Florida B.E.S.T. MA.912.T.4.1
The Standard
Define and plot polar coordinates. Convert between polar coordinates and rectangular coordinates with and without the use of technology.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students locate points by turning through an angle and moving a signed distance from the pole. They use x = r cos θ and y = r sin θ, then reverse the process using distance and quadrant information.
What Mastery Looks Like
- A student plots polar points accurately, including points with negative radii and angles outside one full turn. They convert exact and decimal coordinates by hand, then check decimal results with graphing technology.
Common Misconceptions
- Students may swap sine and cosine when finding x and y. They may ignore the quadrant when finding an angle or treat a negative radius as a negative angle. Degree and radian mode errors also cause incorrect results.
How to Assess It
- Give an exit ticket: Plot (-4, π/3), convert it to rectangular coordinates, then convert (-3, 3√3) to polar form with 0 ≤ θ < 2π.
Lesson moves
Ways to Teach It
Use polar grid paper, rulers, and protractors to plot five points with positive and negative radii.
Ask students to explain why (3, π/4) and (-3, 5π/4) name the same point.
Run a card sort matching polar coordinates, rectangular coordinates, and plotted points.
Use a radar screen map to locate an aircraft from its distance and bearing, then report its rectangular position.
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Printable MA.912.T.4.1 Worksheet
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Related Standards
- MA.912.NSO.2.5
Represent complex numbers on the complex plane in rectangular and polar forms.
- 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
Extend rectangular coordinates and equations to polar and parametric forms.
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