Nancy O’Neil 's CU

Math Games Around the World using
Strategy and Chance

Nancy O’Neil

Academic Setting

The setting at Emerson Elementary School in Albuquerque, New Mexico is one of great diversity. It is a large elementary school with 645 students enrolled last academic year. The attendance is great at 96%. The ethnic population is 10.2% Anglo, 3.9% African- American, 69.9% Hispanic, 10.4% Native American, 4% Asian, and 1.6% other ethnicity. Within our school we have 97.4% Free/Reduced Price Meals. With that percentage 100% of the students get free breakfast and lunch. One other important point to be made about the school is that within the 645 students enrollment, only one third of the students return the following year. Also within the school year we have many students enrolling and disenrolling, starting from the first weeks of school and ongoing until the last weeks of school. It is like a revolving door for the admissions office with the population at the school. Students come and go so frequently that it is difficult to keep up with it. For most of the classroom teachers, their class list from the beginning of the year will look vastly different then at the end of the year. It is a very dramatic change and gives one a good idea of the challenges that take place at our school.

            This unit will be used at Emerson Elementary School in Albuquerque, New Mexico. I have designed this unit with fourth grade students in mind. The students that will be using this unit are typical students that enroll at the school. The unit should be used as supplement to the Everyday Math curriculum that exists at the school. Its purpose is to assist the teacher in providing students with understanding in chance and strategy by using games. Also within the games the students will get a better understanding of logic, which will help them in all areas of their mathematical thinking. The rationale for doing so is as follows: students will be able to read, write, and order numbers to 10,000. Through understanding strategies in games, they develop better problem solving skills. This will help them develop their understanding of all the basic math skill. Although it is a regular education classroom, I plan to use many ESL (English as a second language) strategies throughout the lessons.   The need for this emulates the student population at the school. I have been told that there are as many as 19 different languages spoken at the school, and the need to support the understanding of the English language by using ESL strategies is very important.

Goals and Objectives

I would like to create a curriculum that supports the program that we have in place at Emerson (Everyday Math). After using it for the past two years I have found that there are some gaps using this program with students at Emerson. In Everyday Math, games are very important and used everyday. My goal is to support this program using other games which in turn will help support what the students are learning in the Everyday Math lessons.

        The unit will help to reinforce basic math skills. In general, the fourth grade curriculum covers place value, number relationships, addition, subtraction, multiplication, division, 2-D geometry, 3-D geometry, measuring, money, statistics, probability, patterns, and pre-algebra. The students are unable to understand the higher skills because they are lacking in these basic skills, such as adding two digit numbers, multiplying numbers 2-9, so I would like to give them games that will help them while challenging the others.   As they all learn more skills they may still use these games, but are adding more knowledge to the strategies of the games, therefore improving their ability to play the games with others.

            The primary goal of this unit is for the students to be able to play games with an understanding that they are using chance or strategy. This means not just playing games without the knowledge that there is an outcome, not just guessing how to play the games. It also means knowing when the games are affected by chance and when they are affected by strategy, and building on to the strategies with the new ones they learn by playing the game. They will learn games from a variety of cultural backgrounds, which involves talking to the students about where the games originated, who used them and why, how other cultures have come to know the games, and also why they are still around today.

Rationale

There is a big push these days in the teaching community to have a classroom that is interactive and student centered. Through the math and literacy study group resources that I have been involved in over the past year, I believe that it is always focusing between student centered and teacher directed. Through the study groups I learned that for the population that is at Emerson, a teacher directed classroom is the most effective for the students. Although I tend to agree with that, I still feel that the best learning environment for the students is dependent on the students, and that may result in the fluctuation between teacher directed and student centered environments.   I still believe in play based environments.   I feel that they are very useful in the right setting and help support the ESL students as well. Through all these beliefs I feel using games in the math curriculum is an important tool.

Context and Background

When I look at games, I am looking at them as more than play. The games are a tool for which I can reinforce concepts. It is also a way of teaching the students while they think they are not doing math, then after showing them that what they have been doing is math and they have been learning and using math in everyday situations. The mention of games brings to mind a large and varied set of activities- children’s street play, dice games, puzzles, word games, board games, computer games, golf, and team sports. In general, the activities we call games have clearly defined goals toward which the players move while following agreed upon rules. We can also classify games into those involving physical skill and those depending on information other than the rules of play. The mathematical are those that depend on chance or those in which the strategies must rely on logic (Aster 85). The games I am focusing on are games of logic and games of chance.

              The first game of logic was 4,000 years ago. It was an ancient game in Egypt called “Senet”, and was a great fad during the time in Egypt. The boards of the Senet game have been found carved into the a number of tombs and classical references abound. The game has roots to the game Backgammon. I chose not to use it in my curriculum unit because it seemed more advanced than what I was trying to focus on. When people started playing games, whether they were playing for enjoyment, or as a way to decide who would be the next chief, they where playing games as a society. As pointed out in Ethnomathmatics by this statement,

In all these ramifications, each game can be an expression of the culture. But the games are tied to their culture in a deeper way. In one cross-cultural study, games of strategy have been viewed as models of social interaction. A chessboard, for example, may be thought of as a field of battle on which two armies fight in defense of their royal leaders.   The mobility and value of each piece depend on its social status. Another example, the Mancala game, popular throughout Africa, is sometimes used to demonstrate a chieftain’s strategic abilities or even to decide who will be chief. Quite different from chess, however, the Mancala onlookers (as well as the players) are expected to contribute to a noisy, distracting atmosphere.(Aster 87).

The playing of games is not just for the young either. Look at all the casinos that have developed over the last few years. Some popular games in our culture that rely solely on chance are matching coins, craps, bingo, and roulette. All of these games give the player no choice that will affect the outcome of how the game will turn out. This in turn allows the player no control over whether they win or lose, it is beyond their control. When players play games of strategy such as tic-tac-toe, checkers, or chess, on the other hand, each player does make choices; the choices rely on the logical implications of how the player will move in trying to progress toward the end goal and opening or closing further choices for oneself or one’s opponent. People don’t care if it is a game of chance or strategy, they enjoy playing the games. By using these games I want the students to see what the difference is in both types of games, and how their choices can or cannot make a difference in the outcome of the game.   Through the reading that I have done about games from all cultures I have found that they all have social ties and even particular social settings associated with a particular game. Such as “Wari,” when it is played in Africa they call it “Mancala,” as I stated it may decide who would be chief through the strategies that they use and who wins the game. Nevertheless, when playing games of strategy it is evidence that the player shows enjoyment of logical play and logical challenge, and in games of chance the player is involved with concepts of probability (Aster 87).

Because the games I have found are rooted in a social setting, each culture has created a different game that is embedded into that culture. Then, through the years of the game being in existence, it changes. The different cultures throughout the world grow and change, the games change with the society that developed the game. I have found that there are many games that have different names in different cultures but are very similar. Some of them are because the game had been passed from one country to another and some just happened to be similar.

Games of another culture provide us with an unusual window into the ideas of others; we can, in some limited sense, experience them. We cannot, for example, try out another culture’s kin system or world view. Although the context and ambiance of a game are different if we play it, we can at least participate in its formal aspects and so share in some of the same mental process (Ascher 116).

History of the Games of Chance

Lu - Lu

Lu - Lu is a game coming from the Hawaiian Islands from the early Polynesian settlers on the islands. Captain James Cook discovered the islands and landed at Waimea, Kauai, on 20 January 1778. He was an English explorer and navigator . He named them the Sandwich Islands after John Montagu, the earl of Sandwich (Krause 21).

            The Hawaiian Islands are volcanic in origin.   When the Hawaiians began to play the game they used volcanic stones that where disk shaped and 2.5 cm in diameter.   They called these disks that served as stone dice lu - lu. They marked the dice with red paint, the reason is not stated. “To shake” is what the word Lu - Lu means. The game is played with two or more players. The object of the game is counting and the player with the highest score wins.

Patolli

Patolli Indian people who dominated central Mexico were the Aztecs; they were there when the Spaniards under Corte`s arrived in 1519. The Aztecs played patolli on a mat game board in the shape of a cross. Where are many shapes within shapes that makeup the game board. Within the cross there are line segments that form squares, these squares are called houses. The patolli game board resembles the pashisi board. The one-sided dice that are used in the game are beans, and are called patolli.

            Francisco Lopez de Gomara, wrote the earliest Spanish account of patolli 1552, thirty-one years after the conquest, and reveals that Emperor Montezuma sometimes watched as the game was played (Krause 47).

Totolospi

This game is a Hopi game of chance, pronounced to-to`-los-pi. It was played with two or three cane dice and a counting board which was inscribed in stone. The game was enjoyed by children as well as adults.     Interestingly, the game totolospi has been described as resembling checkers, Monopoly, and Parcheesi, which are games of fox and geese. After observing a variety of collections that have been acquired, the conclusion was made that totolospi counting boards varied in great diversity (Krause 72).

            Depending on the number of players playing the game the game board will look differently.   The three versions are 1) an ellipse that is used when two people are playing, 2) two ellipses intersecting to look like a cross, which is used with four players, and 3) the rectangular board that can be used when playing two to four players.

            The object of the game totolospi is to travel around the board and return back home. The first to do so wins the game. With older students, make the game more challenging when two or three cane dice are used; it increases the number of possible outcomes. Students can use tree diagrams as a useful tool for calculating probabilities. For younger students, the game provides practice in counting by ones and twos on the elliptical boards and by five's and tens on the rectangular board (Krause 72).

Game Sticks

Native Americans played a variety of games of chance. The games that they played came in two categories: dice games and guessing games. When they played the dice games, the dice were thrown and the number was determined in that random way. When dice are referred to in Native American games it is not as we traditionally think of dice. The objects were marked with a design on the face side and plain or marked differently on the other side. The materials that were used to create the dice varied. They used such found objects as wood, bones, animal teeth, walnut shells, peach pits, pottery disks, grains of corn, and shells. They would throw the objects that were made into dice in the air or against a blanket or animal hide. Other ways were tossing them in baskets or bowls, or allowing them to fall freely to the ground. The dice would be tossed from their hands in a variety of ways (GEMS 121).

Two methods of scoring were used to keep track of the game: counters were used and passed hand-to-hand until one player had all the counters, or, sometimes, a counting board or abacus was used. The games were usually played for items of value. It is thought that many of the games were originally played for arrows or arrowheads. Other items of value included shells, obsidian, blankets, or ponies. (GEMS 121).

            The indigenous people of west and southwest North America, which include parts of what is now the United States, Mexico, and Canada, played dice games. Game Sticks is an adaptation of a game played by Native Californians. It was a game that was played mostly by women. Indigenous people still play game sticks in many different parts of the state. Similar games are likely to still be played in the states of Washington, Oregon, Wyoming, Idaho, North and South Dakota, Utah, Arizona, and New Mexico, as well as in British Columbia, Canada, and parts of Mexico (GEMS 122).

History of the Games of Strategy

Ko - No

This is a game from China and Korea. Ko - No means games played on a diagram coming from Korea and the Chinese version is called K’i.    It is played by two players that use black and white stones as the game pieces. The object of the game is to block the opponent so that he or she cannot move. This is a game of logic and strategy, the players need to think of all the options and then make a move.

Nine Men’s Morris

Nine men’s morris, also called merels, mill, and morelles, is an ancient game for two. This game can be traced back to about 1400 BC, for the game board was one of the seven cut into the roofing slabs of the temple on Karnak, Egypt (“Kurna” in some references). Similar diagrams have been found in Sri Lanka, formerly Ceylon. There, two diagrams dating from AD 9-21 were carved into the flight of steps on the lower part of the hill at Mihintale. Evidence shows that the game was known to the inhabitants of the first city of Troy as well as to the Vikings. A Bronze Age burial site in County Wicklow, Ireland, also revealed a morris board carved in stone (Krause 27).

During the height of its popularity, nine men’s morris was being played in Europe during the fourteenth century, according to Bell (1979). Shakespeare knew about the game and mentioned it in the play A Midsummer Night’s Dream in 1598.

            The game is played by two players using 9 pieces each.   The playing pieces are the color of red and green. The object of the game is for each player to attempt either to block an opponent’s playing pieces so they may not move or having the opponent ending up with only two playing pieces.

Wari

Wari is a board game that is played around many parts of the world. Where they all originated from was Egypt and are generically called mancala. These games have been played for thousands of years in Egypt and were found carved into the stone of the pyramid of Cheops and the temples at Luxor and Karnak. As the game spred through Asia and Africa, the Arabs changed the way the game was played to make variations of the game from the original ways of play. As it moved into the nineteenth century, people of Europe would play the game over coffee in cafes and the loser would have to pay the bill (Grunfeld 20).

            In Africa children create the board out of scoops into the ground. This way they may play it at any place or any time. The way they play the game in Africa has been unchanged since the slaves brought it to Surinam and the West Indies and is still called mancala. Although the game is considered a ‘man’s game’, the women of Africa do play the game. If a women is known to be a very good player, a man will not challenge her to a game. For if they were to lose to a women he would be teased by his peers in the village (Grunfeld 20).

This game is know for being played for fun and not as a gambling game. In some areas wari has religious significance. What people do to amuse the sprits is play wari the day before the funeral. Since the spirit has not yet departed it is thought that it will amuse them. Also if the game is played at night, ghosts will come around the players as they play and then fly off with their spirit (Grunfeld 20).

Hex

The game of hex is the newest game out of all the games in this unit. It was developed in 1945 in Denmark by a man named Piet Hein. This game is a very challenging to the players, requiring them to cross the board in a continuous path. The board is made up of hexagons and the sides are of equal length. John F. Nash, who some of you may have heard of from the movie, A Beautiful Mind , reinvented the game in 1948 on his bathroom floor. The tiles on his floor inspired him to create a pathway across the floor from one direction. The opponent has to try to create a pathway in the perpendicular direction. While playing the game of Hex the players need to think of strategies to create their pathway, while also thinking of ways to block their opponent from completing their pathway (GEMS 143).

NIM

NIM is a game that is said to be of ancient Chinese origin. Although the game is old, the name was created fairly recently, in 1901, by a man from the Harvard mathematics department named Charles L. Boston. He came up with the name as he wrote a paper analyzing the way the game is played. Although the origins of the game of NIM are in China the game is played throughout the world today with people playing different versions of the game. Basically, all of the games have only two people playing the game that use a finite set of elements that decrease as each player eliminates pieces (GEMS 13).

Yote`

The game yote` because of the ease of setting up the game has grown to be very popularthroughout West Africa. This board is also created for the ground and made up of five rows of six holes that are scooped from the ground. The game pieces are made up of pebbles or parts of a stick. Although the set-up and pieces are easy and can be found any where don’t think this is a simple game, it is not. The rules are such that it allows many varieties of moves for the players. This game is one that demands good strategies and quick thinking.

Implementation

The way I introduced the games was to alternate a game of strategy and a game of chance, but if you so choose they may be introduced in any order. All of the game board diagrams are in the back of the unit. The lessons are set up to compare them with each other. This will create other lessons which I will not go into detail as to how to do them. Please refer to the history section when talking to students about where the games originated. Also I thought using geography with this part of the lesson would go along excellently.

Assessment will be on going. The teacher will be doing this though observations and discussions in small groups and whole group setting. Also to assess the students the students will be teaching all of their games to other younger students. These students are their math buddies. These lessons are not in the unit, but the lessons will look very similar to the lessons in this unit, and include having the students go over how to play the game and playing them with the younger students.

Lesson 1 :         Introduction to the game Ko-No

Objectives:       Students will learn the background of where the game came from and how               to play the game.

Benchmarks:     New Mexico Content Standards:

            6.30.2.14- Mathematics
                        A ( 1,4) using problem solving
                        B (1) using communication
                        C(1) use Mathematical reasoning
                        6.30.2.16- Social Studies
                        A (3) recognize that the world is made up of many people

Materials:         Game board

            2 black playing pieces
                        2 white playing pieces

How to play:     One player chooses one of the colors of game pieces, the other player gets the other color. Whoever chooses the black piece gets to choose where they what to place their piece first, on A or B. The white player chooses C or D to move on to . The players take turns placing their other game pieces one empty spaces. They keep moving, without jumping, until one of the players is blocked and cannot move.

Procedure:     1. Introduce to the students where the game originated from, China.

            2. Have a map in the front of the room.

            3. Ask the students if any one knows where China is. Have the student come up and show the others where it is located on the map. If no one volunteers show the students where it is on the map.

            4. Then go over the history of the game with the students. While you are going over the history of the game, ask the students questions such as...

            -Why do you think they played with only two game pieces each?
                        -Why do you think they used black and white as the colors for the game pieces?
                        - Who do you think were the people that played the game the most?

            5. Next have the students sit in the circle or semicircle so every student will be able to see how to play the game.
                        -Have one student volunteer to help you demonstrate the game.
                        -Talk about the number of pieces needed, the game board, and how to start the game.                         -Once you have started I would ask the students to help you in your decisions as to                              where to move.

            6. Answer any questions about the game so that it is clear how to play.

            7. Have the students play the game in pairs, either your choice or let them choose                               partners.

            -Let them play for about 15 to 20 minutes, while you walk around and observe the                             games.

            8. After the students are finished call their attention back to you.

            -First ask them to stay in their groups.
                        -Ask them questions like...
                        -Who won the most?
                        -Did that person see a strategy in how they were able to win?
                        -Did any players play logically and how did that happened?
                  - Are strategies and logical play one in the same?
                  -What could the person that did not win do next time playing the game?

Extensions:       1. Have the students make their own game board and pieces to use at home.

            2. Have the students write a letter to a friend telling them about the game. Include where it came from, how to play the game, and if they like playing the game or not.

            3. The students could research China. Find out what the people are like, what their schools are like, the weather and basic politics of the people. Then they can draw a map of China and write on the back of the map if they would like or not like living in China. They would incorporate the information that they found during their research.

Lesson 2:          Introduction to the game Lu-Lu

Objectives:       Students will learn the background of where the game came from and how to play the game.

Benchmarks:     New Mexico Content Standards:

            6.30.2.14 - Mathematics
                        B (1) using communication
                        C (3) Mathematics in reasoning
                        D (3) Mathematical connections
                        F (1) number systems and number theory
                        K(2) understanding and use probability

            6.30.2.16 - Social Studies
                        A(3) recognize that the world is made up of many people
                        D(2,4) view themselves and others over time

Materials:         Four playing pieces marked on one side only as follow:

            The playing pieces can be made out of things such as clay, wood, stones,            buttons, or shells. If needed use masking tape over the side you are marking so you are able to make the marks with a pen.

How to play:     Two or more players play at a time. One of the players shakes the pieces and tosses them. One turn consists of two tosses.

            * If all of the pieces are turned up on a toss the player gets ten points and tosses all of the pieces the second time.

            * If all four pieces do not turn up the player counts the number of dots on the turned up pieces and then tosses only the pieces that were turned down. For the second toss the player counts the pieces that are turned up on that toss.

            * The winner is determined by who reaches 100 first or another designated score you have agreed on.

Procedure:     1. Introduce the students to where Lu-Lu came from and the history of the game.

            1. Ask them questions such as:

          -Where are the Hawaiian Islands?
                        -What country are they part of?
                        -How many islands are there in Hawaii?

            2. Based on the responses from your questions have the students draw where they think the Hawaiian Islands are.

            -Give them a map of the USA or have them draw the USA, depending on their prior knowledge.

            3. After you have discussed where the islands are show them the playing pieces.

            4. Call on two volunteers to play the game. Remember you have not told them exactly how to play the game yet.

            5. Have the first player toss the pieces. Depending on what was tossed write the score on the board for every student to see.

            6. Have them throw their second toss.

            7. Write it on the board.

            8. Do the same for the second player.

            9. Then discuss how the scoring works for this game. Try to get the students to tell you how to score the game.

            10. Once the students understand the scoring and how to play have them go in groups of four to start playing the game.

            -I think groups of four will work best to begin with. This will create more discussion within the groups. You may want to choose the groups.

            11. Bring the whole class back together once they have had sufficient amount of time to play the game. Talk about how the games went. Perhaps let them do that in their small groups first, then call on one person to talk for the group.

            12. Ask them questions
                        -Do they think there were any strategies for winning the game?
                        -If so, what were they?

Extensions:       1. Have them read books that you have brought in about Hawaii.

            2. Create an art poster about Hawaii from magazine pictures. Then have them write about what it is they have on their poster and why it represents Hawaii to them.

            3. Have them make the Lu-Lu game to take home.

Lesson 3:          Introduction to the game Nine Men’s Morris

Objectives:       Students will learn the background of where the game came from and how to play the game.

Benchmarks:     New Mexico Content Standards:

            6.30.2.14 - Mathematics
                        B(2) students will use Mathematica in communication
                        C(1,3) Mathematics in reasoning
                        D(2,3,5) Mathematical connections
                        K(1) understanding probability
                        6.30.2.16 - Social Studies
                        A(3) recognize that the world is made up of many people
                        F(1,2) how personal and group identities are shaped by culture
                        K(2) understanding of diverse cultures
                        N(1) role of globe connections and interdependence between societies

Materials:         nine men’s morris board

            9 red playing pieces
                        9 green playing pieces

How to play:     After the players have decided who is playing first, the game board is clear and the first player places their first piece anywhere on the board. The player take turns placing their playing pieces on the board, one at a time. They place them at the angles and intersections on the board. After all of the playing pieces are on the board, play continues by the players moving the pieces to empty angles or intersections. The pieces have to be moved along the lines of the playing board. Jumping the pieces is not allowed.

            A mill is made when a row of three playing pieces are on a line vertically or horizontally. Once this is achieved the player with the mill may remove one of the opponent’s playing piece. Any piece that is not part of an opponent’s mill can be removed. If it is part of a mill it can not be removed.

            A player can make new mills by existing mills. That is, a playing piece can be moved to form a mill and then returned on the next turn. Each time a mill is made, the player is entitled to remove one of the opponent’s playing piece.

            If a player is left with just three playing pieces and forms a mill, that mill will have to be broken on the next move. This may result in the player losing the game. When a player has won the opponent has only two playing pieces left on the board or is unable to move their playing pieces.

Procedure:        1. Have a large world map in front of the class.

            2. Tell the students that the next country we will be talking about in which our games are from is Egypt.

            3. Ask the students if anyone knows what continent it is on.
                        -If they do not tell them.

            4. Then ask if any of the students can come up and show the class where Egypt is in                            Africa.

            5. After you have talked about the geography of Egypt tell them the history of the game Nine Men’s Morris.

            6. Once you have gone over the history of the game, ask them if they think this game will be one of strategy or of chance? Don’t tell them the answer at this time.

            7. Show them the game board and the playing pieces.

            8. Have two volunteers come up to play the game as you direct them as to how to play the game.

            9. Once they have all the pieces placed and you have told them the other rules of movement let them continue play without direction.

            10. When the game is complete talk to the students about the question, it is a game of chance or strategy?

            -As you talk about it with them give them ideas of strategies that the two players used in the example game. This will help those students that may not have seen them.

            11. Let them choose or have partners chosen for them to begin play.

            - Have them play for about 20-30 minutes. This give them the opportunity to play more than one game so they may see more strategies.

            12. Once the time is up have the class talk in small groups about how the game went. What were some of the strategies? Then have a few share with the entire class.

Extensions:       1. Have the students make the game to bring home.

            2. Have them teach the game to someone at home and play it with them. Then they can either write or talk about how the game went with the class.

            3. After the students have become knowledgeable about the game have them change one of the rules or add a rule to the game. See how this affects the play. Which way do they like better and why?

            4. Have the students research the Egyptian numeration system. They could look for it on the Internet or through books. Have them create a chart of the Egyptian numerals, the number name, and the meaning of the symbols. They could write puzzles using the numerals and have others try to decode them.

Lesson 4 :         Introduction to the game Totolospi

Objectives:       Students will learn the background of where the game came from and how to play the game.

Benchmarks:     New Mexico Content Standards:

            6.30.2.14 -Mathematics
                        C(3) Mathematics in reasoning
                        D(2,3,5) Mathematical connections
                        K(2,3) understanding probability
                        6.30.2.16 - Social Studies
                        A(3) recognize that the world is made up of many people
                        F(1,2) how personal and group identities are shaped by culture
                        K(2) understand the diverse culture

Materials:         counting board

2 or 3 cane dice (half round dowels can be used for the cane dice. Cut each 9.5 cm. in length. If desired, paint the round sides white and the flat sides red. If half round dowels are not available, use popsicle sticks. Another thing that would work well are tongue depressors.)

2 or 4 counters called “animals” (The Hopi used kernels of colored corn for the animals. Each player has a different color.)

How to play:     1. Totolospi for two: Elliptical counting board

Each player places a counter (or animal) on the nearest circle. Alternate turns are taken. The players move along the line segments on the board, not the spaces between the segments. The moves are determined when the players hold the cane dice and drop them on end. If three round (white sides) land up, the player advances 2 line. If three flat (red side) land up, the player advances 1 line. If a combination is thrown, the player loses his or her turn. The player reaching the opposite side first wins.

            2. Totolospi for four: Cross shaped counting board

Each player places an animal on the circle of the arm of the cross nearest to the player. Players take turns doing this. The players will count just as if they were playing with two players. The player that reaches the other side of the arm is the winner.

            3. Totolospi for two to four: Rectangle counting board

For this version, movement is on the spaces rather than the lines. The players place the animals in the center circle of the board. The center circle at the end of the rectangular strip is called the house. Movement is determined by dropping two cane dice. If both round sides land up, the player moves 10 spaces. If both flat sides land up, the player moves 5 spaces. A player continues to play as long as the cane dice show both sides alike. If the cane dice land with two different sides showing, it is the next player’s turn.   Two animals may not be in the same space. So, the second animal that lands in the space that is occupied sends the player that is there back home again.

The players are first moving along the inside path, the rectangle. Once they reach the outside path, which is called “the home road,” the player may choose to turn right or left. Once a player has gone around the board and is at the last corner, that player needs to get the flat sides up. This will allow the player to go in the door and later proceed inside to the starting point. If, however, the player’s dice land round side up, they have gone past the door and must go around the board again. The winner is the first player to return to the starting point. If, after a second trip around the board, the player goes past the door of the house again, they lose.

Procedure:        1. Have the students make the cane dice first.

            2. Next talk to the students about the game and the history of the game.

            3. After showing them the different game boards I would start with going over the rules of the elliptical board and the cross shaped board, because they are almost the same.

            4. After they understand the rules have them play the game. Either 2 or 3 players.

            5. Next I would talk to them about the rules of the rectangular board. This may even be on another day.

            6. Have them play with the rectangular board.

            7. After the students have played both game boards talk about the possible outcomes of the different game boards.

Extensions:       1. Have the students research the Hopi people.

            2. Have the students research the different kinds of Native Americans that live in their area.

Lesson 5 :         Introduction to the game Wari

Objectives:       Students will learn the background of where the game came from and how to play the game.

Benchmarks:     New Mexico Content Standards:

            6.30.2.14 -Mathematics
                        C(1) Mathematical reasoning
                        6.30.2.16 - Social Studies

            A(3) recognize that the world is made up of many people

Materials:         1 egg carton
                        48 beans or pebbles

            -Remove the lid of the egg carton and cut it in half. Attach each half of the lid to the ends of the egg carton.

How to play:     To start the game the beans are placed in the egg carton. Four beans are placed in each cup. Players face each other with the board between them side to side. The player’s side is the six cups closest to them, and the lid to the right. The player’s move their playing pieces to the right, counterclockwise.

The first player removes four beans from any cup on the board and sows them one by one in the next four cups. Even on the first move player may be placing beans in their opponents cups. The pots at each end of the game board are not to be used when moving the beans, they are only for holding captured beans. The play is continued by the next player removing beans from any cup and sowing them into the following cups. This is how the play is continued.

As play continues the cups may accumulate many beans. Players may go around the board more than once. When a cup becomes empty the players skip that cup for that turn.

How to capture beans:

1. If the bean a player sows lands in a cup on the opponent’s side that contains only one or two beans, that cup is then captured. This last bean plus the opponent’s bean or beans must total no more than three.

2. When this condition is met, the player is also permitted to take beans from all cups preceding it if (a) each cup has two or three beans, (b) the cups are on the opponent’s side of the board, and (c) the cups are consecutive.

The captured beans with the last placed bean are placed in the player’s pot.

Procedure:        1. Have the students make the game board. Have them bring in egg cartons from home.

            2. The students should already be familiar with Egypt, from the game Nine Men’s Morris. Have the students in group of four see which group is able to write down the most things they remember about Egypt. This will help them remember the things you talked about earlier about Egypt.

           3. Go over the history of the game Wari with the students.

            4. Have the students sit so they can see you demonstrate the game and rules of the game for them.

            5. Have one of the students play you so they can see how the game is played. Ask the students to help you with the moves. You probably will not play an entire game in front of the class. Play until all of the rules happen , this will give the students a chance to see what to do.

            6. Have the students get their game boards and play in pairs.

            7. Have the students play for about 30 minutes.

            8. After the students have cleaned up have them discuss in small groups, it does not matter if they are in their pairs still.

            - the type of game it is, chance or strategy?
                        - What were the strategies that they used?
                        - Were there any strategies that they learned from playing?

            9. As a whole class discuss the different types of games that they have played so far and what they are.

            10. Then discuss the games that were from Egypt.

            - How were they the same, different?
                        - Do you think the people enjoyed playing both games?
                        - Knowing that they played these games in Egypt, what other games do you think they would enjoy playing?

Extentions:       1. Have the students make up a new game that they think would be played in Egypt.

Lesson 6 :         Introduction to the game Game Sticks

Objectives:       Students will learn the background of where the game came from and how to play the game.

Benchmarks:     New Mexico Content Standards: