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Quote of the Day: "What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of mathematics?" -- Benjamin Franklin Objectives: The student will understand how the Free Response questions on the A.P. Exam are graded. 1. Hand out a copy of the 1991 Free Response Questions for the A.P. Calculus AB Exam. Have students work on question #1. 2. After 8 to 10 minutes, go over the answer. Then hand out the 1991 Grading Standards and show students what needs to be included in their answers. 3. Discuss coloring a map. Put several on the board and have students determine the number of colors necessary to color them. Discuss the Four Color Theorem. The Four Color Problem dates back to 1852 when Francis Guthrie, while trying to color the map of counties of England noticed that four colors sufficed. He asked his brother Frederick if it was true that any map can be colored using four colors in such a way that adjacent regions (i.e. those sharing a common boundary segment, not just a point) receive different colors. Frederick Guthrie then communicated the conjecture to DeMorgan. It wasn't until over 100 years later that this conjecture was finally proven. It was with the help of a computer that Appel and Haken in 1976 published their proof of the Four Color Theorem. 4. Distribute copies of maps to color.
5. Assignment
Work on 1991 Free Response Problems
Work on Coloring Sheets
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