Making estimates about space

Do astronauts cut their hair in space? Recently, I’ve been exploring space in my mathematics classroom. The new curriculum requires students to study mathematics in an unfamiliar context, and the setting of space can provide an engaging way of covering familiar mathematical ideas.

Additionally, the new GCSEs in science and design and technology include an increased amount of mathematical content. In the same way that other departments can help my student’s progress in mathematics, the more science and engineering content I can include in mathematics the better.

Nobel Prize winner Enrico Fermi was an Italian physicist, born in 1901. He is primarily known for creating the world’s first nuclear bomb but was also known for his ability to make good approximate calculations to questions with little, or no information available.

These types of problems are now known as Fermi questions (or Fermi problems, or estimates) and typically involve making good approximate calculations with little, or no actual information. The classic Fermi question asks “How many piano tuners are there in Chicago?” Recently I’ve been using these types of problems, which can be solved in a series of steps using a set of plausible estimates, in my mathematics lessons when looking at space exploration.

Tim Peake’s mission lasted roughly six months. Do astronauts cut their hair in space? If not, how long would it be when he returned? How long would his fingernails be? Do you think he recorded his favourite TV shows when he was away? How many Match of the Day episodes did he miss? How many goals do you think that would be?

Once returned to Earth, many students would love to meet Tim Peake, but how likely is that? How many people do you meet a day? A week? A year? What are the chances of ever bumping into an astronaut in daily life?

There are more serious matters that these plausible estimates can relate to. It takes six hours in a cramped capsule to get to the ISS - how much oxygen is needed to ensure the three astronauts arrive safely? Living in a zero gravity environment can put a lot of strain on the body. Muscle mass reduces, including that of the heart muscle. If his heart has to beat 10% more frequently to compensate, could this be an extra million heartbeats?

The more often our mathematics students can be exposed open-ended questions, in a variety of contexts, the better equipped they will be when applying their mathematics in other subjects, now increasingly important in GCSE science and design and technology, as well as in their future careers. Why not use Fermi estimates to explore what your students know about space?

You never know, in your classroom might just be the next Tim Peake.

All of the ideas discussed above, and more, can be found in the ‘Principia Mission- maths in space’ resource, found  here.

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