Florida B.E.S.T. MA.912.GR.7.9
The Standard
Graph and solve mathematical and real-world problems that are modeled with an equation of a hyperbola. 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 rewrite equations in standard form and use them to graph hyperbolas. They find the center, vertices, foci, asymptotes, orientation, and branch locations. They solve contextual problems and explain what those features mean.
What Mastery Looks Like
- Given an equation, a student correctly identifies the center, opening direction, vertices, foci, and asymptotes, then draws both branches. The student checks solutions and explains what coordinates, distances, or branches mean in the situation.
Common Misconceptions
- Students often read center signs incorrectly or choose the opening direction from the larger denominator instead of the positive term. They may reverse the asymptote slope, draw only one branch, or treat asymptotes as part of the graph. In context, they may keep solutions that do not fit the stated distances or region.
How to Assess It
- Exit ticket: For (x − 2)²/9 − (y + 1)²/16 = 1, find the center, vertices, and asymptotes, then sketch both branches. Decide whether (5, −1) is a solution and justify by substitution.
Lesson moves
Ways to Teach It
Place two pushpins as foci on graph paper, test points with rulers, and mark those with a fixed distance difference.
Compare two hyperbola equations and write how changing the center, signs, and denominator values moves or reshapes the graph.
Run a card sort matching hyperbola equations, graphs, centers, vertices, and asymptotes, then require partners to justify every match.
Model possible ship locations from a fixed difference in distances to two radio towers, then interpret the relevant hyperbola branch.
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