Wheels in Motion
(Reference Copy)

Activity  6:  Gear Ratios

Gears are numbered on a bicycle with first being the slowest (smallest sprocket on the front, largest on the back), second being the next slowest (smallest on the front,  second largest on the back), and so forth.

The first gear (lowest) has the smallest sprocket on the front and the largest on the back;  the second gear still has the smallest sprocket on the front but the second largest on the back.  When you want to change from the fifth to the sixth gear (assuming you have five sprockets on the back), you have to go from the smallest sprocket in the front and smallest in the back, to the largest sprocket in the front and the largest in the back.  Finally, when you get to the tenth gear you will have the largest sprocket on the front and the smallest on the back.

A major factor in deciding which gears to put on a bicycle is how to avoid having too much gear overlap.  In other words, if the speed you are going is about the same with several combinations of front and rear sprockets, you have fewer choices of speeds that you can travel when pedalling at a constant pace.  Look at different types of bicycles and determine how much overlap there is in the gears they have.