Mastering Multi-Step Equations

Curriculum Standards (US Education)

This lesson aligns with 8th Grade Common Core Math Standards for Expressions and Equations: CCSS.MATH.CONTENT.8.EE.C.7 - "Solve linear equations in one variable, including equations with coefficients represented by letters."

Learning Objective

By the end of this 30-minute lesson, students will confidently solve multi-step equations using inverse operations, parentheses, distribution, and variable isolation. They will also understand how to check their solution for accuracy.

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Overview/Key Vocabulary

1. Multi-step equation
2. Inverse operations (addition, subtraction, multiplication, division)
3. Distribution
4. Like terms
5. Solution verification

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Materials Needed

1. Whiteboard/Chalkboard
2. Dry-erase markers/chalk
3. Student notebooks or graph paper
4. Prepared handout or worksheet with 4–5 multi-step equations
5. Colored pencils (optional for organizing steps visually)

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Lesson Breakdown

1. Warm-Up (5 Minutes)

Purpose: Activate prior knowledge

• Write on the board:
  “2x + 5 = 15. How would you solve this?”
  • Ask students for their ideas (focus on inverse operations).
  • Quickly solve it step-by-step, emphasizing:
    • Subtraction to isolate variable terms.
    • Division to finish solving.
  • Highlight that today we’ll deal with equations requiring multiple steps and distribution.

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2. Guided Practice (10 Minutes)

This section uses I Do, We Do, You Do (gradual release of responsibility) teaching strategy.

Step 1: "I Do" (4 Minutes)

Present Example 1: Distributing First
Write on the board: 3(2x - 4) = 18

• Show students:
  1. Distribute: 6x - 12 = 18
  2. Add 12 to both sides: 6x = 30
  3. Divide both sides by 6: x = 5
  4. Solution Check: Plug x = 5 into the original equation to verify.
• Use a different color for each step to show clear separation in solving.

Step 2: "We Do" (4 Minutes)

Collaborative Example 2
Write on the board: 5x + 3 = 2(x + 6)

• Work through step-by-step with students helping:
  1. Distribute on the right-hand side: 5x + 3 = 2x + 12
  2. Subtract 2x from both sides: 3x + 3 = 12
  3. Subtract 3 from both sides: 3x = 9
  4. Divide by 3: x = 3
  5. Solution Check

Step 3: "You Do" (2 Minutes)

Students Practice Independently with Immediate Support
Write on the board: 4(x - 2) = 8

• Ask students to solve on their own while you circulate among desks.

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3. Small Group Activity: Equation Challenge (10 Minutes)

Purpose: Reinforce learning through collaboration.

• Divide the class into 3 small groups (3-4 students each).

• Task: Each group receives a prepared worksheet with 3 progressively challenging multi-step equations, e.g.:

  1. 2(3x + 1) = 14
  2. 4x - 3(x + 5) = 8
  3. (x/2) + 7 = 10

• Groups work together to solve each equation step-by-step. Encourage students to color-code the steps if needed for clarity.

• One student from each group presents their solution and reasoning to the class.

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4. Cool Down & Exit Ticket (5 Minutes)

Recap Key Points on the Board:

• Always start with distribution and combine like terms.
• Use inverse operations in reverse “PEMDAS” order.
• Always verify your solution by substitution.

Ask students for one thing they’ve learned that was new or interesting about multi-step equations.

Exit Ticket Activity:
Hand out a sticky note to each student. Ask them to solve this final equation independently:
6x + 4 = 2(x + 10)

Students write their name and solution to turn in as they leave.

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Differentiation Strategies

• Advanced Learners: Give a multi-step equation that involves fractions or decimals (e.g., (1/3)x + 5 = 14).
• Struggling Learners: Provide a visual checklist (e.g., “1. Distribute, 2. Combine like terms, 3. Isolate the variable, 4. Check solution”). Offer one-on-one support during “You Do” practice.
• ELL Students: Include vocabulary prompts (e.g., definitions of “isolate,” “distribute”) and allow use of colored pencils to highlight terms for visual learners.

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Assessment

• Evaluate participation during group work and presentations.
• Quickly review exit tickets to identify misconceptions.
• Use this data to inform the next lesson—further practice or moving toward real-world applications of equations.

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Reflection for Teacher

• Which students excelled or struggled in solving multi-step equations?
• Was there enough time during group work for all students to contribute?
• Did the teacher’s gradual release of responsibility support independent problem-solving?

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