Tag Archives: Cross Curricular

I Need Some Space…

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It hurts quite a bit when you stub your toe. Try being hit by a whole galaxy! Because that’s exactly what’s going to happen. The galaxy Andromeda (our closest spiral galaxy) is speeding towards us a massive 260,000 miles an hour…

Before you start planning for doomsday you might want to consider galactic distances. It is absolutely true that Andromeda is speeding towards us at an incredibly high speed, however, due to the gargantuan distance between us it will be more than 4 billion years before it gets anywhere near us. So you can stop breathing into a paper bag now.

This beautifully demonstrates the vastness of the universe in which we live. Something which we consider massive (take the earth for instance of which the diameter is 1.2756 × 10^7 or 12756000 meters in diameter) is tiny compared to the size of the universe (9.2 × 10^26 meters or 10 billion kilometres in diameter). This also illustrates the importance of fundamental areas of mathematics such as base systems. For example when using very large or very small numbers we use standard notation (used above) instead of attaching many zeros to a number to demonstrate its size. An example that shows why we switch when using extreme numbers is; imagine trying to give directions to Edinburgh using only millimetres. This would be very confusing, so instead we switch to using kilometres.

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Pictured: Ngc 2207, Spiral Galaxy

However telling you that the universe is 10 billion kilometres wide does nothing really to explain just how massive it is. An area which I find fascinating is light years. This is the distance which light will have travelled within a year. As I am sure you are away, light travels unbelievably quickly (just think about how fast a room changes from light to dark when you switch a light on, it is near instantaneous). The actual distance light can travel in a year is 9.46 × 10^15 meters or 9.5 trillion miles. Now, the nearest star to our sun is Proxima Centauri, and I stress that this is the nearest to us. For light (the fastest moving thing we know of) to travel from Proxima Centauri to us would take 4 years (Yes, that does mean we see 4 years into the past when looking at Proxima Centauri). Now imagine how long it would take for light to travel across the universe! Or how long it would take for a human spacecraft to travel that far!

Before we were given an input on astronomy earlier this week, I knew very little of the content explored within this blog. This is something I think is a shame, as I’m sure this is an area I would have found hugely interesting as a child in primary, much more so than simply learning the names of the planets in our solar system and that they all go round the sun (though of course I concede this is vital knowledge to have).

As a future practitioner this is an area I would very much like to explore with my class. To learn about the solar system which we live in, but to also introduce the notion of fundamental mathematics within this subject area to further explore the world of astronomy and mathematics in an exciting and engaging way.

It’s maths, Jim, but not as we know it…

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When a string is plucked, it vibrates at a particular rate creating a note. A familiar concept to violinists, guitarists, cellists and…well anybody who plays a stringed instrument, and I’m sure anyone who has ever fired an elastic band across a room. The rate at which this string vibrates is known as the frequency (determined by string thickness, density, length and tension, f=(1/2L)√(T/μ)) which is measured in Hertz(Hz). As humans we perceive these frequencies within a given range as pitch. The range begins at about 20Hz and goes up to approximately 20,000Hz. For example concert A (the tuning pitch for orchestras) is 440Hz and middle C is 261.63Hz.

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It’s probably at this point you’re beginning to wonder “In what way could this information possibly be useful?”.

Well, as many of you will know some notes sound better together than others (if you’re not aware of this, have a look at this video, about 3 minutes in). This has to do with how the two note’s frequencies are related. Notes whose frequencies are related by simple fractions tend to sound better together. Let’s take for example the note of A which we know to be 440Hz. If we half the frequency to 220Hz we arrive at another note of A only an octave down. Similarly if we double the frequency to 880Hz this is also the note of A, this time an octave up.

Taking this to the next level we can apply more complex fractions. If we take 3/2 of 440Hz we arrive at 660Hz or E and if we take 5/4 we arrive at 550Hz or C#. These are the fractional relationships between a major chord and by playing A, C#, and E we are actually playing the chord of A major. It is because of this fractional relationship we find harmonics (demonstrated rather nicely in this piece of music by Daniel Padim) situated exactly halfway, one third along, and one fifth along the string length of a guitar.

So, after all that, why would I write a blog about this? Apart from the fact that this is a very exciting application of maths. I suppose this was my rather long-winded way of demonstrating the often forgotten, cross-curricular nature of mathematics, and that perhaps (despite a very finely categorised curriculum) we should embrace the concept of learning in a way that accommodates individual difference and that allows for the blending of curriculum areas of which (Savage, 2010) describes as ‘sending a positive message to the children’ and as ‘rich pedagody’.

It seems that wherever I look there is always some aspect of maths to be found. Perhaps it could be combined with more curricular areas than just music…