Florida B.E.S.T. MA.912.GR.7.7
The Standard
Graph and solve mathematical and real-world problems that are modeled with an equation of an ellipse. Determine and interpret key features in terms of the context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students read an ellipse equation and find its center, axis lengths, vertices, covertices, and foci. They graph the ellipse, solve for points on it, and interpret those features in context.
What Mastery Looks Like
- Students can graph an ellipse accurately and label its center, vertices, covertices, foci, and axes. They can solve for missing coordinates and explain what each feature means in a real situation.
Common Misconceptions
- Students may treat the denominators as axis lengths instead of squared semi-axis lengths. They may swap the major and minor axes or use the wrong relationship, c² = a² − b², for the foci.
How to Assess It
- Give students (x − 2)²/25 + (y + 1)²/9 = 1. Ask them to sketch it, label its center, vertices, and foci, then state both axis lengths.
Lesson moves
Ways to Teach It
Use two thumbtacks, string, and a pencil to draw an ellipse, then measure the axes and verify the constant distance sum.
Compare two ellipse equations with switched denominators, then write how the switch changes the major axis, vertices, and foci.
Run a card sort matching ellipse equations, graphs, centers, vertices, and foci, with students correcting any unmatched cards.
Model an elliptical running track from given dimensions, write its equation, and locate entrances placed at the vertices and covertices.
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