2x + 3 = 11
-3      -3
2x = 8
÷2   ÷2
x = 4

x + 5 = 12
3x – 4 = 11

2x + 3 = 11

4x + 2 = 18
x/3 + 5 = 9

2x + 3 = x + 9

2x + 3 = x + 9
- x        - x
x + 3 = 9
-3     -3
x = 6

3x + 2 = x + 8

x + 4 = 10
2x – 6 = 8
3x + 2 = x + 10

Overview

This 4-day scaffolded small-group sequence supports 8th grade Level C students with moderate disabilities to confidently solve multi-step linear equations—including those with variables on both sides—directly aligned to Common Core State Standard 8.EE.C.7. The lessons emphasize explicit modeling, step-by-step strategies, visual supports, and frequent formative checks to build fluency and conceptual understanding.

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Unit Objective

Students will solve multi-step linear equations using inverse operations and organize their solution process clearly.

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Day 1: Understanding Multi-Step Equations

🎯 I Can Statement

I can solve a multi-step equation by using steps and checking my answer.

📚 Success Criteria

• Identify terms in an equation (variable term, constants)
• Correctly perform inverse operations in order
• Organize work neatly and clearly

⏰ Time breakdown (20 minutes)

Activity	Time
Anticipatory Set	2 min
I Do (Teacher Model)	5 min
We Do (Guided Practice)	5 min
You Do (Independent Practice)	5 min
Check for Understanding/Exit Ticket	3 min

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Detailed Activities

Anticipatory Set (2 min)

Write on board:
2x + 3 = 11

Ask aloud:

• “Can I solve this in one step? Why or why not?”
• “What should I undo first?”

Explain briefly that some equations need multiple steps.

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I Do: Model Step-by-Step (5 min)

Use a large color-coded anchor chart with these steps shown in different colors:

2x + 3 = 11
-3       -3    (Undo addition first - green)
2x = 8
÷2      ÷2     (Undo multiplication - blue)
x = 4

Think aloud:

• "Since addition or subtraction is closest outside the variable, I undo that first.”
• Emphasize neat alignment and showing each step clearly.

Display an explicitly numbered and color-coded equation.

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We Do: Guided Practice (5 min)

Solve together on whiteboards:

1. x + 5 = 12
2. 3x – 4 = 11

Use step cards to remind students of order: Subtract → Divide.

Encourage students to verbalize steps aloud.

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You Do: Independent Practice (5 min)

Students solve 1–2 problems independently using a visual step checklist with reminders:

• Circle variable term
• Undo addition or subtraction
• Undo multiplication or division
• Check answer by substitution

Example problems:

• x + 4 = 9
• 5x – 2 = 13

Teacher circulates offering individual support as needed.

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Check For Understanding & Exit Ticket (3 min)

Thumb signals for confidence:

• 👍 = I can do it
• 👉 = I need help

Exit Ticket:

• Solve and show steps for x + 7 = 15
• Teacher quickly reviews and provides positive feedback.

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Differentiation Strategies

• Provide dyslexia-friendly fonts on anchor charts and handouts (e.g., OpenDyslexic)
• Use color coding consistently to highlight operations
• Allow verbal explanations for students who struggle with writing
• Pair stronger students with those needing more support during "We Do"

Extension Activity (for accelerated learners)

• Introduce equations requiring fractions or decimals, e.g.,
  1/2 x + 3 = 7
• Challenge students to explain why inverse operations undo the original operation.

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Day 2: Equations with Variables on One Side

🎯 I Can Statement

I can solve multi-step equations with variables on one side by following steps and checking my work.

📚 Success Criteria

• Identify variables on one side only
• Execute inverse operations in correct order
• Use strategies to write neat, organized steps

⏰ Time breakdown (20 minutes)

Activity	Time
Anticipatory Set	2 min
I Do (Teacher Model)	5 min
We Do (Guided Practice with Partners)	5 min
You Do (Independent Practice)	5 min
Check For Understanding/Exit Ticket	3 min

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Detailed Activities

Anticipatory Set (2 min)

Real-life example on board:

“You pay a $3 fee plus $2 per item. Your total is $11. How many items did you buy?”

Write the equation:
2x + 3 = 11

Ask: “What does x represent?” and “How do we solve this?”

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I Do: Model (5 min)

Solve the equation step-by-step on anchor chart emphasizing:

• Variable terms only on the left
• Undo addition/subtraction first
• Undo multiplication/division second

Write:

2x + 3 = 11
-3       -3
2x = 8
÷2       ÷2
x = 4

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We Do: Guided Practice (Kagan “Rally Coach” Structure) (5 min)

In pairs:

• Partner A solves 4x + 2 = 18 aloud while Partner B supports with step-checklist prompts
• Switch roles using x/3 + 5 = 9

Encourage language: “First we undo __ because ___.”

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You Do: Independent Practice (5 min)

Students solve:

• 5x + 4 = 19
• 3x – 7 = 8

Include visual step checklist for self-monitoring.

Teacher supports students who need help and prompts to explain reasoning.

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Check For Understanding + Exit Ticket (3 min)

Quick verbal questions:

• “What do we undo first in this equation?”
• “Why do we undo addition/subtraction before multiplication?”

Exit Ticket:
Solve 3x + 1 = 10 showing all steps.

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Differentiation Strategies

• Use manipulatives or balance scales for kinesthetic learners
• Provide fill-in-the-blank equation templates to reduce writing load
• Allow calculators only for checking final answers if needed
• Pair verbal processors with students who need articulation practice

Extension Activities

• Introduce more complex problems involving negative coefficients, e.g.,
  -3x + 5 = 11
• Encourage students to create their own real-world problems that model equations with variables on one side.

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Day 3: Variables on Both Sides

🎯 I Can Statement

I can solve multi-step equations with variables on both sides by moving all variables to one side first and solving step-by-step.

📚 Success Criteria

• Identify variable terms on both sides
• Move variables first, then constants
• Use arrows and color-coded steps to organize thinking

⏰ Time Breakdown (20 minutes)

Activity	Time
Anticipatory Set	2 min
I Do (Teacher Model)	5 min
We Do (Guided Practice with T-Chart)	5 min
You Do (Supported Independent)	5 min
Check For Understanding/Exit Ticket	3 min

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Detailed Activities

Anticipatory Set (2 min)

Write on board:
2x + 3 = x + 9

Ask: “Which side has more x’s? What should we do first?”

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I Do: Model Stepwise (5 min)

Use color coding for variable terms and constants, arrows to show movement:

2x + 3  =  x + 9
- x     - x    (Move variable term on right to left)
x + 3   = 9
-3     -3
x       = 6

Explain clearly:

• Move variable terms first to keep work organized
• Undo addition/subtraction next
• Divide if needed

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We Do: Guided Practice (5 min)

Use a T-Chart on the board or whiteboard for left side / right side terms.

Solve together:
3x + 2 = x + 8

Have students help decide which term to move first, then walk through each step collaboratively.

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You Do: Independent Practice with Support (5 min)

Student attempts:
4x + 5 = 2x + 11

Teacher supports: asks guiding questions, points to checklist, assists with color-coded steps and T-Chart use.

Encourage students to verbalize their reasoning.

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Check for Understanding & Exit Ticket (3 min)

Rich discussion:

• “What do we move first—numbers or variable terms? Why?”
• Exit Ticket: Circle the first step shown in this equation:
  2x + 7 = x + 13

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Differentiation Strategies

• Provide color-coded printed T-Charts to students
• Use voice notes or video modeling for review outside class
• Offer sentence starters to guide explanation (e.g., “I will move ___ first because ___.”)

Extension Activities

• Challenge students with literal equations involving distributing before solving, e.g.,
  2(x + 3) = x + 9
• Analyze “what if” scenarios changing coefficients or constants and predict solution changes.

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Day 4: Review & Application

🎯 I Can Statement

I can solve multi-step equations and reflect on the first step I take when solving them.

📚 Success Criteria

• Correctly solve various multi-step equations
• Identify errors and explain corrections
• Express the first step taken with reasoning

⏰ Time breakdown (20 minutes)

Activity	Time
Anticipatory Set (Mistake Analysis)	3 min
Kagan "Quiz-Quiz-Trade" Practice	7 min
Independent Practice (Mixed Review)	5 min
CFU & Exit Ticket	5 min

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Detailed Activities

Anticipatory Set: Analyze a Mistake (3 min)

Show a deliberately incorrect solution:

5x + 2 = 17
÷5       ÷5
x + 0.4 = 3.4   ← Incorrect first step

Ask:

• “What is wrong here?”
• “What should have been the first step?”

Discuss emphasizing order of operations.

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Kagan Structure: Quiz-Quiz-Trade (7 min)

Students each get an equation card to solve quickly, then join a partner to check each other’s answers and provide coaching. Then trade cards and repeat.

Sample cards:

• x + 4 = 10
• 2x – 6 = 8
• 3x + 2 = x + 10

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You Do: Independent Practice (Mixed Review) (5 min)

Complete two equations independently on whiteboards or paper, showing all steps.

• 4x + 3 = 11
• 2x + 5 = x + 9

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Check for Understanding & Exit Ticket (5 min)

1. Solve and turn in: x – 7 = 15

2. Reflection prompt:

   “The first step I take is _______ because _______.”

Teacher reads responses and provides targeted feedback.

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Differentiation Strategies

• Provide sentence frames for reflection writing
• Allow oral exit tickets for students with writing challenges
• Scaffold quiz cards by varying difficulty; simpler equations for those needing support

Extension Activity

• Create one original multi-step equation and exchange with a partner to solve.

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Supports Built-In Throughout Unit

• Visual step checklist to guide procedure
• Color-coded operations and variable terms for clarity
• Reduced problem set to avoid cognitive overload
• Verbal think-aloud modeling to foster metacognition
• Peer partner coaching using structured Kagan strategies
• Frequent, formative checks every ~3–5 minutes to gauge understanding
• Dyslexia-friendly fonts and layouts for anchor charts and printed materials
• Use of manipulatives and T-Charts for students needing concrete representations

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Alignment to Common Core Standard 8.EE.C.7

• Solve linear equations in one variable, including those with variables on both sides
• Emphasizes use of inverse operations and multi-step solution strategy
• Supports foundational algebraic understanding necessary for high school math

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This tightly scaffolded, explicit instruction plan respects the attention span and learning needs of Level C students and engenders confidence in solving multi-step equations with strong procedural skill and conceptual understanding. It models best practices for inclusive math instruction aligned to Common Core standards.