The Fraction Wheel Addition Machine
Note: This pure HTML application is completely self-contained. Running it does not require internet access. All that is required is a reasonably up to date browser like chrome or firefox.
This is the second in a series of interactive applications that use pulleys to create animated models of fractions. The idea is analogous to the way bicycle gears work. A pulley of a given size is attached to a fraction wheel in the same way that the gears on the back of bicycle are attached to the rear wheel of the bike. A crank, analogous to the pedals of the bike, is connected by a belt, analogous to the chain on a bike, to the pulley so that turning the crank turns the pulley which turns the fraction wheel. How much the fraction wheel turns depends on the ratio of the size of the crank pulley to the size of fraction wheel pulley. This ratio is analogous to the gear ratio on a bike. For example if the fraction wheel pulley is 4 times as large as the crank pulley, corresponding to a ratio of 1:4, 4 full turns of the crank will be required to produce 1 full turn of the fraction wheel. Thus one turn of the crank produces a quarter turn of the fraction wheel providing both a mechanical and a visual model of 1/4. By changing pulleys students can observe the behavior of different fractions.
In the first application, 'The Fraction Wheel Pulley Machine', students observed fraction families for different base fractions by turn the crank multiple times for a given pulley until the fraction wheel had turned completely. In this application we model addition of fractions by allowing the student to change pulleys without restarting.
The thumbnails for this product illustrate how it works. The first image shows the result of connecting the '1:4' pulley and turning the crank once. We then click on the '1:3' pulley and turn the crank once. The result is shown in the second image. Finally we click on the '1:6' pulley and turn the crank once resulting in the third image.
Notice that when we change fractions the fraction wheel is marked off in units of the least common denominator of the fractions. In the example, when we add 1/3 to 1/4 the fraction wheel is marked off in units of 1/12 so that we can observer that 1/3 = 4/12 and 1/4 = 3/12 and so the sum is 7/12. Adding 1/6 doesn't change the least common denominator as 1/6 = 2/12 and we see the final sum is 9/12 = 3/4. Thus the application provides a visual model of least common denominator and why we use them in adding fractions.