ARITHMETIC LESSONS
At Mr. X, we practice arithmetic. Then we practice some more. The benefits of knowing and understanding basic arithmetic relationships are priceless. Mastering arithmetic is essential to understanding algebra and all higher mathematics. We have a library of sample arithmetic problems with examples of solved problems for each arithmetic lesson. Check out our free samples below, as well as the arithmetic curriculum.Arithmetic Curriculum
Addition
Title DescriptionAddition Makes Counting Easier  How many birds are two birds and five birds? We sum objects with the conjunction "and."  
Addition by 8  This video lesson, appropriate for children starting to learn addition, goes over adding by 8  
Addition of 1  Repeating simple addition facts helps children master early arithmetic. This video lesson, appropriate for children starting to learn addition, goes over adding by 1. 

Addition by 4  This video lesson, appropriate for children starting to learn addition, goes over adding by 4. 

Addition by 9  This video lesson, appropriate for children starting to learn addition, goes over adding by 9. 

Adding by 11 and 12  We use an addition table to review addition of 11 and 12.  
Addition Tables  You need to know all of these facts for simple addition. Learn these tables, they are very important! 

Addition by 7  This video lesson, appropriate for children starting to learn addition, goes over adding by 7. 

Addition by 6  This video lesson, appropriate for children starting to learn addition, goes over adding by 6. 

Addition by 5  This video lesson, appropriate for children starting to learn addition, goes over adding by 5. 

Addition by 10  This video lesson, appropriate for children starting to learn addition, goes over adding by 10. 

Addition by 2  This video lesson, appropriate for children starting to learn addition, goes over adding by 2. 

Addition by 3  This video lesson, appropriate for children starting to learn addition, goes over adding by 3. 

Review of Simple Addition  We read word problems to reinforce the basic facts of addition for small positive integers.  
Adding Whole Numbers up to 20  Before adding larger sums, it's good to have substantial practice with smallvalue integers.  
Adding Whole Numbers up to 99  Before adding larger sums, it's good to have substantial practice with smallvalue integers.  
Addition of One or Two Digit  Two Addends  Practicing with Addition. Repetitive practice is an important element to learning these basics. The student's goal should be to answer these problems with very little effort. 

Addition of Multiple Integers  Just as we add two integers together, we may add any number of integers almost as easily, and in any order we choose. A sum of terms does not rely on the order or sequence in which we take the terms; order of the terms does not matter. 

A Lesson in Japanese Money  The Yen  A brief discussion of the Yen, the unit of both coinage and currency in Japan.  
A Lesson in British Currency  We briefly discuss British paper money, or currency.  
A Lesson in British Coins  We learn a few facts about coinage in Great Britain.  
Adding with US Pennies  At the 3 minute mark we visually use US Coins to practice addition.  
Adding United States coins  To add the value of coinage we simply learn the denominations of coins used in the U.S.  
38 Cents in US Coins  How many ways can we get 38 cents using pennies, nickles, dimes and/or a quarter?  
Making the Transition from Addition to Subtraction  Subtracting a positive value is equivalent to adding the negative of that value. This concept is easy to understand with the visualization on the real number line. 

A Lesson in Adding English Measurements  This lesson adds English units of length to the nearest sixteenth of an inch. 
Decimals
Title DescriptionLong Division with ThreeDigit Divisors  Three digits in the divisor means long, long division.  
Comparing Decimals Lesson 1  We read math statements lefttoright. For this worksheet we need the Correct Comparison Symbol: >, = or <. 

Comparing Decimals Lesson 2  Real Values on the Real Number Line can be compared then expressed with greaterthan, lessthan, or equalto symbols.  
Decimals on the Real Number Line  Decimals, or decimal values, are to be placed at their proper location on the Real Number Line.  
The Real Number Line, a General Lesson  There is only one Real Number Line, strictly speaking. But we can describe The Real Number Line or draw parts of The Real Number Line an infinite number of different and unique ways. 

Multiplying by Powers of Ten, Lesson  This video emphasizes that you simply have to learn how to do this. ONLY YOU CAN DO THIS. These types of products need to be "automatic." Thank you. 
Division
Title DescriptionA Lesson in Integer Divisibility  Our rules for divisibility assist us in knowing how to divide numbers evenly and what real values will divide by 2, 3, 4, 5, 6, 8, or 9.  
Factors of 1368 with Divisibility Rules  We divide 1368 into factors as we discuss divisibility rules.  
Divisibility of 360  The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility.  
Division with 7  We practice the facts of division with sevens by practicing the facts of multiplication that have a factor of seven.  
Division with 8  We practice the facts of division with eights by practicing the facts of multiplication that have a factor of eight.  
A Lesson for the Division Facts Table  We master the facts of division by mastering the facts from the Multiplication Table.  
Division with 9  We practice the facts of division with nines by practicing the facts of multiplication that have a factor of nine.  
Division Table  Knowing the multiplication facts makes division easy.  
Division with 10  Because we use a baseten system, dividing by ten means to move the decimal point. We practice the facts of division with tens by practicing the facts of multiplication that have a factor of ten. 

Division with 2  When we divide by 2, we divide the number in half.  
Division with 6  We practice the facts of division with sixes by practicing the facts of multiplication that have a factor of six.  
Division with 4  We practice the facts of division with fours by practicing the facts of multiplication that have a factor of four.  
Division with 5  We practice the facts of division with fives by practicing the facts of multiplication that have a factor of five.  
Division with 3  We practice the facts of division with threes by practicing the facts of multiplication that have a factor of three.  
An Introduction to Division  We learn that division is actually a form of multiplication. So we focus on multiplication to learn division. 

Dividing and Rounding Large Numbers  The problems in this lessons require the skills of long division and rounding.  
Long Division with ThreeDigit Divisors  Three digits in the divisor means long, long division.  
Lesson in Division to Solve for Missing Number  Using numbers 30 through 99, we solve division problems for the "missing number." We are building a bridge from arithmetic to algebra.  
A Lesson in Negative Division  At some point we involve negative values into our approach to arithmetic, to start building a bridge toward algebra. We review that the product of two negative values is positive. 

Division in Three Different Formats  We can write a statement of division horizontally, or as traditional long division, or as a fraction. 
Estimation
Title DescriptionExponents & Radicals
Title DescriptionAn Overview of Rules for Exponents  We take a look at the MathAids handout for rules of exponents.  
An Introduction to Negative Exponents  An introduction to negative exponents. We reference reciprocals without detail about them. 

More Work with Negative Exponents  More explanations of working with negative exponents. Both our bases and exponents employ negative integers. 

The World of Negative Exponents  We jump into the world of negative exponents. So we employ both Positive and Negative values for both bases and exponents. 

Introducing Fractional Exponents  We introduce the equivalence of fractional exponents as roots: square roots, cube roots, and fourth roots.  
Introducing Fraction Exponents  We introduce the equivalence of fractional exponents as roots: square roots, cube roots, and fourth roots.  
Multiplying with Exponents  An introductory lesson for multiplication of terms with exponents.  
A Lesson in Evaluating Exponential Functions  We examine the nature of functions before we jump into the evaluation of Exponential Functions.  
More Detailed Examples with Simplifying Radicals  Simplifying radicals (square roots) is really a test of your mastery of basic facts of multiplication. Identifying the factors of the radicand will make it easy to work these problems. 

Simplifying Square Roots  A few words about the simplifcation of radicals and square roots. Sometimes simpler is not so simple. 

Square Roots and Absolute Values  A review of square roots and absolute values. 

Detailed Examples with Simplifying Radicals  Simplifying radicals (square roots) is really a test of your mastery of basic facts of multiplication. Identifying the factors of the radicand will make it easy to work these problems. 

Additional Examples with Simplifying Radicals  Simplifying radicals (square roots) is really a test of your mastery of basic facts of multiplication. Identifying the factors of the radicand will make it easy to work these problems. 

A Lesson in Simplifying Radicals  Preaching the need to learn the Facts of Multiplication. Learn the facts of the Times Table. Please. 

A Lesson in Simplifying Radical Expressions  The game is to "pull out" the factors that lurk about within the factors raised to a specific power. This is a game. 

A Lesson in Multiplying Radical Expressions  Hard Problems: Now we are making our way from Algebra toward Advanced Algebra. We multiply binomials with radical expressions. 

Dividing Radical Expressions (Level: Medium)  Level: Medium. Simplify fractions by cancelling factors top and bottom. Make sure to rationalize the denominator. 

Dividing Radical Expressions (Level: Hard)  Level: Medium. Simplify fractions by cancelling factors top and bottom. Make sure to rationalize the denominator. 

Dividing Radical Expressions (Level: Easy)  Level: Easy. We simplify fractions that contain radicals in the numerator and the denominator. We cancel out factors simultaneously from topandbottom. 

Scientific Notation with Negative Exponents 2  This lesson in Scientific Notation uses only Negative Powers of Ten.  
Scientific Notation with Positive Exponents 2  This lesson in Scientific Notation uses only Positive Powers of Ten.  
Scientific Notation with Positive and Negative Powers  A lesson in Scientific Notation discusses the difference between Positive Exponents and Negative Exponents.  
Scientific Notation, Positive and Negative Exponents  A lesson in Scientific Notation discusses the difference between Positive Exponents and Negative Exponents.  
Scientific Notation with Positive and Negative Exponents  A lesson where we multiply numbers in Scientific Notation with a little multiplication and a smidgen of addition.  
Scientific Notation with both Positive and Negative Exponents  We raise values expressed in Scientific Notation to both Positive Exponents and Negative Exponents.  
Scientific Notation and Operations  Mr. X does the HARD Long Division and the student gets the EASY Long Division.  
Scientific Notation Operations  We show all answers and work toward them. As we do we emphasize that reliance on a calculator may not be entirely helpful. 
Fact Family
Title DescriptionAn Overview of Fact Families  We tout the importance of Fact Families with two games: SumorProduct, and SumandProduct.  
Multiplication Fact Family Lessson  A quick lesson for the six ways to order the three integers from a Multiplication Fact Family. 
Factors
Title DescriptionPrime Factor Trees  A basic lesson in Prime Factorization with Factor Trees.  
Divisibility of 360  The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility.  
GCF, Greatest Common Factor  A lesson in finding the Greatest Common Factor, or GCF, for two given integers.  
Greatest Common Factor Lesson  Twenty problems for GCF. Mr. X knocks out the first ten in highspeed fashion. 

LCM  Least Common Multiple  We discuss the methods to determine the Least Common Multiple for a pair of given Integers.  
Least Common Multiple Methods  Explanations of LCM with the list method and the Prime Factorization method.  
Least Common Multiples  More explanations of LCM with the list method and the Prime Factorization method.  
A Lesson in Prime Factorization  A brief lesson in Prime Factorization of Integers less than ninesquared.  
Prime Factorization Lesson  Prime factorization means to find the factors (or divisors) of an integer that are themselves prime numbers. These problems are also part of Prime Factorization Lesson 20. 
Flash Cards
Title DescriptionAddition Makes Counting Easier  How many birds are two birds and five birds? We sum objects with the conjunction "and."  
Addition of 1  Repeating simple addition facts helps children master early arithmetic. This video lesson, appropriate for children starting to learn addition, goes over adding by 1. 

Addition by 9  This video lesson, appropriate for children starting to learn addition, goes over adding by 9. 

Addition by 8  This video lesson, appropriate for children starting to learn addition, goes over adding by 8  
Addition by 7  This video lesson, appropriate for children starting to learn addition, goes over adding by 7. 

Addition by 6  This video lesson, appropriate for children starting to learn addition, goes over adding by 6. 

Adding by 11 and 12  We use an addition table to review addition of 11 and 12.  
Addition by 5  This video lesson, appropriate for children starting to learn addition, goes over adding by 5. 

Addition by 10  This video lesson, appropriate for children starting to learn addition, goes over adding by 10. 

Addition by 2  This video lesson, appropriate for children starting to learn addition, goes over adding by 2. 

Addition by 3  This video lesson, appropriate for children starting to learn addition, goes over adding by 3. 

Addition by 4  This video lesson, appropriate for children starting to learn addition, goes over adding by 4. 

The Subtraction Table  You need to know these facts. They are basic facts of subtraction and they are essential to understanding what comes later. Learn these facts. 

Subtraction of 5  We practice subtracting by 5. Students should be able to memorize these facts. 

Subtraction of 6  We practice subtracting by 6. Students should be able to memorize these facts. 

Subtraction of 7  We practice subtracting by 7. Students should be able to memorize these facts. 

Subtraction of 8  We practice subtracting by 8. Students should be able to memorize these facts. 

Subtraction of 4  We practice subtracting by 4. Students should be able to memorize these facts. 

Subtraction of 9  We practice subtracting by 9. Students should be able to memorize these facts. 

Subtraction of 3  Learn the facts of subtracting by 3.  
Making the Transition from Addition to Subtraction  Subtracting a positive value is equivalent to adding the negative of that value. This concept is easy to understand with the visualization on the real number line. 

Subtraction of 2  Learn the facts of subtracting by 2.  
Subtraction of 10  We practice subtracting by 10. Students should be able to memorize these facts. 

Subtraction of 1  Learn the facts of subtracting by 1.  
Multiplying by 9  We review the multiplication table for 9. We also work some sample problems. 

Building a Times Table in Excel  We design a multiplication table using a standard spreadsheet. The facts are universal, but your design for its look should be your own. 

Multiplying by 7  We review the multiplication table for 7. We also work some sample problems. 

Multiplying by 6  We review the multiplication table for 6. We also work some sample problems. 

Multiplying by 5  When we multiply by 5, we quintuple the number.  
Multiplying by 1  When we multiply by one, we employ the multiplicative identity.  
Multiplication by 4  When we multiply by 4, we quadruple the number.  
Multiplication by 3  When we multiply by 3, we triple the number.  
Multiplication by 2  When we multiply by 2, we double the number.  
Elements of Basic Multiplication  The basic facts of multiplication must be memorized. There is no substitute for this knowledge. Learn these facts. Note that what used to be termed "multiplicand" and "multiplier" are now called factors. 

Multiplication by 10  We practice the basic facts of multiplication with a factor of ten. We multiply an integer by ten by writing a following zero. 

Multiplying by 8  We review the multiplication table for 8. We also work some sample problems. 

Division with 4  We practice the facts of division with fours by practicing the facts of multiplication that have a factor of four.  
Division with 10  Because we use a baseten system, dividing by ten means to move the decimal point. We practice the facts of division with tens by practicing the facts of multiplication that have a factor of ten. 

Division with 9  We practice the facts of division with nines by practicing the facts of multiplication that have a factor of nine.  
Division with 8  We practice the facts of division with eights by practicing the facts of multiplication that have a factor of eight.  
Division with 7  We practice the facts of division with sevens by practicing the facts of multiplication that have a factor of seven.  
Division Table  Knowing the multiplication facts makes division easy.  
Division with 2  When we divide by 2, we divide the number in half.  
Division with 5  We practice the facts of division with fives by practicing the facts of multiplication that have a factor of five.  
A Lesson for the Division Facts Table  We master the facts of division by mastering the facts from the Multiplication Table.  
Division with 3  We practice the facts of division with threes by practicing the facts of multiplication that have a factor of three.  
Division with 6  We practice the facts of division with sixes by practicing the facts of multiplication that have a factor of six.  
Telling Time on Analog Clocks  Five Minute Increments  We tell the time on an analog clock in fiveminute increments. Then we follow a Minute Hand clockwise in a very fast fashion. 

38 Cents in US Coins  How many ways can we get 38 cents using pennies, nickles, dimes and/or a quarter?  
Adding United States coins  To add the value of coinage we simply learn the denominations of coins used in the U.S.  
A Lesson in Roman Numerals  A very brief lesson in Roman Numerals with a converter from NovaRoma.org.  
An Overview of Fact Families  We tout the importance of Fact Families with two games: SumorProduct, and SumandProduct.  
Multiplication Fact Family Lessson  A quick lesson for the six ways to order the three integers from a Multiplication Fact Family.  
Reading Numbers 1  100  You should be able to read numbers from 1 to 100. The numbers in this set are considered Counting Numbers. 

Counting 61 though 100  We continue counting, reading number names, through one hundred.  
Counting 31 though 60  We continue counting through sixty.  
Learning Numbers 1 through 10  Counting and recognizing digits comes early with practice. We first discuss numbers 1 through 10. 

Learning Numbers 11 through 30  Counting and recognizing digits comes early with practice. In this video we learn numbers 11  30. 

Numbers to be Written  Learn your digits, how to read them, how to write them, how to recognize them. We focus on twodigit numbers in this lesson. 

A Lesson in Japanese Money  The Yen  A brief discussion of the Yen, the unit of both coinage and currency in Japan.  
A Lesson in British Currency  We briefly discuss British paper money, or currency.  
A Lesson in British Coins  We learn a few facts about coinage in Great Britain. 
Fractions
Title DescriptionFractions Visualized as Sections of a Pie  This handout provides a handy graphic for learning basic fractions. Because all the graphics are the same size, children at early primary age could use them with scissors and crayons. Fractions range from a whole to twelfths. 

Fractions Visualized as Sections of a Rectangular Bar  We look at the concept of a whole divided by successive numbers. Our fractions range from 1/2 to 1/12. 

Basic Fractions in a Bar  A lesson in dividing a Bar into Twelfths.  
Fractions within Shaded Triangles  Basic fractions from shaded triangles within polygons.  
Fractions within Shaded Bars  Basic fractions with shaded boxes. Don't just count. Think. 

Reading and Writing Fractions  Fractions need to be understood in several different ways. In this lesson we read and write fractions, including mixed fractions. 

Visually Adding Simple Fractions  We visually add simple fractions with the same (common) denominator.  
A Lesson in Visualizing Fractions  One entire object is called a "unit" or a "whole." We introduce fractions as parts of a whole. When we use a pie chart, the entire pie is a whole, or 100%. 

Adding Simple Fractions, a Lesson  A simple lesson in addition of simple fractions, with like denominators.  
Adding Two Fractions, a Lesson  A lesson in the basics of adding fractions with different denominators.  
A Lesson in Adding Two or More Fractions  When adding two or more fractions, we want a common denominator. This allows us to add the numerators of the fractions with equivalent denominators. 

The Basic Idea of Mixed Numbers  Increasingly, the term "improper fraction" is really a mixed number, which can be expressed as a whole number followed by a fraction, or as a decimal with the fractional part to the right of the decimal point.  
Visual Subtraction Lesson  Subtract simple fractions with a visual approach to understanding.  
Subtracting Simple Fractions  A simple lesson in subtraction of simple fractions, with like denominators.  
Subtract Fractions from Whole Numbers  We subtract fractions from Whole Numbers by understanding the language, not by following a recipe or algorithm.  
Subtracting Mixed Numbers  Subtracting Mixed Numbers involves a thorough knowledge of the facts of multiplication.  
Multiply Fractions, a Lesson  When we multiply fractions keep numerator factors on top, and keep denominator factors on the bottom.  
Multiply Fractions, Cancel Factors  We reinforce the cancellation of factors topandbottom as we multiply fractions.  
Multiplying Mixed Fractions  In this lesson we practice multipling fractions with mixed numbers. We also use cross cancelling where appropriate. 

Multiplying with CrossCancelling, a Lesson  Crosscanceling is a technique to reduce fractions as we multiply.  
Multiplying a Mixed Fraction with a Whole Number  We introduce mixed fractions in this lesson, starting with multiplication of a Mixed Fraction with a Whole Number. The manipulation of fractions needs to become easy and secondnature to you. 

Multiply Mixed Numbers  There are several techniques to multiply Mixed Numbers. Heavy fractions often lighten the load. 

Introducing Reciprocals  Reciprocals are handy for dividing fractions. This lesson introduces the concept of Reciprocals. 

Don't Divide. Multiply. To Divide.  Keep the first fraction. Change the operation to Multiplication. Invert the second fraction. 

A Lesson in Division and Reciprocals  Realworld examples for using reciprocals to help us understand division are provided in this lesson.  
A Lesson in Dividing Mixed Numbers  To divide Mixed Numbers, change them to Heavy Fractions, invert and multiply.  
Divisibility of 360  The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility.  
A Lesson in Prime Factorization  Prime factorization means to find the factors (or divisors) of an integer that are themselves prime numbers. 

Prime Factorization Lesson  Prime factorization means to find the factors (or divisors) of an integer that are themselves prime numbers. These problems are also part of Prime Factorization Lesson 20. 

Prime Factor Trees  A basic lesson in Prime Factorization with Factor Trees.  
Greatest Common Factor Lesson  Twenty problems for GCF. Mr. X knocks out the first ten in highspeed fashion. 

GCF, Greatest Common Factor  A lesson in finding the Greatest Common Factor, or GCF, for two given integers.  
Least Common Multiples  More explanations of LCM with the list method and the Prime Factorization method.  
Least Common Multiple Methods  Explanations of LCM with the list method and the Prime Factorization method.  
LCM  Least Common Multiple  We discuss the methods to determine the Least Common Multiple for a pair of given Integers.  
Converting to Equivalent Fractions  A lesson in converting fractions to an equivalent fraction, just with a different denominator.  
Moving Tomatoes  A fastmoving lesson in Moving Tomatoes.  
Reducing Fractions Problem Set 1  Reduction of simple fractions is an essential skill. The reduced fractions will have denominators ranging from 2 to 10. 

Reducing Fractions to the Lowest Term  A fraction is in its lowest term when no number greater than 1 can divide both terms. This lesson shows examples on how to reduce fractions. 

Reducing Fractions Problem Set 2  Many reductions in basic fractions should be automatic. You need to learn the basic ones. The reduced fractions will have denominators ranging from 2 to 12. 

Reinforcing our work with 9ths  Know the facts, know the truth about ninths and how they convert to decimals. Learn these and you will have them forever. Just learn them. 

Reinforcing our work with 8ths  It is important to know eighths. There is no substitute for practice with fractions, decimals, and percents. 

Converting 8ths to Decimals and Percentages  Instead of using a calculator every time you encounter a multiple of one eighth, just remember a few facts about them.  
Converting 9ths to Decimals and Percentages  You should know your ninths, which are exceptionally easy to convert to decimals or percents. 

Converting 11ths to Decimals and Percentages  You should know your elevenths. When you see the patterns, 11ths are extremely easy to understand in terms of decimals or percents. 

Converting 12ths to Decimals and Percentages  You should learn your twelfths. This little lesson reinforces basic twelfths in terms of both decimals and percentages. 

Practice with 12ths  Look for patterns in basic fractions. Converting twelfths to decimals or percents is actually pretty easy once you catch onto them. 

Converting 20ths to Decimals and Percentages  If you can count by fives, you can quickly understand decimal and percent equivalence for 20ths.  
Comparing Fractions, Absolute Value  Greater values reside to the right on the Real Number Line. We also introduce the notion of Absolute Value. 

Comparing Fractions Left and Right  The relative position (left or right) of two real values on the Real Number Line determines lessthan or greaterthan.  
Comparing Fractions, a Lesson  Several methods are presented for the comparison of fractions, using " < , > , or = ."  
A Lesson for Fractions with Like Tops or Bottoms  There are a couple of principles to keep in mind when either numerators agree or when denominators agree.  
Comparing Fractions and Decimals  Fractions on the left, decimals on the right, and a comparison symbol in between the two values, and we read lefttoright.  
The Master PDF Chart, Lesson One  We take a close look at eighths and ninths at the Official Mr. X PDF Master File for Mastering Fractions. We learn equivalent Percents, Decimals, and Fractional Values. 

The Master PDF Chart, Lesson Two  Sixths, fifths, twentieths, sevenths and elevenths are detailed as percents, decimals, and fractions. Learn these, please. 

A Lesson in Improper Fractions and Mixed Numbers  Improper Fractions can be expressed as Mixed Numbers. Both the improper (heavy) fraction and the mixed number are equivalent! 

Introducing Fraction Exponents  We introduce the equivalence of fractional exponents as roots: square roots, cube roots, and fourth roots.  
A Lesson in Adding English Measurements  This lesson adds English units of length to the nearest sixteenth of an inch.  
A Chart for Decimals Equivalents for Fractions of Inches  We discuss the chart for fractions of an inch. Know your eighths. Machinists should learn them all. 

A Lesson in Multiplying Fractions with Whole Numbers  Some very basic calculations merit practice and fundamental understanding.  
Multiplying Fractions with Whole Numbers  We introduce multiplying fractions by first working examples involving one fraction and a whole number. The manipulation of fractions needs to become easy and secondnature to you. 

Multiplying Fractions with Whole Numbers 2  We continue showing examples of multiplying fractions with whole numbers. The manipulation of fractions needs to become easy and secondnature to you. 

Multiplying Fractions with Whole Numbers 3  We continue showing examples of multiplying fractions with whole numbers. The manipulation of fractions needs to become easy and secondnature to you. 
Function Table
Title DescriptionCompute the Output of Functions  To complete each Function Table we calculate y as a function of x. Indeed, y = f(x). 

Computing Outputs of Functions  Complete the Function Table with very simple arithmetic. Each function is linear. 
General Topics
Title Description25!  A close look at the product of the first 25 positive integers, or 25! It's a banquet of numbers!  
An Additional Look at Addition  Just a few thoughts about the very nature of addition.  
An Interesting Relationship  It turns out that xÂ² = (x1)(x+1) + 1. We look at this algebraic relationship with the standard multiplication table. If you prefer, equivalently, xÂ²  1 = (x1)(x+1). 

Coins 38 cents  How many different ways using U.S. coins can one have exactly 38 cents? 

Master PercentDecimalFraction Chart 1  Let's take a look at the "official" Mr. X PDF chart.  
Master PercentDecimalFraction Chart 2  You have to learn a few fractions in this life. Just a few. Learn them. 

Master PercentDecimalFraction Chart 3  We all know that 50 percent is the same as onehalf. Learn just a few more fractions. You'll be glad you did! 

Master PercentDecimalFraction Chart 4  Here is a nice, long look at the "official" Mr. X master PDF Chart.  
New Primary 001  Numbers and Figures  Counting and recognizing digits comes early.  
New Primary 002  Counting 11 though 30  We continue counting through thirty.  
New Primary 003  Counting 31 though 60  We continue counting through sixty.  
New Primary 004  Counting 61 though 100  We continue counting, reading number names, through one hundred.  
New Primary 005  Numbers to be Read  You should be able to read any of the numbers in this lesson.  
New Primary 006  Numbers to be Written  Learn your digits, how to read them, how to write them, how to recognize them. We focus on twodigit numbers in this lesson. 

New Primary 007  Oral Exercises for Objects  Associate a number made from digits to represent a set of objects. You should be able to answer all of the questions in this lesson. 

New Primary 008  Oral Exercises  We begin arithmetic with no operators or operational symbols. Instead, we rely on "and" for sums and "times" for products. How many are two and six? This is the beginning of arithmetic. 

New Primary 009  Oral Exercises  More questions with "and" and "times" for addition and multiplication, with no operators. "One from nine leaves how many?" This is the beginning of subtraction. 

New Primary 010  Addition  How many birds are two birds and five birds? We sum objects with the conjunction "and."  
New Primary 011  Addition of One  We practice the facts of addition that include adding a single unit to another (integer) value.  
New Primary 012  Addition of Two  We practice sums that add two to a value.  
New Primary 013  Addition of Three  We practice sums that include addition of three to a value.  
New Primary 014  Addition of Four  Addition with four. This lesson practices adding 4. 

New Primary 015  Addition of Five  We practice addition facts with addends of fives.  
New Primary 016  Addition of Six  Addition of six is practiced with a list of facts.  
New Primary 017  Addition of Seven  We practice the facts of basic addition with sevens.  
New Primary 018  Addition of Eight  We practice the facts of adding eight to other onedigit integers.  
New Primary 019  Addition of Nine  Addition of nine includes facts to be learned, to be able to be recalled without effort.  
New Primary 020  Addition of Ten  In our BaseTen system, addition of ten is especially convenient.  
New Primary 021  Review of Simple Addition  We answer many questions quickly, such as, "How many are two and nine?" We practice the facts and reinforce that the order in which we sum terms does not matter. We sum three terms. 

New Primary 022  Addition with Triple Sets of Integers  We sum three terms. We reduce the work by combining terms to reduce the number of terms. We review basic addition. 

New Primary 023  Reading Review of Simple Addition  We read word problems to reinforce the basic facts of addition for small positive integers.  
New Primary 024  Subtraction  The words "leaves" and "less" and "left" are key to learning the basic concept of subtraction. We still have no operational symbol. 

New Primary 025  Subtraction of One  We practice the facts of subtraction with a subtrahend or difference of one.  
New Primary 026  Subtraction of Two  We practice the facts of subtraction with a subtrahend or difference of two.  
New Primary 027  Subtraction of Three  We practice the facts of subtraction with a subtrahend or difference of three.  
New Primary 028  Subtraction of Four  We practice the facts of subtraction with a subtrahend or difference of four.  
New Primary 029  Subtraction of Five  We practice the facts of subtraction with a subtrahend or difference of five.  
New Primary 030  Subtraction of Six  We practice the facts of subtraction with a subtrahend or difference of six.  
New Primary 031  Subtraction of Seven  We practice the facts of subtraction with a subtrahend or difference of seven.  
New Primary 032  Subtraction of Eight  We practice the facts of subtraction with a subtrahend or difference of eight.  
New Primary 033  Subtraction of Nine  We practice the facts of subtraction with a subtrahend or difference of nine.  
New Primary 034  Subtraction of Ten  We practice the facts of subtraction with a subtrahend or difference of ten.  
New Primary 035  Review Subtraction  You need to recall quickly and easily the basic facts of subtraction.  
New Primary 036  Review Addition and Subtraction  Singular or plural stateofbeing verbs do not matter in the language of arithmetic. We may correctly say that "seven less three are four," or "seven less three is four." 

New Primary 037  Review with Sequential Subtraction  We count by numbers other than one, and we count toward lesser values with subtraction. Multiplication is implied in some of the word problems in this lesson. 

New Primary 038  Multiplication  Don't be too quick to enter the world of multiplication before mastering the basic facts of addition and subtraction. Plural versus singular forms of stateofbeing verbs do not matter in equating the factors to the product. 

New Primary 039  Multiplicative Identity  When we multiply by one, we employ the multiplicative identity.  
New Primary 040  Multiplication Doubling  Multiplication by two effectively doubles the first (or other) factor or factors.  
New Primary 041  Multiplication Tripling  When we triple a number we multiply that number by three.  
New Primary 042  Multiplication by Four  We practice the basic products that include a factor of four.  
New Primary 043  Multiplication by Five  We practice the basic facts of multiplication with a factor of five.  
New Primary 044  Multiplication by Six  We practice the basic facts of multiplication with a factor of six.  
New Primary 045  Multiplication by Seven  We practice the basic facts of multiplication with a factor of seven.  
New Primary 046  Multiplication by Eight  We practice the basic facts of multiplication with a factor of eight.  
New Primary 047  Multiplication by Nine  We practice the basic facts of multiplication with a factor of nine.  
New Primary 048  Multiplication by Ten  We practice the basic facts of multiplication with a factor of ten. We multiply an integer by ten by writing a following zero. 

New Primary 049  Multiplication Review with Two and Three Simple Factors  We reinforce the basic facts of multiplication. Again, plural versus singular forms of verbs do no matter within the language of arithmetic. We also multiple three factors. 

New Primary 050  Multiplication Around Subtraction  We deal with more complicated forms of math statements in English. We read lefttoright. 

New Primary 051  Promiscuous Questions  Diverse, casual, and random questions related to addition, subtraction, and multiplication.  
New Primary 052  Division  We learn that division is actually a form of multiplication. So we focus on multiplication to learn division. 

New Primary 053  Division with Two  When we divide by two we take half. Two divides evenly into even numbers. 

New Primary 054  Division with Three  We practice the facts of division with threes by practicing the facts of multiplication that have a factor of three.  
New Primary 055  Division with Four  We practice the facts of division with fours by practicing the facts of multiplication that have a factor of four.  
New Primary 056  Division with Five  We practice the facts of division with fives by practicing the facts of multiplication that have a factor of five.  
New Primary 057  Division with Six  We practice the facts of division with sixes by practicing the facts of multiplication that have a factor of six.  
New Primary 058  Division with Seven  We practice the facts of division with sevens by practicing the facts of multiplication that have a factor of seven.  
New Primary 059  Division with Eight  We practice the facts of division with eights by practicing the facts of multiplication that have a factor of eight.  
New Primary 060  Division with Nine  We practice the facts of division with nines by practicing the facts of multiplication that have a factor of nine.  
New Primary 061  Division with Ten  Because we use a baseten system, dividing by ten means to move the decimal point. We practice the facts of division with tens by practicing the facts of multiplication that have a factor of ten. 

New Primary 062  Cognitive Division  If you learn your times tables you can answer these questions quickly and easily.  
New Primary 063  Review Situational Division  Simple and straightforward word problems give us a glimpse into the nature of both division and multiplication.  
New Primary 064  Arithmetic Operators  We introduce the operators of arithmetic, the signs (or symbols) for addition, subtraction, multiplication, and division. These are generally read "plus," "minus," "times," and "divided by," respectively. We also officially introduce the equal sign. 

New Primary 065  Addition with Operators  The familiar facts of addition are now presented with the plussign operator for taking sums.  
New Primary 066  Practice with Addition Operator  Technically, we transposed lessons LXV and LXVI from Ray's New Primary Arithmetic from 1877. It really does not matter, because Lesson 66 and Lesson 65 both practice with the addition operator, the plus sign. 

New Primary 067  Simple Additional Situations  Word problems allow us to practice basic addition with the powerful symbolism of the language of mathematics.  
New Primary 068  Practice with Situational Operations  Basic statements in mathematics derive from simple situations.  
New Primary 069  Statements with Addition and Subtraction  Read math statements lefttoright, just as we do in English. However, there is no one way to combine terms in a math statement. That is, there is no single or unique way to correctly think about arithmetic. 

New Primary 070  Situations with Addition and Subtraction  Basic word problems allow us to write basic math statements. Generally, there is no single way to do this correctly. 

New Primary 071  Statements with Addition, Subtraction and Multiplication  We look at mathematical statements to begin thinking of numbers a little more abstractly, as entities unto themselves.  
New Primary 072A  Cognitive Grouping  The difference between writing a decimal point and writing a multiplication dot for the operation to multiply factors can be a very small distance on the page.  
New Primary 072B  Build a Multiplication Table  We design a multiplication table using a standard spreadsheet. The facts are universal, but your design for its look should be your own. 

New Primary 072C  Counting with Different Values  With the assistance of the multiplication table, we count by various small integers.  
New Primary 072D  Counting with Different Values  With the multiplication table, we count by different values.  
New Primary 072E  Uncover Ten Covers  Ten little black "manhole covers" are revealed atop the multiplication table.  
New Primary 073  More Cognitive Grouping  Multiplication, addition, and subtraction commingle in various forms, so that division appears naturally as a consequence of understanding numbers.  
New Primary 074  Promiscuous Questions  Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality. 

New Primary 075  Promiscuous Questions  Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality. 

New Primary 076  Promiscuous Questions  Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality. 

New Primary 077  Promiscuous Questions  Promiscuous means casual, random, or diverse. We employ the operations of addition, subtraction, multiplication, and division, as well as equality. 

PercentDecimalFraction Lesson in 11ths  You should know your elevenths. When you see the patterns, 11ths are extremely easy to understand in terms of decimals or percents. 

PercentDecimalFraction Lesson in 12ths  You should learn your twelfths. This little lesson reinforces basic twelfths in terms of both decimals and percentages. 

PercentDecimalFraction Lesson in 20ths  If you can count by fives, you can quickly understand decimal and percent equivalence for 20ths.  
PercentDecimalFraction Lesson in 8ths  Instead of using a calculator every time you encounter a multiple of one eighth, just remember a few facts about them.  
PercentDecimalFraction Lesson in 9ths  You should know your ninths, which are exceptionally easy to convert to decimals or percents. 

PercentDecimalFraction Lesson in eighths  It is important to know eighths. There is no substitute for practice with fractions, decimals, and percents. 

PercentDecimalFraction Lesson in ninths  Know the facts, know the truth about ninths and how they convert to decimals. Learn these and you will have them forever. Just learn them. 

PercentDecimalFraction Lesson in twelfths  Look for patterns in basic fractions. Converting twelfths to decimals or percents is actually pretty easy once you catch onto them. 

Prime Factorization Lesson 20  Prime factorization means to find the factors (or divisors) of an integer that are themselves prime numbers. These problems are also part of a Problem Set: Prime Factorization Problem Set 20. 

Prime or Composite?  If an integer is prime its only factors (or divisors) are itself and one. This lesson is, essentially, a lesson in the facts of multiplication, which you should know. 

Ray Intellectual Arithmetic 007  Subtraction Table  You need to know these facts. They are basic facts of subtraction and they are essential to understanding what comes later. Learn these facts. They need to reside between your ears, in the circuits of your brain. 

Ray's Intellectual Arithmetic 001  Cognitive Addition  An initial review of counting and simple addition from Ray's New Intellectual Arithmetic ,from 1877.  
Ray's Intellectual Arithmetic 002  More Cognitive Addition  Make sure you understand that the order we take terms to sum does not matter at all. The Commutative Law of Addition is emphasized. 

Ray's Intellectual Arithmetic 003  Addition Table  You need to know all of these facts for simple addition. You need to infuse these facts to the gray matter between your ears. You need to know every single one of these facts. 

Ray's Intellectual Arithmetic 004  Addition of Pairs of One and TwoDigit Integers  These questions should be automatic. You need to be able to answer all of the questions in this lesson quickly and effortlessly. 

Ray's Intellectual Arithmetic 005  Addition of Multiple Integers  Just as we add two integers together, we may add any number of integers almost as easily, and in any order we choose. A sum of terms does not rely on the order or sequence in which we take the terms; order of the terms does not matter. 

Ray's Intellectual Arithmetic 006  Subtraction  We hope you can answer all of these questions. Your previous practice of arithmetic should make this lesson exceptionally easy and straightforward. Subtraction provides the difference between two values. 

Ray's Intellectual Arithmetic 008  Cognitive Subtraction  Simple word problems provide a glimpse into the meaning of subtraction as a difference between two values.  
Ray's Intellectual Arithmetic 009  Review  Word problems provide a fundamental understanding to the meaning of subtraction and taking the difference between two values.  
Ray's Intellectual Arithmetic 010  Addition and Subtraction with Operators  This is some really good practice with simple integers with both plus and minus signs. You need to get used to working with these symbols. You should do every single one of these problems on your own. Have a knowledgeable person check your answers. Don't use a calculator. Learn these facts to understand the basics of the language of arithmetic. 

Ray's Intellectual Arithmetic 011  Cognitive Addition and Subtraction  Word problems illustrate the concepts of both addition and subtraction. Basic addition facts and basic subtraction facts are reinforced. We express in English and in mathematics the same ideas. 

Ray's Intellectual Arithmetic 012  Multiplication  Basic arithmetic includes our facts from the multiplication table. Simple word problems emphasize these facts, which need to be memorized. 

Ray's Intellectual Arithmetic 013  Multiplication Table with Exercises  What used to be termed "multiplicand" and "multiplier" are now called, simply, factors. The basic facts of multiplication must be memorized. There is no substitute for this knowledge. Learn these facts. 

Ray's Intellectual Arithmetic 014  Cognitive Multiplication  Simple word problems reinforce the basic facts of multiplication.  
Ray's Intellectual Arithmetic 015  More Cognitive Multiplication  This lesson continues the application of your knowledge of the basic facts of multiplication. It is important to build a good foundation in arithmetic. 

Ray's Intellectual Arithmetic 016  Division  Division is just another way to look at multiplication. If you know your facts of multiplication, then division is very straightforward. We define "dividend," "divisor," and "quotient." 

Ray's Intellectual Arithmetic 017  Division Table  This is a systematic review of basic multiplication, as division facts. We recommend learning these facts as multiplication facts. If you memorize the facts of multiplication, then this lesson is a piece of cake. 

Ray's Intellectual Arithmetic 018  Practice in Division  You have to know how many times a smaller number is contained in a larger number.  
Ray's Intellectual Arithmetic 019  Operative Arithmetic Practice  From word problems we practice the basic facts of multiplication, addition, subtraction, and division.  
Ray's Intellectual Arithmetic 020  Fractions  One entire object is called a "unit" or a "whole." We introduce fractions as parts of a whole (unit).  
Ray's Intellectual Arithmetic 021  Reading and Writing Fractions  Fractions need to be understood in several different ways. We do not like the terms "proper fraction" and "improper fraction." Fractions are easy as pie. 

Ray's Intellectual Arithmetic 022  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 023  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 024  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 025  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 026  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 027  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 028  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 029  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 030  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 031  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 032  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 033  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 034  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 035  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 036  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 037  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 038  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 039  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 040  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 041  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 042  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Ray's Intellectual Arithmetic 043  Practice with Fractions  We have a lot of work to do in the practice of fractions. The manipulation of fractions needs to become easy and secondnature to you. 

Rounding Integers Lesson 17  A lesson in rounding, accompanied by a Problem Set. This basic skill of rounding is important for almost everyone. 
Graph Paper
Title DescriptionPractice with Cartesian Coordinates  Practice (x, y) coordinate location until it is secondnature to you.  
Polar Graph Paper, an Overview  An overview of Polar Graph Paper. We plot a single point as (r, Î˜) as well as (x, y). 

Opposite Directions  Get comfortable moving in opposite directions before tackling negative values.  
Graph Paper: An Overview  The general format for Cornell Notes is detailed in a specialized Mr. X video.  
Cornell Notes, a brief lesson  An overview of Cornell Notes, a template for taking quality notes in class. 
Graphing
Title DescriptionPractice with Cartesian Coordinates  Practice (x, y) coordinate location until it is secondnature to you. 
Greater Than Less Than
Title DescriptionComparing Integers Lesson  We compare both positive and negative pairs of Integers for their position on the Real Number Line. If the values a and b are not equal, then either a > b or b> a. 

Comparing Fractions, Absolute Value  Greater values reside to the right on the Real Number Line. We also introduce the notion of Absolute Value. 

Comparing Fractions, a Lesson  Several methods are presented for the comparison of fractions, using " < , > , or = ."  
Comparing Fractions Left and Right  The relative position (left or right) of two real values on the Real Number Line determines lessthan or greaterthan.  
Comparing Decimals Lesson 1  We read math statements lefttoright. For this worksheet we need the Correct Comparison Symbol: >, = or <. 

Comparing Decimals Lesson 2  Real Values on the Real Number Line can be compared then expressed with greaterthan, lessthan, or equalto symbols.  
The Master PDF Chart, Lesson One  We take a close look at eighths and ninths at the Official Mr. X PDF Master File for Mastering Fractions. We learn equivalent Percents, Decimals, and Fractional Values. 

Comparing Fractions and Decimals  Fractions on the left, decimals on the right, and a comparison symbol in between the two values, and we read lefttoright.  
The Master PDF Chart, Lesson Two  Sixths, fifths, twentieths, sevenths and elevenths are detailed as percents, decimals, and fractions. Learn these, please. 
Hundreds Chart
Title DescriptionCounting 31 though 60  We continue counting through sixty.  
Counting 61 though 100  We continue counting, reading number names, through one hundred.  
Learning Numbers 1 through 10  Counting and recognizing digits comes early with practice. We first discuss numbers 1 through 10. 

Learning Numbers 11 through 30  Counting and recognizing digits comes early with practice. In this video we learn numbers 11  30. 

Reading Numbers 1  100  You should be able to read numbers from 1 to 100. The numbers in this set are considered Counting Numbers. 
In and Out Boxes
Title DescriptionIntegers
Title DescriptionReading Numbers 1  100  You should be able to read numbers from 1 to 100. The numbers in this set are considered Counting Numbers. 

Numbers to be Written  Learn your digits, how to read them, how to write them, how to recognize them. We focus on twodigit numbers in this lesson. 

Integers One Less & One More Lesson  Simple, but important is this notion of "one more." So, equally important, is "one less." Make sure you "get it." 

Comparing Integers Lesson  We compare both positive and negative pairs of Integers for their position on the Real Number Line. If the values a and b are not equal, then either a > b or b> a. 

Addition of One or Two Digit  Two Addends  Practicing with Addition. Repetitive practice is an important element to learning these basics. The student's goal should be to answer these problems with very little effort. 

Addition of Multiple Integers  Just as we add two integers together, we may add any number of integers almost as easily, and in any order we choose. A sum of terms does not rely on the order or sequence in which we take the terms; order of the terms does not matter. 

A Lesson in Negative Division  At some point we involve negative values into our approach to arithmetic, to start building a bridge toward algebra. We review that the product of two negative values is positive. 
Kindergarten
Title DescriptionNumbers to be Written  Learn your digits, how to read them, how to write them, how to recognize them. We focus on twodigit numbers in this lesson. 

A Lesson in British Currency  We briefly discuss British paper money, or currency.  
Counting 31 though 60  We continue counting through sixty.  
Reading Numbers 1  100  You should be able to read numbers from 1 to 100. The numbers in this set are considered Counting Numbers. 

Counting 61 though 100  We continue counting, reading number names, through one hundred.  
Learning Numbers 11 through 30  Counting and recognizing digits comes early with practice. In this video we learn numbers 11  30. 

Learning Numbers 1 through 10  Counting and recognizing digits comes early with practice. We first discuss numbers 1 through 10. 

Counting Coins Lesson  As we learn to count money, this video has just a little extra explanation.  
Skip Counting by 7's and 12's  Using the times table is a good way to practice skip counting. In this video we skip count by 7's and 12's. 

Skip Counting by 3's and 8's  Using the times table is a good way to practice skip counting. In this video we skip count by 3's and 8's. 

Complete the Number Series  A discussion for teachers and parents about the appropriateness of negative values in Kindergarten. It's fine to expect Kindergarten students to understand negative values, but only with some quality instruction. We're not born with this concept of negative values. 

Addition Makes Counting Easier  How many birds are two birds and five birds? We sum objects with the conjunction "and."  
The Subtraction Table  You need to know these facts. They are basic facts of subtraction and they are essential to understanding what comes later. Learn these facts. 
Mean Mode Median
Title DescriptionHousehold Income, Median is a better "Average"  For some statistical measures, median provides a better value for what we think of as "average." Median household Income is a good example of this.  
MMMR: Mean, Mode, Median, and Range  This lesson describes some concepts related to the most basic ideas in statistics. These really are basics we all should know. 
Measurement
Title DescriptionA Chart for Decimals Equivalents for Fractions of Inches  We discuss the chart for fractions of an inch. Know your eighths. Machinists should learn them all. 

A Lesson in Temperature Conversion  If you can remember these numbers: 100180212, then you can remember the formulas for converting between temperature scales.  
A Quiz in Liquid Measures  This Quiz is actually a lesson. You should learn the basic equivalent measures for the kitchen, especially if you live in the United States. 

A Lesson in LiquidandDryMeasure Conversions  Relax. Learn the equivalent measures. A gallon of milk (or water, gasoline, or ketchup) is the same volume as 16 halfpints or 16 cups. 

General Conversions Table Lesson  The physical entities of Length, Weight, Area, and Speed are discussed in terms of Conversion Factors, along with their reciprocals for conversion of English units. Those units include: miles, inches, yards, feet, tons, ounces, square feet, square yards, acres, miles per hour and feet per second. 

Conversions between English and Metric  Our understanding of Conversion Factors is enhanced with an appreciation of reciprocal values.  
Producing Protactor Images Lesson  A worksheet with "blank" protractors, printable as oneperpage, or 2, 4, or 6toapage.  
Circles, Angles, Degrees  An introduction to angles includes a look at hands on a clock face. Angles need to be understood early in Geometry. 

Angles on a Clock Face  More angles on a clock face help us see the values of angles as we move around the circle.  
A Lesson in Reading Angles  A lesson in the nature of angles, with reading integervalue angle measurements with a protractor.  
Angles and Protactors  We look at equal fifths of a rotation, which are 72°. We also look at an angle greater than 180°. 
Mixed Problems
Title DescriptionReview Addition and Subtraction  Adding and subtracting single digit problems is quick if you have learned the addition and subtraction tables.  
Addition and Subtraction Statements  Read math statements lefttoright, just as we do in English. However, there is no one way to combine terms in a math statement. That is, there is no single or unique way to correctly think about arithmetic. 

A Lesson in Japanese Money  The Yen  A brief discussion of the Yen, the unit of both coinage and currency in Japan.  
A Lesson in British Currency  We briefly discuss British paper money, or currency.  
A Lesson in British Coins  We learn a few facts about coinage in Great Britain. 
Money
Title DescriptionCounting Coins Lesson  As we learn to count money, this video has just a little extra explanation.  
38 Cents in US Coins  How many ways can we get 38 cents using pennies, nickles, dimes and/or a quarter?  
Adding United States coins  To add the value of coinage we simply learn the denominations of coins used in the U.S.  
A Lesson in British Currency  We briefly discuss British paper money, or currency.  
US Coins Lesson  Print a handout full of images of pennies, nickles, dimes, quarters and halfdollars right here. Or go to MathAids.com to print them individually. 

US Bills Lesson  Print a handout full of images of onedollar, twodollar, fivedollar, tendollar, twentydollar, fiftydollar and onehundreddollar bills right here. Or go to MathAids.com to print them individually. 
Multiplication
Title DescriptionBuilding a Times Table in Excel  We design a multiplication table using a standard spreadsheet. The facts are universal, but your design for its look should be your own. 

Elements of Basic Multiplication  The basic facts of multiplication must be memorized. There is no substitute for this knowledge. Learn these facts. Note that what used to be termed "multiplicand" and "multiplier" are now called factors. 

Multiplication by 10  We practice the basic facts of multiplication with a factor of ten. We multiply an integer by ten by writing a following zero. 

Multiplication by 2  When we multiply by 2, we double the number.  
Multiplication by 3  When we multiply by 3, we triple the number.  
Multiplication by 4  When we multiply by 4, we quadruple the number.  
Multiplying by 8  We review the multiplication table for 8. We also work some sample problems. 

Multiplying by 7  We review the multiplication table for 7. We also work some sample problems. 

Multiplying by 1  When we multiply by one, we employ the multiplicative identity.  
Multiplying by 5  When we multiply by 5, we quintuple the number.  
Multiplying by 6  We review the multiplication table for 6. We also work some sample problems. 

Multiplying by 9  We review the multiplication table for 9. We also work some sample problems. 

Multiplication Review with Two and Three Simple Factors  We reinforce the basic facts of multiplication. Again, plural versus singular forms of verbs do no matter within the language of arithmetic. We also multiple three factors. 

Multiplication of Integers  This video shows a detailed approach to multiplying larger integers together. Do not use a calculator for these problems. 
Number Bonds
Title DescriptionNumber Lines
Title DescriptionGraph Paper: An Overview  There are many types of paper used in the study of mathematics. Some are quite specialized, others are just lines on a page. The Real Number Line can be depicted in uncountable ways. 

Opposite Directions  Get comfortable moving in opposite directions before tackling negative values.  
Making the Transition from Addition to Subtraction  Subtracting a positive value is equivalent to adding the negative of that value. This concept is easy to understand with the visualization on the real number line. 

Fractions on Number Lines, Lesson 1  An understanding of fractions on The Real Number Line is a foundation for all math that comes later.  
Fractions on Number Lines, Lesson 2  Place the Fractions on The Real Number Line. Your understanding of the language will be greatly enhanced. 

Decimals on the Real Number Line  Decimals, or decimal values, are to be placed at their proper location on the Real Number Line.  
The Real Number Line, a General Lesson  There is only one Real Number Line, strictly speaking. But we can describe The Real Number Line or draw parts of The Real Number Line an infinite number of different and unique ways. 
Order of Operations
Title DescriptionArithmetic Operators  We introduce the operators of arithmetic, the signs (or symbols) for addition, subtraction, multiplication, and division. These are generally read "plus," "minus," "times," and "divided by," respectively. We also officially introduce the equal sign. 
Patterns
Title DescriptionComplete the Number Series  A discussion for teachers and parents about the appropriateness of negative values in Kindergarten. It's fine to expect Kindergarten students to understand negative values, but only with some quality instruction. We're not born with this concept of negative values. 

Skip Counting by 3's and 8's  Using the times table is a good way to practice skip counting. In this video we skip count by 3's and 8's. 

Skip Counting by 7's and 12's  Using the times table is a good way to practice skip counting. In this video we skip count by 7's and 12's. 

How to Solve Skip Counting Problems  This lesson uses the attached worksheet to give examples on how to find the rule for the skip counting, and solve the problems. We use positive and integer values up to 999 in these advanced skip counting problems. 

Patterns in Advanced Skip Counting  There is a very wide variety of difficulty levels to be practiced with the MathAids.com Advanced Skip Counting worksheets. 
Percent
Title DescriptionMultiplying Percents that are Powers of Ten Problem Set 1  This lesson is really about moving the decimal point. Practice with these problems makes the effort almost effortless. So practice. 

A Lesson in Percentage Calculations  To calculate percentages we first learn to do it manually. Only then should we rely on a calculator. 

Comparing Fractions and Decimals  Fractions on the left, decimals on the right, and a comparison symbol in between the two values, and we read lefttoright.  
The Master PDF Chart, Lesson One  We take a close look at eighths and ninths at the Official Mr. X PDF Master File for Mastering Fractions. We learn equivalent Percents, Decimals, and Fractional Values. 

The Master PDF Chart, Lesson Two  Sixths, fifths, twentieths, sevenths and elevenths are detailed as percents, decimals, and fractions. Learn these, please. 
Place Value
Title DescriptionPlace Value Chart with Decimals  The names of Place Values are detailed in a basic graphic from MathAids.com.  
Place Value Chart with Integers  The names of Place Values for an integer (a Whole Mumber, or Counting Number) are detailed in a graphic from MathAids.com.  
Counting 61 though 100  We continue counting, reading number names, through one hundred.  
Counting 31 though 60  We continue counting through sixty.  
Learning Numbers 1 through 10  Counting and recognizing digits comes early with practice. We first discuss numbers 1 through 10. 

Reading Numbers 1  100  You should be able to read numbers from 1 to 100. The numbers in this set are considered Counting Numbers. 

Learning Numbers 11 through 30  Counting and recognizing digits comes early with practice. In this video we learn numbers 11  30. 

Addition in Expanded Form  This lesson in addition also gives examples of expanding integers to expanded form. 

A Lesson in Expanded Notation  Expanding numbers means taking positive numbers and expressing them as sums of single digits times powers of ten. This lesson shows how to express numbers in expanded notation, and how to find the number for a given expanded notation. 

Matching Decimal Number Names  The worksheet is selfexplanatory. The audio portion is Mr. X on his soapbox. 
Probability
Title DescriptionProbability Handout: Complements  All probabilities are between zero and one. Every probability has a complement, the difference between itself and 100 percent. 

Probability Handout: Independent and Dependent Events  Three colors of socks reside in a drawer. You dress in the dark. What is the probability of drawing out two matching socks? This video discusses when to multiply and when to add to determine probability. 

Probability on Numbers  We reach into our bag of tricks to understand very basic probabilities. 

Probability Using a Single Die  This die has nothing to do with morbidity. This die is a cube, a regular solid with six square faces. Probabilities for a single die have denominators of six. 

Probability Using a Pair of Dice  Dice can be nice, but do not gamble with your future. Learn basic probabilities. Please. Thank you. 

Probability Using a Deck of Cards  Do not gamble; learn the language of probabilities and statistics.  
Probability Using a Spinner  Spinners are very much like pie charts. Probabilities are as easy as pie. 
Properties
Title DescriptionDivision and Subtraction Defined  Differences and quotients are explained with our most basic operations. We may define both subtraction and division as addition and multiplication, respectively. 

Ignorance of the Law is No Excuse  The Commutative Law and the Distributive Law are discussed.  
Inverses, Additive and Reciprocal  We discuss the additive inverse of addition as well as reciprocals in multiplication. These properties are very important to understand, especially as you start a course in Basic Algebra. 

Properties of Math  
Rearrange the Furniture  Using the Commutative Laws  The terms of a sum may be arranged in any order. The terms of a product may be arranged in any order. 

Sum Groups are Worth Joining  Grouping terms according to the Associative Law is exceptionally easy to see.  
Two Laws of Arithmetic  A discussion of the Commutative Laws and the Associative Laws for addition and multiplication. 
Pythagorean
Title DescriptionThe Classic Ladder Before and After Moving the Base  Alternate Approach  In this solution to the Ladder Before and After problem, we use a Pythagorean relation instead of a trig function to derive the answer.  
Pythagorean Relations with Irrational Lengths  We solve right triangles with various lengths of the sides. The Pythagorean relation holds, where the sum of the squares of the legs (the perpendicular sides) is equal to the square of the hypotenuse (the square of the longest side). 

Pythagorean Triples  Basic right triangles are solved with integer values for the lengths of the sides. We call these Pythagorean Triples. No irrational numbers are required. 

Distance Formula as Pythagorean Relation  A basic lesson in the Distance Formula and its close cousin, the Pythagorean Relation.  
The Distance Formula and the Pythagorean Theorem  We find the distance between two points in rectangular (or Cartesian) coordinates. We also look at the familiar Pythagorean Theorem for the relationship between sides of a right triangle. 

The Pythagorean Theorem  The Pythagorean Theorem is a pretty important thing. At some point, you should learn it. 
Radicals
Title DescriptionRatios
Title DescriptionA Lesson in Equivalent Ratios  Moving Tomatos  "Moving Tomatos" is a nice skill to develop. You say "tomatoes," and I say "tomattoes." Let's call the whole thing math. 

A Lesson in Rates and Unit Rates  Rates and Unit Rates are very straightforward, very easy, and very important.  
Growing with a Little Algebra  Algebra helps us calculate rates with different units. Ratios and rates make perfect sense with a little Algebra. 
Rounding
Title DescriptionDividing and Rounding Large Numbers  The problems in this lessons require the skills of long division and rounding.  
Rounding Integers  A lesson in rounding integers. Examples in rounding to the nearest Ten and the nearest Hundred are included in this lesson. 
Significant Figures
Title DescriptionA Lesson with the Significant Figure Rules Handout  Only zeroes are confused when speaking of Significant Figures, and only when they are not situated between nonzero digits. Trailing zeroes at the rightend of a published or written decimal value are significant figures. 

A Lesson in Significant Figures  We look at a football player whose weight of 300 pounds could be regarded with one Significant Digit, or three Significant Digits. 
Skip Counting
Title DescriptionCounting 31 though 60  We continue counting through sixty.  
Counting 61 though 100  We continue counting, reading number names, through one hundred.  
Skip Counting by 7's and 12's  Using the times table is a good way to practice skip counting. In this video we skip count by 7's and 12's. 

Learning Numbers 1 through 10  Counting and recognizing digits comes early with practice. We first discuss numbers 1 through 10. 

Reading Numbers 1  100  You should be able to read numbers from 1 to 100. The numbers in this set are considered Counting Numbers. 

Skip Counting by 3's and 8's  Using the times table is a good way to practice skip counting. In this video we skip count by 3's and 8's. 

Learning Numbers 11 through 30  Counting and recognizing digits comes early with practice. In this video we learn numbers 11  30. 

Patterns in Advanced Skip Counting  There is a very wide variety of difficulty levels to be practiced with the MathAids.com Advanced Skip Counting worksheets.  
How to Solve Skip Counting Problems  This lesson uses the attached worksheet to give examples on how to find the rule for the skip counting, and solve the problems. We use positive and integer values up to 999 in these advanced skip counting problems. 
Subtraction
Title DescriptionThe Subtraction Table  You need to know these facts. They are basic facts of subtraction and they are essential to understanding what comes later. Learn these facts. 

Subtraction of 9  We practice subtracting by 9. Students should be able to memorize these facts. 

Subtraction of 8  We practice subtracting by 8. Students should be able to memorize these facts. 

Subtraction of 7  We practice subtracting by 7. Students should be able to memorize these facts. 

Subtraction of 6  We practice subtracting by 6. Students should be able to memorize these facts. 

Subtraction of 5  We practice subtracting by 5. Students should be able to memorize these facts. 

Subtraction of 4  We practice subtracting by 4. Students should be able to memorize these facts. 

Subtraction of 3  Learn the facts of subtracting by 3.  
Subtraction of 2  Learn the facts of subtracting by 2.  
Subtraction of 1  Learn the facts of subtracting by 1.  
Subtraction of 10  We practice subtracting by 10. Students should be able to memorize these facts. 

A Lesson on Subtraction  We hope you can answer all of these questions. Your previous practice of arithmetic should make this lesson exceptionally easy and straightforward. Subtraction provides the difference between two values. 

Introduction to Subtraction  The words "leaves" and "less" and "left" are key to learning the basic concept of subtraction.  
Making the Transition from Addition to Subtraction  Subtracting a positive value is equivalent to adding the negative of that value. This concept is easy to understand with the visualization on the real number line. 

Review Subtraction Zero to Twenty  You need to recall quickly and easily the basic facts of subtraction. Review and memorize the subtraction tables if you can't answer these problems quickly. 

Subtracting within a Number Problem Set  Part Lesson, part Problem Set, this video encourages your memory. Sometimes we simply learn facts. Period. While it is good to see "why" these facts are true, they're still facts. So learn them. 

A Lesson in Japanese Money  The Yen  A brief discussion of the Yen, the unit of both coinage and currency in Japan.  
A Lesson in British Currency  We briefly discuss British paper money, or currency.  
A Lesson in British Coins  We learn a few facts about coinage in Great Britain.  
A Lesson in Adding English Measurements  This lesson adds English units of length to the nearest sixteenth of an inch. 
Time
Title DescriptionCreating Blank Clock Faces Worksheet Example  Not so much a lesson as a description of clock graphics available at MathAids.com.  
Telling Time on Analog Clocks  Five Minute Increments  We tell the time on an analog clock in fiveminute increments. Then we follow a Minute Hand clockwise in a very fast fashion. 

Talking about Elapsed Days, Weeks, Months and Years  A lesson in Ambiguity. Sometimes one language is not precise when translated into another language.  
A Lesson in Elapsed Time  This lesson will be effective only if you already know how to tell time on a traditional clock. Learn to tell time. Then you may calculate Elapsed Times. 

Making a Calendar  You can make a calendar at MathAids.com. 
Venn Diagrams
Title DescriptionDeMorgan's Theorem, a Lesson  DeMorgan's Theorem applies to Venn Diagrams as well as it applies to Digital Logic Gates, as in our computers.  
Finite vs Infinite  Appreciate infinity and the infinitesimal as you delve in Geometry. "Uncountable" and "infinite" will be different ideas for us in Geometry. 

Set Theory Symbols and Definitions  A brief overview of the Set Theory handout includes a mnemonic device for remembering that OR goes with UNION. UNION means "or." INTERSECTION means "and." 

Venn Diagram Basics for Two Sets  A brief look at Venn Diagram basics.  
Venn Diagram Basics for Three Sets  A description of a Venn Diagram with three sets. 
Word Problems
Title DescriptionAddition of One or Two Digit  Two Addends  Practicing with Addition. Repetitive practice is an important element to learning these basics. The student's goal should be to answer these problems with very little effort. 

Growing with a Little Algebra  Algebra helps us calculate rates with different units. Ratios and rates make perfect sense with a little Algebra. 