Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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

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

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

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

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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27 matches:

  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:   4 Computation Rules and Function Notation/
  11.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  12.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  13.    wt: 2:   B Real Numbers Extrinsic Development/
  14.    wt: 2:   A Origins of Counting and Figuring Methods/
  15.    wt: 2:   10 Examples of Algebraic Reasoning/
  16.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  17.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  18.    wt: 2:   5 Real Numbers/
  19.    wt: 2:   Step 4 Gaussian Elimination/
  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:   Advanced Calculus Volume 3 Appendices/
  25.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  26.    wt: 1:   Volume 2 Three Skills For Algebra/
  27.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

228 matches:

  1.    wt: 5:   20 Chain Rule for Pulley Systems
  2.    wt: 3:   28 Chain Rule Preparation for a Proof
  3.    wt: 3:   22 Chain Rule for polynomials
  4.    wt: 3:   21 Chain Rule for powers
  5.    wt: 3:   19 Chain Rule for linear functions
  6.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  7.    wt: 2:   formal or informal peer review
  8.    wt: 2:   Prequel In For A Penny In For A Pound
  9.    wt: 2:   5 Function notation for geometric transformations
  10.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  11.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  12.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  13.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  14.    wt: 2:   26 Formulas for products of sines and cosines
  15.    wt: 2:   17E Trig Formulas for dot and cross Products
  16.    wt: 2:   17D cis formulas for sine cosines and tangent
  17.    wt: 2:   13 Trig Formulas for dot and cross Products
  18.    wt: 2:   12 cis formulas for sine cosines and tangent
  19.    wt: 2:   4 Equations for lines three forms
  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:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  24.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  25.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  26.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  27.    wt: 2:   3 Two Chain Rule Method Exercises
  28.    wt: 2:   1 Chain Rule in Reverse Integration Method
  29.    wt: 2:   A Chain Rule Real Player video examples
  30.    wt: 2:   38 Formulas and derivatives for powers and roots
  31.    wt: 2:   33 Chain Rule Real Player video examples
  32.    wt: 2:   30Chain Rule A Proof
  33.    wt: 2:   29 Chain Rule Optional Reading
  34.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  35.    wt: 2:   26 Chain Rule Recognising outer inner functions
  36.    wt: 2:   25 Chain Rule Animated Examples Continued
  37.    wt: 2:   24 Chain Rule Animated Examples
  38.    wt: 2:   23 Chain Rule in general
  39.    wt: 2:   18 Chain Rule Introduction
  40.    wt: 2:   10 Power rule for negative integers
  41.    wt: 2:   6 Power rule from product rule
  42.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  43.    wt: 2:   Postscript For Better Performance
  44.    wt: 2:   Chapter 18. Rules for Algebra
  45.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  46.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  47.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  48.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  49.    wt: 2:   G. Written work formats for developing and showing skill
  50.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  51.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  52.    wt: 2:   Chapter 3 Algebra Starter Lessons
  53.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  54.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  55.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  56.    wt: 1:   Skills Chapter 5 Calculus
  57.    wt: 1:   three goals to set for students
  58.    wt: 1:   permissions for teachers
  59.    wt: 1:   activities for students
  60.    wt: 1:   Education Reform Inconsistencies
  61.    wt: 1:   geometric implications for algebra
  62.    wt: 1:   three goals for Mathematics Education
  63.    wt: 1:   02 21 words for teachers
  64.    wt: 1:   three aims for mathematics students
  65.    wt: 1:   standards for course material
  66.    wt: 1:   Four ways to improve education reform
  67.    wt: 1:   need for a mixed mathematics curriculum
  68.    wt: 1:   fairness and inductive principles for instruction
  69.    wt: 1:   words for mathematics instructor
  70.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  71.    wt: 1:   chapitre 06 00 Chaines de la raison
  72.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  73.    wt: 1:   C Electromotive force conventional current02
  74.    wt: 1:   B Electromotive force conventional current01
  75.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  76.    wt: 1:   24 Standards For Skill Develoment Take II
  77.    wt: 1:   24 Standards For Skill Develoment
  78.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  79.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  80.    wt: 1:   17 Math Booklets for children and young teenagers
  81.    wt: 1:   15 Counting For Parents
  82.    wt: 1:   12 Goals and Objectives For Mathematics
  83.    wt: 1:   10 Ends values for work study instruction
  84.    wt: 1:   5 Patience Please for Yourself and Your Charges
  85.    wt: 1:   4 Learning Takes Time and Effort
  86.    wt: 1:   3 Preparing for Science Studies
  87.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  88.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  89.    wt: 1:   19 Horizontal line rule and method
  90.    wt: 1:   18 Vertical Line Rule and Method
  91.    wt: 1:   6 Set Existence Formation and Notation
  92.    wt: 1:   3 Formula or function graphing exercise
  93.    wt: 1:   8 quadratics backward use of various formulas
  94.    wt: 1:   7 quadratic formulla derivation
  95.    wt: 1:   1 Calculator Starter Exercises
  96.    wt: 1:   8 Notes for instructors or tutors
  97.    wt: 1:   7 Links Lessons Elsewhere
  98.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  99.    wt: 1:   12 motivation for term arctan
  100.    wt: 1:   9 motivation for name arcsin
  101.    wt: 1:   4 possible motivation for term arccos
  102.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  103.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  104.    wt: 1:   8 Straight Lines Equation for vertical
  105.    wt: 1:   17 tangent function angle sum formulas
  106.    wt: 1:   29 secant cosecant and cotangent for acute angles
  107.    wt: 1:   25 tangent double angle formula Slope connection
  108.    wt: 1:   24 tangent Angle Difference Formula
  109.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  110.    wt: 1:   21 sine and cosine Half Angle Formulas
  111.    wt: 1:   20 sine and cosine Double Angle Formulas
  112.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  113.    wt: 1:   17C sine and cosine double triple angle formulas
  114.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  115.    wt: 1:   12 Graph of tangent function for one period
  116.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  117.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  118.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  119.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  120.    wt: 1:   11 sine and cosine double triple angle formulas
  121.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  122.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  123.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  124.    wt: 1:   12 Links Lessons elsewhere
  125.    wt: 1:   8 Mid Point Formula
  126.    wt: 1:   6 Intersection of lines by solving linear systems
  127.    wt: 1:   3 Slope product for perpendicular lines
  128.    wt: 1:   2 point slope equation for a line
  129.    wt: 1:   13 Pythagorean spatial distance formulas
  130.    wt: 1:   10 Pythagorean plane distance formula
  131.    wt: 1:   PS H Distributive Law For Complex Numbers
  132.    wt: 1:   6 Ruler and compass Angle Bisection
  133.    wt: 1:   A Measurement with Ruler Proper Use
  134.    wt: 1:   6 Column Methods for Decimal Multiplication
  135.    wt: 1:   5 Distributive Law for Whole Numbers
  136.    wt: 1:   4 Commutative Law Groups Counting Form
  137.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  138.    wt: 1:   6 Compound Interest Forward and Backwards
  139.    wt: 1:   5 Triangle Area Formula Backwards
  140.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  141.    wt: 1:   6 Equations and Systems Equivalent or Implied
  142.    wt: 1:   3 Product Axioms Two Forms
  143.    wt: 1:   1 Equivalent Computation Rules
  144.    wt: 1:   2 More and Less Than for Counts and Measures
  145.    wt: 1:   9 Coordinates for Regions in Space
  146.    wt: 1:   8 Coordinates for Maps and Planes
  147.    wt: 1:   3 Geometric Formulas and Function Notation
  148.    wt: 1:   2 Computation Rules Evaluation
  149.    wt: 1:   1 Formulas Dependence and Function Notation
  150.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  151.    wt: 1:   Using Letters for Physical Quantities
  152.    wt: 1:   13 Naming Identifying Formulas with Words
  153.    wt: 1:   8 Compound Interest Formula Evaluation
  154.    wt: 1:   7 Compound Interest Formula Introduction
  155.    wt: 1:   5 Box Volume Formula Example
  156.    wt: 1:   4 Circle Area Formula Example
  157.    wt: 1:   3 Triangle Area Formula Example
  158.    wt: 1:   2 Another Rectangle Area Formula Example
  159.    wt: 1:   1 Three Skills For Algebra
  160.    wt: 1:   arithmetic videos Real Player Format
  161.    wt: 1:   1 More and Less Than for Counts and Measures
  162.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  163.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  164.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  165.    wt: 1:   4 Counting with Trees Product Rule Take I
  166.    wt: 1:   4 signed coordinates for regions in space
  167.    wt: 1:   3 signed coordinates for maps and planes
  168.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  169.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  170.    wt: 1:   21 Reciprocals for Fractions and Wholes
  171.    wt: 1:   D Remainders Modulo 11 Pair Rule
  172.    wt: 1:   11 Adding Integers Formulas and Examples
  173.    wt: 1:   10 Integer Multiplication Formulas
  174.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  175.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  176.    wt: 1:   11 Efficient Square Rule Use
  177.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  178.    wt: 1:   5 Prime Factorization and a Square Rule
  179.    wt: 1:   Long Division forwards and backwards Example 3
  180.    wt: 1:   Long Division forwards and backwards Example 2
  181.    wt: 1:   Long Division forwards and backwards Example 1
  182.    wt: 1:   A Elementary Basis for Multiplication Methods
  183.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  184.    wt: 1:   5 A Tip for Efficent Subtraction
  185.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  186.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  187.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  188.    wt: 1:   Formula Evaluation how to show work
  189.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  190.    wt: 1:   A Related lessons in Volume 3
  191.    wt: 1:   12 Quotient rule examples
  192.    wt: 1:   11 Quotient rule
  193.    wt: 1:   9 Reciprocal rule
  194.    wt: 1:   5 Product Rule
  195.    wt: 1:   4 Sum Rule
  196.    wt: 1:   3 Motivation for Limit Definition Take 2
  197.    wt: 1:   2 Motivation for Limit Definition Take 1
  198.    wt: 1:   3 Decimal insights for limits continuity convergence
  199.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  200.    wt: 1:   PostScript For and Against Decimal Perspectives
  201.    wt: 1:   Chapter 9 About First Courses in Calculus
  202.    wt: 1:   Fall 1983 Calculus Appetizer
  203.    wt: 1:   Foreword
  204.    wt: 1:   Postscript More on Better Performance
  205.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  206.    wt: 1:   Chapter 23. Notation For Sums
  207.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  208.    wt: 1:   Chapter 8 Three Skills For Algebra
  209.    wt: 1:   Solutions For Arithmetic Exercises
  210.    wt: 1:   Chapter 4 Longer Chains of Reason
  211.    wt: 1:   Chapter 3 Chains of Reason
  212.    wt: 1:   Foreword
  213.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  214.    wt: 1:   Chapter 2 For and Against Mathematics
  215.    wt: 1:   Foreword
  216.    wt: 1:   Postscript C Consistency as a Tool for Reason
  217.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  218.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  219.    wt: 1:   Chapter 7 Longer Chains of Reason
  220.    wt: 1:   Chapter 6 Chains of Reason
  221.    wt: 1:   Foreword
  222.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  223.    wt: 1:   N Mathematics Prepare for College Studies
  224.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  225.    wt: 1:   7 Games and Activities for Instruction
  226.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  227.    wt: 1:   More Algebra and Slope based Calculus Preview
  228.    wt: 1:   The Math Forum and Site Content

Extended Search

470 matches:

  1.    wt: 8:   28 Chain Rule Preparation for a Proof
  2.    wt: 8:   22 Chain Rule for polynomials
  3.    wt: 8:   21 Chain Rule for powers
  4.    wt: 8:   19 Chain Rule for linear functions
  5.    wt: 7:   3 Two Chain Rule Method Exercises
  6.    wt: 7:   1 Chain Rule in Reverse Integration Method
  7.    wt: 7:   A Chain Rule Real Player video examples
  8.    wt: 7:   38 Formulas and derivatives for powers and roots
  9.    wt: 7:   33 Chain Rule Real Player video examples
  10.    wt: 7:   30Chain Rule A Proof
  11.    wt: 7:   29 Chain Rule Optional Reading
  12.    wt: 7:   27 Chain Rule sinusoidal outer inner functions EGS
  13.    wt: 7:   26 Chain Rule Recognising outer inner functions
  14.    wt: 7:   25 Chain Rule Animated Examples Continued
  15.    wt: 7:   24 Chain Rule Animated Examples
  16.    wt: 7:   23 Chain Rule in general
  17.    wt: 7:   18 Chain Rule Introduction
  18.    wt: 7:   10 Power rule for negative integers
  19.    wt: 7:   6 Power rule from product rule
  20.    wt: 6:   1 Written work formats for developing and showing skill
  21.    wt: 6:   A Related lessons in Volume 3
  22.    wt: 6:   12 Quotient rule examples
  23.    wt: 6:   11 Quotient rule
  24.    wt: 6:   9 Reciprocal rule
  25.    wt: 6:   5 Product Rule
  26.    wt: 6:   4 Sum Rule
  27.    wt: 6:   3 Motivation for Limit Definition Take 2
  28.    wt: 6:   2 Motivation for Limit Definition Take 1
  29.    wt: 6:   3 Decimal insights for limits continuity convergence
  30.    wt: 5:   9 Circle Area and Perimeter Formula Backwards Forwards
  31.    wt: 5:   13 Naming Identifying Formulas with Words
  32.    wt: 5:   8 Compound Interest Formula Evaluation
  33.    wt: 5:   7 Compound Interest Formula Introduction
  34.    wt: 5:   5 Box Volume Formula Example
  35.    wt: 5:   4 Circle Area Formula Example
  36.    wt: 5:   3 Triangle Area Formula Example
  37.    wt: 5:   2 Another Rectangle Area Formula Example
  38.    wt: 5:   Example 2 volume of a cone
  39.    wt: 5:   Example 1 volume of a pyramid
  40.    wt: 5:   Volume of Solid by Cross Sections Lesson
  41.    wt: 5:   Example 1. Area Between x and x squared
  42.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  43.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  44.    wt: 5:   Example 4 with x function of y
  45.    wt: 5:   Example 3
  46.    wt: 5:   Example 2
  47.    wt: 5:   Example 1
  48.    wt: 5:   Area Between Curves Lesson Take 2
  49.    wt: 5:   Area Between Curves Lesson Take 1
  50.    wt: 5:   Summary
  51.    wt: 5:   A Related Material in Volume 3
  52.    wt: 5:   5 Area Under Curve Exercise
  53.    wt: 5:   4 Definite Integrals Evaluation Exercises
  54.    wt: 5:   2 Indefinite Integrals Exercises
  55.    wt: 5:   4 Second derivative test exercise example
  56.    wt: 5:   3 Second derivative test
  57.    wt: 5:   2 Second derivative test prequel
  58.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  59.    wt: 5:   36 Cube root derivative animated
  60.    wt: 5:   34 Derivative of exponential function
  61.    wt: 5:   31 Derivatives of inverse functions
  62.    wt: 5:   17 Derivatives of quotients of sine and cosine
  63.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  64.    wt: 5:   15 sine and cosine derivatives 3rd step
  65.    wt: 5:   14 sine and cosine derivatives 2nd step
  66.    wt: 5:   13 sine and cosine derivatives 1st step
  67.    wt: 5:   8 Differentiation of polynomials
  68.    wt: 5:   7 Animated Differentiation Examples
  69.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  70.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  71.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  72.    wt: 5:   11 Limits at infinity Three Examples
  73.    wt: 5:   10 Three one sided limits with infinite values
  74.    wt: 5:   9 Limits Continuity and Composition
  75.    wt: 5:   8 Four Animated Examples
  76.    wt: 5:   7 Evaluation by immediate or delayed substitution
  77.    wt: 5:   6 Continuity at a point
  78.    wt: 5:   5 Jumps and absence of unlimited error control
  79.    wt: 5:   4 Numerical properties
  80.    wt: 5:   2 Algebraic codification
  81.    wt: 5:   1 Numerical introduction
  82.    wt: 4:   8 Pythagorean Relation Forwards Backwards
  83.    wt: 4:   6 Compound Interest Forward and Backwards
  84.    wt: 4:   5 Triangle Area Formula Backwards
  85.    wt: 4:   4 Rectangle Area and Like Formulas Backwards
  86.    wt: 4:   3 Geometric Formulas and Function Notation
  87.    wt: 4:   2 Computation Rules Evaluation
  88.    wt: 4:   1 Formulas Dependence and Function Notation
  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:   6 Column Methods for Decimal Multiplication
  97.    wt: 3:   5 Distributive Law for Whole Numbers
  98.    wt: 3:   4 Commutative Law Groups Counting Form
  99.    wt: 3:   5 Proportionality in Equivalent Fractions
  100.    wt: 3:   4 Rates Ratios and Proporitionality
  101.    wt: 3:   3 Proportionality Examples
  102.    wt: 3:   2 Algebraic View
  103.    wt: 3:   1 What is Proportionality
  104.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  105.    wt: 3:   3 Linear Equation Literal Solution More
  106.    wt: 3:   2 Linear Equation Literal Solution
  107.    wt: 3:   1 Changing Calculations
  108.    wt: 3:   6 Equations and Systems Equivalent or Implied
  109.    wt: 3:   3 Product Axioms Two Forms
  110.    wt: 3:   1 Equivalent Computation Rules
  111.    wt: 3:   2 More and Less Than for Counts and Measures
  112.    wt: 3:   9 Coordinates for Regions in Space
  113.    wt: 3:   8 Coordinates for Maps and Planes
  114.    wt: 3:   5 Independent versus Dependent Variables
  115.    wt: 3:   4 Changing Letters
  116.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  117.    wt: 3:   4 Solving a triangular system exercise
  118.    wt: 3:   3 Solving triangular system example
  119.    wt: 3:   2 Essentially one exercises three with solution
  120.    wt: 3:   1 Essentially One Unknown
  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:   1 Three Skills For Algebra
  129.    wt: 3:   G.2 Lipshitz Conditions Integration Calculus Reform
  130.    wt: 3:   Postscript For Better Performance
  131.    wt: 3:   Chapter 18. Rules for Algebra
  132.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  133.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  134.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  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:   9 Formulas for Real Exponents with Logarithms
  139.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  140.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  141.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  142.    wt: 2:   26 Formulas for products of sines and cosines
  143.    wt: 2:   17E Trig Formulas for dot and cross Products
  144.    wt: 2:   17D cis formulas for sine cosines and tangent
  145.    wt: 2:   13 Trig Formulas for dot and cross Products
  146.    wt: 2:   12 cis formulas for sine cosines and tangent
  147.    wt: 2:   4 Equations for lines three forms
  148.    wt: 2:   musings do not puiblish real numbers
  149.    wt: 2:   A Modular and Remainder Arithmetic
  150.    wt: 2:   A Signed Number Arithmetic Review
  151.    wt: 2:   26 More Less Greater Than Comparison
  152.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  153.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  154.    wt: 2:   23 Distributive Law Two Derivations
  155.    wt: 2:   22 Multiplication of Signed Numbers
  156.    wt: 2:   21 Addition of Multiples of a Single Vector
  157.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  158.    wt: 2:   19 Signed Multiples of Vectors
  159.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  160.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  161.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  162.    wt: 2:   15 Head to Tails in place Addition Associative
  163.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  164.    wt: 2:   13 Arrows and Vectors in a Plane
  165.    wt: 2:   12 Real Numbers Line Signed Coordinates
  166.    wt: 2:   11 Signed Number Addition and Addition Properties
  167.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  168.    wt: 2:   9 Division with Digits after Decimal Point
  169.    wt: 2:   8 Division and Mulplication of Compound Fractions
  170.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  171.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  172.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  173.    wt: 2:   4 Location of Point in Decimal Addition
  174.    wt: 2:   3 Location of Point in Decimal Multiplication
  175.    wt: 2:   2 Counting Digits in Decimal Multiplication
  176.    wt: 2:   1 Fractions with Finite Decimal Expansions
  177.    wt: 2:   E Long Division Methods more
  178.    wt: 2:   D Long Division Methods
  179.    wt: 2:   C Three Decimal Subtraction Methods
  180.    wt: 2:   B Decimal Comparison and Subtraction
  181.    wt: 2:   A Decimal Addition Columm Methods
  182.    wt: 2:   8 Column Multiplication Methods in General
  183.    wt: 2:   7 Decimals Multiplication Methods Examples
  184.    wt: 2:   3 Multiplicative Counting Skills Principles
  185.    wt: 2:   2 Combing Counts Addition Skills and Principles
  186.    wt: 2:   1 The Counting Origins of Numbers
  187.    wt: 2:   5 Areas of Rectangles Revisited
  188.    wt: 2:   4 Fraction Operations Axiomatic Development
  189.    wt: 2:   3 Inequalities Algebraically
  190.    wt: 2:   2 Fraction Operations Physical Development
  191.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  192.    wt: 2:   5 Equality in Algebra
  193.    wt: 2:   4 Subtraction and Division Axioms
  194.    wt: 2:   2 Addition and Multiplication Axioms
  195.    wt: 2:   5 Greater More Less Than Signs in General
  196.    wt: 2:   4 Comparison of Negative Numbers
  197.    wt: 2:   3 More and Less Than with Unlike Signs
  198.    wt: 2:   1 Real Numbers Comparison
  199.    wt: 2:   16 Real Numbers Comparison
  200.    wt: 2:   15 Real Number Division
  201.    wt: 2:   14 Real Number Multiplication
  202.    wt: 2:   13 Real Number Subtraction
  203.    wt: 2:   12 Real Number Additive Inverses or Negatives
  204.    wt: 2:   11 Real Number Addition
  205.    wt: 2:   10 Real Number Lengths and Signs
  206.    wt: 2:   7 Real Numbers as Line Cordinates
  207.    wt: 2:   6 Unsigned Real Numbers
  208.    wt: 2:   5 Rational Numbers More
  209.    wt: 2:   4 Rational Numbers
  210.    wt: 2:   3 Fractions
  211.    wt: 2:   2 Integers
  212.    wt: 2:   1 Whole and Natural Numbers
  213.    wt: 2:   More Exercises
  214.    wt: 2:   Simple Exercises
  215.    wt: 2:   4 GE III Animated Examples
  216.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  217.    wt: 2:   3 GE III Equation Addition and Multiplication
  218.    wt: 2:   2 GE II Comparison
  219.    wt: 2:   1 GE Substitution four examples
  220.    wt: 2:   Skill Development Notes
  221.    wt: 2:   10 One Example
  222.    wt: 2:   9 Three Examples
  223.    wt: 2:   8 One Example
  224.    wt: 2:   7 Two Examples
  225.    wt: 2:   6 Three Examples
  226.    wt: 2:   5 Three Examples
  227.    wt: 2:   4 Two Examples
  228.    wt: 2:   3 Two Examples
  229.    wt: 2:   2 Three Examples
  230.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  231.    wt: 2:   9 Sets in Probability and Statistics
  232.    wt: 2:   8 Sets of Numbers
  233.    wt: 2:   7 Cautious or Safe Set Construction
  234.    wt: 2:   6 Power Set Notation
  235.    wt: 2:   5 Product Builder Notation
  236.    wt: 2:   4 Subset Builder Notation
  237.    wt: 2:   3 Counting with Sets etc
  238.    wt: 2:   2 Venn Diagrams
  239.    wt: 2:   1 Finite Sets
  240.    wt: 2:   6 Three Notions of What is a Variable
  241.    wt: 2:   5 Talking about Numbers and Quantities
  242.    wt: 2:   4 A Brief Story of numbers and algebra
  243.    wt: 2:   3 Adding Words To Arithmetic
  244.    wt: 2:   2 What is a Variable
  245.    wt: 2:   About Folder Contents
  246.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  247.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  248.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  249.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  250.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  251.    wt: 2:   PostScript For and Against Decimal Perspectives
  252.    wt: 2:   Chapter 9 About First Courses in Calculus
  253.    wt: 2:   Fall 1983 Calculus Appetizer
  254.    wt: 2:   Foreword
  255.    wt: 2:   Postscript More on Better Performance
  256.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  257.    wt: 2:   Chapter 23. Notation For Sums
  258.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  259.    wt: 2:   Chapter 8 Three Skills For Algebra
  260.    wt: 2:   Solutions For Arithmetic Exercises
  261.    wt: 2:   Chapter 4 Longer Chains of Reason
  262.    wt: 2:   Chapter 3 Chains of Reason
  263.    wt: 2:   Foreword
  264.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  265.    wt: 2:   G. Written work formats for developing and showing skill
  266.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  267.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  268.    wt: 2:   Chapter 3 Algebra Starter Lessons
  269.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  270.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  271.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  272.    wt: 1:   Skills Chapter 5 Calculus
  273.    wt: 1:   three goals to set for students
  274.    wt: 1:   permissions for teachers
  275.    wt: 1:   activities for students
  276.    wt: 1:   Education Reform Inconsistencies
  277.    wt: 1:   geometric implications for algebra
  278.    wt: 1:   three goals for Mathematics Education
  279.    wt: 1:   02 21 words for teachers
  280.    wt: 1:   three aims for mathematics students
  281.    wt: 1:   standards for course material
  282.    wt: 1:   Four ways to improve education reform
  283.    wt: 1:   need for a mixed mathematics curriculum
  284.    wt: 1:   fairness and inductive principles for instruction
  285.    wt: 1:   words for mathematics instructor
  286.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  287.    wt: 1:   chapitre 06 00 Chaines de la raison
  288.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  289.    wt: 1:   C Electromotive force conventional current02
  290.    wt: 1:   B Electromotive force conventional current01
  291.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  292.    wt: 1:   24 Standards For Skill Develoment Take II
  293.    wt: 1:   24 Standards For Skill Develoment
  294.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  295.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  296.    wt: 1:   17 Math Booklets for children and young teenagers
  297.    wt: 1:   15 Counting For Parents
  298.    wt: 1:   12 Goals and Objectives For Mathematics
  299.    wt: 1:   10 Ends values for work study instruction
  300.    wt: 1:   5 Patience Please for Yourself and Your Charges
  301.    wt: 1:   4 Learning Takes Time and Effort
  302.    wt: 1:   3 Preparing for Science Studies
  303.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  304.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  305.    wt: 1:   19 Horizontal line rule and method
  306.    wt: 1:   18 Vertical Line Rule and Method
  307.    wt: 1:   6 Set Existence Formation and Notation
  308.    wt: 1:   3 Formula or function graphing exercise
  309.    wt: 1:   8 quadratics backward use of various formulas
  310.    wt: 1:   7 quadratic formulla derivation
  311.    wt: 1:   1 Calculator Starter Exercises
  312.    wt: 1:   8 Notes for instructors or tutors
  313.    wt: 1:   7 Links Lessons Elsewhere
  314.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  315.    wt: 1:   12 motivation for term arctan
  316.    wt: 1:   9 motivation for name arcsin
  317.    wt: 1:   4 possible motivation for term arccos
  318.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  319.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  320.    wt: 1:   8 Straight Lines Equation for vertical
  321.    wt: 1:   17 tangent function angle sum formulas
  322.    wt: 1:   29 secant cosecant and cotangent for acute angles
  323.    wt: 1:   25 tangent double angle formula Slope connection
  324.    wt: 1:   24 tangent Angle Difference Formula
  325.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  326.    wt: 1:   21 sine and cosine Half Angle Formulas
  327.    wt: 1:   20 sine and cosine Double Angle Formulas
  328.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  329.    wt: 1:   17C sine and cosine double triple angle formulas
  330.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  331.    wt: 1:   12 Graph of tangent function for one period
  332.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  333.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  334.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  335.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  336.    wt: 1:   11 sine and cosine double triple angle formulas
  337.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  338.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  339.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  340.    wt: 1:   12 Links Lessons elsewhere
  341.    wt: 1:   8 Mid Point Formula
  342.    wt: 1:   6 Intersection of lines by solving linear systems
  343.    wt: 1:   3 Slope product for perpendicular lines
  344.    wt: 1:   2 point slope equation for a line
  345.    wt: 1:   13 Pythagorean spatial distance formulas
  346.    wt: 1:   10 Pythagorean plane distance formula
  347.    wt: 1:   PS H Distributive Law For Complex Numbers
  348.    wt: 1:   6 Ruler and compass Angle Bisection
  349.    wt: 1:   A Measurement with Ruler Proper Use
  350.    wt: 1:   arithmetic videos Real Player Format
  351.    wt: 1:   1 More and Less Than for Counts and Measures
  352.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  353.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  354.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  355.    wt: 1:   4 Counting with Trees Product Rule Take I
  356.    wt: 1:   4 signed coordinates for regions in space
  357.    wt: 1:   3 signed coordinates for maps and planes
  358.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  359.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  360.    wt: 1:   21 Reciprocals for Fractions and Wholes
  361.    wt: 1:   D Remainders Modulo 11 Pair Rule
  362.    wt: 1:   11 Adding Integers Formulas and Examples
  363.    wt: 1:   10 Integer Multiplication Formulas
  364.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  365.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  366.    wt: 1:   11 Efficient Square Rule Use
  367.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  368.    wt: 1:   5 Prime Factorization and a Square Rule
  369.    wt: 1:   Long Division forwards and backwards Example 3
  370.    wt: 1:   Long Division forwards and backwards Example 2
  371.    wt: 1:   Long Division forwards and backwards Example 1
  372.    wt: 1:   A Elementary Basis for Multiplication Methods
  373.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  374.    wt: 1:   5 A Tip for Efficent Subtraction
  375.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  376.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  377.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  378.    wt: 1:   Formula Evaluation how to show work
  379.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  380.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  381.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  382.    wt: 1:   G.5 Motions With Bounded Velocities
  383.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  384.    wt: 1:   G.3 Constant Difference Theorem Proof
  385.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  386.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  387.    wt: 1:   F.5b Extreme Value Theorem
  388.    wt: 1:   F.5a Equicontinuity Theorems
  389.    wt: 1:   F.4 Finite Covering Theorem
  390.    wt: 1:   F.3 Intermediate Value Theorem
  391.    wt: 1:   F.2 Closed Range Theorem
  392.    wt: 1:   F.1 What Functions are Continuous
  393.    wt: 1:   E2 Algebraic Properties of Limits
  394.    wt: 1:   E1 Error Control Inequalities
  395.    wt: 1:   D2 Limits of Monotone Sequences
  396.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  397.    wt: 1:   C Triangle Inequalities
  398.    wt: 1:   B3 Bolzano Weierstrass Theorem
  399.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  400.    wt: 1:   A1. Introduction
  401.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  402.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  403.    wt: 1:   Chapter 23 Links To Trigonometry
  404.    wt: 1:   Chapter 22 Complex Numbers
  405.    wt: 1:   Chapter 21 Arrow Addition
  406.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  407.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  408.    wt: 1:   Chapter 18. Slopes Areas Integration
  409.    wt: 1:   Chapter 17. Area Approximation
  410.    wt: 1:   Chapter 16. Velocity Approximation
  411.    wt: 1:   Chapter 15. Slope Approximation
  412.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  413.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  414.    wt: 1:   Chapter 13. Acceleration
  415.    wt: 1:   Chapter 12. Units and Slopes
  416.    wt: 1:   Chapter 11. Graphing Slope versus Position
  417.    wt: 1:   Chapter 10 Slopes and Units
  418.    wt: 1:   Chapter 8. Slope Interpretation
  419.    wt: 1:   Chapter 7 Slopes and Velocity
  420.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  421.    wt: 1:   Chapter 5. Slope Sign Tests
  422.    wt: 1:   Chapter 4. More Slope Sign Analysis
  423.    wt: 1:   Chapter 3. Slope Sign Analysis
  424.    wt: 1:   Chapter 2. Slopes and Ski Trails
  425.    wt: 1:   Chapter 1.Introduction
  426.    wt: 1:   Appendix E. How To Study Mathematics and Why
  427.    wt: 1:   Appendix D. What to do in School and Why
  428.    wt: 1:   Appendix C. How to Read
  429.    wt: 1:   Appendix B. How To Learn
  430.    wt: 1:   Chapter 31 Direct and Indirect Reason
  431.    wt: 1:   Chapter 30 Truth Tables
  432.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  433.    wt: 1:   Chapter 28 Occurrence Tables
  434.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  435.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  436.    wt: 1:   Chapter 25. Mathematical Induction Examples
  437.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  438.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  439.    wt: 1:   Chapter 21. Third Reading Guide
  440.    wt: 1:   Chapter 20. Degrees and Radians
  441.    wt: 1:   Chapter 19. Functions and Sets
  442.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  443.    wt: 1:   Chapter 16. Painless Theorem Proving
  444.    wt: 1:   Chapter 15. Solving Linear Equations
  445.    wt: 1:   Chapter 13. Second Reading Guide
  446.    wt: 1:   Chapter 12. Shorthand Usage Guide
  447.    wt: 1:   Chapter 11. Why Shorthand
  448.    wt: 1:   Chapter 10 Describing and Changing Calculations
  449.    wt: 1:   Postscript What is a Variable
  450.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  451.    wt: 1:   Chapter 6 Change of Language
  452.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  453.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  454.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  455.    wt: 1:   Chapter 2 For and Against Mathematics
  456.    wt: 1:   Foreword
  457.    wt: 1:   Postscript C Consistency as a Tool for Reason
  458.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  459.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  460.    wt: 1:   Chapter 7 Longer Chains of Reason
  461.    wt: 1:   Chapter 6 Chains of Reason
  462.    wt: 1:   Foreword
  463.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  464.    wt: 1:   N Mathematics Prepare for College Studies
  465.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  466.    wt: 1:   7 Games and Activities for Instruction
  467.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  468.    wt: 1:   More Algebra and Slope based Calculus Preview
  469.    wt: 1:   The Math Forum and Site Content
  470.    wt: 10:   20 Chain Rule for Pulley Systems

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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