Return to Mathematics IndexUSING VARIABLES AND RATIOS TO GET YOU IN THE RIGHT GEARGEORGE K. SMITH DUNBAR VHS 3000 SO. KING DRIVE CHICAGO, IL 60616 1-312-567-5400OBJECTIVES: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 techniqueMATERIALS: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 ratioSTRATEGY 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<>0bubble sort- a programming technique where data is stored from "lowest" to "highest" or vice-versaPSEUDO-BASIC- a simplified version of BASIC for students not familiar with programming languages