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Web www.onemathematicalcat.org

ONE MATHEMATICAL CAT, PLEASE!
A First Course in Algebra

You're about to learn that  x  is to mathematics as "cat" is to English.
The hope is that the next time you find yourself faced with  x , you'll think:
One Mathematical Cat, Please!
and laugh a bit...
making mathematics a little less stressful,
and a little more fun.

JUMP RIGHT TO THE WEB EXERCISES

First time to this web site? Welcome!
Please do the  expressions versus sentences  web exercise in  Section 1: The Language of Mathematics  first.
This particular exercise doesn't require MathPlayer, and it will guide you in using the web exercises.
After you've installed MathPlayer, you might want to try out
multi-step exponent law practice     or     adding and subtracting fractions with variables
to see how Math Markup Language and JavaScript can work together to create randomly-generated math exercises on the web. Enjoy!

Please check out the requirements for using this web site.

Section 1: The Language of Mathematics
Section 2: Brushing Up On Basic Arithmetic Skills
Section 3: The Real Numbers
Section 4: Addition of Signed Numbers
Section 5: Subtraction of Signed Numbers
Section 6: Average
Section 7: The Base Ten Number System
Section 8: Decimals
Section 9: Mathematicians are Fond of Collections
Section 10: Holding This, Holding That
Section 10.5: Solving For A Particular Variable
Section 10.7: Scientific Notation and Significant Figures
Section 11: Introduction to Fractions
Section 12: Multiplying Fractions
Section 13: Adding Fractions
Section 14: I Live Two Blocks West Of You
Section 15: Numbers Have Lots of Different Names!
Section 16: Exact versus Approximate
Section 17: Rounding
Section 18: Unit Conversion
Section 19: More Unit Conversion
Section 20: Exponent Notation
Section 21: Exponent Laws
Section 22: Radicals
Section 23: Rational Exponents
Section 24: The Distributive Law
Section 25: Revisiting Exponents
Section 26: FOIL and more
Section 27: These Sentences Certainly Look Different!
Section 28: Introduction to Factoring
Section 29: Greatest Common Factor
Section 30: Transforming Tool #1 (the Addition Property of Equality)
Section 31: Transforming Tool #2 (the Multiplication Property of Equality)
Section 32: Solving Linear Equations in One Variable
Section 32.5: Applications and More
Section 33: Solving Linear Inequalities in One Variable
Section 34: Introduction to Absolute Value
Section 34.5: Additional Practice
Section 35: Solving Absolute Value Equations
Section 36: Solving Absolute Value Inequalities Involving "Less Than"
Section 37: Finishing Up Absolute Value Sentences
Section 38: Factoring a Difference of Squares
Section 39: Solving Equations Involving Perfect Squares
Section 40: Factoring Trinomials
Section 41: Solving Quadratic Equations by Factoring
Section 42: More on Quadratic Equations
Section 42.5: Arithmetic with Fractions Involving Variables
Section 43: Percent Increase and Decrease
Section 44: Introduction to the Coordinate Plane
Section 45: Lines
Section 46: More On Lines
Section 47: Functions

Title Page and Dedication: One Mathematical Cat, Please! A First Course in Algebra
(incomplete) Annotated Table of Contents



ALL WEB EXERCISES and  FUN STUFF  LINKS OPEN IN A NEW WINDOW

Section 1: The Language of Mathematics
Back to the top!
Web Exercise:
•  expressions versus sentences
Read the text
Solutions to text exercises

FUN STUFF:
Learn about your favorite number
(type in your favorite number and click ENTER)
Improve your vocabulary and feed the hungry at the same time
Section 2: Brushing Up On Basic Arithmetic Skills
Back to the top!
Web Exercises:
•  addition
•  multiplication
•  divisibility
•   basic properties of zero and one
Read the text
(solutions to text exercises are included)

FUN STUFF:
Addition Bingo     Multiplication Bingo     Division Bingo
Circle 21 game
Timed Flashcards—try to beat others in your age group
Section 3: The Real Numbers
Back to the top!
Web Exercises:
•  deciding if a number is a whole number, an integer, etc.
Read the text
Solutions to text exercises

Math Fun Facts!  Squares Ending in Five

FUN STUFF:
Use logical skills to locate the counterfeit coin
Word game
(try it yourself, before you click "generate")
Section 4: Addition of Signed Numbers
Back to the top!
Web Exercises:
•  addition of signed numbers
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Four Fours Problem

FUN STUFF:
Circle 0 game
Classic Peg Puzzle
(click "instructions" to see what you're trying to do;
red can only move left-to-right; blue can only move right-to-left)
Section 5: Subtraction of Signed Numbers
Back to the top!
Web Exercises:
•  subtraction of signed numbers
•  mixed addition and subtraction of signed numbers
Read the text
(solutions to text exercises are included)

FUN STUFF:
Color Chips to explore subtraction
Diffy, a fun subtraction game
(press "ENTER" after typing a difference in a square)
Number Line Bounce
MULTI-SECTION QUIZZES, Sections 1–5
Section 6: Average
Back to the top!
Web Exercises:
•  fractions with a denominator of 2 to decimal form
•   the average of two signed numbers
•   the average of three signed numbers
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Formula for Primes

FUN STUFF:
Wolf and Rabbit (in this game, ":" means "divided by")
Towers of Hanoi
(move a stack of disks from one peg to another
in as few moves as possible)
Section 7: The Base Ten Number System
Back to the top!
Web Exercises:
•  identifying place values
•  multiplying by powers of ten
Read the text
(solutions to text exercises are included)

FUN STUFF:
Base Blocks
SET is a really fun game
(click "Daily Puzzle" to play online;
if you're never played before, click "How To Play")
Section 8: Decimals
Back to the top!
Web Exercises:
•  changing decimals to fractions
•  multiplying and dividing decimals by powers of ten
•  changing decimals to percents
•  changing percents to decimals
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Mind-Reading Number Trick

FUN STUFF:
Explore Percentages
Circle 3 game
Section 9: Mathematicians are Fond of Collections
Back to the top!
Web Exercises:
•   introduction to sets
•  interval and list notation
Read the text
Solutions to text exercises

Math Fun Facts!  Nine Point Circle

FUN STUFF:
Play with Pentominoes
(click on "Activities" for some fun things to do)
Cough in your sleeve and keep us all healthy!
Section 10: Holding This, Holding That
Back to the top!
Web Exercises:
•   introduction to variables
•   reading set notation
•   going from a sequence of operations to an expression
•   going from an expression to a sequence of operations
•   solving simple sentences by inspection
•   using mathematical conventions
Read the text
Solutions to text exercises

Math Fun Facts!  Spherical Bands

FUN STUFF:
Number Puzzle    (math solution to a number puzzle)

Play BLOKUS online    Rules for Blokus
(click "Quick Play" to play against computer)
MULTI-SECTION QUIZZES, Sections 6–10
Section 10.5: Solving For A Particular Variable

IMPORTANT FOR SCIENCE CLASSES!
Back to the top!
Web Exercises:
•   "undoing" a sequence of operations
•   solving for a particular variable
•   Getting bigger? Getting smaller?
Math Fun Facts!  Divisibility By Seven

FUN STUFF:
Arrange numbers by sliding tiles
(go to bottom of page;
you may want to start with level 3)
Section 10.7: Scientific Notation and Significant Figures

IMPORTANT FOR SCIENCE CLASSES!
Back to the top!
Web Exercises:
•   scientific notation
•   significant figures and related concepts
FUN STUFF:
Fill and Pour
SUDOKU: a new game every day
(play online or print it out)
Section 11: Introduction to Fractions
Back to the top!
Web Exercises:
•   rewriting fractions as a whole number plus a fraction
•   locating fractions on a number line
•  fractions involving zero
Read the text
(solutions to text exercises are included)

FUN STUFF:
Play with Pattern blocks to visualize fractions
(hover your mouse over any corner to rotate pieces)
Renaming Fractions
Soda Constructor
Bored? Click on one of the images, and have fun!
Section 12: Multiplying Fractions
Back to the top!
Web Exercises:
•  finding reciprocals
•  determining if a product is positive or negative
•   multiplying and dividing fractions
•   practice with the form  a(b/c)
•   more practice with the form  a(b/c)
•   renaming fractional expressions
Read the text
(solutions to text exercises are included)

FUN STUFF:
Multiplying Fractions
Dividing Fractions
Fighter Pilot Training  (test your reflexes)
MULTI-SECTION QUIZZES, Sections 10.5–12
Section 13: Adding Fractions
Back to the top!
Web Exercises:
•  practice with multiples
•  finding least common multiples
•  renaming fractions with a specified denominator
•  practice with factors
•   adding and subtracting fractions
•   adding and subtracting simple fractions with variables
•  divisibility equivalences
Read the text
(solutions to text exercises are included)

FUN STUFF:
Renaming fractions
Have fun adding fractions
Sieve of Eratosthenes
(a classic method for determining prime numbers)
Math Cartoons
Section 14: I Live Two Blocks West Of You
Back to the top!
Web Exercises:
•  identifying inequalities as true or false
•   bigger, smaller, greater, lesser
•  practice with the phrases "at least" and "at most"
•  identifying inequalities with variables as true or false
•  solving equations of the form xy = 0
Read the text
Solutions to text exercises

FUN STUFF:
ExploreLearning
You can only use each "gizmo" for five minutes each day unless you subscribe (and pay), but these are really cool!
Section 15: Numbers Have Lots of Different Names!
Back to the top!
Web Exercises:
•   recognizing zero and one
Read the text
Solutions to text exercises

FUN STUFF:
Have fun with some CHOCOLATE MATH!
How does "Chocolate Math" work?
Section 16: Exact versus Approximate
Back to the top!
Web Exercises:
•  writing fractions in simplest form
•  deciding if a fraction is a finite or infinite repeating decimal
•  deciding if numbers are equal or approximately equal
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Area of an Ellipse

FUN STUFF:
Word Search
MULTI-SECTION QUIZZES, Sections 13–16
Section 17: Rounding
Back to the top!
Web Exercises:
•  rounding decimals to a specified number of places
Read the text
(solutions to text exercises are included)

FUN STUFF:
Rounding Flash Cards
Math Words
(fascinating origins and information on a wide variety of mathematical words)
Section 18: Unit Conversion
Back to the top!
Web Exercises:
•  Tables of Unit Conversion Information
•  classifying units as length, time, volume, weight/mass
•  practice with unit abbreviations
•  practice with unit names
•  practice with unit conversion information
•   one-step conversions
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Wilson's Theorem

FUN STUFF:
Practice with Unit Conversion
Improve your memory by playing CONCENTRATION
(press "refresh" to restart timer)
Section 19: More Unit Conversion
Back to the top!
Web Exercises:
•   multi-step conversions
•   rate problems
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Fermat's Little Theorem

FUN STUFF:
Optical Illusions
Snowflakes (practice paying attention to details)
Section 20: Exponent Notation
Back to the top!
Web Exercises:
•  practice with exponents
•  practice with order of operations
•  basic exponent practice with fractions
Read the text
(solutions to text exercises are included)

FUN STUFF:
Play HANGMAN online
Section 21: Exponent Laws
Back to the top!
Web Exercises:
•  practice with  xmxn = xm+n
•  practice with  (xm)n = xmn
•  practice with  xm/xn = xm-n
•  practice with  x-p = 1/xp
•  one-step exponent law practice
•   multi-step exponent law practice
Read the text
(solutions to text exercises are included)

FUN STUFF:
Think you might have ESP?
MULTI-SECTION QUIZZES, Sections 17–21
Section 22: Radicals
Back to the top!
Web Exercises:
•   practice with radicals   OR
    no MathPlayer required version
•   approximating radicals
Read the text
(solutions to text exercises are included)

Math Fun Facts!  One Equals Zero!

FUN STUFF:
Square Root Flashcards
Give this a try—it's fun!
Section 23: Rational Exponents
Back to the top!
Web Exercises:
•   writing radicals in rational exponent form
•   writing rational exponents as radicals
•  practice with rational exponents
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Multiplication by 11

FUN STUFF:
Stereograms are 3D images hidden within another picture.
Take the time to "see" these—my first one took me almost an hour—it's worth it! (I have to take my glasses off.)
Section 24: The Distributive Law
Back to the top!
Web Exercises:
•   practice with  x  and  -x
•  practice with products of signed variables
•  practice with the distributive law
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Pizza Slices

FUN STUFF:
Use Algebra Tiles to visualize the distributive law
(press INSTRUCTIONS to learn how to rotate the tiles)
Section 25: Revisiting Exponents
Back to the top!
Web Exercises:
•  equal or opposites?
•  recognizing the patterns xn and (-x)n
•  writing expressions in the form kxn
•  writing more complicated expressions in the form kxn
•  writing quite complicated expressions in the form kxn
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Suspended Rope Trick

FUN STUFF:
Play BOGGLE online (click "Start Game")
MULTI-SECTION QUIZZES, Sections 22–25
Section 26: FOIL and more
Back to the top!
Web Exercises:
•  identifying variable parts and coefficients of terms
•  combining like terms
•  simplifying expressions like -a(3b - 2c - d)
•  basic FOIL
•  more complicated FOIL
•  simplifying  (a + b)2  and  (a - b)2 
•  simplifying expressions like (a - b)(c + d - e)
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Domino and Square Tilings

Section 27: These Sentences Certainly Look Different!
Back to the top!
Web Exercises:
•   practice with the mathematical words and, or, and is equivalent to
Read the text
Solutions to text exercises

Math Fun Facts!  Making Magic Squares

Section 28: Introduction to Factoring
Back to the top!
Web Exercises:
•  recognizing products and sums; identifying factors and terms
•  identifying common factors
•  factoring simple expressions
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Birthday Problem

Section 29: Greatest Common Factor
Back to the top!
Web Exercises:
•  listing all the factors of a whole number
•  finding the greatest common factor of 2 or 3 numbers
•  finding the greatest common factor of variable expressions
•  factoring out the greatest common factor
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Pick's Theorem

FUN STUFF:
Create Factor Trees
MULTI-SECTION QUIZZES, Sections 26–29
Section 30: Transforming Tool #1 (the Addition Property of Equality)
Back to the top!
Web Exercises:
•  practice with the Addition Property of Equality
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Goldbach's Conjecture

FUN STUFF:
Tangrams
Section 31: Transforming Tool #2 (the Multiplication Property of Equality)
Back to the top!
Web Exercises:
•  practice with the Multiplication Property of Equality
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Proofs Without Words

Section 32: Solving Linear Equations in One Variable
Back to the top!
Web Exercises:
•  solving simple linear equations with integer coefficients
•  solving more complicated linear equations with integer coefficients
•   solving linear equations involving fractions
•   solving linear equations, all mixed up
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Pascal's Triangle

FUN STUFF:
Use a balance beam to solve linear equations (positive integers)
(press CONTINUE once you have the equation balanced)
Solve linear equations using negative integers
Algebra Planet Blaster
Section 32.5: Applications and More
Back to the top!
Web Exercises:
•   simple word problems resulting in linear equations
FUN STUFF:
Play Text Twist online (click "Play Web Game")
Section 33: Solving Linear Inequalities in One Variable
Back to the top!
Web Exercises:
•  solving simple linear inequalities with integer coefficients
•  solving linear inequalities with integer coefficients
•   solving linear inequalities involving fractions
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Magic Squares, Indeed!

FUN STUFF:
How to draw an impossible triangle
Section 34: Introduction to Absolute Value
Back to the top!
Web Exercises:
•  simplifying basic absolute value expressions
•  determining the sign (plus or minus) of absolute value expressions
•  solving simple absolute value sentences
•  solving sentences like 2x - 1 = ±5
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Reflecting on the Hyperbola

FUN STUFF:
Math Gems
(this is a beautiful assortment of mathematical marvels;
print it out and hang it on the wall for mathematical inspiration)
Section 34.5: Additional Practice
Back to the top!
Web Exercises:
•  Additional Practice
 
Section 35: Solving Absolute Value Equations
Back to the top!
Web Exercises:
•  solving absolute value equations
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Bike with Square Wheels

MULTI-SECTION QUIZZES, Sections 30–35
Section 36: Solving Absolute Value Inequalities Involving "Less Than"
Back to the top!
Web Exercises:
•  solving absolute value inequalities involving "less than"
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Toggling Light Switches

Section 37: Finishing Up Absolute Value Sentences
Back to the top!
Web Exercises:
•  solving absolute value inequalities involving "greater than"
•  solving absolute value sentences (all types)
Read the text
(solutions to text exercises are included)

Math Fun Facts!  Largest Known Primes
Section 38: Factoring a Difference of Squares
Back to the top!
Web Exercises:
•  identifying perfect squares
•  writing expressions in the form A2
•  factoring a difference of squares
Math Fun Facts!  Matching Problem

Section 39: Solving Equations Involving Perfect Squares
Back to the top!
Web Exercises:
•  solving simple equations involving perfect squares
•  solving more complicated equations involving perfect squares
•  translating simple mathematical phrases
•  word problems involving perfect squares
Math Fun Facts!  Euler Characteristic

Section 40: Factoring Trinomials
Back to the top!
Web Exercises:
•  basic concepts involved in factoring trinomials
•  factoring x2 + bx + c,   c > 0
•  factoring x2 + bx + c,   c < 0
•  factoring trinomials, all mixed up
Math Fun Facts!  Difference of Squares

FUN STUFF:
Take a look at the stars!
MULTI-SECTION QUIZZES, Sections 36–40
Section 41: Solving Quadratic Equations by Factoring
Back to the top!
Web Exercises:
•  identifying quadratic equations
•  writing quadratic equations in standard form
•  solving simple quadratic equations by factoring
Math Fun Facts!  Successive Differences of Powers

Section 42: More on Quadratic Equations
Back to the top!
Web Exercises:
•  factoring ax2 + bx + c
•  solving more complicated quadratic equations by factoring
Math Fun Facts!  Drunken Walker and Fly
Section 42.5: Arithmetic with Fractions Involving Variables
Back to the top!
Web Exercises:
•   multiplying and dividing fractions with variables
•   adding and subtracting fractions with variables
Math Fun Facts!  Proof With Words
Section 43: Percent Increase and Decrease
Back to the top!
Web Exercises:
•  writing expressions involving percent increase and decrease
•  calculating percent increase and decrease
•  problems involving percent increase and decrease
•  more problems involving percent increase and decrease
Math Fun Facts!  Math Limerick

Section 44: Introduction to the Coordinate Plane
Back to the top!
Web Exercises:
•  locating points in quadrants and on axes
•  practice with points
•   the Pythagorean Theorem
•   the distance formula
•   the midpoint formula
•  introduction to equations and inequalities in two variables
Math Fun Facts!  Fibonacci Formula

FUN STUFF:
Play MASTERMIND online
(this is a great game of logic;
BLACK means a correct color in a correct position;
WHITE means a correct color in an incorrect position)
MULTI-SECTION QUIZZES, Sections 41–44
Section 45: Lines
Back to the top!
Web Exercises:
•  introduction to the slope of a line
•  practice with slope
•  graphing lines
•  finding equations of lines
Math Fun Facts!  Kaprekar's Constant


FUN STUFF:
Bake some cornbread!
(ingredients have been renamed
so you don't have many dishes to wash)
Section 46: More On Lines
Back to the top!
Web Exercises:
•   point-slope form
•   horizontal and vertical lines
•   parallel and perpendicular lines
FUN STUFF:
Bored? Flip a coin!
Section 47: Functions
Back to the top!
Web Exercises:
•  introduction to functions
•  introduction to function notation
•   more practice with function notation
•   domain and range of a function
FUN STUFF:
Play with this Function Machine
THINK CLEAR!
(click on the little guy in the lower right corner to move from page to page)
MULTI-SECTION QUIZZES, Sections 45–47


copyright 2004–2007 Carol J.V. Fisher

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