Solving Two-Step Equations

Lesson Overview

Grade: 9
Subject: Mathematics
Duration: 30 minutes
Curriculum Area: Algebra - Expressions and Equations
Standards: California Common Core State Standards for Mathematics – CCSS.MATH.CONTENT.HSA.REI.B.3

Learning Objectives

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

1. Solve two-step equations with integer solutions.
2. Understand and apply inverse operations to isolate variables.
3. Verify solutions by substituting values back into the original equation.

Materials Needed

• Whiteboard and markers
• Student handouts with 20 equations
• Calculators (optional)
• Pencils and erasers

Lesson Plan

1. Introduction (5 minutes)

Objective: Introduce the concept of two-step equations.

• Begin with a brief recap of one-step equations using integers.
• Explain that two-step equations involve two operations.
• Show a simple example on the board: e.g., 2x + 3 = 11.
• Discuss the importance of inverse operations to solve for the variable.

2. Direct Instruction (10 minutes)

Objective: Demonstrate solving techniques for two-step equations.

• Write a two-step equation on the board: 2x + 5 = 15.

• Step 1: Discuss subtracting 5 from both sides to undo addition.

  • 2x = 10

• Step 2: Divide both sides by 2 to isolate x.

  • x = 5

• Highlight the importance of maintaining equation balance.

• Activity: Solve another equation with students: 3x - 4 = 11.

  • Add 4 to both sides and divide by 3.
  • Solution: x = 5

3. Practice (10 minutes)

Objective: Students practice solving equations in pairs.

• Distribute handouts with 20 different two-step equations.
• In pairs, students solve each equation ensuring both partners agree on the solution.
• Encourage students to check solutions by substituting values back.

Sample Equations

1. 4x - 3 = 13
2. 5 + 2x = 19
3. -2x + 6 = 4
4. 7x + 8 = 29
5. x/3 - 2 = 4 (Multiply first)

4. Review and Conclusion (5 minutes)

Objective: Review solutions and reinforce concepts.

• Randomly select pairs to present one solution each.
• Solve any challenging equations together.
• Quick quiz: Pose two more oral questions; students solve on scrap paper.

5. Differentiation Strategies

• Advanced students: Offer more complex equations with fractions.
• Struggling students: Focus on guiding with one handout for each step, and provide additional examples if needed.

Assessment

• Observe students' participation during pair work.
• Evaluate understanding based on accuracy of solved equations presented during class share-out.

Close the Lesson

• Reiterate key strategies for solving two-step equations.
• Encourage students to practice more outside class using similar examples.
• Ask students to reflect on inverse operations used today.

This structured lesson plan aims to provide not just a clear pathway to solving two-step equations but also to bolster confidence through practice and collaboration, adhering to California's educational standards.