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Mathemagical Showtime Book
Investigating the Math Behind Numerical Magic Tricks
Carl Sherrill

Mathemagical Showtime at a Glance

If you love helping students experience the magic of mathematics, this dynamic, creative approach is just what you're looking for. Mathemagical Showtime links children's natural love of magic tricks with important standards-based concepts. This high-quality program gets results because it sparks interest while it supports understanding.

Mathemagical Showtime provides a meaningful context for investigating patterns and functions – along with lots of mental math and basic skills practice.

The investigations cover a range of difficulty appropriate for upper elementary and middle school students. Supporting the blackline masters are classroom-tested, teacher-friendly directions and a commentary featuring actual student examples.

To help each student develop:

• A powerful repertoire of problem-solving strategies
• The ability to represent mathematical ideas using words, charts, and tables
• The recognition of patterns and functional relationships
• Facility with basic math facts and operations
• Confidence in self as a problem solver

Mathematical ContentThe lessons emphasize algebra, number, geometry, logic and language.

Ability Levels:  Recommended for ages 10 to 13. Problem sets of varying difficulty are provided.

Integrations Reading, writing, and oral language



Investigation 1
It's All Done with Numbers!

Tattletale Dice
The Reverso Phenomenon
Menu Activities
Uno . . . and Other Lucky Numbers
The Power of Zero—It's No Secret!
Designer Magic

Investigation 3
Mind Over Machine

See Ya Later, Calculator
The Fabulous Fibonacci Pattern
Menu Activities
Seeing Double
Nine Power . . . and More
Why 3367?

Investigation 2
Magic Squares and Their Magic Cousins

Square Magic
Secrets of the Magic Square
Constructing Magic Square Puzzles
Menu Activities
Mastering the Magic Square
Magic Triangles
and Other Magic Shapes Assessment
Transforming Magic Squares

Investigation 4
Geomagic Circles

Geomagic Circle, Make Me a Star!
Menu Activities
Geomagic Explorations
Taming a Geo-Monster

Sample Lessons

Tattletale Dice

Draw three short lines, one above the other.
Give the other person the dice. Turn your back.
Tell the other person to do the following:

   1. Choose a number and write it on the first line.
   2. Roll the dice.
   3. Add the numbers on the tops of the dice,
       and write the sum on the second line.
   4. Add the numbers on the bottoms of the dice,
       and write the sum on the third line.
   5. Add up the three lines and give the final sum out loud.
   6. Think hard for a few seconds.
       Then tell which number the other person picked.

How is the trick done? Find out for yourself!
   • Choose a number and follow the steps above to get a final sum.
   • Repeat this many times, choosing a different starting number each time.
   • Keep careful track of the starting and ending numbers. Organize your data.
   • Look for a pattern in the data.

Follow-Up Question: How would the trick work with 3 dice? With 1 die?


Magic Sum Magic

Explain to the other person that you have a special "square power" that allows you to create a magic square with any given sum.

   1. Show the other person Magic Square 15 (at right).
   2. Show that the rows, columns, and diagonals all add up to 15.
   3. Ask the other person to pick a number between 18 and 48
      — one that can be divided by 3.
He or she should pick one of these "magic sums":
18 21 24 27 30 33 36 39 42 45 48
   4. Draw the new magic square.
   5. Have the other person check to make sure that the sums are correct.

How is the trick done? Here are some hints:
   • It helps to know the middle number of the new square.
       How can you figure that out?
   • Compare the middle number of the new square
       to the middle number of Magic Square 15.
What is the difference?
   • Look for patterns in Magic Square 15 that might help you
       create the new square.

Note: If you are not getting anywhere, spend some more time working on Constructing Magic Square Puzzles I. Also, look for solutions to Magic Squares 12 and 18 that are similar to Magic Square 15.

4 9 2
3 5 7
8 1 6


"I have never learned that much in such a short time. . . Let every school have the book and teach all of them because they would all be looking forward to learn all the tricks." 
— Mayra, 6th Grade Student

"Mathemagical Showtime was very valuable. . . It encouraged students to think algebraically, to use appropriate symbols, and to explain their thinking in mathematically rigorous terms. I had a number of parents comment at Open House as to how much their family enjoyed working on the tricks after dinner.”  — Erik Bennett, 6th Grade Middle School Teacher

“We have enjoyed watching and participating in the math tricks. It is fun to see our son astound our friends as well as ourselves.”  — Michelle Townsend, Parent

Mathemagical Showtime was very exciting. I never knew math could be done that way."
— David, 5th Grade Student

“Even though this was a ‘math’ class, as my daughter would say, she had something new and fun to share with her family every day. I consider that a success.”  — Greg Curtis, Parent

Author's Note on "Mathemagic"

To many students, mathematics is a kind of magic—an "occult science" whose secrets are somehow, mysteriously, revealed to some but not to others. The paradoxical message of Mathemagical Showtime! is that math is not magic, and that it doesn't take a "mathemagician" to understand the basic logic and language of mathematics.

Mathemagical Showtime! provides a high-interest context for investigating important mathematical ideas, with a particular focus on patterns and functions. Using magic tricks and stunts to enrich the math curriculum is certainly not a new idea—the math education literature is full of suggestions for "mathemagical" demonstrations. To date, however, there has been no effort to group these activities into a teachable classroom unit organized around a coherent body of mathematical ideas. Moreover, most suggestions for using numerical magic tricks call for the teacher to reveal the "math behind the magic"—rather than having students discover the magician's secret in the course of an investigation.

For the latter idea, I am indebted to Marilyn Burns, who was kind enough to look over an early, very rough draft of the unit. Marilyn helped reword the first investigation and piloted it with a group of students. This was a turning point in the evolution of the unit. What had been up to this point an enjoyable and stimulating set of enrichment activities became a series of serious—and much more engaging—investigations.

Many thanks to Carl Sherrill for permission to display these lyric excerpts.
© Carl Sherrill. All rights reserved. Used with permission.




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