In his Metamagical Themas: Questing for the Essence of Mind and Pattern, Douglas Hofstadter talks about numerical literacy, the ability to understand large numbers. This is especially important when state budgets are thrown around which deal with billions of pounds or euros. At some point you just lose all feeling for quantities, as they are all so unimaginably large and abstract. He then goes on to pose some rough calculation questions, such as “How many cigarettes are smoked in the US every day?” – you start with some estimates, and then work out an answer, which might be near the order of magnitude of the right answer (which we of course don’t know). Quite an interesting and useful mental exercise.
Yesterday we had Fish & Chips for dinner. The girls were comparing the sizes of their chips, and then we came on to the topic of the longest chip in the world. Obviously, with ‘proper’ chips this is limited by the size of the source potato. However, assuming that industrially produced chips are made of mashed potato formed into chip-shapes, there is not really any fixed limit on the length. So, thinking of Hofstadter, I asked them how many potatoes we would need to make a chip that spans around the whole world.
Rough assumptions: one potato contains enough matter to produce 10cm worth of chip (the thickness is not specified). So, how many potatoes do we need for one metre of chip? This is also useful to practice basic primary-school-level maths… – 10. How many for a kilometre? 10,000. How many kilometres do we need to span the world? Roughly 40,000 km. So how many potatoes do we need? 400 million.
The next question is whether there are enough potatoes in the world to do this. Assuming a potato weighs 100g, how much do our 400 million potatoes weigh? 40 million kilogrammes, or 40,000 (metric) tons. What is the world’s potato production? According to Wikipedia, this is 315 million metric tons, so plenty enough. Now, if we were to turn the annual potato crop into one long chip, how many times would it go round the Earth? 7,875 times.
So, with a bit of basic maths (and Wikipedia for the data) you can make maths exciting for kids, practice how to multiply and divide, teach problem-solving, and have fun at the same time. And they also get a feeling for numbers: 400 million – that’s how many potatoes you need for a chip to span the Earth.