Tangram and Fractions

Author:
Simona Riva
Topic:
Area, Fractions, Geometry, Isosceles Triangles, Parallelogram, Right Triangles, Square, Triangles
In the picture below, the Tangram pieces have been put together to form a square. You have already discovered here that:
  • the area of the big triangle is twice the area of the medium triangle
  • the medium triangle, the square and the parallelogram have the same area
  • the area of the medium triangle is twice the area of the small triangle

Fractionization!

Now consider the Tangram pieces as fractions of the square that they form in the picture. Compare the areas of the pieces and answer the following questions.

If the big square, built using all the Tangram pieces, represents one whole, assign a fraction value to each of the other Tangram pieces. Explain your answer.

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Among the Tangram pieces there are two (congruent) small triangles: if one of them represents one whole, assign a fraction value to each of the other Tangram pieces. In this case, the values corresponding to the other pieces are integers or fractions? Explain your answer.

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Among the Tangram pieces there is a small square: if it represents one whole, assign a fraction value to each of the other Tangram pieces. Explain your answer.

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Among the Tangram pieces there is a medium triangle: if it represents one whole, assign a fraction value to each of the other Tangram pieces. Explain your answer.

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