Tangrams
Introduction
The Chinese tangram puzzle (see picture on the right) was know as far back as 1813 and it has remained popular ever since. It consists of seven simple geometric pieces that form a a square.
2 Piece Tangram
Let's begin with an easier version with only 2 pieces though. Look at the green square on right that has been cut into two pieces. It is possible to fit the pieces together again to make a new shape. If you must match whole sides to each other so that the corners meet, how many new shapes can you make? Either use this (PRINT ME) to explore or try interactively on nRich here.
7 Piece Tangram
Now, let's try to make a tangram with a piece of square paper. Can you do it? If you need a hint, look here or below.
For each of the smaller shape, can you find all the angles?
What have you noticed about the angles? Hint: think multiples.
Can you name each of the smaller shapes? How may line and rotational symmetries do they have?
World of Tan
Let's now dive into the world of Granma T, who owns a removals business in China. Here you will find a series of stories relating to Granma T, her grandchildren and colleagues, each one accompanied by one or more interactive tangrams. Join them on their adventures and enjoy creating different pictures from the seven tangram pieces. Alternatively, you may prefer to explore the interactive tangrams (CLICK ME) separately from the stories.
Further Questions and Challenges
There are altogether 13 possible convex polygons you can make with tangrams (click on the hyperlink if you are not sure what a convex polygon is). As a class, can we make all 13 of them? Use this interactive tangram to help.
For each one:
Classify the shape.
Describe the symmetries.
Calculate the sum of interior angles of each polygon. What can you conclude?
Find the perimeter.
Easier option – measure the side and the length of the completed tangram square – ie their original square piece of paper.
Harder option – if x = side length of original square and b= ½ the diagonal, find expressions for the perimeter.