Solving Two-Step Equations

Overview

Curriculum Area: Algebra (Common Core Standards – CCSS.MATH.CONTENT.HSA.REI.B.3)
Grade Level: 9-12 (High School)
Duration: 45 minutes
Skill Focus: Solving two-step equations with positive and negative integers, understanding inverse operations, enhancing algebraic reasoning.
Objective: Students will learn to solve two-step equations involving positive and negative integers by observing modeling, practicing scaffolded examples, and applying their learning independently.

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Materials Needed

1. Whiteboard and markers
2. Graph paper
3. Printed worksheets (scaffolded and challenge problems)
4. Mini whiteboards or scratch paper for student practice
5. A deck of integer cards (-10 to 10) for group activities (to be explained in activities)

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Lesson Structure

1. Warm-Up Activity (5 minutes)

Objective: Activating prior knowledge of integer operations and single-step equations.

1. Write 5 quick problems on the whiteboard:
   • Example:
     1. Solve: ( x + 5 = 12 )
     2. Solve: ( 2x = -8 )
     3. What is the result of ( -7 + (-3) )?
2. Have students solve these independently. After 3 minutes, review solutions as a class.

Purpose: This primes students for the use of integers and inverse operations.

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2. Direct Instruction (10 minutes)

Objective: Explain and model solving two-step equations.
Teacher Demonstration (on the whiteboard):

1. Define the Steps to Solve Two-Step Equations:

   • Step 1: Undo addition or subtraction (use inverse)
   • Step 2: Undo multiplication or division (use inverse)

2. Examples:

   • Solve ( 3x - 5 = 16 ):
     • Add 5 to both sides: ( 3x = 21 )
     • Divide both sides by 3: ( x = 7 )
   • Solve ( -4x + 8 = -12 ):
     • Subtract 8 from both sides: ( -4x = -20 )
     • Divide by ( -4 ) on both sides: ( x = 5 )

3. Think Aloud Methodology:
   Walk students through your thinking process for each step, emphasizing why we reverse certain operations. Use color-coded markers for each step to improve their visual understanding.

Interactive Question: Ask, "Why do we do addition first in ( 3x - 5 = 16 ), not division?" Let them reason and explain.

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3. Guided Practice (10 minutes)

Objective: Students practice solving two-step equations with teacher guidance.

1. Hand out mini whiteboards to each student.
2. Teacher writes problems on the board, one at a time:
   • ( 2x + 3 = 11 )
   • ( -6x - 4 = 14 )
   • ( 5x - 7 = -12 )
3. Students solve on their mini whiteboards, holding them up when finished.
4. Review steps together, using student responses to address common errors (e.g., forgetting to reverse the sign when dividing by a negative).

Scaffolding Tip: For students struggling, re-model the inverse steps on the board for one of the questions.

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4. Group Activity: Equation Challenge (15 minutes)

Objective: Reinforce learning through collaborative and engaging activities.

1. Activity Setup:

   • Arrange students into pairs or small groups.
   • Provide each group with a deck of integer cards (cards labeled -10 to 10).

2. Instructions:

   • Each group picks two cards to form a two-step equation for the other group to solve.
     Example: Pick 3 and -5 → Create ( 3x - 5 = 10 ).
   • Once they create the equation, they hand it to a different group to solve.
   • Groups earn points for creating equations as well as accurately solving others’ equations.

3. Encourage friendly competition—keep a tally on the board to track which group solves the most equations.

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5. Independent Practice and Exit Ticket (5 minutes)

Objective: Assess individual student understanding.

1. Distribute a short worksheet with 4-5 equations:

   • ( -2x + 6 = 12 )
   • ( 5x - 9 = 16 )
   • ( 4x + 3 = -5 )
   • ( -3x - 7 = -13 )

2. Students solve as independently as possible.

3. Collect their work as an exit ticket before they leave.

Purpose: This allows the teacher to check each student’s mastery and plan further instruction as needed.

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Differentiation Strategies

1. For Advanced Learners: Add word problems where they need to formulate the equation themselves before solving. Example: “A number multiplied by 3, and then reduced by 4, equals 11. What is the number?”
2. For Struggling Learners: Use color-coded “hints” next to the steps when giving them scaffolded problems. Spend extra intervention time working one-on-one, if necessary.

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Homework Extension (Optional)

Students can practice on additional scaffolded problems at home, which include both simple two-step equations and more challenging ones like fractions or decimals.

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Teacher Reflection

After the lesson, answer these:

• Did students grasp inverse operations effectively?
• Were there common errors or misconceptions?
• Did all students participate during the group activity?

This reflective process will help fine-tune future lessons.

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Note for the Teacher: You’re introducing a core algebraic skill that will scaffold into future topics like systems of equations and functions. Use this as an opportunity to build their confidence by celebrating their successes!