Notes on a triangle
Can you describe what happens in this film?
Age
11 to 14
Challenge level
Problem
For this task, you will need to watch the short film Notes on a Triangle, on the National Film Board of Canada's website.
How would you describe what happens in the film?
Can you describe what happens in different sections of the film?
For example, 1 - 34 seconds and 35 - 45 seconds may provide two natural sections to focus on at the beginning.
What mathematical properties remain constant throughout your chosen clip?
Could a section of the dance be performed by a different shape?
Imagine replacing the triangle with a kite, or a rhombus, or an arrowhead, or ...
How would you cut up your new shape to produce congruent pieces?
Can your new shape(s) still achieve the same movements and symmetries?
If you produce a wall display do send us some photos.
Here is a sheet of equilateral triangles for you to print off and cut out (using coloured paper might be a good idea) if you want to recreate some of the images in the film.
Getting Started
You can pause the film at any point to look carefully at the images.
Teachers' Resources
Watching the film may stimulate lots of discussion about properties of triangles, symmetry and rotation.
If you want to watch it directly from the National Film Board of Canada's website, go here
You could ask students to watch it twice, then talk about what they saw in pairs before having a whole group discussion. Students might notice the different ways in which the initial triangle is split during the film and it might be handy to have some large copies of the triangle available so that they can demonstrate what they saw in the film.
This initial discussion offers a good opportunity for you to draw out well articulated descriptions.
Choose a section of the film and ask students to describe what happens there.
eg 1 - 34 seconds and 35 - 45 seconds may be two natural chunks for students to start to focus on.
What mathematical properties remain constant throughout the clip?
Students can recreate short sequences using cut-out triangles.
Here is a sheet of triangles that can be printed off and cut out.
Ask students to consider if a section of the dance can be performed by a different shape.
If the triangle is replaced with a kite, or a rhombus, or an arrowhead, or ...
can the new shape be bisected into
congruent halves?
can the new shape be trisected into
equal thirds?
can dissections be carried out in
different ways?
Which shapes will allow the same range of movements and symmetries?