Teacher
Mr. Dustin Guntle
6th Grade Mathematics
Magic Squares
Illinois Learning Goals and Standards:
State Goal 6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations (addition, subtraction, multiplication, division), patterns, ratios and proportions.
B. Investigate, represent and solve problems using number facts, operations (addition, subtraction, multiplication, division) and their properties, algorithms and relationships.
6.B.3a. Solve practical computation problems involving whole numbers, integers, and rational numbers.
C. Computer and estimate using mental mathematics, paper-and-pencil methods, calculators and computers.
6.C.3a. Select computational procedures and solve problems with whole numbers, fractions, decimals, percents and proportions.
6.C.3b. Show evidence that computational results using whole numbers, fractions, deciamls, percents and proportions are correct and/or that estimates are reasonable
NET-S
1. Creativity and Innovation
a. apply existing knowledge to generate new ideas, products, or processes.
2. Communication and Collaboration
d. contribute to project teams to produce original works or solve problems
6. Technology Operations and Concepts
a. understand and use technology systems.
Introduction
In this project, your group will become experts on magic squares. Each group will have three members with distinct roles. In order to help your group become experts, each individual will have to do research on particular magic squares and search for the possible existence of a magical formula that enables one to create such a square. The group will need to put together a power point presentation with information about magic squares, present a possible formula for magic squares, and also present one that they have created (minimal 4X4).
Task
ü Research background information on the Lo Shu, Benjamin Franklin, or The Sator magic squares.
ü Give examples of magic squares and see if it is possible for magic squares to be generalized using equations.
ü Create your own magic square- either from guess of check or from the use of the equation, if it exist.
Process/Resources
The Researcher
The Researcher will be the main person to research the history of magic squares.
Steps:
1.) Research the history of magic squares.
2.) Find out as much information as possible about The Sator magic square and the Benjamin Franklin magic square.
Helpful Sites:
1.) http://pballew.net/magsquar.html
2.) http://mathforum.org/alejandre/magic.square/sator.html
3.) http://www.grogono.com/magic/history.php
The Historian
The Historian is in charge of finding out all the available information about the Lo Shu magic square.
Steps:
1.) Research the Lo Shu magic square and figure out where it came from.
2.) Find a picture of the magic square and figure out what everything adds up to.
3.) Is this a special magic square, meaning for than just the columns and rows add up to equal the same thing?
Helpful Sites:
1.) http://mathforum.org/alejandre/magic.square/loshu.html
2.) http://pballew.net/magsquar.html
The Mathematician
The mathematician is in charge of figuring out if a “magic” formula excists and creating a personalized magic square for the group. (DO NOT SIMPLY SEARCH FOR ONE ON THE INTERNET!)
Steps:
1.) If the formula excists, state it.
2.) Create your own magic square. This must be at least a 4X4. And remember, simply do not search for one on the internet. ( I can find out with ease and that would not settle well with your group members!)
Helpful Sites:
1.) http://www.grogono.com/magic/formula.php
2.) http://www.halexandria.org/dward090.htm
Evaluation- see attached rubric
Conclusion
Congratulations! You and your group are now experts on magic squares. Anytime your parents need a magician, you can tell them to hire you because you know magic. As a group, you have also become historians and became knowledgeable about the history of a culture, a subject in school, and of a particular magic. If you feel the need to learn more about this magic, the local library has books about the history of mathematics and it will definately answer any questions you may have. Just don't use your newfound magical powers on the librarian!
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