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A few years ago, someone sent me a video of the latest in warehouse (or fulfilment centre) design. I remembered seeing a wide-angle photo of an Amazon centre at Christmas a few months previously, and I was stuck by the piles of ‘stuff’ and the hundreds of workers, apparently moving around like ants collecting items for the packers. The video showed a different approach: no people, but thousands of pods (containing items stored at random) and, most strikingly, an army of suitcase-sized robots, carrying pods and navigating their way effortlessly around a complex grid system to the packers.

Amazon Robots
Inventory Pods – items packed at random

Videos such as these cannot fail to grab students’ attention, whatever their age or, indeed, prior perceptions of maths. Just about everyone is familiar with ordering online from Amazon and other retailers; they just don’t know exactly how their order is processed, and the part that maths has to play in the operation.

My initial thoughts were to tie in the grid movements of the robots to a well-known maths puzzle, often referred to as the Manhattan Taxi Problem. This involves calculating the number of routes from top left to bottom right in a rectangular array, using an ‘efficiency’ rule of leftwards and downwards movements only. This gives rise to Pascal’s Triangle: some students will recognize it, and others can experience the pleasure of discovering this remarkable mathematical object for the first time.

The Manhattan Taxi Problem
Increasing the complexity of the initial problem

Early iterations of this project for Year 12 students incorporated a research element, involving an in-depth exploration of some of the properties of Pascal’s Triangle, which worked very well. For younger students, and to maintain the focus on real-world problem-solving, features of increasing complexity were introduced to give students opportunities for greater challenge. Feedback so far suggests that students enjoy the activities and, in particular, appreciate the real-world context to which they relate.

Amazon themselves have expressed a significant interest in developing resources for schools and the AMSP is working closely with the company to trial larger-scale enrichment days, based initially at the Amazon Fulfilment Centre adjacent to Manchester Airport.

By Martin Bamber

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