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Under the Ribbon

Age 14 to 16
Challenge Level

One reason for using this problem with students is to show how a spreadsheet approach can give access to problems where other analysis, in this case algebra, is very difficult.

A second reason is that the answer to the problem is surprising.

Somehow the brain doesn't expect such a large answer - perhaps we imagine that because there isn't much extra length extending the ribbon ( 4 cm of slack ) there will not be much scope for displacing the ribbon vertically.

This problem also needs approaching in stages, and it is good for students to experience that by solving for the symmetric central position first then giving consideration to the asymmetric case.

Perhaps students could extend the enquiry to consider how different degrees of slack : 3 cm, 2 cm, 1 cm, effect the result.

Some students will be very familiar with using a spreadsheet to help with this kind of mathematical context, but many will not be at all confident, or even think to try a spreadsheet.

Making calculations for several different cube sizes on a calculator first, helps students to see that the calculation process is the same each time only using different input values. It also helps students to grasp that the ability to cover input values at intervals systematically across a chosen range could guide us closer and closer towards an optimal position or value.