Maryland Math P.IPE.A.1

MathGrades 9–12INTERPRETING PARAMETRIC EQUATIONS

The Standard

Sketch the curve defined by parametric equations.

Maryland College and Career Ready Standards for Mathematics (2025) · Analyze parametric equations.

Teacher's field guide

What Students Need to Do: Students choose values of t and calculate the matching x and y coordinates. They plot the points, sketch the path, and show which way it moves as t increases.
What Mastery Looks Like: A student can sketch the curve from a table of values without treating t as an axis. They mark endpoints when t is limited and add arrows to show direction.
Common Misconceptions: Students may plot t as the x-coordinate instead of calculating x from the equation. They may connect points in left-to-right order rather than time order, or extend the curve past the allowed values of t.
How to Assess It: Exit ticket: Sketch x=t+1 and y=t² for t=-2,-1,0,1,2. Label each point and add an arrow showing direction as t increases.

Lesson moves

On grid paper, plot x=t² and y=t for t=-2,-1,0,1,2 using numbered stickers, then connect the points and add arrows.
Ask: For x=t and y=t², what part of the curve disappears if t is limited to 0 through 2?
Match cards showing x=t, y=t² and x=t², y=t to sketched curves, then mark direction as t increases.
Plot a ball’s path using x=4t and y=8t-4t² at t=0, 0.5, 1, 1.5, 2 seconds, then mark its highest point.

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