Maryland Math G.GPE.D.12

MathGrades 9–12EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS

The Standard

Graph polar equations by hand and using technology.

Maryland College and Career Ready Standards for Mathematics (2025) · Polar Equations.

Teacher's field guide

What Students Need to Do: Students make a table of angles and radii for a polar equation, then plot the points on a polar grid. They sketch the curve and check its shape with a graphing tool.
What Mastery Looks Like: A student plots points for r=2cos θ, placing negative radii on the opposite ray. Their hand sketch matches the graphing tool, and they can explain the curve's symmetry.
Common Misconceptions: Students may place a negative radius on the named ray instead of the opposite ray. They may treat θ as an x-coordinate or leave the graphing tool in degree mode when using radians.
How to Assess It: Exit ticket: For r=2cos θ, find and plot the points at θ=0, π/2, π, and 3π/2. Explain where the point at θ=π goes when r=-2.

Lesson moves

Tape a polar grid to the floor, then use string to mark points for r=2+2cos θ at 45-degree steps.
Ask partners: Why does r=2cos θ at θ=π land at (2,0)? Have them explain with a sketch.
Give pairs angle cards for r=3sin(2θ); have them race to plot the points, then check the rose in Desmos.
Show a cardioid microphone pickup pattern, then have students compare its outline to a graph of r=2+2cos θ.

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