Simplifying Expressions: Combining Like Terms Like a Pro!

Mathematics Grades 7th Grade 3:43 Video
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Lesson Description

Learn how to simplify complex algebraic expressions by identifying and combining like terms. This lesson reinforces the concept of coefficients and variables and how to manipulate them effectively.

Video Resource

How to simplify a big expression by combining like terms | Algebra I | Khan Academy

Khan Academy

Duration: 3:43
Watch on YouTube

Key Concepts

  • Variables and Coefficients
  • Like Terms
  • Combining Like Terms

Learning Objectives

  • Students will be able to identify like terms in an algebraic expression.
  • Students will be able to simplify algebraic expressions by combining like terms.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concepts of variables, coefficients, and terms in an algebraic expression. Briefly discuss why simplifying expressions is important in algebra.
  • Video Viewing (10 mins)
    Play the Khan Academy video "How to simplify a big expression by combining like terms". Encourage students to take notes on the key steps and examples provided.
  • Guided Practice (15 mins)
    Work through example problems on the board, similar to those in the video. Emphasize the importance of identifying like terms (terms with the same variable raised to the same power) and correctly adding or subtracting their coefficients. Reinforce the 'common sense' approach as described in the video.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing various algebraic expressions to simplify. Circulate the room to provide assistance and address any misconceptions.
  • Wrap-up (5 mins)
    Review the key concepts and steps for combining like terms. Answer any remaining questions and preview the next lesson.

Interactive Exercises

  • Term Sorting
    Write several terms on the board (e.g., 3x, 5y, -2x, 7, 4y, -1). Have students group the like terms together.
  • Expression Challenge
    Present students with increasingly complex algebraic expressions and challenge them to simplify them as quickly and accurately as possible. This can be gamified with points for correct answers and time bonuses.

Discussion Questions

  • What are 'like terms', and why can we only combine them?
  • How does the coefficient affect the variable in an expression?
  • Can you think of real-world scenarios where combining like terms would be helpful?

Skills Developed

  • Identifying Like Terms
  • Simplifying Algebraic Expressions
  • Applying Properties of Operations

Multiple Choice Questions

Question 1:

Which of the following terms is a 'like term' with 5x?

Correct Answer: -2x

Question 2:

What is the coefficient in the term -3y?

Correct Answer: -3

Question 3:

Simplify the expression: 2x + 5x - x

Correct Answer: 6x

Question 4:

Which of the following expressions is already fully simplified?

Correct Answer: 2c + 5d

Question 5:

What is the simplified form of 8z - 3z + z?

Correct Answer: 6z

Question 6:

What should you do first when simplifying a big expression?

Correct Answer: Reorder and group like terms

Question 7:

Simplify the expression: 7 + 2x + 3 + 4x

Correct Answer: 6x + 10

Question 8:

What is the equivalent of subtracting z?

Correct Answer: Subtracting 1z

Question 9:

You have 9 apples and give away 4. How many do you have left? Relate this to combining like terms.

Correct Answer: 5 apples

Question 10:

Simplify: 12y - 5y + 2

Correct Answer: 7y + 2

Fill in the Blank Questions

Question 1:

Terms that have the same variable raised to the same power are called ________ ________.

Correct Answer: like terms

Question 2:

The number multiplied by a variable is called the ________.

Correct Answer: coefficient

Question 3:

5x and -2x can be ________ because they are like terms.

Correct Answer: combined

Question 4:

To simplify 8y - 3y, you subtract the ________.

Correct Answer: coefficients

Question 5:

The simplified form of 4a + 6b - a is 3a + ________.

Correct Answer: 6b

Question 6:

When simplifying, you can only combine ________ ________.

Correct Answer: like terms

Question 7:

Implicitly, subtracting a 'z' is the same as subtracting ________ z.

Correct Answer: 1

Question 8:

If you have 10 of something and add 5 more, you have a total of ________.

Correct Answer: 15

Question 9:

The simplified expression for 5x + 2y - 2x + y is 3x + ________.

Correct Answer: 3y

Question 10:

The most simplified form of 7z + 3 - 2z is 5z + ________.

Correct Answer: 3

Educational Standards

7.A.4:Use order of operations and properties of operations to generate and evaluate equivalent numerical and algebraic expressions. 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.

Teaching Materials

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