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Algebra Text Set
Tammy Mickey
March 7, 2012
CONTENTS
FOREWORD ................................................................................................................................................ 3
YOUNG ADULT FICTION ......................................................................................................................... 4
A GEBRA NAMED AL ........................................................................................................................... 5
THE WITCH OF AGNESI ....................................................................................................................... 7
THE PHANTOM TOLLBOOTH ............................................................................................................. 9
PLAYING THE FIELD .......................................................................................................................... 11
THE WRITING ON THE WALL .......................................................................................................... 13
PICTURE BOOKS ..................................................................................................................................... 15
MYSTERY MATH: A FIRST BOOK OF ALGEBRA.......................................................................... 15
MATH ATTACK.................................................................................................................................... 17
ANNO’S MYSTERIOUS MULTIPLYING JAR................................................................................... 19
MATH CURSE ....................................................................................................................................... 21
LAST TO FINISH, A STORY ABOUT THE SMARTEST BOY IN MATH CLASS ......................... 23
NONFICTION BOOKS.............................................................................................................................. 25
ALGEBRA UNPLUGGED .................................................................................................................... 25
ALGEBRA: SETS, SYMBOLS & THE LANGUAGE OF THOUGHT ............................................... 29
HOT X: ALGEBRA EXPOSED............................................................................................................. 31
WACKY WORD PROBLEMS .............................................................................................................. 33
MATHEMAGIC! NUMBER TRICKS .................................................................................................. 35
WEBSITES ................................................................................................................................................. 37
NCTM ILLUMINATIONS .................................................................................................................... 37
WEB SUDOKU ...................................................................................................................................... 39
XY ALGEBRA ....................................................................................................................................... 41
EQUATION BUSTER............................................................................................................................ 43
COOLMATH ALGEBRA ...................................................................................................................... 45
OTHER SOURCES .................................................................................................................................... 47
T-SHIRTS ............................................................................................................................................... 47
ALGEBRA IN THE REAL WORLD..................................................................................................... 49
MATH EXCERPT FROM DIE HARD .................................................................................................. 51
COMIC COLLECTION ......................................................................................................................... 53
STAND AND DELIVER EXCERPT ..................................................................................................... 57
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FOREWORD
Algebra represents two of the five core-area high school math standards. Furthermore,
Algebra is a gatekeeper for further math studies in geometry, statistics, calculus and college
math. Students not proficient in Algebra will face much difficulty in those other classes as well
as chemistry and physics. Many students fear Algebra because they struggle with the concept of
a letter variable and its applications in solving problems. However, I experienced the opposite
result when I studied Algebra as a student. Prior to taking Algebra I was a mediocre math
student, but the concept of being able to use variables as place holders for unknowns opened the
world of math to me and allowed me to become math proficient, not perfect, but proficient. I
would like to share that experience with other students, and teach them not to be afraid.
This text set is a compilation of books and other media, each of which has applications to
the very broad topic of Algebra. The text set has specific applications to the SC High School
Math Standards pertaining to Algebra I typically taken in eighth or ninth grade. It focuses on the
standards for writing and solving linear equations, graphs and characteristics of linear equations,
the real number system, complex numbers, nonlinear relationships, patterns, and sequences.
Some of the texts in the set also require students to judge the reasonableness of solutions (EA
1.4) and understand how relationships can be represented in models (EA 1.6). Given that
Algebra is such a large and important topic in math, this text set is not intended to be complete,
but can and should be augmented as new resources are discovered.
.
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YOUNG ADULT FICTION
A GEBRA NAMED AL
Isdell, Wendy. (1993). A gebra named Al. Minneapolis, MN: Free Spirit Publishing, Inc.
Summary
Julie takes Algebra I and hates it. While working on her algebra homework and
struggling to fix her incorrect answers, she dozes off dreaming about the order of operations.
Even in her dreams, her answers are wrong. In the middle of her dream a cloudy imaginary
number comes to visit chiding her for not following the order of operations. When the imaginary
number disappears, she chases after him through a portal into the Land of Mathematics. The
portal closes, and she finds herself in a strange place with no obvious way back home. Julie
meets the extraordinary residents of the Land of Mathematics including a herd of Gebras, who
sport equations all over their coats, and the Periodics, a group of quasi horses each representing
an element or isotope. The Gebras and Periodics reason that the Mathematician can help her find
her way home, so she travels with them through the Caves of Parentheses, the Towers of
Exponents, the Desert of Division, the Field of Multiplication, Addition Mountain and
Subtraction Valley to reach the Mathematician’s Castle. As they travel, she learns she can solve
math problems she did not realize she was capable of solving.
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Commentary
This book, while not captivating, does an excellent job creating a visual representation
for the order of operations. Julie cannot remember the order of operations for solving problems,
but her travels through the Land of Mathematics clarify those rules for her. Through Julie, the
first chapter expresses frustrations many students feel about rules of math and the requisite order
of certain math processes.
I would use portions of this text as a read-aloud shortly after introducing or reviewing the
order of operations in an Algebra I class. Students would have had time to work one or more
homework selections and determine where they struggled. Introducing the order of operations as
a series of travels through a world of visual math would help make remembering those rules
easier.
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THE WITCH OF AGNESI
Spiller, Robert. The witch of Agnesi. (2006). Aurora, IL: Medallion Press, Inc.
Summary
Set in East Plains, Colorado, Bonnie Pinkwater is a recently widowed high school algebra
teacher. She is also the teacher-sponsor of the high school Knowledge Bowl team. One night
after a disappointing finish in the Knowledge Bowl finals, one member of Bonnie’s team
disappears, and the team captain is violently murdered. Bonnie and her new science teacher beau
embark on trying to solve the mystery of the children’s disappearances and murders. A third
student dies, and the school bully, Jesse, is framed for all three murders. Bonnie and science
teacher Armen Callahan investigate Wiccan rituals, an abusive father, the life of a precocious
thirteen year old genius, and the very strong and agile wheel-chair bound sister of the final
victim. After a particularly long and tiring weekend of sleuthing, Bonnie finds herself with little
energy to review the homework assigned to her Algebra class over the weekend. Instead she tells
the story of Maria Agnesi and the Witch of Agnesi, the famous algebraic equation of a curve
linked to a circle. The children in her class are spellbound by how English Mathematician John
Colson’s mistranslation of the Italian word versiera, the word used by Maria Agnesi to describe
the curve, to aversiera, meaning bride of the devil propagated evil name for the curve. Bonnie’s
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retelling of the Witch of Agnesi ultimately jogs her memory about events and facts she
overlooked in the mysterious deaths of her Knowledge Bowl team.
Commentary
This novel should appeal to a wide range of high school students given the prevalence of
non-graphic violence, mature themes involving abusive homes and adult relationships, and
inappropriate language. Accordingly, most of the book is not suitable as a read-aloud. However,
Bonnie Pinkwater’s telling of the story of the Witch of Agnesi is particularly compelling and
fitting for a classroom read-aloud and subsequent discussion. Within the story we find a link
between geometry and algebra and the significant history resulting from one man’s minor
mistranslation of a single word. Although the parametric curve Maria Agnesi studied had nothing
to do with witchcraft, she was frequently remembered in history books as a witch, a complete
misnomer since she desired to lead life as a nun.
While the equation for the curve itself is more complicated than would be studied in
Algebra I, this story could be used to help students realize that math has affected history and vice
versa. In fact, the study of Algebra and the people behind the science are uniquely tied to history
and culture. I would use this text as an introduction to algebraic equations and the different
applications algebraic equations have to society and the advancement of knowledge.
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THE PHANTOM TOLLBOOTH
Juster, Norton. (2011). The annotated phantom tollbooth. New York: Alfred A. Knopf.
Summary
Milo is a young man who is never happy with where he is. “When he was in school he
longed to be out, and when he was out he longed to be in” (Juster, 2011, p. 9). One day when he
arrives home from school, he finds a large box with coins, a map, and instructions for assembling
a tollbooth. He assembles the tollbooth and using the toll coins drives his toy car right through
into the Kingdom of Wisdom. He joins forces with Tock the Watch Dog and the Humbug as they
try to reconcile the brothers, King Azaz of Dictionopolis and the Mathemagician ruler of
Digitopolis, who have been at odds ever since they banished the princesses, Rhyme and Reason.
Azaz thinks words are more important than numbers, and the Mathemagician thinks numbers are
more important than words. Neither can agree with the other about anything, and the Kingdom of
Wisdom is on the verge of disaster. Milo, Tock, and the Humbug must attempt to rescue the
banished princesses from exile to save the Kingdom of Wisdom.
The novel is full of plays on words and double entendres sure to appeal to any teenager or
adult. As the story climaxes, Milo and his companions meet the demons who try to prevent the
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rescue of the princesses. The Terrible Trivium, demon of petty tasks and worthless jobs, the
demon of insincerity who leads them astray, and the Senses Taker who lures them from their
quest by distracting them with pleasant hallucinations are but a few of the monsters whose job it
is to sidetrack the trio. They are saved when Milo drops a box filled with laughter, for the Senses
Taker cannot keep them spellbound while they retain their sense of humor. They eventually
rescue the princesses, the brother kings reconcile, and Milo returns home full of the wonder of
learning.
Commentary
I would use this book as a read-aloud in my lesson plans to introduce the concept of
infinity. When Milo and friends find themselves in the number-mining caves of the
Mathemagician, Milo asks the Mathemagician to show him the biggest number that exists. The
Mathemagician opens a door to a room with a huge numeral 3. Milo rephrases his question to
request the longest number. Again the Mathemagician opens a closet to reveal a very wide
numeral 8. Finally the Mathemagician understands that Milo is asking about the number of
greatest magnitude. Through a repeated dialog of silly questions and answers, the
Mathemagician constructs the concept of infinity by getting Milo to keep adding one more to the
largest number he can think of. When Milo asks when to stop, the Mathemagician answers,
“Never” (Juster, 2011, p. 190). And so the concept of infinity becomes concrete.
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PLAYING THE FIELD
Rallison, Janette. (2002). Playing the field. New York: Walker and Company.
Summary
McKay is thirteen years old and in the eighth grade. He lives for baseball, but McKay has
a problem. His parents have demanded he pass Algebra or quit the team. McKay’s friend Tony
suggests he ask Serena, the prettiest and smartest girl in the eighth grade, for help; but McKay is
not interested in asking a girl for help. “Girls just had a way of changing everything. That was a
good enough reason not to get involved with them” (Rallison, 2002, p. 47). One day during gym
class McKay runs over Serena in the outfield while chasing down a ball, and she injures her
knee. When McKay goes to her house to apologize they become friends. McKay agrees to tape
the Algebra teacher’s lessons, and Serena works with McKay one-on-one to help him with his
homework. On the next exam, McKay earns a B+.
The story is peppered with teenage angst and witty dialog. McKay struggles with real
Algebra problems embedded into the text of the story, and the author also pokes fun at math
teachers by introducing impossible problems. As McKay struggles with how to get Serena to
speak to him after a disagreement, McKay ponders the question:
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If McKay looks over at Serena at a rate of once every 2 minutes, and class lasts
for 55 minutes every day, how long will it take before he goes absolutely insane?
(Rallison, 2002, p. 146).
This book is a fast read and should appeal to boys and girls alike regardless of age. The
subtle theme of the novel is that a little hard work and effort can make a difference in someone’s
academic performance.
Commentary
With only thirteen short chapters, this book is an excellent text to read on a daily basis
while teaching students how to solve equations with one variable. Most chapters can be read in
five to ten minutes. As McKay attempts problems he cannot solve, the class could work together
or independently to help McKay figure out how to solve those problems. I think every student in
the class can sympathize with McKay when he daydreams while working on Algebra worksheets
to figure out how to get Serena to speak to him.
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THE WRITING ON THE WALL
Lichtman, Wendy. (2008). The writing on the wall. New York: Greenwillow Books.
Summary
Tess enjoys math, and just like her teacher Ms. Saltzman, Tess sees patterns in
everything. She sees patterns in people’s behavior, she sees patterns in numbers, and she sees
patterns in the graffiti on the church wall behind the school. Tess thinks there is a code in the
graffiti, and she concludes there is a possibility the fire in Mr. Z’s class is related to the graffiti.
Eventually Tess begins conversing at the church wall in number code with the author of the
graffiti. She uses the problem of the four 4’s to code all the letters of the alphabet from 1-26. Is
the graffiti artist bragging about setting the fire, or do they actually know who started it?
Almost every chapter of the book is titled with an Algebra application, and Tess relates
the math to real life. In the chapter “Graphic Stories,” Tess decides to modify the technique of
graphing equations for solving systems of linear equations to figure out the person who has been
writing on the wall. She reasons that if a person knows about the arson, knows the problem of the
four 4’s, and is not afraid to write on the wall even after the principal’s warning, then at the
intersection of those three qualities (lines) is the person who has been writing the code. She
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ultimately determines the identity of the graffiti author and finds out who set the fire. Tess’s
sleuthing is revealed in an expose for the first issue of the school newspaper.
Commentary
This novel has a myriad of applications extending from a read-aloud. Certainly it is short
enough to be read throughout the semester to the class. Of more interest are the possibilities for
enrichment activities. For example, Tess likes to give her friends code names with mathematical
symbols. She identifies her friend Miranda with the absolute value sign because Miranda always
has a “positive” attitude. An Algebra class could be given the task of choosing several math
symbols and associating them with friends or people of interest in the media. They would be
tasked with explaining how the qualities of the math symbol were appropriate to describe their
person of interest.
Another option for math comprehension relates to the x-y coordinate plane. Students
often confuse the properties of the 4 quadrants of the coordinate plane, but Tess uses the
properties of the coordinate plane to analyze character traits of the students in her school. As
students in an Algebra I class are introduced to graphing lines and plotting coordinate pairs, they
could be assigned the task of applying character traits to each quadrant of the plane to reinforce
its properties.
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PICTURE BOOKS
MYSTERY MATH: A FIRST BOOK OF ALGEBRA
Adler, David A. (2011). Mystery math: A first book of algebra. New York: Holiday House.
Summary
Adler’s picture book is a Halloween-themed work which follows the children Mandy and
Billy through the mystery of solving for unknown variables on Halloween night. The text
introduces the concept of a “mystery number or variable” and discusses balancing equations and
using variables for solving word problems. Each page discusses a problem about a Halloween
creature (spiders, bats, ravens, skeletons, etc.). On their way to the haunted house, Mandy and
Billy calculate the value of unknown numbers of ravens, pumpkins, and owls. At the haunted
house, they meet the zombie caretaker Igor who chaperones them on the rest of their journey as
they figure out the number of skeletons and little black kittens in the haunted house.
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Commentary
This text is obviously an excellent resource at Halloween. While the problems are basic
and involve equations with single variables, the class could complete the problems as the
instructor read the story. The advantage to this picture book is that the problems are not
explained in so much detail as to give away the solution. Students must think. It is also a fun
approach to word problems without test anxiety. Students could work together in Halloween
groups (the bats, the pumpkins, the ravens, and so on) to set up and solve the problems.
At the end of the text is an activity to make an Algebra scale to calculate the solutions to
basic Algebra problems. The materials needed are a hangar, large paperclips, masking tape,
pennies, and a clothes line. Students solve for an unknown variable by adding groups of pennies
until the improvised hangar scale is balanced. Thus the concept of balancing an equation is
reinforced.
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MATH ATTACK
Horton, Joan. (2009). Math attack. New York: Farrar, Straus and Grioux.
Summary
On Monday a pig-tailed little girl is sitting in math class when her teacher, Ms. Glass
announces it is time to practice multiplication tables. The teacher asks, “Can somebody tell me
what’s seven times ten?” (Horton, 2009, p. 1). Then the pig-tailed girl’s brain explodes. Numbers
literally fly out of her head, bounce off the floor and out the door into the town. The numbers
attack the school nurse, the police, and the town utilities. The numbers pile up in grocery carts at
the supermarket. When the TV station tries to interview the little girl about what happened, the
numbers fly out of her head all over again. Finally she remembers how to compute 7 times 10,
and the number attack stops.
Written in a rhythmic, past-paced rhyme the illustrations and text conjure comical images
of the sometimes tortuous rote practice of the multiplication tables. Adults and students alike can
sympathize with the unnamed little pig-tailed girl who cannot remember 7 times 10.
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Commentary
I would use this book the first week of school. While multiplication tables have been
taught since third grade, a firm grasp of multiplication facts are a requisite basic skill for solving
algebra problems. Not only must students be able to multiply, but they ultimately must be able to
factor multiplication products to solve for unique algebraic solutions. Addition and
multiplication are perhaps the most heavily utilized math operations in Algebra. They are so
important, in fact, that entire college algebra courses are devoted to the theory behind
multiplication and addition.
A read-aloud from this text would be a fun introduction to reinforcing the times tables via
a team relay race the first week of school. After the instructor reads the book, teams would be
formed and the relay race would begin with the students sitting in groups at their desks.
Questions would be on index cards, and as the team solves problems, the solved index card
would be placed in a basket. The group with the most cards in the basket at the end of the timed
period wins. As a follow up activity, students could create multiplication fact cards to put on a
reference ring to use during homework, and maybe the first couple weeks of class.
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ANNO’S MYSTERIOUS MULTIPLYING JAR
Anno, Masaichiro and Mitsumasa. (1983). Anno’s mysterious multiplying jar. New York:
Philomel Books.
Summary
This is a story about factorials and combinatorial math. The reader begins the story by
opening the jar to find it is filled with water rippling like a breeze over the ocean. As the reader
travels the ocean he finds an island with countries, mountains, kingdoms, villages, houses,
cupboards, boxes, and jars. The fantasy ends where it began, except now there are 10 jars. The
authors mathematically emphasize the number of items that were in the first jar, a total of
3,628,800 items. They then proceed to decode the pattern of the combinatorial growth by
introducing the concept of factorials for each new discovery within the jar. In an “Afterword,”
the authors discuss the theory and symbol for the concept of factorial.
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Commentary
Most students are not introduced to the concept of factorial until Algebra II or
Intermediate Algebra. The factorial symbol, like scientific notation, is a short-hand method to
express numbers of large magnitude. However, unlike scientific notation, the factorial
presentation represents a very specific pattern. Students must learn not only what the factorial
symbol (!) means, but they must learn how to work with factorials within the context of math and
Algebra problems. This very basic illustrated text provides an excellent introduction to the
concept of factorial. It is much more interesting than an instructor standing at the board to
explain that 3! = 3 x 2 x 1 = 6. Instead, the authors present a visual and offer conceptual input
about what a factorial integer means. In short, I would use this text as an introduction to and
reinforcement of the concept of factorials.
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MATH CURSE
Scieszka, Jon and Lane Smith. (1995). Math curse. New York: Penguin Books, Inc.
Summary
Mrs. Fibonacci tells her math class that they can think of almost everything as a math
problem. The next morning, one student is in a panic. The day starts as a word problem, and the
problems keep coming nonstop. The milk for the cereal causes consternation over conversion
units. Is there enough time to get to school? How many fingers are on the students in the math
class?
Mrs. Fibonacci’s student is convinced Mrs. Fibonacci uttered a curse. Even social studies
turns into a problem when daydreaming about M&Ms. What is the length of the Mississippi
River in M&Ms? Compound words in English become logical subtraction problems. “If mail +
box = mailbox, does lipstick – stick = lip?” (Scieszka and Smith, 1995, p. 13). What’s a student
to do? Finally a weird dream and some convoluted math logic solve the problem of the curse.
In Math Curse, the illustrations are reminiscent of the animation from the movie James
and the Giant Peach. They give the illusion that the androgynous looking student is caught in a
nightmare from which they cannot escape thus highlighting the frustrations every student
experiences at some point when overwhelmed by math.
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Commentary
Math Curse intersperses real life math problems with zany unsolvable situations. It is up
to the reader to figure out which is which. The questions in the text provide an excellent
opportunity to exercise Algebra students’ logic skills. One page tackles conversions of different
denominations of paper money followed up by a silly, but perfectly valid multiple choice
question. The read-aloud with the ensuing questions should be used as a forum for class
discussion. The discussion could focus on what is a legitimate question versus what needs to be
reorganized into a legitimate question. Standardized tests often ask students to determine if a
solution to a problem is possible (i.e., is there enough information to solve the problem?).
Students must learn to discern when a problem can be solved, when more information is needed,
and when the wrong question is being asked altogether. Math Curse is an excellent resource in
the midst of a unit on word problems.
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LAST TO FINISH, A STORY ABOUT THE SMARTEST BOY IN MATH CLASS
Esham, Barbara. (2008). Last to finish: A story about the smartest boy in math class. Ocean City,
MD: Mainstream Connections.
Summary
Max is in third grade at Perryville Elementary, and he cannot complete the timed
multiplication facts quizzes. Whenever he hears the tick, tick, tick of the timer, he panics and
cannot think. To make matters worse, the bully David Peterson comes up with the chant, “Max,
Max, last in math” (Esham, 2008, p. 10). As a complete ending to a bad day, he loses his math
homework folder and then finds out he and his parents have been called to a conference with his
math teacher and the principal.
The day of the conference arrives. Everyone, including Max, is surprised to learn that
Max has been recognized for his math abilities in Algebra. He has been using his older brother’s
algebra book to solve math puzzles. The principal found Max’s work when he picked up the
math folder Max left at school.
Last to Finish is a story about talents. The theme is that learning obstacles can be
inhibitors for students with real aptitudes for a subject.
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Commentary
It is difficult to link this story to a specific high school Algebra standard. While the
setting of the story is a math class, the crux of the story is to accentuate that everyone has hidden
talents. We just have to find them by disabling our fears. This book could best be utilized as a
read-aloud in the early weeks of a school year or semester as a reminder to the teacher not to
give up on students and as a reminder to students not to give up on learning. Students have a
responsibility to figure out how they learn best, and teachers need to try different techniques in
an effort to reach all students.
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NONFICTION BOOKS
ALGEBRA UNPLUGGED
Amdahl, Kenn and Jim Loats, PhD. (1995). Algebra unplugged. Broomfield, Colorado:
Clearwater Publishing Co.
Summary
Algebra Unplugged is a cooperative effort between Kenn Amdahl, a literature-loving
artist and musician, and Jim Loats, a professor of mathematics. Their idea was to compile a
readable book about Algebra that entertains. There are absolutely no practice problems and very
few examples. Amdahl takes the approach that Algebra is a game, and like other games has
certain rules to be followed. The game theme permeates the text with silly analogies that make
the reader laugh while at the same time providing insight into the various “how-to” aspects of
Algebra. A chapter-long introduction is devoted to letting the reader know that his or her fear of
math is a close-to-universal emotion. The authors poke fun at math teachers and acknowledge:
Most of us love games, but aren’t crazy about mathematics. We’ve been bored by
math, frightened by it, and made to feel stupid by it. We haven’t loved it.
(Amdahl and Loats, 1995, p. 3).
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Finally, the authors jump into the meat of Algebra by describing the game pieces (different sets
of numbers, the moves (Algebra strategies), and the rules (properties of one, zero and the
multiplication sign). They sum up their game of Algebra with a story about an overweight
student nicknamed Braindead and his excursion into a weightwatchers-like math club. Braindead
learns about multiplication of negative numbers from fellow club member Mrs. Jeffries. Mrs.
Jeffries is trying to lose weight without much success. She is convinced that at different times
throughout her weight-loss endeavors her husband has been injecting her with gravy. Regardless,
Mrs. Jeffries must give up one of her silver badges as she gained weight since the last meeting.
By the end of the meeting, Braindead understands the concept of multiplying negative numbers.
(While very funny, for obvious reasons an instructor would need to exercise judgment in the
read-aloud of this particular story.)
Throughout the book, the authors tell funny stories and use ridiculous anecdotes for each
“lesson” of Algebra while enlightening the reader about solving algebraic problems. This text is
an excellent resource for the Algebra I teacher. Its humor and sarcastic approach to the topic of
Algebra offer the opportunity to inject levity into classroom.
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Commentary
Algebra Unplugged is a text which can be used throughout the entire year or semester of
Algebra I. It addresses almost every Algebra I standard as well as offers novel approaches to
basic math operations. (For instance, the authors explain the distributive property in terms of a
hysterical new operation, the flogging of tenors.) I would use this text as a read-aloud to
introduce new lessons in Algebra. The comic approach to the subject should help students better
remember the “rules” of the game. Some of the activities described could be incorporated into
the lesson plan. For example, the authors reference using a dart board divided into four sections,
analogous to the coordinate plane, as a means of initiating students to the concept of slope.
Students would have the opportunity to throw two darts, corresponding to two coordinate pairs,
and then calculate the slope between the points on the dart board. This example is just one of the
numerous opportunities for integration of the text into classroom instruction.
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ALGEBRA: SETS, SYMBOLS & THE LANGUAGE OF THOUGHT
Tabak, John. (2004). Algebra: Sets, symbols & the language of thought. New York: Facts on
File, Inc.
Summary
Tabak’s Algebra: Sets, Symbols & the Language of Thought offers a historical
perspective on the development of Algebra as a mathematical science. He begins his text with
the stirrings of algebraic theory by the Mesopotamians and carries on through the Greeks,
Indians, and Northern Africans. Tabak biographies the lives of individuals with important
contributions to Algebra and chronicles the history behind the development of those theorems.
Much of the text pertaining to development of theorems is quite complex and would not be
discussed until upper level college math classes. However, the biographies of the inventors of
Algebra are quite interesting and appropriate for any high school math student.
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Commentary
I would use this text to integrate the study of math with social studies. Brief class
discussions following a short read-aloud from the text about some of the famous mathematicians
could immediately precede the introduction of the relevant algebraic topic. Alternatively,
students could be given a short extra credit assignment or quiz grade assignment to write a one to
three paragraph biography of some of the famous mathematicians. The lives of many famous
mathematicians are well documented, and most led quite interesting professional and personal
lives. A number suffered insanity before death, a fact sure to interest and entertain students.
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HOT X: ALGEBRA EXPOSED
McKellar, Danica. (2010). Hot X: Algebra exposed. New York: Hudson Street Press.
Summary
Danica McKellar, actress and author, has written several books about math specifically
for girls who struggle with math. She uses romantic analogies and cutesy ideas and drawings to
catch the attention of girls while presenting technically accurate algebraic examples. She
encourages girls to take a somewhat irreverent stance towards Algebra, renaming the subject
Alge-blah-blah-blah. McKellar also suggests thinking of the math symbol x as something happy,
especially since in other contexts x can mean a kiss. Much of the text is written in diary or
journal form infused with sketches of Barbie icons, kitty cats, and designer shoes in the margin
to highlight her points. She encourages girls to journal their progress in math and includes
excerpts from her own diary and others’ into the body of the book. Like Algebra Unplugged,
Algebra Exposed tackles the basic standards of Algebra I but in more detail. She outlines tricks
and strategies for solving Algebra problems not typically found in a math textbook.
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Commentary
Like Algebra Unplugged, Hot X: Algebra Exposed can be utilized throughout the entire
school year or semester. Even better, the two texts can be used in tandem, with Algebra
Unplugged providing the conceptual framework for lesson plans and Algebra Exposed providing
some nifty how-to shortcuts. Alternatively, groups of girls versus boys could be formed
providing the boys with excerpts of the Algebra Unplugged text and the girls with the
corresponding Hot X: Algebra Exposed text to work as competitive teams to solve a given set of
Algebra problems. Of course, permission would have to be obtained from the publisher to
reproduce excerpts.
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WACKY WORD PROBLEMS
Long, Lynette. (2005). Wacky word problems. San Francisco, CA: Jossey-Bass.
Summary
Wacky Word Problems was written to help students understand that they solve math
problems every day. The introduction briefly introduces the concept of word problems by
relating the excitement associated with driving to an amusement park to a math problem. After
all, doesn’t someone want to know how long it will take to get there? .... A math problem. Long
convinces the reader that they use math every day, they just need to practice solving word
problems to master the skill.
The text is artfully broken down into various sections so the reader can practice one
aspect of solving a word problem and build on that mastery to work through the remainder of the
problem. The first chapter is dedicated to interpreting word clues which represent different math
operations. Subsequent chapters are devoted to fun math activities to enhance word problem
interpretations skills. Most games utilize inexpensive items such as dice, paper cups, and index
cards. The rest of the text is broken down into sections which tackle typical types of word
problems with activities to reinforce the concepts of measurement, counting and logic,
percentages, distance, algebra, and geometry. Some activities require students solve problems
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while others require the students to create problems, thus reinforcing math strategies in two
directions.
Commentary
This text has several in-class applications. A read-aloud of the two-page introduction can
introduce the applications of using Algebra to solve word problems. Second, Wacky Word
Problems suggests activities applying the concept of a variable to solve a word problem.
Specifically, I would incorporate the word interpretation activities into a first lesson in using
Algebra to solve word problems. Recognizing the vocabulary pertinent to a specific math
operation goes a long way in helping students master word problems. The text includes many
other games and contests that could be used in the classroom to get students up and moving
while reinforcing concepts of Algebra. Many of the games Long recommends, while fun, require
students collect their own data and then use the data to answer a question or solve a problem.
This aspect of the activities creates a personal connection to the learning objective.
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MATHEMAGIC! NUMBER TRICKS
Colgan, Lynda. (2011). Mathemagic! Number tricks.Tonawanda, NY: Kids Can Press, Ltd.
Summary
Mathemagic! Number Tricks is a compilation of 10 math tricks based on applications of
the rules of multiplication and divisibility. Some of the activities rely on glorified finger
counting, some are card or dice tricks, and the others simply use paper and pencil. The author
explains the steps of each trick in detail and then provides a several page summary of the math
theory which underpins how the trick works. Readers are introduced to the Sieve of
Eratosthenes, the history of the talus bone, how ancient Egyptians multiplied, the West African
history of binary systems in drum beat communication, and John Napier’s multiplication bones –
one of the first examples of a calculator.
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Commentary
Most of the number tricks introduced in Mathemagic! require significant practice before
the student/teacher performer could adequately demonstrate the activity. However, two of the
finger multiplying tricks could easily be demonstrated to students at the beginning of a school
year. These would be especially useful for students who have difficulty remember their
multiplication facts. The first trick involves labeling the digits of both the right and left hands
from 1 to 10 to calculate multiplying by 9. The corresponding finger of the number being
multiplied by 9 is dropped to the palm, and the remaining fingers to the left of the dropped digit
are the tens of the product, and the fingers to the right of the dropped digit are the ones. A second
finger trick involving multiplying by 6 and up is handy (no pun intended) for those who have
trouble remembering their 6, 7, 8, and 9 tables. Both tricks could be taught and practiced in one
class period.
The remainder of the book offers the opportunity for students to research basic integer
patterns. The instructor could assign group activities based on the remaining tricks in the books
for a group project in which students would perform a math “trick” and then present the history
and theory behind the trick. This project provides an opportunities for cooperative learning and
cross content teaching into social studies.
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WEBSITES
NCTM ILLUMINATIONS
NCTM illuminations website. Retrieved from
http://illuminations.nctm.org/ActivitySearch.aspx?grade=4
Hyperlink:
NCTM Illuminations Website
Summary
The National Council of Teachers of Mathematics Illuminations website is a free website
resource for math teachers and students of all grade levels. The hyperlink above takes the user to
the activities page of the Illuminations website where the student chooses the appropriate grade
level. The student may choose from a large list of grade appropriate math activities. Instructions
are provided, and the interactive activity allows the student to practice a particular math skill.
These activities are available free of charge.
Clicking on the Lessons tab at the top of the page allows the teacher-user to choose grade
level and math topic lessons. The lessons are subdivided into subcategories of Numbers and
Operations, Algebra, Geometry, Measurement, and Data Analysis & Probability. Choosing one
of the subcategories retrieves a long list of lesson plans. These lessons include detailed plans
which involve interactive activities for the students. The lesson plans also include possibilities
for assessment, student questions, teacher reflections, and references to the applicable NCTM
standards.
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Commentary
Students can access the activities on the NCTM website according to teacher instructions
or on their own. Each activity is descriptively titled and includes a brief summary so the student
is aware of the skill being reinforced. Two activities are specifically designed to enhance
Algebra skills: “Algebra Tiles” and “Proof without Words – Completing the Square.” “Algebra
Tiles” is an interactive game in which the student uses geometric figures to solve equations,
substitute, expand, and factor algebraic equations. This game offers a link between an algorithm
and a visual geometric presentation. The “Proof without Words” activity allows the student to
see the geometric presentation behind the technique of solving quadratic equations using the
completing the square algorithm.
The lesson plans tabs is even more useful for the teacher as over 55 detailed Algebra
plans for different standards are available. Typically each lesson includes a detailed list of
student learning objectives and an interactive exploration requiring student participation. For
example, the Barbie Bungee lesson plan explores the concept of lines of best fit by having
students make bungee cords for Barbie dolls and then collecting and plotting data for the
distance Barbie drops. Not only is the concept of the line of best fit introduced, but the standards
for equations of lines and slopes are reinforced. The lesson is introduced with brief video links to
bungee jumping sites to pique student interest. Many other lessons are equally viable for
classroom integration.
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WEB SUDOKU
Web sudoku. Retrieved from http://www.websudoku.com/
Hyperlink: Sudoku Puzzles
Summary
Web Sudoku is one of many Sudoku websites which offer free daily puzzles with
solutions. Users can choose the puzzle which appears or change the level of difficulty from easy
to medium to hard. Web Sudoku also allows the user to print the puzzle if they do not wish to
solve the puzzle online. Instructions are available in English, German, French, and Spanish.
A Sudoku puzzle is a 9 x 9 square table of positive integers (whole numbers) divided into
nine separate smaller grids of nine. The object of the game is to find the sequence of numbers
one through nine with one digit in each grid box such that no single digit is repeated in any given
column or row. Like a rubix cube, a Sudoku puzzle is a game of logic requiring the contestant to
determine the correct sequence of numbers to solve the problem.
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Commentary
Web Sudoku is a fun application of logic, patterns, and sequences which tacitly train
students in discrete propositional logic. In short, students must think about the solutions in terms
of if-then statements. “If I place a 2 in this box, then a 9 must go in this box.”
Easy Sudoku puzzles could be used as warm-ups or after lunch to get the class thinking
after being in a loud and busy lunch room. Sudoku puzzles could even be solved in groups.
While there is only one solution to any given Sudoku puzzle, there are multiple ways and steps to
solve each problem. Working together on a puzzle allows team members to see the strategy
which others employ to get to the answer.
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XY ALGEBRA
Miller, John C. (2011). XY algebra version 6.4 [computer software]. Available from
www.xyalgebra.org. New York: The City College of C.U.N.Y.
Hyperlink:
XYAlgebra Website
Summary
XYAlgebra software is free software available from the website listed above. Both
students and teachers may download the program. The software helps students work through
solving algebraic equations by providing line by line feedback as the student types in a solution
for a problem. Students download the Student Programs and choose a topic from the following:
1.
signed number expressions
2.
expression evaluation
3.
simplifying polynomials
4.
algebraic fractions
5.
solving linear equations
6.
plotting and graphing
7. solving quadratic equations.
As the students work problems, an incorrect answer initiates prompts for the student to
try a practice problem with additional hints and suggestions before allowing the student to return
to the original problem. The software can be tailored as extra practice or as a homework
assignment. An added option allows the student to print a progress report to be turned in to the
teacher.
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Commentary
This software is a good technology-based supplement to the basic topics introduced in
Algebra I. That students receive line by line feedback as they work problems should alleviate the
frustration often associated with solving math problems independently. The downloadable
software can be used in the classroom via a promethean board, as assigned homework, or just
made available before a quiz or test. The workspace is not very interesting, but the comments are
helpful in working through problems.
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EQUATION BUSTER
Mathsnet interactive equation buster. (2004). Retrieved from
http://mathsnet.net/algebra/l1_equation.html
Hyperlink: Equation Buster
Summary
Like the software from XYAlgebra, MathsNet Equation Buster provides interactive
student practice for balancing and solving equations of one variable. The website allows the user
to choose the level of difficulty which refers to the minimum number of steps needed to solve the
problem correctly. If the student solves the problem in the minimum number of steps, the
website provides a red double check mark when the solution is reached. If the student uses more
than the minimum number of steps but answers the problem correctly, the website provides a
single checkmark. This lets the student know their final answer is correct, but they could have
achieved the solution more efficiently.
This website is more user-friendly and visually appealing than the xyAlgebra software. It
is not necessary to key in numbers or algebraic symbols. The user chooses operations, variables,
and numbers from a chart at the bottom of the screen by clicking on their selection. However,
Equation Buster offers significantly fewer cues when the student makes arithmetic mistakes or
errors of logic.
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Commentary
While perhaps less instructive than XYAlgebra, the Equation Buster moves faster, has
fewer instructions, and is more attractive. As such, it is probably better suited to the more adept
Algebra student who wants to quickly review or practice balancing equations. This website could
easily be adapted to classroom use by running it to a screen or promethean board for a game of
practice problems to be solved by students individually or in groups for prizes or bonus points on
quizzes or tests.
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COOLMATH ALGEBRA
Coolmath algebra. CoolMath.com. Retrieved from http://www.coolmath.com/algebra/index.html
Hyperlink: Coolmath Website
Summary
The Coolmath website offers activities, games, and lessons for a variety of math
disciplines including pre-algebra, Algebra, precalculus, and geometry. The hyperlink above takes
the user directly to the area reserved for Algebra. Scrolling toward the bottom of the page reveals
a list of Algebra help topics written in an easy-to- read conversational tone and large font with
accompanying examples. The student can click the topic desired, find an index of subtopics,
choose the subtopic they need help with, and read a brief but reasonably thorough explanation of
the topic.
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Commentary
I would recommend this site to students as a resource to use at home while doing
homework. Many of the topics not only include a brief review, but several practice examples.
The site should first be introduced in the classroom, so students can see the tabs they need to
follow to end up in the section on Algebra. The xyz234 floating colored cursor can be annoying
at times as it distracts from the user’s target destination, but it is also somewhat entertaining.
When the student is finished using the reference material, they can tackle some of the logic
games found in the tab near the top of the page.
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OTHER SOURCES
T-SHIRTS
I (i) “greater than” you
I (i) ate (8) some (sum) pie (Π).
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Summary and Commentary
A collection of math or Algebra t-shirts on the walls in the classroom can lighten the
mood for students as they often feel math is too heavy a subject. Math teachers need to be able to
poke fun at themselves and their content area to give students the opportunity to relax in class.
With the exception of the Dear Algebra letter, the t-shirts on the facing page use math symbols
correctly, and their application in silly plays on words should help students remember how to
correctly apply them in math. For instance, students often have trouble interpreting the greater
than/less than symbol, and its applications are as important in Algebra as they are in earlier math
classes. The haughty t-shirt on the top left should help students remember that if the symbol
opens to the left, than it represents greater than. As students begin Algebra, they must learn to
discern between the different categories of numbers. The “Be rational – get real” t-shirt is a
reminder that it is important to understand the classifications of numbers. The value of the
discriminant of quadratic equation provides information about the number of real solutions
which solve an equation. For some reason, while students can remember the quadratic formula
they have difficulty remembering to use the discriminant to help them find real roots of quadratic
equations. The t-shirt at the bottom right on the facing page should serve as a reminder to make
use of the discriminant when solving quadratic equations.
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ALGEBRA IN THE REAL WORLD
Algebra in the real world [DVD]. (2010). United States: Futures Channel.
Summary
The Algebra in the Real World DVD is an educational DVD with 18 short scientific
videos in which Algebra has been applied in a real life situation. The development of Maglev
trains, saving Bald Eagles, and testing robotic hands are but a few of the video topics included in
the collection. The videos provide a concrete link between Algebra and its application in the
sciences, and the supplementary information includes detailed, grade-specific lesson plans for
Algebra activities related to each video. Student worksheets and references to the common core
math standards are also provided. Briefs of the videos along with sample lesson plans and
student materials may be viewed on the Futures Channel website.
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Commentary
This DVD and accompanying materials are somewhat expensive at $95.00. However, the
short videos and lesson plans may well be worth the investment. They are designed to be used in
the Algebra classroom, and students are encouraged to work together on the mini-projects and
worksheets. These lessons should be used as reinforcement, enrichment, and expansion of skills
previously acquired. The videos and lesson plans provide obvious links between the science of
Algebra and its real life applications.
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MATH EXCERPT FROM DIE HARD
McTiernan J. (Producer/ Director). (1995). Die hard with a vengeance [DVD]. United States:
Cingergi Pictures.
Math movies. Mathbits.com. Retrieved from
http://mathbits.com/MathBits/MathMovies/ResourceList.htm.
Hyperlink: MathBits.com (and scroll down to the Die Hard Link)
Summary
Die Hard with a Vengeance is the second in the series of the Die Hard movies. The
protagonists are played by actors Bruce Willis and Samuel L. Jackson, police detectives trying to
stop a villain from setting off bombs in New York City. In one clip, the detectives must solve a
logical algebra riddle to diffuse a bomb. They must figure out how to place 4 gallons of water on
a scale using only a 5 gallon jug and a 3 gallon jug.
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Commentary
This movie is rated R for language, so the only clip which should be shown is the clip
mentioned, then only after receiving administrative permission. If permission is not granted, the
teacher can set the stage of the story and allow students to read redacted dialog from the script to
set up the problem of the 4 gallon math jug. Assuming the teacher is allowed to show the clip, it
should be stopped before Willis and Jackson discover the solution. The scenario posed to the
detectives is an algebraic riddle which, given a little thought, the students in the class should be
able to solve. The solution makes use of linear Diophantine Equations, which have solutions if
the coefficients in the equation are relatively prime, as are 3 and 5. Like Willis and Jackson, the
students should be divided into groups to work in detective pairs. They should be instructed to
work quickly and quietly. A timer could be used to simulate the scene from the movie.
Afterwards, students may discuss their solutions with the class. Worksheet problems pertaining
to this movie clip are available at the mathbits.com website cited on the facing page, or the
instructor can simply request students solve the movie riddle.
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COMIC COLLECTION
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Summary
Most of the comics on the previous pages are self-explanatory, although a few require
clarification. In the first comic, Peter is supposed to expand the algebraic expression into all of
its component parts. Instead, Peter just keeps writing the terms of the original equation further
and further apart, his literal interpretation of “expand.” The Wise/Aldrich comic is a play on
words dealing with the slope of a line. A parallel line would have exactly the same slope as the
original line. A perpendicular line has the opposite sign and is the multiplicative inverse of the
slope of the original line. The comic strip with the -1 under the radical sign is funny if you
understand that in mathematics the square root of a negative number is an imaginary number.
Commentary
As a CPA, I am required to take continuing education classes annually. Tax is a fairly
dry subject, and sitting through an eight-hour day of tax can be mind-numbing. Twelve years ago
I attended a tax workshop led by a tax professor from North Carolina. This professor recognized
that to keep his audience awake and engaged, he needed to inject levity into his presentation.
Every twenty minutes or so, he stopped his lecture and presented several comics from his
collection on the overhead projector. Those comics went a long way to making the tax seminar
bearable.
When I decided to become a math teacher I promised myself I would follow Walter
Nunnallee’s lead and continue his tradition of comic breaks. Like tax, any math subject can be
dry. A collection of comics along the lines of those pictured on pages 49 and 50 sprinkled
throughout the lesson should help orient the students’ attention back to the lesson. Since I am not
a natural comedienne, I plan to let the comics do the entertaining. A large enough collection of
comics should yield some lesson-related humor. Others should help relieve test anxiety. After
seeing enough comics, students could be assigned a comic project in which they designed their
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own Algebra comic or comic strip. This should appeal to the natural comedians and artists and
require students to think about the relationship between the language of math and English.
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Works Cited
(2010). [Brainy-yak proves pythagorean theorem – comic]. Retrieved 5 Mar 2012 from
www.comicmath.com.
[8’s Imaginary friend – comic]. Retrieved 5 Mar 2012 from http://humorsoffice.com.
Creators Syndicate, Inc. (2008). [Self-Help/Math – comic]. Retrieved 5 Mar 2012 from
http://comicsidont understand.com.
Glasbergen, Rancy. (1996). [The square root of 9 – comic]. Retrieved 5 Mar 2012 from
http://www.grahamisd.com.
Glasbergen, Rancy. (1997). [Algebra class – comic]. Retrieved 5 Mar 2012 from
http://www.grahamisd.com.
Glasbergen, Rancy. (2005). [Tech support – comic]. Retrieved 5 Mar 2012 from
http://www.grahamisd.com.
[Never ever give up! – comic]. Retrieved 5 Mar 2012 from http://webmaths.wordpress.com.
[Peter: expand – comic homework example]. Retrieved 5 Mar 2012 from:
AllFunnyPictures.com.
Traves, Louis. (1994). “Frank and Earnest [comic].” Retrieved 5 Mar 2012 from
http://www.thecomics.com.
Wise and Aldrich. “Real life adventures [comic].” Retrieved 5 Mar 2012 from
http://www.dsollberger.com.
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STAND AND DELIVER EXCERPT
Musco, T. (Producer), and Menendez, R. (Director). (1988). Stand and deliver [DVD]. United
States: Available from Warner Bros., Inc., 4000 Warner Boulevard, Burbank, CA 91522.
Hyperlink: Stand and Deliver Excerpt (“Fill the Hole”)
Summary
Stand and Deliver is a film about the math teaching endeavors of a Hispanic
businessman, Jaime Escalante, in Garfield High, a predominantly Latino high school in
California. He is assigned to teach a low-track group of upperclassmen basic math. He decides
they are capable of achieving much more and proceeds to train them in advanced Algebra and
calculus. By the end of their senior year, many sit for the AP Calculus Exam with astounding
results. This is the story of the faith of a teacher and the achievement of his students in the face
of great adversity. The movie clip above takes place early in the plot as Escalante begins to teach
his class the concept of negative numbers.
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Commentary
This plot, based in part on true events at Garfield High during the late 1970s and early
1980s, has many implications for the system of tracking and overcoming perceived challenges
facing minority communities. From an Algebra perspective, the film offers insight into how to
introduce or approach various Algebraic topics. In particular, the excerpt “Fill the Hole”
provides an innovative way to introduce the concept of negative numbers. Escalante describes a
negative number as a hole in the sand at the beach. The sand that comes out of the hole is a
positive number, the hole itself is negative. The concept of negative numbers is often difficult for
beginning Algebra students to comprehend, and Escalante’s description supplies students with a
connective concept. This five-minute excerpt could be shown independently as part of a unit
about negative numbers and the number line, or time permitting, the instructor could play the
entire DVD which is rated PG.
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