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 Subject  
 Preface  
PURPOSE :
PowerMath Arithmetic®
is a complete course suitable for Grades 6 on up. The curriculum includes 9 chapters, 62 lessons, totaling 16.13 hours (or 968 minutes)
of continuous animated mathematical instruction (in virtualreality).
Based on the "Foundations of Mathematics," the buildingblocks where it all starts, you will be
guided stepbystep through the initial formalization of mathematics. Arithmetic affects our daily lives in order to count, measure or estimate numerical quantities. Whether your are
a "firsttime learner" or wishes to "relearn it" in a formal manner to prepare you for a better understanding of
fundamental mathematics, then this course was designed for you!
APPLICATION :
The course assumes no prior mathematical knowledge nor experience, other than basic reading skills in the English language.
Combining theory proved by logical reasoning with plenty of examples and illustrations, stressing both the
theoretical and computational aspects, this course is a rigorous representation of traditional topics in Arithmetic.
For Students, lessons are selfpaced and selflearning requiring no instructional intervention.
For Teachers, lessons are content specific and optimal to augment their own classroom lectures.
RECOMMENDATION :
LessonShows were designed to be watched sequentially, to build your mathematical knowledge and confidence incrementally.
Skipping any portion of the course (lessons and/or chapters) is not advised. We suggest that you start with the very first lesson of the subject (Chapter One  Lesson One), while working your way up.
Your startingpoint (depending on your abilities), is when you find a specific lesson content challenging.
Alternatively, match your instructor most recent lecture topic or corresponding part of your textbook, with
any lesson Title & Description below.
 Contents  
In PDF Format
 Lessons  
SHOW 1005 
Reading the Numbers
Counting and Spelling the Cardinal & Ordinal Numbers 
runtime 10 minutes requires None 

SHOW 1010 
The Decimal System
The Expanded Form of Decimal Numbers 
runtime 10 minutes requires SHOW 1005 

SHOW 1012 
Introduction to Number Operations
Add, Subtract, Multiply and Divide, explained 
runtime 14 minutes requires SHOW 1010 

SHOW 1015 
Integer Addition
Addition, Graphic Representation, and Properties 
runtime 16 minutes requires SHOW 1010 

SHOW 1020 
Integer Subtraction
Subtraction, Graphic Representation, and Properties 
runtime 16 minutes requires SHOW 1015 

SHOW 1025 
Integer Multiplication
Multiplication, Graphic Representation, and Properties 
runtime 18 minutes requires SHOW 1015 

SHOW 1030 
Integer Division
Division, Graphic Representation, and Properties 
runtime 20 minutes requires SHOW 1025 

SHOW 1035 
Rules of Arithmetic
Signed Numbers and Arithmetical Notation 
runtime 14 minutes requires SHOW 1030 

SHOW 1040 
Introduction to Sets
A Study of Union, Intersect, and Complement of Sets 
runtime 19 minutes requires SHOW 1035 
SHOW 1100 
Basic Number Systems
A Look at Natural, Whole and Integer Numbers 
runtime 14 minutes requires None 

SHOW 1105 
Advanced Number Systems
A Look at Rational, Irrational and Real Numbers 
runtime 18 minutes requires SHOW 1100 
SHOW 1140 
Adding Real Numbers by Hand
Leading & Trailing Zeros, and the Column Method 
runtime 15 minutes requires SHOW 1105 

SHOW 1145 
Subtracting Real Numbers by Hand
Leading & Trailing Zeros, and the Column Method 
runtime 17 minutes requires SHOW 1140 

SHOW 1150 
Part 1  Multiplication of Real Numbers by Hand
Leading & Trailing Zeros, and the Column Method with Integers 
runtime 16 minutes requires SHOW 1145 

SHOW 1155 
Part 2  Multiplication of Real Numbers by Hand
Leading & Trailing Zeros, and the Column Method with Decimals 
runtime 23 minutes requires SHOW 1150 

SHOW 1160 
Real Numbers x Multiples of 10
Small & Large Number Patterns in Multiplication 
runtime 18 minutes requires SHOW 1155 

SHOW 1165 
Part 1  Division of Real Numbers by Hand
Leading & Trailing Zeros, and the Long Division Method with Integers 
runtime 19 minutes requires SHOW 1160 

SHOW 1170 
Part 2  Division of Real Numbers by Hand
Leading & Trailing Zeros, and the Long Division Method with Decimals 
runtime 22 minutes requires SHOW 1165 

SHOW 1175 
Part 3  Division Special Case
When Divisor is greater than Dividend 
runtime 18 minutes requires SHOW 1170 

SHOW 1180 
Real Numbers / Multiples of 10
Small & Large Number Patterns in Division 
runtime 16 minutes requires SHOW 1175 

SHOW 1185 
Order of Operations
The PEMDAS Method 
runtime 9 minutes requires SHOW 1180 

SHOW 1190 
The Prime Numbers
Prime & Composite Numbers, and Prime Factors 
runtime 15 minutes requires SHOW 1185 

SHOW 1195 
Prime Factorization
Reducing Composite Numbers into Prime Factors 
runtime 11 minutes requires SHOW 1190 

SHOW 1196 
The Greatest Common Divisor
Technique to Compute the G.C.D. 
runtime 16 minutes requires SHOW 1195 

SHOW 1198 
The Least Common Multiple
Technique to Compute the L.C.M. 
runtime 17 minutes requires SHOW 1196 
SHOW 1200 
The Concept of Fraction
Defining Mathematical Fractions 
runtime 13 minutes requires SHOW 1198 

SHOW 1205 
An Introduction to Fractions
Similar Fractions, Reducing Fractions, Ratio of Fractions and Types of Fractions 
runtime 13 minutes requires SHOW 1200 

SHOW 1210 
The Multiplication of Fractions
Standard & Mixed Forms, and Fraction Multiplication 
runtime 9 minutes requires SHOW 1205 

SHOW 1215 
The Division of Fractions
Standard & Mixed Forms, and Fraction Division 
runtime 10 minutes requires SHOW 1210 

SHOW 1220 
The Least Common Denominator
Least Common Denominator explained 
runtime 12 minutes requires SHOW 1215 

SHOW 1225 
Addition & Subtraction of Fractions
Finding the Least Common Denominator 
runtime 19 minutes requires SHOW 1220 

SHOW 1230 
Mixed Fractions
Adding & Subtracting 
runtime 12 minutes requires SHOW 1225 
SHOW 1300 
The Concept of Exponents
Graphic Simulation of Exponents 
runtime 11 minutes requires SHOW 1225 

SHOW 1305 
Properties of Exponents
A Detailed Look at the Base and the Power 
runtime 16 minutes requires SHOW 1300 

SHOW 1310 
The Laws of Exponents
Basic Rules of Exponentiation 
runtime 22 minutes requires SHOW 1305 

SHOW 1315 
Operations with Exponential Numbers
Adding, Subtracting, Multiplying & Dividing Exponentials 
runtime 17 minutes requires SHOW 1310 
SHOW 1350 
The Concept of Roots
The Notion of Roots, Principal & Alternate Roots 
runtime 12 minutes requires SHOW 1315 

SHOW 1355 
Roots of Real Numbers
Square, Cubic and Higher Roots 
runtime 24 minutes requires SHOW 1350 

SHOW 1360 
The Properties of Radicals
The Behavior of Roots & Radicals 
runtime 12 minutes requires SHOW 1355 

SHOW 1365 
Working with Roots & Radicals
Numeric Guidelines for Roots & Radicals 
runtime 18 minutes requires SHOW 1360 

SHOW 1370 
Operations with Radicals 1
Addition & Subtraction of Radicals 
runtime 11 minutes requires SHOW 1365 

SHOW 1375 
Operations with Radicals 2
Multiplication of Radical Numbers and the Index 
runtime 21 minutes requires SHOW 1370 

SHOW 1380 
Operations with Radicals 3
Division of Radical Numbers & Rationalizing Denominators 
runtime 22 minutes requires SHOW 1375 

SHOW 1385 
Square Roots by Hand
Computing Square Roots Manually 
runtime 22 minutes requires SHOW 1380 
SHOW 1400 
Rounding Off Decimal Numbers
When to RoundOff Numbers UP or DOWN 
runtime 16 minutes requires SHOW 1385 

SHOW 1405 
Numeric Forms: Fractional Numbers
Form of Representing Numbers 
runtime 17 minutes requires SHOW 1400 

SHOW 1410 
Numeric Forms: Scientific Notation
Form of Representing Numbers 
runtime 11 minutes requires SHOW 1405 

SHOW 1415 
Numeric Forms: Percent
Form of Representing Numbers 
runtime 13 minutes requires SHOW 1410 

SHOW 1420 
Conversion of Equivalent Numerical Forms
Converting Decimal, Fraction, Scientific & Percent 
runtime 16 minutes requires SHOW 1415 
SHOW 1500 
Handling Money
The Value of Money 
runtime 10 minutes requires SHOW 1420 

SHOW 1505 
Gauging Temperature
Examining the Celsius, Fahrenheit, and Kelvin Scales 
runtime 18 minutes requires SHOW 1500 

SHOW 1510 
The Unit of Time
Understanding Time 
runtime 17 minutes requires SHOW 1505 

SHOW 1515 
Length
One Dimensional Unit of Measurement 
runtime 12 minutes requires SHOW 1510 

SHOW 1520 
Weight
One Dimensional Unit of Measurement 
runtime 11 minutes requires SHOW 1515 

SHOW 1525 
Area
Two Dimensional Unit of Measurement 
runtime 22 minutes requires SHOW 1520 

SHOW 1530 
Volume
Three Dimensional Unit of Measurement 
runtime 24 minutes requires SHOW 1525 
SHOW 1600 
Mathematical Proportion
The CrossMultiplying Approach 
runtime 13 minutes requires SHOW 1530 

SHOW 1605 
Factorial Numbers
An Introduction to Factorials 
runtime 17 minutes requires SHOW 1600 

SHOW 1610 
Permutation
Permutation Explained 
runtime 14 minutes requires SHOW 1605 

SHOW 1615 
Combination
Combination Explained 
runtime 13 minutes requires SHOW 1610 

SHOW 1620 
Data Analysis I
The Study of Information (Tables & Charts) 
runtime 14 minutes requires SHOW 1615 

SHOW 1625 
Data Analysis II
The Study of Information (Sample Statistics) 
runtime 13 minutes requires SHOW 1620 
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