Florida B.E.S.T. MA.912.T.4.3
The Standard
Graph equations in the polar coordinate plane with and without the use of graphing technology.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students choose angle values, calculate the matching radius, and plot the resulting points on a polar grid. They sketch curves by hand and use graphing technology to verify shape, symmetry, and key features.
What Mastery Looks Like
- Students create a useful table of θ and r values, plot positive and negative radii correctly, and connect points into an accurate curve. They use graphing technology to check the result and explain any differences in window, mode, or scale.
Common Misconceptions
- Students may treat r and θ like x and y, or ignore that a negative r plots in the opposite direction. They may also use degree mode when angles are given in radians or choose too few θ-values to reveal the shape.
How to Assess It
- Give students r = 2 + 2cos θ and a blank polar grid. Ask them to make a value table, sketch the curve, and label its symmetry and maximum radius.
Lesson moves
Ways to Teach It
Use a paper polar grid and movable arrow to plot ordered pairs, including negative radii, before connecting points for r = 3cos θ.
Ask students to compare r = 2sin θ and r = 2cos θ, then write how sine and cosine change the graph’s orientation.
Run a matching game with cards showing polar equations, value tables, and graphs for circles, roses, limaçons, and spirals.
Model a rotating radar beam with θ as direction and r as distance, then plot several detected objects on a polar grid.
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Printable MA.912.T.4.3 Worksheet
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Related Standards
- 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.4.4
Identify and graph special polar equations, including circles, cardioids, limacons, rose curves and lemniscates.
- MA.912.T.4
Extend rectangular coordinates and equations to polar and parametric forms.
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