Procedures
1.  Design a clown face using only graphs (or parts of graphs) of parabolas.  When you have a design you like, record the equations  you use, including any restrictions on the domain or range of each.  Give the equations for your clown face to two classmates.  Ask them to sketch the face from the equations.  Compare their sketches with yours.  Check your equations to resolve any differences
among the graphs.

Equations for Parabolas will vary.  Check students work.

2.  Design several clown faces using graphs (or parts of graphs) of conic sections.  Each face should convey a different emotion, such as anger, sadness, joy, or surprise.  For each face, record the equations you use, including any restrictions.

check students work

3.  Find two classmates.  Collect measurements for the distance h from the top of the head to the chin and the distance w across the face at the eyes.  Analyze
the data to design an elliptical outline for a clown face that will fit the "average" student.  Record the equation you use.  How well does your ellipse fit your own face?  Do you think an ellipse is a good approximation for the shape of a human face?  Why or why not?
An ellipse is good to simulate the shape of a face.  My face was a little smaller than the people that I measured.

4.   Create a display for your designs.  Choose any medium you like and be creative.  Set your display in the glass case in the foyer by the office.

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