Mississippi Math C.A.17
The Standard
Predict and explain the relationships between functions and their derivatives.
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
- Students use the slope of a function’s graph to predict its derivative. They use the derivative to tell where the original function rises, falls, or has a flat tangent.
What Mastery Looks Like
- Given a function graph, a student can sketch a plausible derivative graph with the right signs and zeros. Given a derivative graph, they can explain what it says about the original function.
Common Misconceptions
- Students may read the derivative as the height of the original graph rather than its slope. They may think a negative derivative means the function is below the x-axis, or that every zero derivative is a turning point.
How to Assess It
- Give students a printed graph of y = x³ − 3x. Ask them to sketch its derivative, mark its zeros, and explain where the original graph rises and falls.
Lesson moves
Ways to Teach It
Give pairs a printed function graph and colored stickers to mark where its slope is positive, negative, or zero.
Ask, “Can a function decrease while its derivative increases?” Have students sketch an example and explain their answer.
Play graph-match with six function graphs and six derivative graphs; pairs justify each match using slope signs and zeros.
Show a bike ride’s distance-versus-time graph; students sketch speed versus time and mark stops and fastest stretches.
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Printable C.A.17 Worksheet
A ready-to-print activity worksheet aligned to C.A.17, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- C.A.4
Predict and explain the characteristics and behavior of functions and their graphs (domain, range, increasing/decreasing intervals, intercepts, symmetry, and en...
- C.N.2
Estimate numerical derivatives from graphs or tables of data.
- C.A.7
Solve mathematical situations and application problems involving or using derivatives, including exponential, logarithmic, and trigonometric functions.
- C.A.10
State and apply the formal definition of a derivative.
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