INVESTIGATING THE MATH BEHIND NUMERICAL
have never learned that much in such a short time. . ."
will amaze their classmates, friends, and families as
they read minds . . . predict the future
. . . and compute large sums instantly . . .
with mind-boggling mathemagical tricks such as Tattletale
Dice, The Red-Hot Kid, and See Ya Later, Calculator. The
math detectives are then challenged to discover the intriguing
math behind the magic.
. . It encouraged students to think algebraically . . .
and to explain their thinking in mathematically rigorous terms."
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.
. . . had something new and fun to share with her family every
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.
"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
It's All Done with Numbers!
The Reverso Phenomenon
Uno . . . and Other Lucky Numbers
The Power of Zero—It's No Secret!
Mind Over Machine
See Ya Later, Calculator
The Fabulous Fibonacci Pattern
Nine Power . . . and More
Magic Squares and Their Magic Cousins
Secrets of the Magic Square
Constructing Magic Square Puzzles
Mastering the Magic Square
Magic Triangles and Other Magic Shapes
Transforming Magic Squares
Geomagic Circle, Make Me a Star!
Taming a Geo-Monster
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
• Choose a number and follow the steps above to get a
• 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?
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
— 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
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.
Showtime! at a Glance
To help each student develop:
• A powerful repertoire of problem-solving
• 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 Content: The 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
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.
ISBN 0-9704459-1-1 140 pages
Online . . .
Phone . . . 800-649-5514