Florida B.E.S.T. MA.912.GR.7.1

MathGrades 9–12Apply geometric and algebraic representations of conic sections.

The Standard

Given a conic section, describe how it can result from the slicing of two cones.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students connect each conic shape to the position of a plane cutting a double cone. They describe the plane’s angle and whether it crosses one cone or both cones.
What Mastery Looks Like: Students correctly match circles, ellipses, parabolas, and hyperbolas to their cutting planes. They explain each match using the plane’s angle and whether it crosses one cone or both cones.
Common Misconceptions: Students may call every tilted slice an ellipse and miss that a plane parallel to the cone’s side makes a parabola. They may think a hyperbola comes from cutting only one cone. Some also think every horizontal slice makes an ellipse rather than a circle.
How to Assess It: Give students four conic diagrams. For each, have them sketch the cutting plane and label whether it crosses one cone or both cones.

Lesson moves

Build a double cone from modeling clay, then use cardstock planes to model slices that form each conic.
Show four slice diagrams and ask students to explain how changing the plane turns an ellipse into a parabola or hyperbola.
Give groups cards showing conic graphs, names, and cone slices, then have them race to make four correct sets.
Shine a flashlight straight and diagonally onto a wall, then compare the circular and elliptical light regions to cone slices.

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