Introducing the CLAA's New Modern Arithmetic Program

For years, families in the Classical Liberal Arts Academy have asked me how they should teach their children modern, grade-level Arithmetic. My answer, until now, has been to recommend outside programs, because I had nothing better to offer them. That has changed. The Academy now offers a complete Modern Arithmetic program of its own, and in this article I'd like to explain what it is, why I created it, and how it works. THE PROBLEM WITH MODERN MATH PROGRAMS If you open a modern math textbook, you will find a chaotic mess of colored boxes, cartoon illustrations, sidebars, and scattered exercises. Publishers design these books as if children are incapable of reading, and so must be entertained. The result is that students never actually study mathematics — they hunt around busy pages for answers, follow along with videos, and click through software. Mathematics becomes a subject unlike every other subject, one that is not read, not studied, and not understood, but merely endured. In the Classical Liberal Arts Academy, students learn by reading and studying text. They do this in Grammar, in Reasoning, in Latin, in every subject. There is no reason why Arithmetic should be any different. A student who can read and study should be able to learn Arithmetic the same way he learns everything else: by reading a clear lesson, understanding what it teaches, committing its key points to memory, and proving his mastery through assessment. LEARNING FROM THE PAST Many Christian parents have seen this problem, which is why the old "Ray's Arithmetic" series remains popular today, more than a century after it was written. The content of the Ray's books, and especially its arrangement, is excellent. The series moves through the whole of Arithmetic in an orderly way, from counting to the threshold of Algebra, with each part building on what came before. However, the Ray's books were never written for students. They were written as source books for teachers, who were expected to supply all of the explanations, drills, and discussion in the classroom. A child cannot sit down with Ray's Arithmetic and simply study it — and this is exactly what homeschooled students need to do. Moreover, the books are filled with the commercial arithmetic of the 1870s — stocks, bank discounts, partnerships — while lacking topics every modern student must know. What was needed was a program that preserved the excellent arrangement of the old books, but rewrote the content as lessons students could actually read and study on their own, and brought the material up to date for modern students. That is what I have produced. HOW THE PROGRAM WORKS Every lesson in the Modern Arithmetic program is a simple prose lesson. There are no info boxes, no cartoons, no clutter — just clear, straightforward teaching, written to be read and understood. Each lesson teaches one concept, explains it fully, and works through it with the student. The textbook is the teacher. Every lesson is accompanied by Memory Work — the definitions and rules of the lesson stated in fixed, exact language, which students commit to memory. This is how students studied in the classical tradition, and it is how students study in every CLAA course. As students progress, their memory work builds into a complete, ordered knowledge of Arithmetic. Mastery is proven through assessments — quizzes, tests, and written examinations — provided with the courses in the new CLAA study center. The program is arranged in concentric levels, like the old catechisms: each course covers the whole subject of Arithmetic, and each course covers it again at greater depth. A student who completes the program will have studied Arithmetic thoroughly three times over, and will be fully prepared both for standardized testing and for the regular high school courses in Mathematics — Algebra, Geometry, and beyond. THE THREE COURSES Modern Arithmetic I (Grades 2–4) covers the content of Ray's Primary and Intellectual Arithmetic in 62 lessons: counting and numbers, the four operations, money and measures, parts of things, and mental arithmetic. MAT-051 Lesson 001 - Counting Things MAT-051 Lesson 002 - The Figures: Writing One to Ten MAT-051 Lesson 003 - Numbers to Twenty MAT-051 Lesson 004 - Counting to One Hundred MAT-051 Lesson 005 - Reading and Writing Numbers to One Hundred MAT-051 Lesson 006 - Numbers to One Thousand MAT-051 Lesson 007 - Reading and Writing Numbers to One Thousand MAT-051 Lesson 008 - Roman Numerals to Twelve: Reading the Clock Face MAT-051 Lesson 009 - About How Many: Making a Good Guess MAT-051 Lesson 010 - What Addition Is MAT-051 Lesson 011 - The Addition Table: Adding One and Two MAT-051 Lesson 012 - The Addition Table: Adding Three and Four MAT-051 Lesson 013 - The Addition Table: Adding Five and Six MAT-051 Lesson 014 - The Addition Table: Adding Seven, Eight, and Nine MAT-051 Lesson 015 - Adding in the Head: Three or More Small Numbers MAT-051 Lesson 016 - Writing Addition Down MAT-051 Lesson 017 - Adding Larger Numbers on Paper MAT-051 Lesson 018 - What Subtraction Is MAT-051 Lesson 019 - The Subtraction Table: Taking Away One and Two MAT-051 Lesson 020 - The Subtraction Table: Taking Away Three and Four MAT-051 Lesson 021 - The Subtraction Table: Taking Away Five and Six MAT-051 Lesson 022 - The Subtraction Table: Taking Away Seven, Eight, and Nine MAT-051 Lesson 023 - Writing Subtraction Down MAT-051 Lesson 024 - Taking Away with Borrowing MAT-051 Lesson 025 - How Addition and Subtraction Undo Each Other MAT-051 Lesson 026 - Addition and Subtraction Together MAT-051 Lesson 027 - What Multiplication Is MAT-051 Lesson 028 - The Table of Twos MAT-051 Lesson 029 - The Table of Threes MAT-051 Lesson 030 - The Table of Fours MAT-051 Lesson 031 - The Table of Fives and Tens MAT-051 Lesson 032 - The Table of Sixes MAT-051 Lesson 033 - The Table of Sevens MAT-051 Lesson 034 - The Table of Eights MAT-051 Lesson 035 - The Table of Nines MAT-051 Lesson 036 - Writing Multiplication Down MAT-051 Lesson 037 - What Division Is: Equal Sharing MAT-051 Lesson 038 - The Division Table from the Twos and Threes MAT-051 Lesson 039 - The Division Table from the Fours and Fives MAT-051 Lesson 040 - The Division Table from the Sixes and Sevens MAT-051 Lesson 041 - The Division Table from the Eights, Nines, and Tens MAT-051 Lesson 042 - Something Left Over: Remainders MAT-051 Lesson 043 - Writing Division Down MAT-051 Lesson 044 - How Multiplication and Division Undo Each Other MAT-051 Lesson 045 - Cents, Nickels, and Dimes MAT-051 Lesson 046 - Quarters and the Dollar MAT-051 Lesson 047 - Making Change MAT-051 Lesson 048 - The Clock: Hours and Half Hours MAT-051 Lesson 049 - The Clock: Minutes MAT-051 Lesson 050 - The Calendar: Days, Weeks, and Months MAT-051 Lesson 051 - The Ruler: Inches, Feet, and the Yard MAT-051 Lesson 052 - The Pound: Weighing Things MAT-051 Lesson 053 - The Quart: Measuring What Pours MAT-051 Lesson 054 - Measuring the Metric Way: The Centimeter, the Meter, and the Liter MAT-051 Lesson 055 - Keeping Count: Tally Marks and Picture Graphs MAT-051 Lesson 056 - Halves: One Thing Made Into Two Equal Parts MAT-051 Lesson 057 - Quarters: Half of a Half MAT-051 Lesson 058 - Thirds MAT-051 Lesson 059 - Finding Half or a Quarter of a Number MAT-051 Lesson 060 - Arithmetic in the Head: Adding and Taking Away MAT-051 Lesson 061 - Arithmetic in the Head: Multiplying and Dividing MAT-051 Lesson 062 - Arithmetic in the Head: Money, Measures, and Parts of Things MAT-051 Lesson 063 - The Completion of Modern Arithmetic I Modern Arithmetic II (Grades 4–6) covers the content of Ray's Practical Arithmetic in 166 lessons, carrying students through the whole subject — from numbers and the four operations through fractions, decimals, measurement, percentage, ratio and proportion, and progressions — to the door of Algebra. MAT-151 Lesson 001 - The Unit, the Number, and Arithmetic MAT-151 Lesson 002 - The Ten Figures MAT-151 Lesson 003 - Units, Tens, and Hundreds MAT-151 Lesson 004 - The Period of Thousands MAT-151 Lesson 005 - Millions and Beyond MAT-151 Lesson 006 - Writing Numbers Exactly MAT-151 Lesson 007 - Rounding and Estimation MAT-151 Lesson 008 - The Roman System I MAT-151 Lesson 009 - The Roman System II MAT-151 Lesson 010 - What Addition Is MAT-151 Lesson 011 - The Addition Facts MAT-151 Lesson 012 - Written Addition MAT-151 Lesson 013 - Carrying MAT-151 Lesson 014 - Addition at Scale MAT-151 Lesson 015 - Proving Addition MAT-151 Lesson 016 - What Subtraction Is MAT-151 Lesson 017 - The Subtraction Facts MAT-151 Lesson 018 - Written Subtraction MAT-151 Lesson 019 - Borrowing MAT-151 Lesson 020 - Subtraction at Scale MAT-151 Lesson 021 - Proving Subtraction MAT-151 Lesson 022 - What Multiplication Is MAT-151 Lesson 023 - The Multiplication Table I MAT-151 Lesson 024 - The Multiplication Table II MAT-151 Lesson 025 - Multiplying by One Figure MAT-151 Lesson 026 - Multiplying by Two or More Figures MAT-151 Lesson 027 - Zeros in Multiplication MAT-151 Lesson 028 - Contractions in Multiplication MAT-151 Lesson 029 - Proving Multiplication MAT-151 Lesson 030 - What Division Is MAT-151 Lesson 031 - The Division Facts MAT-151 Lesson 032 - Short Division MAT-151 Lesson 033 - Remainders MAT-151 Lesson 034 - Long Division I MAT-151 Lesson 035 - Long Division II MAT-151 Lesson 036 - Long Division III MAT-151 Lesson 037 - Contractions in Division MAT-151 Lesson 038 - The General Principles of Division MAT-151 Lesson 039 - Proving Division and the Four Operations Together MAT-151 Lesson 040 - Dollars and Cents MAT-151 Lesson 041 - Reduction of Money MAT-151 Lesson 042 - Adding and Subtracting Money MAT-151 Lesson 043 - Multiplying and Dividing Money MAT-151 Lesson 044 - Bills and Receipts MAT-151 Lesson 045 - Money Problems MAT-151 Lesson 046 - Simple and Compound Numbers MAT-151 Lesson 047 - Measures of Time MAT-151 Lesson 048 - Reduction of Time MAT-151 Lesson 049 - Long Measure MAT-151 Lesson 050 - The Metric Idea MAT-151 Lesson 051 - Metric Length MAT-151 Lesson 052 - Square Measure MAT-151 Lesson 053 - Metric Square Measure MAT-151 Lesson 054 - Cubic Measure MAT-151 Lesson 055 - Metric Capacity MAT-151 Lesson 056 - Liquid Measure MAT-151 Lesson 057 - Weight and the Pound MAT-151 Lesson 058 - Metric Weight MAT-151 Lesson 059 - Counting Measures MAT-151 Lesson 060 - Between the Systems MAT-151 Lesson 061 - Addition of Compound Numbers MAT-151 Lesson 062 - Subtraction of Compound Numbers MAT-151 Lesson 063 - Multiplication of Compound Numbers MAT-151 Lesson 064 - Division of Compound Numbers MAT-151 Lesson 065 - Longitude and Time MAT-151 Lesson 066 - Factors, Primes, and Composites MAT-151 Lesson 067 - The Tests of Divisibility MAT-151 Lesson 068 - Prime Factoring MAT-151 Lesson 069 - Greatest Common Divisor I MAT-151 Lesson 070 - Greatest Common Divisor II MAT-151 Lesson 071 - Least Common Multiple I MAT-151 Lesson 072 - Least Common Multiple II MAT-151 Lesson 073 - Cancellation MAT-151 Lesson 074 - What a Fraction Is MAT-151 Lesson 075 - Kinds of Fractions MAT-151 Lesson 076 - The Principles of Fractions MAT-151 Lesson 077 - Reduction to Lowest Terms MAT-151 Lesson 078 - Improper Fractions and Mixed Numbers MAT-151 Lesson 079 - Common Denominators MAT-151 Lesson 080 - Comparing Fractions MAT-151 Lesson 081 - Addition of Fractions MAT-151 Lesson 082 - Addition of Mixed Numbers MAT-151 Lesson 083 - Subtraction of Fractions MAT-151 Lesson 084 - Subtraction of Mixed Numbers MAT-151 Lesson 085 - Multiplication of Fractions I MAT-151 Lesson 086 - Multiplication of Fractions II MAT-151 Lesson 087 - Division of Fractions I MAT-151 Lesson 088 - Division of Fractions II MAT-151 Lesson 089 - Fractions of Compound Numbers in Practice MAT-151 Lesson 090 - What a Decimal Is MAT-151 Lesson 091 - Reading and Writing Decimals MAT-151 Lesson 092 - The Principles of Decimals MAT-151 Lesson 093 - Rounding and Estimating Decimals MAT-151 Lesson 094 - Decimals to Common Fractions MAT-151 Lesson 095 - Common Fractions to Decimals MAT-151 Lesson 096 - Addition of Decimals MAT-151 Lesson 097 - Subtraction of Decimals MAT-151 Lesson 098 - Multiplication of Decimals MAT-151 Lesson 099 - Powers of Ten MAT-151 Lesson 100 - Division of Decimals MAT-151 Lesson 101 - Decimals of Compound Numbers MAT-151 Lesson 102 - What Percent Means MAT-151 Lesson 103 - Finding a Percent of a Number MAT-151 Lesson 104 - What Percent One Number Is of Another MAT-151 Lesson 105 - Finding the Whole from a Part MAT-151 Lesson 106 - Increase and Decrease MAT-151 Lesson 107 - The Cases Mixed MAT-151 Lesson 108 - Sales Tax and Tips MAT-151 Lesson 109 - Commission MAT-151 Lesson 110 - Trade Discount MAT-151 Lesson 111 - Profit and Loss I MAT-151 Lesson 112 - Profit and Loss II MAT-151 Lesson 113 - Percentage Problems MAT-151 Lesson 114 - What Interest Is MAT-151 Lesson 115 - Computing Simple Interest MAT-151 Lesson 116 - Interest for Months and Days MAT-151 Lesson 117 - The Cases of Interest MAT-151 Lesson 118 - Borrowing and Lending MAT-151 Lesson 119 - Compound Interest I MAT-151 Lesson 120 - Compound Interest II MAT-151 Lesson 121 - Taxes MAT-151 Lesson 122 - What a Ratio Is MAT-151 Lesson 123 - The Principles of Ratio MAT-151 Lesson 124 - What a Proportion Is MAT-151 Lesson 125 - Simple Proportion I MAT-151 Lesson 126 - Simple Proportion II MAT-151 Lesson 127 - Simple Proportion III MAT-151 Lesson 128 - Compound Proportion I MAT-151 Lesson 129 - Compound Proportion II MAT-151 Lesson 130 - Rates MAT-151 Lesson 131 - Scale Drawings and Maps MAT-151 Lesson 132 - The Average I MAT-151 Lesson 133 - The Average II MAT-151 Lesson 134 - Powers and Exponents MAT-151 Lesson 135 - What Evolution Is MAT-151 Lesson 136 - Square Root I MAT-151 Lesson 137 - Square Root II MAT-151 Lesson 138 - Applications of Square Root MAT-151 Lesson 139 - Cube Root I MAT-151 Lesson 140 - Cube Root II MAT-151 Lesson 141 - Applications of Powers and Roots MAT-151 Lesson 142 - Mensuration and the Rectangle MAT-151 Lesson 143 - Parallelograms and Triangles MAT-151 Lesson 144 - The Trapezoid and Irregular Figures MAT-151 Lesson 145 - The Circle MAT-151 Lesson 146 - The Surfaces of Solids MAT-151 Lesson 147 - Volume and the Rectangular Solid MAT-151 Lesson 148 - Volume of Prisms and Cylinders MAT-151 Lesson 149 - Pyramids, Cones, and Spheres MAT-151 Lesson 150 - Applications of Mensuration I MAT-151 Lesson 151 - Applications of Mensuration II MAT-151 Lesson 152 - Collecting and Ordering Data MAT-151 Lesson 153 - Bar Graphs MAT-151 Lesson 154 - Line Graphs MAT-151 Lesson 155 - Circle Graphs MAT-151 Lesson 156 - Mean, Median, Mode, and Range MAT-151 Lesson 157 - The Coordinate Grid I MAT-151 Lesson 158 - The Coordinate Grid II MAT-151 Lesson 159 - Simple Probability I MAT-151 Lesson 160 - Simple Probability II MAT-151 Lesson 161 - Arithmetical Progression MAT-151 Lesson 162 - The Last Term of a Progression MAT-151 Lesson 163 - The Sum of a Progression MAT-151 Lesson 164 - Geometrical Progression MAT-151 Lesson 165 - Terms and Sums of Geometrical Progressions MAT-151 Lesson 166 - Progressions and the Door to Algebra Modern Arithmetic III (Grades 6–8) covers the content of Ray's Higher Arithmetic in 152 lessons, treating the whole subject a third time with the depth and rigor that prepares students for high school Mathematics. 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 Engine, 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 A MATH PROGRAM FOR CLAA STUDENTS I know of no other Arithmetic program like this available anywhere: a complete, text-based Arithmetic program that students can read and study like any other subject. It was produced for CLAA families, to solve a real problem they have faced for years, and it makes Arithmetic what it should always have been in a classical Catholic curriculum — not a strange exception handled by outside programs, but one more subject in which students learn to read, study, memorize, and master. Enrollment will be open shortly in the new CLAA site. God bless, Mr. William C. Michael, O.P. Headmaster Classical Liberal Arts Academy