Mississippi Math C.A.18

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

The Standard

Model rates of change to solve related rate 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 an equation linking quantities that change over time. They differentiate it with respect to time, then use known values to find an unknown rate.
What Mastery Looks Like: For a sliding ladder, students use its fixed length to relate the foot and top. They calculate how fast the top moves, include units, and say whether it rises or falls.
Common Misconceptions: Students sometimes substitute lengths before differentiating, treating changing quantities as constants. They may leave out factors such as dx/dt or give a positive rate for a falling height.
How to Assess It: Exit ticket: A 10-foot ladder has its foot 6 feet from a wall, moving outward at 2 feet per second. How fast is its top moving? Show your equation, units, and direction.

Lesson moves

Inflate a balloon with a hand pump; measure its circumference with string every 10 seconds, then estimate how fast its radius grows.
Draw a 10-foot ladder against a wall; ask students why the top's rate is negative when the foot moves outward.
Give pairs cards with ladder, balloon, and tank situations; have them match each situation to a differentiated equation and explain the signs.
A cylindrical tank fills at 0.2 cubic meters per minute; use its 1-meter radius to calculate how fast the water level rises.

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