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.

Home << Search

[1] [2] [3] [4]

Key Word Search

Folder Search

46 matches:

  1.    wt: 6:   12 Webvideo Lessons on Area and Volume Calculation/
  2.    wt: 5:   5 Lessons on Integration/
  3.    wt: 5:   4 Lessons on Using Derivatives/
  4.    wt: 5:   38 Lessons on Calculating Derivatives/
  5.    wt: 5:   13 Lessons on Limits and Continuity/
  6.    wt: 4:   70 Calculus Starter Lessons/
  7.    wt: 3:   6 Trigonometry first steps/
  8.    wt: 3:   6 More Less Greater Than Inequalities and Comparison/
  9.    wt: 2:   B Real Numbers Extrinsic Development/
  10.    wt: 2:   A Origins of Counting and Figuring Methods/
  11.    wt: 2:   10 Examples of Algebraic Reasoning/
  12.    wt: 2:   9 Proportionality Backwards and Forwards/
  13.    wt: 2:   8 Unifying Theme For Algebra/
  14.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  15.    wt: 2:   5 Real Numbers/
  16.    wt: 2:   4 Computation Rules and Function Notation/
  17.    wt: 2:   Step 4 Gaussian Elimination/
  18.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  19.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  20.    wt: 2:   Step 1 Stick diagram and fractions/
  21.    wt: 2:   3 Solving Linear Equations/
  22.    wt: 2:   2 Formula Forward Use Evaluation/
  23.    wt: 2:   1 Working With Sets/
  24.    wt: 2:   Algebra Starter Lessons/
  25.    wt: 2:   6 Fractions and Ratios/
  26.    wt: 2:   Volume 3 Why Slopes A Calculus Intro Etc/
  27.    wt: 2:   Mathematics 506 Lessons/
  28.    wt: 1:   Direct Current Electric Circuits/
  29.    wt: 1:   Parent Center/
  30.    wt: 1:   Mathematics Skills Year by Year/
  31.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  32.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  33.    wt: 1:   13 Vectors/
  34.    wt: 1:   12 Function Translating and Rescaling/
  35.    wt: 1:   11 Parallel Straight Lines and Transversals/
  36.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  37.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  38.    wt: 1:   8 Unit Circle Trigonometry/
  39.    wt: 1:   7 Complex Numbers/
  40.    wt: 1:   5 What is Similarity/
  41.    wt: 1:   4 Lines and Slopes Take 1/
  42.    wt: 1:   3 Cartesian and Polar Coordinates/
  43.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  44.    wt: 1:   1 Maps Plans Measurement/
  45.    wt: 1:   Geometry maps plans trigonometry vectors/
  46.    wt: 1:   Advanced Calculus Volume 3 Appendices/

Web Page Search

134 matches:

  1.    wt: 3:   Area Between Crossing Curves Lesson Take 2
  2.    wt: 3:   Area Between Crossing Curves Lesson Take 1
  3.    wt: 3:   Area Between Curves Lesson Take 2
  4.    wt: 3:   Area Between Curves Lesson Take 1
  5.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  6.    wt: 2:   Example 1. Area Between x and x squared
  7.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  8.    wt: 2:   Chapter 3 Algebra Starter Lessons
  9.    wt: 1:   Skills Chapter 5 Calculus
  10.    wt: 1:   6 polynomials etc
  11.    wt: 1:   chapitre 06 00 Chaines de la raison
  12.    wt: 1:   chapitre 04 06 engagements
  13.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  14.    wt: 1:   1 Energy Power Heat06
  15.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  16.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  17.    wt: 1:   16 Secondary Mathematics Tips
  18.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  19.    wt: 1:   Ages 6 to 7
  20.    wt: 1:   26 Function definitions done and coming
  21.    wt: 1:   16 Increasing or decreasing on intervals
  22.    wt: 1:   6 Set Existence Formation and Notation
  23.    wt: 1:   6 quadratics numerical approach
  24.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  25.    wt: 1:   1 Calculator Starter Exercises
  26.    wt: 1:   7 Links Lessons Elsewhere
  27.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  28.    wt: 1:   16 cotangent function Definition Graph and Inverse
  29.    wt: 1:   6 Graph of arccos function
  30.    wt: 1:   6 Radian Measure to Degrees
  31.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  32.    wt: 1:   6 Vectors with Coordinates
  33.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  34.    wt: 1:   26 Formulas for products of sines and cosines
  35.    wt: 1:   16 Right Triangle Complementary Angle Relations
  36.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  37.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  38.    wt: 1:   16 References and Originality Question
  39.    wt: 1:   6 Field Properties of Complex Number
  40.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  41.    wt: 1:   6 Geometric Diagrams in Class
  42.    wt: 1:   12 Links Lessons elsewhere
  43.    wt: 1:   6 Intersection of lines by solving linear systems
  44.    wt: 1:   8 Distance Between Points on a Line
  45.    wt: 1:   6 Polar Multiplication and Rotation
  46.    wt: 1:   16 Angles Subtended By Chords and Diameters
  47.    wt: 1:   6 Ruler and compass Angle Bisection
  48.    wt: 1:   2 Correspondence between Triangles
  49.    wt: 1:   6 Figuring with Maps Not to Scale
  50.    wt: 1:   3 Lengths and Areas on Maps and Plans
  51.    wt: 1:   2 Measuring Area Directly
  52.    wt: 1:   26 More Less Greater Than Comparison
  53.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  54.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  55.    wt: 1:   6 Column Methods for Decimal Multiplication
  56.    wt: 1:   5 Areas of Rectangles Revisited
  57.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  58.    wt: 1:   6 Compound Interest Forward and Backwards
  59.    wt: 1:   5 Triangle Area Formula Backwards
  60.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  61.    wt: 1:   6 Equations and Systems Equivalent or Implied
  62.    wt: 1:   16 Real Numbers Comparison
  63.    wt: 1:   6 Unsigned Real Numbers
  64.    wt: 1:   6 Algebraic Solution Example
  65.    wt: 1:   6 Three Examples
  66.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  67.    wt: 1:   4 Circle Area Formula Example
  68.    wt: 1:   3 Triangle Area Formula Example
  69.    wt: 1:   2 Another Rectangle Area Formula Example
  70.    wt: 1:   6 Power Set Notation
  71.    wt: 1:   6 Three Notions of What is a Variable
  72.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  73.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  74.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  75.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  76.    wt: 1:   6 GCD from Prime
  77.    wt: 1:   5 Common Divisors 60 45 via Prime
  78.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  79.    wt: 1:   6 adding signed numbers
  80.    wt: 1:   6 Simplification of Fractions with Units
  81.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  82.    wt: 1:   16 Addition Subtraction Comparision Compared
  83.    wt: 1:   6 Multiplication of Mixed Numbers
  84.    wt: 1:   6 Multiplication Algebraically Take II
  85.    wt: 1:   6 Multiplication by Natural Numbers
  86.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  87.    wt: 1:   26 Divisibility by 2 3 5 Example
  88.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  89.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  90.    wt: 1:   16 video Factors of 980 using prime
  91.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  92.    wt: 1:   2 Prime and Composites less than 16
  93.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  94.    wt: 1:   C Counting Areas with Powers of Ten
  95.    wt: 1:   6 Multiplication Commutes Order Not Important
  96.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  97.    wt: 1:   6. Counting and adding units and mixed units
  98.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  99.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  100.    wt: 1:   016 Numbering Occidental Calendar Days
  101.    wt: 1:   6 How long is a million seconds
  102.    wt: 1:   5 Area Under Curve Exercise
  103.    wt: 1:   A Related lessons in Volume 3
  104.    wt: 1:   36 Cube root derivative animated
  105.    wt: 1:   26 Chain Rule Recognising outer inner functions
  106.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  107.    wt: 1:   6 Power rule from product rule
  108.    wt: 1:   6 Continuity at a point
  109.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  110.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  111.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  112.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  113.    wt: 1:   Chapter 18. Slopes Areas Integration
  114.    wt: 1:   Chapter 17. Area Approximation
  115.    wt: 1:   Chapter 16. Velocity Approximation
  116.    wt: 1:   Chapter 9 About First Courses in Calculus
  117.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  118.    wt: 1:   Fall 1983 Calculus Appetizer
  119.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  120.    wt: 1:   Chapter 16. Painless Theorem Proving
  121.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  122.    wt: 1:   Chapter 6 Change of Language
  123.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  124.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  125.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  126.    wt: 1:   Chapter 6 Chains of Reason
  127.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  128.    wt: 1:   Chapter 6 More Algebra and Geometry
  129.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  130.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  131.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  132.    wt: 1:   More Algebra and Slope based Calculus Preview
  133.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  134.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

702 matches:

  1.    wt: 9:   Area Between Crossing Curves Lesson Take 2
  2.    wt: 9:   Area Between Crossing Curves Lesson Take 1
  3.    wt: 9:   Area Between Curves Lesson Take 2
  4.    wt: 9:   Area Between Curves Lesson Take 1
  5.    wt: 8:   Example 1. Area Between x and x squared
  6.    wt: 7:   Example 2 volume of a cone
  7.    wt: 7:   Example 1 volume of a pyramid
  8.    wt: 7:   Volume of Solid by Cross Sections Lesson
  9.    wt: 7:   6 Continuity at a point
  10.    wt: 6:   Example 4 with x function of y
  11.    wt: 6:   Example 3
  12.    wt: 6:   Example 2
  13.    wt: 6:   Example 1
  14.    wt: 6:   Summary
  15.    wt: 6:   5 Area Under Curve Exercise
  16.    wt: 6:   4 Definite Integrals Evaluation Exercises
  17.    wt: 6:   A Related lessons in Volume 3
  18.    wt: 6:   36 Cube root derivative animated
  19.    wt: 6:   27 Chain Rule sinusoidal outer inner functions EGS
  20.    wt: 6:   26 Chain Rule Recognising outer inner functions
  21.    wt: 6:   25 Chain Rule Animated Examples Continued
  22.    wt: 6:   16 Derivatives of reciprocals of sine and cosine
  23.    wt: 6:   13 sine and cosine derivatives 1st step
  24.    wt: 6:   8 Differentiation of polynomials
  25.    wt: 6:   6 Power rule from product rule
  26.    wt: 5:   A Related Material in Volume 3
  27.    wt: 5:   3 Two Chain Rule Method Exercises
  28.    wt: 5:   2 Indefinite Integrals Exercises
  29.    wt: 5:   1 Chain Rule in Reverse Integration Method
  30.    wt: 5:   4 Second derivative test exercise example
  31.    wt: 5:   3 Second derivative test
  32.    wt: 5:   2 Second derivative test prequel
  33.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  34.    wt: 5:   A Chain Rule Real Player video examples
  35.    wt: 5:   38 Formulas and derivatives for powers and roots
  36.    wt: 5:   34 Derivative of exponential function
  37.    wt: 5:   33 Chain Rule Real Player video examples
  38.    wt: 5:   31 Derivatives of inverse functions
  39.    wt: 5:   30Chain Rule A Proof
  40.    wt: 5:   29 Chain Rule Optional Reading
  41.    wt: 5:   28 Chain Rule Preparation for a Proof
  42.    wt: 5:   24 Chain Rule Animated Examples
  43.    wt: 5:   23 Chain Rule in general
  44.    wt: 5:   22 Chain Rule for polynomials
  45.    wt: 5:   21 Chain Rule for powers
  46.    wt: 5:   20 Chain Rule for Pulley Systems
  47.    wt: 5:   19 Chain Rule for linear functions
  48.    wt: 5:   18 Chain Rule Introduction
  49.    wt: 5:   17 Derivatives of quotients of sine and cosine
  50.    wt: 5:   15 sine and cosine derivatives 3rd step
  51.    wt: 5:   14 sine and cosine derivatives 2nd step
  52.    wt: 5:   12 Quotient rule examples
  53.    wt: 5:   11 Quotient rule
  54.    wt: 5:   10 Power rule for negative integers
  55.    wt: 5:   9 Reciprocal rule
  56.    wt: 5:   7 Animated Differentiation Examples
  57.    wt: 5:   5 Product Rule
  58.    wt: 5:   4 Sum Rule
  59.    wt: 5:   3 Motivation for Limit Definition Take 2
  60.    wt: 5:   2 Motivation for Limit Definition Take 1
  61.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  62.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  63.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  64.    wt: 5:   11 Limits at infinity Three Examples
  65.    wt: 5:   10 Three one sided limits with infinite values
  66.    wt: 5:   9 Limits Continuity and Composition
  67.    wt: 5:   8 Four Animated Examples
  68.    wt: 5:   7 Evaluation by immediate or delayed substitution
  69.    wt: 5:   5 Jumps and absence of unlimited error control
  70.    wt: 5:   4 Numerical properties
  71.    wt: 5:   3 Decimal insights for limits continuity convergence
  72.    wt: 5:   2 Algebraic codification
  73.    wt: 5:   1 Numerical introduction
  74.    wt: 4:   6 Trigonometry Sines of Supplementary Angles
  75.    wt: 4:   6 Column Methods for Decimal Multiplication
  76.    wt: 4:   6 Algebraic Solution Example
  77.    wt: 4:   6 Three Examples
  78.    wt: 4:   6 Multiplication of Mixed Numbers
  79.    wt: 4:   6 Multiplication Algebraically Take II
  80.    wt: 4:   Chapter 16. Velocity Approximation
  81.    wt: 4:   Chapter 6. Slopes and Vertical Shifts
  82.    wt: 3:   1 Energy Power Heat06
  83.    wt: 3:   16 Secondary Mathematics Tips
  84.    wt: 3:   6 Discipline Who is in Charge Conserving Authority
  85.    wt: 3:   16 References and Originality Question
  86.    wt: 3:   6 Field Properties of Complex Number
  87.    wt: 3:   8 Triangles Cascade Problem Solving
  88.    wt: 3:   7 Trignometric Ratios Unit Circle
  89.    wt: 3:   5 Trigonometric Ratios For Tangent and Special Triangles
  90.    wt: 3:   4 Trigonometric Ratios For Two Special Triangles
  91.    wt: 3:   3 Trigonometric Ratios sine and cosine
  92.    wt: 3:   2 Similar Triangles Equality of Corresponding Side Ratios
  93.    wt: 3:   1 Angle Measurement with Degrees
  94.    wt: 3:   Why Trigonometry the whyslopes view
  95.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  96.    wt: 3:   6 Geometric Diagrams in Class
  97.    wt: 3:   6 Intersection of lines by solving linear systems
  98.    wt: 3:   6 Polar Multiplication and Rotation
  99.    wt: 3:   16 Angles Subtended By Chords and Diameters
  100.    wt: 3:   6 Ruler and compass Angle Bisection
  101.    wt: 3:   26 More Less Greater Than Comparison
  102.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  103.    wt: 3:   6 Infinite Decimals Ending in 9 repeating
  104.    wt: 3:   5 Areas of Rectangles Revisited
  105.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  106.    wt: 3:   6 Compound Interest Forward and Backwards
  107.    wt: 3:   5 Triangle Area Formula Backwards
  108.    wt: 3:   4 Rectangle Area and Like Formulas Backwards
  109.    wt: 3:   6 Equations and Systems Equivalent or Implied
  110.    wt: 3:   5 Greater More Less Than Signs in General
  111.    wt: 3:   4 Comparison of Negative Numbers
  112.    wt: 3:   3 More and Less Than with Unlike Signs
  113.    wt: 3:   2 More and Less Than for Counts and Measures
  114.    wt: 3:   1 Real Numbers Comparison
  115.    wt: 3:   16 Real Numbers Comparison
  116.    wt: 3:   6 Unsigned Real Numbers
  117.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  118.    wt: 3:   4 Circle Area Formula Example
  119.    wt: 3:   3 Triangle Area Formula Example
  120.    wt: 3:   2 Another Rectangle Area Formula Example
  121.    wt: 3:   6 Power Set Notation
  122.    wt: 3:   6 Three Notions of What is a Variable
  123.    wt: 3:   A Similarities between Fractions and Two Term Ratios
  124.    wt: 3:   16 Addition Subtraction Comparision Compared
  125.    wt: 3:   9 Improper Fractions and Mixed Numbers
  126.    wt: 3:   8 Numerals Fractionals Quantals Take II
  127.    wt: 3:   7 Numerals Fractionals Quantals
  128.    wt: 3:   Chapter 18. Slopes Areas Integration
  129.    wt: 3:   Chapter 17. Area Approximation
  130.    wt: 3:   Chapter 9 About First Courses in Calculus
  131.    wt: 3:   Fall 1983 Calculus Appetizer
  132.    wt: 2:   6 polynomials etc
  133.    wt: 2:   D Wire Resistance Calculation02
  134.    wt: 2:   E Kirchoffs Second Law
  135.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  136.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  137.    wt: 2:   Ages 6 to 7
  138.    wt: 2:   26 Function definitions done and coming
  139.    wt: 2:   16 Increasing or decreasing on intervals
  140.    wt: 2:   6 Set Existence Formation and Notation
  141.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  142.    wt: 2:   16 cotangent function Definition Graph and Inverse
  143.    wt: 2:   6 Graph of arccos function
  144.    wt: 2:   6 Radian Measure to Degrees
  145.    wt: 2:   5 Degrees to Radian Measure
  146.    wt: 2:   4 Circle Sector Area proportional to Central Angle
  147.    wt: 2:   6 Vectors with Coordinates
  148.    wt: 2:   Parallel Lines and Parallel Transversals
  149.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  150.    wt: 2:   4 Tangent Function Properties
  151.    wt: 2:   17 tangent function angle sum formulas
  152.    wt: 2:   27 Logarithmic use of products of sines and cosines
  153.    wt: 2:   26 Formulas for products of sines and cosines
  154.    wt: 2:   16 Right Triangle Complementary Angle Relations
  155.    wt: 2:   9 Graphs of sine and cosine over one period
  156.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  157.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  158.    wt: 2:   5 Similarity of Circles Squares and Rectangles
  159.    wt: 2:   12 Links Lessons elsewhere
  160.    wt: 2:   8 Distance Between Points on a Line
  161.    wt: 2:   PS F Scalar Multiplication Distributes over Addition
  162.    wt: 2:   2 Correspondence between Triangles
  163.    wt: 2:   6 Figuring with Maps Not to Scale
  164.    wt: 2:   3 Lengths and Areas on Maps and Plans
  165.    wt: 2:   2 Measuring Area Directly
  166.    wt: 2:   musings do not puiblish real numbers
  167.    wt: 2:   A Modular and Remainder Arithmetic
  168.    wt: 2:   A Signed Number Arithmetic Review
  169.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  170.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  171.    wt: 2:   23 Distributive Law Two Derivations
  172.    wt: 2:   22 Multiplication of Signed Numbers
  173.    wt: 2:   21 Addition of Multiples of a Single Vector
  174.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  175.    wt: 2:   19 Signed Multiples of Vectors
  176.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  177.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  178.    wt: 2:   15 Head to Tails in place Addition Associative
  179.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  180.    wt: 2:   13 Arrows and Vectors in a Plane
  181.    wt: 2:   12 Real Numbers Line Signed Coordinates
  182.    wt: 2:   11 Signed Number Addition and Addition Properties
  183.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  184.    wt: 2:   9 Division with Digits after Decimal Point
  185.    wt: 2:   8 Division and Mulplication of Compound Fractions
  186.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  187.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  188.    wt: 2:   4 Location of Point in Decimal Addition
  189.    wt: 2:   3 Location of Point in Decimal Multiplication
  190.    wt: 2:   2 Counting Digits in Decimal Multiplication
  191.    wt: 2:   1 Fractions with Finite Decimal Expansions
  192.    wt: 2:   E Long Division Methods more
  193.    wt: 2:   D Long Division Methods
  194.    wt: 2:   C Three Decimal Subtraction Methods
  195.    wt: 2:   B Decimal Comparison and Subtraction
  196.    wt: 2:   A Decimal Addition Columm Methods
  197.    wt: 2:   8 Column Multiplication Methods in General
  198.    wt: 2:   7 Decimals Multiplication Methods Examples
  199.    wt: 2:   5 Distributive Law for Whole Numbers
  200.    wt: 2:   4 Commutative Law Groups Counting Form
  201.    wt: 2:   3 Multiplicative Counting Skills Principles
  202.    wt: 2:   2 Combing Counts Addition Skills and Principles
  203.    wt: 2:   1 The Counting Origins of Numbers
  204.    wt: 2:   4 Fraction Operations Axiomatic Development
  205.    wt: 2:   3 Inequalities Algebraically
  206.    wt: 2:   2 Fraction Operations Physical Development
  207.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  208.    wt: 2:   5 Proportionality in Equivalent Fractions
  209.    wt: 2:   4 Rates Ratios and Proporitionality
  210.    wt: 2:   3 Proportionality Examples
  211.    wt: 2:   2 Algebraic View
  212.    wt: 2:   1 What is Proportionality
  213.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  214.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  215.    wt: 2:   3 Linear Equation Literal Solution More
  216.    wt: 2:   2 Linear Equation Literal Solution
  217.    wt: 2:   1 Changing Calculations
  218.    wt: 2:   5 Equality in Algebra
  219.    wt: 2:   4 Subtraction and Division Axioms
  220.    wt: 2:   3 Product Axioms Two Forms
  221.    wt: 2:   2 Addition and Multiplication Axioms
  222.    wt: 2:   1 Equivalent Computation Rules
  223.    wt: 2:   15 Real Number Division
  224.    wt: 2:   14 Real Number Multiplication
  225.    wt: 2:   13 Real Number Subtraction
  226.    wt: 2:   12 Real Number Additive Inverses or Negatives
  227.    wt: 2:   11 Real Number Addition
  228.    wt: 2:   10 Real Number Lengths and Signs
  229.    wt: 2:   9 Coordinates for Regions in Space
  230.    wt: 2:   8 Coordinates for Maps and Planes
  231.    wt: 2:   7 Real Numbers as Line Cordinates
  232.    wt: 2:   5 Rational Numbers More
  233.    wt: 2:   4 Rational Numbers
  234.    wt: 2:   3 Fractions
  235.    wt: 2:   2 Integers
  236.    wt: 2:   1 Whole and Natural Numbers
  237.    wt: 2:   5 Independent versus Dependent Variables
  238.    wt: 2:   4 Changing Letters
  239.    wt: 2:   3 Geometric Formulas and Function Notation
  240.    wt: 2:   2 Computation Rules Evaluation
  241.    wt: 2:   1 Formulas Dependence and Function Notation
  242.    wt: 2:   More Exercises
  243.    wt: 2:   Simple Exercises
  244.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  245.    wt: 2:   4 GE III Animated Examples
  246.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  247.    wt: 2:   3 GE III Equation Addition and Multiplication
  248.    wt: 2:   2 GE II Comparison
  249.    wt: 2:   1 GE Substitution four examples
  250.    wt: 2:   4 Solving a triangular system exercise
  251.    wt: 2:   3 Solving triangular system example
  252.    wt: 2:   2 Essentially one exercises three with solution
  253.    wt: 2:   1 Essentially One Unknown
  254.    wt: 2:   5 Algebraic Solutions Introduction
  255.    wt: 2:   4 Four Examples Fractional Coefficients
  256.    wt: 2:   3 Four Examples
  257.    wt: 2:   2 Three Examples
  258.    wt: 2:   1 Proper Equal Sign Usage
  259.    wt: 2:   Skill Development Notes
  260.    wt: 2:   10 One Example
  261.    wt: 2:   9 Three Examples
  262.    wt: 2:   8 One Example
  263.    wt: 2:   7 Two Examples
  264.    wt: 2:   5 Three Examples
  265.    wt: 2:   4 Two Examples
  266.    wt: 2:   3 Two Examples
  267.    wt: 2:   2 Three Examples
  268.    wt: 2:   Using Letters for Physical Quantities
  269.    wt: 2:   Formula Usage Show Work Format
  270.    wt: 2:   13 Naming Identifying Formulas with Words
  271.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  272.    wt: 2:   11 Volume of Sphere
  273.    wt: 2:   10 Volume of Pyramid
  274.    wt: 2:   9 Volume of Cone
  275.    wt: 2:   8 Compound Interest Formula Evaluation
  276.    wt: 2:   7 Compound Interest Formula Introduction
  277.    wt: 2:   5 Box Volume Formula Example
  278.    wt: 2:   1 Written work formats for developing and showing skill
  279.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  280.    wt: 2:   9 Sets in Probability and Statistics
  281.    wt: 2:   8 Sets of Numbers
  282.    wt: 2:   7 Cautious or Safe Set Construction
  283.    wt: 2:   5 Product Builder Notation
  284.    wt: 2:   4 Subset Builder Notation
  285.    wt: 2:   3 Counting with Sets etc
  286.    wt: 2:   2 Venn Diagrams
  287.    wt: 2:   1 Finite Sets
  288.    wt: 2:   5 Talking about Numbers and Quantities
  289.    wt: 2:   4 A Brief Story of numbers and algebra
  290.    wt: 2:   3 Adding Words To Arithmetic
  291.    wt: 2:   2 What is a Variable
  292.    wt: 2:   1 Three Skills For Algebra
  293.    wt: 2:   About Folder Contents
  294.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  295.    wt: 2:   5 Common Divisors 60 45 via Prime
  296.    wt: 2:   LCM 60 45 Avoid List Method Use Prime
  297.    wt: 2:   6 adding signed numbers
  298.    wt: 2:   6 Simplification of Fractions with Units
  299.    wt: 2:   D Three Term Ratios
  300.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  301.    wt: 2:   B Fractions and Two Term Ratios
  302.    wt: 2:   22 Complex Compound Fractions
  303.    wt: 2:   21 Working With Signs
  304.    wt: 2:   21 Reciprocals for Fractions and Wholes
  305.    wt: 2:   20 Dividing Fractions the Why
  306.    wt: 2:   19 Dividing Fractions How TO
  307.    wt: 2:   18 Efficient Ways to Multiply
  308.    wt: 2:   17 Efficient Ways to Add and Subtract
  309.    wt: 2:   15 Adding and Subtracting with Unlike Denominators
  310.    wt: 2:   14 Adding and Subtracting with Like Denominators
  311.    wt: 2:   13 Fraction Comparison Algebraic View
  312.    wt: 2:   12 Fraction Comparison
  313.    wt: 2:   11 Simplification an Algebraic View
  314.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  315.    wt: 2:   5 Equivalent Fractions
  316.    wt: 2:   4 Fraction Multiplication
  317.    wt: 2:   3 Unit fraction of a fraction
  318.    wt: 2:   2 Unit Fraction Multiplication
  319.    wt: 2:   1 What is a fraction Take II
  320.    wt: 2:   1 What is a fraction
  321.    wt: 2:   Fraction Operations by Raising Terms A Simple Innovation
  322.    wt: 2:   6 Multiplication by Natural Numbers
  323.    wt: 2:   16 video Factors of 980 using prime
  324.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  325.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  326.    wt: 2:   6 Multiplication Commutes Order Not Important
  327.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  328.    wt: 2:   6. Counting and adding units and mixed units
  329.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  330.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  331.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  332.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  333.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  334.    wt: 2:   D2 Limits of Monotone Sequences
  335.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  336.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  337.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  338.    wt: 2:   Chapter 23 Links To Trigonometry
  339.    wt: 2:   Chapter 22 Complex Numbers
  340.    wt: 2:   Chapter 21 Arrow Addition
  341.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  342.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  343.    wt: 2:   Chapter 15. Slope Approximation
  344.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  345.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  346.    wt: 2:   Chapter 13. Acceleration
  347.    wt: 2:   Chapter 12. Units and Slopes
  348.    wt: 2:   Chapter 11. Graphing Slope versus Position
  349.    wt: 2:   Chapter 10 Slopes and Units
  350.    wt: 2:   Chapter 8. Slope Interpretation
  351.    wt: 2:   Chapter 7 Slopes and Velocity
  352.    wt: 2:   Chapter 5. Slope Sign Tests
  353.    wt: 2:   Chapter 4. More Slope Sign Analysis
  354.    wt: 2:   Chapter 3. Slope Sign Analysis
  355.    wt: 2:   Chapter 2. Slopes and Ski Trails
  356.    wt: 2:   Chapter 1.Introduction
  357.    wt: 2:   Foreword
  358.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  359.    wt: 2:   Chapter 16. Painless Theorem Proving
  360.    wt: 2:   Chapter 6 Change of Language
  361.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  362.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  363.    wt: 2:   Chapter 6 Chains of Reason
  364.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  365.    wt: 2:   Chapter 6 More Algebra and Geometry
  366.    wt: 2:   Chapter 3 Algebra Starter Lessons
  367.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  368.    wt: 1:   Skills Chapter 5 Calculus
  369.    wt: 1:   Ramblings Extrinsic numbers theory
  370.    wt: 1:   three goals to set for students
  371.    wt: 1:   Teach the teachers plus goals
  372.    wt: 1:   permissions for teachers
  373.    wt: 1:   Math Ed if it must be short make it lean effective
  374.    wt: 1:   Applied Maths Program14092009 POMME variant
  375.    wt: 1:   activities for students
  376.    wt: 1:   links Education Resources online
  377.    wt: 1:   teaching tips
  378.    wt: 1:   Operational Viewpoint to Value
  379.    wt: 1:   formal or informal peer review
  380.    wt: 1:   Motivation and Context Problem
  381.    wt: 1:   chapitre 06 00 Chaines de la raison
  382.    wt: 1:   chapitre 04 06 engagements
  383.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  384.    wt: 1:   logique deux enigme
  385.    wt: 1:   4 Energy Power Heat09
  386.    wt: 1:   3 Energy Power Heat08
  387.    wt: 1:   2 Energy Power Heat07
  388.    wt: 1:   E Energy Power05
  389.    wt: 1:   D Energy Power04
  390.    wt: 1:   C Energy Power03
  391.    wt: 1:   B Energy Power02
  392.    wt: 1:   A Energy Power01
  393.    wt: 1:   2 Conductance Resistance Duality02
  394.    wt: 1:   1 Conductance Resistance Duality01
  395.    wt: 1:   F Wire Resistance Calculation04
  396.    wt: 1:   E Wire Resistance Calculation03
  397.    wt: 1:   C Wire Resistance Calculation01
  398.    wt: 1:   B Wire Resistance Qualitative02
  399.    wt: 1:   A Wire Resistance Qualitative01
  400.    wt: 1:   3 Like resistors in parallel
  401.    wt: 1:   2 Unlike resistors in parallel01
  402.    wt: 1:   1 Like resistors in series
  403.    wt: 1:   H Series Circuit02
  404.    wt: 1:   G Series Circuit01
  405.    wt: 1:   F Unlike Resistors in Series
  406.    wt: 1:   D Kirchoff First Law
  407.    wt: 1:   C Electromotive force conventional current02
  408.    wt: 1:   B Electromotive force conventional current01
  409.    wt: 1:   A Circuit Elements
  410.    wt: 1:   Home Tutoring and Home Schooling
  411.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  412.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  413.    wt: 1:   24 Standards For Skill Develoment Take II
  414.    wt: 1:   24 Standards For Skill Develoment
  415.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  416.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  417.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  418.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  419.    wt: 1:   22 Student Centered Highschool Mathematics
  420.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  421.    wt: 1:   18 Primary School Mathematics
  422.    wt: 1:   17 Math Booklets for children and young teenagers
  423.    wt: 1:   15 Counting For Parents
  424.    wt: 1:   14 Multiplication and Times Tables
  425.    wt: 1:   13 Addition and Addition Tables
  426.    wt: 1:   12 Goals and Objectives For Mathematics
  427.    wt: 1:   11 Help and Defend Your Child or Teens Education
  428.    wt: 1:   10 Ends values for work study instruction
  429.    wt: 1:   9 Streaming by Student Cooperation
  430.    wt: 1:   8 The Effect of Negative Remarks
  431.    wt: 1:   7 Student Motivation
  432.    wt: 1:   5 Patience Please for Yourself and Your Charges
  433.    wt: 1:   4 Learning Takes Time and Effort
  434.    wt: 1:   3 Preparing for Science Studies
  435.    wt: 1:   2 Reading and Writing Skills
  436.    wt: 1:   1 Speaking Skills
  437.    wt: 1:   Ages 12 to 14 Skills with take home value
  438.    wt: 1:   Ages 12 to 14 Geometry
  439.    wt: 1:   Ages 12 to 14 Arithmetic
  440.    wt: 1:   Ages 10 to 12 Geometry
  441.    wt: 1:   Ages 10 to 12 Arithmetic
  442.    wt: 1:   Ages 9 to 10
  443.    wt: 1:   Ages 8 to 9
  444.    wt: 1:   Ages 7 to 8
  445.    wt: 1:   Ages 4 plus to 5 plus
  446.    wt: 1:   Ages 3 plus to 4 plus
  447.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  448.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  449.    wt: 1:   6 quadratics numerical approach
  450.    wt: 1:   1 Calculator Starter Exercises
  451.    wt: 1:   7 Links Lessons Elsewhere
  452.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  453.    wt: 1:   15 cosecant function Definition Graph and Inverse
  454.    wt: 1:   14 secant function Definition Graph and Inverse
  455.    wt: 1:   13 cosecant function Definition Graph and Inverse
  456.    wt: 1:   12 motivation for term arctan
  457.    wt: 1:   11 arctan left inverse of tangent Graph
  458.    wt: 1:   10 arctan left inverse of tangent Definition
  459.    wt: 1:   9 motivation for name arcsin
  460.    wt: 1:   8 arcsin left inverse of sine Graph
  461.    wt: 1:   7 arcsin left inverse of sine Definition
  462.    wt: 1:   5 Swapping Coordinates is a reflection
  463.    wt: 1:   4 possible motivation for term arccos
  464.    wt: 1:   3 Left Inverse of cosine arccos definition
  465.    wt: 1:   2 cosine function more properties
  466.    wt: 1:   1 cosine function properties
  467.    wt: 1:   9 Summary Degrees to Radians and back
  468.    wt: 1:   8 Radian Measures of Common Angles
  469.    wt: 1:   7 Radian Measures in special Triangles
  470.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  471.    wt: 1:   2 Radian Measure Numerical Value of one degree
  472.    wt: 1:   1 Degrees and Radians Introduction
  473.    wt: 1:   A Global Time and Navigation
  474.    wt: 1:   15 Dot and Cross Product
  475.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  476.    wt: 1:   13 Velocity Vectors in Physics
  477.    wt: 1:   12 From Applied To Pure Mathematics
  478.    wt: 1:   11 Component Method
  479.    wt: 1:   10 Parallelogram Addition Method
  480.    wt: 1:   9 Head to Tail Coordinate View
  481.    wt: 1:   8 Parallel Vectors
  482.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  483.    wt: 1:   5 Head To Tail Arrow Addition
  484.    wt: 1:   4 Resultant of a Sum of Movements
  485.    wt: 1:   3 Navigation with Arrows or Vectors
  486.    wt: 1:   2 Signed Coordinates
  487.    wt: 1:   1 Unsigned Coordinates
  488.    wt: 1:   Vector and Complex Number Applet
  489.    wt: 1:   4 graphing y=Asin(x c)
  490.    wt: 1:   3 graphing y=f(x c) plus K
  491.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  492.    wt: 1:   1 graphing y=f(x a)
  493.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  494.    wt: 1:   Triangle Angles Sum To 180 Degrees
  495.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  496.    wt: 1:   Parallel Lines and Interior Angles
  497.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  498.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  499.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  500.    wt: 1:   Straight Lines ASA Intersection Study More
  501.    wt: 1:   Straight Lines ASA Intersection Study
  502.    wt: 1:   Straight Lines Instersection Solving Equations
  503.    wt: 1:   Straight Lines Intersection of
  504.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  505.    wt: 1:   C Straight Lines Slope from Coordinates
  506.    wt: 1:   B Straight Line Slope Scaling Properties More
  507.    wt: 1:   A Straight Line Slope Scaling Properties
  508.    wt: 1:   14 Straight Lines Equations General Case
  509.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  510.    wt: 1:   12 Straight Lines Graphing mx plus b
  511.    wt: 1:   11 Straight Lines Graphing y=mx
  512.    wt: 1:   10 Straight Lines through Origin Equations More
  513.    wt: 1:   9 Straight Lines through Origin Equations
  514.    wt: 1:   8 Straight Lines Equation for vertical
  515.    wt: 1:   7 Tangent Function is odd on this domain
  516.    wt: 1:   5 Tangent Function Graph
  517.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  518.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  519.    wt: 1:   1 Straight Lines Slope Concept
  520.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  521.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  522.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  523.    wt: 1:   32 seven rows of pascals triangle
  524.    wt: 1:   31 basic secant cosecant cotangent trig identities
  525.    wt: 1:   30 unit circle calculation of six trigonometric functions
  526.    wt: 1:   29 secant cosecant and cotangent for acute angles
  527.    wt: 1:   28 Expressing products of sines cosines as sums
  528.    wt: 1:   25 tangent double angle formula Slope connection
  529.    wt: 1:   24 tangent Angle Difference Formula
  530.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  531.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  532.    wt: 1:   21 sine and cosine Half Angle Formulas
  533.    wt: 1:   20 sine and cosine Double Angle Formulas
  534.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  535.    wt: 1:   18 sum of sinusoidal waves as a single wave
  536.    wt: 1:   17G Pythagorean Theorem Converse
  537.    wt: 1:   17F Law of cosines
  538.    wt: 1:   17E Trig Formulas for dot and cross Products
  539.    wt: 1:   17D cis formulas for sine cosines and tangent
  540.    wt: 1:   17C sine and cosine double triple angle formulas
  541.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  542.    wt: 1:   17A The complex number valued trig function cis
  543.    wt: 1:   15 sine cosine Complementary Angle Relations
  544.    wt: 1:   14 cosine even and sine and tangent are odd
  545.    wt: 1:   13 Graph of tangent function many periods
  546.    wt: 1:   12 Graph of tangent function for one period
  547.    wt: 1:   11 tangent function undefined when terminal side vertical
  548.    wt: 1:   10 Graphs of sines and cosines many periods
  549.    wt: 1:   8 period of tangent function
  550.    wt: 1:   7 period of sine and cosine
  551.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  552.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  553.    wt: 1:   2 Quadrant I reference Angles
  554.    wt: 1:   1 Unit Points Reflections Rotations
  555.    wt: 1:   Unit Circle Development of Trigonometry
  556.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  557.    wt: 1:   21 Logarithms Powers and Exponentials
  558.    wt: 1:   20 N th Roots of Complex Numbers
  559.    wt: 1:   19 N th Roots of Unity
  560.    wt: 1:   18 Sixth Roots of Unity
  561.    wt: 1:   17 Cube Roots of unity
  562.    wt: 1:   15 Pythagorean Theorem Converse
  563.    wt: 1:   14 Law of cosines
  564.    wt: 1:   13 Trig Formulas for dot and cross Products
  565.    wt: 1:   12 cis formulas for sine cosines and tangent
  566.    wt: 1:   11 sine and cosine double triple angle formulas
  567.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  568.    wt: 1:   9 The complex number valued trig function cis
  569.    wt: 1:   8 Unit Circle Development of Trigonometry
  570.    wt: 1:   7 Second Way to Calculate Products
  571.    wt: 1:   5 An Easy Proof of the Distributive Law
  572.    wt: 1:   4 Multiplication Properties
  573.    wt: 1:   3 Addition Properties
  574.    wt: 1:   2 Complex Numbers made easier we hope
  575.    wt: 1:   1 Rectangular Polar Coordinates Review
  576.    wt: 1:   Appetizer A Complex Number Applet
  577.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  578.    wt: 1:   12 Triangles Similarity More Problems
  579.    wt: 1:   11 Triangle Similarity Missing Side Problem
  580.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  581.    wt: 1:   9 Similarity of Triangles Usual Criteria
  582.    wt: 1:   8 Similarity of Triangles and Polygons
  583.    wt: 1:   7 Translations Rotations Reflections Dilatations
  584.    wt: 1:   4 Similarity Definition with Coordinate
  585.    wt: 1:   3 Similarity by Design with coordinates
  586.    wt: 1:   2 Similarity By Design
  587.    wt: 1:   1 Early Concept of Like or Similar Shapes
  588.    wt: 1:   Four Simple Exercises
  589.    wt: 1:   11 A Partial Summary
  590.    wt: 1:   10 Midpoint of [a b] and [b a]
  591.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  592.    wt: 1:   8 Mid Point Formula
  593.    wt: 1:   7 Exercises to test skill and concept mastery
  594.    wt: 1:   5 Algebraic View of Slopes
  595.    wt: 1:   4 Equations for lines three forms
  596.    wt: 1:   3 Slope product for perpendicular lines
  597.    wt: 1:   2 point slope equation for a line
  598.    wt: 1:   1 Numerical view of lines and their equations
  599.    wt: 1:   What is and is not here
  600.    wt: 1:   13 Pythagorean spatial distance formulas
  601.    wt: 1:   12 Spatial Coordinates
  602.    wt: 1:   11 Triangle Inequality
  603.    wt: 1:   10 Pythagorean plane distance formula
  604.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  605.    wt: 1:   7 Complex Numbers Appetizer
  606.    wt: 1:   5 Cartesian Addition and Translation
  607.    wt: 1:   4 Polar Coordinates to and from
  608.    wt: 1:   3 Rectangular Coordinates Review
  609.    wt: 1:   2 Cartesian Coordinates with signs
  610.    wt: 1:   1 Cartesian Coordinates sans signs
  611.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  612.    wt: 1:   PS H Distributive Law For Complex Numbers
  613.    wt: 1:   PS G Rotation Distributes over Addition
  614.    wt: 1:   PS E Multiplication with Polar Coordinates
  615.    wt: 1:   PS D Addition with Cartesian Coordinates
  616.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  617.    wt: 1:   PS B Parallelogram Construction Methods
  618.    wt: 1:   PS A Kite Construction Methods
  619.    wt: 1:   21 Parallelograms
  620.    wt: 1:   19 Right Triangle Similarity
  621.    wt: 1:   18 Triangle Similarity Take 1
  622.    wt: 1:   17 Right Bisectors of Triangle Sides
  623.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  624.    wt: 1:   14 Parallel Lines Postulate
  625.    wt: 1:   13 Angle Side Angle Failure
  626.    wt: 1:   12 Side Angle Side Failure
  627.    wt: 1:   11 Triangle Construction Fails
  628.    wt: 1:   10 Dropping a perpendicular to line
  629.    wt: 1:   9 Construction of a right bisector
  630.    wt: 1:   8 Isoceles Triangles
  631.    wt: 1:   7 Angle Side Angle
  632.    wt: 1:   5 Side Angle Side
  633.    wt: 1:   4 Side Side Side
  634.    wt: 1:   3 Isometry of Triangles Congruence
  635.    wt: 1:   1 Initial Concepts and Terms
  636.    wt: 1:   Short Course on Euclidean Geometry
  637.    wt: 1:   A Measurement with Ruler Proper Use
  638.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  639.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  640.    wt: 1:   4 Angles on Maps Plans drawn to scale
  641.    wt: 1:   1 Length Measurement
  642.    wt: 1:   About Folder Contents
  643.    wt: 1:   3 Properties of Square Roots with example
  644.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  645.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  646.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  647.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  648.    wt: 1:   6 GCD from Prime
  649.    wt: 1:   2 Least Common Multiple LCM intro via list method
  650.    wt: 1:   12 GCD 2700 288 via Prime
  651.    wt: 1:   2 Counting with Tables and Trees I
  652.    wt: 1:   7 Converting or Changing Units
  653.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  654.    wt: 1:   4 Fractions with Units
  655.    wt: 1:   3 Multiplying Units and Numbers
  656.    wt: 1:   2 Equality and Units
  657.    wt: 1:   1 Addition and Subtraction with Units
  658.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  659.    wt: 1:   26 Divisibility by 2 3 5 Example
  660.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  661.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  662.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  663.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  664.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  665.    wt: 1:   2 Prime and Composites less than 16
  666.    wt: 1:   C Counting Areas with Powers of Ten
  667.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  668.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  669.    wt: 1:   Quick history of numbers and algebra
  670.    wt: 1:   016 Numbering Occidental Calendar Days
  671.    wt: 1:   6 How long is a million seconds
  672.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  673.    wt: 1:   G.5 Motions With Bounded Velocities
  674.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  675.    wt: 1:   G.3 Constant Difference Theorem Proof
  676.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  677.    wt: 1:   F.5b Extreme Value Theorem
  678.    wt: 1:   F.5a Equicontinuity Theorems
  679.    wt: 1:   F.4 Finite Covering Theorem
  680.    wt: 1:   F.3 Intermediate Value Theorem
  681.    wt: 1:   F.2 Closed Range Theorem
  682.    wt: 1:   F.1 What Functions are Continuous
  683.    wt: 1:   E2 Algebraic Properties of Limits
  684.    wt: 1:   E1 Error Control Inequalities
  685.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  686.    wt: 1:   C Triangle Inequalities
  687.    wt: 1:   B3 Bolzano Weierstrass Theorem
  688.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  689.    wt: 1:   PostScript For and Against Decimal Perspectives
  690.    wt: 1:   A1. Introduction
  691.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  692.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  693.    wt: 1:   Postscript B More on Story Telling and Reason
  694.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  695.    wt: 1:   F. The student teacher tutor feedback loop
  696.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  697.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  698.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  699.    wt: 1:   Implementation Notes
  700.    wt: 1:   More Algebra and Slope based Calculus Preview
  701.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  702.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

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.

Return to Page Top

Home << Search

[1] [2] [3] [4]

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

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.