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:   Volume 1 Elements of Reason/
  4.    wt: 1:   10 Examples of Algebraic Reasoning/
  5.    wt: 1:   8 Unifying Theme For Algebra/
  6.    wt: 1:   9 Combinatorics Trees Tables and Products/
  7.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  8.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  9.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  10.    wt: 1:   Volume 2 Three Skills For Algebra/
  11.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  12.    wt: 1:   Mathematics 506 Lessons/
  13.    wt: 1:   Quebec Material/

Web Page Search

78 matches:

  1.    wt: 2:   Different Kinds of Reasoning in maths
  2.    wt: 2:   A Related Material in Volume 3
  3.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  4.    wt: 1:   Math Ed if it must be short make it lean effective
  5.    wt: 1:   teacher certification
  6.    wt: 1:   five decades make a difference
  7.    wt: 1:   three difficulties
  8.    wt: 1:   mathematics curriculum shifts
  9.    wt: 1:   geometric implications for algebra
  10.    wt: 1:   teaching tutoring algebraic reason
  11.    wt: 1:   Lessening Algebra Difficulties
  12.    wt: 1:   standards for course material
  13.    wt: 1:   three kinds of reason in mathematics
  14.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  15.    wt: 1:   chapitre 04 05 Implication versus suggestion
  16.    wt: 1:   chapitre 04 00 Les regles d implication
  17.    wt: 1:   14 Multiplication and Times Tables
  18.    wt: 1:   13 Addition and Addition Tables
  19.    wt: 1:   4 quadratics difference of two squares
  20.    wt: 1:   2 Square Root Simplification a prequel
  21.    wt: 1:   24 tangent Angle Difference Formula
  22.    wt: 1:   13 Naming Identifying Formulas with Words
  23.    wt: 1:   11 Volume of Sphere
  24.    wt: 1:   10 Volume of Pyramid
  25.    wt: 1:   9 Volume of Cone
  26.    wt: 1:   5 Box Volume Formula Example
  27.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  28.    wt: 1:   3 Counting with Tables and Trees II
  29.    wt: 1:   2 Counting with Tables and Trees I
  30.    wt: 1:   6 Simplification of Fractions with Units
  31.    wt: 1:   11 Simplification an Algebraic View
  32.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  33.    wt: 1:   17 Identify and Count Factors using Primes
  34.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  35.    wt: 1:   3 video Primes and Composites from 9 times table
  36.    wt: 1:   1. Explaining Addition Table
  37.    wt: 1:   The 20 Times Table
  38.    wt: 1:   The 12 Times Table Visually
  39.    wt: 1:   015 School and work day counting tables
  40.    wt: 1:   013 Travel Time Tables
  41.    wt: 1:   Example 2 volume of a cone
  42.    wt: 1:   Example 1 volume of a pyramid
  43.    wt: 1:   Volume of Solid by Cross Sections Lesson
  44.    wt: 1:   A Related lessons in Volume 3
  45.    wt: 1:   8 Differentiation of polynomials
  46.    wt: 1:   7 Animated Differentiation Examples
  47.    wt: 1:   2 Algebraic codification
  48.    wt: 1:   G.3 Constant Difference Theorem Proof
  49.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  50.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  51.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  52.    wt: 1:   Chapter 31 Direct and Indirect Reason
  53.    wt: 1:   Chapter 30 Truth Tables
  54.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  55.    wt: 1:   Chapter 28 Occurrence Tables
  56.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  57.    wt: 1:   Chapter 4 Longer Chains of Reason
  58.    wt: 1:   Chapter 3 Chains of Reason
  59.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  60.    wt: 1:   Annotated Links to Material Elsehwere
  61.    wt: 1:   Chapter 3 Algebra Difficulties
  62.    wt: 1:   Postscript C Consistency as a Tool for Reason
  63.    wt: 1:   Postscript B More on Story Telling and Reason
  64.    wt: 1:   Chapter 24 Direct and Indirect Reason
  65.    wt: 1:   Chapter 23 Truth Tables
  66.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  67.    wt: 1:   Chapter 21 Occurrence Tables
  68.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  69.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  70.    wt: 1:   Chapter 11 Accidental Patterns
  71.    wt: 1:   Chapter 7 Longer Chains of Reason
  72.    wt: 1:   Chapter 6 Chains of Reason
  73.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  74.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  75.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  76.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  77.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  78.    wt: 1:   More Algebra and Slope based Calculus Preview

Extended Search

234 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 23 Truth Tables
  5.    wt: 7:   Chapter 22 Contrapositive and Vacuously True Implications
  6.    wt: 7:   Chapter 21 Occurrence Tables
  7.    wt: 7:   Chapter 16 Origins and Limitations of Rules and Patterns
  8.    wt: 7:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  9.    wt: 7:   Chapter 11 Accidental Patterns
  10.    wt: 7:   Chapter 7 Longer Chains of Reason
  11.    wt: 7:   Chapter 6 Chains of Reason
  12.    wt: 7:   Chapter 4 Implication Rules Forwards and Backwards
  13.    wt: 6:   Postscript D Reflections on Law of the Excluded Middle
  14.    wt: 6:   Postscript A Story Telling
  15.    wt: 6:   Chapter 20 Shorthand Symbols as Pronouns
  16.    wt: 6:   Chapter 19 What is in chapters 20 to 24
  17.    wt: 6:   Chapter 18 Sense and Knowledge
  18.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  19.    wt: 6:   Chapter 15 Objective Processes
  20.    wt: 6:   Chapter 14 Deductive and Empirical Views of Mathematics
  21.    wt: 6:   Chapter 12 Islands and Divisions of Knowledge
  22.    wt: 6:   Chapter 10 Responsibility
  23.    wt: 6:   Chapter 9 What is in Chapters 10 to 18
  24.    wt: 6:   Chapter 8 Change of Language
  25.    wt: 6:   Chapter 5 Deception
  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:   chapitre 04 07 RepetablesEtReproductibles
  32.    wt: 3:   chapitre 04 05 Implication versus suggestion
  33.    wt: 3:   chapitre 04 00 Les regles d implication
  34.    wt: 3:   A Related Material in Volume 3
  35.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  36.    wt: 2:   Different Kinds of Reasoning in maths
  37.    wt: 2:   chapitre 12 00 les iles et division
  38.    wt: 2:   chapitre 07 01 principle D induction mathematique
  39.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  40.    wt: 2:   chapitre 06 00 Chaines de la raison
  41.    wt: 2:   chapitre 05 00 Deception
  42.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  43.    wt: 2:   chapitre 04 09 Regles accidentelles
  44.    wt: 2:   chapitre 04 08 Limitations et benefices
  45.    wt: 2:   chapitre 04 06 engagements
  46.    wt: 2:   chapitre 04 04 Parlons de la logique
  47.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  48.    wt: 2:   chapitre 04 02 Deuxieme enigme
  49.    wt: 2:   chapitre 04 01 Premiere enigme
  50.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  51.    wt: 2:   chapitre 02 00 La Communication des idees
  52.    wt: 2:   chapitre 01 00 Introduction
  53.    wt: 2:   5 Counting with Tables Trees Product Rule Take II
  54.    wt: 2:   3 Counting with Tables and Trees II
  55.    wt: 2:   2 Counting with Tables and Trees I
  56.    wt: 2:   Example 2 volume of a cone
  57.    wt: 2:   Example 1 volume of a pyramid
  58.    wt: 2:   Volume of Solid by Cross Sections Lesson
  59.    wt: 2:   Area Between Curves Lesson Take 2
  60.    wt: 2:   G.3 Constant Difference Theorem Proof
  61.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  62.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  63.    wt: 2:   Chapter 6. Slopes and Vertical Shifts
  64.    wt: 2:   Chapter 31 Direct and Indirect Reason
  65.    wt: 2:   Chapter 30 Truth Tables
  66.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  67.    wt: 2:   Chapter 28 Occurrence Tables
  68.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  69.    wt: 2:   Chapter 4 Longer Chains of Reason
  70.    wt: 2:   Chapter 3 Chains of Reason
  71.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  72.    wt: 2:   Annotated Links to Material Elsehwere
  73.    wt: 2:   Chapter 3 Algebra Difficulties
  74.    wt: 1:   Math Ed if it must be short make it lean effective
  75.    wt: 1:   teacher certification
  76.    wt: 1:   five decades make a difference
  77.    wt: 1:   three difficulties
  78.    wt: 1:   mathematics curriculum shifts
  79.    wt: 1:   geometric implications for algebra
  80.    wt: 1:   teaching tutoring algebraic reason
  81.    wt: 1:   Lessening Algebra Difficulties
  82.    wt: 1:   standards for course material
  83.    wt: 1:   three kinds of reason in mathematics
  84.    wt: 1:   14 Multiplication and Times Tables
  85.    wt: 1:   13 Addition and Addition Tables
  86.    wt: 1:   4 quadratics difference of two squares
  87.    wt: 1:   2 Square Root Simplification a prequel
  88.    wt: 1:   24 tangent Angle Difference Formula
  89.    wt: 1:   5 Areas of Rectangles Revisited
  90.    wt: 1:   4 Fraction Operations Axiomatic Development
  91.    wt: 1:   3 Inequalities Algebraically
  92.    wt: 1:   2 Fraction Operations Physical Development
  93.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  94.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  95.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  96.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  97.    wt: 1:   6 Compound Interest Forward and Backwards
  98.    wt: 1:   5 Triangle Area Formula Backwards
  99.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  100.    wt: 1:   3 Linear Equation Literal Solution More
  101.    wt: 1:   2 Linear Equation Literal Solution
  102.    wt: 1:   1 Changing Calculations
  103.    wt: 1:   13 Naming Identifying Formulas with Words
  104.    wt: 1:   11 Volume of Sphere
  105.    wt: 1:   10 Volume of Pyramid
  106.    wt: 1:   9 Volume of Cone
  107.    wt: 1:   5 Box Volume Formula Example
  108.    wt: 1:   4 Counting with Trees Product Rule Take I
  109.    wt: 1:   1 Counting and Counting Methods I
  110.    wt: 1:   6 Simplification of Fractions with Units
  111.    wt: 1:   11 Simplification an Algebraic View
  112.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  113.    wt: 1:   17 Identify and Count Factors using Primes
  114.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  115.    wt: 1:   3 video Primes and Composites from 9 times table
  116.    wt: 1:   1. Explaining Addition Table
  117.    wt: 1:   The 20 Times Table
  118.    wt: 1:   The 12 Times Table Visually
  119.    wt: 1:   015 School and work day counting tables
  120.    wt: 1:   013 Travel Time Tables
  121.    wt: 1:   Example 1. Area Between x and x squared
  122.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  123.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  124.    wt: 1:   Example 4 with x function of y
  125.    wt: 1:   Example 3
  126.    wt: 1:   Example 2
  127.    wt: 1:   Example 1
  128.    wt: 1:   Area Between Curves Lesson Take 1
  129.    wt: 1:   Summary
  130.    wt: 1:   A Related lessons in Volume 3
  131.    wt: 1:   8 Differentiation of polynomials
  132.    wt: 1:   7 Animated Differentiation Examples
  133.    wt: 1:   2 Algebraic codification
  134.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  135.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  136.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  137.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  138.    wt: 1:   G.5 Motions With Bounded Velocities
  139.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  140.    wt: 1:   F.5b Extreme Value Theorem
  141.    wt: 1:   F.5a Equicontinuity Theorems
  142.    wt: 1:   F.4 Finite Covering Theorem
  143.    wt: 1:   F.3 Intermediate Value Theorem
  144.    wt: 1:   F.2 Closed Range Theorem
  145.    wt: 1:   F.1 What Functions are Continuous
  146.    wt: 1:   E2 Algebraic Properties of Limits
  147.    wt: 1:   E1 Error Control Inequalities
  148.    wt: 1:   D2 Limits of Monotone Sequences
  149.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  150.    wt: 1:   C Triangle Inequalities
  151.    wt: 1:   B3 Bolzano Weierstrass Theorem
  152.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  153.    wt: 1:   PostScript For and Against Decimal Perspectives
  154.    wt: 1:   A1. Introduction
  155.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  156.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  157.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  158.    wt: 1:   Chapter 23 Links To Trigonometry
  159.    wt: 1:   Chapter 22 Complex Numbers
  160.    wt: 1:   Chapter 21 Arrow Addition
  161.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  162.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  163.    wt: 1:   Chapter 18. Slopes Areas Integration
  164.    wt: 1:   Chapter 17. Area Approximation
  165.    wt: 1:   Chapter 16. Velocity Approximation
  166.    wt: 1:   Chapter 15. Slope Approximation
  167.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  168.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  169.    wt: 1:   Chapter 13. Acceleration
  170.    wt: 1:   Chapter 12. Units and Slopes
  171.    wt: 1:   Chapter 11. Graphing Slope versus Position
  172.    wt: 1:   Chapter 10 Slopes and Units
  173.    wt: 1:   Chapter 9 About First Courses in Calculus
  174.    wt: 1:   Chapter 8. Slope Interpretation
  175.    wt: 1:   Chapter 7 Slopes and Velocity
  176.    wt: 1:   Chapter 5. Slope Sign Tests
  177.    wt: 1:   Chapter 4. More Slope Sign Analysis
  178.    wt: 1:   Chapter 3. Slope Sign Analysis
  179.    wt: 1:   Chapter 2. Slopes and Ski Trails
  180.    wt: 1:   Chapter 1.Introduction
  181.    wt: 1:   Fall 1983 Calculus Appetizer
  182.    wt: 1:   Foreword
  183.    wt: 1:   Postscript More on Better Performance
  184.    wt: 1:   Postscript For Better Performance
  185.    wt: 1:   Appendix E. How To Study Mathematics and Why
  186.    wt: 1:   Appendix D. What to do in School and Why
  187.    wt: 1:   Appendix C. How to Read
  188.    wt: 1:   Appendix B. How To Learn
  189.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  190.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  191.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  192.    wt: 1:   Chapter 25. Mathematical Induction Examples
  193.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  194.    wt: 1:   Chapter 23. Notation For Sums
  195.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  196.    wt: 1:   Chapter 21. Third Reading Guide
  197.    wt: 1:   Chapter 20. Degrees and Radians
  198.    wt: 1:   Chapter 19. Functions and Sets
  199.    wt: 1:   Chapter 18. Rules for Algebra
  200.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  201.    wt: 1:   Chapter 16. Painless Theorem Proving
  202.    wt: 1:   Chapter 15. Solving Linear Equations
  203.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  204.    wt: 1:   Chapter 13. Second Reading Guide
  205.    wt: 1:   Chapter 12. Shorthand Usage Guide
  206.    wt: 1:   Chapter 11. Why Shorthand
  207.    wt: 1:   Chapter 10 Describing and Changing Calculations
  208.    wt: 1:   Postscript What is a Variable
  209.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  210.    wt: 1:   Chapter 8 Three Skills For Algebra
  211.    wt: 1:   Solutions For Arithmetic Exercises
  212.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  213.    wt: 1:   Chapter 6 Change of Language
  214.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  215.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  216.    wt: 1:   Foreword
  217.    wt: 1:   Postscript B Mathematics Education References
  218.    wt: 1:   Postscript A Three Remarks
  219.    wt: 1:   Chapter 12 Four Phases
  220.    wt: 1:   Chapter 11 Elementary Instruction
  221.    wt: 1:   Chapter 10 Transition
  222.    wt: 1:   Chapter 9 The Two Ends
  223.    wt: 1:   Chapter 8 Modern Instruction
  224.    wt: 1:   Chapter 7 Two Treatments of Geometry
  225.    wt: 1:   Chapter 5 Four References
  226.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  227.    wt: 1:   Chapter 2 For and Against Mathematics
  228.    wt: 1:   Chapter 1 Introduction
  229.    wt: 1:   Foreword
  230.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  231.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  232.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  233.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  234.    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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