Florida B.E.S.T. MA.912.C.2.2
The Standard
Interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect a derivative value to what is happening at one input. They use nearby points, graphs, or formulas to explain its sign, size, and units.
What Mastery Looks Like
- A student can connect a derivative value to a tangent line on a graph and to change in a real situation. The student explains the sign, size, and units correctly.
Common Misconceptions
- Students may confuse the derivative with the function value or use a secant line when asked about one point. They may think a negative derivative means the original quantity is negative, rather than decreasing.
How to Assess It
- Exit ticket: A tank has V'(6) = -3 gallons per minute. Explain what this means and state the slope of the tangent line at t = 6.
Lesson moves
Ways to Teach It
Roll a toy car down a ramp, record positions near two seconds, and estimate its speed using smaller time intervals.
Ask students to explain in writing how a secant slope approaches a tangent slope as two points move closer together.
Give pairs matching cards with graphs, tangent lines, derivative values, and context statements, then have students justify each match.
Use a temperature graph to interpret positive, negative, and zero derivative values at selected times during one day.
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Related Standards
- MA.912.C.2.1
State, understand and apply the definition of derivative. Apply and interpret derivatives geometrically and numerically.
- MA.912.C.3.8
Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a...
- MA.912.C.4.5
Analyze function graphs by using derivative graphs and the Fundamental Theorem of Calculus.
- MA.912.C.4.3
Interpret a definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval.
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