Tangram Race

Hope Campbell
Christine Garcia
Patricia Oliveira


| Instructional Objective | Learners & Context | Object of Game | Game Materials |

| Time Required | Rules | Design Process | References |


Instructional Objectives

The learners will select and position geometric tangram shapes to complete a tangram puzzle. In the advanced level, the learners will apply knowledge of spatial relationships to complete a tangram puzzle silhouette.

These objectives address the National Council of Teachers of Mathematics (NCTM) Standards:
Grades K-4, Standard 9: Geometry and Spatial Sense
Grade 5-8, Standard 12: Geometry


Learners & Context of Use

The game is designed for learners from lower elementary school to adult. The game can be played for reinforcement of names of geometric shapes, spatial relationships and for enjoyment.

For classroom use, sitting at a table or moving desks together will accommodate playing this game which is standard board game size. The multiple cards containing tangram puzzles allow players to have new experiences with each game.

Prior to playing the game, players may review the definition of a tangram puzzle, the names of the shapes and the number of pieces for each shape, and the total number of pieces in a tangram puzzle. This information is available in the Rules for the game and in most dictionaries.

After concluding a game, learners may change tangram cards and play a new game.


Object of the Game

The object of the game is to be the first to complete the tangram puzzle with all the correct pieces in one color.


Game Materials


Time Required

The game is designed for three or four players and can last from 30 minutes to one hour, depending on cooperative strategies or competitive strategies employed by the players. The winner is the first to complete the tangram puzzle with pieces of the same color. Chance cards allow players to trade pieces and the strategy used here can shorten or lengthen the game.

The Set-up

1. Open the board and set the stack of Chance cards, face down, in one of the open black triangular areas of the board.

2. Determine the level of play and have all players select one tangram card. All players will use either the tangram cards indicating the solution or the silhouette tangram shapes.

3. Players select their marker and place it in the Start space.

4. The tangram bank can rest in one convenient location or can be passed from player to player throughout the game.


The Rules

A Tangram is a Chinese puzzle from the 19th century. The puzzle consists of seven pieces, or tans, made from one square: a small square, a parallelogram, two small triangles, one mid-sized triangle, and two large triangles. The purpose of the puzzle is to combine the seven tans to make one figure.

Board Design

The center of the board design contains the seven shapes that make up a tangram. The path of spaces the players follow is the tangram shapes. Spaces that are not a tangram shape are a Chance space. This design reminds players of the seven pieces that make up a tangram.

Rules

1. Players roll the die to determine which player will start. The highest number goes first. Players then take turns in a clockwise order.

2. All player's markers start on the orange start space and move in the direction of the arrow, clockwise, around the board.

3. Players advance around the board by the number that shows on the die.

4. When a player lands on a tangram space he or she takes the equal tangram shape and color from the tangram Bank. For example: landing on the large green triangle at one corner of the board allows the player to take a large green triangle from the Bank.

When a player lands on a Chance space, the player takes a Chance card and completes the action described, and places the card face up on the used pile on the board. If the action is not possible, the player loses the Chance and places the card face up in the used pile.

If a player lands on the start space, he or she may take a tangram piece of their choice from the Bank.

Levels of Play

Introductory Level

Players use the tangram cards with lines filled in to indicate the solution to the puzzle.

Advanced Level

Players use the tangram cards showing only the silhouette of the puzzle. Players must determine where pieces fit in order to complete the puzzle.

Strategies

When a player draws a Chance card to take or trade with another player, two strategies are possible:

a) take or trade a piece from the player closest to winning

b) take or trade a piece to increase his or her own possibility of winning


Design Process

The overarching objective of the board game is to reinforce geometric shapes and spatial relationships. In keeping with accepted board game design concepts we decided to have few ancillary materials. The game pieces are one die, player markers, Chance cards, tangram cards containing a puzzle for each player to complete and three sets of four colors of tangrams.

To maintain integrity between the content and the design, the board was constructed with the race path made of tangram shapes. The interior of the race path is a tangram figure.

The process we experienced was iterative. Initially, we described basic race game rules and began playing the game with rapid prototype pieces. With each iteration of the game we recorded the difficulties and then modified the rules, board design, chance opportunities and number of tangram sets in the Bank. Then we played the game again incorporating these new changes, noting new difficulties and making the next round of changes. Each iteration of the game was with the concept of improving the challenge, curiosity and control as Malone and Lepper (1987) describe. We increased the challenge of winning by requiring players to complete the trangram with one color. We increased the curiosity by making the tangram Bank passed around from player to player, requiring them to find the necessary piece. Initially, we considered placing the tangram pieces in a tray, all pieces separated. We allowed players to decide which color to use to build their figure. Initially we considered making the player build their figure with pieces of the same color as their marker. Players gained control over their figure by analyzing how many pieces of one color they had and then determine which color to capture.

Our first thoughts of the objectives and design of the game were very similar to the final outcome. The basic concept of the race, components and procedures remained the same. The changes were to the number of tangram pieces in the Bank, the number of spaces around the board, the path around the perimeter of the board instead of around the perimeter of a large tangram, and the category of Chance actions.

Initially, we considered playing with one set of each of four colors of tangrams in the Bank. This resulted in no possibility of winning the game. We added a second set, one set each of four colors, which increased the possibility of winning, however it made the game very long. Playing with three sets of tangrams allows the game to be completed in about 30 minutes. The flow of the game improved when we used three sets of four colors of tangrams.

At the outset, Chance cards were very specific about what pieces to trade or give up. In the iterative process we discovered that too often the specific action did not apply, therefore decreasing interest in the game. Making the Chance more generic increased the possibility of taking the Chance action, which increased interest in the game.

We gathered background information by analyzing other race board games with chance cards and by researching tangam figures in books and on Web sites. We also used a math lesson from Mathematics and the Internet, by Hope Campbell, published by DDC Publishing.

Outside feedback for the game design and rules came from a subject matter expert, a former fifth-grade teacher who used game development within his curriculum. One important idea was to make the tangram cards with one design to a card, rather than a design printed on both sides of the card. From a high school student we received feedback that the rules were fair and the game was fun. Fellow graduate students provided feedback regarding the aesthetics of the board design.

To create a prototype game we first made a construction paper game. It was three iterations from original to final design. We transferred the design to a standard-sized game board. Original construction paper tangrams were replaced with purchased tangrams. Chance cards were made from cardstock. Die and markers are standard game pieces. The box is a standard game box.

The lessons learned include: simplicity, simplicity, simplicity. Play the game multiple times, each time modifying the directions to solve any problems and ambiguities.


References

Books & Journals

  • Malone, T. W., & Lepper, M.R. (1987). Making learning fun: A taxonomy of intrinsic motivations for learning. In R. E. Snow & M. J. Farr (Eds.). Aptitude, learning and instruction. Volume 3: Cognitive and affective process analysis. Hillsdale, NJ: Lawrence Erlbaum.
  • Read, R. C. (1965). Tangrams - 330 Puzzles. New York, NY: Dover Publications, Inc.
  • Seymour, D. (1971). Tangramath. Palo Alto, CA: Creative Publications, Inc.
  • Van Note, P. (1966). Tangrams. Picture-making puzzle game. Tokyo, Japan: Charles E. Tuttle Company.

Electronic

  • Java Tangrams
    (http://www.win.bright.net/~gadams/tangrams/javaIndex.html)
  • A Math Forum Web Unit: Tangrams
    (http://forum.swarthmore.edu/trscavo/tangrams.html)
  • Tricon Publishing
    (http://www.triconpub.com/PUZZLES.html#Tangrams)


Game Board

 

Chance Cards Categories

  • Take from bank
  • Take from player
  • Trade with player
  • Trade with bank
  • Combine two small triangles for one parallelogram
  • Combine two small triangles for one medium triangle
  • Combine two small triangles for one square

     

     

Tangram card with lines

Tangram card with tangram silhouette


 

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Last updated October 25 1999