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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15 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:   2 Euclidean Geometry Constructions Theory extras/
  5.    wt: 1:   A Origins of Counting and Figuring Methods/
  6.    wt: 1:   10 Examples of Algebraic Reasoning/
  7.    wt: 1:   D Decimal Long Division Methods/
  8.    wt: 1:   C Decimal Multiplication Methods/
  9.    wt: 1:   B Decimal Comparing and Subtracting Methods/
  10.    wt: 1:   A Decimal Counting and Adding Methods/
  11.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  12.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  13.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  14.    wt: 1:   Volume 2 Three Skills For Algebra/
  15.    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

304 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:   PS B Parallelogram Construction Methods
  53.    wt: 2:   PS A Kite Construction Methods
  54.    wt: 2:   E Long Division Methods more
  55.    wt: 2:   D Long Division Methods
  56.    wt: 2:   C Three Decimal Subtraction Methods
  57.    wt: 2:   A Decimal Addition Columm Methods
  58.    wt: 2:   8 Column Multiplication Methods in General
  59.    wt: 2:   7 Decimals Multiplication Methods Examples
  60.    wt: 2:   6 Column Methods for Decimal Multiplication
  61.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  62.    wt: 2:   D Decimal Multiplication Methods Derived
  63.    wt: 2:   A Elementary Basis for Multiplication Methods
  64.    wt: 2:   4 Two and Three Digit Multipliers
  65.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  66.    wt: 2:   Example 2 volume of a cone
  67.    wt: 2:   Example 1 volume of a pyramid
  68.    wt: 2:   Volume of Solid by Cross Sections Lesson
  69.    wt: 2:   Area Between Curves Lesson Take 2
  70.    wt: 2:   A Related Material in Volume 3
  71.    wt: 2:   Chapter 4 Longer Chains of Reason
  72.    wt: 2:   Chapter 3 Chains of Reason
  73.    wt: 2:   Chapter 9 The Two Ends
  74.    wt: 2:   Chapter 7 Two Treatments of Geometry
  75.    wt: 1:   Secondary Two Mathematics
  76.    wt: 1:   teaching tutoring algebraic reason
  77.    wt: 1:   Different Kinds of Reasoning in maths
  78.    wt: 1:   three kinds of reason in mathematics
  79.    wt: 1:   4 quadratics difference of two squares
  80.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  81.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  82.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  83.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  84.    wt: 1:   PS H Distributive Law For Complex Numbers
  85.    wt: 1:   PS G Rotation Distributes over Addition
  86.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  87.    wt: 1:   PS E Multiplication with Polar Coordinates
  88.    wt: 1:   PS D Addition with Cartesian Coordinates
  89.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  90.    wt: 1:   21 Parallelograms
  91.    wt: 1:   19 Right Triangle Similarity
  92.    wt: 1:   18 Triangle Similarity Take 1
  93.    wt: 1:   17 Right Bisectors of Triangle Sides
  94.    wt: 1:   16 Angles Subtended By Chords and Diameters
  95.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  96.    wt: 1:   14 Parallel Lines Postulate
  97.    wt: 1:   13 Angle Side Angle Failure
  98.    wt: 1:   12 Side Angle Side Failure
  99.    wt: 1:   11 Triangle Construction Fails
  100.    wt: 1:   10 Dropping a perpendicular to line
  101.    wt: 1:   9 Construction of a right bisector
  102.    wt: 1:   8 Isoceles Triangles
  103.    wt: 1:   7 Angle Side Angle
  104.    wt: 1:   6 Ruler and compass Angle Bisection
  105.    wt: 1:   5 Side Angle Side
  106.    wt: 1:   4 Side Side Side
  107.    wt: 1:   3 Isometry of Triangles Congruence
  108.    wt: 1:   2 Correspondence between Triangles
  109.    wt: 1:   1 Initial Concepts and Terms
  110.    wt: 1:   Short Course on Euclidean Geometry
  111.    wt: 1:   23 Distributive Law Two Derivations
  112.    wt: 1:   B Decimal Comparison and Subtraction
  113.    wt: 1:   5 Distributive Law for Whole Numbers
  114.    wt: 1:   4 Commutative Law Groups Counting Form
  115.    wt: 1:   3 Multiplicative Counting Skills Principles
  116.    wt: 1:   2 Combing Counts Addition Skills and Principles
  117.    wt: 1:   1 The Counting Origins of Numbers
  118.    wt: 1:   5 Areas of Rectangles Revisited
  119.    wt: 1:   4 Fraction Operations Axiomatic Development
  120.    wt: 1:   3 Inequalities Algebraically
  121.    wt: 1:   2 Fraction Operations Physical Development
  122.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  123.    wt: 1:   3 Product Axioms Two Forms
  124.    wt: 1:   7 Two Examples
  125.    wt: 1:   4 Two Examples
  126.    wt: 1:   3 Two Examples
  127.    wt: 1:   11 Volume of Sphere
  128.    wt: 1:   10 Volume of Pyramid
  129.    wt: 1:   9 Volume of Cone
  130.    wt: 1:   5 Box Volume Formula Example
  131.    wt: 1:   1 Counting and Counting Methods I
  132.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  133.    wt: 1:   B Fractions and Two Term Ratios
  134.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  135.    wt: 1:   Long Division Backwards more
  136.    wt: 1:   Long Division Backward
  137.    wt: 1:   Division with Counts and Length
  138.    wt: 1:   Long Division forwards and backwards Example 3
  139.    wt: 1:   Long Division forwards and backwards Example 2
  140.    wt: 1:   Long Division forwards and backwards Example 1
  141.    wt: 1:   12 Why Long Division Works Take III
  142.    wt: 1:   11 Another Single Digit Divisor Example
  143.    wt: 1:   10 Division by Five Long and Short Ways
  144.    wt: 1:   9 Why Long Division Works Take II
  145.    wt: 1:   8 Correcting the Mistake
  146.    wt: 1:   7 Long Divison Mistake Catching
  147.    wt: 1:   5 Long Division Include Zeroes or not
  148.    wt: 1:   4 Division with 2 Digit Divsors
  149.    wt: 1:   3 Division Single Digit Divisor Example
  150.    wt: 1:   2 Division with Single Digit Divisors
  151.    wt: 1:   1 Divsion Physical Examples
  152.    wt: 1:   C Counting Areas with Powers of Ten
  153.    wt: 1:   B Powers of Ten
  154.    wt: 1:   6 Multiplication Commutes Order Not Important
  155.    wt: 1:   5 Decimal Fraction Multiplication
  156.    wt: 1:   3 More One Digit Multipliers
  157.    wt: 1:   2 One Digit Multipliers
  158.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  159.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  160.    wt: 1:   Video Power Notation in Decimal Expansion
  161.    wt: 1:   1 Why 3 times 5 gives 15
  162.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  163.    wt: 1:   Subtraction with J Conversions Example
  164.    wt: 1:   Subtraction Another Video Lesson
  165.    wt: 1:   9 22 Minute Subtraction Review Video
  166.    wt: 1:   8 Subtraction with Units of Measure
  167.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  168.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  169.    wt: 1:   5 A Tip for Efficent Subtraction
  170.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  171.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  172.    wt: 1:   2 Subtraction Easy Case Examples
  173.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  174.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  175.    wt: 1:   8 What skills and work habits to require
  176.    wt: 1:   7 Adding decimal fractions using decimal point
  177.    wt: 1:   6. Counting and adding units and mixed units
  178.    wt: 1:   5. How to add decimals C. Examples
  179.    wt: 1:   4. How to add with decimals B with conversions
  180.    wt: 1:   3. How to add with decimals A sans conversions
  181.    wt: 1:   2 Decimal Counting Practices
  182.    wt: 1:   1. Explaining Addition Table
  183.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  184.    wt: 1:   Example 1. Area Between x and x squared
  185.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  186.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  187.    wt: 1:   Example 4 with x function of y
  188.    wt: 1:   Example 3
  189.    wt: 1:   Example 2
  190.    wt: 1:   Example 1
  191.    wt: 1:   Area Between Curves Lesson Take 1
  192.    wt: 1:   Summary
  193.    wt: 1:   3 Two Chain Rule Method Exercises
  194.    wt: 1:   A Related lessons in Volume 3
  195.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  196.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  197.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  198.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  199.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  200.    wt: 1:   G.5 Motions With Bounded Velocities
  201.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  202.    wt: 1:   G.3 Constant Difference Theorem Proof
  203.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  204.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  205.    wt: 1:   F.5b Extreme Value Theorem
  206.    wt: 1:   F.5a Equicontinuity Theorems
  207.    wt: 1:   F.4 Finite Covering Theorem
  208.    wt: 1:   F.3 Intermediate Value Theorem
  209.    wt: 1:   F.2 Closed Range Theorem
  210.    wt: 1:   F.1 What Functions are Continuous
  211.    wt: 1:   E2 Algebraic Properties of Limits
  212.    wt: 1:   E1 Error Control Inequalities
  213.    wt: 1:   D2 Limits of Monotone Sequences
  214.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  215.    wt: 1:   C Triangle Inequalities
  216.    wt: 1:   B3 Bolzano Weierstrass Theorem
  217.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  218.    wt: 1:   PostScript For and Against Decimal Perspectives
  219.    wt: 1:   A1. Introduction
  220.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  221.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  222.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  223.    wt: 1:   Chapter 23 Links To Trigonometry
  224.    wt: 1:   Chapter 22 Complex Numbers
  225.    wt: 1:   Chapter 21 Arrow Addition
  226.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  227.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  228.    wt: 1:   Chapter 18. Slopes Areas Integration
  229.    wt: 1:   Chapter 17. Area Approximation
  230.    wt: 1:   Chapter 16. Velocity Approximation
  231.    wt: 1:   Chapter 15. Slope Approximation
  232.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  233.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  234.    wt: 1:   Chapter 13. Acceleration
  235.    wt: 1:   Chapter 12. Units and Slopes
  236.    wt: 1:   Chapter 11. Graphing Slope versus Position
  237.    wt: 1:   Chapter 10 Slopes and Units
  238.    wt: 1:   Chapter 9 About First Courses in Calculus
  239.    wt: 1:   Chapter 8. Slope Interpretation
  240.    wt: 1:   Chapter 7 Slopes and Velocity
  241.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  242.    wt: 1:   Chapter 5. Slope Sign Tests
  243.    wt: 1:   Chapter 4. More Slope Sign Analysis
  244.    wt: 1:   Chapter 3. Slope Sign Analysis
  245.    wt: 1:   Chapter 2. Slopes and Ski Trails
  246.    wt: 1:   Chapter 1.Introduction
  247.    wt: 1:   Fall 1983 Calculus Appetizer
  248.    wt: 1:   Foreword
  249.    wt: 1:   Postscript More on Better Performance
  250.    wt: 1:   Postscript For Better Performance
  251.    wt: 1:   Appendix E. How To Study Mathematics and Why
  252.    wt: 1:   Appendix D. What to do in School and Why
  253.    wt: 1:   Appendix C. How to Read
  254.    wt: 1:   Appendix B. How To Learn
  255.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  256.    wt: 1:   Chapter 30 Truth Tables
  257.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  258.    wt: 1:   Chapter 28 Occurrence Tables
  259.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  260.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  261.    wt: 1:   Chapter 25. Mathematical Induction Examples
  262.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  263.    wt: 1:   Chapter 23. Notation For Sums
  264.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  265.    wt: 1:   Chapter 21. Third Reading Guide
  266.    wt: 1:   Chapter 20. Degrees and Radians
  267.    wt: 1:   Chapter 19. Functions and Sets
  268.    wt: 1:   Chapter 18. Rules for Algebra
  269.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  270.    wt: 1:   Chapter 16. Painless Theorem Proving
  271.    wt: 1:   Chapter 15. Solving Linear Equations
  272.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  273.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  274.    wt: 1:   Chapter 13. Second Reading Guide
  275.    wt: 1:   Chapter 12. Shorthand Usage Guide
  276.    wt: 1:   Chapter 11. Why Shorthand
  277.    wt: 1:   Chapter 10 Describing and Changing Calculations
  278.    wt: 1:   Postscript What is a Variable
  279.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  280.    wt: 1:   Chapter 8 Three Skills For Algebra
  281.    wt: 1:   Solutions For Arithmetic Exercises
  282.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  283.    wt: 1:   Chapter 6 Change of Language
  284.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  285.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  286.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  287.    wt: 1:   Foreword
  288.    wt: 1:   Annotated Links to Material Elsehwere
  289.    wt: 1:   Postscript B Mathematics Education References
  290.    wt: 1:   Postscript A Three Remarks
  291.    wt: 1:   Chapter 12 Four Phases
  292.    wt: 1:   Chapter 11 Elementary Instruction
  293.    wt: 1:   Chapter 10 Transition
  294.    wt: 1:   Chapter 8 Modern Instruction
  295.    wt: 1:   Chapter 5 Four References
  296.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  297.    wt: 1:   Chapter 3 Algebra Difficulties
  298.    wt: 1:   Chapter 2 For and Against Mathematics
  299.    wt: 1:   Chapter 1 Introduction
  300.    wt: 1:   Foreword
  301.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  302.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  303.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  304.    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.

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:

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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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