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

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

Outcomes

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

Collect resources

You will need:

Watch

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.]

Speaker

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]

Instructions

  • 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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