Dancing by numbers
Almost 120 years ago, Marius Petipa and his assistant Lev Ivanov choreographed a version of Swan Lake that most productions of the ballet since 1895 have been based on. The geometric designs were one of the choreography's most striking features, and the process of creating geometrical shapes through dance is alive and well today in my maths lessons.
I often use movement to illustrate mathematical concepts in lessons, but this time I went a little further, exploring the link between the sequence of triangular and square numbers.
Petipa choreographed ballet by arranging chess pieces on a board, and in similar fashion I organised the patterns in my notes before I entered the dance space. A technique I don't think Petipa used, however, was to hang laminated numbers around the necks of the dancers. I did this with my two classes of 11- and 12-year-olds so that I could keep track of them and make sure they were all in the right place. If you try out this lesson, I highly recommend this strategy.
The idea behind the dance is to illustrate how two consecutive triangular numbers make a square. It is in three parts. First, the students form a sequence of triangular numbers in groups of 1, 3, 6, 10 and 15.
Next, consecutive triangles come together: 3 and 6 make a square of 9; 10 and 15 make a square of 25. They then split into their triangles and reform: 1 and 3 make 4; 6 and 10 become 16.
Finally, all 36 students create a square. They peel off one row and column at a time to demonstrate descending square numbers: 36 to 25, 16, 9, 4, until the last dancer, number 1, is left by herself.
Dance needs an audience, so it is a good idea to give students the opportunity to perform in front of others. Following the example of the wonderful TED talk "Dance vs PowerPoint, a Modest Proposal" (bit.lyTEDDance), in which John Bohannon explores physics with a company of dancers, you may wish to have a narrator explaining what is happening. Alternatively, you could use some instrumental music as an accompaniment - music with lyrics tends to blur the message.
My pupils were delighted to be part of something different and were pleased with what they had created. They were fully engaged and understood the point of what we had done. More importantly, the dance helped them to see that there are no barriers in learning. We do not need to be limited to a classroom to see maths; it exists around us all the time and just needs to be recognised.
I believe that creativity has a key role to play in the future of maths education. This lesson is certainly a riskier way of exploring numbers than getting children to draw patterns in an exercise book, but it is also fun, engaging, memorable and accessible for many different types of learner. My students are already asking when we can create a new maths dance.
Corinne Wolfe was a ballet teacher for 10 years before retraining to teach maths. She has since taught in the UK, China and Hong Kong, and now works at the British International School in Jakarta, Indonesia. To watch a video of the dance, go to bit.lyTriangularSquares
Top 10 dance resources
1 Monster moves
What's that coming over the hill? Is it a monster doing a dance? Get your class to choreograph a routine to the song Monster by Welsh band The Automatic.
2 Dance diagnosis
Turn your class into critics with this structured writing frame for reviewing performances. Can be used for peer assessment.
3 Swan song
Give children an invaluable insight into ballet choreography with this short video from BBC Class Clips, featuring a scene from Swan Lake.
4 Sea change
Make waves by using this set of images and ideas to inspire students to choreograph dances on the theme of oceans.
5 Diary of dance
Learning and rehearsing a dance has many high and low points, and it can be beneficial to chart them. Get students to keep a record of the rehearsal experience.
6 Street spirit
Move away from traditional dance forms and embrace newer styles with this video, which demonstrates some fun and easy street dance moves.
7 Proper preparation
Print and laminate these warm-up cards to make sure your students are prepped and ready for every dance lesson.
8 Safety in numbers
Dance makes extensive demands on the body that can sometimes lead to illness and injury. Use these worksheets to ensure that all students know how to stay safe and well.
9 Indian insight
Bring the glamour of the Bollywood film industry to your classroom with these resources on Bollywood dancing.
10 Fresh look
This video explores how you can encourage students to improve through self- and peer assessment.