Maryland Math G.GPE.C.8

MathGrades 9–12EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS

The Standard

Understand the relationship between polar coordinates and Cartesian coordinates.

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

Teacher's field guide

What Students Need to Do: Students plot a point using its distance from the origin and an angle measured from the positive x-axis. They convert between that description and x-y coordinates using right triangles, sine, and cosine.
What Mastery Looks Like: Given (4, 150°), a student plots the point in quadrant II and finds its x-y coordinates, (−2√3, 2). Given (−3, 3), they find a distance of 3√2 and an angle of 135°.
Common Misconceptions: Students may measure the angle clockwise or start from the positive y-axis. They may treat the distance as the x-coordinate or choose an angle without checking the quadrant.
How to Assess It: Exit ticket: Plot the point (4, 150°) and give its x-y coordinates. Show how you found them.

Lesson moves

Give pairs a protractor, ruler, and coordinate grid; have them plot (5, 120°) and measure its x and y coordinates.
Ask, "How can (3, 0°) and (3, 360°) name the same point?" Have students sketch and explain.
Make matching cards for (2√2, 45°), (2, 2), and a sketch; have teams assemble matching sets.
Show a radar target 10 km away at 30° counterclockwise from east; students calculate its east and north distances.

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