Tangrams (reimagining wholes)

Stage 3 – A thinking mathematically targeted teaching opportunity focussed on investigating the fractional value of tangram pieces using the square piece as the whole


Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023


  • MAO-WM-01
  • MA3-RQF-01
  • MA3-RQF-02

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Watch Tangrams (reimagining wholes) (1:15).

If a square tangram piece is 1, what is the value of the other pieces?

[A title over a navy-blue background: Tangrams 4 – part 1. Small font text in the upper left-hand corner reads: NSW Department of Education. In the lower left-hand corner is the white waratah of the NSW Government logo.

On a blue sheet of paper is a lined notebook with a cut-up green square piece of paper on it.]


All right mathematicians, welcome back. I'm back with your next challenge. Last time we were talking about fractions, and we were saying we defined the whole…

[The speaker traces the outline of the square with her finger.]

…as the outside of the entire tangram put together as a square, our original square sheet of paper. This time, my question for you is, now what are each of the individual pieces of my puzzle worth if one…

[She places a red square with a ‘1’ over the green square.]

…is actually now defined as this square? So if this is one, my parallelogram…

[She points to the bottom green triangles with writing: 1/16.]

…can no longer be 1/16 combined with 1/16, which is 1/8. It has to be worth something to... something else. So back to you mathematicians, to work this out. If this square…

[She points to the red square.]

…is defined as one whole, what are all the other pieces of my tangram now described as? Over to you! Have fun with your sweaty brains.

[Text over a blue background: Over to you!]

Over a grey background, the red waratah of the NSW Government logo appears amongst red, white and blue circles. Text: Copyright State of New South Wales (Department of Education), 2021.]

[End of transcript]


  • If the red square is now defined as 1 whole, what is the value of all the other tangram pieces?
  • Record your thinking in your workbook.
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