Florida B.E.S.T. MA.912.C.2

MA.912.C.2 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.C.2.1

  State, understand and apply the definition of derivative. Apply and interpret derivatives geometrically and numerically.

• MA.912.C.2.10

  Apply the Mean Value Theorem.

• MA.912.C.2.2

  Interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.

• MA.912.C.2.3

  Prove the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule.

• MA.912.C.2.4

  Apply the rules for finding derivatives of constants, sums, products, quotients and the Chain Rule to solve problems with functions limited to algebraic, trigon...

• MA.912.C.2.5

  Find the derivatives of implicitly defined functions.

• MA.912.C.2.6

  Find derivatives of inverse functions.

• MA.912.C.2.7

  Find second derivatives and derivatives of higher order.

• MA.912.C.2.8

  Find derivatives using logarithmic differentiation.

• MA.912.C.2.9

  Demonstrate and use the relationship between differentiability and continuity.

01

What Students Need to Do

Students connect a derivative to the slope of a tangent line and an instantaneous rate of change. They find derivatives from limits, graphs, tables, and rules. They use units and context to explain results.

02

What Mastery Looks Like

Given a function, graph, or table, students can determine the derivative at a point and describe what its sign and size mean. They apply derivative rules accurately. They recognize points where a derivative does not exist.

03

Common Misconceptions

Students may use average rate of change when instantaneous rate is requested. They often confuse f(a) with f'(a), omit the inner derivative in the chain rule, or mishandle negative exponents. They may assume derivatives exist at corners and discontinuities.

04

How to Assess It

Exit ticket: For f(x) = x² - 4x, find f'(3), write the tangent line at x = 3, and explain its slope in words.

1. 01

   Use a motion sensor to collect position data, then calculate velocities over shrinking time intervals around one chosen moment.

2. 02

   Ask students to explain, with a sketch, how secant slopes approach a tangent slope as the two points move closer together.

3. 03

   Run a card sort matching functions, derivative formulas, derivative graphs, and applicable rules, then have pairs defend two matches.

4. 04

   Give a water-tank volume model and ask students to find and interpret the filling rate at a stated time.

• MA.912.C.4

  Develop an understanding for and determine integrals.

• MA.912.C.3

  Apply derivatives to solve problems.

• MA.912.C.1

  Develop an understanding for limits and continuity. Determine limits and continuity.