|
The books annotated below delve into a wide spectrum of mathematical,
problem-solving, and other game-related strategies, concepts,
and skills. Given the range and cultural breadth of this GEMS
guide, we have also sought to represent multicultural problem-solving,
as for example in Stories to Solve and More Stories
to Solve, which contain challenging folktales from around
the world. Other books focus on specific mathematical concepts
raised by the games in this guide, such as networks and topology,
probability and statistics, logical thinking, strategy development,
and real-life applications of mathematics. An "electronic
book" available on the Internet and a magazine on games are
also included.
You and your students may have other favorite books that connect
to mathematical games and problem-solving challenges of diverse
cultures—send us your suggestions and we’ll consider
them when this guide is revised. If you are focusing on a specific
mathematics strand or concept, you may also want to consult the
GEMS literature handbook Once Upon A
GEMS Guide: Connecting Young People’s Literature to Great
Explorations in Math and Science.
Alice’s Adventures in Wonderland
Anno’s Math Games III
Anno’s Mysterious
Multiplying Jar
Do You Wanna Bet?
The Eight
The Eleventh Hour: A Curious Mystery
A Grain of Rice
The Great Adventures of Sherlock Holmes
Jumanji
The King’s Chessboard
Maps, Tracks, and the Bridges of Königsberg
Melisande
More Stories to Solve
The Phantom Tollbooth
Rubber Bands, Baseballs and Doughnuts
Sideways Arithmetic from Wayside
School
Socrates and the Three Little Pigs
Stories to Solve: Folktales
from Around the World
Through the Looking Glass
The Toothpaste Millionaire
Maze
Alice’s Adventures in Wonderland
by Lewis Carroll
Viking Penguin, New York. 1984
Grades: 4–Adult
Logic is turned on its head during Alice’s adventures
in Wonderland. Nearly every page contains some twist on what we
usually perceive and expect to happen. Logical thinking in all
its paradoxes abounds in this classic as the mathematician-author
has a field day caricaturing the processes of human thought. Especially
hilarious, and a test of logical thinking, is Alice’s meeting
with the caterpillar in Chapter 3. Gives students a look at the
lighter side of logic. Ties in "logically" with NIM
(Game 1), Kalah (Game 2), and Hex (Game 8).
Anno’s Math Games III
by Mitsumasa Anno
Philomel Books/Putnam & Grosset, New York. 1991
Grades: 4–10
Picture puzzles, games, and simple activities introduce the
mathematical concepts of abstract thinking, circuitry, geometry,
and topology. The book invites active participation. Chapter 1,
Changing Shapes with Magic Liquid, is a good introduction to topology,
which is then explored further in Chapter 3, Mazes. It is this
chapter which connects best to Game 4, Shongo Networks, in Math
Around the World. There is even an illustration of the Königsberg
Bridge Problem in Chapter 3 and a discussion of it in the Afterword.
Anno’s Mysterious Multiplying
Jar
by Masaichiro and Mitsumasa Anno
Philomel/Putnam & Grosset, New York. 1983
Grades: 3–8
Through an understanding of multiplication, the reader can
learn about factorials and the way that numbers can expand. On
a second reading of the book, students can follow along using
calculators to verify the large number of jars at the end of the
story. Though this book concentrates on factorials, it can lead
students to an understanding of exponential growth, as explored
in Game 3, Tower of Hanoi.
Do You Wanna Bet?
Your Chance to Find Out About Probability
by Jean Cushman; illustrated by Martha Weston
Clarion Books/Houghton Mifflin, New York. 1991
Grades: 4–6
Two boys find that the most ordinary everyday events and activities
such as card games, coin flips, sports scores, and statistics—even
weather prediction—are dependent on the subtle interplay
of many factors of chance and probability. Includes bibliographical
references and index. Ties in very well with Game 6, Game Sticks.
The Eight
by Katherine Neville
Ballantine Books, New York. 1988
Grades: Adult
This is an adult-level novel and is therefore recommended
for older, advanced students. Much of the book involves games
(lots on Magic Squares and chess), logic, and strategy in an intricately
woven plot. It has references to the Knight’s Tour and Benjamin
Franklin as well as math and music. It also refers to Bach, Boswell,
Wordsworth, Blake, Newton, Voltaire, Euler, and Fibonacci numbers.
The Eleventh Hour: A Curious Mystery
by Graeme Base
Harry N. Abrams, New York. 1989
Grades: 3–8
An elephant’s eleventh birthday party is marked by eleven
games preceding the banquet to be eaten at the eleventh hour,
but when the time to eat arrives the birthday feast has disappeared.
Rhyming text and gloriously detailed illustrations contain cryptic
clues and hidden messages to keep sleuths searching for the thief.
A great book for developing visual-discrimination and logical-thinking
skills, thus relates well to all games in Math Around the World.
A Grain of Rice
by Helena C. Pittman
Hastings House, Mamaroneck, New York. 1986
Bantam Books, New York. 1992
Grades: 2–5
A clever, cheerful, hard-working farmer’s son wins the
hand of the Emperor’s daughter by outwitting the father who
treasures her more than all the rice in China. Pong Lo’s
winning strategy is to use a mathematical ruse, asking simply
for a grain of rice that is to be doubled every day for one hundred
days. The book clearly illustrates exponential growth as in Game
3, Tower of Hanoi.
The Great Adventures of Sherlock Holmes
by Arthur Conan Doyle
Viking Penguin, New York. 1990
Grades: 6–Adult
The search for, and discovery of, the unknown by putting together
a number of clues to find the answer is Sherlock Holmes and deductive
reasoning at their best. These, and nearly the entire canon of
Holmes adventures, are classic studies in problem-solving as the
great detective unravels each case logically, clearly, and cleverly.
Ties in with all games in Math Around the World.
Jumanji
by Chris Van Allsburg
Houghton Mifflin, Boston. 1981
Grades: K–6
A bored brother and sister left on their own find a discarded
board game (called Jumanji) which turns their home into an exotic
jungle. A final roll of the dice for two sixes helps them escape
from an erupting volcano. As students play Game Sticks in Game
6 they learn about probability and can then discuss the likelihood
of rolling two sixes.
The King’s Chessboard
by David Birch; illustrated by Devis Grebu
Dial Books, New York. 1988
Grades: K–6
A too proud king learns a valuable lesson when he readily
grants his wise man a special request: one grain of rice on the
first square of a chessboard on the first day, two grains on the
second square on the second day, four grains on the third square
on the third day and so on. After several days the counting of
rice grains gives way to weighing, then the weighing gives way
to counting sackfuls, then to wagonfuls. The king soon realizes
that there is not enough rice in the entire world to fulfill the
wise man’s request. This tale involves exponential growth
as in Game 3, Tower of Hanoi. Students can use manipulatives in
the classroom to see how quickly the rice amasses.
Maps, Tracks, and the Bridges of Königsberg:
A Book About Networks
by Michael Holt; illustrated by Wendy Watson
Thomas Y. Crowell, New York. 1975
Grades: 4–8
The subtitle says it all—this is a book about networks.
Through a series of inviting interactive pictures, the reader
is led in a discussion of networks until finally arriving at the
Königsberg bridge problem. By the time the reader arrives
there, they probably understand networks well enough that the
bridge problem seems a snap. An excellent connection to Game 4,
Shongo Networks.
Melisande
by Edith Nesbit; illustrated by P.J. Lynch
Harcourt Brace Jovanovich, San Diego. 1989
Grades: 1–8
Princess Melisande will grow up to be bald because of a curse
by an evil fairy. Upon being granted one wish, she asks for golden
hair a yard long that will grow an inch every day and twice as
fast when cut. Soon the princess realizes the implications of
her wish. With the help of a determined godmother and a prince,
order is restored. Though traditional fairy tale roles prevail,
this story lends itself to an exploration of exponential growth
and thus connects well to Game 3, Tower of Hanoi. Students can
use yarn as a hands-on tool to understand how Melisande’s
hair grows and to visualize exponential growth.
More Stories to Solve: Fifteen Folktales
from Around the World
by George Shannon; illustrated by Peter Sis
Greenwillow Books/William Morrow, New York. 1990
Grades: 3–8
This further collection of brief folktales from a variety
of cultures invites you to solve a mystery or problem before the
resolution is presented. Notes in the back of the book tell the
source of the folktale and thereby the country of origin. A superb
book for developing divergent-thinking and problem-solving skills,
this book is highly recommended as is its prequel, Stories to
Solve (see below).
The Phantom Tollbooth
by Norton Juster; illustrated by Jules Feiffer
Random House, New York. 1989
Grades: 2–8
Milo has mysterious and magical adventures when he drives
his car past The Phantom Tollbooth and discovers The Lands Beyond.
On his journey Milo encounters amusing situations that involve
numbers, geometry, measurement, and problem-solving. The play
on words in the text is delightful.
Rubber Bands, Baseballs and Doughnuts:
A Book about Topology
by Robert Froman; illustrated by Harvey Weiss
Thomas Y. Crowell, Minneapolis. 1972
Out of print
Grades: 4–8
An introduction into the world of topology through active
reader participation. The activities provide concrete examples
and insights into abstract concepts. Connects well to Game 4,
Shongo Networks.
Sideways Arithmetic from Wayside
School
by Louis Sachar
Scholastic, New York. 1989
Grades: 3–5
This series of problems and puzzles uses "sideways arithmetic"
to stimulate divergent-thinking skills and the funny bone. Sideways
arithmetic approaches arithmetic as you have never seen before.
A variety of problems and puzzles are presented which hold the
interest and stimulate the brain of any reader. Connects well
to all games in Math Around the World, especially Game
5, Magic Squares, which involve the use of addition.
Socrates and the Three Little Pigs
by Tuyosi Mori; illustrated by Mitsumasa Anno
G.P. Putnam, New York. 1986
Grades: 4–8
Socrates, a wolf, attempts to catch one of three pigs for
his wife’s dinner. These three pigs collectively own five
cottages. With the help of his frog friend, the mathematician
Pythagoras, Socrates tries to determine the possible cottages
the pigs might be in. As the story unfolds, the illustrations
show the many possible locations of the pigs, and in doing so,
visually and clearly show the difference between permutations
and combinations. This type of math, known as combinatorial analysis,
forms the basis for computer programming and problem solving and
this connection is explained on a more advanced level in the back
of the book. The problem solving aspect of this book connects
well to all the games in the guide, but by specifically explaining
permutations and combinations the book ties in best to probability
in Game 6, Game Sticks. The book is also published under the title
Anno’s Three Little Pigs.
Stories to Solve: Folktales from
Around the World
by George Shannon: illustrated by Peter Sis
Greenwillow Books/William Morrow, New York. 1985
Grades: 3–8
These brief folktales from a variety of cultures invite you
to solve a mystery or problem before the resolution is presented.
Notes in the back of the book tell the source of the folktale
and thereby the country of origin. A superb book for developing
divergent-thinking and problem-solving skills, this book is highly
recommended as is its sequel, More Stories to Solve.
Through the Looking Glass
by Lewis Carroll
Viking Penguin, New York. 1984
Grades: All ages
Logic keeps doing somersaults during Alice’s further
adventures in Wonderland. She enters Wonderland through a mirror
and finds a world completely opposite of the one she left behind.
Nearly every page contains some twist on what we usually perceive
and expect to happen. Ties in nicely with NIM (Game 1), Kalah
(Game 2), and Hex (Game 8).
The Toothpaste Millionaire
by Jean Merrill; illustrated by Jan Palmer
Houghton Mifflin, Boston. 1972
Grades: 5–8
Twelve-year-old Rufus doesn’t start out to become a millionaire—just
to make toothpaste. Assisted by his friend Kate and his math class
(which becomes known as Toothpaste 1), his company grows from
a laundry room operation to a corporation with stock and bank
loans. Many opportunities for estimations and calculations are
presented including cubic inches, a gross of toothpaste tubes
bought at auction, manufacturing expenses, and profits. An ideal
book to illustrate the need for, and use of, mathematics in real-world
problem solving.
Maze
by Christopher Manson
Henry Holt & Co., Inc., New York. 1995
Grades: 5–Adult
Based on the book, Maze: A Riddle in Words and Pictures by
Christopher Manson (Henry Holt & Co., Inc., New York. 1985),
this new dimension in literature can be found on the Internet
at:
http://www.obs-us.com:80/obs/english/books/holt/books/maze/index.htm
As the Maze Directions say, "This is not really a book.
This is a virtual space in the shape of a book…a maze. Each
numbered page depicts a room in the Maze. The doors in each room
lead to other rooms. Your challenge is to find your way from room
1 to room 45 and then back to room 1 using the shortest possible
path. There are any number of clues in the drawings and in the
story to help you choose the right door in each room." The
reader goes into a room simply by clicking on one of the doors
in the drawing. While not highly imaginative, this "book"
is engaging, represents a new direction for books, and invites
you, as the reader, to "use your head."
|
|
