L059 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.
Solve 3x²−12x=0 and check both roots.
3x(x−4)=0, so x=0 or 4.
Explain why dividing x²=9 by x can lose a solution.
Dividing by x is unsafe if x=0 in general; here taking only x=3 loses x=−3. Factor x²−9 or use ±√9.
Lesson L059: Solving quadratics
Objective: Solve quadratic equations using tier-appropriate methods.
60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.
I represented the algebraic structure accurately, kept each transformation valid and checked the result by substitution, graph or equivalent reasoning.
I will show the missing inverse operation or algebraic step, keep signs and brackets accurate and test the result in the original relationship.
Stretch: Solve 3x²−12x=0 and check both roots.
Deep challenge: Explain why dividing x²=9 by x can lose a solution.