Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
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.

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  1.    wt: 6:   Advanced Calculus Volume 3 Appendices/
  2.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  3.    wt: 3:   13 Lessons on Limits and Continuity/
  4.    wt: 3:   Volume 3 Why Slopes A Calculus Intro Etc/
  5.    wt: 2:   3 Quadratics Geometrically/
  6.    wt: 2:   13 Vectors/
  7.    wt: 2:   3 Cartesian and Polar Coordinates/
  8.    wt: 2:   3 Prime Factorization Skills/
  9.    wt: 2:   12 Webvideo Lessons on Area and Volume Calculation/
  10.    wt: 2:   4 Lessons on Using Derivatives/
  11.    wt: 2:   38 Lessons on Calculating Derivatives/
  12.    wt: 1:   LAMP Lean Applied Mathematics Program/
  13.    wt: 1:   Volume 1A Regles et modeles/
  14.    wt: 1:   Step 4 Gaussian Elimination/
  15.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  16.    wt: 1:   Step 1 Stick diagram and fractions/
  17.    wt: 1:   3 Solving Linear Equations/
  18.    wt: 1:   C Decimal Multiplication Methods/
  19.    wt: 1:   5 Lessons on Integration/
  20.    wt: 1:   70 Calculus Starter Lessons/
  21.    wt: 1:   Volume 2 Three Skills For Algebra/
  22.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  23.    wt: 1:   Volume 1A Pattern Based Reason/
  24.    wt: 1:   Volume 1 Elements of Reason/
  25.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

177 matches:

  1.    wt: 3:   33 sines and cosines of 2A 3A 4A 5A
  2.    wt: 3:   G.4 Lipschitz Continuity implies EquiContinuity
  3.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  4.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  5.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  6.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  7.    wt: 2:   A Related Material in Volume 3
  8.    wt: 2:   A Related lessons in Volume 3
  9.    wt: 2:   33 Chain Rule Real Player video examples
  10.    wt: 2:   3 Decimal insights for limits continuity convergence
  11.    wt: 2:   Fall 1983 Calculus Appetizer
  12.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  13.    wt: 1:   Skills Chapter 5 Calculus
  14.    wt: 1:   Skills Chapter 3 Algebra
  15.    wt: 1:   3 Euclidean Geometry Leanly
  16.    wt: 1:   05 13 OldSiteEntrancePage
  17.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  18.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  19.    wt: 1:   3 Energy Power Heat08
  20.    wt: 1:   C Energy Power03
  21.    wt: 1:   E Wire Resistance Calculation03
  22.    wt: 1:   3 Like resistors in parallel
  23.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  24.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  25.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  26.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  27.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  28.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  29.    wt: 1:   13 Addition and Addition Tables
  30.    wt: 1:   3 Preparing for Science Studies
  31.    wt: 1:   Ages 3 plus to 4 plus
  32.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  33.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  34.    wt: 1:   sign monoticity analysis example 3
  35.    wt: 1:   23 Inverse Functions
  36.    wt: 1:   13 From one to one to many to one
  37.    wt: 1:   3 Formula or function graphing exercise
  38.    wt: 1:   3 quadratics factoring by inspection
  39.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  40.    wt: 1:   3 Polynomials Multiplication Addition
  41.    wt: 1:   13 cosecant function Definition Graph and Inverse
  42.    wt: 1:   3 Left Inverse of cosine arccos definition
  43.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  44.    wt: 1:   13 Velocity Vectors in Physics
  45.    wt: 1:   3 Navigation with Arrows or Vectors
  46.    wt: 1:   3 graphing y=f(x c) plus K
  47.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  48.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  49.    wt: 1:   32 seven rows of pascals triangle
  50.    wt: 1:   31 basic secant cosecant cotangent trig identities
  51.    wt: 1:   30 unit circle calculation of six trigonometric functions
  52.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  53.    wt: 1:   13 Graph of tangent function many periods
  54.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  55.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  56.    wt: 1:   13 Trig Formulas for dot and cross Products
  57.    wt: 1:   3 Addition Properties
  58.    wt: 1:   3 Trigonometric Ratios sine and cosine
  59.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  60.    wt: 1:   3 Similarity by Design with coordinates
  61.    wt: 1:   3 Slope product for perpendicular lines
  62.    wt: 1:   13 Pythagorean spatial distance formulas
  63.    wt: 1:   3 Rectangular Coordinates Review
  64.    wt: 1:   13 Angle Side Angle Failure
  65.    wt: 1:   3 Isometry of Triangles Congruence
  66.    wt: 1:   3 Lengths and Areas on Maps and Plans
  67.    wt: 1:   23 Distributive Law Two Derivations
  68.    wt: 1:   13 Arrows and Vectors in a Plane
  69.    wt: 1:   3 Location of Point in Decimal Multiplication
  70.    wt: 1:   3 Multiplicative Counting Skills Principles
  71.    wt: 1:   3 Inequalities Algebraically
  72.    wt: 1:   3 Proportionality Examples
  73.    wt: 1:   3 Linear Equation Literal Solution More
  74.    wt: 1:   3 Product Axioms Two Forms
  75.    wt: 1:   3 More and Less Than with Unlike Signs
  76.    wt: 1:   13 Real Number Subtraction
  77.    wt: 1:   3 Fractions
  78.    wt: 1:   3 Geometric Formulas and Function Notation
  79.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  80.    wt: 1:   3 GE III Equation Addition and Multiplication
  81.    wt: 1:   3 Solving triangular system example
  82.    wt: 1:   3 Four Examples
  83.    wt: 1:   3 Two Examples
  84.    wt: 1:   13 Naming Identifying Formulas with Words
  85.    wt: 1:   11 Volume of Sphere
  86.    wt: 1:   10 Volume of Pyramid
  87.    wt: 1:   9 Volume of Cone
  88.    wt: 1:   5 Box Volume Formula Example
  89.    wt: 1:   3 Triangle Area Formula Example
  90.    wt: 1:   3 Counting with Sets etc
  91.    wt: 1:   3 Adding Words To Arithmetic
  92.    wt: 1:   3 Comparison of Negative Numbers
  93.    wt: 1:   3 Properties of Square Roots with example
  94.    wt: 1:   13 GCD from given Prime Factorization
  95.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  96.    wt: 1:   3 Counting with Tables and Trees II
  97.    wt: 1:   3 signed coordinates for maps and planes
  98.    wt: 1:   3 Multiplying Units and Numbers
  99.    wt: 1:   13 Fraction Comparison Algebraic View
  100.    wt: 1:   3 Unit fraction of a fraction
  101.    wt: 1:   13 Subtraction with Additive Inverse
  102.    wt: 1:   3 Adding Movements with same direction
  103.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  104.    wt: 1:   26 Divisibility by 2 3 5 Example
  105.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  106.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  107.    wt: 1:   23 Remainder Arithmetic Modulo 2
  108.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  109.    wt: 1:   21 Remainder Arithmetic Modulo 3
  110.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  111.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  112.    wt: 1:   13 video Factors of 24 using prime
  113.    wt: 1:   10 video Prime Factorization upto 23 squared
  114.    wt: 1:   3 video Primes and Composites from 9 times table
  115.    wt: 1:   Long Division forwards and backwards Example 3
  116.    wt: 1:   3 Division Single Digit Divisor Example
  117.    wt: 1:   3 More One Digit Multipliers
  118.    wt: 1:   1 Why 3 times 5 gives 15
  119.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  120.    wt: 1:   3. How to add with decimals A sans conversions
  121.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  122.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  123.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  124.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  125.    wt: 1:   013 Travel Time Tables
  126.    wt: 1:   3 Units and Lengths of Time
  127.    wt: 1:   Example 2 volume of a cone
  128.    wt: 1:   Example 1 volume of a pyramid
  129.    wt: 1:   Volume of Solid by Cross Sections Lesson
  130.    wt: 1:   Example 3
  131.    wt: 1:   3 Two Chain Rule Method Exercises
  132.    wt: 1:   3 Second derivative test
  133.    wt: 1:   38 Formulas and derivatives for powers and roots
  134.    wt: 1:   36 Cube root derivative animated
  135.    wt: 1:   34 Derivative of exponential function
  136.    wt: 1:   31 Derivatives of inverse functions
  137.    wt: 1:   30Chain Rule A Proof
  138.    wt: 1:   23 Chain Rule in general
  139.    wt: 1:   15 sine and cosine derivatives 3rd step
  140.    wt: 1:   13 sine and cosine derivatives 1st step
  141.    wt: 1:   3 Motivation for Limit Definition Take 2
  142.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  143.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  144.    wt: 1:   9 Limits Continuity and Composition
  145.    wt: 1:   6 Continuity at a point
  146.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  147.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  148.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  149.    wt: 1:   G.3 Constant Difference Theorem Proof
  150.    wt: 1:   F.5a Equicontinuity Theorems
  151.    wt: 1:   F.3 Intermediate Value Theorem
  152.    wt: 1:   B3 Bolzano Weierstrass Theorem
  153.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  154.    wt: 1:   Chapter 23 Links To Trigonometry
  155.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  156.    wt: 1:   Chapter 13. Acceleration
  157.    wt: 1:   Chapter 9 About First Courses in Calculus
  158.    wt: 1:   Chapter 3. Slope Sign Analysis
  159.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  160.    wt: 1:   Chapter 31 Direct and Indirect Reason
  161.    wt: 1:   Chapter 30 Truth Tables
  162.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  163.    wt: 1:   Chapter 23. Notation For Sums
  164.    wt: 1:   Chapter 13. Second Reading Guide
  165.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  166.    wt: 1:   Chapter 3 Chains of Reason
  167.    wt: 1:   Chapter 3 Algebra Difficulties
  168.    wt: 1:   Chapter 23 Truth Tables
  169.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  170.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  171.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  172.    wt: 1:   Chapter 3 Algebra Starter Lessons
  173.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  174.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  175.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  176.    wt: 1:   More Algebra and Slope based Calculus Preview
  177.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

530 matches:

  1.    wt: 9:   G.4 Lipschitz Continuity implies EquiContinuity
  2.    wt: 8:   F.5a Equicontinuity Theorems
  3.    wt: 8:   B3 Bolzano Weierstrass Theorem
  4.    wt: 7:   G.2 Lipshitz Conditions Integration Calculus Reform
  5.    wt: 7:   G.1 First Fundamental Theorem of Calculus
  6.    wt: 7:   G.6 Bounded Derivatives implies Lipshitz Continuity
  7.    wt: 7:   G.3 Constant Difference Theorem Proof
  8.    wt: 7:   F.3 Intermediate Value Theorem
  9.    wt: 7:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  10.    wt: 6:   Postscript One Sided and Intermediate Value Theorems
  11.    wt: 6:   G.5 Motions With Bounded Velocities
  12.    wt: 6:   G.2 Differentiable Functions Mean Value Theorem
  13.    wt: 6:   G.1 Differentiable Functions Rolles Theorem
  14.    wt: 6:   F.5b Extreme Value Theorem
  15.    wt: 6:   F.4 Finite Covering Theorem
  16.    wt: 6:   F.2 Closed Range Theorem
  17.    wt: 6:   F.1 What Functions are Continuous
  18.    wt: 6:   E2 Algebraic Properties of Limits
  19.    wt: 6:   E1 Error Control Inequalities
  20.    wt: 6:   D2 Limits of Monotone Sequences
  21.    wt: 6:   D1 Sets and Sequences GLBs and LGBs
  22.    wt: 6:   C Triangle Inequalities
  23.    wt: 6:   B1 Pigeon Hole Principles from combinatorics
  24.    wt: 6:   PostScript For and Against Decimal Perspectives
  25.    wt: 6:   A1. Introduction
  26.    wt: 5:   3 Solving triangular system example
  27.    wt: 5:   3 Decimal insights for limits continuity convergence
  28.    wt: 5:   Chapter 23 Links To Trigonometry
  29.    wt: 5:   Chapter 13. Acceleration
  30.    wt: 5:   Chapter 3. Slope Sign Analysis
  31.    wt: 5:   Fall 1983 Calculus Appetizer
  32.    wt: 4:   13 Velocity Vectors in Physics
  33.    wt: 4:   3 Navigation with Arrows or Vectors
  34.    wt: 4:   34 sines and cosines of 2A 3A 4A 5A
  35.    wt: 4:   33 sines and cosines of 2A 3A 4A 5A
  36.    wt: 4:   13 Pythagorean spatial distance formulas
  37.    wt: 4:   3 Rectangular Coordinates Review
  38.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  39.    wt: 4:   13 video Factors of 24 using prime
  40.    wt: 4:   3 video Primes and Composites from 9 times table
  41.    wt: 4:   Example 3
  42.    wt: 4:   A Related lessons in Volume 3
  43.    wt: 4:   33 Chain Rule Real Player video examples
  44.    wt: 4:   31 Derivatives of inverse functions
  45.    wt: 4:   13 Limits with Parameters and Derivatives Take II
  46.    wt: 4:   9 Limits Continuity and Composition
  47.    wt: 4:   6 Continuity at a point
  48.    wt: 4:   4 Numerical properties
  49.    wt: 4:   Chapter 14 Limits and Continuity with and sans Decimals
  50.    wt: 4:   Chapter 9 About First Courses in Calculus
  51.    wt: 3:   Skills Chapter 3 Algebra
  52.    wt: 3:   3 quadratics factoring by inspection
  53.    wt: 3:   35 sines and cosines of 2A 3A 4A 5A
  54.    wt: 3:   3 GE III Equation Addition and Multiplication
  55.    wt: 3:   4 Solving a triangular system exercise
  56.    wt: 3:   2 Essentially one exercises three with solution
  57.    wt: 3:   1 Essentially One Unknown
  58.    wt: 3:   3 Four Examples
  59.    wt: 3:   3 Two Examples
  60.    wt: 3:   10 video Prime Factorization upto 23 squared
  61.    wt: 3:   3 More One Digit Multipliers
  62.    wt: 3:   3 More on Groups of 3 Multi Digit Place Value
  63.    wt: 3:   Example 2 volume of a cone
  64.    wt: 3:   Example 1 volume of a pyramid
  65.    wt: 3:   Volume of Solid by Cross Sections Lesson
  66.    wt: 3:   Example 4 with x function of y
  67.    wt: 3:   Example 2
  68.    wt: 3:   Example 1
  69.    wt: 3:   A Related Material in Volume 3
  70.    wt: 3:   3 Second derivative test
  71.    wt: 3:   2 Second derivative test prequel
  72.    wt: 3:   38 Formulas and derivatives for powers and roots
  73.    wt: 3:   36 Cube root derivative animated
  74.    wt: 3:   34 Derivative of exponential function
  75.    wt: 3:   30Chain Rule A Proof
  76.    wt: 3:   23 Chain Rule in general
  77.    wt: 3:   22 Chain Rule for polynomials
  78.    wt: 3:   15 sine and cosine derivatives 3rd step
  79.    wt: 3:   13 sine and cosine derivatives 1st step
  80.    wt: 3:   12 Quotient rule examples
  81.    wt: 3:   5 Product Rule
  82.    wt: 3:   3 Motivation for Limit Definition Take 2
  83.    wt: 3:   1 Fall 1983 Why Slopes Appetizer
  84.    wt: 3:   12 Limits with Parameters and Derivatives Take I
  85.    wt: 3:   11 Limits at infinity Three Examples
  86.    wt: 3:   10 Three one sided limits with infinite values
  87.    wt: 3:   8 Four Animated Examples
  88.    wt: 3:   7 Evaluation by immediate or delayed substitution
  89.    wt: 3:   5 Jumps and absence of unlimited error control
  90.    wt: 3:   2 Algebraic codification
  91.    wt: 3:   1 Numerical introduction
  92.    wt: 3:   Postscript Pythagorean Theorem yet another proof
  93.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  94.    wt: 3:   Chapter 22 Complex Numbers
  95.    wt: 3:   Chapter 21 Arrow Addition
  96.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  97.    wt: 3:   Chapter 19. Exponentials and Natural Logarithms
  98.    wt: 3:   Chapter 18. Slopes Areas Integration
  99.    wt: 3:   Chapter 17. Area Approximation
  100.    wt: 3:   Chapter 16. Velocity Approximation
  101.    wt: 3:   Chapter 15. Slope Approximation
  102.    wt: 3:   Chapter 15. Algebraic Evaluation of Limits
  103.    wt: 3:   Chapter 12. Units and Slopes
  104.    wt: 3:   Chapter 11. Graphing Slope versus Position
  105.    wt: 3:   Chapter 10 Slopes and Units
  106.    wt: 3:   Chapter 8. Slope Interpretation
  107.    wt: 3:   Chapter 7 Slopes and Velocity
  108.    wt: 3:   Chapter 6. Slopes and Vertical Shifts
  109.    wt: 3:   Chapter 5. Slope Sign Tests
  110.    wt: 3:   Chapter 4. More Slope Sign Analysis
  111.    wt: 3:   Chapter 2. Slopes and Ski Trails
  112.    wt: 3:   Chapter 1.Introduction
  113.    wt: 3:   Foreword
  114.    wt: 3:   Chapter 31 Direct and Indirect Reason
  115.    wt: 3:   Chapter 30 Truth Tables
  116.    wt: 3:   Chapter 23. Notation For Sums
  117.    wt: 3:   Chapter 13. Second Reading Guide
  118.    wt: 3:   Chapter 3 Chains of Reason
  119.    wt: 3:   Chapter 3 Algebra Difficulties
  120.    wt: 3:   Chapter 23 Truth Tables
  121.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  122.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  123.    wt: 3:   More Algebra and Slope based Calculus Preview
  124.    wt: 3:   Systematic Algebra Skill Development Missing Links
  125.    wt: 3:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  126.    wt: 2:   Skills Chapter 5 Calculus
  127.    wt: 2:   Ramblings Extrinsic numbers theory
  128.    wt: 2:   Ramblings Introduction Algebra Essay
  129.    wt: 2:   3 Euclidean Geometry Leanly
  130.    wt: 2:   Education Reform Inconsistencies
  131.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  132.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  133.    wt: 2:   C Energy Power03
  134.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  135.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  136.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  137.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  138.    wt: 2:   13 Addition and Addition Tables
  139.    wt: 2:   3 Preparing for Science Studies
  140.    wt: 2:   Ages 3 plus to 4 plus
  141.    wt: 2:   sign monoticity analysis example 3
  142.    wt: 2:   23 Inverse Functions
  143.    wt: 2:   13 From one to one to many to one
  144.    wt: 2:   3 Formula or function graphing exercise
  145.    wt: 2:   A Quadratics Summary
  146.    wt: 2:   10 quadratic exercises
  147.    wt: 2:   9 quadratics physical and further context
  148.    wt: 2:   8 quadratics backward use of various formulas
  149.    wt: 2:   7 quadratic formulla derivation
  150.    wt: 2:   6 quadratics numerical approach
  151.    wt: 2:   5 quadratics completing the square
  152.    wt: 2:   4 quadratics difference of two squares
  153.    wt: 2:   2 quadratics graphing in general
  154.    wt: 2:   1 quadratics graphing exercises
  155.    wt: 2:   Quadratics in 10 steps
  156.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  157.    wt: 2:   3 Circle Arclengh Proportional to Central Angle
  158.    wt: 2:   A Global Time and Navigation
  159.    wt: 2:   15 Dot and Cross Product
  160.    wt: 2:   14 Why Scalar Multiplication Distributes Physical Argument
  161.    wt: 2:   12 From Applied To Pure Mathematics
  162.    wt: 2:   11 Component Method
  163.    wt: 2:   10 Parallelogram Addition Method
  164.    wt: 2:   9 Head to Tail Coordinate View
  165.    wt: 2:   8 Parallel Vectors
  166.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  167.    wt: 2:   6 Vectors with Coordinates
  168.    wt: 2:   5 Head To Tail Arrow Addition
  169.    wt: 2:   4 Resultant of a Sum of Movements
  170.    wt: 2:   2 Signed Coordinates
  171.    wt: 2:   1 Unsigned Coordinates
  172.    wt: 2:   Vector and Complex Number Applet
  173.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  174.    wt: 2:   12 Straight Lines Graphing mx plus b
  175.    wt: 2:   32 seven rows of pascals triangle
  176.    wt: 2:   31 basic secant cosecant cotangent trig identities
  177.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  178.    wt: 2:   13 Trig Formulas for dot and cross Products
  179.    wt: 2:   3 Addition Properties
  180.    wt: 2:   13 Navigation Location from Angles to 2 Landmarks
  181.    wt: 2:   3 Similarity by Design with coordinates
  182.    wt: 2:   3 Slope product for perpendicular lines
  183.    wt: 2:   12 Spatial Coordinates
  184.    wt: 2:   11 Triangle Inequality
  185.    wt: 2:   10 Pythagorean plane distance formula
  186.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  187.    wt: 2:   8 Distance Between Points on a Line
  188.    wt: 2:   7 Complex Numbers Appetizer
  189.    wt: 2:   6 Polar Multiplication and Rotation
  190.    wt: 2:   5 Cartesian Addition and Translation
  191.    wt: 2:   4 Polar Coordinates to and from
  192.    wt: 2:   2 Cartesian Coordinates with signs
  193.    wt: 2:   1 Cartesian Coordinates sans signs
  194.    wt: 2:   13 Angle Side Angle Failure
  195.    wt: 2:   3 Isometry of Triangles Congruence
  196.    wt: 2:   23 Distributive Law Two Derivations
  197.    wt: 2:   3 Multiplicative Counting Skills Principles
  198.    wt: 2:   3 Proportionality Examples
  199.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  200.    wt: 2:   3 Comparison of Negative Numbers
  201.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  202.    wt: 2:   3 Unit fraction of a fraction
  203.    wt: 2:   3 Adding Movements with same direction
  204.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  205.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  206.    wt: 2:   20 Uniqueness of Prime Factorization
  207.    wt: 2:   19 video Prime Factorization Unique
  208.    wt: 2:   18 video Count Factors given Prime Factorization
  209.    wt: 2:   17 Identify and Count Factors using Primes
  210.    wt: 2:   16 video Factors of 980 using prime
  211.    wt: 2:   15 video Factors of 20 using Prime Factorization
  212.    wt: 2:   14 video Factors of 24 Take II
  213.    wt: 2:   12 LCD GCD and LCM using Primes
  214.    wt: 2:   11 Efficient Square Rule Use
  215.    wt: 2:   9 video Prime Factorization upto 19 squared
  216.    wt: 2:   8 video Prime Factorization upto 19
  217.    wt: 2:   7 Calculator Usage Notes and Cautions
  218.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  219.    wt: 2:   5 Prime Factorization and a Square Rule
  220.    wt: 2:   4 video Prime Factorization Introduction
  221.    wt: 2:   2 Prime and Composites less than 16
  222.    wt: 2:   1 video how Products are bigger than factor
  223.    wt: 2:   3 Division Single Digit Divisor Example
  224.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  225.    wt: 2:   1 Why 3 times 5 gives 15
  226.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  227.    wt: 2:   3. How to add with decimals A sans conversions
  228.    wt: 2:   Example 1. Area Between x and x squared
  229.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  230.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  231.    wt: 2:   Area Between Curves Lesson Take 2
  232.    wt: 2:   Area Between Curves Lesson Take 1
  233.    wt: 2:   Summary
  234.    wt: 2:   3 Two Chain Rule Method Exercises
  235.    wt: 2:   4 Second derivative test exercise example
  236.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  237.    wt: 2:   A Chain Rule Real Player video examples
  238.    wt: 2:   29 Chain Rule Optional Reading
  239.    wt: 2:   28 Chain Rule Preparation for a Proof
  240.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  241.    wt: 2:   26 Chain Rule Recognising outer inner functions
  242.    wt: 2:   25 Chain Rule Animated Examples Continued
  243.    wt: 2:   24 Chain Rule Animated Examples
  244.    wt: 2:   21 Chain Rule for powers
  245.    wt: 2:   20 Chain Rule for Pulley Systems
  246.    wt: 2:   19 Chain Rule for linear functions
  247.    wt: 2:   18 Chain Rule Introduction
  248.    wt: 2:   17 Derivatives of quotients of sine and cosine
  249.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  250.    wt: 2:   14 sine and cosine derivatives 2nd step
  251.    wt: 2:   11 Quotient rule
  252.    wt: 2:   10 Power rule for negative integers
  253.    wt: 2:   9 Reciprocal rule
  254.    wt: 2:   8 Differentiation of polynomials
  255.    wt: 2:   7 Animated Differentiation Examples
  256.    wt: 2:   6 Power rule from product rule
  257.    wt: 2:   4 Sum Rule
  258.    wt: 2:   2 Motivation for Limit Definition Take 1
  259.    wt: 2:   Appendix C. How to Read
  260.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  261.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  262.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  263.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  264.    wt: 2:   Postscript A Three Remarks
  265.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  266.    wt: 2:   Chapter 3 Algebra Starter Lessons
  267.    wt: 2:   3 Telling Tracking Time Temporal and More Place Sense
  268.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  269.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  270.    wt: 2:   Implementation Notes
  271.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  272.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  273.    wt: 1:   Appendix 2 primary school Arithmetic 01
  274.    wt: 1:   Appendix 1 primary and preschool mathematic
  275.    wt: 1:   K LAMP Musings Science Education
  276.    wt: 1:   J LAMP Introduction Extrinsic Origins
  277.    wt: 1:   I LAMP Introduction Study Habits
  278.    wt: 1:   H LAMP Introduction Instructional Concepts
  279.    wt: 1:   G LAMP Introduction Problem Solving Skills
  280.    wt: 1:   F LAMP Introduction Prerequisites
  281.    wt: 1:   E LAMP Introduction Modern Mathematics
  282.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  283.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  284.    wt: 1:   A Introduction Objectives
  285.    wt: 1:   Skills Chapter 4 Logic
  286.    wt: 1:   Skills Chapter 2 Geometry
  287.    wt: 1:   Skills Chapter 1 Arithmetic
  288.    wt: 1:   Skills Chapter 0 Introduction
  289.    wt: 1:   permissions for teachers
  290.    wt: 1:   Math Ed if it must be short make it lean effective
  291.    wt: 1:   modern education
  292.    wt: 1:   learning takes time
  293.    wt: 1:   grouping students according to ability
  294.    wt: 1:   what should be learnt and When
  295.    wt: 1:   mathematics in context
  296.    wt: 1:   Postscript 2007 01 10
  297.    wt: 1:   five decades make a difference
  298.    wt: 1:   teaching tutoring algebraic reason
  299.    wt: 1:   the trouble with algebra
  300.    wt: 1:   05 13 OldSiteEntrancePage
  301.    wt: 1:   Theory of Knowledge
  302.    wt: 1:   Different Kinds of Reasoning in maths
  303.    wt: 1:   chapitre 12 00 les iles et division
  304.    wt: 1:   chapitre 07 01 principle D induction mathematique
  305.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  306.    wt: 1:   chapitre 06 00 Chaines de la raison
  307.    wt: 1:   chapitre 05 00 Deception
  308.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  309.    wt: 1:   chapitre 04 09 Regles accidentelles
  310.    wt: 1:   chapitre 04 08 Limitations et benefices
  311.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  312.    wt: 1:   chapitre 04 06 engagements
  313.    wt: 1:   chapitre 04 05 Implication versus suggestion
  314.    wt: 1:   chapitre 04 04 Parlons de la logique
  315.    wt: 1:   chapitre 04 02 Deuxieme enigme
  316.    wt: 1:   chapitre 04 01 Premiere enigme
  317.    wt: 1:   chapitre 04 00 Les regles d implication
  318.    wt: 1:   chapitre 02 00 La Communication des idees
  319.    wt: 1:   chapitre 01 00 Introduction
  320.    wt: 1:   liens
  321.    wt: 1:   3 Energy Power Heat08
  322.    wt: 1:   E Wire Resistance Calculation03
  323.    wt: 1:   A Wire Resistance Qualitative01
  324.    wt: 1:   3 Like resistors in parallel
  325.    wt: 1:   B Electromotive force conventional current01
  326.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  327.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  328.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  329.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  330.    wt: 1:   3 Polynomials Multiplication Addition
  331.    wt: 1:   13 cosecant function Definition Graph and Inverse
  332.    wt: 1:   3 Left Inverse of cosine arccos definition
  333.    wt: 1:   3 graphing y=f(x c) plus K
  334.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  335.    wt: 1:   Straight Lines Intersection of
  336.    wt: 1:   14 Straight Lines Equations General Case
  337.    wt: 1:   11 Straight Lines Graphing y=mx
  338.    wt: 1:   10 Straight Lines through Origin Equations More
  339.    wt: 1:   9 Straight Lines through Origin Equations
  340.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  341.    wt: 1:   30 unit circle calculation of six trigonometric functions
  342.    wt: 1:   24 tangent Angle Difference Formula
  343.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  344.    wt: 1:   15 sine cosine Complementary Angle Relations
  345.    wt: 1:   13 Graph of tangent function many periods
  346.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  347.    wt: 1:   3 Trigonometric Ratios sine and cosine
  348.    wt: 1:   6 Geometric Diagrams in Class
  349.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  350.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  351.    wt: 1:   3 Lengths and Areas on Maps and Plans
  352.    wt: 1:   26 More Less Greater Than Comparison
  353.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  354.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  355.    wt: 1:   22 Multiplication of Signed Numbers
  356.    wt: 1:   13 Arrows and Vectors in a Plane
  357.    wt: 1:   3 Location of Point in Decimal Multiplication
  358.    wt: 1:   3 Inequalities Algebraically
  359.    wt: 1:   3 Linear Equation Literal Solution More
  360.    wt: 1:   3 Product Axioms Two Forms
  361.    wt: 1:   3 More and Less Than with Unlike Signs
  362.    wt: 1:   13 Real Number Subtraction
  363.    wt: 1:   3 Fractions
  364.    wt: 1:   3 Geometric Formulas and Function Notation
  365.    wt: 1:   More Exercises
  366.    wt: 1:   Simple Exercises
  367.    wt: 1:   4 GE III Animated Examples
  368.    wt: 1:   2 GE II Comparison
  369.    wt: 1:   1 GE Substitution four examples
  370.    wt: 1:   6 Algebraic Solution Example
  371.    wt: 1:   5 Algebraic Solutions Introduction
  372.    wt: 1:   4 Four Examples Fractional Coefficients
  373.    wt: 1:   2 Three Examples
  374.    wt: 1:   1 Proper Equal Sign Usage
  375.    wt: 1:   Skill Development Notes
  376.    wt: 1:   10 One Example
  377.    wt: 1:   9 Three Examples
  378.    wt: 1:   8 One Example
  379.    wt: 1:   7 Two Examples
  380.    wt: 1:   6 Three Examples
  381.    wt: 1:   5 Three Examples
  382.    wt: 1:   4 Two Examples
  383.    wt: 1:   2 Three Examples
  384.    wt: 1:   Using Letters for Physical Quantities
  385.    wt: 1:   Formula Usage Show Work Format
  386.    wt: 1:   13 Naming Identifying Formulas with Words
  387.    wt: 1:   11 Volume of Sphere
  388.    wt: 1:   10 Volume of Pyramid
  389.    wt: 1:   9 Volume of Cone
  390.    wt: 1:   5 Box Volume Formula Example
  391.    wt: 1:   3 Triangle Area Formula Example
  392.    wt: 1:   3 Counting with Sets etc
  393.    wt: 1:   3 Adding Words To Arithmetic
  394.    wt: 1:   3 Properties of Square Roots with example
  395.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  396.    wt: 1:   13 GCD from given Prime Factorization
  397.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  398.    wt: 1:   2 Least Common Multiple LCM intro via list method
  399.    wt: 1:   3 Counting with Tables and Trees II
  400.    wt: 1:   3 signed coordinates for maps and planes
  401.    wt: 1:   3 Multiplying Units and Numbers
  402.    wt: 1:   13 Fraction Comparison Algebraic View
  403.    wt: 1:   A Associative Law Theorectical Note
  404.    wt: 1:   13 Subtraction with Additive Inverse
  405.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  406.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  407.    wt: 1:   26 Divisibility by 2 3 5 Example
  408.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  409.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  410.    wt: 1:   23 Remainder Arithmetic Modulo 2
  411.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  412.    wt: 1:   21 Remainder Arithmetic Modulo 3
  413.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  414.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  415.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  416.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  417.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  418.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  419.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  420.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  421.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  422.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  423.    wt: 1:   Long Division Backward
  424.    wt: 1:   Long Division forwards and backwards Example 3
  425.    wt: 1:   D Decimal Multiplication Methods Derived
  426.    wt: 1:   C Counting Areas with Powers of Ten
  427.    wt: 1:   B Powers of Ten
  428.    wt: 1:   A Elementary Basis for Multiplication Methods
  429.    wt: 1:   6 Multiplication Commutes Order Not Important
  430.    wt: 1:   5 Decimal Fraction Multiplication
  431.    wt: 1:   4 Two and Three Digit Multipliers
  432.    wt: 1:   2 One Digit Multipliers
  433.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  434.    wt: 1:   Video Power Notation in Decimal Expansion
  435.    wt: 1:   Subtraction Another Video Lesson
  436.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  437.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  438.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  439.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  440.    wt: 1:   Expression Evaluation how to show work
  441.    wt: 1:   013 Travel Time Tables
  442.    wt: 1:   3 Units and Lengths of Time
  443.    wt: 1:   5 Area Under Curve Exercise
  444.    wt: 1:   4 Definite Integrals Evaluation Exercises
  445.    wt: 1:   2 Indefinite Integrals Exercises
  446.    wt: 1:   1 Chain Rule in Reverse Integration Method
  447.    wt: 1:   Postscript More on Better Performance
  448.    wt: 1:   Postscript For Better Performance
  449.    wt: 1:   Appendix E. How To Study Mathematics and Why
  450.    wt: 1:   Appendix D. What to do in School and Why
  451.    wt: 1:   Appendix B. How To Learn
  452.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  453.    wt: 1:   Chapter 28 Occurrence Tables
  454.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  455.    wt: 1:   Chapter 25. Mathematical Induction Examples
  456.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  457.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  458.    wt: 1:   Chapter 21. Third Reading Guide
  459.    wt: 1:   Chapter 20. Degrees and Radians
  460.    wt: 1:   Chapter 19. Functions and Sets
  461.    wt: 1:   Chapter 18. Rules for Algebra
  462.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  463.    wt: 1:   Chapter 16. Painless Theorem Proving
  464.    wt: 1:   Chapter 15. Solving Linear Equations
  465.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  466.    wt: 1:   Chapter 12. Shorthand Usage Guide
  467.    wt: 1:   Chapter 11. Why Shorthand
  468.    wt: 1:   Chapter 10 Describing and Changing Calculations
  469.    wt: 1:   Postscript What is a Variable
  470.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  471.    wt: 1:   Chapter 8 Three Skills For Algebra
  472.    wt: 1:   Solutions For Arithmetic Exercises
  473.    wt: 1:   Chapter 6 Change of Language
  474.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  475.    wt: 1:   Chapter 4 Longer Chains of Reason
  476.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  477.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  478.    wt: 1:   Foreword
  479.    wt: 1:   Annotated Links to Material Elsehwere
  480.    wt: 1:   Postscript B Mathematics Education References
  481.    wt: 1:   Chapter 12 Four Phases
  482.    wt: 1:   Chapter 11 Elementary Instruction
  483.    wt: 1:   Chapter 10 Transition
  484.    wt: 1:   Chapter 9 The Two Ends
  485.    wt: 1:   Chapter 8 Modern Instruction
  486.    wt: 1:   Chapter 7 Two Treatments of Geometry
  487.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  488.    wt: 1:   Chapter 5 Four References
  489.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  490.    wt: 1:   Chapter 2 For and Against Mathematics
  491.    wt: 1:   Chapter 1 Introduction
  492.    wt: 1:   Foreword
  493.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  494.    wt: 1:   Postscript C Consistency as a Tool for Reason
  495.    wt: 1:   Postscript B More on Story Telling and Reason
  496.    wt: 1:   Postscript A Story Telling
  497.    wt: 1:   Chapter 24 Direct and Indirect Reason
  498.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  499.    wt: 1:   Chapter 21 Occurrence Tables
  500.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  501.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  502.    wt: 1:   Chapter 18 Sense and Knowledge
  503.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  504.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  505.    wt: 1:   Chapter 15 Objective Processes
  506.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  507.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  508.    wt: 1:   Chapter 11 Accidental Patterns
  509.    wt: 1:   Chapter 10 Responsibility
  510.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  511.    wt: 1:   Chapter 8 Change of Language
  512.    wt: 1:   Chapter 7 Longer Chains of Reason
  513.    wt: 1:   Chapter 6 Chains of Reason
  514.    wt: 1:   Chapter 5 Deception
  515.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  516.    wt: 1:   Chapter 2 Skill Development
  517.    wt: 1:   Chapter 1 Introduction
  518.    wt: 1:   Three Remarks
  519.    wt: 1:   Foreword
  520.    wt: 1:   M Words to extend arithmetic
  521.    wt: 1:   C. Domino effect of being careful
  522.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  523.    wt: 1:   Helping the Blind in Logic and Mathematics
  524.    wt: 1:   Mathematics Education References
  525.    wt: 1:   Mathematics Education References
  526.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  527.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  528.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  529.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  530.    wt: 1:   Which Way To Go

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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