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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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

57 matches:

  1.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  2.    wt: 1:   teaching tutoring algebraic reason
  3.    wt: 1:   Different Kinds of Reasoning in maths
  4.    wt: 1:   three kinds of reason in mathematics
  5.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  6.    wt: 1:   19 Horizontal line rule and method
  7.    wt: 1:   18 Vertical Line Rule and Method
  8.    wt: 1:   2 Column Multiplication Method
  9.    wt: 1:   11 Component Method
  10.    wt: 1:   10 Parallelogram Addition Method
  11.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  12.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  13.    wt: 1:   PS B Parallelogram Construction Methods
  14.    wt: 1:   PS A Kite Construction Methods
  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:   11 Volume of Sphere
  23.    wt: 1:   10 Volume of Pyramid
  24.    wt: 1:   9 Volume of Cone
  25.    wt: 1:   5 Box Volume Formula Example
  26.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  27.    wt: 1:   2 Least Common Multiple LCM intro via list method
  28.    wt: 1:   1 Counting and Counting Methods I
  29.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  30.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  31.    wt: 1:   D Decimal Multiplication Methods Derived
  32.    wt: 1:   A Elementary Basis for Multiplication Methods
  33.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  34.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  35.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  36.    wt: 1:   Example 2 volume of a cone
  37.    wt: 1:   Example 1 volume of a pyramid
  38.    wt: 1:   Volume of Solid by Cross Sections Lesson
  39.    wt: 1:   A Related Material in Volume 3
  40.    wt: 1:   3 Two Chain Rule Method Exercises
  41.    wt: 1:   1 Chain Rule in Reverse Integration Method
  42.    wt: 1:   A Related lessons in Volume 3
  43.    wt: 1:   Chapter 31 Direct and Indirect Reason
  44.    wt: 1:   Chapter 4 Longer Chains of Reason
  45.    wt: 1:   Chapter 3 Chains of Reason
  46.    wt: 1:   Postscript C Consistency as a Tool for Reason
  47.    wt: 1:   Postscript B More on Story Telling and Reason
  48.    wt: 1:   Chapter 24 Direct and Indirect Reason
  49.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  50.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  51.    wt: 1:   Chapter 11 Accidental Patterns
  52.    wt: 1:   Chapter 7 Longer Chains of Reason
  53.    wt: 1:   Chapter 6 Chains of Reason
  54.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  55.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  56.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  57.    wt: 1:   More Algebra and Slope based Calculus Preview

Extended Search

274 matches:

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

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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