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Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
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Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

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

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
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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: 5:   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:   2 Formula Forward Use Evaluation/
  7.    wt: 4:   70 Calculus Starter Lessons/
  8.    wt: 3:   9 Proportionality Backwards and Forwards/
  9.    wt: 3:   8 Unifying Theme For Algebra/
  10.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  11.    wt: 2:   B Real Numbers Extrinsic Development/
  12.    wt: 2:   A Origins of Counting and Figuring Methods/
  13.    wt: 2:   10 Examples of Algebraic Reasoning/
  14.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  15.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  16.    wt: 2:   5 Real Numbers/
  17.    wt: 2:   4 Computation Rules and Function Notation/
  18.    wt: 2:   Step 4 Gaussian Elimination/
  19.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  20.    wt: 2:   Step 1 Stick diagram and fractions/
  21.    wt: 2:   3 Solving Linear Equations/
  22.    wt: 2:   1 Working With Sets/
  23.    wt: 2:   Algebra Starter Lessons/
  24.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  25.    wt: 1:   5 Integers/
  26.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  27.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  28.    wt: 1:   Volume 2 Three Skills For Algebra/
  29.    wt: 1:   Resources and Reciprocal Links/
  30.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

222 matches:

  1.    wt: 4:   10 Power rule for negative integers
  2.    wt: 3:   38 Formulas and derivatives for powers and roots
  3.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  4.    wt: 2:   formal or informal peer review
  5.    wt: 2:   Prequel In For A Penny In For A Pound
  6.    wt: 2:   5 Function notation for geometric transformations
  7.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  8.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  9.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  10.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  11.    wt: 2:   26 Formulas for products of sines and cosines
  12.    wt: 2:   17E Trig Formulas for dot and cross Products
  13.    wt: 2:   17D cis formulas for sine cosines and tangent
  14.    wt: 2:   13 Trig Formulas for dot and cross Products
  15.    wt: 2:   12 cis formulas for sine cosines and tangent
  16.    wt: 2:   4 Equations for lines three forms
  17.    wt: 2:   PS H Distributive Law For Complex Numbers
  18.    wt: 2:   5 Distributive Law for Whole Numbers
  19.    wt: 2:   4 Commutative Law Groups Counting Form
  20.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  21.    wt: 2:   Formula Usage Show Work Format
  22.    wt: 2:   1 Written work formats for developing and showing skill
  23.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  24.    wt: 2:   21 Reciprocals for Fractions and Wholes
  25.    wt: 2:   11 Adding Integers Formulas and Examples
  26.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  27.    wt: 2:   21 Chain Rule for powers
  28.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  29.    wt: 2:   Postscript For Better Performance
  30.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  31.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  32.    wt: 2:   G. Written work formats for developing and showing skill
  33.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  34.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  35.    wt: 2:   Chapter 3 Algebra Starter Lessons
  36.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  37.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  38.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  39.    wt: 1:   Skills Chapter 5 Calculus
  40.    wt: 1:   three goals to set for students
  41.    wt: 1:   permissions for teachers
  42.    wt: 1:   activities for students
  43.    wt: 1:   Education Reform Inconsistencies
  44.    wt: 1:   geometric implications for algebra
  45.    wt: 1:   three goals for Mathematics Education
  46.    wt: 1:   02 21 words for teachers
  47.    wt: 1:   three aims for mathematics students
  48.    wt: 1:   standards for course material
  49.    wt: 1:   Four ways to improve education reform
  50.    wt: 1:   need for a mixed mathematics curriculum
  51.    wt: 1:   fairness and inductive principles for instruction
  52.    wt: 1:   words for mathematics instructor
  53.    wt: 1:   4 Energy Power Heat09
  54.    wt: 1:   3 Energy Power Heat08
  55.    wt: 1:   2 Energy Power Heat07
  56.    wt: 1:   1 Energy Power Heat06
  57.    wt: 1:   E Energy Power05
  58.    wt: 1:   D Energy Power04
  59.    wt: 1:   C Energy Power03
  60.    wt: 1:   B Energy Power02
  61.    wt: 1:   A Energy Power01
  62.    wt: 1:   E Kirchoffs Second Law
  63.    wt: 1:   D Kirchoff First Law
  64.    wt: 1:   C Electromotive force conventional current02
  65.    wt: 1:   B Electromotive force conventional current01
  66.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  67.    wt: 1:   24 Standards For Skill Develoment Take II
  68.    wt: 1:   24 Standards For Skill Develoment
  69.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  70.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  71.    wt: 1:   17 Math Booklets for children and young teenagers
  72.    wt: 1:   15 Counting For Parents
  73.    wt: 1:   12 Goals and Objectives For Mathematics
  74.    wt: 1:   10 Ends values for work study instruction
  75.    wt: 1:   8 The Effect of Negative Remarks
  76.    wt: 1:   5 Patience Please for Yourself and Your Charges
  77.    wt: 1:   4 Learning Takes Time and Effort
  78.    wt: 1:   3 Preparing for Science Studies
  79.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  80.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  81.    wt: 1:   6 Set Existence Formation and Notation
  82.    wt: 1:   3 Formula or function graphing exercise
  83.    wt: 1:   8 quadratics backward use of various formulas
  84.    wt: 1:   7 quadratic formulla derivation
  85.    wt: 1:   1 Calculator Starter Exercises
  86.    wt: 1:   8 Notes for instructors or tutors
  87.    wt: 1:   7 Links Lessons Elsewhere
  88.    wt: 1:   1 Polynomials Distributive Law
  89.    wt: 1:   12 motivation for term arctan
  90.    wt: 1:   9 motivation for name arcsin
  91.    wt: 1:   4 possible motivation for term arccos
  92.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  93.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  94.    wt: 1:   8 Straight Lines Equation for vertical
  95.    wt: 1:   17 tangent function angle sum formulas
  96.    wt: 1:   29 secant cosecant and cotangent for acute angles
  97.    wt: 1:   25 tangent double angle formula Slope connection
  98.    wt: 1:   24 tangent Angle Difference Formula
  99.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  100.    wt: 1:   21 sine and cosine Half Angle Formulas
  101.    wt: 1:   20 sine and cosine Double Angle Formulas
  102.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  103.    wt: 1:   17F Law of cosines
  104.    wt: 1:   17C sine and cosine double triple angle formulas
  105.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  106.    wt: 1:   12 Graph of tangent function for one period
  107.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  108.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  109.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  110.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  111.    wt: 1:   21 Logarithms Powers and Exponentials
  112.    wt: 1:   14 Law of cosines
  113.    wt: 1:   11 sine and cosine double triple angle formulas
  114.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  115.    wt: 1:   5 An Easy Proof of the Distributive Law
  116.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  117.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  118.    wt: 1:   12 Links Lessons elsewhere
  119.    wt: 1:   8 Mid Point Formula
  120.    wt: 1:   3 Slope product for perpendicular lines
  121.    wt: 1:   2 point slope equation for a line
  122.    wt: 1:   13 Pythagorean spatial distance formulas
  123.    wt: 1:   10 Pythagorean plane distance formula
  124.    wt: 1:   23 Distributive Law Two Derivations
  125.    wt: 1:   6 Column Methods for Decimal Multiplication
  126.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  127.    wt: 1:   6 Compound Interest Forward and Backwards
  128.    wt: 1:   5 Triangle Area Formula Backwards
  129.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  130.    wt: 1:   3 Product Axioms Two Forms
  131.    wt: 1:   4 Comparison of Negative Numbers
  132.    wt: 1:   2 More and Less Than for Counts and Measures
  133.    wt: 1:   12 Real Number Additive Inverses or Negatives
  134.    wt: 1:   9 Coordinates for Regions in Space
  135.    wt: 1:   8 Coordinates for Maps and Planes
  136.    wt: 1:   2 Integers
  137.    wt: 1:   3 Geometric Formulas and Function Notation
  138.    wt: 1:   1 Formulas Dependence and Function Notation
  139.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  140.    wt: 1:   Using Letters for Physical Quantities
  141.    wt: 1:   13 Naming Identifying Formulas with Words
  142.    wt: 1:   8 Compound Interest Formula Evaluation
  143.    wt: 1:   7 Compound Interest Formula Introduction
  144.    wt: 1:   5 Box Volume Formula Example
  145.    wt: 1:   4 Circle Area Formula Example
  146.    wt: 1:   3 Triangle Area Formula Example
  147.    wt: 1:   2 Another Rectangle Area Formula Example
  148.    wt: 1:   6 Power Set Notation
  149.    wt: 1:   1 Three Skills For Algebra
  150.    wt: 1:   arithmetic videos Real Player Format
  151.    wt: 1:   3 Comparison of Negative Numbers
  152.    wt: 1:   1 More and Less Than for Counts and Measures
  153.    wt: 1:   7 negative and additive inverse
  154.    wt: 1:   4 signed coordinates for regions in space
  155.    wt: 1:   3 signed coordinates for maps and planes
  156.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  157.    wt: 1:   A Associative Law Theorectical Note
  158.    wt: 1:   12 Adding Integers More Examples
  159.    wt: 1:   10 Integer Multiplication Formulas
  160.    wt: 1:   9 Multiplying Integers
  161.    wt: 1:   8 Multiplication by Signed Numbers Integers
  162.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  163.    wt: 1:   1 Integers as Coordinates
  164.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  165.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  166.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  167.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  168.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  169.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  170.    wt: 1:   Long Division forwards and backwards Example 3
  171.    wt: 1:   Long Division forwards and backwards Example 2
  172.    wt: 1:   Long Division forwards and backwards Example 1
  173.    wt: 1:   C Counting Areas with Powers of Ten
  174.    wt: 1:   B Powers of Ten
  175.    wt: 1:   A Elementary Basis for Multiplication Methods
  176.    wt: 1:   Video Power Notation in Decimal Expansion
  177.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  178.    wt: 1:   5 A Tip for Efficent Subtraction
  179.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  180.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  181.    wt: 1:   Formula Evaluation how to show work
  182.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  183.    wt: 1:   A Related lessons in Volume 3
  184.    wt: 1:   28 Chain Rule Preparation for a Proof
  185.    wt: 1:   22 Chain Rule for polynomials
  186.    wt: 1:   20 Chain Rule for Pulley Systems
  187.    wt: 1:   19 Chain Rule for linear functions
  188.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  189.    wt: 1:   9 Reciprocal rule
  190.    wt: 1:   6 Power rule from product rule
  191.    wt: 1:   3 Motivation for Limit Definition Take 2
  192.    wt: 1:   2 Motivation for Limit Definition Take 1
  193.    wt: 1:   3 Decimal insights for limits continuity convergence
  194.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  195.    wt: 1:   PostScript For and Against Decimal Perspectives
  196.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  197.    wt: 1:   Chapter 9 About First Courses in Calculus
  198.    wt: 1:   Fall 1983 Calculus Appetizer
  199.    wt: 1:   Foreword
  200.    wt: 1:   Postscript More on Better Performance
  201.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  202.    wt: 1:   Chapter 23. Notation For Sums
  203.    wt: 1:   Chapter 18. Rules for Algebra
  204.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  205.    wt: 1:   Chapter 8 Three Skills For Algebra
  206.    wt: 1:   Solutions For Arithmetic Exercises
  207.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  208.    wt: 1:   Foreword
  209.    wt: 1:   Chapter 2 For and Against Mathematics
  210.    wt: 1:   Foreword
  211.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  212.    wt: 1:   Postscript C Consistency as a Tool for Reason
  213.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  214.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  215.    wt: 1:   Foreword
  216.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  217.    wt: 1:   N Mathematics Prepare for College Studies
  218.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  219.    wt: 1:   7 Games and Activities for Instruction
  220.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  221.    wt: 1:   More Algebra and Slope based Calculus Preview
  222.    wt: 1:   The Math Forum and Site Content

Extended Search

492 matches:

  1.    wt: 9:   10 Power rule for negative integers
  2.    wt: 8:   38 Formulas and derivatives for powers and roots
  3.    wt: 7:   21 Chain Rule for powers
  4.    wt: 6:   1 Written work formats for developing and showing skill
  5.    wt: 6:   A Related lessons in Volume 3
  6.    wt: 6:   28 Chain Rule Preparation for a Proof
  7.    wt: 6:   22 Chain Rule for polynomials
  8.    wt: 6:   20 Chain Rule for Pulley Systems
  9.    wt: 6:   19 Chain Rule for linear functions
  10.    wt: 6:   16 Derivatives of reciprocals of sine and cosine
  11.    wt: 6:   9 Reciprocal rule
  12.    wt: 6:   6 Power rule from product rule
  13.    wt: 6:   3 Motivation for Limit Definition Take 2
  14.    wt: 6:   2 Motivation for Limit Definition Take 1
  15.    wt: 6:   3 Decimal insights for limits continuity convergence
  16.    wt: 5:   9 Circle Area and Perimeter Formula Backwards Forwards
  17.    wt: 5:   13 Naming Identifying Formulas with Words
  18.    wt: 5:   8 Compound Interest Formula Evaluation
  19.    wt: 5:   7 Compound Interest Formula Introduction
  20.    wt: 5:   5 Box Volume Formula Example
  21.    wt: 5:   4 Circle Area Formula Example
  22.    wt: 5:   3 Triangle Area Formula Example
  23.    wt: 5:   2 Another Rectangle Area Formula Example
  24.    wt: 5:   Example 2 volume of a cone
  25.    wt: 5:   Example 1 volume of a pyramid
  26.    wt: 5:   Volume of Solid by Cross Sections Lesson
  27.    wt: 5:   Example 1. Area Between x and x squared
  28.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  29.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  30.    wt: 5:   Example 4 with x function of y
  31.    wt: 5:   Example 3
  32.    wt: 5:   Example 2
  33.    wt: 5:   Example 1
  34.    wt: 5:   Area Between Curves Lesson Take 2
  35.    wt: 5:   Area Between Curves Lesson Take 1
  36.    wt: 5:   Summary
  37.    wt: 5:   A Related Material in Volume 3
  38.    wt: 5:   5 Area Under Curve Exercise
  39.    wt: 5:   4 Definite Integrals Evaluation Exercises
  40.    wt: 5:   3 Two Chain Rule Method Exercises
  41.    wt: 5:   2 Indefinite Integrals Exercises
  42.    wt: 5:   1 Chain Rule in Reverse Integration Method
  43.    wt: 5:   4 Second derivative test exercise example
  44.    wt: 5:   3 Second derivative test
  45.    wt: 5:   2 Second derivative test prequel
  46.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  47.    wt: 5:   A Chain Rule Real Player video examples
  48.    wt: 5:   36 Cube root derivative animated
  49.    wt: 5:   34 Derivative of exponential function
  50.    wt: 5:   33 Chain Rule Real Player video examples
  51.    wt: 5:   31 Derivatives of inverse functions
  52.    wt: 5:   30Chain Rule A Proof
  53.    wt: 5:   29 Chain Rule Optional Reading
  54.    wt: 5:   27 Chain Rule sinusoidal outer inner functions EGS
  55.    wt: 5:   26 Chain Rule Recognising outer inner functions
  56.    wt: 5:   25 Chain Rule Animated Examples Continued
  57.    wt: 5:   24 Chain Rule Animated Examples
  58.    wt: 5:   23 Chain Rule in general
  59.    wt: 5:   18 Chain Rule Introduction
  60.    wt: 5:   17 Derivatives of quotients of sine and cosine
  61.    wt: 5:   15 sine and cosine derivatives 3rd step
  62.    wt: 5:   14 sine and cosine derivatives 2nd step
  63.    wt: 5:   13 sine and cosine derivatives 1st step
  64.    wt: 5:   12 Quotient rule examples
  65.    wt: 5:   11 Quotient rule
  66.    wt: 5:   8 Differentiation of polynomials
  67.    wt: 5:   7 Animated Differentiation Examples
  68.    wt: 5:   5 Product Rule
  69.    wt: 5:   4 Sum Rule
  70.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  71.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  72.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  73.    wt: 5:   11 Limits at infinity Three Examples
  74.    wt: 5:   10 Three one sided limits with infinite values
  75.    wt: 5:   9 Limits Continuity and Composition
  76.    wt: 5:   8 Four Animated Examples
  77.    wt: 5:   7 Evaluation by immediate or delayed substitution
  78.    wt: 5:   6 Continuity at a point
  79.    wt: 5:   5 Jumps and absence of unlimited error control
  80.    wt: 5:   4 Numerical properties
  81.    wt: 5:   2 Algebraic codification
  82.    wt: 5:   1 Numerical introduction
  83.    wt: 4:   5 Distributive Law for Whole Numbers
  84.    wt: 4:   4 Commutative Law Groups Counting Form
  85.    wt: 4:   8 Pythagorean Relation Forwards Backwards
  86.    wt: 4:   6 Compound Interest Forward and Backwards
  87.    wt: 4:   5 Triangle Area Formula Backwards
  88.    wt: 4:   4 Rectangle Area and Like Formulas Backwards
  89.    wt: 4:   Formula Usage Show Work Format
  90.    wt: 4:   12 Cone Cylinder Sphere Lesson Idea
  91.    wt: 4:   11 Volume of Sphere
  92.    wt: 4:   10 Volume of Pyramid
  93.    wt: 4:   9 Volume of Cone
  94.    wt: 4:   6 Pythagorean Hypotenuse Calculation Example
  95.    wt: 4:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  96.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  97.    wt: 3:   8 Formulas for Fractional Exponents with Logarithms
  98.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  99.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  100.    wt: 3:   23 Distributive Law Two Derivations
  101.    wt: 3:   6 Column Methods for Decimal Multiplication
  102.    wt: 3:   5 Proportionality in Equivalent Fractions
  103.    wt: 3:   4 Rates Ratios and Proporitionality
  104.    wt: 3:   3 Proportionality Examples
  105.    wt: 3:   2 Algebraic View
  106.    wt: 3:   1 What is Proportionality
  107.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  108.    wt: 3:   3 Linear Equation Literal Solution More
  109.    wt: 3:   2 Linear Equation Literal Solution
  110.    wt: 3:   1 Changing Calculations
  111.    wt: 3:   3 Product Axioms Two Forms
  112.    wt: 3:   4 Comparison of Negative Numbers
  113.    wt: 3:   2 More and Less Than for Counts and Measures
  114.    wt: 3:   12 Real Number Additive Inverses or Negatives
  115.    wt: 3:   9 Coordinates for Regions in Space
  116.    wt: 3:   8 Coordinates for Maps and Planes
  117.    wt: 3:   2 Integers
  118.    wt: 3:   3 Geometric Formulas and Function Notation
  119.    wt: 3:   1 Formulas Dependence and Function Notation
  120.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  121.    wt: 3:   6 Algebraic Solution Example
  122.    wt: 3:   5 Algebraic Solutions Introduction
  123.    wt: 3:   4 Four Examples Fractional Coefficients
  124.    wt: 3:   3 Four Examples
  125.    wt: 3:   2 Three Examples
  126.    wt: 3:   1 Proper Equal Sign Usage
  127.    wt: 3:   Using Letters for Physical Quantities
  128.    wt: 3:   6 Power Set Notation
  129.    wt: 3:   1 Three Skills For Algebra
  130.    wt: 3:   11 Adding Integers Formulas and Examples
  131.    wt: 3:   G.2 Lipshitz Conditions Integration Calculus Reform
  132.    wt: 3:   Postscript For Better Performance
  133.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  134.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  135.    wt: 2:   formal or informal peer review
  136.    wt: 2:   Prequel In For A Penny In For A Pound
  137.    wt: 2:   5 Function notation for geometric transformations
  138.    wt: 2:   1 Calculator Starter Exercises
  139.    wt: 2:   26 Formulas for products of sines and cosines
  140.    wt: 2:   17E Trig Formulas for dot and cross Products
  141.    wt: 2:   17D cis formulas for sine cosines and tangent
  142.    wt: 2:   13 Trig Formulas for dot and cross Products
  143.    wt: 2:   12 cis formulas for sine cosines and tangent
  144.    wt: 2:   4 Equations for lines three forms
  145.    wt: 2:   PS H Distributive Law For Complex Numbers
  146.    wt: 2:   musings do not puiblish real numbers
  147.    wt: 2:   A Modular and Remainder Arithmetic
  148.    wt: 2:   A Signed Number Arithmetic Review
  149.    wt: 2:   26 More Less Greater Than Comparison
  150.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  151.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  152.    wt: 2:   22 Multiplication of Signed Numbers
  153.    wt: 2:   21 Addition of Multiples of a Single Vector
  154.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  155.    wt: 2:   19 Signed Multiples of Vectors
  156.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  157.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  158.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  159.    wt: 2:   15 Head to Tails in place Addition Associative
  160.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  161.    wt: 2:   13 Arrows and Vectors in a Plane
  162.    wt: 2:   12 Real Numbers Line Signed Coordinates
  163.    wt: 2:   11 Signed Number Addition and Addition Properties
  164.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  165.    wt: 2:   9 Division with Digits after Decimal Point
  166.    wt: 2:   8 Division and Mulplication of Compound Fractions
  167.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  168.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  169.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  170.    wt: 2:   4 Location of Point in Decimal Addition
  171.    wt: 2:   3 Location of Point in Decimal Multiplication
  172.    wt: 2:   2 Counting Digits in Decimal Multiplication
  173.    wt: 2:   1 Fractions with Finite Decimal Expansions
  174.    wt: 2:   E Long Division Methods more
  175.    wt: 2:   D Long Division Methods
  176.    wt: 2:   C Three Decimal Subtraction Methods
  177.    wt: 2:   B Decimal Comparison and Subtraction
  178.    wt: 2:   A Decimal Addition Columm Methods
  179.    wt: 2:   8 Column Multiplication Methods in General
  180.    wt: 2:   7 Decimals Multiplication Methods Examples
  181.    wt: 2:   3 Multiplicative Counting Skills Principles
  182.    wt: 2:   2 Combing Counts Addition Skills and Principles
  183.    wt: 2:   1 The Counting Origins of Numbers
  184.    wt: 2:   5 Areas of Rectangles Revisited
  185.    wt: 2:   4 Fraction Operations Axiomatic Development
  186.    wt: 2:   3 Inequalities Algebraically
  187.    wt: 2:   2 Fraction Operations Physical Development
  188.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  189.    wt: 2:   6 Equations and Systems Equivalent or Implied
  190.    wt: 2:   5 Equality in Algebra
  191.    wt: 2:   4 Subtraction and Division Axioms
  192.    wt: 2:   2 Addition and Multiplication Axioms
  193.    wt: 2:   1 Equivalent Computation Rules
  194.    wt: 2:   5 Greater More Less Than Signs in General
  195.    wt: 2:   3 More and Less Than with Unlike Signs
  196.    wt: 2:   1 Real Numbers Comparison
  197.    wt: 2:   16 Real Numbers Comparison
  198.    wt: 2:   15 Real Number Division
  199.    wt: 2:   14 Real Number Multiplication
  200.    wt: 2:   13 Real Number Subtraction
  201.    wt: 2:   11 Real Number Addition
  202.    wt: 2:   10 Real Number Lengths and Signs
  203.    wt: 2:   7 Real Numbers as Line Cordinates
  204.    wt: 2:   6 Unsigned Real Numbers
  205.    wt: 2:   5 Rational Numbers More
  206.    wt: 2:   4 Rational Numbers
  207.    wt: 2:   3 Fractions
  208.    wt: 2:   1 Whole and Natural Numbers
  209.    wt: 2:   5 Independent versus Dependent Variables
  210.    wt: 2:   4 Changing Letters
  211.    wt: 2:   2 Computation Rules Evaluation
  212.    wt: 2:   More Exercises
  213.    wt: 2:   Simple Exercises
  214.    wt: 2:   4 GE III Animated Examples
  215.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  216.    wt: 2:   3 GE III Equation Addition and Multiplication
  217.    wt: 2:   2 GE II Comparison
  218.    wt: 2:   1 GE Substitution four examples
  219.    wt: 2:   4 Solving a triangular system exercise
  220.    wt: 2:   3 Solving triangular system example
  221.    wt: 2:   2 Essentially one exercises three with solution
  222.    wt: 2:   1 Essentially One Unknown
  223.    wt: 2:   Skill Development Notes
  224.    wt: 2:   10 One Example
  225.    wt: 2:   9 Three Examples
  226.    wt: 2:   8 One Example
  227.    wt: 2:   7 Two Examples
  228.    wt: 2:   6 Three Examples
  229.    wt: 2:   5 Three Examples
  230.    wt: 2:   4 Two Examples
  231.    wt: 2:   3 Two Examples
  232.    wt: 2:   2 Three Examples
  233.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  234.    wt: 2:   9 Sets in Probability and Statistics
  235.    wt: 2:   8 Sets of Numbers
  236.    wt: 2:   7 Cautious or Safe Set Construction
  237.    wt: 2:   5 Product Builder Notation
  238.    wt: 2:   4 Subset Builder Notation
  239.    wt: 2:   3 Counting with Sets etc
  240.    wt: 2:   2 Venn Diagrams
  241.    wt: 2:   1 Finite Sets
  242.    wt: 2:   6 Three Notions of What is a Variable
  243.    wt: 2:   5 Talking about Numbers and Quantities
  244.    wt: 2:   4 A Brief Story of numbers and algebra
  245.    wt: 2:   3 Adding Words To Arithmetic
  246.    wt: 2:   2 What is a Variable
  247.    wt: 2:   About Folder Contents
  248.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  249.    wt: 2:   21 Reciprocals for Fractions and Wholes
  250.    wt: 2:   A Associative Law Theorectical Note
  251.    wt: 2:   12 Adding Integers More Examples
  252.    wt: 2:   10 Integer Multiplication Formulas
  253.    wt: 2:   9 Multiplying Integers
  254.    wt: 2:   8 Multiplication by Signed Numbers Integers
  255.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  256.    wt: 2:   1 Integers as Coordinates
  257.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  258.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  259.    wt: 2:   PostScript For and Against Decimal Perspectives
  260.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  261.    wt: 2:   Chapter 9 About First Courses in Calculus
  262.    wt: 2:   Fall 1983 Calculus Appetizer
  263.    wt: 2:   Foreword
  264.    wt: 2:   Postscript More on Better Performance
  265.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  266.    wt: 2:   Chapter 23. Notation For Sums
  267.    wt: 2:   Chapter 18. Rules for Algebra
  268.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  269.    wt: 2:   Chapter 8 Three Skills For Algebra
  270.    wt: 2:   Solutions For Arithmetic Exercises
  271.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  272.    wt: 2:   Foreword
  273.    wt: 2:   G. Written work formats for developing and showing skill
  274.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  275.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  276.    wt: 2:   Chapter 3 Algebra Starter Lessons
  277.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  278.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  279.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  280.    wt: 1:   Skills Chapter 5 Calculus
  281.    wt: 1:   three goals to set for students
  282.    wt: 1:   permissions for teachers
  283.    wt: 1:   activities for students
  284.    wt: 1:   Education Reform Inconsistencies
  285.    wt: 1:   geometric implications for algebra
  286.    wt: 1:   three goals for Mathematics Education
  287.    wt: 1:   02 21 words for teachers
  288.    wt: 1:   three aims for mathematics students
  289.    wt: 1:   standards for course material
  290.    wt: 1:   Four ways to improve education reform
  291.    wt: 1:   need for a mixed mathematics curriculum
  292.    wt: 1:   fairness and inductive principles for instruction
  293.    wt: 1:   words for mathematics instructor
  294.    wt: 1:   4 Energy Power Heat09
  295.    wt: 1:   3 Energy Power Heat08
  296.    wt: 1:   2 Energy Power Heat07
  297.    wt: 1:   1 Energy Power Heat06
  298.    wt: 1:   E Energy Power05
  299.    wt: 1:   D Energy Power04
  300.    wt: 1:   C Energy Power03
  301.    wt: 1:   B Energy Power02
  302.    wt: 1:   A Energy Power01
  303.    wt: 1:   E Kirchoffs Second Law
  304.    wt: 1:   D Kirchoff First Law
  305.    wt: 1:   C Electromotive force conventional current02
  306.    wt: 1:   B Electromotive force conventional current01
  307.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  308.    wt: 1:   24 Standards For Skill Develoment Take II
  309.    wt: 1:   24 Standards For Skill Develoment
  310.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  311.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  312.    wt: 1:   17 Math Booklets for children and young teenagers
  313.    wt: 1:   15 Counting For Parents
  314.    wt: 1:   12 Goals and Objectives For Mathematics
  315.    wt: 1:   10 Ends values for work study instruction
  316.    wt: 1:   8 The Effect of Negative Remarks
  317.    wt: 1:   5 Patience Please for Yourself and Your Charges
  318.    wt: 1:   4 Learning Takes Time and Effort
  319.    wt: 1:   3 Preparing for Science Studies
  320.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  321.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  322.    wt: 1:   6 Set Existence Formation and Notation
  323.    wt: 1:   3 Formula or function graphing exercise
  324.    wt: 1:   8 quadratics backward use of various formulas
  325.    wt: 1:   7 quadratic formulla derivation
  326.    wt: 1:   11 Growth and Decay in Biology
  327.    wt: 1:   10 Exponential Growth and Decay Models
  328.    wt: 1:   5 Natural Logarithm Calculator Exercises
  329.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  330.    wt: 1:   2 Square Root Simplification a prequel
  331.    wt: 1:   8 Notes for instructors or tutors
  332.    wt: 1:   7 Links Lessons Elsewhere
  333.    wt: 1:   1 Polynomials Distributive Law
  334.    wt: 1:   12 motivation for term arctan
  335.    wt: 1:   9 motivation for name arcsin
  336.    wt: 1:   4 possible motivation for term arccos
  337.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  338.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  339.    wt: 1:   8 Straight Lines Equation for vertical
  340.    wt: 1:   17 tangent function angle sum formulas
  341.    wt: 1:   29 secant cosecant and cotangent for acute angles
  342.    wt: 1:   25 tangent double angle formula Slope connection
  343.    wt: 1:   24 tangent Angle Difference Formula
  344.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  345.    wt: 1:   21 sine and cosine Half Angle Formulas
  346.    wt: 1:   20 sine and cosine Double Angle Formulas
  347.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  348.    wt: 1:   17F Law of cosines
  349.    wt: 1:   17C sine and cosine double triple angle formulas
  350.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  351.    wt: 1:   12 Graph of tangent function for one period
  352.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  353.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  354.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  355.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  356.    wt: 1:   21 Logarithms Powers and Exponentials
  357.    wt: 1:   14 Law of cosines
  358.    wt: 1:   11 sine and cosine double triple angle formulas
  359.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  360.    wt: 1:   5 An Easy Proof of the Distributive Law
  361.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  362.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  363.    wt: 1:   12 Links Lessons elsewhere
  364.    wt: 1:   8 Mid Point Formula
  365.    wt: 1:   3 Slope product for perpendicular lines
  366.    wt: 1:   2 point slope equation for a line
  367.    wt: 1:   13 Pythagorean spatial distance formulas
  368.    wt: 1:   10 Pythagorean plane distance formula
  369.    wt: 1:   arithmetic videos Real Player Format
  370.    wt: 1:   3 Comparison of Negative Numbers
  371.    wt: 1:   1 More and Less Than for Counts and Measures
  372.    wt: 1:   7 negative and additive inverse
  373.    wt: 1:   4 signed coordinates for regions in space
  374.    wt: 1:   3 signed coordinates for maps and planes
  375.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  376.    wt: 1:   D Remainders Modulo 11 Pair Rule
  377.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  378.    wt: 1:   B Integer Long Division Multiple Choices
  379.    wt: 1:   13 Subtraction with Additive Inverse
  380.    wt: 1:   7 Multiplication by Signs
  381.    wt: 1:   6 Multiplication by Natural Numbers
  382.    wt: 1:   5 Zero Movement and Additive Inverses
  383.    wt: 1:   4 Adding Movements wiht opposite directions
  384.    wt: 1:   3 Adding Movements with same direction
  385.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  386.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  387.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  388.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  389.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  390.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  391.    wt: 1:   Long Division forwards and backwards Example 3
  392.    wt: 1:   Long Division forwards and backwards Example 2
  393.    wt: 1:   Long Division forwards and backwards Example 1
  394.    wt: 1:   C Counting Areas with Powers of Ten
  395.    wt: 1:   B Powers of Ten
  396.    wt: 1:   A Elementary Basis for Multiplication Methods
  397.    wt: 1:   Video Power Notation in Decimal Expansion
  398.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  399.    wt: 1:   5 A Tip for Efficent Subtraction
  400.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  401.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  402.    wt: 1:   Formula Evaluation how to show work
  403.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  404.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  405.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  406.    wt: 1:   G.5 Motions With Bounded Velocities
  407.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  408.    wt: 1:   G.3 Constant Difference Theorem Proof
  409.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  410.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  411.    wt: 1:   F.5b Extreme Value Theorem
  412.    wt: 1:   F.5a Equicontinuity Theorems
  413.    wt: 1:   F.4 Finite Covering Theorem
  414.    wt: 1:   F.3 Intermediate Value Theorem
  415.    wt: 1:   F.2 Closed Range Theorem
  416.    wt: 1:   F.1 What Functions are Continuous
  417.    wt: 1:   E2 Algebraic Properties of Limits
  418.    wt: 1:   E1 Error Control Inequalities
  419.    wt: 1:   D2 Limits of Monotone Sequences
  420.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  421.    wt: 1:   C Triangle Inequalities
  422.    wt: 1:   B3 Bolzano Weierstrass Theorem
  423.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  424.    wt: 1:   A1. Introduction
  425.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  426.    wt: 1:   Chapter 23 Links To Trigonometry
  427.    wt: 1:   Chapter 22 Complex Numbers
  428.    wt: 1:   Chapter 21 Arrow Addition
  429.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  430.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  431.    wt: 1:   Chapter 18. Slopes Areas Integration
  432.    wt: 1:   Chapter 17. Area Approximation
  433.    wt: 1:   Chapter 16. Velocity Approximation
  434.    wt: 1:   Chapter 15. Slope Approximation
  435.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  436.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  437.    wt: 1:   Chapter 13. Acceleration
  438.    wt: 1:   Chapter 12. Units and Slopes
  439.    wt: 1:   Chapter 11. Graphing Slope versus Position
  440.    wt: 1:   Chapter 10 Slopes and Units
  441.    wt: 1:   Chapter 8. Slope Interpretation
  442.    wt: 1:   Chapter 7 Slopes and Velocity
  443.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  444.    wt: 1:   Chapter 5. Slope Sign Tests
  445.    wt: 1:   Chapter 4. More Slope Sign Analysis
  446.    wt: 1:   Chapter 3. Slope Sign Analysis
  447.    wt: 1:   Chapter 2. Slopes and Ski Trails
  448.    wt: 1:   Chapter 1.Introduction
  449.    wt: 1:   Appendix E. How To Study Mathematics and Why
  450.    wt: 1:   Appendix D. What to do in School and Why
  451.    wt: 1:   Appendix C. How to Read
  452.    wt: 1:   Appendix B. How To Learn
  453.    wt: 1:   Chapter 31 Direct and Indirect Reason
  454.    wt: 1:   Chapter 30 Truth Tables
  455.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  456.    wt: 1:   Chapter 28 Occurrence Tables
  457.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  458.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  459.    wt: 1:   Chapter 25. Mathematical Induction Examples
  460.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  461.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  462.    wt: 1:   Chapter 21. Third Reading Guide
  463.    wt: 1:   Chapter 20. Degrees and Radians
  464.    wt: 1:   Chapter 19. Functions and Sets
  465.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  466.    wt: 1:   Chapter 16. Painless Theorem Proving
  467.    wt: 1:   Chapter 15. Solving Linear Equations
  468.    wt: 1:   Chapter 13. Second Reading Guide
  469.    wt: 1:   Chapter 12. Shorthand Usage Guide
  470.    wt: 1:   Chapter 11. Why Shorthand
  471.    wt: 1:   Chapter 10 Describing and Changing Calculations
  472.    wt: 1:   Postscript What is a Variable
  473.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  474.    wt: 1:   Chapter 6 Change of Language
  475.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  476.    wt: 1:   Chapter 4 Longer Chains of Reason
  477.    wt: 1:   Chapter 3 Chains of Reason
  478.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  479.    wt: 1:   Chapter 2 For and Against Mathematics
  480.    wt: 1:   Foreword
  481.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  482.    wt: 1:   Postscript C Consistency as a Tool for Reason
  483.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  484.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  485.    wt: 1:   Foreword
  486.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  487.    wt: 1:   N Mathematics Prepare for College Studies
  488.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  489.    wt: 1:   7 Games and Activities for Instruction
  490.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  491.    wt: 1:   More Algebra and Slope based Calculus Preview
  492.    wt: 1:   The Math Forum and Site Content

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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