Florida B.E.S.T. MA.912.T.4.5
The Standard
Sketch the graph of a curve in the plane represented parametrically, indicating the direction of motion.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students make a table of parameter values, plot the resulting ordered pairs, and connect them to sketch the curve. They add arrows to show how the point moves as the parameter increases.
What Mastery Looks Like
- Given parametric equations and a parameter interval, a student plots key points, finds endpoints, and draws the correct curve. The student marks direction accurately, including changes in direction or repeated points.
Common Misconceptions
- Students may treat the parameter as a third coordinate instead of using it to generate ordered pairs. They may graph the full Cartesian relation rather than the portion traced on the given interval. They often omit arrows or assume motion is always left to right.
How to Assess It
- Exit ticket: For x = t² - 1 and y = t, with -2 ≤ t ≤ 2, plot five points, sketch the curve, and add direction arrows.
Lesson moves
Ways to Teach It
Tape a coordinate grid on the floor; one student reads t-values while another walks to each point from x = t, y = t².
Show two identical curve sketches with opposite arrows, then ask students to explain in writing which matches increasing t and why.
Run a card sort matching parametric equations, value tables, graph sketches, and direction arrows for four curves.
Plot a ball's horizontal and vertical position every second, connect the points, and label its direction from launch to landing.
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