Mastering the Art of Combining Like Terms: Level Up!

Algebra 1 Grades High School 4:39 Video
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Lesson Description

This lesson takes you beyond basic like terms and dives into complex expressions with multiple variables and exponents. Learn to identify, reorder, and simplify these expressions like a pro!

Video Resource

Combining like terms, but more complicated | Introduction to algebra | Algebra I | Khan Academy

Khan Academy

Duration: 4:39
Watch on YouTube

Key Concepts

  • Identifying like terms (variables and exponents must match)
  • Understanding that variables represent numbers
  • Reordering expressions using the commutative property
  • Combining coefficients of like terms

Learning Objectives

  • Students will be able to identify like terms within complex algebraic expressions.
  • Students will be able to reorder algebraic expressions to group like terms together.
  • Students will be able to simplify complex algebraic expressions by combining like terms.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic concept of combining like terms (e.g., 2x + 3x = 5x). Briefly discuss the importance of understanding variables and their potential values. Emphasize that 'like terms' must have identical variable parts (including exponents).
  • Video Viewing (10 mins)
    Play the Khan Academy video: "Combining like terms, but more complicated". Instruct students to pay close attention to how the presenter identifies and groups like terms, especially when dealing with multiple variables (x, y) and exponents (x², y²).
  • Guided Practice (15 mins)
    Work through a few example problems similar to the one in the video. Model the process of identifying like terms, reordering the expression (if necessary), and combining the coefficients. Use color-coding or underlining to help students visually track the terms being combined. For example: 5x² + 3xy - 2x² + xy = (5x² - 2x²) + (3xy + xy) = 3x² + 4xy.
  • Independent Practice (15 mins)
    Provide students with a set of practice problems to solve independently. Circulate the classroom to offer assistance and answer questions. Encourage students to show their work and use the techniques demonstrated in the video and guided practice.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts of the lesson and address any remaining questions. Administer the multiple-choice and fill-in-the-blank quizzes to assess student understanding.

Interactive Exercises

  • Like Term Sort
    Create a set of cards with various algebraic terms (e.g., 3x, -2y², 5xy, 7x², -xy, 4y²). Have students work in pairs or small groups to sort the cards into groups of like terms.
  • Expression Builder
    Provide students with a set of coefficients and variable terms (e.g., coefficients: 2, -3, 5; variable terms: x, y, x², xy). Have them create complex algebraic expressions and then simplify them by combining like terms.

Discussion Questions

  • Why is it important to identify like terms correctly before combining them?
  • How does understanding that variables represent numbers help in combining like terms?
  • Can you give an example of two terms that look similar but are NOT like terms and explain why?
  • What properties allow us to reorder expressions?

Skills Developed

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

Multiple Choice Questions

Question 1:

Which of the following terms is like 3x²y?

Correct Answer: -3x²y

Question 2:

What is the simplified form of 5xy + 2xy - xy?

Correct Answer: 6xy

Question 3:

Which property allows you to reorder terms in an expression?

Correct Answer: Commutative Property

Question 4:

Simplify: 4a + 2b - a + 3b

Correct Answer: 3a + 5b

Question 5:

Which of the following is NOT a like term to 7y?

Correct Answer: 7y²

Question 6:

What is the coefficient in the term -5x²?

Correct Answer: -5

Question 7:

Simplify: 2x² + 3x - x² - x

Correct Answer: x² + 2x

Question 8:

Why can't you combine x and x²?

Correct Answer: They have different exponents

Question 9:

What is 0xy equivalent to?

Correct Answer: 0

Question 10:

What is the simplified form of -3y + 5y?

Correct Answer: 2y

Fill in the Blank Questions

Question 1:

Terms that have the exact same variable factors are called _________ terms.

Correct Answer: like

Question 2:

The number in front of a variable is called the _________.

Correct Answer: coefficient

Question 3:

To simplify an expression, you _________ like terms.

Correct Answer: combine

Question 4:

5x and 5x² are _________ like terms.

Correct Answer: not

Question 5:

The expression 3x + 2y + 5x simplifies to _________.

Correct Answer: 8x+2y

Question 6:

When combining like terms, you only add or subtract the _________.

Correct Answer: coefficients

Question 7:

The simplified form of 4xy - 4xy is _________.

Correct Answer: 0

Question 8:

You can only combine terms that have the same _________ and exponents.

Correct Answer: variables

Question 9:

Reordering an expression to group like terms is possible due to the _________ property.

Correct Answer: commutative

Question 10:

When an x term has no written coefficient, the coefficient is understood to be _________.

Correct Answer: 1

Educational Standards

A1.A.3.2:Simplify polynomial expressions by adding, subtracting, or multiplying. A1.A.3:Create and evaluate equivalent algebraic expressions and equations using algebraic properties.

Teaching Materials

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