Colleen BeaudoinFor FCIT

Note: All clipart found on Clipart ETC

Note: With the exception of the hyperbola, the plane intersects only one nappe of the cone.

The plane that intersects the cone is perpendicular to the axis of symmetry of the cone.

The plane that intersects the cone is neither parallel nor perpendicular to the axis of symmetry of the cone and cuts through 2 “sides”.

The plane that intersects the cone is parallel to an element of the cone.

The plane that intersects the cone is parallel to the axis of symmetry of the cone.

 

1. Put students into groups and give each group:

4 cone-shaped paper cups (or party hats) 4 sheets of paper  paint on a paper plate

2. Each group should cut the first cone flat across the bottom as if a plane intersected it perpendicular to its axis. Then, dip the cone into the paint and stamp the paper to see the outline of where the cone was cut. Have each group write down the name of the shape they see on their paper.

3. Cut the second cone as if a plane is intersecting it neither parallel nor perpendicular to the axis.  Be sure to cut all the way through the cone (hitting all “sides”). Dip the edge in paint and stamp the paper. Label the shape produced. 

Have students compare and contrast the two shapes they have on their paper.

 

4. Have students cut the third cone as if a plane is passing through it parallel to the slant of the outside edge.  Again, dip the cut edge in the paint and stamp the paper. Label the shape.

 

5. With the fourth cone, cut the cone as if a plane was passing through it parallel to the axis of symmetry. Dip the cut edge in the paint and stamp the paper. Label the shape.

 

What are the 4 conic sections we discussed and how are they defined?