Maryland Math P.CED.A.2

MathGrades 9–12CREATING EQUATIONS

The Standard

Given a data set, create a parametric equation and a single equation using rectangular coordinates to fit the data.

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 use a data table to write one equation for x and another for y, both in terms of the same parameter, such as time. They then remove the parameter to write one equation relating x and y.
What Mastery Looks Like: Given x=2t and y=t², a student writes y=x²/4. They check the equation against the data and keep track of the x-values covered by the measurements.
Common Misconceptions: Students may treat the parameter as a third location instead of a value shared by x and y. They may write y=x² without accounting for x=2t, or expect a model to pass through every point in a noisy data set.
How to Assess It: Give students t=0,1,2,3; x=0,2,4,6; and y=0,1,4,9. Ask them to write x(t), y(t), and one equation relating x and y.

Lesson moves

Hand pairs cards marked (0,0,0), (1,2,1), (2,4,4), and (3,6,9) for (t,x,y); have them plot the points and write both forms.
Ask why y=x²/4 includes negative x-values when the table shows only x-values from 0 to 6.
Play a card match using the sample table, x=2t and y=t², and y=x²/4; add y=x² as a distractor.
Pause a slow-motion ball video at four timestamps; measure x and y on a grid, then fit x(t), y(t), and y(x).

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