Florida B.E.S.T. MA.912.T.4

MA.912.T.4 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.T.4.1

  Define and plot polar coordinates. Convert between polar coordinates and rectangular coordinates with and without the use of technology.

• MA.912.T.4.2

  Represent equations given in rectangular coordinates in terms of polar coordinates. Represent equations given in polar coordinates in terms of rectangular coord...

• MA.912.T.4.3

  Graph equations in the polar coordinate plane with and without the use of graphing technology.

• MA.912.T.4.4

  Identify and graph special polar equations, including circles, cardioids, limacons, rose curves and lemniscates.

• MA.912.T.4.5

  Sketch the graph of a curve in the plane represented parametrically, indicating the direction of motion.

• MA.912.T.4.6

  Convert from a parametric representation of a plane curve to a rectangular equation, and convert from a rectangular equation to a parametric representation of a...

• MA.912.T.4.7

  Apply parametric equations to model applications involving motion in the plane.

01

What Students Need to Do

Students represent points and curves with rectangular, polar, and parametric coordinates. They convert between forms, graph the results, and interpret parameters, angles, and direction.

02

What Mastery Looks Like

Students accurately convert points and common equations among rectangular, polar, and parametric forms. They graph each form and identify the same curve across representations. They also describe how a parameter controls position and direction.

03

Common Misconceptions

Students may choose the wrong quadrant when finding an angle or mix degrees and radians. They may think a polar point has only one representation. When eliminating a parameter, they often lose the curve’s direction or restrict its domain incorrectly.

04

How to Assess It

Exit ticket: Convert (-√3, 1) to polar form, rewrite r = 4 cos θ in rectangular form, and parametrize x² + y² = 16 counterclockwise.

1. 01

   Give students rulers and protractors to plot polar points on paper, then measure and record the matching rectangular coordinates.

2. 02

   Ask students to explain which form best describes a circle, a spiral, and a moving object, using one equation as evidence.

3. 03

   Run a card match with rectangular equations, polar equations, parametric equations, and graphs that represent the same curve.

4. 04

   Model a Ferris wheel with x = r cos t and y = h + r sin t, then find a rider’s position at given times.

• MA.912.NSO.2.5

  Represent complex numbers on the complex plane in rectangular and polar forms.