Maryland Math G.GPE.C.9

MathGrades 9–12EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS

The Standard

Convert between polar and rectangular coordinates.

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

Teacher's field guide

What Students Need to Do: Students describe a point by its distance from the origin and angle from the positive x-axis, then by its x and y values. They convert in both directions using trig and check the quadrant on a sketch.
What Mastery Looks Like: Given (4, 60°), a student gets (2, 2√3). Given (-3, 3), they get (3√2, 135°) and can plot the point correctly.
Common Misconceptions: Students may swap sine and cosine when finding x and y. When finding an angle, they may use arctan(y/x) without checking the quadrant. Some leave a calculator in radians while working with degrees.
How to Assess It: Exit ticket: Convert (4, 60°) to rectangular coordinates and (-3, 3) to polar coordinates with a positive radius and an angle from 0° to 360°. Show a sketch for each.

Lesson moves

On graph paper, use a ruler and protractor to plot (4, 60°), then measure x and y and compare with calculated values.
Ask students why (-3, 3) has an angle of 135° even though arctan(3/−3) gives −45°.
Play a matching game with cards showing (4, 60°), (2, 2√3), and a matching graph; include points in all four quadrants.
Give a radar reading of 10 km at 30° north of east; have students calculate the east and north distances.

Free download

$Preview of the G.GPE.C.9 printable worksheet$

A ready-to-print activity worksheet aligned to G.GPE.C.9, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.