Maryland Math G.GMD.B.4.a
The Standard
- G.GMD.B.4
- Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Identify the shapes of two-dimensional cross-sections of a right double cone.
Maryland College and Career Ready Standards for Mathematics (2025) · Visualize relationships between two-dimensional and three-dimensional objects.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Picture a flat plane cutting two cones joined tip to tip. Sketch and name the shape made where the plane meets the cones.
What Mastery Looks Like
- Students identify a circle, ellipse, parabola, or hyperbola from the plane’s angle and position. They know a plane that cuts both halves makes two separate curves, unless it passes through the shared tip.
Common Misconceptions
- Students may call every slanted cut an ellipse. They may miss that a plane parallel to a sloping side makes a parabola, or that a cut through both halves makes two curves.
How to Assess It
- Draw a double cone with a horizontal plane above the tip, a tilted plane crossing only the top cone, and a plane crossing both cones. Ask students to sketch and name each cut.
Lesson moves
Ways to Teach It
Press two clay cones tip to tip; cut across one cone and then both with a plastic knife, and trace the exposed edges.
Draw a plane parallel to one sloping side of a double cone; ask why the cut makes an open curve.
Give pairs cards showing cutting planes and cards showing curves; have them match each pair and defend one match.
Aim a flashlight at a wall, then tilt it; sketch how the light patch stretches from a circle toward an ellipse.
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