Integer Matrix

Created by Karen Boe & John Spiegel


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


Instructional Objective

Integer Matrix was created to have the learner practice adding integers.
The game meets the following California State Math Standards.

5th Grade Standard
Number Sense
2.1 Add with negative integers and positive integers.

6th Grade Standard
Number Sense
2.3 Solve addition problems that use positive and negative integers
and combinations of these operations.

7th Grade Standard
Number sense
1.2 Add rational numbers (which includes integers)

The game meets the following National Math Standards:

Grades 6-8
Understand numbers, ways of representing numbers,
relationships among numbers, and number systems.
Develop meaning for integers and represent and compare
quantities with them.


Learners & Context of Use

Integer Matrix is designed for two players, but it can be utilized in a classroom setting with four players with two per team. The game is focused on math students practicing how to add positive and negative integers. This typically occurs in the United States in 5th, 6th, and 7th grade (age 10 to adult). The players needs to have basic prior knowledge on how to add integers at a very introductory level. Integer Matrix will provide the practice to perfect the players ability level. Integer Matrix takes minutes to learn, but a Millennium to master.


Object of the Game

The object of the game is to create a net positive or negative score that is farthest away from zero through the addition of integer matrices.


Game Materials
  • Game board
  • 49 game discs (as detailed by the following table )

1,0

2,0
3,0
4,0
-1,0
-2,0
-3,0
1,-1
2,-1
3,-1
4,-1
-1,1
-2,1
-3,1
1,-2
2,-2
3,-2
4,-2
-1,2
-2,2
-3,2
1,-3
2,-3
3,-3
4,-3
-1,3
-2,3
-3,3
1,-4
2,-4
3,-4
4,-4
-1,4
-2,4
-3,4
0,0
0,2
0,4
0,-2
-4,0
-4,1
-4,3
0,1
0,3
0,-1
0,-3
0,-4
-4,2
-4,4
  • Game disc storage bag
  • Net score sheets
Integer Matrix Score Card
Name:
Negative
Name:
Positive

 

 

 

 

 

 

 

 

 

 

 

 

 


Time Required

Integer Matrix only takes minutes to set up. The length of the game is determined by the skill level of the players, on average a game takes 20 to 35 minutes to complete. To master the matrix may take a millennium. In a classroom setting ideally it should take one hour to explain the game and allow students to play Integer Matrix.


The Rules

Click here to view the official rules of Integer Matrix.


Design Process

  • Brain Storm for Content Analysis
    All ideas and thoughts were compiled onto a paper.
    The focus of the session created a focus on integers as a topic.
    Several game ideas came to mind.

  • Incubation
    Ideas were left to simmer in the gray matter.

  • Chunking
    Pieces: chips
    Patterns: Linear lines such as seen in mathematical equations
    Paths: relate to mathematical equations that contain multiple numbers
    Probabilities: when a player chooses at random the game chips from a bag
    Prizes: the player with the largest score is the winner
    Principles: In theory if the player understands the concept of adding integers she/he
    should be able to play the game at a basic level. Then the player can work on mastering the subtleties of the board game.


  • Aligning
    The general theme of a Othello game was used as a template to start with. The main pattern within the game was adding integers in a linear manner. This transferred to the game board by selecting a linear pattern for the game board by considering plays both horizontally, vertically, and diagonally (see rules). This gave the player various options of where to place their chip and determine their score. Initially when there are few chips on the board a player can remember what number is on the back of the chips, but after a few rounds the player only knows that if the chip is positive on the front the back must be negative or zero and visa versa. The game offers changing conditions with each play. As the chips are turned over the numbers change and so does the possibility of the score for that round. This also affords a bit of random unpredictability to the game based on the fact that you can not predict how the board will look for your next turn. The player must always be thinking and planning there is no down time in this game.

  • Drafting
    Initially we used some foam pieces and wrote numbers on them. A eight by eight game board similar to checkers or Othello was used. The game started out with four pieces two black and two white placed in the middle four squares just like one would do when playing Othello After about four rounds it was determined that four chips to start was too few. We also found that the game board ended up turning one color or the other quite quickly thus ending the game.

  • Incubating
    At this point we walked away from the game. Further research was conducted and a Othello game was purchased, played, and the rules analyzed.

  • Prototype testing
    After further research a board that was 7 by 7 squares was selected. Nine squares in the middle were to be predetermined by random draws and placement based on the players color (see rules). The rule that the game board could not be turned completely one color alleviated the issue of the game ending to quickly. The game was then tested by the creators extensively.

  • Beta Testing
    Several individuals were selected to test the game. The individuals who tested the game were asked how they liked the game afterwards. They stated that it was engaging and after an initial learning curve they were intrigued by the strategy of the game beyond the simple adding of integers. Where you placed your chip had to be well thought out so as to attain the highest possible score and thwart your opponents next move. Further Beta testing is to take place in 6th and 7th grade math classrooms. Currently game production is taking place so as to provide a classroom with an ample supply of games to play in teams of four.

  • Further Thoughts
    After completing the game we thought we had made too simple of a game, but that is actually the beauty of it. It is clear, concise, and easy to learn. In looking toward making another game the challenge would be to maintain the simplicity in the game yet provide a game that is engaging and challenging. Aligning the game with the what is to be learned is the most important challenge of a game designer. It is easy to wander from the main objective if you are not careful.


References

Books & Journals

  • Rouse, Richard. Game Design: theory and practice, Worldware publishing, Inc. Plano Texas. 2001.

Electronic


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Last updated October 2001

Copyrightę2001.