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Product Details
| ISBN-13: | 9781613742396 |
|---|---|
| Publisher: | Chicago Review Press, Incorporated |
| Publication date: | 05/01/1998 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 160 |
| File size: | 7 MB |
| Age Range: | 9 Years |
Read an Excerpt
Math Games & Activities from Around the World
By Claudia Zaslavsky
Chicago Review Press Incorporated
Copyright © 1998 Claudia ZaslavskyAll rights reserved.
ISBN: 978-1-61374-239-6
CHAPTER 1
Three-in-a-Row Games
All over the world children play some form of a three-in-a-row game for two players. Tic-tac-toe is one example of such a game. The object of the game is to be the first player to get three markers in a row on the game board. It seems that people were playing such games long before the time of your great grandparents.
More than one hundred years ago, scientists examining the rooftop of an ancient Egyptian temple found several strange diagrams carved in the sandstone slabs. They looked like this: Figure 0
It turned out that every one of these diagrams is used as a game board for a three-in-a-row game somewhere in the world! Did the ancient Egyptians really play such games? How could the scientists find out?
The temple was built 3,300 years ago to memorialize the king, Pharaoh Seti I. It stands in the town of Qurna. Royal tombs were built on the west side of the Nile River. This was where the setting sun entered the spirit world for the night, according to Egyptian beliefs. Ancient Egyptians believed that people would have a life after death and would need all the things that they enjoyed while they were alive. So the tombs contain many items that were important to them in life, like clothing, jewelry, tools, and even their pets!
The Egyptians painted the walls of their tombs and temples with the scenes from the lives of their kings and queens and other wealthy people. Game boards and carved game pieces for Senet and other games were buried with the mummies of important Egyptians. That's how we know about the games that these people played when they were alive. But no game boards for three-in-a-row games have been found inside the tombs, and no pictures of people playing such games appear on temple walls.
How did these diagrams come to be on the roof of the Pharaoh's temple? Probably the workmen who built the temple played three-in-a-row games on the stone slabs during their lunch break. Instead of drawing a fresh game board in the sand for each game, they carved permanent diagrams in stone.
You may wonder whether Egyptian children played these games. Perhaps fathers played such games with their children at home. But they probably drew game boards in the dirt outside the house and wiped them away when the game was over, leaving no trace.
From Egypt the games could easily have spread all over the world. Greek scholars traveled to Egypt for higher education, just as people nowadays go to college. The Romans, who probably learned the games from the Greeks, spread them when they conquered parts of Europe, the Middle East, and North Africa. By that time the Chinese had already been playing three-in-a-row games for centuries. Game diagrams carved on the tops of stone walls and the steps of important buildings can still be found in many parts of the world.
The first European picture of children playing a three-in-a-row game appeared in Spain more than seven hundred years ago in the Book of Games. In the picture two children sit on either side of a large board for a game called Alquerque de Tres. The Spanish name means "mill with three." The game board they used is just like the board for Tapatan (see page 6).
Arabic-speaking Moors came to Spain from North Africa in the eighth century. They taught the Spanish people how to play games like Chess and Alquerque. Later the Spanish king Alfonso the Wise had this information written down in the Book of Games. Soon these games spread to other parts of Europe and, later, to America.
Now you will have a chance to learn several three-in-a-row games that children play in other parts of the world. As you will see, some of these games are more complicated than Tic-tac-toe. But the object of the game is always the same — to be the first player to get three markers in a row.
Shisima from Kenya TWO PLAYERS
Kenya is a country in East Africa. Children in western Kenya play a three-in-a-row game called Shisima (Shi-SEE-Mah). The word shisima means "body of water" in the Tiriki language. They call the counters imbalavali or water bugs. Water bugs move so rapidly through the water that it is hard to keep them in sight. That's how quickly players of Shisima move their counters on the game board.
Children in Kenya draw the game board in the sand and play with bottle caps, pebbles, or buttons. You might also use coins. Just be sure that you can tell the difference between your counters and the other player's counters.
MATERIALS
• Sheet of unlined paper, at least 8 inches (20cm) square
• Pencil with eraser
• Compass, or about 10 inches (25cm) of string
• Ruler
• Scissors
• Glue
• Piece of cardboard, at least 9 inches (22.5cm) square
• Colored markers or crayons
• 3 counters for each player, of 2 different kinds (buttons, bottle caps, or coins)
DRAWING THE GAME BOARD
The game board has the shape of an octagon (eight-sided polygon).
1. Mark the center of the paper. Use a compass to draw a large circle. If you don't have a compass, attach a piece of string to a pencil. Hold the pencil upright near the edge of the paper. Extend the string to the center and hold it down there. Then draw the circle. Figure 1a
2. Draw a line, called the diameter, through the center of the circle.
3. Draw another diameter, so that the two lines form a cross. These two lines are perpendicular to each other.
4. Draw two more diameters, each halfway between the first two.
5. Connect the endpoints of the diameters with straight lines to form an octagon. Erase the circle. Figure 1b
6. Draw the shisima, or body of water, in the center. Erase the lines in the center.
7. Glue your game board to the cardboard and decorate with colored markers. You might want to draw a border around your game board.
PLAYING THE GAME
Place the counters on the board, as shown in the diagram. Figure 1c
Players take turns moving their counters one space along a line to the next empty point. They continue to take turns moving one counter at a time. A player may move into the center, the shisima, at any time. Jumping over a counter is not allowed.
Each player tries to make a row with his or her three counters. A row must go through the shisima. There are four different ways to make a row. This diagram shows three black counters in a row. Figure 1d
The first player to get all three counters in a row is the winner. If the same set of moves is repeated three times, the game ends in a draw — no winner or loser. It's time to start a new game. Take turns being Player One.
After a few games you may be able to move your counters as fast as the imbalavaliswim in the water.
THINGS TO THINK ABOUT
Is it a good idea to move into the shisima on your first move? Why or why not?
If each player has four counters, can they still play the game? Try it and see what happens.
Tapatan from the Philippines TWO PLAYERS
Tapatan (TAP-uh-tan) is a game that people play in the Philippines, a country of many islands off the southeast coast of the Asian continent. Some families keep beautiful wooden game boards for Tapatan. Other families have the diagrams marked on floors or on doorsteps of their homes. They use special round counters for this game, three of light wood for one player and three of dark wood for the other.
MATERIALS
• Sheet of unlined paper, at least 8 inches (20cm) square
• Pencil
• Ruler
• Colored markers or crayons
• Scissors
• Glue
• Piece of cardboard, at least 9 inches (22.5cm) square
• 3 counters for each player, 3 light and 3 dark (beans, buttons, or coins)
DRAWING THE GAME BOARD
1. Draw a square that measures six inches (15cm) on each side.
2. With your pencil, draw the diagonals.
3. Draw lines that connect the midpoints of the opposite sides.
4. Use a marker or crayon to mark the nine points where the lines meet as shown in the diagram. Figure 2a
5. Glue the paper to the cardboard and decorate your game board.
PLAYING THE GAME
This game is played on the nine points where the lines intersect. Players take turns going first. Player One places a light counter on any point. Then Player Two places a dark counter on any empty point. They take turns until all the counters have been placed on the game board.
Then Player One moves one of her counters along a line to the next empty point. Jumping over a counter is not allowed. Player Two does the same with one of his counters. They continue this way taking turns.
Each player tries to make a row of three counters of one color and block the other player from doing the same. A row can be made in eight different ways: three across, three down, and two along the diagonal. Figure 2b
The winner is the first player to make a row. If neither player can get three in a row and the same set of moves is repeated three times, the game ends in a draw — no winner or loser.
THINGS TO THINK ABOUT
Where should Player One place the first counter in order to win?
Can you play the game with four counters for each player?
How is Tapatan like Tic-tac-toe? How is it different?
Player One can place the first counter on any one of the nine points on the board. Show that there are really only three different ways to place the first counter: center, corner, and side. Figure 2c
CHANGING THE RULES
Children and grown-ups play games similar to Tapatan in many parts of the world, but the rules may be somewhat different. Here are some other versions of the game you might want to try:
Marelle (France). Neither player may make the first move in the center.
Achi (Ghana and Nigeria). Each player may have four counters instead of three.
Tant Fant (India). The game opens with each player's three counters already in position, as in this diagram. In Tant Fant, a row may not be made on the starting lines. There are just six different ways to make a row in this version. Figure 2d
Tsoro Yematatu from Zimbabwe TWO PLAYERS
Zimbabwe is a country in southern Africa. It is named after the complex of buildings called Great Zimbabwe, or the "Great Stone House." In these buildings once lived the rulers of a vast ancient kingdom known for its rich gold mines.
Children in Zimbabwe play Tsoro Yematatu (TSOH-roh Yeh-mah-TAH-too), the "stone game played with three." Today they are most likely to use bottle caps as counters, as soft drinks are just as popular in Africa as they are in the United States.
MATERIALS
• Sheet of unlined paper, at least 8 inches (20cm) square
• Pencil
• Ruler
• Colored markers or crayons
• Scissors
• Glue
• Sheet of cardboard, slightly larger than the paper
• 3 counters for each player, of 2 different kinds (coins, buttons, or bottle caps)
DRAWING THE GAME BOARD
1. The game board is in the shape of an isosceles triangle (it has two equal sides). With a pencil and ruler, draw a triangle on your sheet of paper as shown in the diagram. Figure 3
2. Draw an altitude that divides the triangle in half. Then connect the midpoints of the equal sides.
3. Go over your lines with a marker and mark the seven points where the lines intersect.
4. Glue the paper to the piece of cardboard. You may want to decorate the game board and keep it to use again.
PLAYING THE GAME
Players take turns placing their counters on the empty points of the board. After all the counters have been placed on the board, one empty point remains. Then each player in turn moves one of his or her counters to the empty point on the board. Jumping over a counter is allowed.
Each player tries to make a row of three. There are five different ways to do this. The winner is the first to make a row of three. This game can go on for a long time without a winner. In that case, the players should decide to call it a draw.
THINGS TO THINK ABOUT
Why can't you play the game with four counters for each player?
Picaría Native American TWO PLAYERS
The Pueblo Indians of New Mexico play three-in-a-row games similar to those found halfway around the world. Did they make up these games themselves, or did they learn them from other people?
One clue is the name of the game. Some of the Pueblo people called their games Pitarilla or Picaría (Pick-ah-REE-ah). These words sound like the Spanish name for the game Pedreria, which means "little stone." Most likely the Native Americans of the Southwest learned the games from the Spanish.
In the sixteenth century, the Spanish conquistadores sailed from Spain to America searching for riches. They had heard that some towns in the Southwest were filled with gold. They attacked the towns but found no gold.
The Spanish conquistadores gave the name Pueblo to the people of this region. In Spanish, pueblo means both "people" and "town." The Spanish forced the Pueblo Indians to work like slaves. In 1680 the Pueblos revolted but were free from slavery for only twelve years. Imagine how much the Native Americans must have disliked their Spanish conquerors, and yet they continued to play the games they learned from them.
Pueblo children scratch their game boards on flat stones. For counters they use pebbles, dried corn kernels, or bits of pottery.
MATERIALS
• Sheet of unlined paper, at least 8 inches (20cm) square
• Pencil
• Ruler
• Colored markers or crayons
• Scissors
• Glue
• Piece of cardboard, at least 9 inches (22.5cm) square
• 3 counters for each player, of 2 different kinds (pebbles, coins, or bottle caps)
DRAWING THE GAME BOARD
1. Draw a square that measures six inches (15cm) on each side.
2. Using your pencil, connect the midpoints of the opposite sides to form four small squares.
3. Then draw the diagonals of each of the four smaller squares. Figure 4a
4. Go over the lines with a marker. Mark the nine points on which the game is played — one in the center and eight along the sides, as shown in the diagram.
5. Glue the game board to the cardboard and decorate with markers or crayons. You may want to try a border design like these from Pueblo Indian artwork. Figure 4b
PLAYING THE GAME
The two players take turns placing one counter at a time on an empty point on the board. When all six counters have been placed, the players take turns moving one counter at a time along any line to the next empty point. Jumping over a counter is not allowed.
Each player tries to make a row with his or her three counters. A row can be made across, up and down, or along a diagonal — eight ways altogether.
The winner is the first player to make a row. If neither player can get three in a row, call it a draw and start again.
CHANGING THE RULES
Some people play Picaría on the thirteen points where the lines intersect, as shown in the diagram. Figure 4c Try playing on thirteen points by the game rules just given, with these differences:
1. Neither player may place a counter in the center of the board until all six counters are on the board.
2. Players may make three in a row, with no empty points between, anywhere along a diagonal. There are sixteen different ways to make three in a row.
THINGS TO THINK ABOUT
Which form of Picaría is a better game? Why?
Can you play the first version of Picaría with four counters for each player instead of three? How about the second version of the game?
9 Men's Morris from England TWO PLAYERS
For hundreds of years people in England have played three-in-a-row games. Some had names like Three Men's Morris, Five Men's Morris, Nine Men's Morris, and Twelve Men's Morris. The number told you how many counters each player used in the game.
(Continues...)
Excerpted from Math Games & Activities from Around the World by Claudia Zaslavsky. Copyright © 1998 Claudia Zaslavsky. Excerpted by permission of Chicago Review Press Incorporated.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
Table of Contents
Contents
INTRODUCTION,1: THREE-IN-A-ROW GAMES,
2: MANKALA: BOARD GAMES OF TRANSFER,
3: MORE BOARD GAMES,
4: GAMES OF CHANCE,
5: PUZZLES WITH NUMBERS,
6: PUZZLES WITHOUT NUMBERS,
7: GEOMETRY ALL AROUND US,
8: DESIGNS &8364; SYMMETRY,
9: REPEATING PATTERNS,
10: SELECTED ANSWERS,
BIBLIOGRAPHY,
A WORD ABOUT UNICEF,