Combining Like Terms

Overview

Grade Level: 7th Grade
Subject: Mathematics
Lesson Duration: 60 minutes
Curriculum Standard: CCSS.Math.Content.7.EE.A.1 (Use properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients)

This engaging lesson will teach students how to simplify expressions by combining like terms, ensuring they understand the fundamental concepts behind it. The lesson will include interactive activities, creative practice, and a fun challenge to solidify the concept in a hands-on manner.

---

Objectives

By the end of the lesson, students will be able to:

1. Identify like terms within an algebraic expression.
2. Simplify expressions by combining like terms and applying properties of operations.
3. Explain the reasoning behind their work and demonstrate understanding in a collaborative setting.

---

Materials Needed

• Dry-erase boards and markers (enough for each student or pair)
• Small cut-out algebra tiles (paper or foam), red and blue to represent positive and negative terms
• Chart paper or a whiteboard
• Markers for collaborative work
• “Like Terms Matching Game” cards (differentiated by levels of difficulty)
• Handout: “Combining Like Terms Practice” worksheet
• Two small prizes (for the group challenge)

---

Lesson Structure

1. Introduction (10 Minutes)

Hook: Alphabet Soup Challenge

• Write a scrambled “equation” on the board in bright colors:
  Example: 3x + 4y - 2x + 6 - 7y + 5.
• Ask the class:
  "If these terms were pieces of alphabet soup, how would you group the 'letters' back together into meaningful words?"
• Discuss how grouping similar “letters” (or terms) together makes it more understandable.

Set the Stage

• Briefly explain the concept of like terms (terms with the same variable and exponent) and why combining them is essential for simplifying algebraic expressions.
• Write a quick example: 2x + 3 + 5x → Combine 2x and 5x → 7x + 3.
• Emphasize color coding or grouping as a visual aid for understanding the concept.

---

2. Exploration (20 Minutes)

Guided Practice (10 Minutes)

1. Visual Manipulatives:

   • Hand out small sets of algebra tiles to each pair of students.
   • Show an example on the board using tiles to physically demonstrate grouping: Example: 3x + 2 - 2x + 5
     • Positive x = Blue tiles, Negative x = Red tiles, Constants = Yellow tiles.
     • Students group like tiles together to demonstrate combining terms: (3x - 2x) and (+2 + 5) → x + 7.
   • Reinforce that students can use the tiles to check their work before writing the final simplified expression.

2. On the board: Work through a more complex example with the entire class. Example: 4a - 3 + 5b + 2a + 6 - b.

   • Talk students through step-by-step: Combine 4a + 2a, combine 5b - b, and -3 + 6.

---

Independent Exploration: Think-Pair-Share (10 Minutes)

• Give each student their individual whiteboard and ask:
  Example Problem: 6m + 8 - 4m + 11 - m.
  • Step 1: Solve the problem independently on their whiteboard.
  • Step 2: Turn to their partner to compare answers and explain their reasoning.
  • Step 3: Share their final answer with the class.

Teachers should circulate the room, prompting students with questions like, “How do you know these are like terms?” or “What happens when you add negative and positive terms together?”

---

3. Application (25 Minutes)

Activity 1: Like Terms Matching Game (10 Minutes)

• Divide the class into small groups of 3–4 students.
• Each group receives a set of shuffled algebra card pairs with expressions (e.g., 3x + 4x, 10y - 7y, 5 - 2).
• Their task:
  1. Match the expressions to their correct simplified forms.
  2. Write the finalized expressions on a group whiteboard.
• Groups earn a point for each correct match. Bonus points if they can explain their work!

Activity 2: Team Challenge Relay (15 Minutes)

• Break the class into two teams.
• On the board, write five increasingly complex expressions for each team (Example: 7x + 3y + 2x - y + 4 - x).
• One student at a time from each team runs to the board to simplify a term or combine something, then tags the next person in their team. Teams must explain their final answers while the teacher checks their work.
• First team to finish with correct answers wins a small prize!

---

4. Wrap-Up and Reflection (5 Minutes)

• Present one final example on the board: 8x - 3x + 4y - 6 + 7x + 9.
• As a class, simplify the expression step-by-step for reinforcement.
  Final Answer: 12x + 4y + 3.

Exit Ticket

Provide each student a sticky note with two questions to answer on their way out the door:

1. Simplify: 5a + 2b - 3a + 7 + 6b - 2.
2. In one sentence, explain why combining like terms is essential in math.

Collect these as a formative assessment of their understanding.

---

Differentiation Strategies

• For Struggling Learners: Use more algebra tiles and guided problems with teacher assistance. Work in smaller groups with additional support. Highlight and circle like terms to make grouping visual.
• For Advanced Learners: Provide additional challenge problems that include fractions or decimals (e.g., 1.5x + 3.2 - 0.5x).

---

Assessment

• Observation during group and individual work.
• Team Challenge Relay performance.
• Exit ticket responses to evaluate comprehension.

---

Homework/Extension

• “Like Terms Practice Worksheet” with 10 questions:
  • Simplify increasingly difficult expressions.
  • Final challenge: Write your own expression (minimum 5 terms) and simplify it.

---

By engaging students with hands-on activities, collaborative challenges, and visual aids, this lesson will help 7th graders confidently grasp the concept of combining like terms and apply it to mathematical expressions!