Project Title

It’s all Fun and Games

 

Introduction

In algebra variables are used to represent unknowns.  When first beginning algebra, the symbolic representation can be difficult.  By now you should be quite comfortable with x and y, as symbols for unknowns, however, the roots of mathematics are engrained in complex symbol-based number systems.  Get ready to explore these ancient systems and become an expert at interpreting and using the symbols found within!

 

Task

Working together with your group, you will research one of four ancient number systems.  Then, based upon what you have learned, you will design a team game based on that number system.  The game needs to be complete with rules, scoring guidelines, and dimensions of the field based on the ancient number system.  Finally, you will calculate the perimeter of your field, using the number system.  

 

Instructions

Solve each problem in order.  Save your work along the way, as you will create a presentation at the conclusion of the project.  Your audience will be the Mayan, Egyptian, Sumerian, or Roman people.  You may use multi-media, make a movie, or create a website to highlight your game and how it connects to the number system.

 

1                     First problem:

·                     With your group, choose one of the ancient number systems below to research.  You may use the following links to begin, but there are multiple websites dedicated to the number systems.

 

Egyptian: 

http://www.touregypt.net/featurestories/numbers.htm

 

Mayan: 

http://www-history.mcs.st-and.ac.uk/HistTopics/Mayan_mathematics.html

 

Roman: 

http://turner.faculty.swau.edu/mathematics/materialslibrary/roman/

 

Sumerian: 

http://www.storyofmathematics.com/sumerian.html

 

·                     Use the following questions to guide your research:

How do you write the following numbers:  1, 5, 10, 20, 50, & 100?

What is the base of the number system? 

How has the number system impacted the base ten system that is used today?

How do you perform basic addition using the number system?

 

2                     Second problem:

·                     Once your group has a good understanding of the number system, begin thinking about games that are played today and how they might be adapted to fit with the number system.  For instance, consider football.  The field is based on 100 yards and advancing the ball is based on ten-yard increments.  This game would fit well for the Egyptians and Romans, but not for the Sumerians and Mayan.  Creativity and originality will make your presentation stand out.

 

·                     A good example of a made-up game is “Quidditch” from the Harry Potter book series. Information about the fictional game, including rules and field dimensions can be found at: http://en.wikipedia.org/wiki/Quidditch

 

·                     First, decide the dimensions of your field.  Be sure to keep in mind the foundation of your number system when making your decisions.  Your dimensions should be written using the symbols from the system.  You can draw a picture of your field using drafting software such as, Google Sketchup.  The free download is available at http://sketchup.google.com/.  If you have an artistic flair, a hand-drawn field or court is another option.

 

3          Third Problem:

·                     Now your team needs to work on developing rules and scoring guidelines for your game.  What tools are necessary to play?  How many points are various tasks worth?  How many points are necessary to win?  How many players are on the field at once?  Make sure to consider how the answers to each of these questions would be impacted based on the number system that is studied.

 

Hint:  (Remember that you will be presenting the game at the end of the project.  It may help to actually go outside and attempt to play the game in order to discover what works and what does not.)

 

4          Fourth problem:

·                     Your final task is to calculate the perimeter of the field, using the number system studied.  Begin by learning to add small numbers within the system and then work your way to larger numbers.  You will need to include the detailed process that was used to add the perimeter as part of your presentation.

  

Collaboration

Get together with another group to discuss your game and how it is played.  Discuss how the rules and field dimensions relate to what you have studied about the number system.  Finally, work together to check each other’s perimeter calculations.  While reviewing the perimeter calculations, answer the following questions:

·                     How is adding within your number system related to adding polynomials?

·                     Do you see any other ties to algebra within your calculations?

 

Conclusions

Now you will get to present your game using modern technology to your classmates, who will be considered citizens of the ancient civilization that you researched. Some options for the presentation include using multi-media, making a movie, or creating a website to highlight your game and how it connects to the number system.  Your presentation should include answers to each of the four problems above.    

 

Grade

Your project will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:

 

Score	Content	Presentation
4	Your project appropriately answers each of the problems.  Background research is thorough.  A detailed drawing of the game field is given, with dimensions labeled using the number system.   Rules and scoring guidelines are complete and relate to the number system studied.  A detailed calculation of perimeter, in the number system, is included.	Your project contains information presented in a logical and interesting sequence that is easy to follow.   Your project is professional looking with graphics and attractive use of color.
3	Your project appropriately answers each of the problems.  Background research is thorough.  A detailed drawing of the game field is given, with dimensions labeled using the number system.  Minor errors may be noted.   Rules and scoring guidelines are complete and relate to the number system studied.  A detailed calculation of perimeter, in the number system, is included.  Minor errors may be noted.	Your project contains information presented in a logical sequence that is easy to follow.   Your project is neat with graphics and attractive use of color.
2	Your project attempts to answer each of the problems.  Background research is present, but not complete.  A drawing of the game field is given, with dimensions labeled using the number system.  Major errors may be noted &/or some information is missing.   Rules and scoring guidelines present and relate to the number system studied.  The perimeter is given, but the detailed work used to obtain the answer is not given.  Major errors may also be noted.	Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.   Your project contains low quality graphics and colors that do not add interest to the project.
1	Your project attempts to answer some of the problems. Major errors are noted and information is missing.   Your project has minimal information on rules and scoring guidelines.  The perimeter calculation is missing.	Your project is difficult to understand because there is no sequence of information.   Your project is missing graphics and uses little to no color.