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
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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:   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:   5 Lessons on Integration/
  11.    wt: 2:   4 Lessons on Using Derivatives/
  12.    wt: 2:   38 Lessons on Calculating Derivatives/
  13.    wt: 1:   LAMP Lean Applied Mathematics Program/
  14.    wt: 1:   Volume 1A Regles et modeles/
  15.    wt: 1:   Step 4 Gaussian Elimination/
  16.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  17.    wt: 1:   Step 1 Stick diagram and fractions/
  18.    wt: 1:   3 Solving Linear Equations/
  19.    wt: 1:   C Decimal Multiplication Methods/
  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

179 matches:

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

Extended Search

530 matches:

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