Tangram: A Traditional Game of Geometrical Puzzle
- Apr 25, 2016
- Sudipto Das
Tangram is a type of dissection puzzle that consists of 7 flat shapes. A dissection puzzle, also known as transformation puzzle is a form of puzzle where a number of pieces are assembled in different manners for producing geometric shapes. The 7 flat shapes that are present in a tangram are known as “tans”. The main objective of the players should be to design a specific geometric shape using the 7 flat shapes (“tans”) of this game. The players would have a specific outline of the shape that they have to construct with the 7 pieces. The players should use all the 7 pieces to make the figure. Another thing to remember is that the “tans” should not overlap each other. Let's go through the various attributes of this puzzle in more details.
The 7 “Tans”
- 2 large right-angled triangles,
- 1 medium sized right-angled triangle,
- 2 small right-angled triangles,
- 1 small square,
- 1 parallelogram.
The 7 “tans”
Image courtesy- https://cdn-1.parentingscience.com/images/Tangram-rabbit.jpg
The above shapes can be fitted together to form a variety of complex geometric shapes. The following picture can be taken as an example.
Various geometric shapes made from the 7 “tans”
Image courtesy- https://vickimartinez.com/tangram_pic.jpg
How to Play
There are plenty of ways to play tangrams. Generally as well as traditionally, the rule is to provide the players with a specific shape that they have to create using the 7 flat pieces. That's the target that needs to be fulfilled by the players. But for starters, it's better to avoid the inclusion of targets at least at the start. They should try to make any complex shape as per their choice with the 7 “tans”, provided that the complex shape formed by them carries a meaning from the point of view of geometry. The “tans” can be rotated, placed at different positions as per the players' choice but there's a catch that's already explained above. The “tans” should not overlap each other.
How to make Tangrams
Tangrams are available for purchase here but they are pretty easy to make as well. All you'll be needing is a piece of paper shaped in the form of a rectangle that can be folded easily for your benefit, a ruler and a pair of scissors. You can also use a cardboard in place of a paper to ensure that your tangram pieces are robust enough thereby providing the pieces with more durability. After that you can follow these steps.
Step 1: The rectangular piece of paper needs to be folded in a manner which gives a square in the end. The extra part needs to be cut off by using the scissors. We strongly recommend adult supervision while you are handling sharp objects like scissors. Please go through the following diagram to understand this step in more detail for your reference.
Image courtesy- https://mathforum.org/trscavo/tangrams/graphics/fold-fold-cut.gif
Step 2: The square needs to be cut into 2 triangles like the way it's shown in the picture below.
Image courtesy- https://mathforum.org/trscavo/tangrams/graphics/cut.gif
Step 3: Now pick any triangle of your choice from the ones above and fold it like the way it's shown in the figure. The triangle picked in the figure is the one marked “A”. After that, you can cut it along the fold shown below to make 2 more triangles.
Image courtesy- https://mathforum.org/trscavo/tangrams/graphics/fold-cut.gif
Step 4: Pick the other one “B” and do the following depicted in the picture below. You'll get a trapezoid and another triangle.
Image courtesy- https://mathforum.org/trscavo/tangrams/graphics/crease-fold-cut.gif
Step 5: The trapezoid should then be folded in half followed by another fold like the way it's depicted below. Cut the trapezoid along the folds to get a small triangle, a small square and a smaller trapezoid.
Image courtesy- https://mathforum.org/trscavo/tangrams/graphics/fold-fold-cut2.gif
Step 6: The smaller trapezoid shown above is folded like the way depicted below and is also cut along the fold to get a parallelogram and another small triangle.
Image courtesy- https://mathforum.org/trscavo/tangrams/graphics/fold-cut2.gif
After completion of all the above steps, you'll be set to start with your very own tangram. The figures marked above in numbers i.e. 1, 2, 3, 4, 5, 6, 7 are your seven “tans”.
Tangram figures and solutions
The picture provided below will provide you with some figures that you can construct with tangrams. The solutions are also provided in the same. Try to construct the figure first without looking at the solutions. The best way to do that is to print out the following picture and cut it into two in which one part will contain the problems and the other will contain the solutions. If you are stuck in a problem, you can consult the solution for your reference. There are countless other tangram problems on the internet. You can check them out as well.
Tangram Problems and Solutions
Benefits of this Game
Playing with the "tans" develop the critical thinking ability of the players. They'll develop the various ways to visualize the spatial relationships between geometric shapes mentally and implement it into action for achieving the target which is the final figure that they have to construct using the tangram pieces. This is immensely beneficial in mathematics and in various STEM education. Tangrams can give them an idea of area and perimeter of certain figures. Tangrams are suitable enough for the players to understand the ways to calculate the area of composite geometrical figures where the given problem has to be broken into smaller known figures for the solution. To sum up, the benefits of Tangrams are explained below:
- Tangrams helps the players to identify and classify shapes.
- Increase an affinity to geoometry and also develop a positive attitude in the players to solve certain geometrical problems.
- Increase the players' ability to comprehend spatial relationships.
- Sharpen spatial rotational skills.
- Gives them a clear idea of various ways to manipulate shapes (for example, flip and rotate etc.).
- Develops certain geometrical as well as mensuration skills like similarity, congruency, area, perimeter etc.
Mathematics is dreaded by many students because of the abstract nature of the subject. It may be abstract in nature but its importance can not be ignored in STEM education as well as in many other fields of education and daily life. Certain mathematical games and puzzles will help you out immensely if you fail to grasp certain concepts of Mathematics. Tangram is one such game based on puzzles that may develop your mathematical concepts relatated to geometry. There are various other after-school on-line mathematics classes and activities that might help you out immensely for developing and strengthening your concepts of mathematics. The best thing is that these classes are pretty fun as well as engaging.
Image by Anthony J
Sudipto writes technical and educational content periodically for wizert.com and backs it up with extensive research and relevant examples. He's an avid reader and a tech enthusiast at the same time with a little bit of “Arsenal Football Club” thrown in as well. He's got a B.Tech in Electronics and Instrumentation.
Follow him on twitter @SudiptoDas1993
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