## ARITHMETIC LESSONS

At Mr. X, we practice arithmetic. Then we practice some more. The benefits of knowing and understanding basic arithmetic relationships are priceless. Mastering arithmetic is essential to understanding algebra and all higher mathematics. We have a library of sample arithmetic problems with examples of solved problems for each arithmetic lesson. Check out our free samples below, as well as the arithmetic curriculum.
Arithmetic Sample Lesson 1
Arithmetic Sample Lesson 2
Arithmetic Sample Lesson 3

# Arithmetic Curriculum

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## Decimals

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 Long Division with Three-Digit Divisors Three digits in the divisor means long, long division. Comparing Decimals Lesson 1 We read math statements left-to-right.For this worksheet we need the Correct Comparison Symbol: >, = or <. Comparing Decimals Lesson 2 Real Values on the Real Number Line can be compared then expressed with greater-than, less-than, or equal-to symbols. Decimals on the Real Number Line Decimals, or decimal values, are to be placed at their proper location on the Real Number Line. The Real Number Line, a General Lesson There is only one Real Number Line, strictly speaking.But we can describe The Real Number Line or draw parts of The Real Number Line an infinite number of different and unique ways. Multiplying by Powers of Ten, Lesson This video emphasizes that you simply have to learn how to do this.ONLY YOU CAN DO THIS.These types of products need to be "automatic." Thank you.

## Division

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 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. Factors of 1368 with Divisibility Rules We divide 1368 into factors as we discuss divisibility rules. Divisibility of 360 The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility. Division with 7 We practice the facts of division with sevens by practicing the facts of multiplication that have a factor of seven. Division with 8 We practice the facts of division with eights by practicing the facts of multiplication that have a factor of eight. A Lesson for the Division Facts Table We master the facts of division by mastering the facts from the Multiplication Table. Division with 9 We practice the facts of division with nines by practicing the facts of multiplication that have a factor of nine. Division Table Knowing the multiplication facts makes division easy. Division with 10 Because we use a 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. Division with 2 When we divide by 2, we divide the number in half. Division with 6 We practice the facts of division with sixes by practicing the facts of multiplication that have a factor of six. Division with 4 We practice the facts of division with fours by practicing the facts of multiplication that have a factor of four. Division with 5 We practice the facts of division with fives by practicing the facts of multiplication that have a factor of five. Division with 3 We practice the facts of division with threes by practicing the facts of multiplication that have a factor of three. An Introduction to Division We learn that division is actually a form of multiplication.So we focus on multiplication to learn division. Dividing and Rounding Large Numbers The problems in this lessons require the skills of long division and rounding. Long Division with Three-Digit Divisors Three digits in the divisor means long, long division. Lesson in Division to Solve for Missing Number Using numbers 30 through 99, we solve division problems for the "missing number." We are building a bridge from arithmetic to algebra. A Lesson in Negative Division At some point we involve negative values into our approach to arithmetic, to start building a bridge toward algebra.We review that the product of two negative values is positive. Division in Three Different Formats We can write a statement of division horizontally, or as traditional long division, or as a fraction.

## Estimation

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## Fact Family

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

## Factors

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 Prime Factor Trees A basic lesson in Prime Factorization with Factor Trees. Divisibility of 360 The number 360 was chosen for the number of degrees in a circle because of its extraordinary divisibility. GCF, Greatest Common Factor A lesson in finding the Greatest Common Factor, or GCF, for two given integers. Greatest Common Factor Lesson Twenty problems for GCF.Mr. X knocks out the first ten in high-speed fashion. LCM - Least Common Multiple We discuss the methods to determine the Least Common Multiple for a pair of given Integers. Least Common Multiple Methods Explanations of LCM with the list method and the Prime Factorization method. Least Common Multiples More explanations of LCM with the list method and the Prime Factorization method. A Lesson in Prime Factorization A brief lesson in Prime Factorization of Integers less than nine-squared. Prime Factorization Lesson Prime factorization means to find the factors (or divisors) of an integer that are themselves prime numbers.These problems are also part of Prime Factorization Lesson 20.

## Flash Cards

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## Fractions

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## Function Table

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

## General Topics

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## Graph Paper

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

## Graphing

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

## Greater Than Less Than

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

## Hundreds Chart

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

## In and Out Boxes

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## Integers

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## Kindergarten

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 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. A Lesson in British Currency We briefly discuss British paper money, or currency. Counting 31 though 60 We continue counting through sixty. Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.The numbers in this set are considered Counting Numbers. Counting 61 though 100 We continue counting, reading number names, through one hundred. Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.In this video we learn numbers 11 - 30. Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.We first discuss numbers 1 through 10. Counting Coins Lesson As we learn to count money, this video has just a little extra explanation. Skip Counting by 7's and 12's Using the times table is a good way to practice skip counting.In this video we skip count by 7's and 12's. Skip Counting by 3's and 8's Using the times table is a good way to practice skip counting.In this video we skip count by 3's and 8's. Complete the Number Series A discussion for teachers and parents about the appropriateness of negative values in Kindergarten.It's fine to expect Kindergarten students to understand negative values, but only with some quality instruction.We're not born with this concept of negative values. Addition Makes Counting Easier How many birds are two birds and five birds? We sum objects with the conjunction "and." The Subtraction Table You need to know these facts.They are basic facts of subtraction and they are essential to understanding what comes later.Learn these facts.

## Mean Mode Median

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 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. MMMR: Mean, Mode, Median, and Range This lesson describes some concepts related to the most basic ideas in statistics.These really are basics we all should know.

## Measurement

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 A Chart for Decimals Equivalents for Fractions of Inches We discuss the chart for fractions of an inch.Know your eighths.Machinists should learn them all. A Lesson in Temperature Conversion If you can remember these numbers: 100-180-212, then you can remember the formulas for converting between temperature scales. A Quiz in Liquid Measures This Quiz is actually a lesson.You should learn the basic equivalent measures for the kitchen, especially if you live in the United States. A Lesson in 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. General Conversions Table Lesson The physical entities of Length, Weight, Area, and Speed are discussed in terms of Conversion Factors, along with their reciprocals for conversion of English units.Those units include: miles, inches, yards, feet, tons, ounces, square feet, square yards, acres, miles per hour and feet per second. Conversions between English and Metric Our understanding of Conversion Factors is enhanced with an appreciation of reciprocal values. Producing Protactor Images Lesson A worksheet with "blank" protractors, printable as one-per-page, or 2-, 4-, or 6-to-a-page. Circles, Angles, Degrees An introduction to angles includes a look at hands on a clock face.Angles need to be understood early in Geometry. Angles on a Clock Face More angles on a clock face help us see the values of angles as we move around the circle. A Lesson in Reading Angles A lesson in the nature of angles, with reading integer-value angle measurements with a protractor. Angles and Protactors We look at equal fifths of a rotation, which are 72°.We also look at an angle greater than 180°.

## Mixed Problems

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

## Money

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

## Multiplication

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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. Elements of Basic Multiplication The basic facts of multiplication must be memorized.There is no substitute for this knowledge.Learn these facts.Note that what used to be termed "multiplicand" and "multiplier" are now called factors. Multiplication by 10 We practice the basic facts of multiplication with a factor of ten.We multiply an integer by ten by writing a following zero. Multiplication by 2 When we multiply by 2, we double the number. Multiplication by 3 When we multiply by 3, we triple the number. Multiplication by 4 When we multiply by 4, we quadruple the number. Multiplying by 8 We review the multiplication table for 8.We also work some sample problems. Multiplying by 7 We review the multiplication table for 7.We also work some sample problems. Multiplying by 1 When we multiply by one, we employ the multiplicative identity. Multiplying by 5 When we multiply by 5, we quintuple the number. Multiplying by 6 We review the multiplication table for 6.We also work some sample problems. Multiplying by 9 We review the multiplication table for 9.We also work some sample problems. Multiplication Review with Two and Three Simple Factors We reinforce the basic facts of multiplication.Again, plural versus singular forms of verbs do no matter within the language of arithmetic.We also multiple three factors. Multiplication of Integers This video shows a detailed approach to multiplying larger integers together.Do not use a calculator for these problems.

## Number Bonds

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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. Opposite Directions Get comfortable moving in opposite directions before tackling negative values. Making the Transition from Addition to Subtraction Subtracting a positive value is equivalent to adding the negative of that value. This concept is easy to understand with the visualization on the real number line. Fractions on Number Lines, Lesson 1 An understanding of fractions on The Real Number Line is a foundation for all math that comes later. Fractions on Number Lines, Lesson 2 Place the Fractions on The Real Number Line.Your understanding of the language will be greatly enhanced. Decimals on the Real Number Line Decimals, or decimal values, are to be placed at their proper location on the Real Number Line. The Real Number Line, a General Lesson There is only one Real Number Line, strictly speaking.But we can describe The Real Number Line or draw parts of The Real Number Line an infinite number of different and unique ways.

## Order of Operations

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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.

## 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. Skip Counting by 3's and 8's Using the times table is a good way to practice skip counting.In this video we skip count by 3's and 8's. Skip Counting by 7's and 12's Using the times table is a good way to practice skip counting.In this video we skip count by 7's and 12's. How to Solve Skip Counting Problems This lesson uses the attached worksheet to give examples on how to find the rule for the skip counting, and solve the problems.We use positive and integer values up to 999 in these advanced skip counting problems. Patterns in Advanced Skip Counting There is a very wide variety of difficulty levels to be practiced with the Math-Aids.com Advanced Skip Counting worksheets.

## 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. A Lesson in Percentage Calculations To calculate percentages we first learn to do it manually.Only then should we rely on a calculator. Comparing Fractions and Decimals Fractions on the left, decimals on the right, and a comparison symbol in between the two values, and we read left-to-right. The Master PDF Chart, Lesson One We take a close look at eighths and ninths at the Official Mr. X PDF Master File for Mastering Fractions.We learn equivalent Percents, Decimals, and Fractional Values. The Master PDF Chart, Lesson Two Sixths, fifths, twentieths, sevenths and elevenths are detailed as percents, decimals, and fractions.Learn these, please.

## Place Value

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 Place Value Chart with Decimals The names of Place Values are detailed in a basic graphic from Math-Aids.com. Place Value Chart with Integers The names of Place Values for an integer (a Whole Mumber, or Counting Number) are detailed in a graphic from Math-Aids.com. Counting 61 though 100 We continue counting, reading number names, through one hundred. Counting 31 though 60 We continue counting through sixty. Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.We first discuss numbers 1 through 10. Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.The numbers in this set are considered Counting Numbers. Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.In this video we learn numbers 11 - 30. Addition in Expanded Form This lesson in addition also gives examples of expanding integers to expanded form. A Lesson in Expanded Notation Expanding numbers means taking positive numbers and expressing them as sums of single digits times powers of ten.This lesson shows how to express numbers in expanded notation, and how to find the number for a given expanded notation. Matching Decimal Number Names The worksheet is self-explanatory.The audio portion is Mr. X on his soapbox.

## 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. Probability Handout: Independent and Dependent Events Three colors of socks reside in a drawer.You dress in the dark.What is the probability of drawing out two matching socks? This video discusses when to multiply and when to add to determine probability. Probability on Numbers We reach into our bag of tricks to understand very basic probabilities. Probability Using a Single Die This die has nothing to do with morbidity.This die is a cube, a regular solid with six square faces.Probabilities for a single die have denominators of six. Probability Using a Pair of Dice Dice can be nice, but do not gamble with your future.Learn basic probabilities.Please.Thank you. Probability Using a Deck of Cards Do not gamble; learn the language of probabilities and statistics. Probability Using a Spinner Spinners are very much like pie charts.Probabilities are as easy as pie.

## Properties

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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. Ignorance of the Law is No Excuse The Commutative Law and the Distributive Law are discussed. Inverses, Additive and Reciprocal We discuss the additive inverse of addition as well as reciprocals in multiplication.These properties are very important to understand, especially as you start a course in Basic Algebra. Properties of Math Rearrange the Furniture - Using the Commutative Laws The terms of a sum may be arranged in any order.The terms of a product may be arranged in any order. Sum Groups are Worth Joining Grouping terms according to the Associative Law is exceptionally easy to see. Two Laws of Arithmetic A discussion of the Commutative Laws and the Associative Laws for addition and multiplication.

## Pythagorean

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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. Pythagorean Relations with Irrational Lengths We solve right triangles with various lengths of the sides.The Pythagorean relation holds, where the sum of the squares of the legs (the perpendicular sides) is equal to the square of the hypotenuse (the square of the longest side). Pythagorean Triples Basic right triangles are solved with integer values for the lengths of the sides.We call these Pythagorean Triples.No irrational numbers are required. Distance Formula as Pythagorean Relation A basic lesson in the Distance Formula and its close cousin, the Pythagorean Relation. The Distance Formula and the Pythagorean Theorem We find the distance between two points in rectangular (or Cartesian) coordinates.We also look at the familiar Pythagorean Theorem for the relationship between sides of a right triangle. The Pythagorean Theorem The Pythagorean Theorem is a pretty important thing.At some point, you should learn it.

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

## Rounding

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

## Significant Figures

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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. A Lesson in Significant Figures We look at a football player whose weight of 300 pounds could be regarded with one Significant Digit, or three Significant Digits.

## Skip Counting

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 Counting 31 though 60 We continue counting through sixty. Counting 61 though 100 We continue counting, reading number names, through one hundred. Skip Counting by 7's and 12's Using the times table is a good way to practice skip counting.In this video we skip count by 7's and 12's. Learning Numbers 1 through 10 Counting and recognizing digits comes early with practice.We first discuss numbers 1 through 10. Reading Numbers 1 - 100 You should be able to read numbers from 1 to 100.The numbers in this set are considered Counting Numbers. Skip Counting by 3's and 8's Using the times table is a good way to practice skip counting.In this video we skip count by 3's and 8's. Learning Numbers 11 through 30 Counting and recognizing digits comes early with practice.In this video we learn numbers 11 - 30. Patterns in Advanced Skip Counting There is a very wide variety of difficulty levels to be practiced with the Math-Aids.com Advanced Skip Counting worksheets. How to Solve Skip Counting Problems This lesson uses the attached worksheet to give examples on how to find the rule for the skip counting, and solve the problems.We use positive and integer values up to 999 in these advanced skip counting problems.

## Subtraction

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 The Subtraction Table You need to know these facts.They are basic facts of subtraction and they are essential to understanding what comes later.Learn these facts. Subtraction of 9 We practice subtracting by 9.Students should be able to memorize these facts. Subtraction of 8 We practice subtracting by 8.Students should be able to memorize these facts. Subtraction of 7 We practice subtracting by 7.Students should be able to memorize these facts. Subtraction of 6 We practice subtracting by 6.Students should be able to memorize these facts. Subtraction of 5 We practice subtracting by 5.Students should be able to memorize these facts. Subtraction of 4 We practice subtracting by 4.Students should be able to memorize these facts. Subtraction of 3 Learn the facts of subtracting by 3. Subtraction of 2 Learn the facts of subtracting by 2. Subtraction of 1 Learn the facts of subtracting by 1. Subtraction of 10 We practice subtracting by 10.Students should be able to memorize these facts. A Lesson on Subtraction We hope you can answer all of these questions.Your previous practice of arithmetic should make this lesson exceptionally easy and straightforward.Subtraction provides the difference between two values. Introduction to Subtraction The words "leaves" and "less" and "left" are key to learning the basic concept of subtraction. Making the Transition from Addition to Subtraction Subtracting a positive value is equivalent to adding the negative of that value. This concept is easy to understand with the visualization on the real number line. Review Subtraction Zero to Twenty You need to recall quickly and easily the basic facts of subtraction.Review and memorize the subtraction tables if you can't answer these problems quickly. Subtracting within a Number Problem Set Part Lesson, part Problem Set, this video encourages your memory.Sometimes we simply learn facts. Period.While it is good to see "why" these facts are true, they're still facts.So learn them. A Lesson in Japanese Money - The Yen A brief discussion of the Yen, the unit of both coinage and currency in Japan. A Lesson in British Currency We briefly discuss British paper money, or currency. A Lesson in British Coins We learn a few facts about coinage in Great Britain. A Lesson in Adding English Measurements This lesson adds English units of length to the nearest sixteenth of an inch.

## Time

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 Creating Blank Clock Faces Worksheet Example Not so much a lesson as a description of clock graphics available at Math-Aids.com. 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. Talking about Elapsed Days, Weeks, Months and Years A lesson in Ambiguity. Sometimes one language is not precise when translated into another language. A Lesson in Elapsed Time This lesson will be effective only if you already know how to tell time on a traditional clock.Learn to tell time. Then you may calculate Elapsed Times. Making a Calendar You can make a calendar at Math-Aids.com.

## 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. Finite vs Infinite Appreciate infinity and the infinitesimal as you delve in Geometry."Uncountable" and "infinite" will be different ideas for us in Geometry. Set Theory Symbols and Definitions A brief overview of the Set Theory handout includes a mnemonic device for remembering that OR goes with UNION.UNION means "or." INTERSECTION means "and." Venn Diagram Basics for Two Sets A brief look at Venn Diagram basics. Venn Diagram Basics for Three Sets A description of a Venn Diagram with three sets.

## Word Problems

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