MAT-251 · Modern Arithmetic III

The CLAA's MAT-251 Modern Arithmetic III course provides an advanced study for students in grades 6-8. This course covers complex topics such as advanced fractions, powers and roots, compound numbers, and the application of arithmetic in real-world problem-solving. Designed for students with a solid foundation in arithmetic, this course emphasizes logical reasoning and precision, preparing learners for higher mathematics and practical applications. Ideal for middle and high school students, this course challenges and refines mathematical skills.

Lessons

MAT-251 Lesson 001 - Arithmetic, the Science of Number
MAT-251 Lesson 002 - The Definitions Restated: Unit, Number, and Quantity
MAT-251 Lesson 003 - The Axioms of Arithmetic
MAT-251 Lesson 004 - The Theory of the Decimal Notation
MAT-251 Lesson 005 - Numeration and Notation at Full Scale
MAT-251 Lesson 006 - The Roman Notation
MAT-251 Lesson 007 - The Signs of Arithmetic
MAT-251 Lesson 008 - Addition and Its Reasons
MAT-251 Lesson 009 - The Proofs of Addition
MAT-251 Lesson 010 - Subtraction and Its Reasons
MAT-251 Lesson 011 - The Proofs of Subtraction
MAT-251 Lesson 012 - Multiplication and Its Reasons
MAT-251 Lesson 013 - Multiplication at Full Scale
MAT-251 Lesson 014 - The Contractions of Multiplication
MAT-251 Lesson 015 - Why the Contractions Work
MAT-251 Lesson 016 - Division and Its Reasons
MAT-251 Lesson 017 - Long Division Demonstrated
MAT-251 Lesson 018 - The Contractions of Division
MAT-251 Lesson 019 - The General Principles of Multiplication and Division
MAT-251 Lesson 020 - The Four Operations as One System
MAT-251 Lesson 021 - The Inner Structure of Numbers
MAT-251 Lesson 022 - Divisibility Demonstrated
MAT-251 Lesson 023 - The Properties of the Number Nine
MAT-251 Lesson 024 - Casting Out Nines, Proved
MAT-251 Lesson 025 - Prime Factoring and the One Frame
MAT-251 Lesson 026 - The Greatest Common Divisor in Theory
MAT-251 Lesson 027 - Euclid's Method, Proved
MAT-251 Lesson 028 - The Least Common Multiple in Theory
MAT-251 Lesson 029 - The GCD and LCM Law Demonstrated
MAT-251 Lesson 030 - Cancellation Generalized
MAT-251 Lesson 031 - The Theory of Fractions
MAT-251 Lesson 032 - The Principles of Fractions, Proved
MAT-251 Lesson 033 - Reduction of Fractions Demonstrated
MAT-251 Lesson 034 - The Common Denominator in Theory
MAT-251 Lesson 035 - Addition of Fractions at Full Strength
MAT-251 Lesson 036 - Subtraction of Fractions at Full Strength
MAT-251 Lesson 037 - Multiplication of Fractions, Demonstrated
MAT-251 Lesson 038 - Division of Fractions: Why Invert and Multiply
MAT-251 Lesson 039 - Complex Fractions and Chains
MAT-251 Lesson 040 - The Greatest Common Divisor of Fractions
MAT-251 Lesson 041 - The Least Common Multiple of Fractions
MAT-251 Lesson 042 - Fractions in Full Command
MAT-251 Lesson 043 - Decimal Fractions and the Theory of the Places
MAT-251 Lesson 044 - Reduction Between Common and Decimal Fractions
MAT-251 Lesson 045 - Addition and Subtraction of Decimals at Full Strength
MAT-251 Lesson 046 - Multiplication of Decimals, Demonstrated
MAT-251 Lesson 047 - Division of Decimals, Demonstrated
MAT-251 Lesson 048 - The Powers of Ten and the Point
MAT-251 Lesson 049 - Rounding, Precision, and the Honest Answer
MAT-251 Lesson 050 - Decimals in Full Command
MAT-251 Lesson 051 - Why Some Decimals Repeat
MAT-251 Lesson 052 - Pure and Mixed Circulates
MAT-251 Lesson 053 - Reducing Circulates to Common Fractions
MAT-251 Lesson 054 - Operations with Circulates
MAT-251 Lesson 055 - The Two Families of Decimals: The Border Law Completed
MAT-251 Lesson 056 - The Measures Reviewed as Systems
MAT-251 Lesson 057 - Measures of Value and of Weight
MAT-251 Lesson 058 - Measures of Extension and of Capacity
MAT-251 Lesson 059 - Angular Measure
MAT-251 Lesson 060 - The Measure of Time
MAT-251 Lesson 061 - The Metric System in Full
MAT-251 Lesson 062 - The Comparative Table: Customary and Metric
MAT-251 Lesson 063 - Reduction of Compound Numbers at Speed
MAT-251 Lesson 064 - The Four Operations on Compound Numbers
MAT-251 Lesson 065 - Longitude and Time, Deepened
MAT-251 Lesson 066 - Aliquot Parts and the Reckoner's Art
MAT-251 Lesson 067 - The Measures in Full Command
MAT-251 Lesson 068 - The Doctrine of Ratio
MAT-251 Lesson 069 - The Principles of Ratio, Demonstrated
MAT-251 Lesson 070 - What a Proportion Is: The Theory
MAT-251 Lesson 071 - The Law of the Products, Proved
MAT-251 Lesson 072 - Simple Proportion at Full Strength
MAT-251 Lesson 073 - The Judgment of Proportions: Direct and Inverse
MAT-251 Lesson 074 - Inverse Proportion and the Constant Whole
MAT-251 Lesson 075 - Compound Proportion Demonstrated
MAT-251 Lesson 076 - Compound Proportion at Full Stride
MAT-251 Lesson 077 - Proportion, Rates, and the Average Revisited
MAT-251 Lesson 078 - Percentage Restated as Formulas
MAT-251 Lesson 079 - The Cases by Formula
MAT-251 Lesson 080 - Increase, Decrease, and Successive Percents
MAT-251 Lesson 081 - Profit and Loss at Full Rigor I
MAT-251 Lesson 082 - Profit and Loss at Full Rigor II
MAT-251 Lesson 083 - Commission in the Modern World
MAT-251 Lesson 084 - Trade Discount and Discount Chains
MAT-251 Lesson 085 - Taxes: The Citizen's Ledger Deepened
MAT-251 Lesson 086 - Percentage Problems at Full Stride I
MAT-251 Lesson 087 - Percentage Problems at Full Stride II
MAT-251 Lesson 088 - Interest by Formula
MAT-251 Lesson 089 - The Cases of Interest by Formula
MAT-251 Lesson 090 - Exact and Ordinary Interest
MAT-251 Lesson 091 - Promissory Notes
MAT-251 Lesson 092 - Compound Interest Through Exponents
MAT-251 Lesson 093 - The Rule of 72 Examined
MAT-251 Lesson 094 - Saving: The Mathematics of the Account
MAT-251 Lesson 095 - Borrowing: The Mathematics of the Loan
MAT-251 Lesson 096 - Credit, Rates, and the Modern Borrower
MAT-251 Lesson 097 - The Money Problems at Full Stride
MAT-251 Lesson 098 - Mixtures and the Weighted Average
MAT-251 Lesson 099 - Making a Mixture to a Required Value
MAT-251 Lesson 100 - Mixture Problems at Full Stride
MAT-251 Lesson 101 - Involution and the Theory of Exponents
MAT-251 Lesson 102 - The Laws of Exponents
MAT-251 Lesson 103 - The Square Root Demonstrated
MAT-251 Lesson 104 - Square Root at Full Strength
MAT-251 Lesson 105 - The Cube Root Demonstrated
MAT-251 Lesson 106 - Roots of Any Degree
MAT-251 Lesson 107 - The Applications of Square and Cube Root
MAT-251 Lesson 108 - Parallel Lines and Similar Figures
MAT-251 Lesson 109 - Similar Figures and Their Measures
MAT-251 Lesson 110 - Powers and Roots at Full Stride
MAT-251 Lesson 111 - Arithmetical Progression by Formula
MAT-251 Lesson 112 - The Last Term and the Sum, Demonstrated
MAT-251 Lesson 113 - Geometrical Progression by Formula
MAT-251 Lesson 114 - The Geometric Leap and Sum, Demonstrated
MAT-251 Lesson 115 - The Two Orders Compared and Applied
MAT-251 Lesson 116 - Series at Full Stride
MAT-251 Lesson 117 - Lines and Angles
MAT-251 Lesson 118 - The Measurement of Angles
MAT-251 Lesson 119 - Surfaces and Areas: The Rules Derived I
MAT-251 Lesson 120 - Surfaces and Areas: The Rules Derived II
MAT-251 Lesson 121 - The Circle Demonstrated
MAT-251 Lesson 122 - Solids: Prisms and Cylinders Derived
MAT-251 Lesson 123 - Pyramids, Cones, and the Sphere Derived
MAT-251 Lesson 124 - Surface and Volume at Full Strength
MAT-251 Lesson 125 - The Trades: Masonry and Building Measure
MAT-251 Lesson 126 - The Trades: Lumber, Gauging, and Stored Goods
MAT-251 Lesson 127 - Mensuration Problems at Full Stride I
MAT-251 Lesson 128 - Mensuration Problems at Full Stride II
MAT-251 Lesson 129 - The Number Line in Both Directions
MAT-251 Lesson 130 - What Signed Numbers Are
MAT-251 Lesson 131 - Addition of Signed Numbers
MAT-251 Lesson 132 - Subtraction of Signed Numbers
MAT-251 Lesson 133 - Multiplication of Signed Numbers
MAT-251 Lesson 134 - Division of Signed Numbers
MAT-251 Lesson 135 - The Four Quadrants of the Grid
MAT-251 Lesson 136 - Signed Numbers at Full Stride
MAT-251 Lesson 137 - Angles Measured and Classified
MAT-251 Lesson 138 - Angle Pairs and Parallel Lines
MAT-251 Lesson 139 - The Triangle and Its Angle Sum
MAT-251 Lesson 140 - Classifying Triangles and Quadrilaterals
MAT-251 Lesson 141 - Congruence: Figures That Match
MAT-251 Lesson 142 - Similarity: Figures in Proportion
MAT-251 Lesson 143 - The Pythagorean Theorem at Full Strength
MAT-251 Lesson 144 - Geometry at Full Stride
MAT-251 Lesson 145 - The Order of Operations
MAT-251 Lesson 146 - The Letter That Stands for a Number
MAT-251 Lesson 147 - Expressions and Their Evaluation
MAT-251 Lesson 148 - Formulas: The Course's Rules in Letters
MAT-251 Lesson 149 - Scientific Notation
MAT-251 Lesson 150 - Simple Equations I: The Unknown Member
MAT-251 Lesson 151 - Simple Equations II: Undoing to Solve
MAT-251 Lesson 152 - Through the Door: Arithmetic Complete