Florida B.E.S.T. MA.912.AR.6.6
The Standard
Solve and graph mathematical and real-world problems that are modeled with polynomial functions of degree 3 or higher. Interpret key features and determine constraints in terms of the context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve higher-degree polynomial equations and graph the related functions. They identify zeros, intercepts, turning points, end behavior, and domain or range limits that make sense in a given situation.
What Mastery Looks Like
- Given a higher-degree polynomial model, students can find real zeros and create an accurate graph using algebra or graphing technology. They can explain intercepts, extrema, end behavior, and valid input and output values within the situation.
Common Misconceptions
- Students may assume every zero is real or that every x-intercept crosses the axis. They may ignore repeated zeros, turning points, or end behavior. They also may include negative time, fractional objects, or other values that do not fit the situation.
How to Assess It
- Exit ticket: For d(t)=t(t-2)^2(5-t) on 0 ≤ t ≤ 5, graph the model, label its zeros and maximum, and explain the domain restriction.
Lesson moves
Ways to Teach It
Cut equal corner squares from cardstock, build open boxes, and compare measured volumes with the cubic volume model.
Ask: Which graph features matter to a park manager, and what does each feature mean for a modeled roller coaster?
Play a card sort matching cubic and quartic equations, graphs, zeros, multiplicities, end behavior, and valid contextual domains.
Use a profit model for 0 to 500 items, then identify break-even points, maximum profit, and impossible input values.
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