Main Question

Solve for x: 3x + 7 = 22

But more importantly, can you explain why each step you take is mathematically valid?

Key Concepts to Explore

• Inverse operations and why they work
• The balance/scale model of equations
• Checking solutions by substitution
• The difference between expressions and equations

Expected Follow-up Questions

High-quality student engagement should include questions like:

• “Why can I subtract 7 from both sides?”
• “How do I know when I’ve found the right answer?”
• “What if the number in front of x was negative?”
• “Can you show me how to check if my answer is correct?”
• “What would happen if I did the steps in a different order?”
• “Why does this method work for all linear equations?”

Critical Thinking Indicators

Students demonstrate understanding when they:

• Ask about the reasoning behind each step
• Want to understand why inverse operations work
• Ask how to verify their solution
• Explore what happens with different types of equations
• Make connections to real-world balance/equality concepts
• Question whether there could be other solution methods

Assessment Criteria

Excellent (A): Student asks deep questions about why methods work, explores verification strategies, makes connections to the concept of mathematical balance, demonstrates understanding beyond just getting the answer

Good (B): Student asks relevant questions about solution steps, shows understanding of inverse operations, attempts to verify solutions

Satisfactory (C): Student follows the solution process but asks few follow-up questions, shows basic understanding of the mechanics

Needs Improvement (D/F): Student asks for direct answer without engaging with the solution process, shows no curiosity about why methods work

Sample Conversation Flow

Student Initial Question: “How do I solve 3x + 7 = 22?”

AI Response: “Great question! Before we solve this, let me ask you something: what do you think this equation is telling us? What does the equals sign mean here?”

Expected Student Follow-up: “The equals sign means both sides are equal… so 3x + 7 has the same value as 22?”

AI Guidance: “Exactly! So if both sides are equal, what do you think would happen if we did the same operation to both sides? What operation might help us get closer to having x by itself?”

Teacher Notes

• Emphasize the conceptual understanding over mechanical steps
• Watch for students who want to jump straight to algorithms
• Common misconception: students often want to “move” terms rather than understanding inverse operations
• Connect to balance scales if students struggle with the concept

Extensions

For advanced students or further exploration:

• What happens when the coefficient of x is a fraction?
• How would you solve 2(x + 3) = 14?
• Can you create a word problem that would lead to this equation?
• What if there were x terms on both sides of the equation?