Math9-12+
Solving Quadratics by Factoring: Free Response Review
By Sherwin S.
A 20-question free-response practice set on solving quadratic equations by factoring, aimed at 9th graders and written at DOK levels 2 and 3. It builds fluency with the Zero Product Property and factoring trinomials, and asks students to justify their reasoning in multi-step written answers, with completing the square deliberately left out.
Customize for your classroom
Teacher Guide & Tips
- Use this as a review after students have practiced factoring basics, as a 45-minute independent or partner block, or split across two shorter sessions.
- Discussion question: Why must the equation be set equal to zero before factoring, and what would go wrong if we factored without doing so?
- Scaffold for struggling readers: Have them complete the worked example's factoring steps aloud first, then use a factor-pair chart (products and sums) before attempting the DOK 3 items.
- Extension for advanced students: Ask them to create their own DOK 3 problem that requires explaining why a particular quadratic has no rational roots and what that implies about its graph.
- Estimated time: about 45 to 60 minutes to complete all 20 questions, with more time needed if students are writing full justifications.
Math9-12+
Solving Quadratics by Factoring: Free Response Review
By Sherwin S.
A 20-question free-response practice set on solving quadratic equations by factoring, aimed at 9th graders and written at DOK levels 2 and 3. It builds fluency with the Zero Product Property and factoring trinomials, and asks students to justify their reasoning in multi-step written answers, with completing the square deliberately left out.
Customize for your classroom
Teacher Guide & Tips
- Use this as a review after students have practiced factoring basics, as a 45-minute independent or partner block, or split across two shorter sessions.
- Discussion question: Why must the equation be set equal to zero before factoring, and what would go wrong if we factored without doing so?
- Scaffold for struggling readers: Have them complete the worked example's factoring steps aloud first, then use a factor-pair chart (products and sums) before attempting the DOK 3 items.
- Extension for advanced students: Ask them to create their own DOK 3 problem that requires explaining why a particular quadratic has no rational roots and what that implies about its graph.
- Estimated time: about 45 to 60 minutes to complete all 20 questions, with more time needed if students are writing full justifications.