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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

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 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

ALL WEB EXERCISES and FUN STUFF LINKS OPEN IN A NEW WINDOW
Note: all references to http://fishcaro.crosswinds.net in the text
should be replaced by http://www.onemathematicalcat.org

Section 1: The Language of Mathematics Back to the top!	Web Exercise: expressions versus sentences	Read the text Solutions to text exercises FUN STUFF: WolframAlpha (Type in ANY math—incredible!!) Learn about your favorite number (type in your favorite number and click ENTER) Improve your vocabulary and feed the hungry at the same time Practice basic math skills and feed the hungry at the same time
Section 2: Brushing Up On Basic Arithmetic Skills Back to the top!	Web Exercises: basic addition practice multiplication divisibility basic properties of zero and one mixed basic add/subtract/multiply/divide practice	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 Kahn Academy Check out this collection of YouTube videos: it includes arithmetic, pre-algebra, algebra, geometry, and more. Practice multiplication tables and feed the hungry at the same time
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 ThatQuiz offers fun number line practice. LOTS of other practice, too! Check it out! 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) 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
Section 6: Average Back to the top!	Web Exercises: fractions with a denominator of 2 to decimal form average of two signed numbers average of signed numbers	Read the text (solutions to text exercises are included) 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) 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 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 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)
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?	Divisibility By Seven
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 $\,a\cdot\frac{b}{c}\,$ more practice with the form $\,a\cdot\frac{b}{c}\,$ renaming fractional expressions	Read the text (solutions to text exercises are included) FUN STUFF: Multiplying Fractions Dividing Fractions Fighter Pilot Training (test your reflexes)
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)
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) Area of an Ellipse Buffon Needle Problem (estimate pi!) FUN STUFF: Daily Word Search
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) Wilson's Theorem FUN STUFF: Practice with Unit Conversion Improve your memory by playing CONCENTRATION
Section 19: More Unit Conversion Back to the top!	Web Exercises: multi-step conversions rate problems work problems (This web exercise is an experiment with a very different style. Enjoy!)	Read the text (solutions to text exercises are included) Fermat's Little Theorem FUN STUFF: Optical Illusions Snowflakes (practice paying attention to details)
Section 20: Exponent Notation Back to the top!	Web Exercises: 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 $\,x^mx^n = x^{m+n}\,$ practice with $\,(x^m)^n = x^{mn}\,$ practice with $\,x^m/x^n = x^{m-n}$ practice with $\,x^{-p} = 1/x^p$ one-step exponent law practice multi-step exponent law practice	Read the text (solutions to text exercises are included) Sums of Reciprocal Powers
Section 22: Radicals Back to the top!	Web Exercises: practice with radicals approximating radicals	Read the text (solutions to text exercises are included) 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) Multiplication by 11 Leapfrog Addition 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 mental math: addition Don't mix up $\,3x\,$ versus $\,x^3\,$!	Read the text (solutions to text exercises are included) 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 $\,x^n\,$ 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) Suspended Rope Trick FUN STUFF: Play BOGGLE online (click "Start Game")
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 and $\,(a-b)^2\,$ simplifying expressions like (a - b)(c + d - e)	Read the text (solutions to text exercises are included) Domino and Square Tilings FUN STUFF: KenKen (similar to Sudoku)
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 Making Magic Squares FUN STUFF: Kakuro (easy) (similar to Sudoku) Kakuro (harder) (similar to Sudoku)
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) 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) Pick's Theorem FUN STUFF: Create Factor Trees
Section 30: Transforming Tool #1 (the Addition Property of Equality) Back to the top!	Web Exercises: the Addition Property of Equality	Read the text (solutions to text exercises are included) Goldbach's Conjecture FUN STUFF: Tangrams
Section 31: Transforming Tool #2 (the Multiplication Property of Equality) Back to the top!	Web Exercises: the Multiplication Property of Equality	Read the text (solutions to text exercises are included) 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) 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 solving linear inequalities, all mixed up	Read the text (solutions to text exercises are included) 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 involving "plus or minus"	Read the text (solutions to text exercises are included) 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 35: Solving Absolute Value Equations Back to the top!	Web Exercises: solving absolute value equations	Read the text (solutions to text exercises are included) Bike with Square Wheels
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) 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) 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	Matching Problem Make a jigsaw puzzle online
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	Euler Characteristic Why an International Date Line?
Section 40: Factoring Trinomials Back to the top!	Web Exercises: basic concepts involved in factoring trinomials factoring $\,x^2 + bx + c\,$, $\,c > 0\,$ factoring $\,x^2 + bx + c\,$, $\,c < 0\,$ factoring trinomials, all mixed up	Difference of Squares FUN STUFF: Take a look at the stars!
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	Successive Differences of Powers Six Degrees of Separation FUN STUFF: Optical Illusions
Section 42: More on Quadratic Equations Back to the top!	Web Exercises: factoring $\,ax^2 + bx + c\,$ solving more complicated quadratic equations by factoring	Drunken Walker and Fly Conic Sections
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	Proof With Words Red-Black Card Trick FUN STUFF: Mathematical Artwork (by the creator of MathJax)
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 Limerick Magic 1089 FUN STUFF: Create your own Jeopardy game! (Teachers—you'll love this!)
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	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)
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	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	Binary Card Trick Wallis' Formula 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	Four Color Theorem 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)

ONE MATHEMATICAL CAT, PLEASE! A First Course in Algebra

ONE MATHEMATICAL CAT, PLEASE!
A First Course in Algebra