Florida B.E.S.T. MA.912.T.4.7

MathGrades 9–12Extend rectangular coordinates and equations to polar and parametric forms.

The Standard

Apply parametric equations to model applications involving motion in the plane.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students describe horizontal and vertical position with separate equations that use the same time variable. They use those equations to locate an object, graph its path, and interpret direction.
What Mastery Looks Like: Students can write x(t) and y(t) from a starting point and horizontal and vertical rates. They can find positions at given times, graph the path, and show its direction.
Common Misconceptions: Students often omit the starting coordinates, swap the horizontal and vertical rates, or write only one equation. They may graph the path without showing direction or treat time as another coordinate.
How to Assess It: Exit ticket: A cyclist starts at (2, -1) and moves 3 units per second east and 2 units per second north. Write x(t) and y(t), then find the cyclist’s position at 4 seconds.

Lesson moves

Roll a ball across grid paper, record its coordinates at timed intervals, then write parametric equations for its path.
Show x = 2t + 1 and y = 5 - t, then ask students to explain the start, direction, and position at t = 3.
Use matching cards with motion stories, coordinate tables, graphs, and parametric equations; teams justify each four-card set.
Model a drone flying east while drifting north, then determine when it reaches a marked boundary on a coordinate map.

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