homepage: Dr. Carol JVF Burns
Many thanks to Miss Hall's School in Pittsfield, Massachusetts for their support of this site.

ONE MATHEMATICAL CAT, PLEASE!
A First Course in Algebra

Free Online Algebra I Course
with Unlimited Randomly-Generated Practice Problems and Worksheets
in Every Section

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

Khan 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!

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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

opens in a new window  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

opens in a new window  Spherical Bands

FUN STUFF:
Number Puzzle    (math solution to a number puzzle)
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?
opens in a new window  Divisibility By Seven

FUN STUFF:
Make a Tri-Hexa-Flexagon

Make a Paper Tree
(Don't use too many pieces,
or you won't be able to make the cuts.)
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)

opens in a new window  Area of an Ellipse

opens in a new window  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)

opens in a new window  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)

opens in a new window  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
  taking PEMDAS too literally: don't make this mistake!
  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  Multiplication by 11

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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)

opens in a new window  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
opens in a new window  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
opens in a new window  Euler Characteristic

opens in an new window  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
opens in a new window  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
opens in a new window  Successive Differences of Powers

opens in an new window  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
opens in a new window  Drunken Walker and Fly

opens in a new window  Conic Sections

FUN STUFF:
Cool Math: Factory Balls   (Good brain exercise!)
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
opens in a new window  Proof With Words

opens in a new window  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
opens in a new window  Math Limerick

opens in a new window  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
opens in a new window  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
opens in a new window  Kaprekar's Constant

FUN STUFF:
Bake some cornbread!
(ingredients have been renamed
so you don't have many dishes to wash)

Cool Math: Doggnations   (Great brain exercise; 50 levels)
Section 46: More On Lines
Back to the top!
Web Exercises:
  point-slope form
  horizontal and vertical lines
  parallel and perpendicular lines
opens in a new window  Binary Card Trick

opens in a new window  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
opens in a new window  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)