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### Number and algebra

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# Notes on a Triangle

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 ...

Which shapes will allow the same range of movements and symmetries?

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Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 11 to 14

Challenge Level

- Problem
- Getting Started
- 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?

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?