12 equilateral triangles

The prompt

Mathematical inquiry processes: Interpret; explore; find rules; generalise. Conceptual field of inquiry: Angle properties of equilateral triangles; tessellation.

The prompt was devised by David Aaron (a primary teacher in Blackpool, UK) for his year 6 class. The inquiries that developed from the prompt covered, amongst other things:

  • Angles in triangles

  • Angles on a straight line

  • Angles around a point

  • Symmetry

  • Angle properties of parallel lines

  • Exterior angles

  • 2-d shapes composed of equilateral triangles

  • The number of equilateral triangles of different sizes in the prompt.

David said: "All this in one lesson! I had to rein things in, but it personalised the learning brilliantly."

An alternative prompt

Billy Adamson, Head of Mathematics at Thurston Community College (Bury St Edmunds, UK), used this prompt (originally from the SMILE Wealth of Worksheets) with year 8 classes as an introduction to shapes and angles. He reported that the prompt led to "great exploration" (see an example below) and he "loved the energy and excitement the students displayed."

A year 8 student annotated the diagram.

Exploring the prompts

The pictures come from pupils in a Year 5 class at Living Waters Lutheran School (Alice Springs, Australia). Rebekah Clark, their teacher, describes the inquiry: "I gave the pupils the choice of the two prompts at the beginning of the unit on angles. Most of them chose to label and classify angles first, then started to find the degrees by using other angles in the image." Rebekah concluded that it was an "awesome start to our unit on angles that involved fascinating discussions and misconceptions."