From Hypothesis To Conclusion...Reading Maps To Understand Proofs

Blaszak, Maryann South Shore Community Academy

Objectives: 1. The student will write directions to any given situation using a map. 2. The student will be able to fill in missing data for any given situation. 3. The student will understand the importance of diagrams while writing proofs. 4. The student will develop a tentative understanding of writing proofs. Materials: Maps and transparencies of: 1. CTA Bus Routes 2. State of Illinois 3. Chicago Distance Classic 4. Washington, D.C. Strategy: This mini teach is directed toward 10th grade students who will soon begin to write two column proofs. To understand the step by step method in writing a proof, students will use their map reading skills to give directions to various places of interest in cities like Chicago and Washington D.C. and also other places of interest in Illinois. Students will rearrange their desks to form groups, each group containing four members. Four situations with maps will be given to each group, one situation at a time, in which they will write out the necessary directions. Group discussion of each situation will be approximately five minutes. Only after the first situation will the class come back together to discuss their set of directions. One student from each group will read their directions as I follow along on a map on the overhead projector. If other groups have the same directions we will move on. Otherwise, we will discuss the variety of ways a person can reach the same destination. The students will regroup and discuss the remaining situations which will be given to them in five minute intervals. Again, as a class we will discuss their outcomes. Next activity the groups will work together filling in missing directions to a given situation. After five minutes, a class discussion will be held. Lastly, together we will write a geometric proof. Emphasize the statements and reasons of a proof must contain any of the following: 1. a given 2. a postulate 3. a theorem 4. a definition.
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