Arithmetic_lessons

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.

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Arithmetic Sample Lesson 1

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Arithmetic Sample Lesson 2

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Arithmetic Sample Lesson 3

Arithmetic Curriculum

Addition

Title Description
Addition Makes Counting Easier How many birds are two birds and five birds? We sum objects with the conjunction "and." Play_video
Addition by 8 This video lesson, appropriate for children starting to learn addition, goes over adding by 8 Play_video
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.
Play_video
Addition by 4 This video lesson, appropriate for children starting to learn addition, goes over adding by 4.
Play_video
Addition by 9 This video lesson, appropriate for children starting to learn addition, goes over adding by 9.
Play_video
Adding by 11 and 12 We use an addition table to review addition of 11 and 12. Play_video
Addition Tables You need to know all of these facts for simple addition.
Learn these tables, they are very important!
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Addition by 7 This video lesson, appropriate for children starting to learn addition, goes over adding by 7.
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Addition by 6 This video lesson, appropriate for children starting to learn addition, goes over adding by 6.
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Addition by 5 This video lesson, appropriate for children starting to learn addition, goes over adding by 5.
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Addition by 10 This video lesson, appropriate for children starting to learn addition, goes over adding by 10.
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Addition by 2 This video lesson, appropriate for children starting to learn addition, goes over adding by 2.
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Addition by 3 This video lesson, appropriate for children starting to learn addition, goes over adding by 3.
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Review of Simple Addition We read word problems to reinforce the basic facts of addition for small positive integers. Play_video
Adding Whole Numbers up to 20 Before adding larger sums, it's good to have substantial practice with small-value integers. Play_video
Adding Whole Numbers up to 99 Before adding larger sums, it's good to have substantial practice with small-value integers. Play_video
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.
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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.
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A Lesson in Japanese Money - The Yen A brief discussion of the Yen, the unit of both coinage and currency in Japan. Play_video
A Lesson in British Currency We briefly discuss British paper money, or currency. Play_video
A Lesson in British Coins We learn a few facts about coinage in Great Britain. Play_video
Adding with US Pennies At the 3 minute mark we visually use US Coins to practice addition. Play_video
Adding United States coins To add the value of coinage we simply learn the denominations of coins used in the U.S. Play_video
38 Cents in US Coins How many ways can we get 38 cents using pennies, nickles, dimes and/or a quarter? Play_video
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.
Play_video
A Lesson in Adding English Measurements This lesson adds English units of length to the nearest sixteenth of an inch. Play_video

Decimals

Title Description
Long Division with Three-Digit Divisors Three digits in the divisor means long, long division. Play_video
Comparing Decimals Lesson 1 We read math statements left-to-right.
For this worksheet we need the Correct Comparison Symbol: >, = or <.
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Comparing Decimals Lesson 2 Real Values on the Real Number Line can be compared then expressed with greater-than, less-than, or equal-to symbols. Play_video
Decimals on the Real Number Line Decimals, or decimal values, are to be placed at their proper location on the Real Number Line. Play_video
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.
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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.
Play_video

Division

Title Description
A 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. Play_video
Factors of 1368 with Divisibility Rules We divide 1368 into factors as we discuss divisibility rules. Play_video
Divisibility of 360 The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility. Play_video
Division with 7 We practice the facts of division with sevens by practicing the facts of multiplication that have a factor of seven. Play_video
Division with 8 We practice the facts of division with eights by practicing the facts of multiplication that have a factor of eight. Play_video
A Lesson for the Division Facts Table We master the facts of division by mastering the facts from the Multiplication Table. Play_video
Division with 9 We practice the facts of division with nines by practicing the facts of multiplication that have a factor of nine. Play_video
Division Table Knowing the multiplication facts makes division easy. Play_video
Division with 10 Because we use a base-ten 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.
Play_video
Division with 2 When we divide by 2, we divide the number in half. Play_video
Division with 6 We practice the facts of division with sixes by practicing the facts of multiplication that have a factor of six. Play_video
Division with 4 We practice the facts of division with fours by practicing the facts of multiplication that have a factor of four. Play_video
Division with 5 We practice the facts of division with fives by practicing the facts of multiplication that have a factor of five. Play_video
Division with 3 We practice the facts of division with threes by practicing the facts of multiplication that have a factor of three. Play_video
An Introduction to Division We learn that division is actually a form of multiplication.
So we focus on multiplication to learn division.
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Dividing and Rounding Large Numbers The problems in this lessons require the skills of long division and rounding. Play_video
Long Division with Three-Digit Divisors Three digits in the divisor means long, long division. Play_video
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. Play_video
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.
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Division in Three Different Formats We can write a statement of division horizontally, or as traditional long division, or as a fraction. Play_video

Estimation

Title Description

Exponents & Radicals

Title Description
An Overview of Rules for Exponents We take a look at the Math-Aids handout for rules of exponents. Play_video
An Introduction to Negative Exponents An introduction to negative exponents.
We reference reciprocals without detail about them.
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More Work with Negative Exponents More explanations of working with negative exponents.
Both our bases and exponents employ negative integers.
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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.
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Introducing Fractional Exponents We introduce the equivalence of fractional exponents as roots: square roots, cube roots, and fourth roots. Play_video
Introducing Fraction Exponents We introduce the equivalence of fractional exponents as roots: square roots, cube roots, and fourth roots. Play_video
Multiplying with Exponents An introductory lesson for multiplication of terms with exponents. Play_video
A Lesson in Evaluating Exponential Functions We examine the nature of functions before we jump into the evaluation of Exponential Functions. Play_video
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.
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Simplifying Square Roots A few words about the simplifcation of radicals and square roots.
Sometimes simpler is not so simple.
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Square Roots and Absolute Values A review of square roots and absolute values.
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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.
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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.
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A Lesson in Simplifying Radicals Preaching the need to learn the Facts of Multiplication.
Learn the facts of the Times Table.
Please.
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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.
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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.
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Dividing Radical Expressions (Level: Medium) Level: Medium.
Simplify fractions by cancelling factors top and bottom.
Make sure to rationalize the denominator.
Play_video
Dividing Radical Expressions (Level: Hard) Level: Medium.
Simplify fractions by cancelling factors top and bottom.
Make sure to rationalize the denominator.
Play_video
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 top-and-bottom.
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Scientific Notation with Negative Exponents 2 This lesson in Scientific Notation uses only Negative Powers of Ten. Play_video
Scientific Notation with Positive Exponents 2 This lesson in Scientific Notation uses only Positive Powers of Ten. Play_video
Scientific Notation with Positive and Negative Powers A lesson in Scientific Notation discusses the difference between Positive Exponents and Negative Exponents. Play_video
Scientific Notation, Positive and Negative Exponents A lesson in Scientific Notation discusses the difference between Positive Exponents and Negative Exponents. Play_video
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. Play_video
Scientific Notation with both Positive and Negative Exponents We raise values expressed in Scientific Notation to both Positive Exponents and Negative Exponents. Play_video
Scientific Notation and Operations Mr. X does the HARD Long Division and the student gets the EASY Long Division. Play_video
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.
Play_video

Fact Family

Title Description
An Overview of Fact Families We tout the importance of Fact Families with two games: Sum-or-Product, and Sum-and-Product. Play_video
Multiplication Fact Family Lessson A quick lesson for the six ways to order the three integers from a Multiplication Fact Family. Play_video

Factors

Title Description
Prime Factor Trees A basic lesson in Prime Factorization with Factor Trees. Play_video
Divisibility of 360 The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility. Play_video
GCF, Greatest Common Factor A lesson in finding the Greatest Common Factor, or GCF, for two given integers. Play_video
Greatest Common Factor Lesson Twenty problems for GCF.
Mr. X knocks out the first ten in high-speed fashion.
Play_video
LCM - Least Common Multiple We discuss the methods to determine the Least Common Multiple for a pair of given Integers. Play_video
Least Common Multiple Methods Explanations of LCM with the list method and the Prime Factorization method. Play_video
Least Common Multiples More explanations of LCM with the list method and the Prime Factorization method. Play_video
A Lesson in Prime Factorization A brief lesson in Prime Factorization of Integers less than nine-squared. Play_video
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.
Play_video

Flash Cards

Title Description
Addition Makes Counting Easier How many birds are two birds and five birds? We sum objects with the conjunction "and." Play_video
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.
Play_video
Addition by 9 This video lesson, appropriate for children starting to learn addition, goes over adding by 9.
Play_video
Addition by 8 This video lesson, appropriate for children starting to learn addition, goes over adding by 8 Play_video
Addition by 7 This video lesson, appropriate for children starting to learn addition, goes over adding by 7.
Play_video
Addition by 6 This video lesson, appropriate for children starting to learn addition, goes over adding by 6.
Play_video
Adding by 11 and 12 We use an addition table to review addition of 11 and 12. Play_video
Addition by 5 This video lesson, appropriate for children starting to learn addition, goes over adding by 5.
Play_video
Addition by 10 This video lesson, appropriate for children starting to learn addition, goes over adding by 10.
Play_video
Addition by 2 This video lesson, appropriate for children starting to learn addition, goes over adding by 2.
Play_video
Addition by 3 This video lesson, appropriate for children starting to learn addition, goes over adding by 3.
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Addition by 4 This video lesson, appropriate for children starting to learn addition, goes over adding by 4.
Play_video
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.
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Subtraction of 5 We practice subtracting by 5.
Students should be able to memorize these facts.
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Subtraction of 6 We practice subtracting by 6.
Students should be able to memorize these facts.
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Subtraction of 7 We practice subtracting by 7.
Students should be able to memorize these facts.
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Subtraction of 8 We practice subtracting by 8.
Students should be able to memorize these facts.
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Subtraction of 4 We practice subtracting by 4.
Students should be able to memorize these facts.
Play_video
Subtraction of 9 We practice subtracting by 9.
Students should be able to memorize these facts.
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Subtraction of 3 Learn the facts of subtracting by 3. Play_video
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.
Play_video
Subtraction of 2 Learn the facts of subtracting by 2. Play_video
Subtraction of 10 We practice subtracting by 10.
Students should be able to memorize these facts.
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Subtraction of 1 Learn the facts of subtracting by 1. Play_video
Multiplying by 9 We review the multiplication table for 9.
We also work some sample problems.
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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.
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Multiplying by 7 We review the multiplication table for 7.
We also work some sample problems.
Play_video
Multiplying by 6 We review the multiplication table for 6.
We also work some sample problems.
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Multiplying by 5 When we multiply by 5, we quintuple the number. Play_video
Multiplying by 1 When we multiply by one, we employ the multiplicative identity. Play_video
Multiplication by 4 When we multiply by 4, we quadruple the number. Play_video
Multiplication by 3 When we multiply by 3, we triple the number. Play_video
Multiplication by 2 When we multiply by 2, we double the number. Play_video
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.
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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.
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Multiplying by 8 We review the multiplication table for 8.
We also work some sample problems.
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Division with 4 We practice the facts of division with fours by practicing the facts of multiplication that have a factor of four. Play_video
Division with 10 Because we use a base-ten 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.
Play_video
Division with 9 We practice the facts of division with nines by practicing the facts of multiplication that have a factor of nine. Play_video
Division with 8 We practice the facts of division with eights by practicing the facts of multiplication that have a factor of eight. Play_video
Division with 7 We practice the facts of division with sevens by practicing the facts of multiplication that have a factor of seven. Play_video
Division Table Knowing the multiplication facts makes division easy. Play_video
Division with 2 When we divide by 2, we divide the number in half. Play_video
Division with 5 We practice the facts of division with fives by practicing the facts of multiplication that have a factor of five. Play_video
A Lesson for the Division Facts Table We master the facts of division by mastering the facts from the Multiplication Table. Play_video
Division with 3 We practice the facts of division with threes by practicing the facts of multiplication that have a factor of three. Play_video
Division with 6 We practice the facts of division with sixes by practicing the facts of multiplication that have a factor of six. Play_video
Telling Time on Analog Clocks - Five Minute Increments We tell the time on an analog clock in five-minute increments.
Then we follow a Minute Hand clockwise in a very fast fashion.
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38 Cents in US Coins How many ways can we get 38 cents using pennies, nickles, dimes and/or a quarter? Play_video
Adding United States coins To add the value of coinage we simply learn the denominations of coins used in the U.S. Play_video
A Lesson in Roman Numerals A very brief lesson in Roman Numerals with a converter from NovaRoma.org. Play_video
An Overview of Fact Families We tout the importance of Fact Families with two games: Sum-or-Product, and Sum-and-Product. Play_video
Multiplication Fact Family Lessson A quick lesson for the six ways to order the three integers from a Multiplication Fact Family. Play_video
Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.
The numbers in this set are considered Counting Numbers.
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Counting 61 though 100 We continue counting, reading number names, through one hundred. Play_video
Counting 31 though 60 We continue counting through sixty. Play_video
Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.
We first discuss numbers 1 through 10.
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Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.
In this video we learn numbers 11 - 30.
Play_video
Numbers to be Written Learn your digits, how to read them, how to write them, how to recognize them.
We focus on two-digit numbers in this lesson.
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A Lesson in Japanese Money - The Yen A brief discussion of the Yen, the unit of both coinage and currency in Japan. Play_video
A Lesson in British Currency We briefly discuss British paper money, or currency. Play_video
A Lesson in British Coins We learn a few facts about coinage in Great Britain. Play_video

Fractions

Title Description
Fractions 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.
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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.
Play_video
Basic Fractions in a Bar A lesson in dividing a Bar into Twelfths. Play_video
Fractions within Shaded Triangles Basic fractions from shaded triangles within polygons. Play_video
Fractions within Shaded Bars Basic fractions with shaded boxes.
Don't just count.
Think.
Play_video
Reading and Writing Fractions Fractions need to be understood in several different ways.
In this lesson we read and write fractions, including mixed fractions.
Play_video
Visually Adding Simple Fractions We visually add simple fractions with the same (common) denominator. Play_video
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%.
Play_video
Adding Simple Fractions, a Lesson A simple lesson in addition of simple fractions, with like denominators. Play_video
Adding Two Fractions, a Lesson A lesson in the basics of adding fractions with different denominators. Play_video
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.
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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. Play_video
Visual Subtraction Lesson Subtract simple fractions with a visual approach to understanding. Play_video
Subtracting Simple Fractions A simple lesson in subtraction of simple fractions, with like denominators. Play_video
Subtract Fractions from Whole Numbers We subtract fractions from Whole Numbers by understanding the language, not by following a recipe or algorithm. Play_video
Subtracting Mixed Numbers Subtracting Mixed Numbers involves a thorough knowledge of the facts of multiplication. Play_video
Multiply Fractions, a Lesson When we multiply fractions keep numerator factors on top, and keep denominator factors on the bottom. Play_video
Multiply Fractions, Cancel Factors We reinforce the cancellation of factors top-and-bottom as we multiply fractions. Play_video
Multiplying Mixed Fractions In this lesson we practice multipling fractions with mixed numbers.
We also use cross cancelling where appropriate.
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Multiplying with Cross-Cancelling, a Lesson Cross-canceling is a technique to reduce fractions as we multiply. Play_video
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 second-nature to you.
Play_video
Multiply Mixed Numbers There are several techniques to multiply Mixed Numbers.
Heavy fractions often lighten the load.
Play_video
Introducing Reciprocals Reciprocals are handy for dividing fractions.
This lesson introduces the concept of Reciprocals.
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Don't Divide. Multiply. To Divide. Keep the first fraction.
Change the operation to Multiplication.
Invert the second fraction.
Play_video
A Lesson in Division and Reciprocals Real-world examples for using reciprocals to help us understand division are provided in this lesson. Play_video
A Lesson in Dividing Mixed Numbers To divide Mixed Numbers, change them to Heavy Fractions, invert and multiply. Play_video
Divisibility of 360 The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility. Play_video
A Lesson in Prime Factorization Prime factorization means to find the factors (or divisors) of an integer that are themselves prime numbers.
Play_video
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.
Play_video
Prime Factor Trees A basic lesson in Prime Factorization with Factor Trees. Play_video
Greatest Common Factor Lesson Twenty problems for GCF.
Mr. X knocks out the first ten in high-speed fashion.
Play_video
GCF, Greatest Common Factor A lesson in finding the Greatest Common Factor, or GCF, for two given integers. Play_video
Least Common Multiples More explanations of LCM with the list method and the Prime Factorization method. Play_video
Least Common Multiple Methods Explanations of LCM with the list method and the Prime Factorization method. Play_video
LCM - Least Common Multiple We discuss the methods to determine the Least Common Multiple for a pair of given Integers. Play_video
Converting to Equivalent Fractions A lesson in converting fractions to an equivalent fraction, just with a different denominator. Play_video
Moving Tomatoes A fast-moving lesson in Moving Tomatoes. Play_video
Reducing Fractions Problem Set 1 Reduction of simple fractions is an essential skill.
The reduced fractions will have denominators ranging from 2 to 10.
Play_video
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.
Play_video
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.
Play_video
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.
Play_video
Reinforcing our work with 8ths It is important to know eighths.
There is no substitute for practice with fractions, decimals, and percents.
Play_video
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. Play_video
Converting 9ths to Decimals and Percentages You should know your ninths, which are exceptionally easy to convert to decimals or percents.
Play_video
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.
Play_video
Converting 12ths to Decimals and Percentages You should learn your twelfths.
This little lesson reinforces basic twelfths in terms of both decimals and percentages.
Play_video
Practice with 12ths Look for patterns in basic fractions.
Converting twelfths to decimals or percents is actually pretty easy once you catch onto them.
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Converting 20ths to Decimals and Percentages If you can count by fives, you can quickly understand decimal and percent equivalence for 20ths. Play_video
Comparing Fractions, Absolute Value Greater values reside to the right on the Real Number Line.
We also introduce the notion of Absolute Value.
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Comparing Fractions Left and Right The relative position (left or right) of two real values on the Real Number Line determines less-than or greater-than. Play_video
Comparing Fractions, a Lesson Several methods are presented for the comparison of fractions, using " < , > , or = ." Play_video
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. Play_video
Comparing Fractions and Decimals Fractions on the left, decimals on the right, and a comparison symbol in between the two values, and we read left-to-right. Play_video
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.
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The Master PDF Chart, Lesson Two Sixths, fifths, twentieths, sevenths and elevenths are detailed as percents, decimals, and fractions.
Learn these, please.
Play_video
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!
Play_video
Introducing Fraction Exponents We introduce the equivalence of fractional exponents as roots: square roots, cube roots, and fourth roots. Play_video
A Lesson in Adding English Measurements This lesson adds English units of length to the nearest sixteenth of an inch. Play_video
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.
Play_video
A Lesson in Multiplying Fractions with Whole Numbers Some very basic calculations merit practice and fundamental understanding. Play_video
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 second-nature to you.
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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 second-nature to you.
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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 second-nature to you.
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Function Table

Title Description
Compute the Output of Functions To complete each Function Table we calculate y as a function of x.
Indeed, y = f(x).
Play_video
Computing Outputs of Functions Complete the Function Table with very simple arithmetic.
Each function is linear.
Play_video

General Topics

Title Description
25! A close look at the product of the first 25 positive integers, or 25! It's a banquet of numbers! Play_video
An Additional Look at Addition Just a few thoughts about the very nature of addition. Play_video
An Interesting Relationship It turns out that x² = (x-1)(x+1) + 1.
We look at this algebraic relationship with the standard multiplication table.
If you prefer, equivalently, x² - 1 = (x-1)(x+1).
Play_video
Coins 38 cents How many different ways using U.S.
coins can one have exactly 38 cents?
Play_video
Master Percent-Decimal-Fraction Chart 1 Let's take a look at the "official" Mr. X PDF chart. Play_video
Master Percent-Decimal-Fraction Chart 2 You have to learn a few fractions in this life.
Just a few.
Learn them.
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Master Percent-Decimal-Fraction Chart 3 We all know that 50 percent is the same as one-half.
Learn just a few more fractions.
You'll be glad you did!
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Master Percent-Decimal-Fraction Chart 4 Here is a nice, long look at the "official" Mr. X master PDF Chart. Play_video
New Primary 001 - Numbers and Figures Counting and recognizing digits comes early. Play_video
New Primary 002 - Counting 11 though 30 We continue counting through thirty. Play_video
New Primary 003 - Counting 31 though 60 We continue counting through sixty. Play_video
New Primary 004 - Counting 61 though 100 We continue counting, reading number names, through one hundred. Play_video
New Primary 005 - Numbers to be Read You should be able to read any of the numbers in this lesson. Play_video
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 two-digit numbers in this lesson.
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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.
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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.
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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.
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New Primary 010 - Addition How many birds are two birds and five birds? We sum objects with the conjunction "and." Play_video
New Primary 011 - Addition of One We practice the facts of addition that include adding a single unit to another (integer) value. Play_video
New Primary 012 - Addition of Two We practice sums that add two to a value. Play_video
New Primary 013 - Addition of Three We practice sums that include addition of three to a value. Play_video
New Primary 014 - Addition of Four Addition with four.
This lesson practices adding 4.
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New Primary 015 - Addition of Five We practice addition facts with addends of fives. Play_video
New Primary 016 - Addition of Six Addition of six is practiced with a list of facts. Play_video
New Primary 017 - Addition of Seven We practice the facts of basic addition with sevens. Play_video
New Primary 018 - Addition of Eight We practice the facts of adding eight to other one-digit integers. Play_video
New Primary 019 - Addition of Nine Addition of nine includes facts to be learned, to be able to be recalled without effort. Play_video
New Primary 020 - Addition of Ten In our Base-Ten system, addition of ten is especially convenient. Play_video
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.
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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.
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New Primary 023 - Reading Review of Simple Addition We read word problems to reinforce the basic facts of addition for small positive integers. Play_video
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.
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New Primary 025 - Subtraction of One We practice the facts of subtraction with a subtrahend or difference of one. Play_video
New Primary 026 - Subtraction of Two We practice the facts of subtraction with a subtrahend or difference of two. Play_video
New Primary 027 - Subtraction of Three We practice the facts of subtraction with a subtrahend or difference of three. Play_video
New Primary 028 - Subtraction of Four We practice the facts of subtraction with a subtrahend or difference of four. Play_video
New Primary 029 - Subtraction of Five We practice the facts of subtraction with a subtrahend or difference of five. Play_video
New Primary 030 - Subtraction of Six We practice the facts of subtraction with a subtrahend or difference of six. Play_video
New Primary 031 - Subtraction of Seven We practice the facts of subtraction with a subtrahend or difference of seven. Play_video
New Primary 032 - Subtraction of Eight We practice the facts of subtraction with a subtrahend or difference of eight. Play_video
New Primary 033 - Subtraction of Nine We practice the facts of subtraction with a subtrahend or difference of nine. Play_video
New Primary 034 - Subtraction of Ten We practice the facts of subtraction with a subtrahend or difference of ten. Play_video
New Primary 035 - Review Subtraction You need to recall quickly and easily the basic facts of subtraction. Play_video
New Primary 036 - Review Addition and Subtraction Singular or plural state-of-being 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."
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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.
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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 state-of-being verbs do not matter in equating the factors to the product.
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New Primary 039 - Multiplicative Identity When we multiply by one, we employ the multiplicative identity. Play_video
New Primary 040 - Multiplication Doubling Multiplication by two effectively doubles the first (or other) factor or factors. Play_video
New Primary 041 - Multiplication Tripling When we triple a number we multiply that number by three. Play_video
New Primary 042 - Multiplication by Four We practice the basic products that include a factor of four. Play_video
New Primary 043 - Multiplication by Five We practice the basic facts of multiplication with a factor of five. Play_video
New Primary 044 - Multiplication by Six We practice the basic facts of multiplication with a factor of six. Play_video
New Primary 045 - Multiplication by Seven We practice the basic facts of multiplication with a factor of seven. Play_video
New Primary 046 - Multiplication by Eight We practice the basic facts of multiplication with a factor of eight. Play_video
New Primary 047 - Multiplication by Nine We practice the basic facts of multiplication with a factor of nine. Play_video
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.
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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.
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New Primary 050 - Multiplication Around Subtraction We deal with more complicated forms of math statements in English.
We read left-to-right.
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New Primary 051 - Promiscuous Questions Diverse, casual, and random questions related to addition, subtraction, and multiplication. Play_video
New Primary 052 - Division We learn that division is actually a form of multiplication.
So we focus on multiplication to learn division.
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New Primary 053 - Division with Two When we divide by two we take half.
Two divides evenly into even numbers.
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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. Play_video
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. Play_video
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. Play_video
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. Play_video
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. Play_video
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. Play_video
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. Play_video
New Primary 061 - Division with Ten Because we use a base-ten 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.
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New Primary 062 - Cognitive Division If you learn your times tables you can answer these questions quickly and easily. Play_video
New Primary 063 - Review Situational Division Simple and straightforward word problems give us a glimpse into the nature of both division and multiplication. Play_video
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.
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New Primary 065 - Addition with Operators The familiar facts of addition are now presented with the plus-sign operator for taking sums. Play_video
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.
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New Primary 067 - Simple Additional Situations Word problems allow us to practice basic addition with the powerful symbolism of the language of mathematics. Play_video
New Primary 068 - Practice with Situational Operations Basic statements in mathematics derive from simple situations. Play_video
New Primary 069 - Statements with Addition and Subtraction Read math statements left-to-right, 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.
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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.
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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. Play_video
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. Play_video
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.
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New Primary 072C - Counting with Different Values With the assistance of the multiplication table, we count by various small integers. Play_video
New Primary 072D - Counting with Different Values With the multiplication table, we count by different values. Play_video
New Primary 072E - Uncover Ten Covers Ten little black "manhole covers" are revealed atop the multiplication table. Play_video
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. Play_video
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.
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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.
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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.
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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.
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Percent-Decimal-Fraction 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.
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Percent-Decimal-Fraction Lesson in 12ths You should learn your twelfths.
This little lesson reinforces basic twelfths in terms of both decimals and percentages.
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Percent-Decimal-Fraction Lesson in 20ths If you can count by fives, you can quickly understand decimal and percent equivalence for 20ths. Play_video
Percent-Decimal-Fraction Lesson in 8ths Instead of using a calculator every time you encounter a multiple of one eighth, just remember a few facts about them. Play_video
Percent-Decimal-Fraction Lesson in 9ths You should know your ninths, which are exceptionally easy to convert to decimals or percents.
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Percent-Decimal-Fraction Lesson in eighths It is important to know eighths.
There is no substitute for practice with fractions, decimals, and percents.
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Percent-Decimal-Fraction 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.
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Percent-Decimal-Fraction Lesson in twelfths Look for patterns in basic fractions.
Converting twelfths to decimals or percents is actually pretty easy once you catch onto them.
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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.
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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.
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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.
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Ray's Intellectual Arithmetic 001 - Cognitive Addition An initial review of counting and simple addition from Ray's New Intellectual Arithmetic ,from 1877. Play_video
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.
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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.
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Ray's Intellectual Arithmetic 004 - Addition of Pairs of One- and Two-Digit Integers These questions should be automatic.
You need to be able to answer all of the questions in this lesson quickly and effortlessly.
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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.
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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.
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Ray's Intellectual Arithmetic 008 - Cognitive Subtraction Simple word problems provide a glimpse into the meaning of subtraction as a difference between two values. Play_video
Ray's Intellectual Arithmetic 009 - Review Word problems provide a fundamental understanding to the meaning of subtraction and taking the difference between two values. Play_video
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.
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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.
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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.
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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.
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Ray's Intellectual Arithmetic 014 - Cognitive Multiplication Simple word problems reinforce the basic facts of multiplication. Play_video
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.
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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."
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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.
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Ray's Intellectual Arithmetic 018 - Practice in Division You have to know how many times a smaller number is contained in a larger number. Play_video
Ray's Intellectual Arithmetic 019 - Operative Arithmetic Practice From word problems we practice the basic facts of multiplication, addition, subtraction, and division. Play_video
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). Play_video
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.
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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 second-nature to you.
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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 second-nature to you.
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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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
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 second-nature to you.
Play_video
Rounding Integers Lesson 17 A lesson in rounding, accompanied by a Problem Set.
This basic skill of rounding is important for almost everyone.
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Graph Paper

Title Description
Practice with Cartesian Coordinates Practice (x, y) coordinate location until it is second-nature to you. Play_video
Polar Graph Paper, an Overview An overview of Polar Graph Paper.
We plot a single point as (r, Θ) as well as (x, y).
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Opposite Directions Get comfortable moving in opposite directions before tackling negative values. Play_video
Graph Paper: An Overview The general format for Cornell Notes is detailed in a specialized Mr. X video. Play_video
Cornell Notes, a brief lesson An overview of Cornell Notes, a template for taking quality notes in class. Play_video

Graphing

Title Description
Practice with Cartesian Coordinates Practice (x, y) coordinate location until it is second-nature to you. Play_video

Greater Than Less Than

Title Description
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.
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Comparing Fractions, Absolute Value Greater values reside to the right on the Real Number Line.
We also introduce the notion of Absolute Value.
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Comparing Fractions, a Lesson Several methods are presented for the comparison of fractions, using " < , > , or = ." Play_video
Comparing Fractions Left and Right The relative position (left or right) of two real values on the Real Number Line determines less-than or greater-than. Play_video
Comparing Decimals Lesson 1 We read math statements left-to-right.
For this worksheet we need the Correct Comparison Symbol: >, = or <.
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Comparing Decimals Lesson 2 Real Values on the Real Number Line can be compared then expressed with greater-than, less-than, or equal-to symbols. Play_video
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.
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Comparing Fractions and Decimals Fractions on the left, decimals on the right, and a comparison symbol in between the two values, and we read left-to-right. Play_video
The Master PDF Chart, Lesson Two Sixths, fifths, twentieths, sevenths and elevenths are detailed as percents, decimals, and fractions.
Learn these, please.
Play_video

Hundreds Chart

Title Description
Counting 31 though 60 We continue counting through sixty. Play_video
Counting 61 though 100 We continue counting, reading number names, through one hundred. Play_video
Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.
We first discuss numbers 1 through 10.
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Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.
In this video we learn numbers 11 - 30.
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Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.
The numbers in this set are considered Counting Numbers.
Play_video

In and Out Boxes

Title Description

Integers

Title Description
Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.
The numbers in this set are considered Counting Numbers.
Play_video
Numbers to be Written Learn your digits, how to read them, how to write them, how to recognize them.
We focus on two-digit numbers in this lesson.
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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."
Play_video
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.
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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.
Play_video
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.
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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.
Play_video

Kindergarten

Title Description
Numbers to be Written Learn your digits, how to read them, how to write them, how to recognize them.
We focus on two-digit numbers in this lesson.
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A Lesson in British Currency We briefly discuss British paper money, or currency. Play_video
Counting 31 though 60 We continue counting through sixty. Play_video
Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.
The numbers in this set are considered Counting Numbers.
Play_video
Counting 61 though 100 We continue counting, reading number names, through one hundred. Play_video
Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.
In this video we learn numbers 11 - 30.
Play_video
Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.
We first discuss numbers 1 through 10.
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Counting Coins Lesson As we learn to count money, this video has just a little extra explanation. Play_video
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.
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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.
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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.
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Addition Makes Counting Easier How many birds are two birds and five birds? We sum objects with the conjunction "and." Play_video
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.
Play_video

Mean Mode Median

Title Description
Household 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. Play_video
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.
Play_video

Measurement

Title Description
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.
Play_video
A Lesson in Temperature Conversion If you can remember these numbers: 100-180-212, then you can remember the formulas for converting between temperature scales. Play_video
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.
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A Lesson in Liquid-and-Dry-Measure Conversions Relax.
Learn the equivalent measures.
A gallon of milk (or water, gasoline, or ketchup) is the same volume as 16 half-pints or 16 cups.
Play_video
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.
Play_video
Conversions between English and Metric Our understanding of Conversion Factors is enhanced with an appreciation of reciprocal values. Play_video
Producing Protactor Images Lesson A worksheet with "blank" protractors, printable as one-per-page, or 2-, 4-, or 6-to-a-page. Play_video
Circles, Angles, Degrees An introduction to angles includes a look at hands on a clock face.
Angles need to be understood early in Geometry.
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Angles on a Clock Face More angles on a clock face help us see the values of angles as we move around the circle. Play_video
A Lesson in Reading Angles A lesson in the nature of angles, with reading integer-value angle measurements with a protractor. Play_video
Angles and Protactors We look at equal fifths of a rotation, which are 72°.
We also look at an angle greater than 180°.
Play_video

Mixed Problems

Title Description
Review Addition and Subtraction Adding and subtracting single digit problems is quick if you have learned the addition and subtraction tables. Play_video
Addition and Subtraction Statements Read math statements left-to-right, 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.
Play_video
A Lesson in Japanese Money - The Yen A brief discussion of the Yen, the unit of both coinage and currency in Japan. Play_video
A Lesson in British Currency We briefly discuss British paper money, or currency. Play_video
A Lesson in British Coins We learn a few facts about coinage in Great Britain. Play_video

Money

Title Description
Counting Coins Lesson As we learn to count money, this video has just a little extra explanation. Play_video
38 Cents in US Coins How many ways can we get 38 cents using pennies, nickles, dimes and/or a quarter? Play_video
Adding United States coins To add the value of coinage we simply learn the denominations of coins used in the U.S. Play_video
A Lesson in British Currency We briefly discuss British paper money, or currency. Play_video
US Coins Lesson Print a handout full of images of pennies, nickles, dimes, quarters and half-dollars right here.
Or go to Math-Aids.com to print them individually.
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US Bills Lesson Print a handout full of images of one-dollar, two-dollar, five-dollar, ten-dollar, twenty-dollar, fifty-dollar and one-hundred-dollar bills right here.
Or go to Math-Aids.com to print them individually.
Play_video

Multiplication

Title Description
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.
Play_video
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.
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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.
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Multiplication by 2 When we multiply by 2, we double the number. Play_video
Multiplication by 3 When we multiply by 3, we triple the number. Play_video
Multiplication by 4 When we multiply by 4, we quadruple the number. Play_video
Multiplying by 8 We review the multiplication table for 8.
We also work some sample problems.
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Multiplying by 7 We review the multiplication table for 7.
We also work some sample problems.
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Multiplying by 1 When we multiply by one, we employ the multiplicative identity. Play_video
Multiplying by 5 When we multiply by 5, we quintuple the number. Play_video
Multiplying by 6 We review the multiplication table for 6.
We also work some sample problems.
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Multiplying by 9 We review the multiplication table for 9.
We also work some sample problems.
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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.
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Multiplication of Integers This video shows a detailed approach to multiplying larger integers together.
Do not use a calculator for these problems.
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Number Bonds

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Number Lines

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Graph 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.
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Opposite Directions Get comfortable moving in opposite directions before tackling negative values. Play_video
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.
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Fractions on Number Lines, Lesson 1 An understanding of fractions on The Real Number Line is a foundation for all math that comes later. Play_video
Fractions on Number Lines, Lesson 2 Place the Fractions on The Real Number Line.
Your understanding of the language will be greatly enhanced.
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Decimals on the Real Number Line Decimals, or decimal values, are to be placed at their proper location on the Real Number Line. Play_video
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.
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Order of Operations

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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.
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Patterns

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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.
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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.
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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.
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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.
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Patterns in Advanced Skip Counting There is a very wide variety of difficulty levels to be practiced with the Math-Aids.com Advanced Skip Counting worksheets. Play_video

Percent

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Multiplying 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.
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A Lesson in Percentage Calculations To calculate percentages we first learn to do it manually.
Only then should we rely on a calculator.
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Comparing Fractions and Decimals Fractions on the left, decimals on the right, and a comparison symbol in between the two values, and we read left-to-right. Play_video
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.
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The Master PDF Chart, Lesson Two Sixths, fifths, twentieths, sevenths and elevenths are detailed as percents, decimals, and fractions.
Learn these, please.
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Place Value

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Place Value Chart with Decimals The names of Place Values are detailed in a basic graphic from Math-Aids.com. Play_video
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 Math-Aids.com. Play_video
Counting 61 though 100 We continue counting, reading number names, through one hundred. Play_video
Counting 31 though 60 We continue counting through sixty. Play_video
Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.
We first discuss numbers 1 through 10.
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Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.
The numbers in this set are considered Counting Numbers.
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Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.
In this video we learn numbers 11 - 30.
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Addition in Expanded Form This lesson in addition also gives examples of expanding integers to expanded form.
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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.
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Matching Decimal Number Names The worksheet is self-explanatory.
The audio portion is Mr. X on his soapbox.
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Probability

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Probability Handout: Complements All probabilities are between zero and one.
Every probability has a complement, the difference between itself and 100 percent.
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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.
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Probability on Numbers We reach into our bag of tricks to understand very basic probabilities.
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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.
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Probability Using a Pair of Dice Dice can be nice, but do not gamble with your future.
Learn basic probabilities.
Please.
Thank you.
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Probability Using a Deck of Cards Do not gamble; learn the language of probabilities and statistics. Play_video
Probability Using a Spinner Spinners are very much like pie charts.
Probabilities are as easy as pie.
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Properties

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Division 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.
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Ignorance of the Law is No Excuse The Commutative Law and the Distributive Law are discussed. Play_video
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.
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Properties of Math Play_video
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.
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Sum Groups are Worth Joining Grouping terms according to the Associative Law is exceptionally easy to see. Play_video
Two Laws of Arithmetic A discussion of the Commutative Laws and the Associative Laws for addition and multiplication. Play_video

Pythagorean

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The 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. Play_video
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).
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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.
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Distance Formula as Pythagorean Relation A basic lesson in the Distance Formula and its close cousin, the Pythagorean Relation. Play_video
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.
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The Pythagorean Theorem The Pythagorean Theorem is a pretty important thing.
At some point, you should learn it.
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Radicals

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Ratios

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A 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.
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A Lesson in Rates and Unit Rates Rates and Unit Rates are very straightforward, very easy, and very important. Play_video
Growing with a Little Algebra Algebra helps us calculate rates with different units. Ratios and rates make perfect sense with a little Algebra. Play_video

Rounding

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Dividing and Rounding Large Numbers The problems in this lessons require the skills of long division and rounding. Play_video
Rounding Integers A lesson in rounding integers.
Examples in rounding to the nearest Ten and the nearest Hundred are included in this lesson.
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Significant Figures

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A Lesson with the Significant Figure Rules Handout Only zeroes are confused when speaking of Significant Figures, and only when they are not situated between non-zero digits.
Trailing zeroes at the right-end of a published or written decimal value are significant figures.
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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. Play_video

Skip Counting

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Counting 31 though 60 We continue counting through sixty. Play_video
Counting 61 though 100 We continue counting, reading number names, through one hundred. Play_video
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.
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Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.
We first discuss numbers 1 through 10.
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Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.
The numbers in this set are considered Counting Numbers.
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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.
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Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.
In this video we learn numbers 11 - 30.
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Patterns in Advanced Skip Counting There is a very wide variety of difficulty levels to be practiced with the Math-Aids.com Advanced Skip Counting worksheets. Play_video
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.
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Subtraction

Title Description
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.
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Subtraction of 9 We practice subtracting by 9.
Students should be able to memorize these facts.
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Subtraction of 8 We practice subtracting by 8.
Students should be able to memorize these facts.
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Subtraction of 7 We practice subtracting by 7.
Students should be able to memorize these facts.
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Subtraction of 6 We practice subtracting by 6.
Students should be able to memorize these facts.
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Subtraction of 5 We practice subtracting by 5.
Students should be able to memorize these facts.
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Subtraction of 4 We practice subtracting by 4.
Students should be able to memorize these facts.
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Subtraction of 3 Learn the facts of subtracting by 3. Play_video
Subtraction of 2 Learn the facts of subtracting by 2. Play_video
Subtraction of 1 Learn the facts of subtracting by 1. Play_video
Subtraction of 10 We practice subtracting by 10.
Students should be able to memorize these facts.
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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.
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Introduction to Subtraction The words "leaves" and "less" and "left" are key to learning the basic concept of subtraction. Play_video
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.
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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.
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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.
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A Lesson in Japanese Money - The Yen A brief discussion of the Yen, the unit of both coinage and currency in Japan. Play_video
A Lesson in British Currency We briefly discuss British paper money, or currency. Play_video
A Lesson in British Coins We learn a few facts about coinage in Great Britain. Play_video
A Lesson in Adding English Measurements This lesson adds English units of length to the nearest sixteenth of an inch. Play_video

Time

Title Description
Creating Blank Clock Faces Worksheet Example Not so much a lesson as a description of clock graphics available at Math-Aids.com. Play_video
Telling Time on Analog Clocks - Five Minute Increments We tell the time on an analog clock in five-minute increments.
Then we follow a Minute Hand clockwise in a very fast fashion.
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Talking about Elapsed Days, Weeks, Months and Years A lesson in Ambiguity. Sometimes one language is not precise when translated into another language. Play_video
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.
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Making a Calendar You can make a calendar at Math-Aids.com. Play_video

Venn Diagrams

Title Description
DeMorgan's Theorem, a Lesson DeMorgan's Theorem applies to Venn Diagrams as well as it applies to Digital Logic Gates, as in our computers. Play_video
Finite vs Infinite Appreciate infinity and the infinitesimal as you delve in Geometry.
"Uncountable" and "infinite" will be different ideas for us in Geometry.
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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."
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Venn Diagram Basics for Two Sets A brief look at Venn Diagram basics. Play_video
Venn Diagram Basics for Three Sets A description of a Venn Diagram with three sets. Play_video

Word Problems

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