Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

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

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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13 matches:

  1.    wt: 6:   Volume 1A Pattern Based Reason/
  2.    wt: 2:   Volume 1A Regles et modeles/
  3.    wt: 2:   2 Formula Forward Use Evaluation/
  4.    wt: 2:   Volume 2 Three Skills For Algebra/
  5.    wt: 2:   Volume 1 Elements of Reason/
  6.    wt: 1:   10 Examples of Algebraic Reasoning/
  7.    wt: 1:   9 Proportionality Backwards and Forwards/
  8.    wt: 1:   8 Unifying Theme For Algebra/
  9.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  10.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  11.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  12.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  13.    wt: 1:   Volume 1B Mathematics Curriculum Notes/

Web Page Search

198 matches:

  1.    wt: 2:   formal or informal peer review
  2.    wt: 2:   Prequel In For A Penny In For A Pound
  3.    wt: 2:   fairness and inductive principles for instruction
  4.    wt: 2:   5 Function notation for geometric transformations
  5.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  6.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  7.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  8.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  9.    wt: 2:   26 Formulas for products of sines and cosines
  10.    wt: 2:   17E Trig Formulas for dot and cross Products
  11.    wt: 2:   17D cis formulas for sine cosines and tangent
  12.    wt: 2:   13 Trig Formulas for dot and cross Products
  13.    wt: 2:   12 cis formulas for sine cosines and tangent
  14.    wt: 2:   4 Equations for lines three forms
  15.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  16.    wt: 2:   Formula Usage Show Work Format
  17.    wt: 2:   5 Box Volume Formula Example
  18.    wt: 2:   1 Written work formats for developing and showing skill
  19.    wt: 2:   38 Formulas and derivatives for powers and roots
  20.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  21.    wt: 2:   Postscript For Better Performance
  22.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  23.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  24.    wt: 2:   Postscript C Consistency as a Tool for Reason
  25.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  26.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  27.    wt: 2:   G. Written work formats for developing and showing skill
  28.    wt: 1:   three goals to set for students
  29.    wt: 1:   permissions for teachers
  30.    wt: 1:   activities for students
  31.    wt: 1:   Education Reform Inconsistencies
  32.    wt: 1:   geometric implications for algebra
  33.    wt: 1:   teaching tutoring algebraic reason
  34.    wt: 1:   three goals for Mathematics Education
  35.    wt: 1:   02 21 words for teachers
  36.    wt: 1:   three aims for mathematics students
  37.    wt: 1:   standards for course material
  38.    wt: 1:   Different Kinds of Reasoning in maths
  39.    wt: 1:   three kinds of reason in mathematics
  40.    wt: 1:   Four ways to improve education reform
  41.    wt: 1:   need for a mixed mathematics curriculum
  42.    wt: 1:   words for mathematics instructor
  43.    wt: 1:   C Electromotive force conventional current02
  44.    wt: 1:   B Electromotive force conventional current01
  45.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  46.    wt: 1:   24 Standards For Skill Develoment Take II
  47.    wt: 1:   24 Standards For Skill Develoment
  48.    wt: 1:   17 Math Booklets for children and young teenagers
  49.    wt: 1:   15 Counting For Parents
  50.    wt: 1:   12 Goals and Objectives For Mathematics
  51.    wt: 1:   10 Ends values for work study instruction
  52.    wt: 1:   5 Patience Please for Yourself and Your Charges
  53.    wt: 1:   4 Learning Takes Time and Effort
  54.    wt: 1:   3 Preparing for Science Studies
  55.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  56.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  57.    wt: 1:   6 Set Existence Formation and Notation
  58.    wt: 1:   3 Formula or function graphing exercise
  59.    wt: 1:   8 quadratics backward use of various formulas
  60.    wt: 1:   7 quadratic formulla derivation
  61.    wt: 1:   8 Notes for instructors or tutors
  62.    wt: 1:   12 motivation for term arctan
  63.    wt: 1:   9 motivation for name arcsin
  64.    wt: 1:   4 possible motivation for term arccos
  65.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  66.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  67.    wt: 1:   8 Straight Lines Equation for vertical
  68.    wt: 1:   17 tangent function angle sum formulas
  69.    wt: 1:   29 secant cosecant and cotangent for acute angles
  70.    wt: 1:   25 tangent double angle formula Slope connection
  71.    wt: 1:   24 tangent Angle Difference Formula
  72.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  73.    wt: 1:   21 sine and cosine Half Angle Formulas
  74.    wt: 1:   20 sine and cosine Double Angle Formulas
  75.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  76.    wt: 1:   17C sine and cosine double triple angle formulas
  77.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  78.    wt: 1:   12 Graph of tangent function for one period
  79.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  80.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  81.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  82.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  83.    wt: 1:   11 sine and cosine double triple angle formulas
  84.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  85.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  86.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  87.    wt: 1:   8 Mid Point Formula
  88.    wt: 1:   3 Slope product for perpendicular lines
  89.    wt: 1:   2 point slope equation for a line
  90.    wt: 1:   13 Pythagorean spatial distance formulas
  91.    wt: 1:   10 Pythagorean plane distance formula
  92.    wt: 1:   PS H Distributive Law For Complex Numbers
  93.    wt: 1:   6 Column Methods for Decimal Multiplication
  94.    wt: 1:   5 Distributive Law for Whole Numbers
  95.    wt: 1:   4 Commutative Law Groups Counting Form
  96.    wt: 1:   3 Multiplicative Counting Skills Principles
  97.    wt: 1:   2 Combing Counts Addition Skills and Principles
  98.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  99.    wt: 1:   6 Compound Interest Forward and Backwards
  100.    wt: 1:   5 Triangle Area Formula Backwards
  101.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  102.    wt: 1:   3 Product Axioms Two Forms
  103.    wt: 1:   2 More and Less Than for Counts and Measures
  104.    wt: 1:   9 Coordinates for Regions in Space
  105.    wt: 1:   8 Coordinates for Maps and Planes
  106.    wt: 1:   3 Geometric Formulas and Function Notation
  107.    wt: 1:   1 Formulas Dependence and Function Notation
  108.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  109.    wt: 1:   Using Letters for Physical Quantities
  110.    wt: 1:   13 Naming Identifying Formulas with Words
  111.    wt: 1:   11 Volume of Sphere
  112.    wt: 1:   10 Volume of Pyramid
  113.    wt: 1:   9 Volume of Cone
  114.    wt: 1:   8 Compound Interest Formula Evaluation
  115.    wt: 1:   7 Compound Interest Formula Introduction
  116.    wt: 1:   4 Circle Area Formula Example
  117.    wt: 1:   3 Triangle Area Formula Example
  118.    wt: 1:   2 Another Rectangle Area Formula Example
  119.    wt: 1:   1 Three Skills For Algebra
  120.    wt: 1:   arithmetic videos Real Player Format
  121.    wt: 1:   1 More and Less Than for Counts and Measures
  122.    wt: 1:   4 signed coordinates for regions in space
  123.    wt: 1:   3 signed coordinates for maps and planes
  124.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  125.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  126.    wt: 1:   21 Reciprocals for Fractions and Wholes
  127.    wt: 1:   11 Adding Integers Formulas and Examples
  128.    wt: 1:   10 Integer Multiplication Formulas
  129.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  130.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  131.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  132.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  133.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  134.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  135.    wt: 1:   Long Division forwards and backwards Example 3
  136.    wt: 1:   Long Division forwards and backwards Example 2
  137.    wt: 1:   Long Division forwards and backwards Example 1
  138.    wt: 1:   A Elementary Basis for Multiplication Methods
  139.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  140.    wt: 1:   5 A Tip for Efficent Subtraction
  141.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  142.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  143.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  144.    wt: 1:   Formula Evaluation how to show work
  145.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  146.    wt: 1:   Example 2 volume of a cone
  147.    wt: 1:   Example 1 volume of a pyramid
  148.    wt: 1:   Volume of Solid by Cross Sections Lesson
  149.    wt: 1:   A Related Material in Volume 3
  150.    wt: 1:   A Related lessons in Volume 3
  151.    wt: 1:   28 Chain Rule Preparation for a Proof
  152.    wt: 1:   22 Chain Rule for polynomials
  153.    wt: 1:   21 Chain Rule for powers
  154.    wt: 1:   20 Chain Rule for Pulley Systems
  155.    wt: 1:   19 Chain Rule for linear functions
  156.    wt: 1:   10 Power rule for negative integers
  157.    wt: 1:   3 Motivation for Limit Definition Take 2
  158.    wt: 1:   2 Motivation for Limit Definition Take 1
  159.    wt: 1:   3 Decimal insights for limits continuity convergence
  160.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  161.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  162.    wt: 1:   PostScript For and Against Decimal Perspectives
  163.    wt: 1:   Foreword
  164.    wt: 1:   Postscript More on Better Performance
  165.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  166.    wt: 1:   Chapter 31 Direct and Indirect Reason
  167.    wt: 1:   Chapter 23. Notation For Sums
  168.    wt: 1:   Chapter 18. Rules for Algebra
  169.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  170.    wt: 1:   Chapter 8 Three Skills For Algebra
  171.    wt: 1:   Solutions For Arithmetic Exercises
  172.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  173.    wt: 1:   Chapter 4 Longer Chains of Reason
  174.    wt: 1:   Chapter 3 Chains of Reason
  175.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  176.    wt: 1:   Foreword
  177.    wt: 1:   Chapter 2 For and Against Mathematics
  178.    wt: 1:   Foreword
  179.    wt: 1:   Postscript B More on Story Telling and Reason
  180.    wt: 1:   Chapter 24 Direct and Indirect Reason
  181.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  182.    wt: 1:   Chapter 11 Accidental Patterns
  183.    wt: 1:   Chapter 10 Responsibility
  184.    wt: 1:   Chapter 7 Longer Chains of Reason
  185.    wt: 1:   Chapter 6 Chains of Reason
  186.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  187.    wt: 1:   Foreword
  188.    wt: 1:   N Mathematics Prepare for College Studies
  189.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  190.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  191.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  192.    wt: 1:   7 Games and Activities for Instruction
  193.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  194.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  195.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  196.    wt: 1:   More Algebra and Slope based Calculus Preview
  197.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  198.    wt: 1:   The Math Forum and Site Content

Extended Search

356 matches:

  1.    wt: 8:   Postscript C Consistency as a Tool for Reason
  2.    wt: 8:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  3.    wt: 7:   Postscript B More on Story Telling and Reason
  4.    wt: 7:   Chapter 24 Direct and Indirect Reason
  5.    wt: 7:   Chapter 16 Origins and Limitations of Rules and Patterns
  6.    wt: 7:   Chapter 11 Accidental Patterns
  7.    wt: 7:   Chapter 10 Responsibility
  8.    wt: 7:   Chapter 7 Longer Chains of Reason
  9.    wt: 7:   Chapter 6 Chains of Reason
  10.    wt: 7:   Chapter 4 Implication Rules Forwards and Backwards
  11.    wt: 7:   Foreword
  12.    wt: 6:   Postscript D Reflections on Law of the Excluded Middle
  13.    wt: 6:   Postscript A Story Telling
  14.    wt: 6:   Chapter 23 Truth Tables
  15.    wt: 6:   Chapter 22 Contrapositive and Vacuously True Implications
  16.    wt: 6:   Chapter 21 Occurrence Tables
  17.    wt: 6:   Chapter 20 Shorthand Symbols as Pronouns
  18.    wt: 6:   Chapter 19 What is in chapters 20 to 24
  19.    wt: 6:   Chapter 18 Sense and Knowledge
  20.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  21.    wt: 6:   Chapter 15 Objective Processes
  22.    wt: 6:   Chapter 14 Deductive and Empirical Views of Mathematics
  23.    wt: 6:   Chapter 12 Islands and Divisions of Knowledge
  24.    wt: 6:   Chapter 9 What is in Chapters 10 to 18
  25.    wt: 6:   Chapter 8 Change of Language
  26.    wt: 6:   Chapter 5 Deception
  27.    wt: 6:   Chapter 3 What is in chapters 4 to 8
  28.    wt: 6:   Chapter 2 Skill Development
  29.    wt: 6:   Chapter 1 Introduction
  30.    wt: 6:   Three Remarks
  31.    wt: 4:   5 Box Volume Formula Example
  32.    wt: 4:   1 Written work formats for developing and showing skill
  33.    wt: 4:   Postscript For Better Performance
  34.    wt: 4:   Chapter 14. Forward and Backward Use of a Formula
  35.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  36.    wt: 3:   13 Naming Identifying Formulas with Words
  37.    wt: 3:   11 Volume of Sphere
  38.    wt: 3:   10 Volume of Pyramid
  39.    wt: 3:   9 Volume of Cone
  40.    wt: 3:   8 Compound Interest Formula Evaluation
  41.    wt: 3:   7 Compound Interest Formula Introduction
  42.    wt: 3:   4 Circle Area Formula Example
  43.    wt: 3:   3 Triangle Area Formula Example
  44.    wt: 3:   2 Another Rectangle Area Formula Example
  45.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  46.    wt: 3:   Postscript More on Better Performance
  47.    wt: 3:   Appendix A. Reading Guide For Next Appendices
  48.    wt: 3:   Chapter 31 Direct and Indirect Reason
  49.    wt: 3:   Chapter 23. Notation For Sums
  50.    wt: 3:   Chapter 18. Rules for Algebra
  51.    wt: 3:   Postscript Unifying Theme A Fourth Skill For Algebra
  52.    wt: 3:   Chapter 8 Three Skills For Algebra
  53.    wt: 3:   Solutions For Arithmetic Exercises
  54.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  55.    wt: 3:   Chapter 4 Longer Chains of Reason
  56.    wt: 3:   Chapter 3 Chains of Reason
  57.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  58.    wt: 3:   Foreword
  59.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  60.    wt: 2:   formal or informal peer review
  61.    wt: 2:   Prequel In For A Penny In For A Pound
  62.    wt: 2:   fairness and inductive principles for instruction
  63.    wt: 2:   chapitre 12 00 les iles et division
  64.    wt: 2:   chapitre 07 01 principle D induction mathematique
  65.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  66.    wt: 2:   chapitre 06 00 Chaines de la raison
  67.    wt: 2:   chapitre 05 00 Deception
  68.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  69.    wt: 2:   chapitre 04 09 Regles accidentelles
  70.    wt: 2:   chapitre 04 08 Limitations et benefices
  71.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  72.    wt: 2:   chapitre 04 06 engagements
  73.    wt: 2:   chapitre 04 05 Implication versus suggestion
  74.    wt: 2:   chapitre 04 04 Parlons de la logique
  75.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  76.    wt: 2:   chapitre 04 02 Deuxieme enigme
  77.    wt: 2:   chapitre 04 01 Premiere enigme
  78.    wt: 2:   chapitre 04 00 Les regles d implication
  79.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  80.    wt: 2:   chapitre 02 00 La Communication des idees
  81.    wt: 2:   chapitre 01 00 Introduction
  82.    wt: 2:   5 Function notation for geometric transformations
  83.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  84.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  85.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  86.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  87.    wt: 2:   26 Formulas for products of sines and cosines
  88.    wt: 2:   17E Trig Formulas for dot and cross Products
  89.    wt: 2:   17D cis formulas for sine cosines and tangent
  90.    wt: 2:   13 Trig Formulas for dot and cross Products
  91.    wt: 2:   12 cis formulas for sine cosines and tangent
  92.    wt: 2:   4 Equations for lines three forms
  93.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  94.    wt: 2:   6 Compound Interest Forward and Backwards
  95.    wt: 2:   5 Triangle Area Formula Backwards
  96.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  97.    wt: 2:   Formula Usage Show Work Format
  98.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  99.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  100.    wt: 2:   Example 2 volume of a cone
  101.    wt: 2:   Example 1 volume of a pyramid
  102.    wt: 2:   Volume of Solid by Cross Sections Lesson
  103.    wt: 2:   Area Between Curves Lesson Take 2
  104.    wt: 2:   A Related Material in Volume 3
  105.    wt: 2:   38 Formulas and derivatives for powers and roots
  106.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  107.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  108.    wt: 2:   PostScript For and Against Decimal Perspectives
  109.    wt: 2:   Foreword
  110.    wt: 2:   Appendix E. How To Study Mathematics and Why
  111.    wt: 2:   Appendix D. What to do in School and Why
  112.    wt: 2:   Appendix C. How to Read
  113.    wt: 2:   Appendix B. How To Learn
  114.    wt: 2:   Chapter 30 Truth Tables
  115.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  116.    wt: 2:   Chapter 28 Occurrence Tables
  117.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  118.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  119.    wt: 2:   Chapter 25. Mathematical Induction Examples
  120.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  121.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  122.    wt: 2:   Chapter 21. Third Reading Guide
  123.    wt: 2:   Chapter 20. Degrees and Radians
  124.    wt: 2:   Chapter 19. Functions and Sets
  125.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  126.    wt: 2:   Chapter 16. Painless Theorem Proving
  127.    wt: 2:   Chapter 15. Solving Linear Equations
  128.    wt: 2:   Chapter 13. Second Reading Guide
  129.    wt: 2:   Chapter 12. Shorthand Usage Guide
  130.    wt: 2:   Chapter 11. Why Shorthand
  131.    wt: 2:   Chapter 10 Describing and Changing Calculations
  132.    wt: 2:   Postscript What is a Variable
  133.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  134.    wt: 2:   Chapter 6 Change of Language
  135.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  136.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  137.    wt: 2:   Chapter 2 For and Against Mathematics
  138.    wt: 2:   Foreword
  139.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  140.    wt: 2:   G. Written work formats for developing and showing skill
  141.    wt: 1:   three goals to set for students
  142.    wt: 1:   permissions for teachers
  143.    wt: 1:   activities for students
  144.    wt: 1:   Education Reform Inconsistencies
  145.    wt: 1:   geometric implications for algebra
  146.    wt: 1:   teaching tutoring algebraic reason
  147.    wt: 1:   three goals for Mathematics Education
  148.    wt: 1:   02 21 words for teachers
  149.    wt: 1:   three aims for mathematics students
  150.    wt: 1:   standards for course material
  151.    wt: 1:   Different Kinds of Reasoning in maths
  152.    wt: 1:   three kinds of reason in mathematics
  153.    wt: 1:   Four ways to improve education reform
  154.    wt: 1:   need for a mixed mathematics curriculum
  155.    wt: 1:   words for mathematics instructor
  156.    wt: 1:   C Electromotive force conventional current02
  157.    wt: 1:   B Electromotive force conventional current01
  158.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  159.    wt: 1:   24 Standards For Skill Develoment Take II
  160.    wt: 1:   24 Standards For Skill Develoment
  161.    wt: 1:   17 Math Booklets for children and young teenagers
  162.    wt: 1:   15 Counting For Parents
  163.    wt: 1:   12 Goals and Objectives For Mathematics
  164.    wt: 1:   10 Ends values for work study instruction
  165.    wt: 1:   5 Patience Please for Yourself and Your Charges
  166.    wt: 1:   4 Learning Takes Time and Effort
  167.    wt: 1:   3 Preparing for Science Studies
  168.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  169.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  170.    wt: 1:   6 Set Existence Formation and Notation
  171.    wt: 1:   3 Formula or function graphing exercise
  172.    wt: 1:   8 quadratics backward use of various formulas
  173.    wt: 1:   7 quadratic formulla derivation
  174.    wt: 1:   8 Notes for instructors or tutors
  175.    wt: 1:   12 motivation for term arctan
  176.    wt: 1:   9 motivation for name arcsin
  177.    wt: 1:   4 possible motivation for term arccos
  178.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  179.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  180.    wt: 1:   8 Straight Lines Equation for vertical
  181.    wt: 1:   17 tangent function angle sum formulas
  182.    wt: 1:   29 secant cosecant and cotangent for acute angles
  183.    wt: 1:   25 tangent double angle formula Slope connection
  184.    wt: 1:   24 tangent Angle Difference Formula
  185.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  186.    wt: 1:   21 sine and cosine Half Angle Formulas
  187.    wt: 1:   20 sine and cosine Double Angle Formulas
  188.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  189.    wt: 1:   17C sine and cosine double triple angle formulas
  190.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  191.    wt: 1:   12 Graph of tangent function for one period
  192.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  193.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  194.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  195.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  196.    wt: 1:   11 sine and cosine double triple angle formulas
  197.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  198.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  199.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  200.    wt: 1:   8 Mid Point Formula
  201.    wt: 1:   3 Slope product for perpendicular lines
  202.    wt: 1:   2 point slope equation for a line
  203.    wt: 1:   13 Pythagorean spatial distance formulas
  204.    wt: 1:   10 Pythagorean plane distance formula
  205.    wt: 1:   PS H Distributive Law For Complex Numbers
  206.    wt: 1:   6 Column Methods for Decimal Multiplication
  207.    wt: 1:   5 Distributive Law for Whole Numbers
  208.    wt: 1:   4 Commutative Law Groups Counting Form
  209.    wt: 1:   3 Multiplicative Counting Skills Principles
  210.    wt: 1:   2 Combing Counts Addition Skills and Principles
  211.    wt: 1:   5 Areas of Rectangles Revisited
  212.    wt: 1:   4 Fraction Operations Axiomatic Development
  213.    wt: 1:   3 Inequalities Algebraically
  214.    wt: 1:   2 Fraction Operations Physical Development
  215.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  216.    wt: 1:   5 Proportionality in Equivalent Fractions
  217.    wt: 1:   4 Rates Ratios and Proporitionality
  218.    wt: 1:   3 Proportionality Examples
  219.    wt: 1:   2 Algebraic View
  220.    wt: 1:   1 What is Proportionality
  221.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  222.    wt: 1:   3 Linear Equation Literal Solution More
  223.    wt: 1:   2 Linear Equation Literal Solution
  224.    wt: 1:   1 Changing Calculations
  225.    wt: 1:   3 Product Axioms Two Forms
  226.    wt: 1:   2 More and Less Than for Counts and Measures
  227.    wt: 1:   9 Coordinates for Regions in Space
  228.    wt: 1:   8 Coordinates for Maps and Planes
  229.    wt: 1:   3 Geometric Formulas and Function Notation
  230.    wt: 1:   1 Formulas Dependence and Function Notation
  231.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  232.    wt: 1:   6 Algebraic Solution Example
  233.    wt: 1:   5 Algebraic Solutions Introduction
  234.    wt: 1:   4 Four Examples Fractional Coefficients
  235.    wt: 1:   3 Four Examples
  236.    wt: 1:   2 Three Examples
  237.    wt: 1:   1 Proper Equal Sign Usage
  238.    wt: 1:   Using Letters for Physical Quantities
  239.    wt: 1:   1 Three Skills For Algebra
  240.    wt: 1:   arithmetic videos Real Player Format
  241.    wt: 1:   1 More and Less Than for Counts and Measures
  242.    wt: 1:   4 signed coordinates for regions in space
  243.    wt: 1:   3 signed coordinates for maps and planes
  244.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  245.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  246.    wt: 1:   21 Reciprocals for Fractions and Wholes
  247.    wt: 1:   11 Adding Integers Formulas and Examples
  248.    wt: 1:   10 Integer Multiplication Formulas
  249.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  250.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  251.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  252.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  253.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  254.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  255.    wt: 1:   Long Division forwards and backwards Example 3
  256.    wt: 1:   Long Division forwards and backwards Example 2
  257.    wt: 1:   Long Division forwards and backwards Example 1
  258.    wt: 1:   A Elementary Basis for Multiplication Methods
  259.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  260.    wt: 1:   5 A Tip for Efficent Subtraction
  261.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  262.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  263.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  264.    wt: 1:   Formula Evaluation how to show work
  265.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  266.    wt: 1:   Example 1. Area Between x and x squared
  267.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  268.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  269.    wt: 1:   Example 4 with x function of y
  270.    wt: 1:   Example 3
  271.    wt: 1:   Example 2
  272.    wt: 1:   Example 1
  273.    wt: 1:   Area Between Curves Lesson Take 1
  274.    wt: 1:   Summary
  275.    wt: 1:   A Related lessons in Volume 3
  276.    wt: 1:   28 Chain Rule Preparation for a Proof
  277.    wt: 1:   22 Chain Rule for polynomials
  278.    wt: 1:   21 Chain Rule for powers
  279.    wt: 1:   20 Chain Rule for Pulley Systems
  280.    wt: 1:   19 Chain Rule for linear functions
  281.    wt: 1:   10 Power rule for negative integers
  282.    wt: 1:   3 Motivation for Limit Definition Take 2
  283.    wt: 1:   2 Motivation for Limit Definition Take 1
  284.    wt: 1:   3 Decimal insights for limits continuity convergence
  285.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  286.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  287.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  288.    wt: 1:   G.5 Motions With Bounded Velocities
  289.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  290.    wt: 1:   G.3 Constant Difference Theorem Proof
  291.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  292.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  293.    wt: 1:   F.5b Extreme Value Theorem
  294.    wt: 1:   F.5a Equicontinuity Theorems
  295.    wt: 1:   F.4 Finite Covering Theorem
  296.    wt: 1:   F.3 Intermediate Value Theorem
  297.    wt: 1:   F.2 Closed Range Theorem
  298.    wt: 1:   F.1 What Functions are Continuous
  299.    wt: 1:   E2 Algebraic Properties of Limits
  300.    wt: 1:   E1 Error Control Inequalities
  301.    wt: 1:   D2 Limits of Monotone Sequences
  302.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  303.    wt: 1:   C Triangle Inequalities
  304.    wt: 1:   B3 Bolzano Weierstrass Theorem
  305.    wt: 1:   A1. Introduction
  306.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  307.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  308.    wt: 1:   Chapter 23 Links To Trigonometry
  309.    wt: 1:   Chapter 22 Complex Numbers
  310.    wt: 1:   Chapter 21 Arrow Addition
  311.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  312.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  313.    wt: 1:   Chapter 18. Slopes Areas Integration
  314.    wt: 1:   Chapter 17. Area Approximation
  315.    wt: 1:   Chapter 16. Velocity Approximation
  316.    wt: 1:   Chapter 15. Slope Approximation
  317.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  318.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  319.    wt: 1:   Chapter 13. Acceleration
  320.    wt: 1:   Chapter 12. Units and Slopes
  321.    wt: 1:   Chapter 11. Graphing Slope versus Position
  322.    wt: 1:   Chapter 10 Slopes and Units
  323.    wt: 1:   Chapter 9 About First Courses in Calculus
  324.    wt: 1:   Chapter 8. Slope Interpretation
  325.    wt: 1:   Chapter 7 Slopes and Velocity
  326.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  327.    wt: 1:   Chapter 5. Slope Sign Tests
  328.    wt: 1:   Chapter 4. More Slope Sign Analysis
  329.    wt: 1:   Chapter 3. Slope Sign Analysis
  330.    wt: 1:   Chapter 2. Slopes and Ski Trails
  331.    wt: 1:   Chapter 1.Introduction
  332.    wt: 1:   Fall 1983 Calculus Appetizer
  333.    wt: 1:   Annotated Links to Material Elsehwere
  334.    wt: 1:   Postscript B Mathematics Education References
  335.    wt: 1:   Postscript A Three Remarks
  336.    wt: 1:   Chapter 12 Four Phases
  337.    wt: 1:   Chapter 11 Elementary Instruction
  338.    wt: 1:   Chapter 10 Transition
  339.    wt: 1:   Chapter 9 The Two Ends
  340.    wt: 1:   Chapter 8 Modern Instruction
  341.    wt: 1:   Chapter 7 Two Treatments of Geometry
  342.    wt: 1:   Chapter 5 Four References
  343.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  344.    wt: 1:   Chapter 3 Algebra Difficulties
  345.    wt: 1:   Chapter 1 Introduction
  346.    wt: 1:   N Mathematics Prepare for College Studies
  347.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  348.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  349.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  350.    wt: 1:   7 Games and Activities for Instruction
  351.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  352.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  353.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  354.    wt: 1:   More Algebra and Slope based Calculus Preview
  355.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  356.    wt: 1:   The Math Forum and Site Content

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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