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    Pupils Square Up for Menger Challenge

    48 000 pieces of card plus over 1000 person hours later and we had a giant Menger Sponge to display in the QKB. Here's the story about how and why we did it...

    Last week saw the culmination of a huge mathematics project involving over 450 Senior School pupils and many staff.  Using 48 000 standard business card pieces of card – but no fixings or adhesives -  pupils and staff successfully constructed a level 3 Menger Sponge which is now on display in the Queen Katharine Building (QKB).

    The giant cube is a great example of a fractal, an object whose component parts are identical to the whole thing but on a smaller scale.  Since half term, pupils in our First to Fourth Forms plus our Lower Sixth mathematicians have each spent at least one Maths lesson building 8000 small (level 0) cube components and then making these in turn into 400 level 1, then 20 level 2 cubes before the construction by staff and Sixth Formers of the final level 3 Sponge. Many non-Maths staff also joined in, building cubes during lunch breaks.

    Designed to serve as a bit of downtime following the intensity of the end of year exams, the Menger Sponge project has stimulated plenty of discussion of mathematical concepts while giving the more senior pupils hands-on time to explore the bizarre relationship between surface area and volume as the Sponge moves down through its levels towards infinity.

    “I was inspired to build a Sponge with our pupils by a UK Mathematics Trust lecture that I attended last year,” explained Mathematics teacher, Mr Andrew Wilkinson. “It’s taken around 1000 person-hours to build and, aside from being a really interesting project that everyone has been able to contribute meaningfully to, it has become a stunning piece of mathematical art for the QKB.  It is thought that a level 4 Sponge could not be constructed from card as it would collapse under its own weight. To have the largest possible one on display – in Kimbolton colours, of course – is a tribute to the tenacity and dexterity of our pupils and staff.”

    • For more about Menger Sponges, please see this article.
    • More photos of pupils constructing the Sponge are here.


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