Florida B.E.S.T. MA.912.C.5

MA.912.C.5 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.C.5.1

  Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from veloci...

• MA.912.C.5.2

  Solve separable differential equations.

• MA.912.C.5.3

  Solve differential equations of the form dY/dt=kY as applied to growth and decay problems.

• MA.912.C.5.4

  Display a graphic representation of the solution to a differential equation by using slope fields, and locate particular solutions to the equation.

• MA.912.C.5.5

  Find the area between a curve and the x-axis or between two curves by using definite integrals.

• MA.912.C.5.6

  Find the average value of a function over a closed interval by using definite integrals.

• MA.912.C.5.7

  Find the volume of a figure with known cross-sectional area, including figures of revolution, by using definite integrals.

01

What Students Need to Do

Students identify what quantity is accumulating and choose suitable limits. They write and evaluate a definite integral, then interpret its sign, size, and units in context.

02

What Mastery Looks Like

Given a graph, formula, table, or context, students can choose bounds and write the correct definite integral. They evaluate it and explain the answer using the situation and correct units.

03

Common Misconceptions

Students may treat all area as positive, even when the graph lies below the axis. They may reverse bounds, omit units, or confuse net change with total change.

04

How to Assess It

Exit ticket: A particle has velocity v(t) = 3t² − 6t meters per second from t = 0 to t = 3. Find its displacement and total distance, showing both integrals.

1. 01

   Give students graph cutouts and unit-square grids to estimate signed area, then write and evaluate the matching definite integral.

2. 02

   Ask students to explain why displacement and total distance can differ when a velocity graph crosses the time axis.

3. 03

   Run a card sort matching contexts, graphs, definite integrals, numerical answers, and units.

4. 04

   Use hourly water-flow data to estimate total gallons delivered with trapezoids, then compare the estimate with a definite integral.

• MA.912.C.4

  Develop an understanding for and determine integrals.

• MA.912.C.3

  Apply derivatives to solve problems.

• MA.912.C.4.4

  Evaluate definite integrals by using the Fundamental Theorem of Calculus.

• MA.912.C.4.6

  Evaluate or solve problems using the properties of definite integrals.