Solving Equations: Unlocking the Mystery of ax = b

Mathematics Grades 7th Grade 11:06 Video
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Lesson Description

This lesson introduces 7th-grade students to solving basic algebraic equations in the form ax = b. Students will learn how to isolate the variable and find its value, using inverse operations. Emphasis is placed on understanding the concept of equality and checking solutions.

Video Resource

How to solve equations of the form ax = b | Linear equations | Algebra I | Khan Academy

Khan Academy

Duration: 11:06
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Key Concepts

  • Variable: A symbol (usually a letter) representing an unknown value.
  • Coefficient: The number multiplied by the variable in an algebraic term.
  • Inverse Operation: The operation that undoes another operation (e.g., division is the inverse of multiplication).
  • Isolate: To get a variable alone on one side of an equation.
  • Equality: Showing that two equations or expressions are equal to each other.

Learning Objectives

  • Students will be able to identify the variable and coefficient in an equation of the form ax = b.
  • Students will be able to solve for the variable in an equation of the form ax = b using inverse operations.
  • Students will be able to check their solution by substituting it back into the original equation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of a variable and its purpose in algebra. Ask students for examples of situations where they might need to find an unknown quantity. Briefly introduce the equation form ax = b, explaining what each symbol represents.
  • Video Viewing (10 mins)
    Play the Khan Academy video: 'How to solve equations of the form ax = b'. Encourage students to take notes on the steps involved in solving the equations. Pause the video at key points to discuss the concepts being presented.
  • Guided Practice (15 mins)
    Work through several example problems of the form ax = b on the board. Emphasize the importance of showing all steps, including the inverse operation used to isolate the variable. Model how to check the solution by substituting it back into the original equation. Start with easier problems (e.g., 2x = 6) and gradually increase the difficulty (e.g., 4x = 20). Ask students to explain their reasoning for each step.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing a variety of equations of the form ax = b. Have them work independently to solve each equation and check their solutions. Circulate the room to provide assistance as needed. Encourage students to work together and discuss their approaches.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts of the lesson. Ask students to summarize the steps involved in solving equations of the form ax = b. Collect the worksheets for assessment. Preview the next lesson on solving more complex one-step equations.

Interactive Exercises

  • Equation Matching Game
    Create cards with equations on one set and solutions on another. Students match the equations to their correct solutions.
  • Online Practice on Khan Academy
    Have students practice solving equations of the form ax = b on the Khan Academy website using the link provided in the video description.

Discussion Questions

  • What does the variable represent in the equation ax = b?
  • Why do we use inverse operations to solve equations?
  • How can you check if your solution is correct?
  • Can 'a' or 'b' be negative numbers? How would that affect the solution?

Skills Developed

  • Problem-solving
  • Algebraic thinking
  • Critical thinking
  • Attention to detail

Multiple Choice Questions

Question 1:

What is the variable in the equation 3x = 12?

Correct Answer: x

Question 2:

What operation should you use to solve the equation 5x = 25?

Correct Answer: Division

Question 3:

What is the value of x in the equation 4x = 16?

Correct Answer: 4

Question 4:

If 2x = 10, what is the value of x?

Correct Answer: 5

Question 5:

What is the solution to the equation 7x = 49?

Correct Answer: 7

Question 6:

In the equation 'ax = b', what does 'a' represent?

Correct Answer: The coefficient

Question 7:

To check your answer in the equation 6x=30, what do you do with the solution?

Correct Answer: Multiply it by 6

Question 8:

Solve: 9x = 81

Correct Answer: 9

Question 9:

Which operation is the inverse of multiplication?

Correct Answer: Division

Question 10:

What is the value of 'x' in the equation 1x = 5?

Correct Answer: 5

Fill in the Blank Questions

Question 1:

In the equation ax = b, 'x' is called the ________.

Correct Answer: variable

Question 2:

The number multiplied by the variable is called the ________.

Correct Answer: coefficient

Question 3:

To solve for x in 3x = 9, you should ________ both sides by 3.

Correct Answer: divide

Question 4:

The solution to the equation 5x = 35 is x = ________.

Correct Answer: 7

Question 5:

To check if x = 4 is the correct solution for 2x = 8, you can ________ 4 for x in the original equation.

Correct Answer: substitute

Question 6:

The goal when solving equations is to __________ the variable.

Correct Answer: isolate

Question 7:

If 8x = 24, then x = ________.

Correct Answer: 3

Question 8:

Division is the __________ operation of multiplication.

Correct Answer: inverse

Question 9:

In the equation 6x = 42, the coefficient is __________.

Correct Answer: 6

Question 10:

The solution to 10x = 100 is x = ________.

Correct Answer: 10

Educational Standards

7.A.3.1:Write and solve problems leading to linear equations with one variable in the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. 7.A.4.1:Use properties of operations (associative, commutative, and distributive) to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. 7.A.4.2:Evaluate numerical expressions using calculators and other technologies and justify solutions using order of operations and grouping symbols.

Teaching Materials

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