Florida B.E.S.T. MA.912.AR.3.3
The Standard
Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a situation into a quadratic inequality in one variable. They find the boundary values, determine which intervals work, and show the answer with symbols or a number line.
What Mastery Looks Like
- Students find the boundary values, test the intervals, and select every interval that makes the inequality true. They use correct endpoint symbols and restrict answers to values that make sense in context.
Common Misconceptions
- Students often report only the roots instead of the intervals that satisfy the inequality. They may always choose the region between the roots or include endpoints when the inequality is strict.
How to Assess It
- Exit ticket: A garden has width x and length x + 3, with area at least 40 square feet. Write and solve an inequality, graph the solution, and state the possible widths.
Lesson moves
Ways to Teach It
Place root cards on a floor number line, then have students stand in intervals where a given quadratic is positive or negative.
Ask students to compare x² − 5x + 6 ≤ 0 and x² − 5x + 6 ≥ 0, then explain why the solutions differ.
Run a card sort matching quadratic inequalities with factored forms, number line graphs, and interval notation solutions.
Model when a thrown ball is at least 10 feet high, then solve and interpret the resulting time interval.
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Related Standards
- MA.912.AR.3.1
Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.
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- MA.912.AR.2.6
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