equation.

Question 9:

Which of these equations has x = 3 as a solution?

Correct Answer: 2x - 1 = 4

Question 10:

Consider the equation 7 - 2b = 1. Which of the following values for 'b' makes the equation true?

Correct Answer: 3

Fill in the Blank Questions

Question 1:

The process of replacing a variable with a specific value is called ___________.

Correct Answer: substitution

Question 2:

A ___________ to an equation is a value that makes the equation true.

Correct Answer: solution

Question 3:

In the expression 4x + 2, if x = 3, the value of the expression is ___________.

Correct Answer: 14

Question 4:

If 2y - 5 = 11, then y = ___________ is the solution.

Correct Answer: 8

Question 5:

Following the ___________ is essential to get correct solutions during substitution.

Correct Answer: order of operations

Question 6:

If 5(x - 2) = 15, then x = _______ is a solution.

Correct Answer: 5

Question 7:

A value is NOT a solution if the substitution results in a ___________ statement.

Correct Answer: false

Question 8:

In the equation x/4 = 3, then the value of x is _______.

Correct Answer: 12

Question 9:

To check if x = 4 is a solution to 2x + 1 = 9, you would substitute 4 for _______ in the equation.

Correct Answer: x

Question 10:

After substituting, you must ___________ both sides of the equation to determine if the solution is correct.

Correct Answer: simplify

Educational Standards

A1.A.1:Represent and solve mathematical and real-world problems using linear equations, absolute value equations, and systems of equations; interpret solutions in the original context. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties. A1.A.3.4:Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y.

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