|Conic Sections Classroom
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Distribute 4 cone-shaped paper cups (for cooperative learning groups),
or construct 4 cones from posterboard (for class demonstration).
Also distribute a large sheet of newsprint and fold it into four sections.
2. Cut the first cone flat across the bottom so that the bottom remains in a circle. Dip this cone in tempera paint and "stamp" the sheet of newsprint in the first section. Note that the shape produced is a circle, and label it accordingly.
3. Cut the second cone diagonally across the bottom. Again dip in tempera paint and stamp in the second section of the newsprint. Note that this time the shape produced is oval. Discuss the shape with the students by asking how it is like and how it is different from the circle produced in Step 2. If they are not familiar with the word "ellipse", introduce the term at this time. Then ask the students to draw and label a circle, then draw and label an ellipse.
To further develop vocabulary and concepts about the ellipse, have students identify its center and label it. Also describe the foci, a pair of points symmetrically placed about the center on the long axis of the ellipse. The playground ellipse activity will show students how the foci can be used to draw the ellipse.
4. Ask the students what they already know about these two shapes ( both are closed figures, no corners, etc.). Demonstrate on a computer drawing program the tool that lets students draw ellipses.
The rest of this activity introduces the remaining two conic sections, and can serve as an extension for more advanced students. These next two shapes may be new to students and will be open figures.
5. Take the third cone and cut it parallel to the slant of the outside edge. The shape created will resemble a "U". This shape is open at one end and is called a parabola. Dip the cut edge, paint, print and label its image in the third section of the newsprint.
6. Take the fourth cone and this time cut a section perpendicular to the base. The shape created will resemble a rounded "V". This shape is open at one end and is called a hyperbola. Again, dip the cut edge in paint, print and label its image in the final section of the newsprint.
Newtons work showed that objects in closed orbits must have circular or elliptical paths. However, if the velocity of an orbiting body were increased, its orbital path would change to a parabola or hyperbola, and it would escape the gravitational pull of the Sun and leave the solar system.