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Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

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

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
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Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

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

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  1.    wt: 6:   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/

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134 matches:

  1.    wt: 4:   Area Between Crossing Curves Lesson Take 2
  2.    wt: 4:   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

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702 matches:

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

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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