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Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
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Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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  1.    wt: 6:   12 Webvideo Lessons on Area and Volume Calculation/
  2.    wt: 6:   5 Lessons on Integration/
  3.    wt: 5:   5 Real Numbers/
  4.    wt: 5:   4 Lessons on Using Derivatives/
  5.    wt: 5:   38 Lessons on Calculating Derivatives/
  6.    wt: 5:   13 Lessons on Limits and Continuity/
  7.    wt: 4:   15 Arc or Inverse Trigonometric Function/
  8.    wt: 4:   5 What is Similarity/
  9.    wt: 4:   10 Examples of Algebraic Reasoning/
  10.    wt: 4:   9 Proportionality Backwards and Forwards/
  11.    wt: 4:   8 Unifying Theme For Algebra/
  12.    wt: 4:   7 Axioms Logic and Equivalent Equations/
  13.    wt: 4:   6 More Less Greater Than Inequalities and Comparison/
  14.    wt: 4:   4 Computation Rules and Function Notation/
  15.    wt: 4:   Step 4 Gaussian Elimination/
  16.    wt: 4:   Step 3 Easy systems in 2 or more unknowns/
  17.    wt: 4:   Step 2 Algebraic solutions for one unknown/
  18.    wt: 4:   Step 1 Stick diagram and fractions/
  19.    wt: 4:   3 Solving Linear Equations/
  20.    wt: 4:   2 Formula Forward Use Evaluation/
  21.    wt: 4:   1 Working With Sets/
  22.    wt: 4:   70 Calculus Starter Lessons/
  23.    wt: 4:   Mathematics 506 Lessons/
  24.    wt: 3:   5 Factored Polynomial Sign Analysis Examples/
  25.    wt: 3:   B Real Numbers Extrinsic Development/
  26.    wt: 3:   A Origins of Counting and Figuring Methods/
  27.    wt: 3:   Algebra Starter Lessons/
  28.    wt: 3:   5 Integers/
  29.    wt: 2:   4 Functions/
  30.    wt: 2:   3 Quadratics Geometrically/
  31.    wt: 2:   2 Natural Logarithms Exponentials Powers Roots/
  32.    wt: 2:   1 Five Polynomial Operations/
  33.    wt: 2:   14 Degrees to Radians and Radians to Degrees/
  34.    wt: 2:   13 Vectors/
  35.    wt: 2:   12 Function Translating and Rescaling/
  36.    wt: 2:   11 Parallel Straight Lines and Transversals/
  37.    wt: 2:   10 Intersecting Straight Lines and Transversals/
  38.    wt: 2:   9 Lines and Slopes Take 2 with tangent function/
  39.    wt: 2:   8 Unit Circle Trigonometry/
  40.    wt: 2:   7 Complex Numbers/
  41.    wt: 2:   6 Trigonometry first steps/
  42.    wt: 2:   4 Lines and Slopes Take 1/
  43.    wt: 2:   3 Cartesian and Polar Coordinates/
  44.    wt: 2:   2 Euclidean Geometry Constructions Theory extras/
  45.    wt: 2:   1 Maps Plans Measurement/
  46.    wt: 2:   Geometry maps plans trigonometry vectors/
  47.    wt: 1:   More Algebra/
  48.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  49.    wt: 1:   11 Squares and Square Roots/
  50.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  51.    wt: 1:   9 Combinatorics Trees Tables and Products/
  52.    wt: 1:   8 Arithmetic with Signed Numbers/
  53.    wt: 1:   7 Arithmetic and Fractions with Units/
  54.    wt: 1:   6 Fractions and Ratios/
  55.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  56.    wt: 1:   3 Prime Factorization Skills/
  57.    wt: 1:   D Decimal Long Division Methods/
  58.    wt: 1:   C Decimal Multiplication Methods/
  59.    wt: 1:   B Decimal Comparing and Subtracting Methods/
  60.    wt: 1:   A Decimal Counting and Adding Methods/
  61.    wt: 1:   2 Arithmetic with Decimals/
  62.    wt: 1:   1 Decimal Place Value/
  63.    wt: 1:   Arithmetic and Number Theory Skills/
  64.    wt: 1:   Time Date Matters/
  65.    wt: 1:   Skills with take home value/
  66.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  67.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  68.    wt: 1:   Resources and Reciprocal Links/

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137 matches:

  1.    wt: 3:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  2.    wt: 2:   Skills Chapter 5 Calculus
  3.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  4.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  5.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  6.    wt: 2:   5 Common Divisors 60 45 via Prime
  7.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  8.    wt: 2:   5 Remainder Arithmetic Modulo 5
  9.    wt: 2:   1 Why 3 times 5 gives 15
  10.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  11.    wt: 2:   Chapter 3 Algebra Starter Lessons
  12.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  13.    wt: 1:   5 logarithms and exponentials etc
  14.    wt: 1:   05 13 OldSiteEntrancePage
  15.    wt: 1:   04 25 when to stop or suspend mathemat
  16.    wt: 1:   chapitre 05 00 Deception
  17.    wt: 1:   chapitre 04 05 Implication versus suggestion
  18.    wt: 1:   E Energy Power05
  19.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  20.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  21.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  22.    wt: 1:   15 Counting For Parents
  23.    wt: 1:   5 Patience Please for Yourself and Your Charges
  24.    wt: 1:   Ages 4 plus to 5 plus
  25.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  26.    wt: 1:   15 Sign analysis of functions
  27.    wt: 1:   5 Function notation for geometric transformations
  28.    wt: 1:   5 quadratics completing the square
  29.    wt: 1:   5 Natural Logarithm Calculator Exercises
  30.    wt: 1:   1 Calculator Starter Exercises
  31.    wt: 1:   7 Links Lessons Elsewhere
  32.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  33.    wt: 1:   15 cosecant function Definition Graph and Inverse
  34.    wt: 1:   5 Swapping Coordinates is a reflection
  35.    wt: 1:   5 Degrees to Radian Measure
  36.    wt: 1:   15 Dot and Cross Product
  37.    wt: 1:   5 Head To Tail Arrow Addition
  38.    wt: 1:   5 Tangent Function Graph
  39.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  40.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  41.    wt: 1:   25 tangent double angle formula Slope connection
  42.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  43.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  44.    wt: 1:   15 sine cosine Complementary Angle Relations
  45.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  46.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  47.    wt: 1:   15 Pythagorean Theorem Converse
  48.    wt: 1:   5 An Easy Proof of the Distributive Law
  49.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  50.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  51.    wt: 1:   12 Links Lessons elsewhere
  52.    wt: 1:   5 Algebraic View of Slopes
  53.    wt: 1:   5 Cartesian Addition and Translation
  54.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  55.    wt: 1:   5 Side Angle Side
  56.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  57.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  58.    wt: 1:   15 Head to Tails in place Addition Associative
  59.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  60.    wt: 1:   5 Distributive Law for Whole Numbers
  61.    wt: 1:   5 Areas of Rectangles Revisited
  62.    wt: 1:   5 Proportionality in Equivalent Fractions
  63.    wt: 1:   5 Triangle Area Formula Backwards
  64.    wt: 1:   5 Equality in Algebra
  65.    wt: 1:   5 Greater More Less Than Signs in General
  66.    wt: 1:   15 Real Number Division
  67.    wt: 1:   5 Rational Numbers More
  68.    wt: 1:   5 Independent versus Dependent Variables
  69.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  70.    wt: 1:   5 Algebraic Solutions Introduction
  71.    wt: 1:   5 Three Examples
  72.    wt: 1:   5 Box Volume Formula Example
  73.    wt: 1:   5 Product Builder Notation
  74.    wt: 1:   5 Talking about Numbers and Quantities
  75.    wt: 1:   5 Square Roots with primes more still
  76.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  77.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  78.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  79.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  80.    wt: 1:   5 lengths and signs of numbers
  81.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  82.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  83.    wt: 1:   5 Equivalent Fractions
  84.    wt: 1:   5 Zero Movement and Additive Inverses
  85.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  86.    wt: 1:   26 Divisibility by 2 3 5 Example
  87.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  88.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  89.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  90.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  91.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  92.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  93.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  94.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  95.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  96.    wt: 1:   15 video Factors of 20 using Prime Factorization
  97.    wt: 1:   5 Prime Factorization and a Square Rule
  98.    wt: 1:   5 Long Division Include Zeroes or not
  99.    wt: 1:   5 Decimal Fraction Multiplication
  100.    wt: 1:   5 A Tip for Efficent Subtraction
  101.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  102.    wt: 1:   5. How to add decimals C. Examples
  103.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  104.    wt: 1:   015 School and work day counting tables
  105.    wt: 1:   5 Conversion Arithmetic
  106.    wt: 1:   5 Area Under Curve Exercise
  107.    wt: 1:   2 Indefinite Integrals Exercises
  108.    wt: 1:   A Related lessons in Volume 3
  109.    wt: 1:   25 Chain Rule Animated Examples Continued
  110.    wt: 1:   15 sine and cosine derivatives 3rd step
  111.    wt: 1:   5 Product Rule
  112.    wt: 1:   5 Jumps and absence of unlimited error control
  113.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  114.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  115.    wt: 1:   G.5 Motions With Bounded Velocities
  116.    wt: 1:   F.5b Extreme Value Theorem
  117.    wt: 1:   F.5a Equicontinuity Theorems
  118.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  119.    wt: 1:   Chapter 15. Slope Approximation
  120.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  121.    wt: 1:   Chapter 9 About First Courses in Calculus
  122.    wt: 1:   Chapter 5. Slope Sign Tests
  123.    wt: 1:   Fall 1983 Calculus Appetizer
  124.    wt: 1:   Chapter 25. Mathematical Induction Examples
  125.    wt: 1:   Chapter 15. Solving Linear Equations
  126.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  127.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  128.    wt: 1:   Chapter 5 Four References
  129.    wt: 1:   Chapter 15 Objective Processes
  130.    wt: 1:   Chapter 5 Deception
  131.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  132.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  133.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  134.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  135.    wt: 1:   More Algebra and Slope based Calculus Preview
  136.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  137.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

881 matches:

  1.    wt: 7:   Example 1 volume of a pyramid
  2.    wt: 7:   Example 1. Area Between x and x squared
  3.    wt: 7:   5 Area Under Curve Exercise
  4.    wt: 7:   3 Two Chain Rule Method Exercises
  5.    wt: 7:   2 Indefinite Integrals Exercises
  6.    wt: 7:   15 sine and cosine derivatives 3rd step
  7.    wt: 7:   5 Jumps and absence of unlimited error control
  8.    wt: 6:   5 Similarity of Circles Squares and Rectangles
  9.    wt: 6:   5 Proportionality in Equivalent Fractions
  10.    wt: 6:   15 Real Number Division
  11.    wt: 6:   5 Rational Numbers More
  12.    wt: 6:   5 Gaussian Elimination for 3 unknowns 2nd example
  13.    wt: 6:   5 Algebraic Solutions Introduction
  14.    wt: 6:   5 Three Examples
  15.    wt: 6:   Example 2 volume of a cone
  16.    wt: 6:   Volume of Solid by Cross Sections Lesson
  17.    wt: 6:   Area Between Crossing Curves Lesson Take 2
  18.    wt: 6:   Area Between Crossing Curves Lesson Take 1
  19.    wt: 6:   Example 4 with x function of y
  20.    wt: 6:   Example 3
  21.    wt: 6:   Example 2
  22.    wt: 6:   Example 1
  23.    wt: 6:   Area Between Curves Lesson Take 2
  24.    wt: 6:   Area Between Curves Lesson Take 1
  25.    wt: 6:   Summary
  26.    wt: 6:   A Related Material in Volume 3
  27.    wt: 6:   4 Definite Integrals Evaluation Exercises
  28.    wt: 6:   1 Chain Rule in Reverse Integration Method
  29.    wt: 6:   A Related lessons in Volume 3
  30.    wt: 6:   4 Second derivative test exercise example
  31.    wt: 6:   26 Chain Rule Recognising outer inner functions
  32.    wt: 6:   25 Chain Rule Animated Examples Continued
  33.    wt: 6:   24 Chain Rule Animated Examples
  34.    wt: 6:   20 Chain Rule for Pulley Systems
  35.    wt: 6:   17 Derivatives of quotients of sine and cosine
  36.    wt: 6:   16 Derivatives of reciprocals of sine and cosine
  37.    wt: 6:   7 Animated Differentiation Examples
  38.    wt: 6:   5 Product Rule
  39.    wt: 6:   13 Limits with Parameters and Derivatives Take II
  40.    wt: 6:   3 Decimal insights for limits continuity convergence
  41.    wt: 5:   15 cosecant function Definition Graph and Inverse
  42.    wt: 5:   5 Swapping Coordinates is a reflection
  43.    wt: 5:   7 Translations Rotations Reflections Dilatations
  44.    wt: 5:   5 Distributive Law for Whole Numbers
  45.    wt: 5:   5 Areas of Rectangles Revisited
  46.    wt: 5:   5 Triangle Area Formula Backwards
  47.    wt: 5:   5 Equality in Algebra
  48.    wt: 5:   5 Greater More Less Than Signs in General
  49.    wt: 5:   16 Real Numbers Comparison
  50.    wt: 5:   14 Real Number Multiplication
  51.    wt: 5:   13 Real Number Subtraction
  52.    wt: 5:   12 Real Number Additive Inverses or Negatives
  53.    wt: 5:   11 Real Number Addition
  54.    wt: 5:   10 Real Number Lengths and Signs
  55.    wt: 5:   9 Coordinates for Regions in Space
  56.    wt: 5:   8 Coordinates for Maps and Planes
  57.    wt: 5:   7 Real Numbers as Line Cordinates
  58.    wt: 5:   6 Unsigned Real Numbers
  59.    wt: 5:   4 Rational Numbers
  60.    wt: 5:   3 Fractions
  61.    wt: 5:   2 Integers
  62.    wt: 5:   1 Whole and Natural Numbers
  63.    wt: 5:   5 Independent versus Dependent Variables
  64.    wt: 5:   More Exercises
  65.    wt: 5:   5 Box Volume Formula Example
  66.    wt: 5:   5 Product Builder Notation
  67.    wt: 5:   5 Zero Movement and Additive Inverses
  68.    wt: 5:   3 Second derivative test
  69.    wt: 5:   2 Second derivative test prequel
  70.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  71.    wt: 5:   A Chain Rule Real Player video examples
  72.    wt: 5:   38 Formulas and derivatives for powers and roots
  73.    wt: 5:   36 Cube root derivative animated
  74.    wt: 5:   34 Derivative of exponential function
  75.    wt: 5:   33 Chain Rule Real Player video examples
  76.    wt: 5:   31 Derivatives of inverse functions
  77.    wt: 5:   30Chain Rule A Proof
  78.    wt: 5:   29 Chain Rule Optional Reading
  79.    wt: 5:   28 Chain Rule Preparation for a Proof
  80.    wt: 5:   27 Chain Rule sinusoidal outer inner functions EGS
  81.    wt: 5:   23 Chain Rule in general
  82.    wt: 5:   22 Chain Rule for polynomials
  83.    wt: 5:   21 Chain Rule for powers
  84.    wt: 5:   19 Chain Rule for linear functions
  85.    wt: 5:   18 Chain Rule Introduction
  86.    wt: 5:   14 sine and cosine derivatives 2nd step
  87.    wt: 5:   13 sine and cosine derivatives 1st step
  88.    wt: 5:   12 Quotient rule examples
  89.    wt: 5:   11 Quotient rule
  90.    wt: 5:   10 Power rule for negative integers
  91.    wt: 5:   9 Reciprocal rule
  92.    wt: 5:   8 Differentiation of polynomials
  93.    wt: 5:   6 Power rule from product rule
  94.    wt: 5:   4 Sum Rule
  95.    wt: 5:   3 Motivation for Limit Definition Take 2
  96.    wt: 5:   2 Motivation for Limit Definition Take 1
  97.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  98.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  99.    wt: 5:   11 Limits at infinity Three Examples
  100.    wt: 5:   10 Three one sided limits with infinite values
  101.    wt: 5:   9 Limits Continuity and Composition
  102.    wt: 5:   8 Four Animated Examples
  103.    wt: 5:   7 Evaluation by immediate or delayed substitution
  104.    wt: 5:   6 Continuity at a point
  105.    wt: 5:   4 Numerical properties
  106.    wt: 5:   2 Algebraic codification
  107.    wt: 5:   1 Numerical introduction
  108.    wt: 4:   25 Absolute Value greatest integer and saw tooth functions
  109.    wt: 4:   15 Sign analysis of functions
  110.    wt: 4:   5 Function notation for geometric transformations
  111.    wt: 4:   5 Natural Logarithm Calculator Exercises
  112.    wt: 4:   16 cotangent function Definition Graph and Inverse
  113.    wt: 4:   14 secant function Definition Graph and Inverse
  114.    wt: 4:   13 cosecant function Definition Graph and Inverse
  115.    wt: 4:   12 motivation for term arctan
  116.    wt: 4:   11 arctan left inverse of tangent Graph
  117.    wt: 4:   10 arctan left inverse of tangent Definition
  118.    wt: 4:   9 motivation for name arcsin
  119.    wt: 4:   8 arcsin left inverse of sine Graph
  120.    wt: 4:   7 arcsin left inverse of sine Definition
  121.    wt: 4:   6 Graph of arccos function
  122.    wt: 4:   4 possible motivation for term arccos
  123.    wt: 4:   3 Left Inverse of cosine arccos definition
  124.    wt: 4:   2 cosine function more properties
  125.    wt: 4:   1 cosine function properties
  126.    wt: 4:   15 Dot and Cross Product
  127.    wt: 4:   Proportionality of Line Segments From Parallel Transversals
  128.    wt: 4:   35 sines and cosines of 2A 3A 4A 5A
  129.    wt: 4:   15 Pythagorean Theorem Converse
  130.    wt: 4:   5 An Easy Proof of the Distributive Law
  131.    wt: 4:   13 Navigation Location from Angles to 2 Landmarks
  132.    wt: 4:   12 Triangles Similarity More Problems
  133.    wt: 4:   11 Triangle Similarity Missing Side Problem
  134.    wt: 4:   10 Similarity of Triangles Equivalent of Two Criteria
  135.    wt: 4:   9 Similarity of Triangles Usual Criteria
  136.    wt: 4:   8 Similarity of Triangles and Polygons
  137.    wt: 4:   6 Geometric Diagrams in Class
  138.    wt: 4:   4 Similarity Definition with Coordinate
  139.    wt: 4:   3 Similarity by Design with coordinates
  140.    wt: 4:   2 Similarity By Design
  141.    wt: 4:   1 Early Concept of Like or Similar Shapes
  142.    wt: 4:   5 Algebraic View of Slopes
  143.    wt: 4:   5 Cartesian Addition and Translation
  144.    wt: 4:   15 Triangle Angle Sum is 180 degrees
  145.    wt: 4:   5 Side Angle Side
  146.    wt: 4:   25 Mid way Convergence to Axiomatic Approach
  147.    wt: 4:   15 Head to Tails in place Addition Associative
  148.    wt: 4:   5 Fractions with Infinite Decimal Expansions
  149.    wt: 4:   4 Fraction Operations Axiomatic Development
  150.    wt: 4:   3 Inequalities Algebraically
  151.    wt: 4:   2 Fraction Operations Physical Development
  152.    wt: 4:   1 Decimals Modular and Remainder Arithmetic
  153.    wt: 4:   4 Rates Ratios and Proporitionality
  154.    wt: 4:   3 Proportionality Examples
  155.    wt: 4:   2 Algebraic View
  156.    wt: 4:   1 What is Proportionality
  157.    wt: 4:   9 Circle Area and Perimeter Formula Backwards Forwards
  158.    wt: 4:   8 Pythagorean Relation Forwards Backwards
  159.    wt: 4:   7 Pythagorean Theorem Chinese Square Proof
  160.    wt: 4:   6 Compound Interest Forward and Backwards
  161.    wt: 4:   4 Rectangle Area and Like Formulas Backwards
  162.    wt: 4:   3 Linear Equation Literal Solution More
  163.    wt: 4:   2 Linear Equation Literal Solution
  164.    wt: 4:   1 Changing Calculations
  165.    wt: 4:   6 Equations and Systems Equivalent or Implied
  166.    wt: 4:   4 Subtraction and Division Axioms
  167.    wt: 4:   3 Product Axioms Two Forms
  168.    wt: 4:   2 Addition and Multiplication Axioms
  169.    wt: 4:   1 Equivalent Computation Rules
  170.    wt: 4:   4 Comparison of Negative Numbers
  171.    wt: 4:   3 More and Less Than with Unlike Signs
  172.    wt: 4:   2 More and Less Than for Counts and Measures
  173.    wt: 4:   1 Real Numbers Comparison
  174.    wt: 4:   4 Changing Letters
  175.    wt: 4:   3 Geometric Formulas and Function Notation
  176.    wt: 4:   2 Computation Rules Evaluation
  177.    wt: 4:   1 Formulas Dependence and Function Notation
  178.    wt: 4:   Simple Exercises
  179.    wt: 4:   4 GE III Animated Examples
  180.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  181.    wt: 4:   3 GE III Equation Addition and Multiplication
  182.    wt: 4:   2 GE II Comparison
  183.    wt: 4:   1 GE Substitution four examples
  184.    wt: 4:   4 Solving a triangular system exercise
  185.    wt: 4:   3 Solving triangular system example
  186.    wt: 4:   2 Essentially one exercises three with solution
  187.    wt: 4:   1 Essentially One Unknown
  188.    wt: 4:   6 Algebraic Solution Example
  189.    wt: 4:   4 Four Examples Fractional Coefficients
  190.    wt: 4:   3 Four Examples
  191.    wt: 4:   2 Three Examples
  192.    wt: 4:   1 Proper Equal Sign Usage
  193.    wt: 4:   Skill Development Notes
  194.    wt: 4:   10 One Example
  195.    wt: 4:   9 Three Examples
  196.    wt: 4:   8 One Example
  197.    wt: 4:   7 Two Examples
  198.    wt: 4:   6 Three Examples
  199.    wt: 4:   4 Two Examples
  200.    wt: 4:   3 Two Examples
  201.    wt: 4:   2 Three Examples
  202.    wt: 4:   Using Letters for Physical Quantities
  203.    wt: 4:   Formula Usage Show Work Format
  204.    wt: 4:   13 Naming Identifying Formulas with Words
  205.    wt: 4:   12 Cone Cylinder Sphere Lesson Idea
  206.    wt: 4:   11 Volume of Sphere
  207.    wt: 4:   10 Volume of Pyramid
  208.    wt: 4:   9 Volume of Cone
  209.    wt: 4:   8 Compound Interest Formula Evaluation
  210.    wt: 4:   7 Compound Interest Formula Introduction
  211.    wt: 4:   6 Pythagorean Hypotenuse Calculation Example
  212.    wt: 4:   4 Circle Area Formula Example
  213.    wt: 4:   3 Triangle Area Formula Example
  214.    wt: 4:   2 Another Rectangle Area Formula Example
  215.    wt: 4:   1 Written work formats for developing and showing skill
  216.    wt: 4:   10 Set View of Wordy Extensions To Arithmetic
  217.    wt: 4:   9 Sets in Probability and Statistics
  218.    wt: 4:   8 Sets of Numbers
  219.    wt: 4:   7 Cautious or Safe Set Construction
  220.    wt: 4:   6 Power Set Notation
  221.    wt: 4:   4 Subset Builder Notation
  222.    wt: 4:   3 Counting with Sets etc
  223.    wt: 4:   2 Venn Diagrams
  224.    wt: 4:   1 Finite Sets
  225.    wt: 4:   5 Talking about Numbers and Quantities
  226.    wt: 4:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  227.    wt: 4:   5 Common Divisors 60 45 via Prime
  228.    wt: 4:   D Remainders Modulo 11 Pair Rule
  229.    wt: 4:   C Divisibility by 11 Integer Recognition Method
  230.    wt: 3:   Skills Chapter 5 Calculus
  231.    wt: 3:   sign monoticity analysis example 4
  232.    wt: 3:   sign monoticity analysis example 3
  233.    wt: 3:   sign monoticity analysis example 2
  234.    wt: 3:   sign monoticity analysis example 1
  235.    wt: 3:   A Quadratics Summary
  236.    wt: 3:   5 quadratics completing the square
  237.    wt: 3:   1 Calculator Starter Exercises
  238.    wt: 3:   7 Links Lessons Elsewhere
  239.    wt: 3:   5 Polynomials Long division Nonlinear divisor
  240.    wt: 3:   5 Degrees to Radian Measure
  241.    wt: 3:   6 Vectors with Coordinates
  242.    wt: 3:   5 Head To Tail Arrow Addition
  243.    wt: 3:   Parallel Lines and Parallel Transversals
  244.    wt: 3:   Triangle Angles Sum To 180 Degrees
  245.    wt: 3:   Parallel Lines and Alternating Corresponding Angles
  246.    wt: 3:   Parallel Lines and Interior Angles
  247.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  248.    wt: 3:   D Straight Lines Slope from Coordinates Examples
  249.    wt: 3:   C Straight Lines Slope from Coordinates
  250.    wt: 3:   B Straight Line Slope Scaling Properties More
  251.    wt: 3:   A Straight Line Slope Scaling Properties
  252.    wt: 3:   14 Straight Lines Equations General Case
  253.    wt: 3:   5 Tangent Function Graph
  254.    wt: 3:   3 Straight Lines Slope as Tangent of Inclination Angle
  255.    wt: 3:   34 sines and cosines of 2A 3A 4A 5A
  256.    wt: 3:   33 sines and cosines of 2A 3A 4A 5A
  257.    wt: 3:   26 Formulas for products of sines and cosines
  258.    wt: 3:   25 tangent double angle formula Slope connection
  259.    wt: 3:   23 sine and cosine of 180 plus 22.5 degrees
  260.    wt: 3:   22 sine of 22.5 degrees via half angle formulas
  261.    wt: 3:   17G Pythagorean Theorem Converse
  262.    wt: 3:   17F Law of cosines
  263.    wt: 3:   17E Trig Formulas for dot and cross Products
  264.    wt: 3:   17D cis formulas for sine cosines and tangent
  265.    wt: 3:   17C sine and cosine double triple angle formulas
  266.    wt: 3:   17B sine cosine Angle Sum Formulas via cis
  267.    wt: 3:   17A The complex number valued trig function cis
  268.    wt: 3:   15 sine cosine Complementary Angle Relations
  269.    wt: 3:   8 period of tangent function
  270.    wt: 3:   5 sines and cosines for reference angle 60 degrees
  271.    wt: 3:   4 sines and cosines for reference angle 45 degrees
  272.    wt: 3:   Unit Circle Development of Trigonometry
  273.    wt: 3:   5 Trigonometric Ratios For Tangent and Special Triangles
  274.    wt: 3:   12 Links Lessons elsewhere
  275.    wt: 3:   PS E Multiplication with Polar Coordinates
  276.    wt: 3:   5 Drawing to Scale Avoids Angle Distortions
  277.    wt: 3:   musings do not puiblish real numbers
  278.    wt: 3:   A Modular and Remainder Arithmetic
  279.    wt: 3:   A Signed Number Arithmetic Review
  280.    wt: 3:   26 More Less Greater Than Comparison
  281.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  282.    wt: 3:   23 Distributive Law Two Derivations
  283.    wt: 3:   22 Multiplication of Signed Numbers
  284.    wt: 3:   21 Addition of Multiples of a Single Vector
  285.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  286.    wt: 3:   19 Signed Multiples of Vectors
  287.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  288.    wt: 3:   17 Arrows Rotate to Reverse with Length Unchanged
  289.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  290.    wt: 3:   14 Vector Head to Tail Sums and Resultants
  291.    wt: 3:   13 Arrows and Vectors in a Plane
  292.    wt: 3:   12 Real Numbers Line Signed Coordinates
  293.    wt: 3:   11 Signed Number Addition and Addition Properties
  294.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  295.    wt: 3:   9 Division with Digits after Decimal Point
  296.    wt: 3:   8 Division and Mulplication of Compound Fractions
  297.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  298.    wt: 3:   6 Infinite Decimals Ending in 9 repeating
  299.    wt: 3:   4 Location of Point in Decimal Addition
  300.    wt: 3:   3 Location of Point in Decimal Multiplication
  301.    wt: 3:   2 Counting Digits in Decimal Multiplication
  302.    wt: 3:   1 Fractions with Finite Decimal Expansions
  303.    wt: 3:   E Long Division Methods more
  304.    wt: 3:   D Long Division Methods
  305.    wt: 3:   C Three Decimal Subtraction Methods
  306.    wt: 3:   B Decimal Comparison and Subtraction
  307.    wt: 3:   A Decimal Addition Columm Methods
  308.    wt: 3:   8 Column Multiplication Methods in General
  309.    wt: 3:   7 Decimals Multiplication Methods Examples
  310.    wt: 3:   6 Column Methods for Decimal Multiplication
  311.    wt: 3:   4 Commutative Law Groups Counting Form
  312.    wt: 3:   3 Multiplicative Counting Skills Principles
  313.    wt: 3:   2 Combing Counts Addition Skills and Principles
  314.    wt: 3:   1 The Counting Origins of Numbers
  315.    wt: 3:   6 Three Notions of What is a Variable
  316.    wt: 3:   4 A Brief Story of numbers and algebra
  317.    wt: 3:   3 Adding Words To Arithmetic
  318.    wt: 3:   2 What is a Variable
  319.    wt: 3:   1 Three Skills For Algebra
  320.    wt: 3:   About Folder Contents
  321.    wt: 3:   16 GCD and LCM of 650 225 via Prime
  322.    wt: 3:   10 Euclid Algorithm with 129 125 and with 45 14
  323.    wt: 3:   5 lengths and signs of numbers
  324.    wt: 3:   5 Reciprocals and Division for Fractions with Units
  325.    wt: 3:   5 Equivalent Fractions
  326.    wt: 3:   B Integer Long Division Multiple Choices
  327.    wt: 3:   A Associative Law Theorectical Note
  328.    wt: 3:   13 Subtraction with Additive Inverse
  329.    wt: 3:   12 Adding Integers More Examples
  330.    wt: 3:   11 Adding Integers Formulas and Examples
  331.    wt: 3:   10 Integer Multiplication Formulas
  332.    wt: 3:   9 Multiplying Integers
  333.    wt: 3:   8 Multiplication by Signed Numbers Integers
  334.    wt: 3:   7 Multiplication by Signs
  335.    wt: 3:   6 Multiplication by Natural Numbers
  336.    wt: 3:   4 Adding Movements wiht opposite directions
  337.    wt: 3:   3 Adding Movements with same direction
  338.    wt: 3:   2 Integers Multiplies of a Unit Moverment
  339.    wt: 3:   1 Integers as Coordinates
  340.    wt: 3:   27 Divisibility by 2 3 6 5 9 10 Example
  341.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  342.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  343.    wt: 3:   5 Remainder Arithmetic Modulo 5
  344.    wt: 3:   15 video Factors of 20 using Prime Factorization
  345.    wt: 3:   5 Prime Factorization and a Square Rule
  346.    wt: 3:   5 Long Division Include Zeroes or not
  347.    wt: 3:   5 Decimal Fraction Multiplication
  348.    wt: 3:   1 Why 3 times 5 gives 15
  349.    wt: 3:   5 A Tip for Efficent Subtraction
  350.    wt: 3:   5. How to add decimals C. Examples
  351.    wt: 3:   5 More on Groups of 3 Place Value in Decimal Fractions
  352.    wt: 3:   Chapter 15. Slope Approximation
  353.    wt: 3:   Chapter 15. Algebraic Evaluation of Limits
  354.    wt: 3:   Chapter 5. Slope Sign Tests
  355.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  356.    wt: 2:   5 logarithms and exponentials etc
  357.    wt: 2:   site origins
  358.    wt: 2:   What to Tell Students
  359.    wt: 2:   E Energy Power05
  360.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  361.    wt: 2:   15 Counting For Parents
  362.    wt: 2:   5 Patience Please for Yourself and Your Charges
  363.    wt: 2:   26 Function definitions done and coming
  364.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  365.    wt: 2:   23 Inverse Functions
  366.    wt: 2:   22 Square Root function graphically
  367.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  368.    wt: 2:   20 Interchanging coordinates a reflection
  369.    wt: 2:   19 Horizontal line rule and method
  370.    wt: 2:   18 Vertical Line Rule and Method
  371.    wt: 2:   17 Function maxima minima and their location
  372.    wt: 2:   16 Increasing or decreasing on intervals
  373.    wt: 2:   14 Surjections Injections Bijections
  374.    wt: 2:   13 From one to one to many to one
  375.    wt: 2:   12 Function Domain Recognition Exercises
  376.    wt: 2:   11 Function Domain Range Source and Targets
  377.    wt: 2:   10 Interval Notation
  378.    wt: 2:   9 Set theory term relation possible origins
  379.    wt: 2:   8 Set view of relations and functions
  380.    wt: 2:   7 Functions with finite domains
  381.    wt: 2:   6 Set Existence Formation and Notation
  382.    wt: 2:   4 Function notation in and beyond mathematics
  383.    wt: 2:   3 Formula or function graphing exercise
  384.    wt: 2:   2 Algebraic use of function notation
  385.    wt: 2:   1 Geometric Introduction of Function Notation
  386.    wt: 2:   Introduction Reading Guide
  387.    wt: 2:   10 quadratic exercises
  388.    wt: 2:   9 quadratics physical and further context
  389.    wt: 2:   8 quadratics backward use of various formulas
  390.    wt: 2:   7 quadratic formulla derivation
  391.    wt: 2:   6 quadratics numerical approach
  392.    wt: 2:   4 quadratics difference of two squares
  393.    wt: 2:   3 quadratics factoring by inspection
  394.    wt: 2:   2 quadratics graphing in general
  395.    wt: 2:   1 quadratics graphing exercises
  396.    wt: 2:   Quadratics in 10 steps
  397.    wt: 2:   11 Growth and Decay in Biology
  398.    wt: 2:   10 Exponential Growth and Decay Models
  399.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  400.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  401.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  402.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  403.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  404.    wt: 2:   2 Square Root Simplification a prequel
  405.    wt: 2:   8 Notes for instructors or tutors
  406.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  407.    wt: 2:   4 Polynomials Long division linear divisor
  408.    wt: 2:   3 Polynomials Multiplication Addition
  409.    wt: 2:   2 Column Multiplication Method
  410.    wt: 2:   1 Polynomials Distributive Law
  411.    wt: 2:   9 Summary Degrees to Radians and back
  412.    wt: 2:   8 Radian Measures of Common Angles
  413.    wt: 2:   7 Radian Measures in special Triangles
  414.    wt: 2:   6 Radian Measure to Degrees
  415.    wt: 2:   4 Circle Sector Area proportional to Central Angle
  416.    wt: 2:   3 Circle Arclengh Proportional to Central Angle
  417.    wt: 2:   2 Radian Measure Numerical Value of one degree
  418.    wt: 2:   1 Degrees and Radians Introduction
  419.    wt: 2:   A Global Time and Navigation
  420.    wt: 2:   14 Why Scalar Multiplication Distributes Physical Argument
  421.    wt: 2:   13 Velocity Vectors in Physics
  422.    wt: 2:   12 From Applied To Pure Mathematics
  423.    wt: 2:   11 Component Method
  424.    wt: 2:   10 Parallelogram Addition Method
  425.    wt: 2:   9 Head to Tail Coordinate View
  426.    wt: 2:   8 Parallel Vectors
  427.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  428.    wt: 2:   4 Resultant of a Sum of Movements
  429.    wt: 2:   3 Navigation with Arrows or Vectors
  430.    wt: 2:   2 Signed Coordinates
  431.    wt: 2:   1 Unsigned Coordinates
  432.    wt: 2:   Vector and Complex Number Applet
  433.    wt: 2:   4 graphing y=Asin(x c)
  434.    wt: 2:   3 graphing y=f(x c) plus K
  435.    wt: 2:   2 Graphing y=Af(x) Vertical Scaling
  436.    wt: 2:   1 graphing y=f(x a)
  437.    wt: 2:   SAS Method For Isometric Or Proportional Triangle Construction
  438.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  439.    wt: 2:   Straight Lines ASA Intersection Study More
  440.    wt: 2:   Straight Lines ASA Intersection Study
  441.    wt: 2:   Straight Lines Instersection Solving Equations
  442.    wt: 2:   Straight Lines Intersection of
  443.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  444.    wt: 2:   12 Straight Lines Graphing mx plus b
  445.    wt: 2:   11 Straight Lines Graphing y=mx
  446.    wt: 2:   10 Straight Lines through Origin Equations More
  447.    wt: 2:   9 Straight Lines through Origin Equations
  448.    wt: 2:   8 Straight Lines Equation for vertical
  449.    wt: 2:   7 Tangent Function is odd on this domain
  450.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  451.    wt: 2:   4 Tangent Function Properties
  452.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  453.    wt: 2:   1 Straight Lines Slope Concept
  454.    wt: 2:   17 tangent function angle sum formulas
  455.    wt: 2:   32 seven rows of pascals triangle
  456.    wt: 2:   31 basic secant cosecant cotangent trig identities
  457.    wt: 2:   30 unit circle calculation of six trigonometric functions
  458.    wt: 2:   29 secant cosecant and cotangent for acute angles
  459.    wt: 2:   28 Expressing products of sines cosines as sums
  460.    wt: 2:   27 Logarithmic use of products of sines and cosines
  461.    wt: 2:   24 tangent Angle Difference Formula
  462.    wt: 2:   21 sine and cosine Half Angle Formulas
  463.    wt: 2:   20 sine and cosine Double Angle Formulas
  464.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  465.    wt: 2:   18 sum of sinusoidal waves as a single wave
  466.    wt: 2:   16 Right Triangle Complementary Angle Relations
  467.    wt: 2:   14 cosine even and sine and tangent are odd
  468.    wt: 2:   13 Graph of tangent function many periods
  469.    wt: 2:   12 Graph of tangent function for one period
  470.    wt: 2:   11 tangent function undefined when terminal side vertical
  471.    wt: 2:   10 Graphs of sines and cosines many periods
  472.    wt: 2:   9 Graphs of sine and cosine over one period
  473.    wt: 2:   7 period of sine and cosine
  474.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  475.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  476.    wt: 2:   2 Quadrant I reference Angles
  477.    wt: 2:   1 Unit Points Reflections Rotations
  478.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  479.    wt: 2:   21 Logarithms Powers and Exponentials
  480.    wt: 2:   20 N th Roots of Complex Numbers
  481.    wt: 2:   19 N th Roots of Unity
  482.    wt: 2:   18 Sixth Roots of Unity
  483.    wt: 2:   17 Cube Roots of unity
  484.    wt: 2:   16 References and Originality Question
  485.    wt: 2:   14 Law of cosines
  486.    wt: 2:   13 Trig Formulas for dot and cross Products
  487.    wt: 2:   12 cis formulas for sine cosines and tangent
  488.    wt: 2:   11 sine and cosine double triple angle formulas
  489.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  490.    wt: 2:   9 The complex number valued trig function cis
  491.    wt: 2:   8 Unit Circle Development of Trigonometry
  492.    wt: 2:   7 Second Way to Calculate Products
  493.    wt: 2:   6 Field Properties of Complex Number
  494.    wt: 2:   4 Multiplication Properties
  495.    wt: 2:   3 Addition Properties
  496.    wt: 2:   2 Complex Numbers made easier we hope
  497.    wt: 2:   1 Rectangular Polar Coordinates Review
  498.    wt: 2:   Appetizer A Complex Number Applet
  499.    wt: 2:   8 Triangles Cascade Problem Solving
  500.    wt: 2:   7 Trignometric Ratios Unit Circle
  501.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  502.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  503.    wt: 2:   3 Trigonometric Ratios sine and cosine
  504.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  505.    wt: 2:   1 Angle Measurement with Degrees
  506.    wt: 2:   Why Trigonometry the whyslopes view
  507.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  508.    wt: 2:   Four Simple Exercises
  509.    wt: 2:   11 A Partial Summary
  510.    wt: 2:   10 Midpoint of [a b] and [b a]
  511.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  512.    wt: 2:   8 Mid Point Formula
  513.    wt: 2:   7 Exercises to test skill and concept mastery
  514.    wt: 2:   6 Intersection of lines by solving linear systems
  515.    wt: 2:   4 Equations for lines three forms
  516.    wt: 2:   3 Slope product for perpendicular lines
  517.    wt: 2:   2 point slope equation for a line
  518.    wt: 2:   1 Numerical view of lines and their equations
  519.    wt: 2:   What is and is not here
  520.    wt: 2:   13 Pythagorean spatial distance formulas
  521.    wt: 2:   12 Spatial Coordinates
  522.    wt: 2:   11 Triangle Inequality
  523.    wt: 2:   10 Pythagorean plane distance formula
  524.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  525.    wt: 2:   8 Distance Between Points on a Line
  526.    wt: 2:   7 Complex Numbers Appetizer
  527.    wt: 2:   6 Polar Multiplication and Rotation
  528.    wt: 2:   4 Polar Coordinates to and from
  529.    wt: 2:   3 Rectangular Coordinates Review
  530.    wt: 2:   2 Cartesian Coordinates with signs
  531.    wt: 2:   1 Cartesian Coordinates sans signs
  532.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  533.    wt: 2:   PS H Distributive Law For Complex Numbers
  534.    wt: 2:   PS G Rotation Distributes over Addition
  535.    wt: 2:   PS F Scalar Multiplication Distributes over Addition
  536.    wt: 2:   PS D Addition with Cartesian Coordinates
  537.    wt: 2:   PS C Similarity Use Recognize it in Trigonometry
  538.    wt: 2:   PS B Parallelogram Construction Methods
  539.    wt: 2:   PS A Kite Construction Methods
  540.    wt: 2:   21 Parallelograms
  541.    wt: 2:   19 Right Triangle Similarity
  542.    wt: 2:   18 Triangle Similarity Take 1
  543.    wt: 2:   17 Right Bisectors of Triangle Sides
  544.    wt: 2:   16 Angles Subtended By Chords and Diameters
  545.    wt: 2:   14 Parallel Lines Postulate
  546.    wt: 2:   13 Angle Side Angle Failure
  547.    wt: 2:   12 Side Angle Side Failure
  548.    wt: 2:   11 Triangle Construction Fails
  549.    wt: 2:   10 Dropping a perpendicular to line
  550.    wt: 2:   9 Construction of a right bisector
  551.    wt: 2:   8 Isoceles Triangles
  552.    wt: 2:   7 Angle Side Angle
  553.    wt: 2:   6 Ruler and compass Angle Bisection
  554.    wt: 2:   4 Side Side Side
  555.    wt: 2:   3 Isometry of Triangles Congruence
  556.    wt: 2:   2 Correspondence between Triangles
  557.    wt: 2:   1 Initial Concepts and Terms
  558.    wt: 2:   Short Course on Euclidean Geometry
  559.    wt: 2:   A Measurement with Ruler Proper Use
  560.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  561.    wt: 2:   6 Figuring with Maps Not to Scale
  562.    wt: 2:   4 Angles on Maps Plans drawn to scale
  563.    wt: 2:   3 Lengths and Areas on Maps and Plans
  564.    wt: 2:   2 Measuring Area Directly
  565.    wt: 2:   1 Length Measurement
  566.    wt: 2:   About Folder Contents
  567.    wt: 2:   5 Square Roots with primes more still
  568.    wt: 2:   2 Square Roots with Prime
  569.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  570.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  571.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  572.    wt: 2:   LCM 60 45 Avoid List Method Use Prime
  573.    wt: 2:   5 Counting with Tables Trees Product Rule Take II
  574.    wt: 2:   1 Counting and Counting Methods I
  575.    wt: 2:   7 Converting or Changing Units
  576.    wt: 2:   6 Simplification of Fractions with Units
  577.    wt: 2:   4 Fractions with Units
  578.    wt: 2:   3 Multiplying Units and Numbers
  579.    wt: 2:   2 Equality and Units
  580.    wt: 2:   1 Addition and Subtraction with Units
  581.    wt: 2:   15 Adding and Subtracting with Unlike Denominators
  582.    wt: 2:   Fraction Operations by Raising Terms A Simple Innovation
  583.    wt: 2:   26 Divisibility by 2 3 5 Example
  584.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  585.    wt: 2:   21 Remainder Arithmetic Modulo 3
  586.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  587.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  588.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  589.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  590.    wt: 2:   8 Remainder Arithmetic Morulo 5 Examples II
  591.    wt: 2:   7 Remainder Arithmetic Modulo 5 Examples I
  592.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  593.    wt: 2:   1 Remainder Arithmetic Modulo 10
  594.    wt: 2:   Division with Counts and Length
  595.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  596.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  597.    wt: 2:   Exact Arithmetic Wholes and Fractions
  598.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  599.    wt: 2:   015 School and work day counting tables
  600.    wt: 2:   5 Conversion Arithmetic
  601.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  602.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  603.    wt: 2:   G.5 Motions With Bounded Velocities
  604.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  605.    wt: 2:   F.5b Extreme Value Theorem
  606.    wt: 2:   F.5a Equicontinuity Theorems
  607.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  608.    wt: 2:   PostScript For and Against Decimal Perspectives
  609.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  610.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  611.    wt: 2:   Chapter 9 About First Courses in Calculus
  612.    wt: 2:   Fall 1983 Calculus Appetizer
  613.    wt: 2:   Chapter 25. Mathematical Induction Examples
  614.    wt: 2:   Chapter 15. Solving Linear Equations
  615.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  616.    wt: 2:   Chapter 5 Four References
  617.    wt: 2:   Chapter 15 Objective Processes
  618.    wt: 2:   Chapter 5 Deception
  619.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  620.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  621.    wt: 2:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  622.    wt: 2:   Chapter 3 Algebra Starter Lessons
  623.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  624.    wt: 2:   More Algebra and Slope based Calculus Preview
  625.    wt: 1:   K LAMP Musings Science Education
  626.    wt: 1:   J LAMP Introduction Extrinsic Origins
  627.    wt: 1:   I LAMP Introduction Study Habits
  628.    wt: 1:   H LAMP Introduction Instructional Concepts
  629.    wt: 1:   G LAMP Introduction Problem Solving Skills
  630.    wt: 1:   F LAMP Introduction Prerequisites
  631.    wt: 1:   E LAMP Introduction Modern Mathematics
  632.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  633.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  634.    wt: 1:   A Introduction Objectives
  635.    wt: 1:   Ramblings Introduction Algebra Essay
  636.    wt: 1:   three goals to set for students
  637.    wt: 1:   site eurekas
  638.    wt: 1:   About site lesson plans
  639.    wt: 1:   key notes and themes
  640.    wt: 1:   Postscript 2007 01 10
  641.    wt: 1:   five decades make a difference
  642.    wt: 1:   Maps Plans Drawings
  643.    wt: 1:   mathematics curriculum shifts
  644.    wt: 1:   Lessening Algebra Difficulties
  645.    wt: 1:   05 13 OldSiteEntrancePage
  646.    wt: 1:   04 25 when to stop or suspend mathemat
  647.    wt: 1:   formal or informal peer review
  648.    wt: 1:   Theory of Knowledge
  649.    wt: 1:   mathematics instruction in general
  650.    wt: 1:   need for a mixed mathematics curriculum
  651.    wt: 1:   words for mathematics instructor
  652.    wt: 1:   chapitre 05 00 Deception
  653.    wt: 1:   chapitre 04 05 Implication versus suggestion
  654.    wt: 1:   C Wire Resistance Calculation01
  655.    wt: 1:   2 Unlike resistors in parallel01
  656.    wt: 1:   D Kirchoff First Law
  657.    wt: 1:   Home Tutoring and Home Schooling
  658.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  659.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  660.    wt: 1:   Ages 6 to 7
  661.    wt: 1:   Ages 4 plus to 5 plus
  662.    wt: 1:   Rewriting algebraic substitution as function substitutions
  663.    wt: 1:   arithmetic videos Real Player Format
  664.    wt: 1:   4 Greater More Less Than Signs in General
  665.    wt: 1:   3 Comparison of Negative Numbers
  666.    wt: 1:   2 More and Less Than with Unlike Signs
  667.    wt: 1:   1 More and Less Than for Counts and Measures
  668.    wt: 1:   4 Square Roots with primes more
  669.    wt: 1:   3 Properties of Square Roots with example
  670.    wt: 1:   1 Squares and Square Roots Introduction
  671.    wt: 1:   13 GCD from given Prime Factorization
  672.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  673.    wt: 1:   8 GCD from Euclidean Algorithm
  674.    wt: 1:   7 GCD and LCM from prime factorization
  675.    wt: 1:   6 GCD from Prime
  676.    wt: 1:   4 LCM of 8 and 10 via Prime
  677.    wt: 1:   2 Least Common Multiple LCM intro via list method
  678.    wt: 1:   1 Least Common Multiples LCM Introduction
  679.    wt: 1:   12 GCD 2700 288 via Prime
  680.    wt: 1:   4 Counting with Trees Product Rule Take I
  681.    wt: 1:   3 Counting with Tables and Trees II
  682.    wt: 1:   2 Counting with Tables and Trees I
  683.    wt: 1:   11 What are real lengths and numbers
  684.    wt: 1:   10 dividing signed numbers
  685.    wt: 1:   9 subtracting signed numbers
  686.    wt: 1:   8 multiplying signed numbers
  687.    wt: 1:   7 negative and additive inverse
  688.    wt: 1:   6 adding signed numbers
  689.    wt: 1:   4 signed coordinates for regions in space
  690.    wt: 1:   3 signed coordinates for maps and planes
  691.    wt: 1:   2 signed and unsigned numbers as coordinates
  692.    wt: 1:   D Three Term Ratios
  693.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  694.    wt: 1:   B Fractions and Two Term Ratios
  695.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  696.    wt: 1:   22 Complex Compound Fractions
  697.    wt: 1:   21 Working With Signs
  698.    wt: 1:   21 Reciprocals for Fractions and Wholes
  699.    wt: 1:   20 Dividing Fractions the Why
  700.    wt: 1:   19 Dividing Fractions How TO
  701.    wt: 1:   18 Efficient Ways to Multiply
  702.    wt: 1:   17 Efficient Ways to Add and Subtract
  703.    wt: 1:   16 Addition Subtraction Comparision Compared
  704.    wt: 1:   14 Adding and Subtracting with Like Denominators
  705.    wt: 1:   13 Fraction Comparison Algebraic View
  706.    wt: 1:   12 Fraction Comparison
  707.    wt: 1:   11 Simplification an Algebraic View
  708.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  709.    wt: 1:   9 Improper Fractions and Mixed Numbers
  710.    wt: 1:   8 Numerals Fractionals Quantals Take II
  711.    wt: 1:   7 Numerals Fractionals Quantals
  712.    wt: 1:   6 Multiplication of Mixed Numbers
  713.    wt: 1:   6 Multiplication Algebraically Take II
  714.    wt: 1:   4 Fraction Multiplication
  715.    wt: 1:   3 Unit fraction of a fraction
  716.    wt: 1:   2 Unit Fraction Multiplication
  717.    wt: 1:   1 What is a fraction Take II
  718.    wt: 1:   1 What is a fraction
  719.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  720.    wt: 1:   23 Remainder Arithmetic Modulo 2
  721.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  722.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  723.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  724.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  725.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  726.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  727.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  728.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  729.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  730.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  731.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  732.    wt: 1:   20 Uniqueness of Prime Factorization
  733.    wt: 1:   19 video Prime Factorization Unique
  734.    wt: 1:   18 video Count Factors given Prime Factorization
  735.    wt: 1:   17 Identify and Count Factors using Primes
  736.    wt: 1:   16 video Factors of 980 using prime
  737.    wt: 1:   14 video Factors of 24 Take II
  738.    wt: 1:   13 video Factors of 24 using prime
  739.    wt: 1:   12 LCD GCD and LCM using Primes
  740.    wt: 1:   11 Efficient Square Rule Use
  741.    wt: 1:   10 video Prime Factorization upto 23 squared
  742.    wt: 1:   9 video Prime Factorization upto 19 squared
  743.    wt: 1:   8 video Prime Factorization upto 19
  744.    wt: 1:   7 Calculator Usage Notes and Cautions
  745.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  746.    wt: 1:   4 video Prime Factorization Introduction
  747.    wt: 1:   3 video Primes and Composites from 9 times table
  748.    wt: 1:   2 Prime and Composites less than 16
  749.    wt: 1:   1 video how Products are bigger than factor
  750.    wt: 1:   Long Division Backwards more
  751.    wt: 1:   Long Division Backward
  752.    wt: 1:   Long Division forwards and backwards Example 3
  753.    wt: 1:   Long Division forwards and backwards Example 2
  754.    wt: 1:   Long Division forwards and backwards Example 1
  755.    wt: 1:   12 Why Long Division Works Take III
  756.    wt: 1:   11 Another Single Digit Divisor Example
  757.    wt: 1:   10 Division by Five Long and Short Ways
  758.    wt: 1:   9 Why Long Division Works Take II
  759.    wt: 1:   8 Correcting the Mistake
  760.    wt: 1:   7 Long Divison Mistake Catching
  761.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  762.    wt: 1:   4 Division with 2 Digit Divsors
  763.    wt: 1:   3 Division Single Digit Divisor Example
  764.    wt: 1:   2 Division with Single Digit Divisors
  765.    wt: 1:   1 Divsion Physical Examples
  766.    wt: 1:   D Decimal Multiplication Methods Derived
  767.    wt: 1:   C Counting Areas with Powers of Ten
  768.    wt: 1:   B Powers of Ten
  769.    wt: 1:   A Elementary Basis for Multiplication Methods
  770.    wt: 1:   6 Multiplication Commutes Order Not Important
  771.    wt: 1:   4 Two and Three Digit Multipliers
  772.    wt: 1:   3 More One Digit Multipliers
  773.    wt: 1:   2 One Digit Multipliers
  774.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  775.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  776.    wt: 1:   Video Power Notation in Decimal Expansion
  777.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  778.    wt: 1:   Subtraction with J Conversions Example
  779.    wt: 1:   Subtraction Another Video Lesson
  780.    wt: 1:   9 22 Minute Subtraction Review Video
  781.    wt: 1:   8 Subtraction with Units of Measure
  782.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  783.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  784.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  785.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  786.    wt: 1:   2 Subtraction Easy Case Examples
  787.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  788.    wt: 1:   8 What skills and work habits to require
  789.    wt: 1:   7 Adding decimal fractions using decimal point
  790.    wt: 1:   6. Counting and adding units and mixed units
  791.    wt: 1:   4. How to add with decimals B with conversions
  792.    wt: 1:   3. How to add with decimals A sans conversions
  793.    wt: 1:   2 Decimal Counting Practices
  794.    wt: 1:   1. Explaining Addition Table
  795.    wt: 1:   11 Place Value SI Standard International way
  796.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  797.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  798.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  799.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  800.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  801.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  802.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  803.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  804.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  805.    wt: 1:   Quick history of numbers and algebra
  806.    wt: 1:   Formula Evaluation how to show work
  807.    wt: 1:   Expression Evaluation how to show work
  808.    wt: 1:   The 20 Times Table
  809.    wt: 1:   The 12 Times Table Visually
  810.    wt: 1:   About folder contents
  811.    wt: 1:   016 Numbering Occidental Calendar Days
  812.    wt: 1:   014 Counting Days with Calendars
  813.    wt: 1:   013 Travel Time Tables
  814.    wt: 1:   012 Division of Time Intervals by Time Intervals
  815.    wt: 1:   011 Division of Time Intervals By Numbers
  816.    wt: 1:   010 Repeated Addition of Time Intervals
  817.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  818.    wt: 1:   8 Addition of Time Intervals via subtotaling
  819.    wt: 1:   7 Addition of Time Intervals
  820.    wt: 1:   6 How long is a million seconds
  821.    wt: 1:   4 Mixing and Changing Units of Time
  822.    wt: 1:   3 Units and Lengths of Time
  823.    wt: 1:   2 Time and Date Matters in School
  824.    wt: 1:   1 Intro of Kids To Time Date Skills
  825.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  826.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  827.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  828.    wt: 1:   G.3 Constant Difference Theorem Proof
  829.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  830.    wt: 1:   F.4 Finite Covering Theorem
  831.    wt: 1:   F.3 Intermediate Value Theorem
  832.    wt: 1:   F.2 Closed Range Theorem
  833.    wt: 1:   F.1 What Functions are Continuous
  834.    wt: 1:   E2 Algebraic Properties of Limits
  835.    wt: 1:   E1 Error Control Inequalities
  836.    wt: 1:   D2 Limits of Monotone Sequences
  837.    wt: 1:   C Triangle Inequalities
  838.    wt: 1:   B3 Bolzano Weierstrass Theorem
  839.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  840.    wt: 1:   A1. Introduction
  841.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  842.    wt: 1:   Chapter 23 Links To Trigonometry
  843.    wt: 1:   Chapter 22 Complex Numbers
  844.    wt: 1:   Chapter 21 Arrow Addition
  845.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  846.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  847.    wt: 1:   Chapter 18. Slopes Areas Integration
  848.    wt: 1:   Chapter 17. Area Approximation
  849.    wt: 1:   Chapter 16. Velocity Approximation
  850.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  851.    wt: 1:   Chapter 13. Acceleration
  852.    wt: 1:   Chapter 12. Units and Slopes
  853.    wt: 1:   Chapter 11. Graphing Slope versus Position
  854.    wt: 1:   Chapter 10 Slopes and Units
  855.    wt: 1:   Chapter 8. Slope Interpretation
  856.    wt: 1:   Chapter 7 Slopes and Velocity
  857.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  858.    wt: 1:   Chapter 4. More Slope Sign Analysis
  859.    wt: 1:   Chapter 3. Slope Sign Analysis
  860.    wt: 1:   Chapter 2. Slopes and Ski Trails
  861.    wt: 1:   Chapter 1.Introduction
  862.    wt: 1:   Foreword
  863.    wt: 1:   Postscript More on Better Performance
  864.    wt: 1:   Postscript For Better Performance
  865.    wt: 1:   Appendix E. How To Study Mathematics and Why
  866.    wt: 1:   Postscript What is a Variable
  867.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  868.    wt: 1:   Annotated Links to Material Elsehwere
  869.    wt: 1:   Postscript A Story Telling
  870.    wt: 1:   O On Learning Mathematics and Science
  871.    wt: 1:   H more Routine to non routine problem solving
  872.    wt: 1:   E. When and how to correct errors
  873.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  874.    wt: 1:   Helping the Blind in Logic and Mathematics
  875.    wt: 1:   Mathematics Education References
  876.    wt: 1:   Mathematics Education References
  877.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  878.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  879.    wt: 1:   Which Way To Go
  880.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  881.    wt: 1:   Road Safety Questions

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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