Florida B.E.S.T. MA.912.T.4.6
The Standard
Convert from a parametric representation of a plane curve to a rectangular equation, and convert from a rectangular equation to a parametric representation of a plane curve.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students rewrite a parametric curve as an equation involving only x and y. They also choose parameter equations that trace a given rectangular curve and state any needed parameter restrictions.
What Mastery Looks Like
- Students eliminate the parameter by solving one coordinate equation and substituting into the other, while keeping any restrictions. They can create a parametrization and verify it by substitution into the original rectangular equation.
Common Misconceptions
- Students may replace the parameter inconsistently or make algebra errors when solving for it. They may assume a curve has only one parametrization or drop parameter restrictions, adding points or branches that were not traced.
How to Assess It
- Exit ticket: Convert x = 2t - 1, y = t², t ≥ 0, to a rectangular equation with restrictions, then parametrize x² + y² = 16.
Lesson moves
Ways to Teach It
Have pairs make a t-table for x = 2t + 1 and y = t², plot the points, then eliminate t.
Ask students to explain why x = 3cos t, y = 3sin t traces a circle and how the graph changes as t increases.
Run a card sort matching rectangular equations, parametric equations, graphs, and parameter restrictions for lines, parabolas, and circles.
Model a projectile with x = 20t and y = 1.5 + 15t - 4.9t², then eliminate t to find its path.
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Related Standards
- MA.912.T.4.2
Represent equations given in rectangular coordinates in terms of polar coordinates. Represent equations given in polar coordinates in terms of rectangular coord...
- MA.912.T.4.5
Sketch the graph of a curve in the plane represented parametrically, indicating the direction of motion.
- MA.912.T.4.7
Apply parametric equations to model applications involving motion in the plane.
- MA.912.T.4
Extend rectangular coordinates and equations to polar and parametric forms.
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