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Centre for Innovation in Mathematics Teaching
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Reduction Mill
The reduction mill reduces the thickness of a strip of steel using a series of rollers, each roller making the steel slightly thinner. The percentage reduction is constant on each pair of rollers. The mathematics used to calculate the actual reduction is similar to that used when calculating compound interest. Students are required to find the thickness of the steel at different stages of the process. The first problem asks students to calculate the number of rollers required to produce the required reduction in thickness given the percentage reduction of each pair of rollers and then to generalise the result. Activities two and three consider the speed at which the steel leaves the rollers given that the thickness is reduced but the width stays constant. Problem two requires students to solve an equation in n where n is a power. This can be achieved by trial and improvement or by use of logarithms.
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