Teacher's Guide for ODYSSEY^TM Magic in Math

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      Summary
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"The Puzzling Business of Sam Loyd and Enro Rubik," pg. 6

• The Fifteen Square of the 1800s and the Rubik's Cube of the 1980s captivated with their unique brands of wizardry. The puzzle masters who invented these "toys" are profiled briefly, and Web sites direct interested "gamers" to find out more.
• Invention, Logic

"Number Secrets" (Activity), pg. 10

• Discover Pythagoras's secret history of friendly, perfect, and prime numbers. Then grab some scissors and prove Pythagoras was right about right triangles.
• Vocabulary, Following Directions

"What's So Magical About Magic Squares?" pg. 13

• Magic squares may seem like mathematical madness, but anyone who knows the rules can produce them. Explore the history of this ancient pastime and discover the shortcuts that make constructing them a little less magical.
• Vocabulary, Deductive Reasoning

"Magic Square Mix-Up" (Brain Strain) pg. 17

• Help Susie rebuild her magic square and save her cat from a scolding. Stuck? Reread the prior article!
• Following Directions, Inductive Reasoning

"Tesseracts: Cubes Get Hyper," pg. 18

• Author Madeleine L'Engle uses tesseracts for space travel in her novel A Wrinkle in Time. Although "real" tesseracts may not serve as transportation, these four-dimensional hypercubes are a "trip" nonetheless.
• Spatial Relations, Extrapolation

"John Hendricks: Math Magician" (People to Discover) pg. 19

• He worked as a meteorologist and as a forest ranger, but even after nearly perishing in a forest fire, John Hendricks was grateful that his math notes didn't burn. Hendricks looks back on his 70+ years and recalls the bimagic cubes he has created.
• Vocabulary, Extrapolation

"Martin Gardner: Recreational Math Master" People to Discover) pg. 22

• Although his college training was in philosophy, Martin Gardner is best known for his math puzzles, riddles, and tricks. His puzzle columns have appeared in magazines ranging from Humpty Dumpty to Scientific American.
• Divergent Thinking, Logic

"Make a Hexa-Hexa-Flexagon!" (Activity), pg. 25

• A few careful folds and you can have your own hexa-hexa-flexagon, complete with hidden faces.
• Spatial Reasoning, Following Directions

"Could We Ever Colonize Mars?" pg. 27

• John Conway thinks so, and he has the mathematical game to prove it! Conway has explored the application of numbers theory to everything from ecology to dominoes. In sidebars, learn how to determine the day of the week for any date in history, and how to win at boxes and dots.
• Deductive Reasoning, Applications

"Rounding Up Camels," pg. 32

• How can 17 camels be divided among three brothers? Adding one camel not only gave each brother more than he thought possible, but also even left that one added camel to be returned to its owner.
• Inductive Reasoning, Problem Solving

"Knot Magic NOT Magic," pg. 36

• Magicians tie what seem to be intricate knots in long strands of rope, only to untie them with a single tug. Mathematicians use a closed loop of rope to design knots. Experiments with the mathematics of knot helps biologists learn more about DNA, drugs, and viruses.
• Applications, Hypothesis Formation

"Taking Math into the Streets," pg. 38

• George Nobl takes math onto the sidewalks of New York. Passersby solve a problem and win a candy bar. Nobl will do whatever it takes to sell the idea that math is fun.
• Mathematical Reasoning, Applications

"Hunter's Moon & Great Planet Hunting" (What's Up and Planet Watch) pg. 40

• Go on a hunt for the evening planets (Saturn and Venus) and the morning planets (Jupiter, Mars, and Mercury). Watch for the Orionid meteor shower on the 22nd.
• Observation, Following Directions

"Solar System Sports!" (You Can Do Astronomy), pg. 42

• Construct a scale model of the solar system using commercially available balls, or construct your own from Styrofoam.
• Following Directions, Mathematical Scale

1. Why do some people love math while others fear it? List reasons, and then discuss ways to change the minds of the "math phobic."
2. Talk about favorite puzzles, brainteasers, and magic tricks. Do any have a basis in math?

Pg. 6 - "The Puzzling Business of Sam Loyd & Enro Rubik"

• Talk It Over:
  1. How did the Fifteen Square and the Rubik's Cube became international crazes? What other puzzles have become fads in recent history? Why do people become obsessed with them?
  2. Neither Loyd nor Rubik amassed great wealth in return for his invention. Why not? Was that fair?
• Connections:
  1. Computer Skills: If your school has a computer lab room, take the class there and have them log onto the on-line Rubik's Cube game site mentioned on page 9. Set up a class competition for solving the cube, with individual or team events.
  2. Visual Arts: Review one of the Web sites or booklets describing how to solve the Rubik's Cube. Simplify this information into four or five clear steps and illustrate these steps on a poster. Challenge classmates to follow your plan for solving the puzzle.
  3. Mathematics: On page 9, the author states: "The nine cubes forming one face can be rotated through 45 rotations. There are 43,252,003,274,489,856,000 different arrangements of the small cubes . . . " Work with a partner (or two) to see if you can figure out how that number was obtained. If you can make the calculation, try explaining it to someone else.
• Student Assessment:
  1. Write an essay comparing and contrasting the lives of Sam Loyd and Enro Rubik. Conclude with your assessment of what it takes to become a puzzle master.
  2. Who should win the title of "The Puzzle King," Sam Loyd or Enro Rubik? Pick your candidate, organize your reasons, and prepare a three-minute speech to persuade a panel of judges.

pg. 18 - "Tesseracts: Cubes Get Hyper"

• Talk It Over:
  1. How does a square become a cube? How can we use that idea to see how a cube becomes a tesseract? Is it possible to think in four dimensions? Imagine and describe what life would be like in a four-dimensional world.
  2. Madeleine L'Engle proposes that time folds in four dimensions. How does that make "tessering" possible? Consider what a fold in three dimensions would do to a two-dimensional letter on a printed page. Can you see how the letter could "step" through the fold and across space?
• Connections:
  1. Visual Arts: (In preparation, photocopy the diagram of a tesseract on page 19 so that each student has two copies.) Just as a three-dimensional cube contains six two-dimensional squares (the sides of the cube), a four-dimensional tesseract will contain eight three-dimensional cubes (the "sides" of the tesseract). Use colored pencils or markers to find and outline the eight cubes in the diagram. (The cubes will look distorted and the sides and angles will not appear equal.) Once you find all eight cubes, use your second copy to make a colorful representation of tesseract "art."
  2. Creative Writing: Pretend that you had a real tesseract, and that you could use it to step across space or time to anywhere or any-when in the universe. Where and when would be your destination? Turn your trip and your "landing" into a short story, complete with conflict and a twist ending.
  3. Geometry: Review the part of the article that describes how a cube becomes a tesseract. Now consider what happens to a circle in order to produce a sphere. Apply that same thinking to explain how a sphere might become a four-dimensional "hyper-sphere." Make a poster illustrating your ideas, with notes to explain the steps involved.
• Student Assessment:
  1. In your own words, explain how mathematicians move from one dimension to two, to three, and to four. Use objects (points, lines, etc.) in your explanation.
  2. You are trying to sell a house to a client. The house looks like a simple cube, but you know that, in fact, it is really a tesseract. Organize and present a sales pitch, convincing your client to buy this rather ordinary looking (at least from the outside) house.

"If 400 hundred grams is a pound,"

Whole-Class Project: In your school's hallway or lobby, design a display of magic squares. In your display, show how magic squares are created. Include space on the display for passersby to make their own magic squares. Give prizes to especially deserving creations.

"Then why do they stutter and stammer"

Small-Group Projects: Divide the class into pairs. Each pair of students is to select a famous mathematician (or puzzle-maker) and write a profile of that "celebrity." Use the library and the Web for research, and find a picture, when possible. Display profiles or have students present them to the class.

"When I ask for some pickles and onion"

Community Connection: Ask one of the advanced mathematics teachers from the high school to visit your classroom and bring his or her class along. Ask the teacher to talk about the fun of working with theoretical and irrational numbers. Ask the high school students to teach math games to your class.

"And cheese on a one-hundred-grammer?"

Whole-Class Activity: Organize a math-game carnival. Have students bring from home Rubik's Cubes, rope to practice knots, tangrams, and any other puzzles. Arrange competitions and invite another class to join the fun.

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Updated: 11/21/09 09:20 am
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