Materials Needed

• Small whiteboard and dry-erase markers (or paper and colored pens)
• 2 different colored highlighters (e.g., yellow for variable terms, pink for constant numbers)
• "Detective Decoder" sheet or standard index card

Lesson Overview & Objectives

Total Duration: 15 Minutes

Target Skill: Solving multi-step linear equations containing like terms and variables on one side using inverse operations.

Learning Objectives:

• Student will identify and combine like terms in an equation.
• Student will isolate the variable using inverse operations in reverse order of operations (SADMEP: Subtraction/Addition, then Multiplication/Division).
• Student will successfully solve 2 multi-step equations independently with 100% accuracy.

Success Criteria: "I can simplify an equation by combining like terms and use inverse operations to find the mystery value of x."

1. Introduction & Hook (2 Minutes)

Hook: "Imagine you are a detective trying to unlock a safe. The variable x is the secret code inside, but it's hidden under layers of traps (numbers). To get to x, we have to undo what was done to it, step-by-step, in exact reverse order!"

Connect to Real World: Compare solving multi-step equations to unwrapping a layered present or undoing a sequence of actions (like putting on socks and shoes, then taking them off in reverse order).

Golden Rule: Whatever you do to one side of the equals sign, you MUST do to the other side to keep the balance!

2. "I Do" - Direct Instruction & Modeling (3 Minutes)

Instructor Action: Write the equation on the board: 3x + 4 + 2x = 19

Step-by-Step Demonstration:

1. Highlight Like Terms: Highlight 3x and + 2x in yellow. Highlight + 4 in pink. "First, I group my team members. 3x and 2x are on the same side, so I combine them."
   Result: 5x + 4 = 19
2. Undo Addition/Subtraction: "Now I need to get 5x by itself. The + 4 is in the way. The opposite (inverse) of adding 4 is subtracting 4."
   Subtract 4 from both sides: 5x + 4 - 4 = 19 - 4
   Result: 5x = 15
3. Undo Multiplication/Division: "5x means 5 times x. The opposite of multiplying by 5 is dividing by 5."
   Divide both sides by 5: 5x / 5 = 15 / 5
   Result: x = 3
4. Check the Solution: Plug 3 back into the original problem: 3(3) + 4 + 2(3) = 9 + 4 + 6 = 19. "The case is solved!"

3. "We Do" - Guided Practice (4 Minutes)

Instructor & Student Joint Action: Work together on the equation: 4x - 2 + x = 13

• Prompt Student: "What is our first step? Use your yellow highlighter to find our variable team members." (Student highlights 4x and + x).
• Guide Math: "Combine them! What is 4x plus 1x?" (Student answers: 5x). Rewrite equation: 5x - 2 = 13.
• Prompt Student: "Look at the pink constant - 2. How do we undo subtracting 2?" (Student answers: Add 2 to both sides).
• Guide Math: Have student write + 2 under both sides. Result: 5x = 15.
• Prompt Student: "Final step! How do we free x from the 5?" (Student divides both sides by 5 to get x = 3).
• Give immediate praise and high-five for accurate step execution!

4. "You Do" - Independent Practice & Challenge (4 Minutes)

Student Independent Action: Hand the student two "Case Files" to solve on their board using highlighters and inverse steps.

Case File 1 (Standard): 2x + 6 + 3x = 21 (Target Answer: x = 3)

Case File 2 (Boss Level): 6x - 4 - 2x = 12 (Target Answer: x = 4)

Instructor Role: Observe quietly. If the student gets stuck, ask guiding questions rather than giving answers (e.g., "Which terms belong to the same family?").

5. Conclusion & Reflection (2 Minutes)

Recap: Ask the student to teach you the "Detective Rules" in 30 seconds.

• Rule 1: Combine like terms first.
• Rule 2: Undo addition/subtraction.
• Rule 3: Undo multiplication/division.
• Rule 4: Keep the scale balanced (do to both sides)!

Adaptations & Differentiation

• For Struggling Learners (Scaffolding): Draw a vertical line straight down through the equals sign to create a visual "wall" keeping the two sides separate. Use physical algebra tiles or blocks to represent $x$ and $1$.
• For Advanced Learners (Extension): Introduce negative numbers or distributive property into the "You Do" round (e.g., $2(x + 3) + x = 15$).
• Context Adaptations:
  • Homeschool: Use real objects (e.g., small mystery bags containing coins for $x$ and loose coins for constants).
  • Classroom: Turn "You Do" into a Think-Pair-Share or quick whiteboard show-me game.