Grandfather Tang's Story

Ann Tompert (Crown Publishers, (New York, 1990)), published a book called Grandfather Tang's Story that uses Tangram 7 pieces as illustrations- you can learn more about Tangram here.
The idea can be very useful in a class room or even at home while playing with our restless.

The story goes like this:

Grandfather Tang

Tangram Grandfather Tang

and Little Soo

Tangram- Little Soo

were sitting under a peach tree in their backyard.

Tangram- Tree

They were amusing each other by making different shapes in their tangram puzzle.

"Let's do a story about the fox fairies, (Chou and Wu Ling)," said Little Soo. So Grandfather Tang arranged his seven tangram pieces into the shape of a fox.

Tangram- Fox

Then Grandfather Tang made another fox with Little Soo's seven tangram pieces. Little Soo clapped her hands as her grandfather began.

Although Chou and Wu Ling were best friends, they were always trying to outdo each other. One day this rivalry almost brought their friendship to a tragic end. They were sitting under their favorite willow tree beside a river talking about their magic powers.

"I can change myself into a rabbit as quick as wink," boasted Wu Ling. "I'll bet you can't do that."

"I can too," said Chou.

"Can not," said Wu Ling. "Anyway, actions speak louder than words." and he changed himself into a rabbit.

Tangram- Rabbit

"Not bad," said Chou, smoothing his whiskers. "But watch me do better than that."

And before Wu Ling could blink, Chou changed from a fox into a dog.

Tangram- Dog

Now, when Chou changed himself into a dog, he not only looked like a dog, but he felt like a dog and acted like a dog. He bared his teeth and lashed his tail. Wu Ling shivered and twitched his nose.

"I love rabbits," Chou growled," and I'm going to get you and gobble you up."

The dog edged closer and closer. Wu Ling's eyes grew bigger and bigger. He was too frightened to move at first. But then he thought, "I'll be safe if I can climb up the willow tree."

His little puff of a tail grew long and bushy and his tall ears shrunk as Wu Ling transformed himself into a squirrel.

Tangram- Squirrel

Wu Ling sprang into the willow tree and scrambled to the top.

"Chou will probably turn himself into a cat so he can climb up the tree after me," Wu Ling said to himself. "But he'll never catch me, I'll jump from tree to tree and he won't be able to follow me."

Of course, Chou thought about changing himself into a cat.

Tangram- Cat

"But that's just what Wu Ling expects me to do," he said to himself. "What can I do to surprise him?" He thought and thought. "I know. I'll swoop down upon him from above" And he turned himself into a hawk.

Tangram- Hawk

Chou circled round and round in the sky above the willow tree, searching for Wu Ling. Wu Ling peered through the leaves of the tree, looking for Chou on the ground. Round and round Chou circled the willow tree until he spied Wu Ling.

"Kek! Kek! Kek!" he shrieked as he zoomed down upon the squirrel.

Wu Ling trembled. Chou's beak looked sharp enough to pierce right through him.

"If only I lived in a shell house," he thought "Then Chou couldn't hurt me."

Chou stuck out his fierce claws to seize Wu Ling, but Wu Ling dove toward the river below the willow tree. And as he dove, he tucked in his head and tail and legs, turned green, and changed into a turtle.

Tangram- Turtle

Wu Ling climbed up on a mossy rock in the middle of the river. He thought he was safe because he looked as if he were a part of the rock. Chou circled round and round, searching and searching, until his sharp eyes spotted the turtle. Then he swooped down, down, down toward him.

But just as Chou reached him, Wu Ling plunged into the water. "Follow me and you'll drown, he cried.

"Don't worry," cried Chou, plunging right behind Wu Ling.

His body grew longer, covered with scales. He whipped the water with his long, wicked tail. And he snapped his spike-toothed jaws as he turned into a crocodile.

Tangram- Corcodile

Wu Ling circled round and round as he plunged down, down, down to the bottom of the river. Chou lashed his wicked tail as he plunged after Wu Ling. Just as they reached the bottom, Chou clamped Wu Ling in his spike-toothed mouth.

"Now, I've got you!" he bellowed through his clenched teeth.

"Oh, no, you haven't," cried Wu Ling, who grew smaller and smaller and changed himself from green to gold as he transformed himself into a goldfish.

Tangram- Goldfish

and he swam out of Chou's mouth between his spiked teeth.

Then he hid in a patch of cattails. Chou churned the water with his lashing tail as he charge into the patch after Wu Ling. With his head swinging back and forth and his eyes darting here and there, he searched for Wu Ling. Wu Ling knew that Chou would not give up until he found him.

"I must fly from here," he thought. And he started to honk as he transformed himself into a goose.

Tangram- Goose

"Honk! Honk! Honk!" called Wu Ling. And he took to the air.

A chorus of honks swelled the air as the flock of geese spread their wings to follow him. While Chou watched, the honking grew fainter, the flock grew smaller, and he felt his anger slowly drain away.

"Why, oh, why did we play that stupid game?" he moaned. "I'll never see Wu Ling again"

He closed his eyes and sank toward the river's bottom. Just as he touched it, however, he had an idea. And up he popped again, a goose himself.

Chou charged after him, but Wu Ling spread his wings and took to the air.

Chou watched him fly to a small island where a flock of geese were feeding. By now he was not only very angry, he was also very hungry. He decided that if he could not catch Wu Ling, any goose would make him a good dinner. He splashed through the water toward the island until he reached it.

Moments later, Chou was flying after Wu Ling and the other geese. He could hardly see or hear them at first. But he did not let this discourage him. Calling upon every last bit of his strength, he forged ahead.

Each flap of his wings brought him closer. The wedge of geese slowly grew bigger. The honking grew louder. At last Chou found himself flying beside Wu Ling.

"I'm tired of our silly game," he cried. "Come back with me to our willow tree."

Before Wu Ling could answer, something stung Chou's right wing. He sank toward the ground.

A hunter had shot him. Wu Ling flew down beside Chou, place his left wing under Chou's smashed right wing, and together they fluttered down to the edge of the forest.

The hunter ran toward them.

"Fly away," Chou urged Wu Ling. "Save yourself. Fly! Fly!"

"I wont' desert you," cried Wu Ling. And with a mighty roar, he changed into a lion.

Tangram- Lion

The hunter raised his bow. Wu Ling sprang toward him and knocked the bow from his hand. The hunter fled, leaving his bow behind.

Wu Ling and Chou returned to their fox shapes. And Wu Ling helped Chou to his den, where he took care of him until he was mended.

"Did they ever play that game again?" asked Little Soo.

"Many times," said her grandfather. "But they were very, very careful,"

"That was a good story," said Little Soo. "Let's do another."

Grandfather arranged his seven tangram pieces.

"Is this story going to be about a man?" asked Little Soo.

"Yes, said her grandfather. "he's old and he's tired. He wants to sit under a tree and rest awhile."

Tangram- Grandfather Tang

"Is he a grandfather like you?" asked Little Soo. "Yes," said her grandfather just like me." Little Soo arranged the seven pieces of her tangram beside her grandfather's.

Tangram- Little Soo

"Is that a little girl?" he asked.

"Yes, said Little Soo. "Just like me. She'll sit and rest beside the man."

"That will make him very happy," said Grandfather Tang. "And now, Little Soo, what will we do?"

"We'll sit and rest together until Mother calls us for supper," said Little Soo.

"That will make me very happy," said her grandfather.

Et Voilá!
Try to make your own stories with the 7 Tans!

Enjoy!

Tangram- some cool videos about this math puzzle

Today, on invited restless mind, we have some videos for you about Tangram:

And to finish, my favourite:

Et voilá!
7 dancing "tans" to make nice images, can you do it?

Enjoy!

Tangram legend- Yu and God of Thunder

We can find a lot of legends about Tangram, its impossible to know witch one is true. we found 4 different versions about the origin of this millenary game. The first three are the most common, but the fourth one is the most surprising and interesting. 

The messenger and the Emperor
"Once upon a time 4000 ago, a messenger came to the Emperor Tan with a square mirror, when he dropped to the ground. But he dropped the mirror on the ground and it shattered into seven pieces.
The messenger tried to join the seven pieces in order to reassemble the square. While trying to solve the problem, the messenger has created hundreds of types of people, animals, plants, until finally he made it. "
from here

The disciple and the master
"Once upon a time a young chinese was saying goobye to his master.He was about to take a great trip around the world.
On this occasion, the master handed him a square mirror and said:
-With this mirror, record everything you see on your trip to show me when you get back.
The disciple, surprised, asked:
-But master, how can I show you, with this simple mirror, all I see during the trip?
At this moment the mirror fell from his hands and broke into seven pieces.
Then the Master said:
- Now, with these seven pieces, you can build figures to illustrate your trip. "from here

Mr. Tan and the tile

"Once upon a time, in a land far away, there was a Chinese gentleman named Tan. Mr. Tan lived in a golden palace, with a lake. He loved walk around the lake for hours ... One day while wandered among the reeds, he saw a bright object on the ground. He bent down and found a magnificent silver tile. He took it and admired it, the tile was smooth as the surface of the lake, soft as a feather, bright as his outfit.
Unfortunately, the beautiful tile escaped from his hands and broke into seven pieces on the floor! Mr. Tan, disappointed, tried to reconstitute it. Putting the pieces together, created a form, a little character!, shifted a few more pieces, and to his astonishment, formed a beautiful house!
Mr. Tan returned to the palace so excited to have invented a new game.
He called it TANGRAM and offered one to everyone in his kingdom!"

from here

All this stories share several things: the object geometry, a square tile or a square mirror; the object falls; the object split in seven pieces (Tans); someone try to reconstruct the square and various forms are formed.
As we said earlier, we found a quite a different story, so that caught my attention, the Legend of Yu and the God of Thunder.

Yu and God of Thunder

 "Thousands and thousands of years ago, Yu , the Great Dragon, lived among humans, who venerated him because he was 'yang', good, and was always ready to help them.

One day, the God of Thunder, jealous of the offerings the men had brought to Yu, in a burst of anger, crushed the sky with his hatchet. So, the sky fell on Earth in seven pieces black like coal. Light disappeared taking with it all existing things.

At first Yu felt sad for the world, and then felt nostalgic. So he decided to collect the seven black pieces of the sky and, in memory of the former world, began to reassemble several kinds of shapes: animals, plants and human beings that had disappeared. But after finishing each shape, its shadow left it and wandered the deserted world crying about its misfortune.

These complaints reached the ears of the God of Thunder who was touched and, to remedy the harm he had caused, he pulled from each shadow the body of a living being to repopulate the Earth.

From that time on, our shadow faithfully follows every move we make and with the seven pieces of the sky, called Qi Qiao Ban (literally 'seven boards of cunning'), everything on Earth can still be shaped".

from here

You can read more about Tangram here.

Sources:
http://www.archimedes-lab.org/tangramagicus/Tangram_legend.html
http://peixinhosnosotao.blogspot.com/2009/02/tangram-lenda.html
http://pt.scribd.com/doc/42133445/A-Lenda-Do-Tangram-1
http://www.eb1-setubal-n17-amoreiras.rcts.pt/projectos/fotostangram/a_lenda_do_tangram.htm

Et Voilá!
We found this story so wonderful and so restless that we couldn’t help sharing it
Enjoy!

Yet about Tangram- Paradox

Tangram paradoxes are designs that can be built with all the 7 pieces of the game but aparently are contradictory- click here to see the game rules, like the image above:

Fig1

In this image the man design is paradoxical, both designs used the 7 polygons as the rules, but the right one has feet, what makes us think that it used one more piece. But all the rules were respected! How this is possible?

This paradox was first idealized by Henryn Dudeney, and the solution is in the next figure:

Fig2

After observe the figure above we can conclude that this two images apparently the same, are in fact two different designs with the same area, since the missing feet are compensated by the larger body.. They have the same area because they both use the same polygons (7 tans).
Try to build these figures with your child, and you will see him/her thinking that’s magic.
Now that we understand this dynamic we can see other examples:

Click to expande

Et Voilá!

Fun with geometry

Enjoy!

Tangram- Craft

What is Tangram?
The Tangram, is one of the most popular puzzles in the world. This enigma is formed by 7 polygons and the goal is to organize all the pieces to form geometric figures.

This mathematic puzzle was, more then 100 years ago, so famous as the Rubik Cube, and it was played for many as entertainment, educational tool or mathematic tool. Tangram makes easier to recognize the geometrical forms by young children, and helps on mathematical problems resolution.
The seven polygons that form Tangram are called "tans" and they are organized like the picture

Tangram goal
The goal of this game is to place all the 7 polygons in the right position to form a given design. Sometimes there is more then one solution, alternatives solutions are acceptable as long as they have exactly the same design that is asked.

Basic rules:

• You must use all the 7 pieces;
• All the pieces must be plain;
• The pieces must touch each other;
• The pieces can't be overlapped;
• Pieces can be rotated and/or turned up side down to form the design.

The first challenge we face when we want to play this millenary game is the Tangram itself. Drawing it from scratch is a good option. you can make it the right size for you and chose the colors you like the most, that’s the first step "to make the game yours", and that’s very important in the learning process.

Today we are going to show you how to do this.

We will need:

1. 1 sheet of cardstock, EVA, cardboard or other material,
2. ruler,
3. square,
4. pencil,
5. eraser,
6. scissors.

This step by step is very simple, just try to be exact on the measures.

1- Use the scissors to cut a square shape:

2- Draw a straight line between B and H, dividing the square into two equal triangles: 

3- Find the exact middle of the line HB, name that point D: 

4- Now draw another line from vertice A to point D, at this time you must have three triangles.

5- Find the exactly middle between B and J, that will be the E point. Now do the same to the H and J, that will be the I point.

6- Now draw a line from E to I.

7- Draw a line that makes a 90º angle between point D and line IE , in other words elongate the line AD.

8- With the help of the ruler and the square draw 1 parallel line to DG and another parallel line to the line AH.

To personalize your Tangram puzzle, and create something really unic, paint it in your favorite color, or use a pattern, after painting cut all the polygons to have the 7 geometrical figures.

Images bellow were found on Internet, and are only a few of many possible images we can form using Tangram pieces.

Although the original form of Tangram is a square, there are other Tangram forms, like the egg and the round shape:

References: http://www.archimedes-lab.org/tangramagicus/pagetang1.html#; http://bloguinhovania.blogspot.com/2010/05/como-fazer-o-tangram-com-dobradura.html

Et voilá!

Fun with geometric forms

Enjoy!