Florida B.E.S.T. MA.912.GR.7
B.E.S.T. Standard (Benchmark Cluster)
Apply geometric and algebraic representations of conic sections.
Florida B.E.S.T. Standards for Mathematics
Cluster contents
Benchmarks in This Standard
MA.912.GR.7 is a B.E.S.T. standard. These are the benchmarks under it.
- MA.912.GR.7.1
Given a conic section, describe how it can result from the slicing of two cones.
- MA.912.GR.7.2
Given a mathematical or real-world context, derive and create the equation of a circle using key features.
- MA.912.GR.7.3
Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context...
- MA.912.GR.7.4
Given a mathematical or real-world context, derive and create the equation of a parabola using key features.
- MA.912.GR.7.5
Graph and solve mathematical and real-world problems that are modeled with an equation of a parabola. Determine and interpret key features in terms of the conte...
- MA.912.GR.7.6
Given a mathematical or real-world context, derive and create the equation of an ellipse using key features.
- 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...
- MA.912.GR.7.8
Given a mathematical or real-world context, derive and create the equation of a hyperbola using key features.
- MA.912.GR.7.9
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 cont...
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students connect equations of conic sections to their graphs and geometric features. They identify, rewrite, graph, and interpret circles, parabolas, ellipses, and hyperbolas.
What Mastery Looks Like
- Students correctly identify circles, parabolas, ellipses, and hyperbolas from equations or graphs. They rewrite equations, find key features, and use those features to make accurate sketches.
Common Misconceptions
- Students often identify a conic from one squared term without checking signs and coefficients. They may confuse vertices with foci or forget to complete the square before finding the center.
How to Assess It
- Give students x² + 4y² − 6x + 16y + 9 = 0. Ask them to rewrite it in standard form, name the conic, label its key features, and sketch it.
Lesson moves
Ways to Teach It
Build ellipses with two pushpins, string, and a pencil, then verify that the sum of distances to the foci stays constant.
Write an explanation of how squared terms, signs, and coefficients help distinguish a circle, parabola, ellipse, and hyperbola.
Match cards showing equations, graphs, names, and labeled features, then justify each completed set to a partner.
Fit a parabola to three points from a bridge arch photograph, then use the equation to estimate its maximum height.
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