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

Web Page Search

1104 matches:

  1.    wt: 9:   9 Circle Area and Perimeter Formula Backwards Forwards
  2.    wt: 9:   Long Division forwards and backwards Example 3
  3.    wt: 9:   Chapter 14. Forward and Backward Use of a Formula
  4.    wt: 9:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  5.    wt: 9:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  6.    wt: 8:   33 sines and cosines of 2A 3A 4A 5A
  7.    wt: 8:   13 Pythagorean spatial distance formulas
  8.    wt: 8:   3 Lengths and Areas on Maps and Plans
  9.    wt: 8:   8 Pythagorean Relation Forwards Backwards
  10.    wt: 8:   4 Rectangle Area and Like Formulas Backwards
  11.    wt: 8:   Long Division forwards and backwards Example 2
  12.    wt: 8:   Long Division forwards and backwards Example 1
  13.    wt: 8:   11 Place Value SI Standard International way
  14.    wt: 8:   Chapter 2 Implication Rules Forwards and Backwards
  15.    wt: 8:   Chapter 4 Implication Rules Forwards and Backwards
  16.    wt: 8:   Primary and Secondary Skills and Practices with Take Home Value
  17.    wt: 7:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  18.    wt: 7:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  19.    wt: 7:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  20.    wt: 7:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  21.    wt: 7:   8 quadratics backward use of various formulas
  22.    wt: 7:   3 Natural Logarithms and Exponentials Basic Properties
  23.    wt: 7:   14 Why Scalar Multiplication Distributes Physical Argument
  24.    wt: 7:   Parallel Lines and Parallel Transversals
  25.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  26.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  27.    wt: 7:   18 sum of sinusoidal waves as a single wave
  28.    wt: 7:   13 Navigation Location from Angles to 2 Landmarks
  29.    wt: 7:   4 Angles on Maps Plans drawn to scale
  30.    wt: 7:   5 Triangle Area Formula Backwards
  31.    wt: 7:   3 Gaussian Elimination 3 unknowns first example
  32.    wt: 7:   C Equality for Fractions and Two Term Ratios and Fractions
  33.    wt: 7:   A Similarities between Fractions and Two Term Ratios
  34.    wt: 7:   13 Fraction Comparison Algebraic View
  35.    wt: 7:   3. How to add with decimals A sans conversions
  36.    wt: 7:   13 Limits with Parameters and Derivatives Take II
  37.    wt: 7:   5 Interpreting and Drawing Maps and Plans.
  38.    wt: 7:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  39.    wt: 6:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  40.    wt: 6:   E Wire Resistance Calculation03
  41.    wt: 6:   A Wire Resistance Qualitative01
  42.    wt: 6:   25 Absolute Value greatest integer and saw tooth functions
  43.    wt: 6:   5 Natural Logarithm Calculator Exercises
  44.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  45.    wt: 6:   3 Navigation with Arrows or Vectors
  46.    wt: 6:   Parallel Lines and Alternating Corresponding Angles
  47.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  48.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  49.    wt: 6:   29 secant cosecant and cotangent for acute angles
  50.    wt: 6:   10 Pythagorean plane distance formula
  51.    wt: 6:   5 Cartesian Addition and Translation
  52.    wt: 6:   PS F Scalar Multiplication Distributes over Addition
  53.    wt: 6:   PS D Addition with Cartesian Coordinates
  54.    wt: 6:   5 Drawing to Scale Avoids Angle Distortions
  55.    wt: 6:   25 Mid way Convergence to Axiomatic Approach
  56.    wt: 6:   23 Distributive Law Two Derivations
  57.    wt: 6:   15 Head to Tails in place Addition Associative
  58.    wt: 6:   13 Arrows and Vectors in a Plane
  59.    wt: 6:   6 Compound Interest Forward and Backwards
  60.    wt: 6:   5 Gaussian Elimination for 3 unknowns 2nd example
  61.    wt: 6:   3 Triangle Area Formula Example
  62.    wt: 6:   2 Another Rectangle Area Formula Example
  63.    wt: 6:   3 signed coordinates for maps and planes
  64.    wt: 6:   8 Numerals Fractionals Quantals Take II
  65.    wt: 6:   Fraction Operations by Raising Terms A Simple Innovation
  66.    wt: 6:   A Associative Law Theorectical Note
  67.    wt: 6:   A Decimals Modular and Remainder Arithmetic
  68.    wt: 6:   3 Harder Cases Convert to Compare and Subtract
  69.    wt: 6:   1 Comparison and Subtraction Easy Direct Cases
  70.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  71.    wt: 6:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  72.    wt: 6:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  73.    wt: 6:   5 More on Groups of 3 Place Value in Decimal Fractions
  74.    wt: 6:   4 Groups of 3 Place Value in Decimal Fractions
  75.    wt: 6:   Formula Evaluation how to show work
  76.    wt: 6:   Example 1. Area Between x and x squared
  77.    wt: 6:   38 Formulas and derivatives for powers and roots
  78.    wt: 6:   33 Chain Rule Real Player video examples
  79.    wt: 6:   12 Limits with Parameters and Derivatives Take I
  80.    wt: 6:   Chapter 19. Exponentials and Natural Logarithms
  81.    wt: 6:   Chapter 14 Limits and Continuity with and sans Decimals
  82.    wt: 6:   Appendix E. How To Study Mathematics and Why
  83.    wt: 6:   Chapter 5 Islands and Divisions of Knowledge
  84.    wt: 6:   Chapter 2 For and Against Mathematics
  85.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  86.    wt: 6:   Chapter 14 Deductive and Empirical Views of Mathematics
  87.    wt: 6:   Chapter 12 Islands and Divisions of Knowledge
  88.    wt: 6:   V Reasons and Motivations for Logic and Mathematics
  89.    wt: 6:   P Exact Arithmetic With Whole Numbers and Fractions
  90.    wt: 6:   More Algebra and Slope based Calculus Preview
  91.    wt: 6:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  92.    wt: 6:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  93.    wt: 5:   Appendix 1 primary and preschool mathematic
  94.    wt: 5:   C LAMP Introduction Culture in Mathematics Education
  95.    wt: 5:   Ramblings Introduction Algebra Essay
  96.    wt: 5:   7 logic review and decimals an odd combination
  97.    wt: 5:   Applied Maths Program14092009 POMME variant
  98.    wt: 5:   Maps Plans Drawings
  99.    wt: 5:   chapitre 07 00 Des chaines plus longues de la raison
  100.    wt: 5:   chapitre 06 00 Chaines de la raison
  101.    wt: 5:   chapitre 03 A Propos Des Prochains Chapitre
  102.    wt: 5:   F Wire Resistance Calculation04
  103.    wt: 5:   D Wire Resistance Calculation02
  104.    wt: 5:   C Wire Resistance Calculation01
  105.    wt: 5:   B Wire Resistance Qualitative02
  106.    wt: 5:   25 Mathematics Education Leaving A Good Impression
  107.    wt: 5:   13 Addition and Addition Tables
  108.    wt: 5:   6 Discipline Who is in Charge Conserving Authority
  109.    wt: 5:   sign monoticity analysis example 3
  110.    wt: 5:   17 Function maxima minima and their location
  111.    wt: 5:   6 quadratics numerical approach
  112.    wt: 5:   8 Formulas for Fractional Exponents with Logarithms
  113.    wt: 5:   6 Polynomial Operations and Equivalent Computation Rules
  114.    wt: 5:   5 Swapping Coordinates is a reflection
  115.    wt: 5:   9 Summary Degrees to Radians and back
  116.    wt: 5:   7 Radian Measures in special Triangles
  117.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  118.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  119.    wt: 5:   2 Radian Measure Numerical Value of one degree
  120.    wt: 5:   A Global Time and Navigation
  121.    wt: 5:   5 Head To Tail Arrow Addition
  122.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  123.    wt: 5:   32 seven rows of pascals triangle
  124.    wt: 5:   31 basic secant cosecant cotangent trig identities
  125.    wt: 5:   5 An Easy Proof of the Distributive Law
  126.    wt: 5:   1 Rectangular Polar Coordinates Review
  127.    wt: 5:   5 Trigonometric Ratios For Tangent and Special Triangles
  128.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  129.    wt: 5:   7 Translations Rotations Reflections Dilatations
  130.    wt: 5:   3 Rectangular Coordinates Review
  131.    wt: 5:   PS E Multiplication with Polar Coordinates
  132.    wt: 5:   8 More Use of Maps Not Drawn to Scale
  133.    wt: 5:   A Modular and Remainder Arithmetic
  134.    wt: 5:   17 Arrows Rotate to Reverse with Length Unchanged
  135.    wt: 5:   B Decimal Comparison and Subtraction
  136.    wt: 5:   3 Inequalities Algebraically
  137.    wt: 5:   1 Decimals Modular and Remainder Arithmetic
  138.    wt: 5:   8 Coordinates for Maps and Planes
  139.    wt: 5:   3 GE III Equation Addition and Multiplication
  140.    wt: 5:   Formula Usage Show Work Format
  141.    wt: 5:   13 Naming Identifying Formulas with Words
  142.    wt: 5:   6 Pythagorean Hypotenuse Calculation Example
  143.    wt: 5:   1 Written work formats for developing and showing skill
  144.    wt: 5:   5 Reciprocals and Division for Fractions with Units
  145.    wt: 5:   17 Efficient Ways to Add and Subtract
  146.    wt: 5:   16 Addition Subtraction Comparision Compared
  147.    wt: 5:   15 Adding and Subtracting with Unlike Denominators
  148.    wt: 5:   14 Adding and Subtracting with Like Denominators
  149.    wt: 5:   11 Simplification an Algebraic View
  150.    wt: 5:   7 Numerals Fractionals Quantals
  151.    wt: 5:   6 Multiplication Algebraically Take II
  152.    wt: 5:   1 What is a fraction Take II
  153.    wt: 5:   7 Calculator Usage Notes and Cautions
  154.    wt: 5:   5 Prime Factorization and a Square Rule
  155.    wt: 5:   6 Why Decimal Long Division Methods Works Take I
  156.    wt: 5:   A Elementary Basis for Multiplication Methods
  157.    wt: 5:   Appendix 1 Decimals Comparison Method Take II
  158.    wt: 5:   7 Subtraction for Decimal Fractions with Exercises
  159.    wt: 5:   6 Subtraction with Conversion Example with Exercises
  160.    wt: 5:   4. How to add with decimals B with conversions
  161.    wt: 5:   3 More on Groups of 3 Multi Digit Place Value
  162.    wt: 5:   Exact Arithmetic Wholes and Fractions
  163.    wt: 5:   Expression Evaluation how to show work
  164.    wt: 5:   Practical Methods Ends and Values for Arithmetic
  165.    wt: 5:   9 Comparison and Subtraction of Time Intervals
  166.    wt: 5:   A Related Material in Volume 3
  167.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  168.    wt: 5:   A Chain Rule Real Player video examples
  169.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  170.    wt: 5:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  171.    wt: 5:   Chapter 24 Logarithms Powers and Exponentials
  172.    wt: 5:   Chapter 18. Slopes Areas Integration
  173.    wt: 5:   Chapter 17. Area Approximation
  174.    wt: 5:   Chapter 15. Algebraic Evaluation of Limits
  175.    wt: 5:   Chapter 3. Slope Sign Analysis
  176.    wt: 5:   Chapter 29 Contrapositive and Vacuously True Implications
  177.    wt: 5:   Chapter 26 What is in chapters 27 to 31
  178.    wt: 5:   Chapter 25. Mathematical Induction Examples
  179.    wt: 5:   Chapter 10 Describing and Changing Calculations
  180.    wt: 5:   Annotated Links to Material Elsehwere
  181.    wt: 5:   Chapter 6 Rule Based Reason in Mathematics
  182.    wt: 5:   Chapter 22 Contrapositive and Vacuously True Implications
  183.    wt: 5:   Chapter 16 Origins and Limitations of Rules and Patterns
  184.    wt: 5:   Chapter 3 What is in chapters 4 to 8
  185.    wt: 5:   Q How Logic and Proofs extend Show Work Practices
  186.    wt: 5:   G. Written work formats for developing and showing skill
  187.    wt: 5:   D. Check work a must with a caution
  188.    wt: 5:   Chapter 7 Calculus Previews and Calculus Lightly
  189.    wt: 5:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  190.    wt: 5:   Chapter 4 Logic for Reading Writing and Geometry etc
  191.    wt: 5:   Chapter 3 Algebra Starter Lessons
  192.    wt: 5:   3 Telling Tracking Time Temporal and More Place Sense
  193.    wt: 5:   2 Identifying Size and Position Place and Spatial Sense
  194.    wt: 5:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  195.    wt: 5:   Talking pdf files for online lessons a webvideo alternative
  196.    wt: 4:   E LAMP Introduction Modern Mathematics
  197.    wt: 4:   B LAMP Introduction Curriculum Development Standards
  198.    wt: 4:   Skills Chapter 3 Algebra
  199.    wt: 4:   5 logarithms and exponentials etc
  200.    wt: 4:   what should be learnt and When
  201.    wt: 4:   Secondary Two Mathematics
  202.    wt: 4:   talk the algebra talk
  203.    wt: 4:   teaching tutoring algebraic reason
  204.    wt: 4:   three goals for Mathematics Education
  205.    wt: 4:   standards for course material
  206.    wt: 4:   Operational Viewpoint to Value
  207.    wt: 4:   Education in mathematics science and technology
  208.    wt: 4:   education an empirical art
  209.    wt: 4:   chapitre 04 10 Etapes pour une meilleur raison
  210.    wt: 4:   2 Conductance Resistance Duality02
  211.    wt: 4:   1 Conductance Resistance Duality01
  212.    wt: 4:   3 Like resistors in parallel
  213.    wt: 4:   27 Graduated Correction and Penalties for Young Offenders
  214.    wt: 4:   23 Modularized Skill Development Modularized Rigor Take IV
  215.    wt: 4:   23 Modularized Skill Development Modularized Rigor Take III
  216.    wt: 4:   23 Modularized Skill Development Modularized Rigor Take II
  217.    wt: 4:   16 Secondary Mathematics Tips
  218.    wt: 4:   12 Goals and Objectives For Mathematics
  219.    wt: 4:   5 Patience Please for Yourself and Your Charges
  220.    wt: 4:   Ages 12 to 14 Skills with take home value
  221.    wt: 4:   sign monoticity analysis example 4
  222.    wt: 4:   sign monoticity analysis example 2
  223.    wt: 4:   sign monoticity analysis example 1
  224.    wt: 4:   11 Function Domain Range Source and Targets
  225.    wt: 4:   6 Set Existence Formation and Notation
  226.    wt: 4:   4 Function notation in and beyond mathematics
  227.    wt: 4:   3 Formula or function graphing exercise
  228.    wt: 4:   A Quadratics Summary
  229.    wt: 4:   9 quadratics physical and further context
  230.    wt: 4:   7 quadratic formulla derivation
  231.    wt: 4:   4 quadratics difference of two squares
  232.    wt: 4:   3 quadratics factoring by inspection
  233.    wt: 4:   2 quadratics graphing in general
  234.    wt: 4:   1 quadratics graphing exercises
  235.    wt: 4:   10 Exponential Growth and Decay Models
  236.    wt: 4:   9 Formulas for Real Exponents with Logarithms
  237.    wt: 4:   7 Formulas for Roots with Logarithms Derivation
  238.    wt: 4:   6 Formulas for Even and Odd Roots with Logarithms
  239.    wt: 4:   1 Calculator Starter Exercises
  240.    wt: 4:   5 Polynomials Long division Nonlinear divisor
  241.    wt: 4:   4 Polynomials Long division linear divisor
  242.    wt: 4:   3 Polynomials Multiplication Addition
  243.    wt: 4:   1 Polynomials Distributive Law
  244.    wt: 4:   Rewriting algebraic substitution as function substitutions
  245.    wt: 4:   13 cosecant function Definition Graph and Inverse
  246.    wt: 4:   11 arctan left inverse of tangent Graph
  247.    wt: 4:   8 Radian Measures of Common Angles
  248.    wt: 4:   1 Degrees and Radians Introduction
  249.    wt: 4:   10 Parallelogram Addition Method
  250.    wt: 4:   9 Head to Tail Coordinate View
  251.    wt: 4:   2 Graphing y=Af(x) Vertical Scaling
  252.    wt: 4:   Parallel Lines and Interior Angles
  253.    wt: 4:   SAS Method For Isometric Or Proportional Triangle Construction
  254.    wt: 4:   Analytic View of Triangle Construction or Line Instersection More
  255.    wt: 4:   14 Straight Lines Equations General Case
  256.    wt: 4:   7 Tangent Function is odd on this domain
  257.    wt: 4:   6 Tangent Function Inclination Angle Take 2
  258.    wt: 4:   2 Straight Lines Slopes As Rise Over Run
  259.    wt: 4:   25 tangent double angle formula Slope connection
  260.    wt: 4:   22 sine of 22.5 degrees via half angle formulas
  261.    wt: 4:   21 sine and cosine Half Angle Formulas
  262.    wt: 4:   20 sine and cosine Double Angle Formulas
  263.    wt: 4:   17D cis formulas for sine cosines and tangent
  264.    wt: 4:   17C sine and cosine double triple angle formulas
  265.    wt: 4:   17B sine cosine Angle Sum Formulas via cis
  266.    wt: 4:   16 Right Triangle Complementary Angle Relations
  267.    wt: 4:   14 cosine even and sine and tangent are odd
  268.    wt: 4:   13 Graph of tangent function many periods
  269.    wt: 4:   11 tangent function undefined when terminal side vertical
  270.    wt: 4:   21 Logarithms Powers and Exponentials
  271.    wt: 4:   12 cis formulas for sine cosines and tangent
  272.    wt: 4:   11 sine and cosine double triple angle formulas
  273.    wt: 4:   10 sine cosine Angle Sum Formulas via cis
  274.    wt: 4:   7 Second Way to Calculate Products
  275.    wt: 4:   4 Trigonometric Ratios For Two Special Triangles
  276.    wt: 4:   2 Similar Triangles Equality of Corresponding Side Ratios
  277.    wt: 4:   Why Trigonometry the whyslopes view
  278.    wt: 4:   9 Similarity of Triangles Usual Criteria
  279.    wt: 4:   5 Similarity of Circles Squares and Rectangles
  280.    wt: 4:   3 Similarity by Design with coordinates
  281.    wt: 4:   11 A Partial Summary
  282.    wt: 4:   5 Algebraic View of Slopes
  283.    wt: 4:   1 Numerical view of lines and their equations
  284.    wt: 4:   What is and is not here
  285.    wt: 4:   8 Distance Between Points on a Line
  286.    wt: 4:   6 Polar Multiplication and Rotation
  287.    wt: 4:   2 Cartesian Coordinates with signs
  288.    wt: 4:   1 Cartesian Coordinates sans signs
  289.    wt: 4:   PS H Distributive Law For Complex Numbers
  290.    wt: 4:   PS G Rotation Distributes over Addition
  291.    wt: 4:   PS B Parallelogram Construction Methods
  292.    wt: 4:   13 Angle Side Angle Failure
  293.    wt: 4:   6 Ruler and compass Angle Bisection
  294.    wt: 4:   6 Figuring with Maps Not to Scale
  295.    wt: 4:   26 More Less Greater Than Comparison
  296.    wt: 4:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  297.    wt: 4:   16 Collinear Horizontal Arrows Vectors
  298.    wt: 4:   14 Vector Head to Tail Sums and Resultants
  299.    wt: 4:   9 Division with Digits after Decimal Point
  300.    wt: 4:   8 Division and Mulplication of Compound Fractions
  301.    wt: 4:   7 Arithmetic with Infinite Decimal Expansions
  302.    wt: 4:   5 Fractions with Infinite Decimal Expansions
  303.    wt: 4:   3 Location of Point in Decimal Multiplication
  304.    wt: 4:   1 Fractions with Finite Decimal Expansions
  305.    wt: 4:   5 Distributive Law for Whole Numbers
  306.    wt: 4:   4 Commutative Law Groups Counting Form
  307.    wt: 4:   5 Areas of Rectangles Revisited
  308.    wt: 4:   4 Fraction Operations Axiomatic Development
  309.    wt: 4:   4 Rates Ratios and Proporitionality
  310.    wt: 4:   3 Linear Equation Literal Solution More
  311.    wt: 4:   4 Subtraction and Division Axioms
  312.    wt: 4:   2 Addition and Multiplication Axioms
  313.    wt: 4:   3 More and Less Than with Unlike Signs
  314.    wt: 4:   2 More and Less Than for Counts and Measures
  315.    wt: 4:   1 Whole and Natural Numbers
  316.    wt: 4:   3 Geometric Formulas and Function Notation
  317.    wt: 4:   4 Solving a triangular system exercise
  318.    wt: 4:   3 Solving triangular system example
  319.    wt: 4:   4 Circle Area Formula Example
  320.    wt: 4:   9 Sets in Probability and Statistics
  321.    wt: 4:   6 Three Notions of What is a Variable
  322.    wt: 4:   5 Talking about Numbers and Quantities
  323.    wt: 4:   4 A Brief Story of numbers and algebra
  324.    wt: 4:   3 Adding Words To Arithmetic
  325.    wt: 4:   2 What is a Variable
  326.    wt: 4:   arithmetic videos Real Player Format
  327.    wt: 4:   3 Comparison of Negative Numbers
  328.    wt: 4:   1 More and Less Than for Counts and Measures
  329.    wt: 4:   3 Properties of Square Roots with example
  330.    wt: 4:   1 Squares and Square Roots Introduction
  331.    wt: 4:   10 Euclid Algorithm with 129 125 and with 45 14
  332.    wt: 4:   9 GCD of 360 110 via Primes and Euclid Algorithm
  333.    wt: 4:   2 Least Common Multiple LCM intro via list method
  334.    wt: 4:   3 Counting with Tables and Trees II
  335.    wt: 4:   11 What are real lengths and numbers
  336.    wt: 4:   1 Addition and Subtraction with Units
  337.    wt: 4:   B Fractions and Two Term Ratios
  338.    wt: 4:   21 Reciprocals for Fractions and Wholes
  339.    wt: 4:   10 Simplification of Fractions and Mixed Numerals
  340.    wt: 4:   3 Unit fraction of a fraction
  341.    wt: 4:   1 What is a fraction
  342.    wt: 4:   13 Subtraction with Additive Inverse
  343.    wt: 4:   11 Adding Integers Formulas and Examples
  344.    wt: 4:   3 Adding Movements with same direction
  345.    wt: 4:   13 Remainder Arithmetic Modulo 5 Example
  346.    wt: 4:   10 video Prime Factorization upto 23 squared
  347.    wt: 4:   1 video how Products are bigger than factor
  348.    wt: 4:   Long Division Backwards more
  349.    wt: 4:   Long Division Backward
  350.    wt: 4:   12 Why Long Division Works Take III
  351.    wt: 4:   10 Division by Five Long and Short Ways
  352.    wt: 4:   9 Why Long Division Works Take II
  353.    wt: 4:   7 Long Divison Mistake Catching
  354.    wt: 4:   3 Division Single Digit Divisor Example
  355.    wt: 4:   C Counting Areas with Powers of Ten
  356.    wt: 4:   Video Decimal Multiplication Geometric View Example 2
  357.    wt: 4:   Video Decimal Multiplication Geometric View Example 2
  358.    wt: 4:   Video Power Notation in Decimal Expansion
  359.    wt: 4:   4 Subtraction with Conversions Borrows and Letter J
  360.    wt: 4:   2 Subtraction Easy Case Examples
  361.    wt: 4:   8 What skills and work habits to require
  362.    wt: 4:   7 Adding decimal fractions using decimal point
  363.    wt: 4:   5. How to add decimals C. Examples
  364.    wt: 4:   10 Names for Big Numbers and Powers of Ten Expansion
  365.    wt: 4:   2 Groups of Three Place Value for Multidigit Decimals
  366.    wt: 4:   Quick history of numbers and algebra
  367.    wt: 4:   016 Numbering Occidental Calendar Days
  368.    wt: 4:   015 School and work day counting tables
  369.    wt: 4:   014 Counting Days with Calendars
  370.    wt: 4:   8 Addition of Time Intervals via subtotaling
  371.    wt: 4:   Area Between Crossing Curves Lesson Take 2
  372.    wt: 4:   Area Between Crossing Curves Lesson Take 1
  373.    wt: 4:   Area Between Curves Lesson Take 2
  374.    wt: 4:   Area Between Curves Lesson Take 1
  375.    wt: 4:   4 Definite Integrals Evaluation Exercises
  376.    wt: 4:   3 Two Chain Rule Method Exercises
  377.    wt: 4:   36 Cube root derivative animated
  378.    wt: 4:   28 Chain Rule Preparation for a Proof
  379.    wt: 4:   25 Chain Rule Animated Examples Continued
  380.    wt: 4:   24 Chain Rule Animated Examples
  381.    wt: 4:   7 Animated Differentiation Examples
  382.    wt: 4:   7 Evaluation by immediate or delayed substitution
  383.    wt: 4:   B3 Bolzano Weierstrass Theorem
  384.    wt: 4:   PostScript For and Against Decimal Perspectives
  385.    wt: 4:   Chapter 21 Arrow Addition
  386.    wt: 4:   Chapter 13. Acceleration
  387.    wt: 4:   Chapter 6. Slopes and Vertical Shifts
  388.    wt: 4:   Chapter 4. More Slope Sign Analysis
  389.    wt: 4:   Chapter 2. Slopes and Ski Trails
  390.    wt: 4:   Fall 1983 Calculus Appetizer
  391.    wt: 4:   Appendix D. What to do in School and Why
  392.    wt: 4:   Appendix A. Reading Guide For Next Appendices
  393.    wt: 4:   Chapter 31 Direct and Indirect Reason
  394.    wt: 4:   Chapter 20. Degrees and Radians
  395.    wt: 4:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  396.    wt: 4:   Postscript What is a Variable
  397.    wt: 4:   Chapter 9 Talking about Numbers or Quantities
  398.    wt: 4:   Chapter 7 Prep for Calculus Arithmetic Exercises
  399.    wt: 4:   Chapter 6 Change of Language
  400.    wt: 4:   Chapter 3 Chains of Reason
  401.    wt: 4:   Chapter 4 Complex Numbers and Why Slopes
  402.    wt: 4:   Chapter 3 Algebra Difficulties
  403.    wt: 4:   Postscript C Consistency as a Tool for Reason
  404.    wt: 4:   Chapter 19 What is in chapters 20 to 24
  405.    wt: 4:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  406.    wt: 4:   Chapter 11 Accidental Patterns
  407.    wt: 4:   Chapter 9 What is in Chapters 10 to 18
  408.    wt: 4:   Chapter 8 Change of Language
  409.    wt: 4:   S Adding words to algebra
  410.    wt: 4:   R Why Learn Mathematics Skills
  411.    wt: 4:   O On Learning Mathematics and Science
  412.    wt: 4:   J. More on written work and showing skill
  413.    wt: 4:   Appendix A Calculus with Proofs for Keen or Gifted
  414.    wt: 4:   Chapter 6 More Algebra and Geometry
  415.    wt: 4:   6 Measuring via counting or arithmetic the role of fractions
  416.    wt: 4:   4 Money Matters Saving Earning Buying Selling and Budgets
  417.    wt: 4:   Multiple Ways to Improve Mathematics Skill Development
  418.    wt: 4:   Systematic Algebra Skill Development Missing Links
  419.    wt: 3:   Appendix 2 primary school Arithmetic 01
  420.    wt: 3:   I LAMP Introduction Study Habits
  421.    wt: 3:   H LAMP Introduction Instructional Concepts
  422.    wt: 3:   F LAMP Introduction Prerequisites
  423.    wt: 3:   8 analytic geometry etc
  424.    wt: 3:   3 Euclidean Geometry Leanly
  425.    wt: 3:   which way to go
  426.    wt: 3:   Teach the teachers plus goals
  427.    wt: 3:   Math Ed if it must be short make it lean effective
  428.    wt: 3:   Mathematics Education Professors
  429.    wt: 3:   five decades make a difference
  430.    wt: 3:   how letters appear
  431.    wt: 3:   Secondary Three Mathematics
  432.    wt: 3:   Secondary One Mathematics
  433.    wt: 3:   geometric implications for algebra
  434.    wt: 3:   the trouble with algebra
  435.    wt: 3:   05 13 OldSiteEntrancePage
  436.    wt: 3:   04 29 New Mathematics Curriculum
  437.    wt: 3:   04 25 when to stop or suspend mathemat
  438.    wt: 3:   02 20 mathematics education references
  439.    wt: 3:   three aims for mathematics students
  440.    wt: 3:   formal or informal peer review
  441.    wt: 3:   mathematics instruction in general
  442.    wt: 3:   three kinds of reason in mathematics
  443.    wt: 3:   Four ways to improve education reform
  444.    wt: 3:   need for a mixed mathematics curriculum
  445.    wt: 3:   Leaner mathematics curriculum
  446.    wt: 3:   words for mathematics instructor
  447.    wt: 3:   chapitre 07 01 principle D induction mathematique
  448.    wt: 3:   chapitre 04 04 Parlons de la logique
  449.    wt: 3:   chapitre 02 00 La Communication des idees
  450.    wt: 3:   Trois Notions qui menent a algebre
  451.    wt: 3:   3 Energy Power Heat08
  452.    wt: 3:   2 Unlike resistors in parallel01
  453.    wt: 3:   24 Standards For Skill Develoment Take II
  454.    wt: 3:   23 Modularized Skill Development Modularized Rigor
  455.    wt: 3:   19 Extending the Oral Dimension of Mathematics
  456.    wt: 3:   18 Primary School Mathematics
  457.    wt: 3:   17 Math Booklets for children and young teenagers
  458.    wt: 3:   14 Multiplication and Times Tables
  459.    wt: 3:   4 Learning Takes Time and Effort
  460.    wt: 3:   2 Reading and Writing Skills
  461.    wt: 3:   22 Square Root function graphically
  462.    wt: 3:   20 Interchanging coordinates a reflection
  463.    wt: 3:   16 Increasing or decreasing on intervals
  464.    wt: 3:   15 Sign analysis of functions
  465.    wt: 3:   8 Set view of relations and functions
  466.    wt: 3:   5 Function notation for geometric transformations
  467.    wt: 3:   2 Algebraic use of function notation
  468.    wt: 3:   10 quadratic exercises
  469.    wt: 3:   5 quadratics completing the square
  470.    wt: 3:   Quadratics in 10 steps
  471.    wt: 3:   11 Growth and Decay in Biology
  472.    wt: 3:   2 Square Root Simplification a prequel
  473.    wt: 3:   16 cotangent function Definition Graph and Inverse
  474.    wt: 3:   15 cosecant function Definition Graph and Inverse
  475.    wt: 3:   14 secant function Definition Graph and Inverse
  476.    wt: 3:   12 motivation for term arctan
  477.    wt: 3:   10 arctan left inverse of tangent Definition
  478.    wt: 3:   9 motivation for name arcsin
  479.    wt: 3:   6 Radian Measure to Degrees
  480.    wt: 3:   5 Degrees to Radian Measure
  481.    wt: 3:   12 From Applied To Pure Mathematics
  482.    wt: 3:   Straight Lines ASA Intersection Study More
  483.    wt: 3:   Straight Lines ASA Intersection Study
  484.    wt: 3:   D Straight Lines Slope from Coordinates Examples
  485.    wt: 3:   A Straight Line Slope Scaling Properties
  486.    wt: 3:   13 Straight Lines Finding Equations from 2 points
  487.    wt: 3:   8 Straight Lines Equation for vertical
  488.    wt: 3:   17 tangent function angle sum formulas
  489.    wt: 3:   30 unit circle calculation of six trigonometric functions
  490.    wt: 3:   24 tangent Angle Difference Formula
  491.    wt: 3:   19 Pythagorean Identity For sine and cosine functions
  492.    wt: 3:   17A The complex number valued trig function cis
  493.    wt: 3:   15 sine cosine Complementary Angle Relations
  494.    wt: 3:   10 Graphs of sines and cosines many periods
  495.    wt: 3:   6 sines and cosines for reference angle 30 degrees
  496.    wt: 3:   3 sines and cosines for reference angle 90 degrees
  497.    wt: 3:   2 Quadrant I reference Angles
  498.    wt: 3:   13 Trig Formulas for dot and cross Products
  499.    wt: 3:   2 Complex Numbers made easier we hope
  500.    wt: 3:   Appetizer A Complex Number Applet
  501.    wt: 3:   8 Triangles Cascade Problem Solving
  502.    wt: 3:   3 Trigonometric Ratios sine and cosine
  503.    wt: 3:   1 Angle Measurement with Degrees
  504.    wt: 3:   11 Triangle Similarity Missing Side Problem
  505.    wt: 3:   8 Similarity of Triangles and Polygons
  506.    wt: 3:   6 Geometric Diagrams in Class
  507.    wt: 3:   4 Similarity Definition with Coordinate
  508.    wt: 3:   1 Early Concept of Like or Similar Shapes
  509.    wt: 3:   10 Midpoint of [a b] and [b a]
  510.    wt: 3:   7 Exercises to test skill and concept mastery
  511.    wt: 3:   12 Spatial Coordinates
  512.    wt: 3:   9 Pythagorean Theorem Chinese Square Proof
  513.    wt: 3:   4 Polar Coordinates to and from
  514.    wt: 3:   21 Parallelograms
  515.    wt: 3:   18 Triangle Similarity Take 1
  516.    wt: 3:   16 Angles Subtended By Chords and Diameters
  517.    wt: 3:   15 Triangle Angle Sum is 180 degrees
  518.    wt: 3:   14 Parallel Lines Postulate
  519.    wt: 3:   3 Isometry of Triangles Congruence
  520.    wt: 3:   A Measurement with Ruler Proper Use
  521.    wt: 3:   2 Measuring Area Directly
  522.    wt: 3:   A Signed Number Arithmetic Review
  523.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  524.    wt: 3:   11 Signed Number Addition and Addition Properties
  525.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  526.    wt: 3:   4 Location of Point in Decimal Addition
  527.    wt: 3:   A Decimal Addition Columm Methods
  528.    wt: 3:   7 Decimals Multiplication Methods Examples
  529.    wt: 3:   2 Fraction Operations Physical Development
  530.    wt: 3:   5 Proportionality in Equivalent Fractions
  531.    wt: 3:   3 Proportionality Examples
  532.    wt: 3:   2 Algebraic View
  533.    wt: 3:   1 What is Proportionality
  534.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  535.    wt: 3:   2 Linear Equation Literal Solution
  536.    wt: 3:   1 Changing Calculations
  537.    wt: 3:   6 Equations and Systems Equivalent or Implied
  538.    wt: 3:   5 Equality in Algebra
  539.    wt: 3:   3 Product Axioms Two Forms
  540.    wt: 3:   5 Greater More Less Than Signs in General
  541.    wt: 3:   4 Comparison of Negative Numbers
  542.    wt: 3:   1 Real Numbers Comparison
  543.    wt: 3:   16 Real Numbers Comparison
  544.    wt: 3:   13 Real Number Subtraction
  545.    wt: 3:   12 Real Number Additive Inverses or Negatives
  546.    wt: 3:   7 Real Numbers as Line Cordinates
  547.    wt: 3:   2 Computation Rules Evaluation
  548.    wt: 3:   1 Formulas Dependence and Function Notation
  549.    wt: 3:   4 GE III Animated Examples
  550.    wt: 3:   2 Essentially one exercises three with solution
  551.    wt: 3:   6 Algebraic Solution Example
  552.    wt: 3:   5 Algebraic Solutions Introduction
  553.    wt: 3:   4 Four Examples Fractional Coefficients
  554.    wt: 3:   3 Two Examples
  555.    wt: 3:   8 Compound Interest Formula Evaluation
  556.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  557.    wt: 3:   3 Counting with Sets etc
  558.    wt: 3:   4 Greater More Less Than Signs in General
  559.    wt: 3:   2 More and Less Than with Unlike Signs
  560.    wt: 3:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  561.    wt: 3:   13 GCD from given Prime Factorization
  562.    wt: 3:   7 GCD and LCM from prime factorization
  563.    wt: 3:   5 Counting with Tables Trees Product Rule Take II
  564.    wt: 3:   2 Counting with Tables and Trees I
  565.    wt: 3:   7 negative and additive inverse
  566.    wt: 3:   2 signed and unsigned numbers as coordinates
  567.    wt: 3:   6 Simplification of Fractions with Units
  568.    wt: 3:   12 Fraction Comparison
  569.    wt: 3:   6 Multiplication by Natural Numbers
  570.    wt: 3:   27 Divisibility by 2 3 6 5 9 10 Example
  571.    wt: 3:   26 Divisibility by 2 3 5 Example
  572.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  573.    wt: 3:   23 Remainder Arithmetic Modulo 2
  574.    wt: 3:   22 Remainder Arithmetic Modulo 3 more
  575.    wt: 3:   21 Remainder Arithmetic Modulo 3
  576.    wt: 3:   16 Remainder Arithmetic Modulo 9 Example 2
  577.    wt: 3:   15 Remainder Arithmetic Modulo 9 Example
  578.    wt: 3:   14 Remainder Arithmetic Modulo 9 Example
  579.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  580.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  581.    wt: 3:   10 Remainder Arithmetic Long Division by 5 Quickly
  582.    wt: 3:   9 Remainder Arithmetic Divisibility by 5
  583.    wt: 3:   8 Remainder Arithmetic Morulo 5 Examples II
  584.    wt: 3:   7 Remainder Arithmetic Modulo 5 Examples I
  585.    wt: 3:   4 Remainder Arithmetic Modulo 10 in general
  586.    wt: 3:   3 Remainder Arithmetic Modulos 10 more still
  587.    wt: 3:   18 video Count Factors given Prime Factorization
  588.    wt: 3:   15 video Factors of 20 using Prime Factorization
  589.    wt: 3:   9 video Prime Factorization upto 19 squared
  590.    wt: 3:   6 Sieve of Eratosthenes and Square Rule
  591.    wt: 3:   4 video Prime Factorization Introduction
  592.    wt: 3:   3 video Primes and Composites from 9 times table
  593.    wt: 3:   Division with Counts and Length
  594.    wt: 3:   11 Another Single Digit Divisor Example
  595.    wt: 3:   2 Division with Single Digit Divisors
  596.    wt: 3:   5 Decimal Fraction Multiplication
  597.    wt: 3:   Appendix 2 Three Decimal Subtraction Methods
  598.    wt: 3:   Subtraction with J Conversions Example
  599.    wt: 3:   8 Subtraction with Units of Measure
  600.    wt: 3:   6. Counting and adding units and mixed units
  601.    wt: 3:   1. Explaining Addition Table
  602.    wt: 3:   8 Review Lesson 1 2 4 and 6 All in One
  603.    wt: 3:   1 Place Value in Three Digit Whole Numbers
  604.    wt: 3:   The 12 Times Table Visually
  605.    wt: 3:   013 Travel Time Tables
  606.    wt: 3:   012 Division of Time Intervals by Time Intervals
  607.    wt: 3:   010 Repeated Addition of Time Intervals
  608.    wt: 3:   6 How long is a million seconds
  609.    wt: 3:   2 Time and Date Matters in School
  610.    wt: 3:   Example 1 volume of a pyramid
  611.    wt: 3:   5 Area Under Curve Exercise
  612.    wt: 3:   A Related lessons in Volume 3
  613.    wt: 3:   4 Second derivative test exercise example
  614.    wt: 3:   34 Derivative of exponential function
  615.    wt: 3:   30Chain Rule A Proof
  616.    wt: 3:   29 Chain Rule Optional Reading
  617.    wt: 3:   23 Chain Rule in general
  618.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  619.    wt: 3:   15 sine and cosine derivatives 3rd step
  620.    wt: 3:   13 sine and cosine derivatives 1st step
  621.    wt: 3:   3 Motivation for Limit Definition Take 2
  622.    wt: 3:   8 Four Animated Examples
  623.    wt: 3:   5 Jumps and absence of unlimited error control
  624.    wt: 3:   2 Algebraic codification
  625.    wt: 3:   Postscript One Sided and Intermediate Value Theorems
  626.    wt: 3:   G.2 Lipshitz Conditions Integration Calculus Reform
  627.    wt: 3:   G.1 First Fundamental Theorem of Calculus
  628.    wt: 3:   G.2 Differentiable Functions Mean Value Theorem
  629.    wt: 3:   F.3 Intermediate Value Theorem
  630.    wt: 3:   Postscript Pythagorean Theorem yet another proof
  631.    wt: 3:   Chapter 16. Velocity Approximation
  632.    wt: 3:   Chapter 15. Slope Approximation
  633.    wt: 3:   Chapter 12. Units and Slopes
  634.    wt: 3:   Chapter 10 Slopes and Units
  635.    wt: 3:   Chapter 9 About First Courses in Calculus
  636.    wt: 3:   Chapter 7 Slopes and Velocity
  637.    wt: 3:   Appendix C. How to Read
  638.    wt: 3:   Appendix B. How To Learn
  639.    wt: 3:   Chapter 30 Truth Tables
  640.    wt: 3:   Chapter 27 Shorthand Symbols as Pronouns
  641.    wt: 3:   Chapter 24. Personal Investment and Pension EGS
  642.    wt: 3:   Chapter 23. Notation For Sums
  643.    wt: 3:   Chapter 18. Rules for Algebra
  644.    wt: 3:   Chapter 15. Solving Linear Equations
  645.    wt: 3:   Postscript Unifying Theme A Fourth Skill For Algebra
  646.    wt: 3:   Chapter 13. Second Reading Guide
  647.    wt: 3:   Chapter 12. Shorthand Usage Guide
  648.    wt: 3:   Chapter 11. Why Shorthand
  649.    wt: 3:   Chapter 8 Three Skills For Algebra
  650.    wt: 3:   Chapter 4 Longer Chains of Reason
  651.    wt: 3:   Chapter 1 Introduction to Chapters 2 to 6
  652.    wt: 3:   Postscript B Mathematics Education References
  653.    wt: 3:   Chapter 7 Two Treatments of Geometry
  654.    wt: 3:   Chapter 24 Direct and Indirect Reason
  655.    wt: 3:   Chapter 23 Truth Tables
  656.    wt: 3:   Chapter 20 Shorthand Symbols as Pronouns
  657.    wt: 3:   Chapter 18 Sense and Knowledge
  658.    wt: 3:   Chapter 7 Longer Chains of Reason
  659.    wt: 3:   Chapter 6 Chains of Reason
  660.    wt: 3:   N Mathematics Prepare for College Studies
  661.    wt: 3:   L Skills with take home value
  662.    wt: 3:   N Improving Marks on Tests and Finals
  663.    wt: 3:   I. Logic and language skills
  664.    wt: 3:   H Jigsaw puzzles and problem solving
  665.    wt: 3:   E. When and how to correct errors
  666.    wt: 3:   Chapter 8 Skipped Topics and Why
  667.    wt: 3:   7 Games and Activities for Instruction
  668.    wt: 3:   1 From Number Recognition and Counting to Arithmetic A
  669.    wt: 3:   Helping the Blind in Logic and Mathematics
  670.    wt: 3:   Mathematics Education References
  671.    wt: 3:   Mathematics Education References
  672.    wt: 3:   Ends Values Methods For Skill Development Framework Prequel
  673.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  674.    wt: 3:   Which Way To Go
  675.    wt: 2:   K LAMP Musings Science Education
  676.    wt: 2:   J LAMP Introduction Extrinsic Origins
  677.    wt: 2:   G LAMP Introduction Problem Solving Skills
  678.    wt: 2:   A Introduction Objectives
  679.    wt: 2:   Skills Chapter 5 Calculus
  680.    wt: 2:   Skills Chapter 1 Arithmetic
  681.    wt: 2:   Skills Chapter 0 Introduction
  682.    wt: 2:   11 pure mathematics
  683.    wt: 2:   10 statistics
  684.    wt: 2:   9 combinatorics probability sets
  685.    wt: 2:   6 polynomials etc
  686.    wt: 2:   4 algebra
  687.    wt: 2:   2 arithmetic with signed numbers
  688.    wt: 2:   1 arithmetic with unsigned numbers
  689.    wt: 2:   What is POMME
  690.    wt: 2:   website reviews
  691.    wt: 2:   permissions for teachers
  692.    wt: 2:   About site lesson plans
  693.    wt: 2:   teacher certification
  694.    wt: 2:   learning takes time
  695.    wt: 2:   grouping students according to ability
  696.    wt: 2:   mathematics in context
  697.    wt: 2:   Education Reform Inconsistencies
  698.    wt: 2:   teaching tips
  699.    wt: 2:   mathematics curriculum shifts
  700.    wt: 2:   Lessening Algebra Difficulties
  701.    wt: 2:   02 21 words for teachers
  702.    wt: 2:   Different Kinds of Reasoning in maths
  703.    wt: 2:   How to be a better instructor
  704.    wt: 2:   Motivation and Context Problem
  705.    wt: 2:   Prequel In For A Penny In For A Pound
  706.    wt: 2:   fairness and inductive principles for instruction
  707.    wt: 2:   chapitre 12 00 les iles et division
  708.    wt: 2:   chapitre 04 09 Regles accidentelles
  709.    wt: 2:   chapitre 04 08 Limitations et benefices
  710.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  711.    wt: 2:   chapitre 04 06 engagements
  712.    wt: 2:   chapitre 04 05 Implication versus suggestion
  713.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  714.    wt: 2:   chapitre 04 00 Les regles d implication
  715.    wt: 2:   chapitre 01 00 Introduction
  716.    wt: 2:   problemes algebre et arithmetique
  717.    wt: 2:   4 Energy Power Heat09
  718.    wt: 2:   2 Energy Power Heat07
  719.    wt: 2:   1 Energy Power Heat06
  720.    wt: 2:   C Energy Power03
  721.    wt: 2:   A Energy Power01
  722.    wt: 2:   E Kirchoffs Second Law
  723.    wt: 2:   D Kirchoff First Law
  724.    wt: 2:   24 Standards For Skill Develoment
  725.    wt: 2:   22 Student Centered Highschool Mathematics
  726.    wt: 2:   11 Help and Defend Your Child or Teens Education
  727.    wt: 2:   10 Ends values for work study instruction
  728.    wt: 2:   9 Streaming by Student Cooperation
  729.    wt: 2:   8 The Effect of Negative Remarks
  730.    wt: 2:   3 Preparing for Science Studies
  731.    wt: 2:   Ages 12 to 14 Arithmetic
  732.    wt: 2:   Ages 10 to 12 Arithmetic
  733.    wt: 2:   Ages 3 plus to 4 plus
  734.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  735.    wt: 2:   19 Horizontal line rule and method
  736.    wt: 2:   18 Vertical Line Rule and Method
  737.    wt: 2:   13 From one to one to many to one
  738.    wt: 2:   12 Function Domain Recognition Exercises
  739.    wt: 2:   10 Interval Notation
  740.    wt: 2:   7 Functions with finite domains
  741.    wt: 2:   1 Geometric Introduction of Function Notation
  742.    wt: 2:   Introduction Reading Guide
  743.    wt: 2:   8 arcsin left inverse of sine Graph
  744.    wt: 2:   6 Graph of arccos function
  745.    wt: 2:   4 possible motivation for term arccos
  746.    wt: 2:   3 Left Inverse of cosine arccos definition
  747.    wt: 2:   8 Parallel Vectors
  748.    wt: 2:   6 Vectors with Coordinates
  749.    wt: 2:   4 Resultant of a Sum of Movements
  750.    wt: 2:   Vector and Complex Number Applet
  751.    wt: 2:   4 graphing y=Asin(x c)
  752.    wt: 2:   3 graphing y=f(x c) plus K
  753.    wt: 2:   1 graphing y=f(x a)
  754.    wt: 2:   Triangle Angles Sum To 180 Degrees
  755.    wt: 2:   Straight Lines Instersection Solving Equations
  756.    wt: 2:   C Straight Lines Slope from Coordinates
  757.    wt: 2:   B Straight Line Slope Scaling Properties More
  758.    wt: 2:   12 Straight Lines Graphing mx plus b
  759.    wt: 2:   11 Straight Lines Graphing y=mx
  760.    wt: 2:   10 Straight Lines through Origin Equations More
  761.    wt: 2:   9 Straight Lines through Origin Equations
  762.    wt: 2:   5 Tangent Function Graph
  763.    wt: 2:   27 Logarithmic use of products of sines and cosines
  764.    wt: 2:   26 Formulas for products of sines and cosines
  765.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  766.    wt: 2:   17G Pythagorean Theorem Converse
  767.    wt: 2:   17F Law of cosines
  768.    wt: 2:   17E Trig Formulas for dot and cross Products
  769.    wt: 2:   12 Graph of tangent function for one period
  770.    wt: 2:   9 Graphs of sine and cosine over one period
  771.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  772.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  773.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  774.    wt: 2:   16 References and Originality Question
  775.    wt: 2:   15 Pythagorean Theorem Converse
  776.    wt: 2:   14 Law of cosines
  777.    wt: 2:   9 The complex number valued trig function cis
  778.    wt: 2:   3 Addition Properties
  779.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  780.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  781.    wt: 2:   12 Triangles Similarity More Problems
  782.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  783.    wt: 2:   3 Slope product for perpendicular lines
  784.    wt: 2:   2 point slope equation for a line
  785.    wt: 2:   11 Triangle Inequality
  786.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  787.    wt: 2:   PS C Similarity Use Recognize it in Trigonometry
  788.    wt: 2:   PS A Kite Construction Methods
  789.    wt: 2:   19 Right Triangle Similarity
  790.    wt: 2:   17 Right Bisectors of Triangle Sides
  791.    wt: 2:   12 Side Angle Side Failure
  792.    wt: 2:   11 Triangle Construction Fails
  793.    wt: 2:   10 Dropping a perpendicular to line
  794.    wt: 2:   9 Construction of a right bisector
  795.    wt: 2:   8 Isoceles Triangles
  796.    wt: 2:   7 Angle Side Angle
  797.    wt: 2:   2 Correspondence between Triangles
  798.    wt: 2:   1 Initial Concepts and Terms
  799.    wt: 2:   musings do not puiblish real numbers
  800.    wt: 2:   21 Addition of Multiples of a Single Vector
  801.    wt: 2:   12 Real Numbers Line Signed Coordinates
  802.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  803.    wt: 2:   2 Counting Digits in Decimal Multiplication
  804.    wt: 2:   C Three Decimal Subtraction Methods
  805.    wt: 2:   8 Column Multiplication Methods in General
  806.    wt: 2:   6 Column Methods for Decimal Multiplication
  807.    wt: 2:   3 Multiplicative Counting Skills Principles
  808.    wt: 2:   2 Combing Counts Addition Skills and Principles
  809.    wt: 2:   1 Equivalent Computation Rules
  810.    wt: 2:   15 Real Number Division
  811.    wt: 2:   14 Real Number Multiplication
  812.    wt: 2:   11 Real Number Addition
  813.    wt: 2:   10 Real Number Lengths and Signs
  814.    wt: 2:   9 Coordinates for Regions in Space
  815.    wt: 2:   5 Rational Numbers More
  816.    wt: 2:   4 Rational Numbers
  817.    wt: 2:   3 Fractions
  818.    wt: 2:   2 GE II Comparison
  819.    wt: 2:   1 Essentially One Unknown
  820.    wt: 2:   3 Four Examples
  821.    wt: 2:   1 Proper Equal Sign Usage
  822.    wt: 2:   7 Two Examples
  823.    wt: 2:   4 Two Examples
  824.    wt: 2:   Using Letters for Physical Quantities
  825.    wt: 2:   7 Compound Interest Formula Introduction
  826.    wt: 2:   5 Box Volume Formula Example
  827.    wt: 2:   7 Cautious or Safe Set Construction
  828.    wt: 2:   6 Power Set Notation
  829.    wt: 2:   2 Venn Diagrams
  830.    wt: 2:   1 Three Skills For Algebra
  831.    wt: 2:   5 Square Roots with primes more still
  832.    wt: 2:   4 Square Roots with primes more
  833.    wt: 2:   2 Square Roots with Prime
  834.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  835.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  836.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  837.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  838.    wt: 2:   8 GCD from Euclidean Algorithm
  839.    wt: 2:   5 Common Divisors 60 45 via Prime
  840.    wt: 2:   4 LCM of 8 and 10 via Prime
  841.    wt: 2:   LCM 60 45 Avoid List Method Use Prime
  842.    wt: 2:   1 Least Common Multiples LCM Introduction
  843.    wt: 2:   4 Counting with Trees Product Rule Take I
  844.    wt: 2:   4 signed coordinates for regions in space
  845.    wt: 2:   4 Fractions with Units
  846.    wt: 2:   3 Multiplying Units and Numbers
  847.    wt: 2:   2 Equality and Units
  848.    wt: 2:   21 Working With Signs
  849.    wt: 2:   20 Dividing Fractions the Why
  850.    wt: 2:   19 Dividing Fractions How TO
  851.    wt: 2:   18 Efficient Ways to Multiply
  852.    wt: 2:   9 Improper Fractions and Mixed Numbers
  853.    wt: 2:   5 Equivalent Fractions
  854.    wt: 2:   4 Fraction Multiplication
  855.    wt: 2:   2 Unit Fraction Multiplication
  856.    wt: 2:   D Remainders Modulo 11 Pair Rule
  857.    wt: 2:   12 Adding Integers More Examples
  858.    wt: 2:   10 Integer Multiplication Formulas
  859.    wt: 2:   5 Zero Movement and Additive Inverses
  860.    wt: 2:   4 Adding Movements wiht opposite directions
  861.    wt: 2:   1 Integers as Coordinates
  862.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  863.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  864.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  865.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  866.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  867.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  868.    wt: 2:   5 Remainder Arithmetic Modulo 5
  869.    wt: 2:   2 Remainder Arithmetic Modulo 10 more
  870.    wt: 2:   1 Remainder Arithmetic Modulo 10
  871.    wt: 2:   20 Uniqueness of Prime Factorization
  872.    wt: 2:   19 video Prime Factorization Unique
  873.    wt: 2:   17 Identify and Count Factors using Primes
  874.    wt: 2:   14 video Factors of 24 Take II
  875.    wt: 2:   13 video Factors of 24 using prime
  876.    wt: 2:   8 video Prime Factorization upto 19
  877.    wt: 2:   2 Prime and Composites less than 16
  878.    wt: 2:   8 Correcting the Mistake
  879.    wt: 2:   4 Division with 2 Digit Divsors
  880.    wt: 2:   1 Divsion Physical Examples
  881.    wt: 2:   D Decimal Multiplication Methods Derived
  882.    wt: 2:   6 Multiplication Commutes Order Not Important
  883.    wt: 2:   4 Two and Three Digit Multipliers
  884.    wt: 2:   1 Why 3 times 5 gives 15
  885.    wt: 2:   Subtraction Another Video Lesson
  886.    wt: 2:   9 22 Minute Subtraction Review Video
  887.    wt: 2:   5 A Tip for Efficent Subtraction
  888.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  889.    wt: 2:   2 Decimal Counting Practices
  890.    wt: 2:   011 Division of Time Intervals By Numbers
  891.    wt: 2:   7 Addition of Time Intervals
  892.    wt: 2:   4 Mixing and Changing Units of Time
  893.    wt: 2:   3 Units and Lengths of Time
  894.    wt: 2:   1 Intro of Kids To Time Date Skills
  895.    wt: 2:   Example 2 volume of a cone
  896.    wt: 2:   Example 4 with x function of y
  897.    wt: 2:   Example 3
  898.    wt: 2:   2 Indefinite Integrals Exercises
  899.    wt: 2:   1 Chain Rule in Reverse Integration Method
  900.    wt: 2:   3 Second derivative test
  901.    wt: 2:   31 Derivatives of inverse functions
  902.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  903.    wt: 2:   26 Chain Rule Recognising outer inner functions
  904.    wt: 2:   22 Chain Rule for polynomials
  905.    wt: 2:   21 Chain Rule for powers
  906.    wt: 2:   19 Chain Rule for linear functions
  907.    wt: 2:   18 Chain Rule Introduction
  908.    wt: 2:   17 Derivatives of quotients of sine and cosine
  909.    wt: 2:   14 sine and cosine derivatives 2nd step
  910.    wt: 2:   10 Power rule for negative integers
  911.    wt: 2:   8 Differentiation of polynomials
  912.    wt: 2:   2 Motivation for Limit Definition Take 1
  913.    wt: 2:   11 Limits at infinity Three Examples
  914.    wt: 2:   10 Three one sided limits with infinite values
  915.    wt: 2:   6 Continuity at a point
  916.    wt: 2:   3 Decimal insights for limits continuity convergence
  917.    wt: 2:   1 Numerical introduction
  918.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  919.    wt: 2:   G.3 Constant Difference Theorem Proof
  920.    wt: 2:   F.1 What Functions are Continuous
  921.    wt: 2:   E2 Algebraic Properties of Limits
  922.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  923.    wt: 2:   C Triangle Inequalities
  924.    wt: 2:   A1. Introduction
  925.    wt: 2:   Chapter 23 Links To Trigonometry
  926.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  927.    wt: 2:   Chapter 11. Graphing Slope versus Position
  928.    wt: 2:   Chapter 8. Slope Interpretation
  929.    wt: 2:   Chapter 1.Introduction
  930.    wt: 2:   Chapter 28 Occurrence Tables
  931.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  932.    wt: 2:   Chapter 21. Third Reading Guide
  933.    wt: 2:   Chapter 19. Functions and Sets
  934.    wt: 2:   Chapter 16. Painless Theorem Proving
  935.    wt: 2:   Solutions For Arithmetic Exercises
  936.    wt: 2:   Postscript A Three Remarks
  937.    wt: 2:   Chapter 12 Four Phases
  938.    wt: 2:   Chapter 11 Elementary Instruction
  939.    wt: 2:   Chapter 10 Transition
  940.    wt: 2:   Chapter 9 The Two Ends
  941.    wt: 2:   Chapter 1 Introduction
  942.    wt: 2:   Postscript D Reflections on Law of the Excluded Middle
  943.    wt: 2:   Postscript B More on Story Telling and Reason
  944.    wt: 2:   Chapter 21 Occurrence Tables
  945.    wt: 2:   Chapter 1 Introduction
  946.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  947.    wt: 2:   M Words to extend arithmetic
  948.    wt: 2:   F. The student teacher tutor feedback loop
  949.    wt: 2:   A. Skill has to be seen to believed
  950.    wt: 2:   How to Build Skills and Confidence
  951.    wt: 2:   Chapter 2 Why Sets
  952.    wt: 2:   Chapter 1 Arithmetic
  953.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  954.    wt: 2:   Road Safety Questions
  955.    wt: 2:   The Math Forum and Site Content
  956.    wt: 1:   Skills Chapter 4 Logic
  957.    wt: 1:   Ramblings Extrinsic numbers theory
  958.    wt: 1:   Skills Chapter 2 Geometry
  959.    wt: 1:   why bother
  960.    wt: 1:   three goals to set for students
  961.    wt: 1:   activities for students
  962.    wt: 1:   links Education Resources online
  963.    wt: 1:   site eurekas
  964.    wt: 1:   key notes and themes
  965.    wt: 1:   modern education
  966.    wt: 1:   What to Tell Students
  967.    wt: 1:   Theory of Knowledge
  968.    wt: 1:   cultivating intelligence
  969.    wt: 1:   chapitre 05 00 Deception
  970.    wt: 1:   chapitre 04 02 Deuxieme enigme
  971.    wt: 1:   chapitre 04 01 Premiere enigme
  972.    wt: 1:   deux definitions pour variable
  973.    wt: 1:   E Energy Power05
  974.    wt: 1:   D Energy Power04
  975.    wt: 1:   B Energy Power02
  976.    wt: 1:   1 Like resistors in series
  977.    wt: 1:   F Unlike Resistors in Series
  978.    wt: 1:   C Electromotive force conventional current02
  979.    wt: 1:   B Electromotive force conventional current01
  980.    wt: 1:   A Circuit Elements
  981.    wt: 1:   Home Tutoring and Home Schooling
  982.    wt: 1:   15 Counting For Parents
  983.    wt: 1:   7 Student Motivation
  984.    wt: 1:   1 Speaking Skills
  985.    wt: 1:   Ages 12 to 14 Geometry
  986.    wt: 1:   Ages 10 to 12 Geometry
  987.    wt: 1:   Ages 9 to 10
  988.    wt: 1:   Ages 8 to 9
  989.    wt: 1:   Ages 7 to 8
  990.    wt: 1:   Ages 6 to 7
  991.    wt: 1:   Ages 4 plus to 5 plus
  992.    wt: 1:   26 Function definitions done and coming
  993.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  994.    wt: 1:   23 Inverse Functions
  995.    wt: 1:   9 Set theory term relation possible origins
  996.    wt: 1:   7 Links Lessons Elsewhere
  997.    wt: 1:   2 Column Multiplication Method
  998.    wt: 1:   7 arcsin left inverse of sine Definition
  999.    wt: 1:   15 Dot and Cross Product
  1000.    wt: 1:   13 Velocity Vectors in Physics
  1001.    wt: 1:   2 Signed Coordinates
  1002.    wt: 1:   1 Unsigned Coordinates
  1003.    wt: 1:   Straight Lines Intersection of
  1004.    wt: 1:   4 Tangent Function Properties
  1005.    wt: 1:   1 Straight Lines Slope Concept
  1006.    wt: 1:   28 Expressing products of sines cosines as sums
  1007.    wt: 1:   8 period of tangent function
  1008.    wt: 1:   7 period of sine and cosine
  1009.    wt: 1:   1 Unit Points Reflections Rotations
  1010.    wt: 1:   4 Multiplication Properties
  1011.    wt: 1:   7 Trignometric Ratios Unit Circle
  1012.    wt: 1:   2 Similarity By Design
  1013.    wt: 1:   Four Simple Exercises
  1014.    wt: 1:   12 Links Lessons elsewhere
  1015.    wt: 1:   8 Mid Point Formula
  1016.    wt: 1:   6 Intersection of lines by solving linear systems
  1017.    wt: 1:   4 Equations for lines three forms
  1018.    wt: 1:   7 Complex Numbers Appetizer
  1019.    wt: 1:   5 Side Angle Side
  1020.    wt: 1:   Short Course on Euclidean Geometry
  1021.    wt: 1:   1 Length Measurement
  1022.    wt: 1:   About Folder Contents
  1023.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  1024.    wt: 1:   22 Multiplication of Signed Numbers
  1025.    wt: 1:   E Long Division Methods more
  1026.    wt: 1:   D Long Division Methods
  1027.    wt: 1:   6 Unsigned Real Numbers
  1028.    wt: 1:   5 Independent versus Dependent Variables
  1029.    wt: 1:   4 Changing Letters
  1030.    wt: 1:   More Exercises
  1031.    wt: 1:   Simple Exercises
  1032.    wt: 1:   1 GE Substitution four examples
  1033.    wt: 1:   2 Three Examples
  1034.    wt: 1:   10 One Example
  1035.    wt: 1:   9 Three Examples
  1036.    wt: 1:   8 One Example
  1037.    wt: 1:   6 Three Examples
  1038.    wt: 1:   5 Three Examples
  1039.    wt: 1:   2 Three Examples
  1040.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  1041.    wt: 1:   10 Volume of Pyramid
  1042.    wt: 1:   5 Product Builder Notation
  1043.    wt: 1:   4 Subset Builder Notation
  1044.    wt: 1:   About Folder Contents
  1045.    wt: 1:   12 GCD 2700 288 via Prime
  1046.    wt: 1:   1 Counting and Counting Methods I
  1047.    wt: 1:   9 subtracting signed numbers
  1048.    wt: 1:   6 adding signed numbers
  1049.    wt: 1:   5 lengths and signs of numbers
  1050.    wt: 1:   7 Converting or Changing Units
  1051.    wt: 1:   D Three Term Ratios
  1052.    wt: 1:   22 Complex Compound Fractions
  1053.    wt: 1:   6 Multiplication of Mixed Numbers
  1054.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  1055.    wt: 1:   B Integer Long Division Multiple Choices
  1056.    wt: 1:   8 Multiplication by Signed Numbers Integers
  1057.    wt: 1:   7 Multiplication by Signs
  1058.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  1059.    wt: 1:   16 video Factors of 980 using prime
  1060.    wt: 1:   12 LCD GCD and LCM using Primes
  1061.    wt: 1:   11 Efficient Square Rule Use
  1062.    wt: 1:   5 Long Division Include Zeroes or not
  1063.    wt: 1:   B Powers of Ten
  1064.    wt: 1:   3 More One Digit Multipliers
  1065.    wt: 1:   The 20 Times Table
  1066.    wt: 1:   About folder contents
  1067.    wt: 1:   5 Conversion Arithmetic
  1068.    wt: 1:   Example 2
  1069.    wt: 1:   Example 1
  1070.    wt: 1:   Summary
  1071.    wt: 1:   2 Second derivative test prequel
  1072.    wt: 1:   20 Chain Rule for Pulley Systems
  1073.    wt: 1:   12 Quotient rule examples
  1074.    wt: 1:   9 Reciprocal rule
  1075.    wt: 1:   6 Power rule from product rule
  1076.    wt: 1:   9 Limits Continuity and Composition
  1077.    wt: 1:   4 Numerical properties
  1078.    wt: 1:   G.5 Motions With Bounded Velocities
  1079.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  1080.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  1081.    wt: 1:   F.5b Extreme Value Theorem
  1082.    wt: 1:   F.5a Equicontinuity Theorems
  1083.    wt: 1:   F.2 Closed Range Theorem
  1084.    wt: 1:   E1 Error Control Inequalities
  1085.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  1086.    wt: 1:   Chapter 22 Complex Numbers
  1087.    wt: 1:   Chapter 5. Slope Sign Tests
  1088.    wt: 1:   Foreword
  1089.    wt: 1:   Postscript More on Better Performance
  1090.    wt: 1:   Postscript For Better Performance
  1091.    wt: 1:   Foreword
  1092.    wt: 1:   Chapter 8 Modern Instruction
  1093.    wt: 1:   Chapter 5 Four References
  1094.    wt: 1:   Foreword
  1095.    wt: 1:   Postscript A Story Telling
  1096.    wt: 1:   Chapter 15 Objective Processes
  1097.    wt: 1:   Chapter 10 Responsibility
  1098.    wt: 1:   Chapter 5 Deception
  1099.    wt: 1:   Chapter 2 Skill Development
  1100.    wt: 1:   Three Remarks
  1101.    wt: 1:   Foreword
  1102.    wt: 1:   C. Domino effect of being careful
  1103.    wt: 1:   Implementation Notes
  1104.    wt: 1:   Site Reviews

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  1.    wt: 9:   Skills Chapter 4 Logic
  2.    wt: 9:   Skills Chapter 2 Geometry
  3.    wt: 9:   8 analytic geometry etc
  4.    wt: 9:   Math Ed if it must be short make it lean effective
  5.    wt: 9:   Education Reform Inconsistencies
  6.    wt: 9:   five decades make a difference
  7.    wt: 9:   Secondary Two Mathematics
  8.    wt: 9:   talk the algebra talk
  9.    wt: 9:   the trouble with algebra
  10.    wt: 9:   three goals for Mathematics Education
  11.    wt: 9:   standards for course material
  12.    wt: 9:   Operational Viewpoint to Value
  13.    wt: 9:   Education in mathematics science and technology
  14.    wt: 9:   education an empirical art
  15.    wt: 9:   chapitre 07 00 Des chaines plus longues de la raison
  16.    wt: 9:   chapitre 06 00 Chaines de la raison
  17.    wt: 9:   chapitre 03 A Propos Des Prochains Chapitre
  18.    wt: 9:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  19.    wt: 9:   6 Polynomial Operations and Equivalent Computation Rules
  20.    wt: 9:   5 Swapping Coordinates is a reflection
  21.    wt: 9:   10 Parallelogram Addition Method
  22.    wt: 9:   9 Head to Tail Coordinate View
  23.    wt: 9:   Straight Lines Instersection Solving Equations
  24.    wt: 9:   Straight Lines Intersection of
  25.    wt: 9:   4 Tangent Function Properties
  26.    wt: 9:   1 Straight Lines Slope Concept
  27.    wt: 9:   32 seven rows of pascals triangle
  28.    wt: 9:   31 basic secant cosecant cotangent trig identities
  29.    wt: 9:   29 secant cosecant and cotangent for acute angles
  30.    wt: 9:   5 Trigonometric Ratios For Tangent and Special Triangles
  31.    wt: 9:   11 Triangle Similarity Missing Side Problem
  32.    wt: 9:   8 Similarity of Triangles and Polygons
  33.    wt: 9:   4 Similarity Definition with Coordinate
  34.    wt: 9:   1 Early Concept of Like or Similar Shapes
  35.    wt: 9:   10 Midpoint of [a b] and [b a]
  36.    wt: 9:   7 Exercises to test skill and concept mastery
  37.    wt: 9:   3 Slope product for perpendicular lines
  38.    wt: 9:   PS H Distributive Law For Complex Numbers
  39.    wt: 9:   PS G Rotation Distributes over Addition
  40.    wt: 9:   PS B Parallelogram Construction Methods
  41.    wt: 9:   6 Ruler and compass Angle Bisection
  42.    wt: 9:   3 Isometry of Triangles Congruence
  43.    wt: 9:   A Modular and Remainder Arithmetic
  44.    wt: 9:   26 More Less Greater Than Comparison
  45.    wt: 9:   17 Arrows Rotate to Reverse with Length Unchanged
  46.    wt: 9:   5 Distributive Law for Whole Numbers
  47.    wt: 9:   4 Commutative Law Groups Counting Form
  48.    wt: 9:   3 Linear Equation Literal Solution More
  49.    wt: 9:   1 Equivalent Computation Rules
  50.    wt: 9:   8 Coordinates for Maps and Planes
  51.    wt: 9:   2 Computation Rules Evaluation
  52.    wt: 9:   1 Formulas Dependence and Function Notation
  53.    wt: 9:   12 Cone Cylinder Sphere Lesson Idea
  54.    wt: 9:   10 Volume of Pyramid
  55.    wt: 9:   9 Sets in Probability and Statistics
  56.    wt: 9:   1 More and Less Than for Counts and Measures
  57.    wt: 9:   5 Square Roots with primes more still
  58.    wt: 9:   4 Square Roots with primes more
  59.    wt: 9:   2 Square Roots with Prime
  60.    wt: 9:   17 GCD LCM of 85 and 60 via Prime
  61.    wt: 9:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  62.    wt: 9:   13 GCD from given Prime Factorization
  63.    wt: 9:   7 GCD and LCM from prime factorization
  64.    wt: 9:   LCM 60 45 Avoid List Method Use Prime
  65.    wt: 9:   1 Least Common Multiples LCM Introduction
  66.    wt: 9:   4 Counting with Trees Product Rule Take I
  67.    wt: 9:   6 Simplification of Fractions with Units
  68.    wt: 9:   B Fractions and Two Term Ratios
  69.    wt: 9:   21 Reciprocals for Fractions and Wholes
  70.    wt: 9:   10 Simplification of Fractions and Mixed Numerals
  71.    wt: 9:   1 What is a fraction
  72.    wt: 9:   A Associative Law Theorectical Note
  73.    wt: 9:   16 video Factors of 980 using prime
  74.    wt: 9:   6 Sieve of Eratosthenes and Square Rule
  75.    wt: 9:   8 Correcting the Mistake
  76.    wt: 9:   4 Division with 2 Digit Divsors
  77.    wt: 9:   1 Divsion Physical Examples
  78.    wt: 9:   B Powers of Ten
  79.    wt: 9:   10 Names for Big Numbers and Powers of Ten Expansion
  80.    wt: 9:   2 Groups of Three Place Value for Multidigit Decimals
  81.    wt: 9:   016 Numbering Occidental Calendar Days
  82.    wt: 9:   015 School and work day counting tables
  83.    wt: 9:   014 Counting Days with Calendars
  84.    wt: 9:   8 Addition of Time Intervals via subtotaling
  85.    wt: 9:   Summary
  86.    wt: 9:   1 Two cubic sketching exercises with 1st derivative
  87.    wt: 9:   34 Derivative of exponential function
  88.    wt: 9:   31 Derivatives of inverse functions
  89.    wt: 9:   30Chain Rule A Proof
  90.    wt: 9:   29 Chain Rule Optional Reading
  91.    wt: 9:   23 Chain Rule in general
  92.    wt: 9:   22 Chain Rule for polynomials
  93.    wt: 9:   16 Derivatives of reciprocals of sine and cosine
  94.    wt: 9:   15 sine and cosine derivatives 3rd step
  95.    wt: 9:   13 sine and cosine derivatives 1st step
  96.    wt: 9:   3 Motivation for Limit Definition Take 2
  97.    wt: 9:   PostScript For and Against Decimal Perspectives
  98.    wt: 9:   Chapter 22 Complex Numbers
  99.    wt: 9:   Chapter 5. Slope Sign Tests
  100.    wt: 9:   Foreword
  101.    wt: 9:   Postscript C Consistency as a Tool for Reason
  102.    wt: 9:   Chapter 23 Truth Tables
  103.    wt: 9:   Chapter 19 What is in chapters 20 to 24
  104.    wt: 9:   Chapter 11 Accidental Patterns
  105.    wt: 9:   Chapter 9 What is in Chapters 10 to 18
  106.    wt: 9:   Chapter 8 Change of Language
  107.    wt: 9:   V Reasons and Motivations for Logic and Mathematics
  108.    wt: 9:   P Exact Arithmetic With Whole Numbers and Fractions
  109.    wt: 9:   7 Games and Activities for Instruction
  110.    wt: 9:   1 From Number Recognition and Counting to Arithmetic A
  111.    wt: 9:   Multiple Ways to Improve Mathematics Skill Development
  112.    wt: 8:   11 pure mathematics
  113.    wt: 8:   10 statistics
  114.    wt: 8:   9 combinatorics probability sets
  115.    wt: 8:   6 polynomials etc
  116.    wt: 8:   4 algebra
  117.    wt: 8:   2 arithmetic with signed numbers
  118.    wt: 8:   1 arithmetic with unsigned numbers
  119.    wt: 8:   What is POMME
  120.    wt: 8:   which way to go
  121.    wt: 8:   Teach the teachers plus goals
  122.    wt: 8:   permissions for teachers
  123.    wt: 8:   Mathematics Education Professors
  124.    wt: 8:   learning takes time
  125.    wt: 8:   grouping students according to ability
  126.    wt: 8:   mathematics in context
  127.    wt: 8:   how letters appear
  128.    wt: 8:   Secondary Three Mathematics
  129.    wt: 8:   Secondary One Mathematics
  130.    wt: 8:   geometric implications for algebra
  131.    wt: 8:   05 13 OldSiteEntrancePage
  132.    wt: 8:   04 29 New Mathematics Curriculum
  133.    wt: 8:   04 25 when to stop or suspend mathemat
  134.    wt: 8:   02 20 mathematics education references
  135.    wt: 8:   three aims for mathematics students
  136.    wt: 8:   formal or informal peer review
  137.    wt: 8:   mathematics instruction in general
  138.    wt: 8:   Different Kinds of Reasoning in maths
  139.    wt: 8:   three kinds of reason in mathematics
  140.    wt: 8:   Four ways to improve education reform
  141.    wt: 8:   need for a mixed mathematics curriculum
  142.    wt: 8:   Leaner mathematics curriculum
  143.    wt: 8:   words for mathematics instructor
  144.    wt: 8:   chapitre 04 10 Etapes pour une meilleur raison
  145.    wt: 8:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  146.    wt: 8:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  147.    wt: 8:   Ages 12 to 14 Skills with take home value
  148.    wt: 8:   25 Absolute Value greatest integer and saw tooth functions
  149.    wt: 8:   5 Polynomials Long division Nonlinear divisor
  150.    wt: 8:   4 Polynomials Long division linear divisor
  151.    wt: 8:   3 Polynomials Multiplication Addition
  152.    wt: 8:   1 Polynomials Distributive Law
  153.    wt: 8:   16 cotangent function Definition Graph and Inverse
  154.    wt: 8:   15 cosecant function Definition Graph and Inverse
  155.    wt: 8:   13 cosecant function Definition Graph and Inverse
  156.    wt: 8:   11 arctan left inverse of tangent Graph
  157.    wt: 8:   12 From Applied To Pure Mathematics
  158.    wt: 8:   5 An Easy Proof of the Distributive Law
  159.    wt: 8:   1 Rectangular Polar Coordinates Review
  160.    wt: 8:   4 Trigonometric Ratios For Two Special Triangles
  161.    wt: 8:   2 Similar Triangles Equality of Corresponding Side Ratios
  162.    wt: 8:   Why Trigonometry the whyslopes view
  163.    wt: 8:   12 Triangles Similarity More Problems
  164.    wt: 8:   9 Midpoint Coordinates Half Endpoint Sum
  165.    wt: 8:   2 point slope equation for a line
  166.    wt: 8:   Euclidean Geometry Elsewhere LINKS
  167.    wt: 8:   PS C Similarity Use Recognize it in Trigonometry
  168.    wt: 8:   21 Parallelograms
  169.    wt: 8:   18 Triangle Similarity Take 1
  170.    wt: 8:   16 Angles Subtended By Chords and Diameters
  171.    wt: 8:   15 Triangle Angle Sum is 180 degrees
  172.    wt: 8:   14 Parallel Lines Postulate
  173.    wt: 8:   1 Length Measurement
  174.    wt: 8:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  175.    wt: 8:   16 Collinear Horizontal Arrows Vectors
  176.    wt: 8:   14 Vector Head to Tail Sums and Resultants
  177.    wt: 8:   9 Division with Digits after Decimal Point
  178.    wt: 8:   8 Division and Mulplication of Compound Fractions
  179.    wt: 8:   7 Arithmetic with Infinite Decimal Expansions
  180.    wt: 8:   5 Fractions with Infinite Decimal Expansions
  181.    wt: 8:   3 Location of Point in Decimal Multiplication
  182.    wt: 8:   1 Fractions with Finite Decimal Expansions
  183.    wt: 8:   A Decimal Addition Columm Methods
  184.    wt: 8:   7 Decimals Multiplication Methods Examples
  185.    wt: 8:   3 Multiplicative Counting Skills Principles
  186.    wt: 8:   7 Pythagorean Theorem Chinese Square Proof
  187.    wt: 8:   2 Linear Equation Literal Solution
  188.    wt: 8:   1 Changing Calculations
  189.    wt: 8:   1 Whole and Natural Numbers
  190.    wt: 8:   Using Letters for Physical Quantities
  191.    wt: 8:   11 Volume of Sphere
  192.    wt: 8:   9 Volume of Cone
  193.    wt: 8:   10 Set View of Wordy Extensions To Arithmetic
  194.    wt: 8:   3 Counting with Sets etc
  195.    wt: 8:   4 Greater More Less Than Signs in General
  196.    wt: 8:   2 More and Less Than with Unlike Signs
  197.    wt: 8:   16 GCD and LCM of 650 225 via Prime
  198.    wt: 8:   14 GCD of 650 110 via Primes LCM via Product Rule
  199.    wt: 8:   11 GCD 2700 288 via Euclid Algorithm
  200.    wt: 8:   8 GCD from Euclidean Algorithm
  201.    wt: 8:   5 Common Divisors 60 45 via Prime
  202.    wt: 8:   4 LCM of 8 and 10 via Prime
  203.    wt: 8:   1 Counting and Counting Methods I
  204.    wt: 8:   11 What are real lengths and numbers
  205.    wt: 8:   4 Fractions with Units
  206.    wt: 8:   3 Multiplying Units and Numbers
  207.    wt: 8:   2 Equality and Units
  208.    wt: 8:   12 Fraction Comparison
  209.    wt: 8:   13 Subtraction with Additive Inverse
  210.    wt: 8:   20 Uniqueness of Prime Factorization
  211.    wt: 8:   17 Identify and Count Factors using Primes
  212.    wt: 8:   2 Prime and Composites less than 16
  213.    wt: 8:   5 Long Division Include Zeroes or not
  214.    wt: 8:   2 One Digit Multipliers
  215.    wt: 8:   8 Review Lesson 1 2 4 and 6 All in One
  216.    wt: 8:   1 Place Value in Three Digit Whole Numbers
  217.    wt: 8:   013 Travel Time Tables
  218.    wt: 8:   012 Division of Time Intervals by Time Intervals
  219.    wt: 8:   010 Repeated Addition of Time Intervals
  220.    wt: 8:   6 How long is a million seconds
  221.    wt: 8:   2 Time and Date Matters in School
  222.    wt: 8:   A Related Material in Volume 3
  223.    wt: 8:   27 Chain Rule sinusoidal outer inner functions EGS
  224.    wt: 8:   26 Chain Rule Recognising outer inner functions
  225.    wt: 8:   21 Chain Rule for powers
  226.    wt: 8:   19 Chain Rule for linear functions
  227.    wt: 8:   18 Chain Rule Introduction
  228.    wt: 8:   17 Derivatives of quotients of sine and cosine
  229.    wt: 8:   14 sine and cosine derivatives 2nd step
  230.    wt: 8:   12 Quotient rule examples
  231.    wt: 8:   10 Power rule for negative integers
  232.    wt: 8:   8 Differentiation of polynomials
  233.    wt: 8:   2 Motivation for Limit Definition Take 1
  234.    wt: 8:   7 Evaluation by immediate or delayed substitution
  235.    wt: 8:   Postscript One Sided and Intermediate Value Theorems
  236.    wt: 8:   G.2 Lipshitz Conditions Integration Calculus Reform
  237.    wt: 8:   G.1 First Fundamental Theorem of Calculus
  238.    wt: 8:   G.2 Differentiable Functions Mean Value Theorem
  239.    wt: 8:   F.3 Intermediate Value Theorem
  240.    wt: 8:   Appendix E. How To Study Mathematics and Why
  241.    wt: 8:   Chapter 5 Islands and Divisions of Knowledge
  242.    wt: 8:   Chapter 2 For and Against Mathematics
  243.    wt: 8:   Chapter 24 Direct and Indirect Reason
  244.    wt: 8:   Chapter 20 Shorthand Symbols as Pronouns
  245.    wt: 8:   Chapter 18 Sense and Knowledge
  246.    wt: 8:   Chapter 7 Longer Chains of Reason
  247.    wt: 8:   Chapter 6 Chains of Reason
  248.    wt: 8:   Q How Logic and Proofs extend Show Work Practices
  249.    wt: 8:   G. Written work formats for developing and showing skill
  250.    wt: 8:   D. Check work a must with a caution
  251.    wt: 8:   1 From Number Recognition and Counting to Arithmetic B
  252.    wt: 8:   Helping the Blind in Logic and Mathematics
  253.    wt: 8:   Mathematics Education References
  254.    wt: 8:   Mathematics Education References
  255.    wt: 8:   Ends Values Methods For Skill Development Framework Prequel
  256.    wt: 8:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  257.    wt: 8:   Which Way To Go
  258.    wt: 7:   website reviews
  259.    wt: 7:   About site lesson plans
  260.    wt: 7:   teacher certification
  261.    wt: 7:   modern education
  262.    wt: 7:   teaching tips
  263.    wt: 7:   mathematics curriculum shifts
  264.    wt: 7:   Lessening Algebra Difficulties
  265.    wt: 7:   02 21 words for teachers
  266.    wt: 7:   Theory of Knowledge
  267.    wt: 7:   How to be a better instructor
  268.    wt: 7:   Motivation and Context Problem
  269.    wt: 7:   Prequel In For A Penny In For A Pound
  270.    wt: 7:   fairness and inductive principles for instruction
  271.    wt: 7:   chapitre 07 01 principle D induction mathematique
  272.    wt: 7:   chapitre 04 04 Parlons de la logique
  273.    wt: 7:   chapitre 02 00 La Communication des idees
  274.    wt: 7:   A Wire Resistance Qualitative01
  275.    wt: 7:   13 Addition and Addition Tables
  276.    wt: 7:   Ages 3 plus to 4 plus
  277.    wt: 7:   17 Function maxima minima and their location
  278.    wt: 7:   3 Formula or function graphing exercise
  279.    wt: 7:   14 secant function Definition Graph and Inverse
  280.    wt: 7:   12 motivation for term arctan
  281.    wt: 7:   10 arctan left inverse of tangent Definition
  282.    wt: 7:   9 motivation for name arcsin
  283.    wt: 7:   13 Velocity Vectors in Physics
  284.    wt: 7:   8 Parallel Vectors
  285.    wt: 7:   6 Vectors with Coordinates
  286.    wt: 7:   4 Resultant of a Sum of Movements
  287.    wt: 7:   Vector and Complex Number Applet
  288.    wt: 7:   25 tangent double angle formula Slope connection
  289.    wt: 7:   24 tangent Angle Difference Formula
  290.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  291.    wt: 7:   21 sine and cosine Half Angle Formulas
  292.    wt: 7:   20 sine and cosine Double Angle Formulas
  293.    wt: 7:   17D cis formulas for sine cosines and tangent
  294.    wt: 7:   17C sine and cosine double triple angle formulas
  295.    wt: 7:   17B sine cosine Angle Sum Formulas via cis
  296.    wt: 7:   16 Right Triangle Complementary Angle Relations
  297.    wt: 7:   15 sine cosine Complementary Angle Relations
  298.    wt: 7:   14 cosine even and sine and tangent are odd
  299.    wt: 7:   13 Graph of tangent function many periods
  300.    wt: 7:   11 tangent function undefined when terminal side vertical
  301.    wt: 7:   6 sines and cosines for reference angle 30 degrees
  302.    wt: 7:   21 Logarithms Powers and Exponentials
  303.    wt: 7:   13 Trig Formulas for dot and cross Products
  304.    wt: 7:   12 cis formulas for sine cosines and tangent
  305.    wt: 7:   11 sine and cosine double triple angle formulas
  306.    wt: 7:   10 sine cosine Angle Sum Formulas via cis
  307.    wt: 7:   7 Second Way to Calculate Products
  308.    wt: 7:   8 Triangles Cascade Problem Solving
  309.    wt: 7:   3 Trigonometric Ratios sine and cosine
  310.    wt: 7:   1 Angle Measurement with Degrees
  311.    wt: 7:   2 Similarity By Design
  312.    wt: 7:   Four Simple Exercises
  313.    wt: 7:   12 Links Lessons elsewhere
  314.    wt: 7:   8 Mid Point Formula
  315.    wt: 7:   6 Intersection of lines by solving linear systems
  316.    wt: 7:   4 Equations for lines three forms
  317.    wt: 7:   PS A Kite Construction Methods
  318.    wt: 7:   19 Right Triangle Similarity
  319.    wt: 7:   17 Right Bisectors of Triangle Sides
  320.    wt: 7:   12 Side Angle Side Failure
  321.    wt: 7:   11 Triangle Construction Fails
  322.    wt: 7:   10 Dropping a perpendicular to line
  323.    wt: 7:   9 Construction of a right bisector
  324.    wt: 7:   8 Isoceles Triangles
  325.    wt: 7:   7 Angle Side Angle
  326.    wt: 7:   2 Correspondence between Triangles
  327.    wt: 7:   1 Initial Concepts and Terms
  328.    wt: 7:   A Signed Number Arithmetic Review
  329.    wt: 7:   18 Geometrically Why Vector Addition Commutes
  330.    wt: 7:   11 Signed Number Addition and Addition Properties
  331.    wt: 7:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  332.    wt: 7:   4 Location of Point in Decimal Addition
  333.    wt: 7:   C Three Decimal Subtraction Methods
  334.    wt: 7:   8 Column Multiplication Methods in General
  335.    wt: 7:   6 Column Methods for Decimal Multiplication
  336.    wt: 7:   2 Combing Counts Addition Skills and Principles
  337.    wt: 7:   16 Real Numbers Comparison
  338.    wt: 7:   13 Real Number Subtraction
  339.    wt: 7:   12 Real Number Additive Inverses or Negatives
  340.    wt: 7:   7 Real Numbers as Line Cordinates
  341.    wt: 7:   5 Independent versus Dependent Variables
  342.    wt: 7:   4 Changing Letters
  343.    wt: 7:   More Exercises
  344.    wt: 7:   Simple Exercises
  345.    wt: 7:   7 Cautious or Safe Set Construction
  346.    wt: 7:   6 Power Set Notation
  347.    wt: 7:   2 Venn Diagrams
  348.    wt: 7:   6 Three Notions of What is a Variable
  349.    wt: 7:   5 Talking about Numbers and Quantities
  350.    wt: 7:   4 A Brief Story of numbers and algebra
  351.    wt: 7:   3 Adding Words To Arithmetic
  352.    wt: 7:   2 What is a Variable
  353.    wt: 7:   12 GCD 2700 288 via Prime
  354.    wt: 7:   7 negative and additive inverse
  355.    wt: 7:   2 signed and unsigned numbers as coordinates
  356.    wt: 7:   7 Converting or Changing Units
  357.    wt: 7:   21 Working With Signs
  358.    wt: 7:   20 Dividing Fractions the Why
  359.    wt: 7:   19 Dividing Fractions How TO
  360.    wt: 7:   18 Efficient Ways to Multiply
  361.    wt: 7:   9 Improper Fractions and Mixed Numbers
  362.    wt: 7:   5 Equivalent Fractions
  363.    wt: 7:   4 Fraction Multiplication
  364.    wt: 7:   2 Unit Fraction Multiplication
  365.    wt: 7:   3 Adding Movements with same direction
  366.    wt: 7:   12 LCD GCD and LCM using Primes
  367.    wt: 7:   11 Efficient Square Rule Use
  368.    wt: 7:   Exact Arithmetic Wholes and Fractions
  369.    wt: 7:   Practical Methods Ends and Values for Arithmetic
  370.    wt: 7:   011 Division of Time Intervals By Numbers
  371.    wt: 7:   7 Addition of Time Intervals
  372.    wt: 7:   4 Mixing and Changing Units of Time
  373.    wt: 7:   3 Units and Lengths of Time
  374.    wt: 7:   1 Intro of Kids To Time Date Skills
  375.    wt: 7:   4 Definite Integrals Evaluation Exercises
  376.    wt: 7:   3 Two Chain Rule Method Exercises
  377.    wt: 7:   A Related lessons in Volume 3
  378.    wt: 7:   4 Second derivative test exercise example
  379.    wt: 7:   20 Chain Rule for Pulley Systems
  380.    wt: 7:   9 Reciprocal rule
  381.    wt: 7:   6 Power rule from product rule
  382.    wt: 7:   5 Product Rule
  383.    wt: 7:   8 Four Animated Examples
  384.    wt: 7:   5 Jumps and absence of unlimited error control
  385.    wt: 7:   2 Algebraic codification
  386.    wt: 7:   G.6 Bounded Derivatives implies Lipshitz Continuity
  387.    wt: 7:   G.3 Constant Difference Theorem Proof
  388.    wt: 7:   F.5a Equicontinuity Theorems
  389.    wt: 7:   F.1 What Functions are Continuous
  390.    wt: 7:   E2 Algebraic Properties of Limits
  391.    wt: 7:   D1 Sets and Sequences GLBs and LGBs
  392.    wt: 7:   C Triangle Inequalities
  393.    wt: 7:   A1. Introduction
  394.    wt: 7:   Chapter 31 Direct and Indirect Reason
  395.    wt: 7:   Chapter 29 Contrapositive and Vacuously True Implications
  396.    wt: 7:   Chapter 26 What is in chapters 27 to 31
  397.    wt: 7:   Chapter 25. Mathematical Induction Examples
  398.    wt: 7:   Chapter 10 Describing and Changing Calculations
  399.    wt: 7:   Chapter 3 Chains of Reason
  400.    wt: 7:   Annotated Links to Material Elsehwere
  401.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  402.    wt: 7:   Chapter 3 Algebra Difficulties
  403.    wt: 7:   Postscript D Reflections on Law of the Excluded Middle
  404.    wt: 7:   Postscript B More on Story Telling and Reason
  405.    wt: 7:   Chapter 21 Occurrence Tables
  406.    wt: 7:   Chapter 1 Introduction
  407.    wt: 7:   S Adding words to algebra
  408.    wt: 7:   R Why Learn Mathematics Skills
  409.    wt: 7:   O On Learning Mathematics and Science
  410.    wt: 7:   J. More on written work and showing skill
  411.    wt: 7:   Implementation Notes
  412.    wt: 6:   why bother
  413.    wt: 6:   three goals to set for students
  414.    wt: 6:   activities for students
  415.    wt: 6:   links Education Resources online
  416.    wt: 6:   site eurekas
  417.    wt: 6:   key notes and themes
  418.    wt: 6:   Postscript 2007 01 10
  419.    wt: 6:   What to Tell Students
  420.    wt: 6:   cultivating intelligence
  421.    wt: 6:   chapitre 12 00 les iles et division
  422.    wt: 6:   chapitre 04 09 Regles accidentelles
  423.    wt: 6:   chapitre 04 08 Limitations et benefices
  424.    wt: 6:   chapitre 04 07 RepetablesEtReproductibles
  425.    wt: 6:   chapitre 04 06 engagements
  426.    wt: 6:   chapitre 04 05 Implication versus suggestion
  427.    wt: 6:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  428.    wt: 6:   chapitre 04 00 Les regles d implication
  429.    wt: 6:   chapitre 01 00 Introduction
  430.    wt: 6:   Trois Notions qui menent a algebre
  431.    wt: 6:   E Wire Resistance Calculation03
  432.    wt: 6:   25 Mathematics Education Leaving A Good Impression
  433.    wt: 6:   23 Modularized Skill Development Modularized Rigor Take IV
  434.    wt: 6:   23 Modularized Skill Development Modularized Rigor Take III
  435.    wt: 6:   23 Modularized Skill Development Modularized Rigor Take II
  436.    wt: 6:   6 Discipline Who is in Charge Conserving Authority
  437.    wt: 6:   Ages 12 to 14 Arithmetic
  438.    wt: 6:   Ages 10 to 12 Arithmetic
  439.    wt: 6:   11 Function Domain Range Source and Targets
  440.    wt: 6:   6 Set Existence Formation and Notation
  441.    wt: 6:   4 Function notation in and beyond mathematics
  442.    wt: 6:   Rewriting algebraic substitution as function substitutions
  443.    wt: 6:   8 arcsin left inverse of sine Graph
  444.    wt: 6:   6 Graph of arccos function
  445.    wt: 6:   4 possible motivation for term arccos
  446.    wt: 6:   3 Left Inverse of cosine arccos definition
  447.    wt: 6:   15 Dot and Cross Product
  448.    wt: 6:   2 Signed Coordinates
  449.    wt: 6:   1 Unsigned Coordinates
  450.    wt: 6:   17 tangent function angle sum formulas
  451.    wt: 6:   30 unit circle calculation of six trigonometric functions
  452.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  453.    wt: 6:   17A The complex number valued trig function cis
  454.    wt: 6:   10 Graphs of sines and cosines many periods
  455.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  456.    wt: 6:   2 Quadrant I reference Angles
  457.    wt: 6:   3 Addition Properties
  458.    wt: 6:   2 Complex Numbers made easier we hope
  459.    wt: 6:   Appetizer A Complex Number Applet
  460.    wt: 6:   6 Trigonometry Sines of Supplementary Angles
  461.    wt: 6:   Right Triangle and Unit Circle Trigonometry
  462.    wt: 6:   5 Side Angle Side
  463.    wt: 6:   Short Course on Euclidean Geometry
  464.    wt: 6:   musings do not puiblish real numbers
  465.    wt: 6:   24 Signed Numbers Arithmmetic Properties
  466.    wt: 6:   22 Multiplication of Signed Numbers
  467.    wt: 6:   21 Addition of Multiples of a Single Vector
  468.    wt: 6:   12 Real Numbers Line Signed Coordinates
  469.    wt: 6:   6 Infinite Decimals Ending in 9 repeating
  470.    wt: 6:   2 Counting Digits in Decimal Multiplication
  471.    wt: 6:   E Long Division Methods more
  472.    wt: 6:   D Long Division Methods
  473.    wt: 6:   15 Real Number Division
  474.    wt: 6:   14 Real Number Multiplication
  475.    wt: 6:   11 Real Number Addition
  476.    wt: 6:   10 Real Number Lengths and Signs
  477.    wt: 6:   9 Coordinates for Regions in Space
  478.    wt: 6:   5 Rational Numbers More
  479.    wt: 6:   4 Rational Numbers
  480.    wt: 6:   3 Fractions
  481.    wt: 6:   5 Product Builder Notation
  482.    wt: 6:   4 Subset Builder Notation
  483.    wt: 6:   arithmetic videos Real Player Format
  484.    wt: 6:   6 GCD from Prime
  485.    wt: 6:   4 signed coordinates for regions in space
  486.    wt: 6:   D Three Term Ratios
  487.    wt: 6:   22 Complex Compound Fractions
  488.    wt: 6:   6 Multiplication of Mixed Numbers
  489.    wt: 6:   D Remainders Modulo 11 Pair Rule
  490.    wt: 6:   11 Adding Integers Formulas and Examples
  491.    wt: 6:   Quick history of numbers and algebra
  492.    wt: 6:   5 Conversion Arithmetic
  493.    wt: 6:   5 Area Under Curve Exercise
  494.    wt: 6:   3 Second derivative test
  495.    wt: 6:   2 Second derivative test prequel
  496.    wt: 6:   11 Quotient rule
  497.    wt: 6:   4 Sum Rule
  498.    wt: 6:   11 Limits at infinity Three Examples
  499.    wt: 6:   10 Three one sided limits with infinite values
  500.    wt: 6:   6 Continuity at a point
  501.    wt: 6:   4 Numerical properties
  502.    wt: 6:   3 Decimal insights for limits continuity convergence
  503.    wt: 6:   1 Numerical introduction
  504.    wt: 6:   G.5 Motions With Bounded Velocities
  505.    wt: 6:   G.4 Lipschitz Continuity implies EquiContinuity
  506.    wt: 6:   G.1 Differentiable Functions Rolles Theorem
  507.    wt: 6:   F.5b Extreme Value Theorem
  508.    wt: 6:   F.2 Closed Range Theorem
  509.    wt: 6:   E1 Error Control Inequalities
  510.    wt: 6:   B1 Pigeon Hole Principles from combinatorics
  511.    wt: 6:   Appendix D. What to do in School and Why
  512.    wt: 6:   Appendix C. How to Read
  513.    wt: 6:   Appendix A. Reading Guide For Next Appendices
  514.    wt: 6:   Chapter 30 Truth Tables
  515.    wt: 6:   Chapter 23. Notation For Sums
  516.    wt: 6:   Chapter 20. Degrees and Radians
  517.    wt: 6:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  518.    wt: 6:   Postscript Unifying Theme A Fourth Skill For Algebra
  519.    wt: 6:   Chapter 13. Second Reading Guide
  520.    wt: 6:   Postscript What is a Variable
  521.    wt: 6:   Chapter 9 Talking about Numbers or Quantities
  522.    wt: 6:   Chapter 7 Prep for Calculus Arithmetic Exercises
  523.    wt: 6:   Chapter 6 Change of Language
  524.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  525.    wt: 6:   Postscript A Story Telling
  526.    wt: 6:   Chapter 15 Objective Processes
  527.    wt: 6:   Chapter 10 Responsibility
  528.    wt: 6:   Chapter 5 Deception
  529.    wt: 6:   Chapter 2 Skill Development
  530.    wt: 6:   Three Remarks
  531.    wt: 6:   Foreword
  532.    wt: 6:   N Mathematics Prepare for College Studies
  533.    wt: 6:   M Words to extend arithmetic
  534.    wt: 6:   L Skills with take home value
  535.    wt: 6:   N Improving Marks on Tests and Finals
  536.    wt: 6:   I. Logic and language skills
  537.    wt: 6:   H Jigsaw puzzles and problem solving
  538.    wt: 6:   E. When and how to correct errors
  539.    wt: 5:   site origins
  540.    wt: 5:   three difficulties
  541.    wt: 5:   chapitre 05 00 Deception
  542.    wt: 5:   chapitre 04 02 Deuxieme enigme
  543.    wt: 5:   chapitre 04 01 Premiere enigme
  544.    wt: 5:   problemes algebre et arithmetique
  545.    wt: 5:   F Wire Resistance Calculation04
  546.    wt: 5:   D Wire Resistance Calculation02
  547.    wt: 5:   C Wire Resistance Calculation01
  548.    wt: 5:   B Wire Resistance Qualitative02
  549.    wt: 5:   27 Graduated Correction and Penalties for Young Offenders
  550.    wt: 5:   23 Modularized Skill Development Modularized Rigor
  551.    wt: 5:   16 Secondary Mathematics Tips
  552.    wt: 5:   12 Goals and Objectives For Mathematics
  553.    wt: 5:   5 Patience Please for Yourself and Your Charges
  554.    wt: 5:   Ages 12 to 14 Geometry
  555.    wt: 5:   Ages 10 to 12 Geometry
  556.    wt: 5:   Ages 9 to 10
  557.    wt: 5:   Ages 8 to 9
  558.    wt: 5:   Ages 7 to 8
  559.    wt: 5:   Ages 6 to 7
  560.    wt: 5:   Ages 4 plus to 5 plus
  561.    wt: 5:   22 Square Root function graphically
  562.    wt: 5:   20 Interchanging coordinates a reflection
  563.    wt: 5:   16 Increasing or decreasing on intervals
  564.    wt: 5:   15 Sign analysis of functions
  565.    wt: 5:   13 From one to one to many to one
  566.    wt: 5:   8 Set view of relations and functions
  567.    wt: 5:   5 Function notation for geometric transformations
  568.    wt: 5:   2 Algebraic use of function notation
  569.    wt: 5:   7 Links Lessons Elsewhere
  570.    wt: 5:   2 Column Multiplication Method
  571.    wt: 5:   7 arcsin left inverse of sine Definition
  572.    wt: 5:   11 Component Method
  573.    wt: 5:   27 Logarithmic use of products of sines and cosines
  574.    wt: 5:   26 Formulas for products of sines and cosines
  575.    wt: 5:   23 sine and cosine of 180 plus 22.5 degrees
  576.    wt: 5:   17G Pythagorean Theorem Converse
  577.    wt: 5:   17F Law of cosines
  578.    wt: 5:   17E Trig Formulas for dot and cross Products
  579.    wt: 5:   12 Graph of tangent function for one period
  580.    wt: 5:   9 Graphs of sine and cosine over one period
  581.    wt: 5:   5 sines and cosines for reference angle 60 degrees
  582.    wt: 5:   4 sines and cosines for reference angle 45 degrees
  583.    wt: 5:   Right Triangle and Unit Circle Trigonometry
  584.    wt: 5:   16 References and Originality Question
  585.    wt: 5:   15 Pythagorean Theorem Converse
  586.    wt: 5:   14 Law of cosines
  587.    wt: 5:   9 The complex number valued trig function cis
  588.    wt: 5:   7 Trignometric Ratios Unit Circle
  589.    wt: 5:   4 Side Side Side
  590.    wt: 5:   1 The Counting Origins of Numbers
  591.    wt: 5:   6 Unsigned Real Numbers
  592.    wt: 5:   8 Sets of Numbers
  593.    wt: 5:   1 Finite Sets
  594.    wt: 5:   1 Three Skills For Algebra
  595.    wt: 5:   9 subtracting signed numbers
  596.    wt: 5:   6 adding signed numbers
  597.    wt: 5:   5 lengths and signs of numbers
  598.    wt: 5:   6 Multiplication by Natural Numbers
  599.    wt: 5:   The 12 Times Table Visually
  600.    wt: 5:   2 Indefinite Integrals Exercises
  601.    wt: 5:   1 Chain Rule in Reverse Integration Method
  602.    wt: 5:   9 Limits Continuity and Composition
  603.    wt: 5:   F.4 Finite Covering Theorem
  604.    wt: 5:   D2 Limits of Monotone Sequences
  605.    wt: 5:   Appendix B. How To Learn
  606.    wt: 5:   Chapter 27 Shorthand Symbols as Pronouns
  607.    wt: 5:   Chapter 24. Personal Investment and Pension EGS
  608.    wt: 5:   Chapter 18. Rules for Algebra
  609.    wt: 5:   Chapter 15. Solving Linear Equations
  610.    wt: 5:   Chapter 12. Shorthand Usage Guide
  611.    wt: 5:   Chapter 11. Why Shorthand
  612.    wt: 5:   Chapter 8 Three Skills For Algebra
  613.    wt: 5:   Chapter 4 Longer Chains of Reason
  614.    wt: 5:   Chapter 1 Introduction to Chapters 2 to 6
  615.    wt: 5:   Postscript B Mathematics Education References
  616.    wt: 5:   Postscript A Three Remarks
  617.    wt: 5:   Chapter 7 Two Treatments of Geometry
  618.    wt: 5:   1 Links to Online Resources Elsewhere Take 1
  619.    wt: 5:   F. The student teacher tutor feedback loop
  620.    wt: 5:   C. Domino effect of being careful
  621.    wt: 5:   A. Skill has to be seen to believed
  622.    wt: 5:   How to Build Skills and Confidence
  623.    wt: 5:   Talking pdf files for online lessons a webvideo alternative
  624.    wt: 4:   liens
  625.    wt: 4:   deux definitions pour variable
  626.    wt: 4:   2 Conductance Resistance Duality02
  627.    wt: 4:   1 Conductance Resistance Duality01
  628.    wt: 4:   3 Like resistors in parallel
  629.    wt: 4:   24 Standards For Skill Develoment Take II
  630.    wt: 4:   19 Extending the Oral Dimension of Mathematics
  631.    wt: 4:   18 Primary School Mathematics
  632.    wt: 4:   17 Math Booklets for children and young teenagers
  633.    wt: 4:   14 Multiplication and Times Tables
  634.    wt: 4:   4 Learning Takes Time and Effort
  635.    wt: 4:   3 Preparing for Science Studies
  636.    wt: 4:   2 Reading and Writing Skills
  637.    wt: 4:   23 Inverse Functions
  638.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  639.    wt: 4:   19 Horizontal line rule and method
  640.    wt: 4:   18 Vertical Line Rule and Method
  641.    wt: 4:   12 Function Domain Recognition Exercises
  642.    wt: 4:   10 Interval Notation
  643.    wt: 4:   7 Functions with finite domains
  644.    wt: 4:   1 Geometric Introduction of Function Notation
  645.    wt: 4:   Introduction Reading Guide
  646.    wt: 4:   8 Notes for instructors or tutors
  647.    wt: 4:   2 cosine function more properties
  648.    wt: 4:   1 cosine function properties
  649.    wt: 4:   28 Expressing products of sines cosines as sums
  650.    wt: 4:   8 period of tangent function
  651.    wt: 4:   7 period of sine and cosine
  652.    wt: 4:   1 Unit Points Reflections Rotations
  653.    wt: 4:   4 Multiplication Properties
  654.    wt: 4:   About Folder Contents
  655.    wt: 4:   19 Signed Multiples of Vectors
  656.    wt: 4:   2 Integers
  657.    wt: 4:   About Folder Contents
  658.    wt: 4:   10 dividing signed numbers
  659.    wt: 4:   8 multiplying signed numbers
  660.    wt: 4:   12 Adding Integers More Examples
  661.    wt: 4:   10 Integer Multiplication Formulas
  662.    wt: 4:   5 Zero Movement and Additive Inverses
  663.    wt: 4:   4 Adding Movements wiht opposite directions
  664.    wt: 4:   1 Integers as Coordinates
  665.    wt: 4:   Chapter 28 Occurrence Tables
  666.    wt: 4:   Chapter 22. Geometric Sums and Sequences
  667.    wt: 4:   Chapter 21. Third Reading Guide
  668.    wt: 4:   Chapter 19. Functions and Sets
  669.    wt: 4:   Chapter 16. Painless Theorem Proving
  670.    wt: 4:   Solutions For Arithmetic Exercises
  671.    wt: 4:   Chapter 12 Four Phases
  672.    wt: 4:   Chapter 11 Elementary Instruction
  673.    wt: 4:   Chapter 10 Transition
  674.    wt: 4:   Chapter 9 The Two Ends
  675.    wt: 4:   Chapter 1 Introduction
  676.    wt: 3:   problemes responses
  677.    wt: 3:   logique deux enigme
  678.    wt: 3:   3 Energy Power Heat08
  679.    wt: 3:   C Energy Power03
  680.    wt: 3:   2 Unlike resistors in parallel01
  681.    wt: 3:   24 Standards For Skill Develoment
  682.    wt: 3:   22 Student Centered Highschool Mathematics
  683.    wt: 3:   11 Help and Defend Your Child or Teens Education
  684.    wt: 3:   10 Ends values for work study instruction
  685.    wt: 3:   9 Streaming by Student Cooperation
  686.    wt: 3:   8 The Effect of Negative Remarks
  687.    wt: 3:   26 Function definitions done and coming
  688.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  689.    wt: 3:   9 Set theory term relation possible origins
  690.    wt: 3:   Unit Circle Development of Trigonometry
  691.    wt: 3:   20 N th Roots of Complex Numbers
  692.    wt: 3:   19 N th Roots of Unity
  693.    wt: 3:   18 Sixth Roots of Unity
  694.    wt: 3:   17 Cube Roots of unity
  695.    wt: 3:   8 Unit Circle Development of Trigonometry
  696.    wt: 3:   6 Field Properties of Complex Number
  697.    wt: 3:   C Divisibility by 11 Integer Recognition Method
  698.    wt: 3:   B Integer Long Division Multiple Choices
  699.    wt: 3:   8 Multiplication by Signed Numbers Integers
  700.    wt: 3:   7 Multiplication by Signs
  701.    wt: 3:   2 Integers Multiplies of a Unit Moverment
  702.    wt: 3:   The 20 Times Table
  703.    wt: 3:   About folder contents
  704.    wt: 3:   Postscript More on Better Performance
  705.    wt: 3:   Postscript For Better Performance
  706.    wt: 3:   Foreword
  707.    wt: 3:   Chapter 8 Modern Instruction
  708.    wt: 3:   Chapter 5 Four References
  709.    wt: 3:   Foreword
  710.    wt: 3:   H more Routine to non routine problem solving
  711.    wt: 3:   B. Domino effect of errors
  712.    wt: 2:   4 Energy Power Heat09
  713.    wt: 2:   2 Energy Power Heat07
  714.    wt: 2:   1 Energy Power Heat06
  715.    wt: 2:   A Energy Power01
  716.    wt: 2:   E Kirchoffs Second Law
  717.    wt: 2:   D Kirchoff First Law
  718.    wt: 2:   B Electromotive force conventional current01
  719.    wt: 2:   Home Tutoring and Home Schooling
  720.    wt: 2:   15 Counting For Parents
  721.    wt: 2:   7 Student Motivation
  722.    wt: 2:   1 Speaking Skills
  723.    wt: 2:   14 Surjections Injections Bijections
  724.    wt: 2:   9 Multiplying Integers
  725.    wt: 2:   Road Safety Questions
  726.    wt: 2:   The Math Forum and Site Content
  727.    wt: 1:   E Energy Power05
  728.    wt: 1:   D Energy Power04
  729.    wt: 1:   B Energy Power02
  730.    wt: 1:   1 Like resistors in series
  731.    wt: 1:   F Unlike Resistors in Series
  732.    wt: 1:   C Electromotive force conventional current02
  733.    wt: 1:   A Circuit Elements
  734.    wt: 1:   Site Reviews
  735.    wt: 19:   13 Pythagorean spatial distance formulas
  736.    wt: 18:   Long Division forwards and backwards Example 3
  737.    wt: 17:   3 Gaussian Elimination 3 unknowns first example
  738.    wt: 17:   Long Division forwards and backwards Example 2
  739.    wt: 17:   Long Division forwards and backwards Example 1
  740.    wt: 17:   3. How to add with decimals A sans conversions
  741.    wt: 16:   Parallel Lines and Parallel Transversals
  742.    wt: 16:   Parallel Lines and Alternating Corresponding Angles
  743.    wt: 16:   10 Pythagorean plane distance formula
  744.    wt: 16:   5 Cartesian Addition and Translation
  745.    wt: 16:   3 Rectangular Coordinates Review
  746.    wt: 16:   3 Harder Cases Convert to Compare and Subtract
  747.    wt: 16:   Example 1. Area Between x and x squared
  748.    wt: 15:   3 Natural Logarithms and Exponentials Basic Properties
  749.    wt: 15:   3 Lengths and Areas on Maps and Plans
  750.    wt: 15:   5 Gaussian Elimination for 3 unknowns 2nd example
  751.    wt: 15:   3 GE III Equation Addition and Multiplication
  752.    wt: 15:   3 Solving triangular system example
  753.    wt: 15:   Video Decimal Multiplication Geometric View Example 2
  754.    wt: 15:   1 Comparison and Subtraction Easy Direct Cases
  755.    wt: 15:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  756.    wt: 14:   Ramblings Introduction Algebra Essay
  757.    wt: 14:   sign monoticity analysis example 3
  758.    wt: 14:   8 quadratics backward use of various formulas
  759.    wt: 14:   3 Circle Arclengh Proportional to Central Angle
  760.    wt: 14:   Proportionality of Line Segments From Parallel Transversals
  761.    wt: 14:   3 Straight Lines Slope as Tangent of Inclination Angle
  762.    wt: 14:   13 Navigation Location from Angles to 2 Landmarks
  763.    wt: 14:   8 Distance Between Points on a Line
  764.    wt: 14:   6 Polar Multiplication and Rotation
  765.    wt: 14:   2 Cartesian Coordinates with signs
  766.    wt: 14:   1 Cartesian Coordinates sans signs
  767.    wt: 14:   4 Angles on Maps Plans drawn to scale
  768.    wt: 14:   4 Rates Ratios and Proporitionality
  769.    wt: 14:   3 Proportionality Examples
  770.    wt: 14:   9 Circle Area and Perimeter Formula Backwards Forwards
  771.    wt: 14:   4 Solving a triangular system exercise
  772.    wt: 14:   3 Two Examples
  773.    wt: 14:   3 Triangle Area Formula Example
  774.    wt: 14:   2 Another Rectangle Area Formula Example
  775.    wt: 14:   Long Division Backward
  776.    wt: 14:   Video Decimal Multiplication Geometric View Example 2
  777.    wt: 14:   Video Power Notation in Decimal Expansion
  778.    wt: 14:   Appendix 1 Decimals Comparison Method Take II
  779.    wt: 14:   Subtraction with J Conversions Example
  780.    wt: 14:   Subtraction Another Video Lesson
  781.    wt: 14:   7 Subtraction for Decimal Fractions with Exercises
  782.    wt: 14:   6 Subtraction with Conversion Example with Exercises
  783.    wt: 14:   4. How to add with decimals B with conversions
  784.    wt: 14:   Area Between Crossing Curves Lesson Take 2
  785.    wt: 14:   Area Between Crossing Curves Lesson Take 1
  786.    wt: 14:   Area Between Curves Lesson Take 2
  787.    wt: 14:   Area Between Curves Lesson Take 1
  788.    wt: 14:   Chapter 19. Exponentials and Natural Logarithms
  789.    wt: 14:   Chapter 14 Limits and Continuity with and sans Decimals
  790.    wt: 14:   Chapter 3. Slope Sign Analysis
  791.    wt: 14:   Chapter 3 Algebra Starter Lessons
  792.    wt: 14:   Primary and Secondary Skills and Practices with Take Home Value
  793.    wt: 14:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  794.    wt: 13:   Appendix 1 primary and preschool mathematic
  795.    wt: 13:   C LAMP Introduction Culture in Mathematics Education
  796.    wt: 13:   Skills Chapter 3 Algebra
  797.    wt: 13:   5 Natural Logarithm Calculator Exercises
  798.    wt: 13:   9 Summary Degrees to Radians and back
  799.    wt: 13:   7 Radian Measures in special Triangles
  800.    wt: 13:   4 Circle Sector Area proportional to Central Angle
  801.    wt: 13:   2 Radian Measure Numerical Value of one degree
  802.    wt: 13:   Parallel Lines and Interior Angles
  803.    wt: 13:   Construction Methods and Criteria for Isometric and Similar Triangles
  804.    wt: 13:   14 Straight Lines Equations General Case
  805.    wt: 13:   12 Spatial Coordinates
  806.    wt: 13:   9 Pythagorean Theorem Chinese Square Proof
  807.    wt: 13:   4 Polar Coordinates to and from
  808.    wt: 13:   5 Drawing to Scale Avoids Angle Distortions
  809.    wt: 13:   5 Proportionality in Equivalent Fractions
  810.    wt: 13:   2 Algebraic View
  811.    wt: 13:   1 What is Proportionality
  812.    wt: 13:   8 Pythagorean Relation Forwards Backwards
  813.    wt: 13:   4 Rectangle Area and Like Formulas Backwards
  814.    wt: 13:   3 More and Less Than with Unlike Signs
  815.    wt: 13:   2 More and Less Than for Counts and Measures
  816.    wt: 13:   2 Essentially one exercises three with solution
  817.    wt: 13:   13 Naming Identifying Formulas with Words
  818.    wt: 13:   6 Pythagorean Hypotenuse Calculation Example
  819.    wt: 13:   1 Written work formats for developing and showing skill
  820.    wt: 13:   A Decimals Modular and Remainder Arithmetic
  821.    wt: 13:   13 Remainder Arithmetic Modulo 5 Example
  822.    wt: 13:   9 Remainder Arithmetic Divisibility by 5
  823.    wt: 13:   Long Division Backwards more
  824.    wt: 13:   A Elementary Basis for Multiplication Methods
  825.    wt: 13:   4 Subtraction with Conversions Borrows and Letter J
  826.    wt: 13:   2 Subtraction Easy Case Examples
  827.    wt: 13:   Appendix 1 Counting Revisited 15 minute video
  828.    wt: 13:   8 What skills and work habits to require
  829.    wt: 13:   7 Adding decimal fractions using decimal point
  830.    wt: 13:   5. How to add decimals C. Examples
  831.    wt: 13:   11 Place Value SI Standard International way
  832.    wt: 13:   Example 1 volume of a pyramid
  833.    wt: 13:   Example 4 with x function of y
  834.    wt: 13:   Example 3
  835.    wt: 13:   Chapter 24 Logarithms Powers and Exponentials
  836.    wt: 13:   Chapter 18. Slopes Areas Integration
  837.    wt: 13:   Chapter 17. Area Approximation
  838.    wt: 13:   Chapter 15. Algebraic Evaluation of Limits
  839.    wt: 13:   Chapter 13. Acceleration
  840.    wt: 13:   Chapter 4 Implication Rules Forwards and Backwards
  841.    wt: 13:   Chapter 7 Calculus Previews and Calculus Lightly
  842.    wt: 13:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  843.    wt: 13:   Chapter 4 Logic for Reading Writing and Geometry etc
  844.    wt: 13:   5 Interpreting and Drawing Maps and Plans.
  845.    wt: 12:   E LAMP Introduction Modern Mathematics
  846.    wt: 12:   B LAMP Introduction Curriculum Development Standards
  847.    wt: 12:   sign monoticity analysis example 4
  848.    wt: 12:   sign monoticity analysis example 2
  849.    wt: 12:   sign monoticity analysis example 1
  850.    wt: 12:   6 quadratics numerical approach
  851.    wt: 12:   8 Formulas for Fractional Exponents with Logarithms
  852.    wt: 12:   8 Radian Measures of Common Angles
  853.    wt: 12:   1 Degrees and Radians Introduction
  854.    wt: 12:   14 Why Scalar Multiplication Distributes Physical Argument
  855.    wt: 12:   3 Navigation with Arrows or Vectors
  856.    wt: 12:   2 Graphing y=Af(x) Vertical Scaling
  857.    wt: 12:   13 Straight Lines Finding Equations from 2 points
  858.    wt: 12:   12 Straight Lines Graphing mx plus b
  859.    wt: 12:   7 Tangent Function is odd on this domain
  860.    wt: 12:   6 Tangent Function Inclination Angle Take 2
  861.    wt: 12:   2 Straight Lines Slopes As Rise Over Run
  862.    wt: 12:   34 sines and cosines of 2A 3A 4A 5A
  863.    wt: 12:   33 sines and cosines of 2A 3A 4A 5A
  864.    wt: 12:   11 Triangle Inequality
  865.    wt: 12:   8 More Use of Maps Not Drawn to Scale
  866.    wt: 12:   3 Inequalities Algebraically
  867.    wt: 12:   1 Decimals Modular and Remainder Arithmetic
  868.    wt: 12:   5 Triangle Area Formula Backwards
  869.    wt: 12:   5 Greater More Less Than Signs in General
  870.    wt: 12:   4 Comparison of Negative Numbers
  871.    wt: 12:   1 Real Numbers Comparison
  872.    wt: 12:   4 GE III Animated Examples
  873.    wt: 12:   1 Essentially One Unknown
  874.    wt: 12:   6 Algebraic Solution Example
  875.    wt: 12:   5 Algebraic Solutions Introduction
  876.    wt: 12:   4 Four Examples Fractional Coefficients
  877.    wt: 12:   3 Four Examples
  878.    wt: 12:   7 Two Examples
  879.    wt: 12:   4 Two Examples
  880.    wt: 12:   4 Circle Area Formula Example
  881.    wt: 12:   C Equality for Fractions and Two Term Ratios and Fractions
  882.    wt: 12:   A Similarities between Fractions and Two Term Ratios
  883.    wt: 12:   13 Fraction Comparison Algebraic View
  884.    wt: 12:   15 Remainder Arithmetic Modulo 9 Example
  885.    wt: 12:   14 Remainder Arithmetic Modulo 9 Example
  886.    wt: 12:   12 Remainder Arithmetic Modulo 10 Example
  887.    wt: 12:   11 Remainder Arithmetic Long Division by 5 Quickly more
  888.    wt: 12:   10 Remainder Arithmetic Long Division by 5 Quickly
  889.    wt: 12:   8 Remainder Arithmetic Morulo 5 Examples II
  890.    wt: 12:   7 Remainder Arithmetic Modulo 5 Examples I
  891.    wt: 12:   10 video Prime Factorization upto 23 squared
  892.    wt: 12:   3 video Primes and Composites from 9 times table
  893.    wt: 12:   1 video how Products are bigger than factor
  894.    wt: 12:   Division with Counts and Length
  895.    wt: 12:   6 Why Decimal Long Division Methods Works Take I
  896.    wt: 12:   3 Division Single Digit Divisor Example
  897.    wt: 12:   C Counting Areas with Powers of Ten
  898.    wt: 12:   Appendix 2 Three Decimal Subtraction Methods
  899.    wt: 12:   8 Subtraction with Units of Measure
  900.    wt: 12:   6. Counting and adding units and mixed units
  901.    wt: 12:   1. Explaining Addition Table
  902.    wt: 12:   Example 2 volume of a cone
  903.    wt: 12:   Example 2
  904.    wt: 12:   Example 1
  905.    wt: 12:   38 Formulas and derivatives for powers and roots
  906.    wt: 12:   33 Chain Rule Real Player video examples
  907.    wt: 12:   Chapter 21 Arrow Addition
  908.    wt: 12:   Chapter 6. Slopes and Vertical Shifts
  909.    wt: 12:   Chapter 4. More Slope Sign Analysis
  910.    wt: 12:   Chapter 2. Slopes and Ski Trails
  911.    wt: 12:   Fall 1983 Calculus Appetizer
  912.    wt: 12:   Appendix A Calculus with Proofs for Keen or Gifted
  913.    wt: 12:   Chapter 6 More Algebra and Geometry
  914.    wt: 12:   3 Telling Tracking Time Temporal and More Place Sense
  915.    wt: 12:   More Algebra and Slope based Calculus Preview
  916.    wt: 12:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  917.    wt: 12:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  918.    wt: 11:   Appendix 2 primary school Arithmetic 01
  919.    wt: 11:   I LAMP Introduction Study Habits
  920.    wt: 11:   H LAMP Introduction Instructional Concepts
  921.    wt: 11:   F LAMP Introduction Prerequisites
  922.    wt: 11:   7 logic review and decimals an odd combination
  923.    wt: 11:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  924.    wt: 11:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  925.    wt: 11:   A Quadratics Summary
  926.    wt: 11:   9 quadratics physical and further context
  927.    wt: 11:   7 quadratic formulla derivation
  928.    wt: 11:   4 quadratics difference of two squares
  929.    wt: 11:   3 quadratics factoring by inspection
  930.    wt: 11:   2 quadratics graphing in general
  931.    wt: 11:   1 quadratics graphing exercises
  932.    wt: 11:   10 Exponential Growth and Decay Models
  933.    wt: 11:   9 Formulas for Real Exponents with Logarithms
  934.    wt: 11:   7 Formulas for Roots with Logarithms Derivation
  935.    wt: 11:   6 Formulas for Even and Odd Roots with Logarithms
  936.    wt: 11:   1 Calculator Starter Exercises
  937.    wt: 11:   6 Radian Measure to Degrees
  938.    wt: 11:   5 Degrees to Radian Measure
  939.    wt: 11:   7 Coordinate Addition and Scalar Multiplication
  940.    wt: 11:   Triangle Angles Sum To 180 Degrees
  941.    wt: 11:   SAS Method For Isometric Or Proportional Triangle Construction
  942.    wt: 11:   Analytic View of Triangle Construction or Line Instersection More
  943.    wt: 11:   D Straight Lines Slope from Coordinates Examples
  944.    wt: 11:   A Straight Line Slope Scaling Properties
  945.    wt: 11:   11 Straight Lines Graphing y=mx
  946.    wt: 11:   10 Straight Lines through Origin Equations More
  947.    wt: 11:   9 Straight Lines through Origin Equations
  948.    wt: 11:   8 Straight Lines Equation for vertical
  949.    wt: 11:   35 sines and cosines of 2A 3A 4A 5A
  950.    wt: 11:   10 Similarity of Triangles Equivalent of Two Criteria
  951.    wt: 11:   7 Translations Rotations Reflections Dilatations
  952.    wt: 11:   3 Similarity by Design with coordinates
  953.    wt: 11:   7 Complex Numbers Appetizer
  954.    wt: 11:   PS F Scalar Multiplication Distributes over Addition
  955.    wt: 11:   PS D Addition with Cartesian Coordinates
  956.    wt: 11:   6 Figuring with Maps Not to Scale
  957.    wt: 11:   25 Mid way Convergence to Axiomatic Approach
  958.    wt: 11:   23 Distributive Law Two Derivations
  959.    wt: 11:   5 Areas of Rectangles Revisited
  960.    wt: 11:   4 Fraction Operations Axiomatic Development
  961.    wt: 11:   6 Compound Interest Forward and Backwards
  962.    wt: 11:   4 Subtraction and Division Axioms
  963.    wt: 11:   2 Addition and Multiplication Axioms
  964.    wt: 11:   2 GE II Comparison
  965.    wt: 11:   1 Proper Equal Sign Usage
  966.    wt: 11:   10 One Example
  967.    wt: 11:   9 Three Examples
  968.    wt: 11:   8 One Example
  969.    wt: 11:   6 Three Examples
  970.    wt: 11:   5 Three Examples
  971.    wt: 11:   2 Three Examples
  972.    wt: 11:   Formula Usage Show Work Format
  973.    wt: 11:   8 Compound Interest Formula Evaluation
  974.    wt: 11:   3 Properties of Square Roots with example
  975.    wt: 11:   1 Squares and Square Roots Introduction
  976.    wt: 11:   9 GCD of 360 110 via Primes and Euclid Algorithm
  977.    wt: 11:   2 Least Common Multiple LCM intro via list method
  978.    wt: 11:   3 Counting with Tables and Trees II
  979.    wt: 11:   5 Reciprocals and Division for Fractions with Units
  980.    wt: 11:   8 Numerals Fractionals Quantals Take II
  981.    wt: 11:   Fraction Operations by Raising Terms A Simple Innovation
  982.    wt: 11:   27 Divisibility by 2 3 6 5 9 10 Example
  983.    wt: 11:   26 Divisibility by 2 3 5 Example
  984.    wt: 11:   25 Divisibility Tests for 2 3 5 9 10 Example
  985.    wt: 11:   23 Remainder Arithmetic Modulo 2
  986.    wt: 11:   22 Remainder Arithmetic Modulo 3 more
  987.    wt: 11:   21 Remainder Arithmetic Modulo 3
  988.    wt: 11:   19 Remainder Arithmetic Rule of 9 for checking sums III
  989.    wt: 11:   16 Remainder Arithmetic Modulo 9 Example 2
  990.    wt: 11:   6 Remainder Arithmetic Modulo 5 Propertie
  991.    wt: 11:   4 Remainder Arithmetic Modulo 10 in general
  992.    wt: 11:   3 Remainder Arithmetic Modulos 10 more still
  993.    wt: 11:   18 video Count Factors given Prime Factorization
  994.    wt: 11:   15 video Factors of 20 using Prime Factorization
  995.    wt: 11:   13 video Factors of 24 using prime
  996.    wt: 11:   9 video Prime Factorization upto 19 squared
  997.    wt: 11:   7 Calculator Usage Notes and Cautions
  998.    wt: 11:   5 Prime Factorization and a Square Rule
  999.    wt: 11:   4 video Prime Factorization Introduction
  1000.    wt: 11:   12 Why Long Division Works Take III
  1001.    wt: 11:   10 Division by Five Long and Short Ways
  1002.    wt: 11:   9 Why Long Division Works Take II
  1003.    wt: 11:   7 Long Divison Mistake Catching
  1004.    wt: 11:   5 Decimal Fraction Multiplication
  1005.    wt: 11:   9 22 Minute Subtraction Review Video
  1006.    wt: 11:   5 A Tip for Efficent Subtraction
  1007.    wt: 11:   2 Decimal Counting Practices
  1008.    wt: 11:   9 Place Value Review Decimal form of Avogrados number included
  1009.    wt: 11:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  1010.    wt: 11:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  1011.    wt: 11:   5 More on Groups of 3 Place Value in Decimal Fractions
  1012.    wt: 11:   4 Groups of 3 Place Value in Decimal Fractions
  1013.    wt: 11:   3 More on Groups of 3 Multi Digit Place Value
  1014.    wt: 11:   A Chain Rule Real Player video examples
  1015.    wt: 11:   1 Fall 1983 Why Slopes Appetizer
  1016.    wt: 11:   13 Limits with Parameters and Derivatives Take II
  1017.    wt: 11:   Postscript Pythagorean Theorem yet another proof
  1018.    wt: 11:   Chapter 23 Links To Trigonometry
  1019.    wt: 11:   Chapter 16. Velocity Approximation
  1020.    wt: 11:   Chapter 15. Slope Approximation
  1021.    wt: 11:   Chapter 12. Units and Slopes
  1022.    wt: 11:   Chapter 10 Slopes and Units
  1023.    wt: 11:   Chapter 9 About First Courses in Calculus
  1024.    wt: 11:   Chapter 7 Slopes and Velocity
  1025.    wt: 11:   Chapter 14. Forward and Backward Use of a Formula
  1026.    wt: 11:   Chapter 17 Objective Ways Trial and Error Discovery
  1027.    wt: 11:   Chapter 14 Deductive and Empirical Views of Mathematics
  1028.    wt: 11:   Chapter 12 Islands and Divisions of Knowledge
  1029.    wt: 11:   Chapter 3 What is in chapters 4 to 8
  1030.    wt: 11:   Chapter 8 Skipped Topics and Why
  1031.    wt: 11:   2 Identifying Size and Position Place and Spatial Sense
  1032.    wt: 11:   Systematic Algebra Skill Development Missing Links
  1033.    wt: 11:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  1034.    wt: 11:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  1035.    wt: 10:   K LAMP Musings Science Education
  1036.    wt: 10:   J LAMP Introduction Extrinsic Origins
  1037.    wt: 10:   G LAMP Introduction Problem Solving Skills
  1038.    wt: 10:   A Introduction Objectives
  1039.    wt: 10:   Skills Chapter 5 Calculus
  1040.    wt: 10:   Ramblings Extrinsic numbers theory
  1041.    wt: 10:   Skills Chapter 1 Arithmetic
  1042.    wt: 10:   Skills Chapter 0 Introduction
  1043.    wt: 10:   5 logarithms and exponentials etc
  1044.    wt: 10:   3 Euclidean Geometry Leanly
  1045.    wt: 10:   Applied Maths Program14092009 POMME variant
  1046.    wt: 10:   what should be learnt and When
  1047.    wt: 10:   Maps Plans Drawings
  1048.    wt: 10:   teaching tutoring algebraic reason
  1049.    wt: 10:   10 quadratic exercises
  1050.    wt: 10:   5 quadratics completing the square
  1051.    wt: 10:   Quadratics in 10 steps
  1052.    wt: 10:   11 Growth and Decay in Biology
  1053.    wt: 10:   2 Square Root Simplification a prequel
  1054.    wt: 10:   A Global Time and Navigation
  1055.    wt: 10:   5 Head To Tail Arrow Addition
  1056.    wt: 10:   4 graphing y=Asin(x c)
  1057.    wt: 10:   3 graphing y=f(x c) plus K
  1058.    wt: 10:   1 graphing y=f(x a)
  1059.    wt: 10:   Straight Lines ASA Intersection Study More
  1060.    wt: 10:   Straight Lines ASA Intersection Study
  1061.    wt: 10:   C Straight Lines Slope from Coordinates
  1062.    wt: 10:   B Straight Line Slope Scaling Properties More
  1063.    wt: 10:   5 Tangent Function Graph
  1064.    wt: 10:   18 sum of sinusoidal waves as a single wave
  1065.    wt: 10:   9 Similarity of Triangles Usual Criteria
  1066.    wt: 10:   6 Geometric Diagrams in Class
  1067.    wt: 10:   5 Similarity of Circles Squares and Rectangles
  1068.    wt: 10:   11 A Partial Summary
  1069.    wt: 10:   5 Algebraic View of Slopes
  1070.    wt: 10:   1 Numerical view of lines and their equations
  1071.    wt: 10:   What is and is not here
  1072.    wt: 10:   PS E Multiplication with Polar Coordinates
  1073.    wt: 10:   13 Angle Side Angle Failure
  1074.    wt: 10:   A Measurement with Ruler Proper Use
  1075.    wt: 10:   2 Measuring Area Directly
  1076.    wt: 10:   15 Head to Tails in place Addition Associative
  1077.    wt: 10:   13 Arrows and Vectors in a Plane
  1078.    wt: 10:   B Decimal Comparison and Subtraction
  1079.    wt: 10:   2 Fraction Operations Physical Development
  1080.    wt: 10:   6 Equations and Systems Equivalent or Implied
  1081.    wt: 10:   5 Equality in Algebra
  1082.    wt: 10:   3 Product Axioms Two Forms
  1083.    wt: 10:   3 Geometric Formulas and Function Notation
  1084.    wt: 10:   1 GE Substitution four examples
  1085.    wt: 10:   2 Three Examples
  1086.    wt: 10:   Skill Development Notes
  1087.    wt: 10:   7 Compound Interest Formula Introduction
  1088.    wt: 10:   5 Box Volume Formula Example
  1089.    wt: 10:   3 Comparison of Negative Numbers
  1090.    wt: 10:   10 Euclid Algorithm with 129 125 and with 45 14
  1091.    wt: 10:   5 Counting with Tables Trees Product Rule Take II
  1092.    wt: 10:   2 Counting with Tables and Trees I
  1093.    wt: 10:   3 signed coordinates for maps and planes
  1094.    wt: 10:   1 Addition and Subtraction with Units
  1095.    wt: 10:   17 Efficient Ways to Add and Subtract
  1096.    wt: 10:   16 Addition Subtraction Comparision Compared
  1097.    wt: 10:   15 Adding and Subtracting with Unlike Denominators
  1098.    wt: 10:   14 Adding and Subtracting with Like Denominators
  1099.    wt: 10:   11 Simplification an Algebraic View
  1100.    wt: 10:   7 Numerals Fractionals Quantals
  1101.    wt: 10:   6 Multiplication Algebraically Take II
  1102.    wt: 10:   3 Unit fraction of a fraction
  1103.    wt: 10:   1 What is a fraction Take II
  1104.    wt: 10:   24 Divisibility Tests for 2 3 5 9 10
  1105.    wt: 10:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  1106.    wt: 10:   18 Remainder Arithmetic Rule of 9 for checking sums II
  1107.    wt: 10:   17 Remainder Arithmetic Rule of 9 for checking sums I
  1108.    wt: 10:   5 Remainder Arithmetic Modulo 5
  1109.    wt: 10:   2 Remainder Arithmetic Modulo 10 more
  1110.    wt: 10:   1 Remainder Arithmetic Modulo 10
  1111.    wt: 10:   19 video Prime Factorization Unique
  1112.    wt: 10:   14 video Factors of 24 Take II
  1113.    wt: 10:   8 video Prime Factorization upto 19
  1114.    wt: 10:   11 Another Single Digit Divisor Example
  1115.    wt: 10:   2 Division with Single Digit Divisors
  1116.    wt: 10:   D Decimal Multiplication Methods Derived
  1117.    wt: 10:   6 Multiplication Commutes Order Not Important
  1118.    wt: 10:   4 Two and Three Digit Multipliers
  1119.    wt: 10:   3 More One Digit Multipliers
  1120.    wt: 10:   1 Why 3 times 5 gives 15
  1121.    wt: 10:   Formula Evaluation how to show work
  1122.    wt: 10:   Expression Evaluation how to show work
  1123.    wt: 10:   9 Comparison and Subtraction of Time Intervals
  1124.    wt: 10:   Volume of Solid by Cross Sections Lesson
  1125.    wt: 10:   36 Cube root derivative animated
  1126.    wt: 10:   28 Chain Rule Preparation for a Proof
  1127.    wt: 10:   25 Chain Rule Animated Examples Continued
  1128.    wt: 10:   24 Chain Rule Animated Examples
  1129.    wt: 10:   7 Animated Differentiation Examples
  1130.    wt: 10:   12 Limits with Parameters and Derivatives Take I
  1131.    wt: 10:   B3 Bolzano Weierstrass Theorem
  1132.    wt: 10:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  1133.    wt: 10:   Chapter 20 Vectors and Complex Numbers
  1134.    wt: 10:   Chapter 11. Graphing Slope versus Position
  1135.    wt: 10:   Chapter 8. Slope Interpretation
  1136.    wt: 10:   Chapter 1.Introduction
  1137.    wt: 10:   Chapter 2 Implication Rules Forwards and Backwards
  1138.    wt: 10:   Chapter 22 Contrapositive and Vacuously True Implications
  1139.    wt: 10:   Chapter 16 Origins and Limitations of Rules and Patterns
  1140.    wt: 10:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  1141.    wt: 10:   Chapter 2 Why Sets
  1142.    wt: 10:   Chapter 1 Arithmetic
  1143.    wt: 10:   6 Measuring via counting or arithmetic the role of fractions
  1144.    wt: 10:   4 Money Matters Saving Earning Buying Selling and Budgets

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

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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