USING VARIABLES AND RATIOS TO GET YOU IN THE RIGHT GEAR

GEORGE K. SMITH                DUNBAR VHS
                               3000 SO. KING DRIVE
                               CHICAGO, IL 60616
                               1-312-567-5400 

OBJECTIVES:
     1) To apply the concepts of variable and ratio in everyday situations. 2) To 
determine the gear ratios and gears for a 12-speed bicycle. 3) To write a computer 
program which will determine gears using the bubble sort technique 

MATERIALS:
    1) Overhead projector and transparency sheets
    2) Blackboard and colored chalk
    3) Erasable laminated memo pads
    4) 12-speed bicycle and bicycle mount
    5) Handout explaining gear ratio

STRATEGY AND PROCEDURE:     
     The session will begin with a brief review of the hierarchy of arithmetic 
operations.  Students will first give examples of various hierarchies (army, 
gov't, school,...). To remember the order of operations the students will use the 
mnemonic device PEDS (Parentheses, Exponents, Division/ Multiplication, 
Subtraction/Addition). 
     The overhead projector will then be used to show the students a short program 
in PSEUDO-BASIC.  They will use the hierarchy to determine the output of this 
program.  The program will motivate a discussion of the concept of a variable.  
The laminated pad will be used to see how once a value for a variable is replaced 
, that value forever disappears.  The program is as follows: 
                        
                        10  READ X
                        20  Y=3+4*X-2
                        30  PRINT X,Y
                        40  IF X<>0 THEN 20
                        99  END
                       110  DATA   4,-2,3,0

     Two practical examples of ratios will then be given.  The first will be a 
baseball player's hits per at-bats.  The second the # of records sold per records 
sent at Honky-Tonk Hick Records in Marengo.  For both variable and ratio I want 
the examples to motivate definitions from the students. 
     We will then turn to an application of variables and ratios.  A student will 
mount a 12-speed bicycle in front of class and try to determine the various gears 
by shifting and judging the tension.  The rest of the students will determine the 
gears by using: 
                                                                             
                                   # of teeth on chainwheel
                      gear ratio = ------------------------
                                   # of teeth on freewheel
                                              
     This will be abbreviated using the variables g=c/f.  Two diagrams of the 
chainwheel, freewheel, and their relationship will be drawn on the board: one to 
show the gears as determined by the student on the bicycle, and the second to be 
used by the other students who determined the gear ratios.  The lower the gear 
ratio, the lower the gear.  A handout will be distributed clarifying these 
concepts. 
2
     The results of the cyclist will then be compared with that of the students 
who computed the gears mathematically.  Any differences which may appear will be 
discussed and accounted for (cyclist error in judging tension, old chain which has 
stretched, wear on chainwheel and freewheel, etc).  Finally, a computer program 
will be distributed which determines gear ratios and gears using the bubble-sort 
technique. 

DEFINITIONS:   variable- a symbol (usually letter) used to represent an
                             unknown #

               ratio- a quotient a/b comparing two elements, where b<>0

               bubble sort- a programming technique where data is stored
                              from "lowest" to "highest" or vice-versa

               PSEUDO-BASIC- a simplified version of BASIC for students
                               not familiar with programming languages