Mississippi Math C.A.15
The Standard
Apply the derivative as a rate of change in varied contexts, including velocity, speed, and acceleration.
2025 Mississippi College- and Career-Readiness Standards for Mathematics · Apply Derivatives to Find Solutions in a Variety of Situations
Teacher's field guide
What This Standard Means
What Students Need to Do
- Differentiate a position function to find velocity at a given time. Use the absolute value of velocity for speed, then differentiate velocity to find acceleration. Explain what the signs and units mean.
What Mastery Looks Like
- A student can calculate velocity in m/s and acceleration in m/s² from a position function. They report speed as nonnegative and use velocity and acceleration together to tell whether an object is speeding up or slowing down.
Common Misconceptions
- Students may report negative velocity as negative speed. They may think positive acceleration always means an object is speeding up, even when it is moving in the negative direction.
How to Assess It
- Exit ticket: A cart's position is s(t)=t²−4t meters, with t in seconds. Find its velocity, speed, and acceleration at t=1, include units, and say whether it is speeding up or slowing down.
Lesson moves
Ways to Teach It
Film a rolling cart beside a meter stick, plot its position every half second, and estimate velocity from tangent slopes.
Ask: Can a cart have negative velocity and positive acceleration? Explain using a cart rolling backward while slowing down.
Give pairs position cards such as s(t)=t²−4t; have them calculate velocity, speed, and acceleration at t=1, then compare answers.
Use an elevator height graph to mark when it moves down, slows, or changes direction, then label velocity and acceleration signs.
Free download
Printable C.A.15 Worksheet
A ready-to-print activity worksheet aligned to C.A.15, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- ATM.F.31
Write a function that describes a relationship between two quantities; and be able to calculate and interpret the average rate of change of a function (presente...
- C.G.22
Demonstrate and explain the differences between average and instantaneous rates of change.
- C.A.10
State and apply the formal definition of a derivative.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson