Florida B.E.S.T. MA.912.AR.3.2
The Standard
Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.
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 equation with one unknown. They solve by factoring, square roots, completing the square, or the quadratic formula. They report real or complex solutions and interpret them in context.
What Mastery Looks Like
- Students define the variable, write a correct quadratic equation, and choose an efficient solving method. They give exact or approximate solutions, identify complex solutions, and check whether each answer fits the original situation.
Common Misconceptions
- Students may use a linear equation for a situation with squared quantities. They may forget to set the equation equal to zero, omit the negative square root, or mishandle the discriminant and i. They may also keep solutions that do not fit the context.
How to Assess It
- Give a two-item exit ticket: A rectangle has width x, length x + 3, and area 40. Write and solve the equation, then solve x² + 4x + 13 = 0.
Lesson moves
Ways to Teach It
Build x² + 5x + 6 with algebra tiles, arrange the tiles into a rectangle, and use the side lengths to identify factors.
Compare factoring, completing the square, and the quadratic formula for one equation, then write which method is most efficient and why.
Match cards showing contexts, quadratic equations, discriminants, and solution sets, then check each completed group with a partner.
Model the height of a tossed ball with h = -16t² + 48t + 5, then find when it reaches the ground.
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Related Standards
- MA.912.AR.4.1
Given a mathematical or real-world context, write and solve one-variable absolute value equations.
- MA.912.AR.3.1
Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.
- MA.912.AR.9.1
Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.
- MA.912.AR.3.3
Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically o...
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