Solving Linear Equations: Balance It Out
Year 11 Mathematics 60-minute lesson Waiheke High School
WALT & Success Criteria
We Are Learning To: Solve one-step linear equations using inverse operations Success Criteria: • Solve at least 5 different one-step linear equations • Use inverse operations correctly to isolate the variable • Check solutions for accuracy by substitution
Curriculum Links
New Zealand Curriculum Refresh - Mathematics & Statistics Algebra Strand Year 11: Form and solve linear equations NCEA Level 1 Achievement Standard (AS 91301) Key Competencies: Thinking, Managing Self, Using Mathematical Language
Warm-Up: Quick Recall Challenge
Solve these mental math problems: 7 + ___ = 12 20 - ___ = 13 6 × ___ = 24 ___ ÷ 4 = 8 Use your mini-whiteboards!
The Balance Scale Metaphor
Equations are like balanced scales Both sides must stay equal Whatever we do to one side, we must do to the other Goal: Get the variable by itself on one side
Direct Teaching: Solving x + 5 = 13
Step 1: Identify the operation (+5) Step 2: Use inverse operation (subtract 5) Step 3: Apply to both sides x + 5 - 5 = 13 - 5 Step 4: Simplify: x = 8 Step 5: Check: 8 + 5 = 13 ✓
Four Types of One-Step Equations
{"left":"Addition: x + 4 = 10 (subtract 4)\nSubtraction: y - 3 = 7 (add 3)","right":"Multiplication: 3z = 15 (divide by 3)\nDivision: w ÷ 2 = 6 (multiply by 2)"}
Guided Practice: Partner Work
Work in pairs with your worksheet Solve 8-10 one-step equations together Explain your reasoning to your partner Check each answer by substitution Raise your hand if you need help!
Independent Practice & Self-Check
Solve 5 equations individually Use your preferred method Check each answer by substitution Extension: Try word problems or two-step equations Time: 10 minutes
Reflection Discussion
What strategies helped you solve equations today? What was the most challenging part? How does the balance scale metaphor help? Where might you use these skills in real life?
Key Takeaways & Next Steps
✓ Linear equations can be solved using inverse operations ✓ Always check your solution by substitution ✓ The balance scale metaphor helps maintain equality Next lesson: Two-step linear equations Practice: Complete homework worksheet