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

Blaszak, Maryann South Shore Community Academy

312-933-8180

**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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