Maryland Math P.CED.A.1

MathGrades 9–12CREATING EQUATIONS

The Standard

Create a single equation, using rectangular coordinates, that is equivalent to a pair of parametric equations.

Maryland College and Career Ready Standards for Mathematics (2025) · Creating equations that describe numbers or relationships.

Teacher's field guide

What Students Need to Do: Students turn two rules that use a parameter, often t, into one equation using x and y. They solve one rule for t, substitute it into the other, and check whether the new equation includes only points the original rules allow.
What Mastery Looks Like: Given x=2t+1 and y=3t-2 for any real t, a student writes 2y=3x-7. They can work backward from a point on the line to find its t value. They notice when eliminating t adds points the original rules cannot make.
Common Misconceptions: Students may replace t with x without first solving for t. For x=t² and y=t², they may write y=x and miss that the original pair cannot make points with negative coordinates.
How to Assess It: Exit ticket: For any real t, x=2t+1 and y=3t-2. Write one equation in x and y for the same points, then check it using t=0.

Lesson moves

On graph paper, plot x=t+1 and y=2t-3 for t from -2 to 2, then use the pattern to find one equation.
Ask, 'For x=t² and y=t², why does y=x include points the pair never makes?'
Put x=t+2, y=3t and x=2t-1, y=t+4 on cards; partners trade cards, eliminate t, and check with t=0.
On a city map, points along a road follow x=2t+1 and y=t-3; find the road's equation without t.

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