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12 equilateral triangles

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."

Prompt sheet

Language acquisition as the first phase of inquiry
Sonya terBorg
blogged about using the prompt with her primary class in Idaho (US). The post describes how the class carried out a preliminary inquiry into concepts and language related to angles. The pupils then conducted an open and collaborative inquiry by applying the language acquired in the earlier phase.

You can follow Sonya on twitter @terSonya.
Alternative prompt
Billy Adamson 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."

Prompt sheet

Billy Adamson is the Head of Mathematics at Thurston Community College (Bury St Edmunds, UK). You can follow Billy on twitter @Billyads_47.