How to do a tangram

How to Play Tangram Puzzles and The Solutions to Solve it – SiamMandalay

Have you ever wondered what is a tangram puzzle and how to solve it? This article shows you how to play tangram puzzles, the rules and solutions to solve the wooden tangram puzzle. Let's explore new fun ways to work with shapes!

The tangram puzzle originated in China and was then brought over to Europe and America via trade ships in the early 19th century. It was immensely popular during this time, and rose back to popularity during World War I. The tangram puzzle challenges you to arrange seven separate pieces, called tans, into one shape. A set of tans consists of two small triangles, one medium triangle, one square, one parallelogram, and two large triangles. The shapes made from these pieces can be geometrical, such as a square or triangle, or something more representational such as animals, objects, or people. There are seemingly infinite different shapes that can be made from these pieces as well as multiple different ways to configure those shapes. Tangram sets are inexpensive to purchase, and are also available to be printed out or to be used virtually.

While the benefits of tangram puzzles can be seen in people of any age, they are most beneficial to young children. They are a great hands-on activity that can be incorporated into the classroom or used at home. Below are the skills that tangram puzzles can help to develop:

• Problem-solving and logistical thinking:
• Creativity
• Geometrical concepts
• Spatial relationships
• Positive relationships with math

As stated above, tangram puzzles help children learn problem-solving skills and geometrical concepts. It is for this reason that they are often utilized in math classrooms. The tans can be used to teach the relationships between different basic shapes. For example, two triangles can be combined to make a square or a parallelogram, a parallelogram and two triangles can make a rectangle, and so on. Tangram puzzles can also be used as an introduction to the concept of area. The students can use each tan as a unit of measurement and count how many tans it takes to fill different figures. Symmetry, congruence, similarity, and even fractions can be taught through different exercises using the tangram pieces. Students not only learn mathematical concepts through the completion of theses puzzles and accompanying exercises, but they also passively develop the problem-solving skills needed to effortlessly figure out the puzzles.

Tangram is very simple to play. First, you need access to the tans themselves. You can purchase a wooden tangram puzzle, print out the pieces from the internet, or find a tangram app or website. Next, arrange the tans to match the provided silhouettes or outlines. The tangram rules are just as simple.

• The pieces must all be connected
• They must be flat
• No pieces may overlap
• The tans may also be rotated and/or flipped to form the shape.
• All seven tans must be used
• Each completed puzzle must contain all seven tans.

Tangrams puzzles and solutions can be found all over the internet, but here I will explain some patterns that will help you in solving them. Firstly, remember that the combination of two triangles makes a square or a diamond. Two triangles can also be put back to back to create one larger triangle. Next, a way to make a second parallelogram piece available to you is to combine the two small triangles. A triangle on top of a square, or on top of two combined triangles, makes a type of barn shape. The points of two triangles can be connected to make a sort of bow shape. All in all, when working through these puzzles it is important to remember how to create basic shapes out of triangles. When you start thinking of the shapes more in terms of triangles, the puzzles should start getting easier and easier to solve.

Tangram puzzles serve as a solid educational tool for children as well as an endless source of entertainment for people of all ages. They are easily accessible and an inexpensive way to have fun and strengthen your brain. This classic game will surely stick around as one of the most popular puzzles in the generations to come.

July 18, 2018 — Aod Prommetchit

Educational tips and a printable template

© 2009 – 2022 Gwen Dewar, Ph.D., all rights reserved

Tangrams for kids: A learning tool for building STEM skills

Like building blocks, tangrams can teach kids about spatial relationships. They may help kids learn geometric terms, and develop stronger problem solving abilities. They might even help children perform better on tests of basic arithmetic. But what is a tangram?

Invented in China approximately 200 years ago, a tangram is a two-dimensional re-arrangement puzzle created by cutting a square into seven pieces — seven geometric shapes called “tans” (Slocum et al 2003).

What are the seven shapes in a tangram? Each tangram puzzle contains the following:

• 2 large right triangles
• 1 medium-sized right triangle
• 2 small right triangles
• 1 small square
• 1 parallelogram

Arranged correctly, these tangram shapes can be fitted together as a large square, rectangle, or triangle. They can also be arranged in a variety of complex shapes, including fanciful ones.

There are many ways to play with tangrams. The simplest way is to let kids create their own complex shapes. But traditionally, tangrams are treated as puzzles.

The player is shown a target shape in outline, so that the “seams” between the composite tans are concealed. Then the player attempts to recreate the shape using the seven pieces.

In essence, it’s an exercise similar to structured block play, where the challenge is to create an exact copy of a structure depicted in a diagram. But there’s a key difference.

In structured block play, the diagram provides you with explicit, visual information about where each piece goes. In a tangram puzzle, you’re left to figure that our for yourself.

As noted by Zhen Yuan and his colleagues, solving tangram puzzles appears to activate parts of the brain associated with creative thinking and trial-and-error problem-solving (Hu et al 2019).

The educational benefits of tangrams

When we play with tans, we consider the shapes from a variety of angles and perspectives. How would the shapes look if we stuck them together? Rotated them? Slide them around into different positions?

Experiments suggest that thinking about such things — visualizing the spatial relationships between shapes in your “mind’s eye” — can boost our visual-spatial skills.

Research hints that it can boost arithmetic performance, too. When Yi Ling Cheng and Kelly Mix asked kids, aged 6-8, to perform a series of tangram-like spatial tasks, the practice session seemed to prime the brain for mathematics.

Kids who spent 40 minutes solving shape rotation puzzles performed better on a pencil-and-paper arithmetic test immediately thereafter. Compared to tangram-like activities, crossword puzzle warm-ups had no such effect (Cheng and Mix 2012).

So there is reason to suspect that playing with tangrams has educational benefits, and many educators recommended their use in the classroom (Bohning and Althouse 1997; Krieger 1991; National Council of Teacher’s Mathematics 2003; Clements and Sarama 2014).

In particular, these teachers argue that playing with tangrams may help kids

• classify shapes
• develop positive feelings about geometry
• gain a stronger grasp of spatial relationships
• develop an understanding of how geometric shapes can be decomposed
• hone spatial rotation skills
• acquire a precise vocabulary for manipulating shapes (e.g., “flip,” “rotate”)
• learn the meaning of congruence

In addition, researchers have argued that tangram play can be an opportunity for kids move away from simplistic (and incorrect) ideas about shapes. Young children, for example, might struggle to explain what features are necessary for a shape to be a square. With guided questioning, a teacher can help kids determine why some attempts to make a square with tangrams are unsuccessful (Nic Mhuirí and Kelly 2021).

Children can also learn new vocabulary to describe the shapes they assemble (e.g., rhombus, trapezoid, hexagon). And Tom Scovo demonstrates how tangrams can help kids calculate areas without formulas. For the details, see his excellent activities using tangrams for kids in grades 4-6.

What about free play with tangrams? That’s good, too. But take note: Kids probably stand to learn much more if their play includes discussion and teamwork. 

Indeed, studies indicate that spatial play — like playing with tangrams — is particularly educational when kids interact with others who use spatial vocabulary.

For example, toddlers tend to develop bigger spatial vocabularies if, during play, their parents expose them to a greater range of spatial words, like “triangle” and “line.” As I explain elsewhere, such kids are also more likely to develop stronger spatial skills.

So it’s likely we can boost the value of tangrams by actively engaging kids in conversation. We can introduce them to words they might not know, like “angle” and “parallelogram.”

It’s also likely that kids will benefit from being asked to make predictions and explain tactics. 

Research suggests that kids are more likely to master concepts when they explain them to others. What will happen if you rotate the triangle? What will happen if you flip the parallelogram? How must we move this shape in order to make it fit?

If we can get children to explain their ideas, we may help them improve their spatial skills and comprehension of geometry (Lee et al 2009; Clements and Sarama 2014).

So while kids may benefit from solitary play with tangrams, some of the best educational experiences may arise from playing with a (talkative) partner. 

Any other teaching tips?

Tangrams offer kids an excellent opportunity to test out different geometric manipulations, and become familiar with the properties of the shapes they use.

But notice the triangles– big, medium, and small — are all the same shape. They represent a special kind of right triangle — an isosceles triangle with two 45-degree angles, and one 90-degree angle. And if you put together two triangles of the same size, you can make a square.

These properties aren’t found in all triangles. On the contrary! But it’s easy for children to come to that conclusion if they don’t get exposed to a variety of triangles — equilateral, isosceles, and scalene. So it’s important to expose kids to that variety, and call their attention to the ways in which triangles can differ (Clement and Sarama 2014). 

Getting started: How to make a tangram

You can make your own tangrams by following the instructions on Tom Scovo’s site, or by printing and cutting out the tangram shapes below.

If you right-click on the image here, you can save it on your computer for printing. Alternatively, after right-clicking, you can open the image in a new tab, and use your browser’s print function.

Looking for more durable tangrams? You can buy some. Classic Tangoes includes two plastic tangram sets and a deck of puzzle cards. But the corners are a bit sharp. You can also find tangrams made from other materials, such as wood, foam, and thick cardboard.

Tangrams for young children

My favorite introduction to tangrams for younger kids is the book Three pigs, one wolf, seven magic shapes by Grace Maccarone. Unfortunately, it’s out of print, but you might be able to pick up a copy used. It includes story (based on the folk tale of the three little pigs), a teaching guide, a set of tangrams to cut out, and some activities created by a math teacher. Although the publisher recommended this book for kids in grades 1-2, the book can be enjoyed by preschoolers.

For another, fanciful story featuring tangrams, see Grandfather Tang’s Story (Dragonfly Books).

Virtual tangrams for kids

You might wonder if computer games are as educational as playing with real, physical tangrams. The National Council of Teachers of Mathematics (NCTM) recommends both.

According to the NCTM, computer games may offer special benefits because “the computer environment is likely to encourage [kids] to think about how they need to manipulate the tangram pieces rather than approach the task mainly by trial and error.”

Read more and try out this online game by the National Council of Teachers of Mathematics.

Ideas for tangram activities

The classic approaches are either (1) to present kids with images of target shapes (and have them attempt to reproduce those shapes with their tangrams), or (2) to encourage kids to be creative, and come up with shapes of their own.

But there are additional games and activities to try as well. You can choose a theme (like “fish” “spaceships” or “houses”) and see how many different examples of each type kids can come up with. For instance, how could challenge kids to create a series of cats.

More to read about the development of STEM skills

Interested in learning more about activities that boost STEM skills? In this article I recommend a number of STEM books and learning resources for kids, including some free ones.

In addition, to read about the many benefits of construction play, see my article, “The benefits of toy blocks.” If you’re specifically interested in structured block play, check out my article, “Can Lego bricks and other construction toys boost your child’s STEM skills?”

And for more information about the development of spatial reasoning in children, see these Parenting Science articles:

• Spatial intelligence: What is it, and how can we enhance it?

• Improving spatial skills in children and teens: 12 evidence-based tips

References: Tangrams for kids

Bohning G and Althouse JK. 1997. Using tangrams to teach geometry to young children. Early childhood education journal. 24(4): 239-242.

Cheng Y-L and Mix KS. 2012. Spatial training improves children’s mathematics ability. Journal of Cognition and Development. Published online DOI:10.1080/15248372.2012.725186.

Clements D and Sarama J. 2014. Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.

Hu Z, Lam KF, Yuan Z. 2019. Effective Connectivity of the Fronto-Parietal Network during the Tangram Task in a Natural Environment. Neuroscience. 422:202-211.

Kriegler S. 1991. The Tangram: It’s More than an Ancient Puzzle. Arithmetic Teacher 38(9) 38-43.

Lee J, Lee JO, and Collins C. 2009. Enhancing children’s spatial sense using tangrams. Childhood Education 86(2):92-94.

National Council of Teacher’s Mathematics. 2003. Developing geometry understandings and spatial skills through puzzlelike problems with tangrams: Tangram challenges. www.nctm.org.

Nic Mhuirí S and Kelly D. 2021. Making squares: children’s responses to a tangram task. In: Eighth Conference on Research in Mathematics Education in Ireland (MEI 8), 15-16 Oct 2021, Dublin, Ireland (Online).

Slocum J, Botermans J, Gebhardt D, Ma M, Ma X, Raizer H, Sonnevald D, and Van Splunteren C. 2003. Tangrams: The world’s first puzzle craze. Sterling: New York.

Title image of child’s hand’s manipulating tangrams by Gwen Dewar

Line drawings of triangles and tangrams by Parenting Science

Image of many different tangram cats by Sveta_Aho / istock

Content of “Tangrams for kids” last modified 9/2022. Portions of the text derive from an earlier version of the article, written by the same author.

DIY Tangram (game schemes, figures)

Category: Crafts from different materials

Tangram - an old oriental puzzle of figures obtained by cutting a square into 7 parts in a special way: 2 large triangles, one medium, 2 small triangles, a square and a parallelogram. As a result of folding these parts with each other, flat figures are obtained, the contours of which resemble all kinds of objects, ranging from humans, animals and ending with tools and household items. These types of puzzles are often referred to as "geometric construction sets", "cardboard puzzles" or "cut puzzles".

With a tangram, a child will learn to analyze images, highlight geometric shapes in them, learn to visually break an entire object into parts, and vice versa - to compose a given model from elements, and most importantly - to think logically.

How to make a tangram

A tangram can be made from cardboard or paper by printing out a template and cutting along the lines. You can download and print the tangram square diagram by clicking on the picture and selecting "print" or "save picture as...".

Also available without template. We draw a diagonal in a square - we get 2 triangles. Cut one of them in half into 2 small triangles. We mark the middle on each side of the second large triangle. We cut off the middle triangle and the rest of the figures at these marks. There are other options for how to draw a tangram, but when you cut it into pieces, they will be exactly the same.

A more practical and durable tangram can be cut from a hard office folder or a plastic DVD box. You can complicate your task a little by cutting out tangrams from pieces of different felt, overcasting them around the edges, or even from plywood or wood.

How to play tangram

Each piece of the game must be made up of seven parts of the tangram, and they must not overlap.

The easiest option for preschool children 4-5 years old is to assemble figures according to diagrams (answers) drawn into elements, like a mosaic. A little practice, and the child will learn to make figures according to the contour pattern and even invent their own figures according to the same principle.

Level one - download and print a colored tangram, so it will be easier to navigate the diagram.

Schemes and figures of the game Tangram

This is such a multifunctional tangram.

• Back
• Forward

Tangram

2. Tangram is a puzzle that is a square cut into 7 pieces in a certain way. For preschoolers, the tangram is a great lesson to prepare for school. And at the age of 5-6 years, children love to play very much. They are interested in puzzles with pictures.

   The goal of the game is to assemble figures of people, animals, birds, numbers, objects from tangram parts ...

   Rules of the tangram game:

   • The assembled figure must include all seven parts.
   • Parts must not overlap.
   • Parts must be adjacent to each other.

   Tangram scheme

   0009

   Parts of a tangram

   This is the tangram itself, from its parts invented pictures are made. You can buy it, but it's easy to do it yourself using the construction scheme. The drawing can be printed on colored paper on a printer or drawn independently using a ruler. Cut out puzzle pieces from colored paper. Then, laying out the desired figure, glue it on a dense sheet.

   An example of a dog scheme - made by 1st grade students for a lesson in mathematics and technology.

   The tangram game for children can be in several levels of difficulty. It is better to start with the simplest - lay out the figure according to the model.

   Scheme - rocket

   This is how you can make a house out of a tangram.

   At the second stage, you can invite the children to lay out the figures in a solid pattern.

   And the third level, the most difficult: come up with your own figures that look like people, animals, birds. We offer pictures invented by children.

   Tangram scheme - fox

   Hare and a camel

   Scheme - people

   Figures - Fish

   Print a residential tangram.
   (fox, cat, hare, camel, horse, dog)

   (Clicking on the image will download a Word document file in docx format, which can be printed using Word)

   0116

   (Clicking on the image will download a Word document file in docx format, which can be printed using Word)

   There are various legends about the appearance of the tangram. Here is one of them…

   Almost two and a half thousand years ago, a long-awaited son and heir was born to an elderly emperor of China. Years passed. The boy grew up healthy and quick-witted beyond his years. One thing bothered the old emperor: his son, the future ruler of a vast country, did not want to study. It gave the boy more pleasure to play with toys all day long.

   The emperor summoned three wise men, one of whom was known as a mathematician, another became famous as an artist, and the third was a famous philosopher, and ordered them to come up with a game, while having fun with it, his son would comprehend the beginnings of mathematics, learn to look at the world around him with close eyes. through the eyes of an artist, would become patient, like a true philosopher, and would understand that often complex things are made up of simple things.

   Three wise men invented "Shi-Chao-Chu" - a square cut into seven parts.

   Many figures can be obtained from tangram parts.

   ---

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