Mississippi Math C.A.19

MathGrades 9–12Algebra (A) Demonstrate Basic Knowledge of Functions, Including their Behavior and Characteristics

The Standard

Solve optimization problems.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Apply Derivatives to Find Solutions in a Variety of Situations

Teacher's field guide

What Students Need to Do: Students write a formula for the quantity they want to maximize or minimize, such as area or cost. They use the given limits to make a one-variable function. Then they use its derivative and check which answer fits the situation.
What Mastery Looks Like: A student can label the variables, write the function, and give a sensible range of possible values. They check critical points and endpoints, then report the best value with units.
Common Misconceptions: Students may use the amount of fencing as the area formula instead of using it to relate the dimensions. Some assume every point where the derivative is zero is a maximum. Others forget to check endpoints or reject impossible dimensions.
How to Assess It: Exit ticket: A pen against a wall uses 40 meters of fencing on three sides. Write an area function, use its derivative to find the largest area, and give the pen's dimensions.

Lesson moves

Give pairs 20 cm paper squares; they cut equal corner squares, fold boxes, measure volumes, and calculate the cut size that maximizes volume.
Ask students to write why solving V'(x)=0 does not finish the paper box problem, including what happens at the endpoints.
Give pairs cards labeled A(x)=x(40-2x), A'(x)=40-4x, and x=10, plus distractors; they race to match the correct set.
Give students V=πr²h and S=2πr²+2πrh for a 1,000-cubic-centimeter soup can; they find dimensions that use the least metal.

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