The Cultural Olympiad which has run parallel to the 2012 Olympics comes to an end on the 9th September as the 2012 London Paralympics draws to a close. This summer’s finale was the end of four years of cultural events that went hand in hand with the preparations for the Olympics. Through art, music, theatre and literature, the Olympiad has sought to exercise our brains and emotions in the same way the sporting events exercised our bodies.
You might think it strange that we can include maths in activities related to the Cultural Olympiad but then maths does pop its head up in the strangest environments.
Activity One – Maths and Music
LO: To be able to recognise the link between maths and music in terms of counting
Recognise how changing the length of notes can change a piece of music
It’s long been recognised that good musicians make good mathematicians and vice versa and this activity seeks to make the link between the two disciplines clearer. In fact the Old English word for number was ‘rim’ from where it is thought the words rhyme and rhythm come.
Music is all about timing – you need to count beats to play a piece as the composer wrote it, then there are the number of beats each note is held for which sets the overall tone of the piece.
This activity lets the children see how counting is linked with the playing of a piece of music.
Use the score from a recorder book and annotate the notes as to the number of beats it has. Play the piece and count the beats as you play.
Talking Point: How many beats are there in a bar? Does it vary with the style of music?
Now change the piece to all notes being the same duration and play it again.
Talking Point: What difference did it make? Can we recognise the piece still? Is it better or worse?
Ask the children to look at the number of beats that each style of note has
Talking Point: What do you notice about the sequence?
Now ask the children to compose a simple piece themselves that they can play on a recorder. Ask them to consider the length of each note they write and then get a partner to play it.
Talking Point: Did it sound like they intended it to?
At Home: Change the duration of the notes in your composition and play it again. Keep experimenting until you find an alternative you like.
Activity Two – Maths and Poetry
LO: Be able to understand how poetry and rhyme depends on number sequences and patterns
Experiment with different number patterns in the syllable count of poems to produce effect
Just like in music, poetry relies on maths through counting to help it rhyme, flow and have structure. This activity helps the children to see the importance of counting syllables to help a poem work.
Read the following poem to the children:
Today I wrote this poem, (7 syllables)
but I’m not sure if it’s good. (7)
It doesn’t have the things (6)
my teacher says it should. (6)
It doesn’t share the feelings (7)
I have deep inside of me. (7)
There are no metaphors (6)
and not one simile. (6)
At this point the metre of the poem changes.
Talking Point: Get the children to count the syllables and then to say if they think the rhythm still sounds right.
It’s missing some narrative.
It isn’t an acrostic,
diamante, or haiku.
There’s nothing that’s personified.
It doesn’t have a plot.
I’m pretty sure that rhyming
is the only thing it’s got.
It sure was fun to write it,
and I think it’s long enough.
It’s just too bad it’s missing
all that great poetic stuff.
I put it on my teacher’s desk
and, wow, she made a fuss.
She handed back my poem
with an A++++!
Now try this one…
I went out to tea with my friend James today
He lives far away
He lives in a big caravan
With his pretty mum called Terri and his clever dad called Dan
Talking Point: Ask the children if they think this is a poem and how they came to their decision.
Some will say that it rhymes so it’s a poem whilst others will notice that the metre is awkward and despite rhyming words, it can hardly be called a poem.
Now investigate the syllable count of Haikus, sonnets, limericks and diamante poems. Do all of them follow the same syllable count? Do you think they all work? Which is your favourite?
At Home: Experiment with your own poem using a number pattern of your own. A simple one is similar to the diamante in doubling the syllables each time or alternate in a pattern such as 4,1,4,1 etc.
Activity Three – Maths and Art – the Golden Ratio
LO: Understand how ratios are calculated
Be able to identify where the golden ratio has been used in art and nature
The Golden Ratio has been talked about now for over 2,400 years and appears in many aspects of our daily lives. The ratio or approximations of it are used for architecture, postcard size, widescreen TVs and more whilst it is believed it’s also seen in nature, most prominently in the spiral of a nautilus shell. For the layman, it’s the measures used to make sure something looks aesthetically pleasing, be it buildings or paintings and is linked to perspective. Its use in art, despite being a mathematical expression, is a hot topic still today with academics arguing whether it was used deliberately in the works of Leonardo da Vinci, Dali and Mondrian or whether their keen artistic eye simply found the best proportions anyway.
If you want the explanation of how to get the Golden Ratio, imagine two numbers. If the ratio of the bigger to the smaller is the same at the ratio of the sum of the two numbers to the bigger one then they said to be in the Golden Ratio.
Now for the activity…
Show the children a picture of a nautilus shell and trace the spiral with a thick pen. The picture the children are going to draw will imitate it using a mathematical sequence.
Give each child a piece of cm2 paper and ask them to draw a square in the middle, 1cm x 1cm adding another above it. Then draw a 2cm x 2cm square alongside it then a 3cm x 3cm square underneath it. Continue drawing squares whose sides are that of the next numbers in the Fibonacci sequence so next they will draw a 5cm x 5cm square alongside it.
There’s no need to draw in the diagonals but instead use the measurements with a compass to make a quadrant where the quarter circles touch each other. Keep going and soon you’ll discover the picture is the same as the spiral of the nautilus shell.
Now get the children to use a calculator to work out the ratio of each of the numbers in the Fibonacci series to each other.
Talking Point: What do they notice about their answers?
They should find that the numbers begin to approach the Golden Ratio of 1.618.
You can follow up this activity with a look at the paintings which use the Golden Ratio in them such as Dali’s sacrament of the Last Supper and Mondrian’s Composition with Grey and Light Brown and ask the children to identify where the ratio has been used.
At Home: How many examples of the golden ratio can you find in your daily lives?
Encourage the children to look at buildings, playing cards, postcards, TV screens etc.