Mississippi Math C.A.14

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

The Standard

Define a derivative and explain the purpose/utility of the derivative.

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 define a derivative as the limit of average rates of change over shrinking intervals. They connect it to the slope of a tangent line and explain how it gives a rate at one instant.
What Mastery Looks Like: Given d(t) = t² meters, a student finds the derivative at 2 seconds as 4 meters per second. They explain that this is the speed at that instant, not the distance traveled.
Common Misconceptions: Students may use the slope over a long interval as the exact slope at one point. They may also confuse a negative derivative with a negative function value.
How to Assess It: Exit ticket: For d(t) = t² meters, calculate [d(2 + h) − d(2)]/h and its limit as h approaches 0. Explain what the limit tells you about the motion.

Lesson moves

On graph paper, plot y = x² and draw secants from x = 2 to x = 3, 2.5, and 2.1; compare their slopes.
Ask: A car travels 100 miles from noon to 2 p.m. Can you tell its speed at noon? Explain what more data you need.
Match position-time graph cards with tangent slopes of −2, 0, and 2 meters per second, then justify each match.
Give bike distances of 120 m at minute 4, 155 m at minute 5, and 200 m at minute 6; estimate speed at minute 5.

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