Mathematics and Society - OS X Lion Server

Have a student bring a 5 or 10 speed bicycle to class. Turn the bike upside down sothat the gears can be shifted. PlIt a piece of tape on the rear wheel of the bicycle.Have the students count the teeth in -, Eeach gear and record in Table 1- (The ..Bnumber is not standard. The front gears rCvary from 52 to 39 teeth and the rearrDAX.-.,;'gears from 34 to 14.):::=:::sa~Write the gear ratios and simplify.(/~Record in Table 2.The following activities afor student investigation:TABLE1. Select a simplegear ratio, for example13 to 4, and set thegears to correspond.Check the gear ratio byslowly turning thepedals. The pedalsshould turn four timesand the wheel thirteen.(Hold the rear tirelightly to aid incounting the turns ofthe wheel.) Checksome other gear ratiosby counting pedal andrear wheel turns.re suggestedTABU: 1Geo.vXyAB2. Select a back gear and use the smallshift to the large front gear. Continuechange do you notice in the back wheel?gear ratios?Numb~of' teetc Xto r.DEGeo.v Ratio of Simplifiednum b erRa.tio of teeth Teeth R.o..+ioXtoAXto BX+oC)( +0 DYtoAYto BYto CYi-o Dyto Efront gear. Turn the pedals slowly andturning the pedals at the same rate. WhatCan you explain? What are the corresponding2((3. Move the gearshifts so the chain is on the smallest back and front gears. Turnthe pedals at a constant rate. Shift only the back gear so that the chain travelsfrom the smallest to the largest gear wheel. What change occurs in the back wheel?Can you explain? What are the corresponding gear ratios?4. If the pedals were turned at a constant rate, which ratio would cause the backwheel to turn the fastest? Order the simplified gear ratios from largest to smallest.Students could use a calculator to change each ratio to a decimal and then order thedecimals.5. In riding the bicycle, which gear setting is the easiest to pedal? the mostdifficult? Experiment on the playground. Which gear setting allows you to travelthe farthest for one turn of the pedal? Devise a method for checking your prediction.4286. In a cross-country bicycle race which gear setting would be best for going up asteep hill? (7. In a cross-country bicycle race which gear setting would be best for the sprint tothe finish line?