Florida B.E.S.T. MA.912.GR.7.6
The Standard
Given a mathematical or real-world context, derive and create the equation of an ellipse using key features.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use an ellipse's center, axis lengths, vertices, co-vertices, or foci to build its equation. They choose the correct orientation and use c² = a² - b² when foci are given.
What Mastery Looks Like
- A student can use a center, vertices, co-vertices, axis lengths, or foci to find the needed values and write the equation. The student can check the equation by locating its center, axis direction, vertices, and foci.
Common Misconceptions
- Students often use full axis lengths as denominators instead of squaring the semiaxis lengths. They may reverse signs in the center, place the larger denominator under the wrong variable, or use the wrong relationship among a, b, and c.
How to Assess It
- Exit ticket: An ellipse has center (2, -1), vertices (7, -1) and (-3, -1), and co-vertices (2, 2) and (2, -4). Write its equation and label a and b.
Lesson moves
Ways to Teach It
Use two pins, string, and graph paper to draw an ellipse, then measure its center and semiaxes and write its equation.
Compare two ellipse equations and explain how each denominator shows the major axis direction and the distances from the center.
Run a card sort matching ellipse graphs, equations, centers, vertices, co-vertices, and foci, then have pairs justify each match.
Given an elliptical tabletop 180 centimeters long and 100 centimeters wide, place its center at the origin and write its boundary equation.
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Related Standards
- MA.912.GR.7.7
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 conte...
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Given a mathematical or real-world context, derive and create the equation of a hyperbola using key features.
- MA.912.GR.7.4
Given a mathematical or real-world context, derive and create the equation of a parabola using key features.
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