Section 1: The Language of Mathematics
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Web Exercise:
expressions versus sentences

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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
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Web Exercises:
basic addition practice
multiplication
divisibility
basic properties of zero and one
mixed basic add/subtract/multiply/divide practice 
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(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, prealgebra, algebra, geometry, and more.
Practice multiplication tables and feed the hungry at the same time 
Section 3: The Real Numbers
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Web Exercises:
deciding if a number is a whole number, an integer, etc.

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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
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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 lefttoright; blue can only move righttoleft) 
Section 5: Subtraction of Signed Numbers
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Web Exercises:
subtraction of signed numbers
mixed addition and subtraction of signed numbers

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(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
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Web Exercises:
fractions with a denominator of 2 to decimal form
average of two signed numbers
average of signed numbers

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(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
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Web Exercises:
identifying place values
multiplying by powers of ten

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(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
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Web Exercises:
changing decimals to fractions
multiplying and dividing decimals by powers of ten
changing decimals to percents
changing percents to decimals

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(solutions to text exercises are included)
MindReading Number Trick
FUN STUFF:
Explore Percentages
Circle 3 game 
Section 9: Mathematicians are Fond of Collections
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Web Exercises:
introduction to sets
interval and list notation

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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
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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

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Solutions to text exercises
Spherical Bands
FUN STUFF:
Number Puzzle
(math solution to a number puzzle)

Section 10.5: Solving For A Particular Variable
IMPORTANT FOR SCIENCE CLASSES!
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Web Exercises:
“undoing” a sequence of operations
solving for a particular variable
Getting bigger? Getting smaller? 
Divisibility By Seven
FUN STUFF:
Make a TriHexaFlexagon
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!
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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
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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
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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
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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

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(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
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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!
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Web Exercises:
recognizing zero and one

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Solutions to text exercises
FUN STUFF:
Have fun with some CHOCOLATE MATH!
How does "Chocolate Math" work? 
Section 16: Exact versus Approximate
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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

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(solutions to text exercises are included)
Area of an Ellipse
Buffon Needle Problem (estimate pi!)
FUN STUFF:
Daily Word Search

Section 17: Rounding
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Web Exercises:
rounding decimals to a specified number of places

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(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
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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
onestep conversions

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(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
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Web Exercises:
multistep conversions
rate problems
work problems
(This web exercise is an experiment with a very different style. Enjoy!)

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(solutions to text exercises are included)
Fermat's Little Theorem
FUN STUFF:
Optical Illusions
Snowflakes (practice paying attention to details)

Section 20: Exponent Notation
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Web Exercises:
exponents
practice with order of operations
basic exponent practice with fractions

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(solutions to text exercises are included)
FUN STUFF:
Play HANGMAN online 
Section 21: Exponent Laws
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Web Exercises:
practice with $\,x^mx^n = x^{m+n}\,$
practice with $\,(x^m)^n = x^{mn}\,$
practice with $\,x^m/x^n = x^{mn}$
practice with $\,x^{p} = 1/x^p$
onestep exponent law practice
multistep exponent law practice

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(solutions to text exercises are included)
Sums of Reciprocal Powers

Section 22: Radicals
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Web Exercises:
practice with radicals
approximating radicals

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(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
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Web Exercises:
writing radicals in rational exponent form
writing rational exponents as radicals
practice with rational exponents

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(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
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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 $\,x^3\,$!

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(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
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Web Exercises:
equal or opposites?
recognizing the patterns $\,x^n\,$ and $\,(x)^n\,$
writing expressions in the form kx^{n}
writing more complicated expressions in the form kx^{n}
writing quite complicated expressions in the form kx^{n}

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(solutions to text exercises are included)
Suspended Rope Trick
FUN STUFF:
Play BOGGLE online (click "Start Game")

Section 26: FOIL and more
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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 $\,(ab)^2\,$
simplifying
expressions like (a  b)(c + d  e)

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(solutions to text exercises are included)
Domino and Square Tilings

Section 27: These Sentences Certainly Look Different!
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Web Exercises:
practice with the mathematical words and, or, and is equivalent to

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Solutions to text exercises
Making Magic Squares
FUN STUFF:
Kakuro (easy) (similar to Sudoku)
Kakuro (harder) (similar to Sudoku)

Section 28: Introduction to Factoring
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Web Exercises:
recognizing products and sums; identifying factors and terms
identifying common factors
factoring simple expressions

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(solutions to text exercises are included)
Birthday Problem

Section 29: Greatest Common Factor
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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

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(solutions to text exercises are included)
Pick's Theorem
FUN STUFF:
Create Factor Trees

Section 30: Transforming Tool #1 (the Addition Property of Equality)
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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)
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Web Exercises:
the Multiplication Property of Equality 
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(solutions to text exercises are included)
Proofs Without Words

Section 32: Solving Linear Equations in One Variable
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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
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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
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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
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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
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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"
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Web Exercises:
solving absolute value inequalities involving "less than" 
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(solutions to text exercises are included)
Toggling Light Switches

Section 37: Finishing Up Absolute Value Sentences
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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
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Web Exercises:
identifying perfect squares
writing expressions in the form A^{2}
factoring a difference of squares

Matching Problem
Make a jigsaw puzzle online

Section 39: Solving Equations Involving Perfect Squares
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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
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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
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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
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Web Exercises:
factoring $\,ax^2 + bx + c\,$
solving more complicated quadratic equations by factoring 
Drunken Walker and Fly
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 
Proof With Words
RedBlack Card Trick
FUN STUFF:
Mathematical Artwork
(by the creator of MathJax)

Section 43: Percent Increase and Decrease
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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
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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
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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)
Cool Math: Doggnations (Great brain exercise; 50 levels)

Section 46: More On Lines
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Web Exercises:
pointslope form
horizontal and vertical lines
parallel and perpendicular lines

Binary Card Trick
Wallis' Formula
FUN STUFF:
Bored? Flip a coin! 
Section 47: Functions
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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) 