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

Blaszak, Maryann                 South Shore Community Academy
3250 S. Carpenter St.            312-933-8180
Chicago, Illinois  60608
312-376-5455

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.