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.

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14 matches:

  1.    wt: 6:   Volume 1A Pattern Based Reason/
  2.    wt: 2:   Volume 1A Regles et modeles/
  3.    wt: 2:   Volume 1 Elements of Reason/
  4.    wt: 1:   A Origins of Counting and Figuring Methods/
  5.    wt: 1:   10 Examples of Algebraic Reasoning/
  6.    wt: 1:   D Decimal Long Division Methods/
  7.    wt: 1:   C Decimal Multiplication Methods/
  8.    wt: 1:   B Decimal Comparing and Subtracting Methods/
  9.    wt: 1:   A Decimal Counting and Adding Methods/
  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 2 Three Skills For Algebra/
  14.    wt: 1:   Volume 1B Mathematics Curriculum Notes/

Web Page Search

61 matches:

  1.    wt: 2:   Chapter 31 Direct and Indirect Reason
  2.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  3.    wt: 2:   Chapter 24 Direct and Indirect Reason
  4.    wt: 1:   Secondary Two Mathematics
  5.    wt: 1:   teaching tutoring algebraic reason
  6.    wt: 1:   Different Kinds of Reasoning in maths
  7.    wt: 1:   three kinds of reason in mathematics
  8.    wt: 1:   4 quadratics difference of two squares
  9.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  10.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  11.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  12.    wt: 1:   PS B Parallelogram Construction Methods
  13.    wt: 1:   PS A Kite Construction Methods
  14.    wt: 1:   23 Distributive Law Two Derivations
  15.    wt: 1:   E Long Division Methods more
  16.    wt: 1:   D Long Division Methods
  17.    wt: 1:   C Three Decimal Subtraction Methods
  18.    wt: 1:   A Decimal Addition Columm Methods
  19.    wt: 1:   8 Column Multiplication Methods in General
  20.    wt: 1:   7 Decimals Multiplication Methods Examples
  21.    wt: 1:   6 Column Methods for Decimal Multiplication
  22.    wt: 1:   3 Product Axioms Two Forms
  23.    wt: 1:   7 Two Examples
  24.    wt: 1:   4 Two Examples
  25.    wt: 1:   3 Two Examples
  26.    wt: 1:   11 Volume of Sphere
  27.    wt: 1:   10 Volume of Pyramid
  28.    wt: 1:   9 Volume of Cone
  29.    wt: 1:   5 Box Volume Formula Example
  30.    wt: 1:   1 Counting and Counting Methods I
  31.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  32.    wt: 1:   B Fractions and Two Term Ratios
  33.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  34.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  35.    wt: 1:   D Decimal Multiplication Methods Derived
  36.    wt: 1:   A Elementary Basis for Multiplication Methods
  37.    wt: 1:   4 Two and Three Digit Multipliers
  38.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  39.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  40.    wt: 1:   Example 2 volume of a cone
  41.    wt: 1:   Example 1 volume of a pyramid
  42.    wt: 1:   Volume of Solid by Cross Sections Lesson
  43.    wt: 1:   A Related Material in Volume 3
  44.    wt: 1:   3 Two Chain Rule Method Exercises
  45.    wt: 1:   A Related lessons in Volume 3
  46.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  47.    wt: 1:   Chapter 4 Longer Chains of Reason
  48.    wt: 1:   Chapter 3 Chains of Reason
  49.    wt: 1:   Chapter 9 The Two Ends
  50.    wt: 1:   Chapter 7 Two Treatments of Geometry
  51.    wt: 1:   Postscript C Consistency as a Tool for Reason
  52.    wt: 1:   Postscript B More on Story Telling and Reason
  53.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  54.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  55.    wt: 1:   Chapter 11 Accidental Patterns
  56.    wt: 1:   Chapter 7 Longer Chains of Reason
  57.    wt: 1:   Chapter 6 Chains of Reason
  58.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  59.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  60.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  61.    wt: 1:   More Algebra and Slope based Calculus Preview

Extended Search

276 matches:

  1.    wt: 8:   Chapter 24 Direct and Indirect Reason
  2.    wt: 7:   Postscript C Consistency as a Tool for Reason
  3.    wt: 7:   Postscript B More on Story Telling and Reason
  4.    wt: 7:   Chapter 16 Origins and Limitations of Rules and Patterns
  5.    wt: 7:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  6.    wt: 7:   Chapter 11 Accidental Patterns
  7.    wt: 7:   Chapter 7 Longer Chains of Reason
  8.    wt: 7:   Chapter 6 Chains of Reason
  9.    wt: 6:   Postscript D Reflections on Law of the Excluded Middle
  10.    wt: 6:   Postscript A Story Telling
  11.    wt: 6:   Chapter 23 Truth Tables
  12.    wt: 6:   Chapter 22 Contrapositive and Vacuously True Implications
  13.    wt: 6:   Chapter 21 Occurrence Tables
  14.    wt: 6:   Chapter 20 Shorthand Symbols as Pronouns
  15.    wt: 6:   Chapter 19 What is in chapters 20 to 24
  16.    wt: 6:   Chapter 18 Sense and Knowledge
  17.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  18.    wt: 6:   Chapter 15 Objective Processes
  19.    wt: 6:   Chapter 14 Deductive and Empirical Views of Mathematics
  20.    wt: 6:   Chapter 12 Islands and Divisions of Knowledge
  21.    wt: 6:   Chapter 10 Responsibility
  22.    wt: 6:   Chapter 9 What is in Chapters 10 to 18
  23.    wt: 6:   Chapter 8 Change of Language
  24.    wt: 6:   Chapter 5 Deception
  25.    wt: 6:   Chapter 4 Implication Rules Forwards and Backwards
  26.    wt: 6:   Chapter 3 What is in chapters 4 to 8
  27.    wt: 6:   Chapter 2 Skill Development
  28.    wt: 6:   Chapter 1 Introduction
  29.    wt: 6:   Three Remarks
  30.    wt: 6:   Foreword
  31.    wt: 3:   Chapter 31 Direct and Indirect Reason
  32.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  33.    wt: 2:   chapitre 12 00 les iles et division
  34.    wt: 2:   chapitre 07 01 principle D induction mathematique
  35.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  36.    wt: 2:   chapitre 06 00 Chaines de la raison
  37.    wt: 2:   chapitre 05 00 Deception
  38.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  39.    wt: 2:   chapitre 04 09 Regles accidentelles
  40.    wt: 2:   chapitre 04 08 Limitations et benefices
  41.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  42.    wt: 2:   chapitre 04 06 engagements
  43.    wt: 2:   chapitre 04 05 Implication versus suggestion
  44.    wt: 2:   chapitre 04 04 Parlons de la logique
  45.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  46.    wt: 2:   chapitre 04 02 Deuxieme enigme
  47.    wt: 2:   chapitre 04 01 Premiere enigme
  48.    wt: 2:   chapitre 04 00 Les regles d implication
  49.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  50.    wt: 2:   chapitre 02 00 La Communication des idees
  51.    wt: 2:   chapitre 01 00 Introduction
  52.    wt: 2:   E Long Division Methods more
  53.    wt: 2:   D Long Division Methods
  54.    wt: 2:   C Three Decimal Subtraction Methods
  55.    wt: 2:   A Decimal Addition Columm Methods
  56.    wt: 2:   8 Column Multiplication Methods in General
  57.    wt: 2:   7 Decimals Multiplication Methods Examples
  58.    wt: 2:   6 Column Methods for Decimal Multiplication
  59.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  60.    wt: 2:   D Decimal Multiplication Methods Derived
  61.    wt: 2:   A Elementary Basis for Multiplication Methods
  62.    wt: 2:   4 Two and Three Digit Multipliers
  63.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  64.    wt: 2:   Example 2 volume of a cone
  65.    wt: 2:   Example 1 volume of a pyramid
  66.    wt: 2:   Volume of Solid by Cross Sections Lesson
  67.    wt: 2:   Area Between Curves Lesson Take 2
  68.    wt: 2:   A Related Material in Volume 3
  69.    wt: 2:   Chapter 4 Longer Chains of Reason
  70.    wt: 2:   Chapter 3 Chains of Reason
  71.    wt: 2:   Chapter 9 The Two Ends
  72.    wt: 2:   Chapter 7 Two Treatments of Geometry
  73.    wt: 1:   Secondary Two Mathematics
  74.    wt: 1:   teaching tutoring algebraic reason
  75.    wt: 1:   Different Kinds of Reasoning in maths
  76.    wt: 1:   three kinds of reason in mathematics
  77.    wt: 1:   4 quadratics difference of two squares
  78.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  79.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  80.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  81.    wt: 1:   PS B Parallelogram Construction Methods
  82.    wt: 1:   PS A Kite Construction Methods
  83.    wt: 1:   23 Distributive Law Two Derivations
  84.    wt: 1:   B Decimal Comparison and Subtraction
  85.    wt: 1:   5 Distributive Law for Whole Numbers
  86.    wt: 1:   4 Commutative Law Groups Counting Form
  87.    wt: 1:   3 Multiplicative Counting Skills Principles
  88.    wt: 1:   2 Combing Counts Addition Skills and Principles
  89.    wt: 1:   1 The Counting Origins of Numbers
  90.    wt: 1:   5 Areas of Rectangles Revisited
  91.    wt: 1:   4 Fraction Operations Axiomatic Development
  92.    wt: 1:   3 Inequalities Algebraically
  93.    wt: 1:   2 Fraction Operations Physical Development
  94.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  95.    wt: 1:   3 Product Axioms Two Forms
  96.    wt: 1:   7 Two Examples
  97.    wt: 1:   4 Two Examples
  98.    wt: 1:   3 Two Examples
  99.    wt: 1:   11 Volume of Sphere
  100.    wt: 1:   10 Volume of Pyramid
  101.    wt: 1:   9 Volume of Cone
  102.    wt: 1:   5 Box Volume Formula Example
  103.    wt: 1:   1 Counting and Counting Methods I
  104.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  105.    wt: 1:   B Fractions and Two Term Ratios
  106.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  107.    wt: 1:   Long Division Backwards more
  108.    wt: 1:   Long Division Backward
  109.    wt: 1:   Division with Counts and Length
  110.    wt: 1:   Long Division forwards and backwards Example 3
  111.    wt: 1:   Long Division forwards and backwards Example 2
  112.    wt: 1:   Long Division forwards and backwards Example 1
  113.    wt: 1:   12 Why Long Division Works Take III
  114.    wt: 1:   11 Another Single Digit Divisor Example
  115.    wt: 1:   10 Division by Five Long and Short Ways
  116.    wt: 1:   9 Why Long Division Works Take II
  117.    wt: 1:   8 Correcting the Mistake
  118.    wt: 1:   7 Long Divison Mistake Catching
  119.    wt: 1:   5 Long Division Include Zeroes or not
  120.    wt: 1:   4 Division with 2 Digit Divsors
  121.    wt: 1:   3 Division Single Digit Divisor Example
  122.    wt: 1:   2 Division with Single Digit Divisors
  123.    wt: 1:   1 Divsion Physical Examples
  124.    wt: 1:   C Counting Areas with Powers of Ten
  125.    wt: 1:   B Powers of Ten
  126.    wt: 1:   6 Multiplication Commutes Order Not Important
  127.    wt: 1:   5 Decimal Fraction Multiplication
  128.    wt: 1:   3 More One Digit Multipliers
  129.    wt: 1:   2 One Digit Multipliers
  130.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  131.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  132.    wt: 1:   Video Power Notation in Decimal Expansion
  133.    wt: 1:   1 Why 3 times 5 gives 15
  134.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  135.    wt: 1:   Subtraction with J Conversions Example
  136.    wt: 1:   Subtraction Another Video Lesson
  137.    wt: 1:   9 22 Minute Subtraction Review Video
  138.    wt: 1:   8 Subtraction with Units of Measure
  139.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  140.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  141.    wt: 1:   5 A Tip for Efficent Subtraction
  142.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  143.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  144.    wt: 1:   2 Subtraction Easy Case Examples
  145.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  146.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  147.    wt: 1:   8 What skills and work habits to require
  148.    wt: 1:   7 Adding decimal fractions using decimal point
  149.    wt: 1:   6. Counting and adding units and mixed units
  150.    wt: 1:   5. How to add decimals C. Examples
  151.    wt: 1:   4. How to add with decimals B with conversions
  152.    wt: 1:   3. How to add with decimals A sans conversions
  153.    wt: 1:   2 Decimal Counting Practices
  154.    wt: 1:   1. Explaining Addition Table
  155.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  156.    wt: 1:   Example 1. Area Between x and x squared
  157.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  158.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  159.    wt: 1:   Example 4 with x function of y
  160.    wt: 1:   Example 3
  161.    wt: 1:   Example 2
  162.    wt: 1:   Example 1
  163.    wt: 1:   Area Between Curves Lesson Take 1
  164.    wt: 1:   Summary
  165.    wt: 1:   3 Two Chain Rule Method Exercises
  166.    wt: 1:   A Related lessons in Volume 3
  167.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  168.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  169.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  170.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  171.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  172.    wt: 1:   G.5 Motions With Bounded Velocities
  173.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  174.    wt: 1:   G.3 Constant Difference Theorem Proof
  175.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  176.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  177.    wt: 1:   F.5b Extreme Value Theorem
  178.    wt: 1:   F.5a Equicontinuity Theorems
  179.    wt: 1:   F.4 Finite Covering Theorem
  180.    wt: 1:   F.3 Intermediate Value Theorem
  181.    wt: 1:   F.2 Closed Range Theorem
  182.    wt: 1:   F.1 What Functions are Continuous
  183.    wt: 1:   E2 Algebraic Properties of Limits
  184.    wt: 1:   E1 Error Control Inequalities
  185.    wt: 1:   D2 Limits of Monotone Sequences
  186.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  187.    wt: 1:   C Triangle Inequalities
  188.    wt: 1:   B3 Bolzano Weierstrass Theorem
  189.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  190.    wt: 1:   PostScript For and Against Decimal Perspectives
  191.    wt: 1:   A1. Introduction
  192.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  193.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  194.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  195.    wt: 1:   Chapter 23 Links To Trigonometry
  196.    wt: 1:   Chapter 22 Complex Numbers
  197.    wt: 1:   Chapter 21 Arrow Addition
  198.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  199.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  200.    wt: 1:   Chapter 18. Slopes Areas Integration
  201.    wt: 1:   Chapter 17. Area Approximation
  202.    wt: 1:   Chapter 16. Velocity Approximation
  203.    wt: 1:   Chapter 15. Slope Approximation
  204.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  205.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  206.    wt: 1:   Chapter 13. Acceleration
  207.    wt: 1:   Chapter 12. Units and Slopes
  208.    wt: 1:   Chapter 11. Graphing Slope versus Position
  209.    wt: 1:   Chapter 10 Slopes and Units
  210.    wt: 1:   Chapter 9 About First Courses in Calculus
  211.    wt: 1:   Chapter 8. Slope Interpretation
  212.    wt: 1:   Chapter 7 Slopes and Velocity
  213.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  214.    wt: 1:   Chapter 5. Slope Sign Tests
  215.    wt: 1:   Chapter 4. More Slope Sign Analysis
  216.    wt: 1:   Chapter 3. Slope Sign Analysis
  217.    wt: 1:   Chapter 2. Slopes and Ski Trails
  218.    wt: 1:   Chapter 1.Introduction
  219.    wt: 1:   Fall 1983 Calculus Appetizer
  220.    wt: 1:   Foreword
  221.    wt: 1:   Postscript More on Better Performance
  222.    wt: 1:   Postscript For Better Performance
  223.    wt: 1:   Appendix E. How To Study Mathematics and Why
  224.    wt: 1:   Appendix D. What to do in School and Why
  225.    wt: 1:   Appendix C. How to Read
  226.    wt: 1:   Appendix B. How To Learn
  227.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  228.    wt: 1:   Chapter 30 Truth Tables
  229.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  230.    wt: 1:   Chapter 28 Occurrence Tables
  231.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  232.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  233.    wt: 1:   Chapter 25. Mathematical Induction Examples
  234.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  235.    wt: 1:   Chapter 23. Notation For Sums
  236.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  237.    wt: 1:   Chapter 21. Third Reading Guide
  238.    wt: 1:   Chapter 20. Degrees and Radians
  239.    wt: 1:   Chapter 19. Functions and Sets
  240.    wt: 1:   Chapter 18. Rules for Algebra
  241.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  242.    wt: 1:   Chapter 16. Painless Theorem Proving
  243.    wt: 1:   Chapter 15. Solving Linear Equations
  244.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  245.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  246.    wt: 1:   Chapter 13. Second Reading Guide
  247.    wt: 1:   Chapter 12. Shorthand Usage Guide
  248.    wt: 1:   Chapter 11. Why Shorthand
  249.    wt: 1:   Chapter 10 Describing and Changing Calculations
  250.    wt: 1:   Postscript What is a Variable
  251.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  252.    wt: 1:   Chapter 8 Three Skills For Algebra
  253.    wt: 1:   Solutions For Arithmetic Exercises
  254.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  255.    wt: 1:   Chapter 6 Change of Language
  256.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  257.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  258.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  259.    wt: 1:   Foreword
  260.    wt: 1:   Annotated Links to Material Elsehwere
  261.    wt: 1:   Postscript B Mathematics Education References
  262.    wt: 1:   Postscript A Three Remarks
  263.    wt: 1:   Chapter 12 Four Phases
  264.    wt: 1:   Chapter 11 Elementary Instruction
  265.    wt: 1:   Chapter 10 Transition
  266.    wt: 1:   Chapter 8 Modern Instruction
  267.    wt: 1:   Chapter 5 Four References
  268.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  269.    wt: 1:   Chapter 3 Algebra Difficulties
  270.    wt: 1:   Chapter 2 For and Against Mathematics
  271.    wt: 1:   Chapter 1 Introduction
  272.    wt: 1:   Foreword
  273.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  274.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  275.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  276.    wt: 1:   More Algebra and Slope based Calculus Preview

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.

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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.

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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

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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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