```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
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,
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:

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

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