Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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

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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22 matches:

  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 2:   D Decimal Long Division Methods/
  3.    wt: 2:   C Decimal Multiplication Methods/
  4.    wt: 2:   B Decimal Comparing and Subtracting Methods/
  5.    wt: 2:   A Decimal Counting and Adding Methods/
  6.    wt: 1:   LAMP Lean Applied Mathematics Program/
  7.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  8.    wt: 1:   Mathematics Education Essays/
  9.    wt: 1:   Volume 1A Regles et modeles/
  10.    wt: 1:   Mathematics Skills Year by Year/
  11.    wt: 1:   2 Arithmetic with Decimals/
  12.    wt: 1:   1 Decimal Place Value/
  13.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  14.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  15.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  16.    wt: 1:   Volume 2 Three Skills For Algebra/
  17.    wt: 1:   Volume 1A Pattern Based Reason/
  18.    wt: 1:   Volume 1 Elements of Reason/
  19.    wt: 1:   Mathematics 506 Lessons/
  20.    wt: 1:   Secondary Mathematics A Practical Approach/
  21.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  22.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

115 matches:

  1.    wt: 2:   mathematics curriculum shifts
  2.    wt: 2:   04 29 New Mathematics Curriculum
  3.    wt: 2:   need for a mixed mathematics curriculum
  4.    wt: 2:   Leaner mathematics curriculum
  5.    wt: 2:   C Three Decimal Subtraction Methods
  6.    wt: 2:   B Decimal Comparison and Subtraction
  7.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  8.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  9.    wt: 2:   7 Adding decimal fractions using decimal point
  10.    wt: 1:   E LAMP Introduction Modern Mathematics
  11.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  12.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  13.    wt: 1:   11 pure mathematics
  14.    wt: 1:   7 logic review and decimals an odd combination
  15.    wt: 1:   key notes and themes
  16.    wt: 1:   Mathematics Education Professors
  17.    wt: 1:   mathematics in context
  18.    wt: 1:   Secondary Three Mathematics
  19.    wt: 1:   Secondary Two Mathematics
  20.    wt: 1:   Secondary One Mathematics
  21.    wt: 1:   three goals for Mathematics Education
  22.    wt: 1:   02 20 mathematics education references
  23.    wt: 1:   three aims for mathematics students
  24.    wt: 1:   mathematics instruction in general
  25.    wt: 1:   Education in mathematics science and technology
  26.    wt: 1:   three kinds of reason in mathematics
  27.    wt: 1:   words for mathematics instructor
  28.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  29.    wt: 1:   22 Student Centered Highschool Mathematics
  30.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  31.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  32.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  33.    wt: 1:   18 Primary School Mathematics
  34.    wt: 1:   16 Secondary Mathematics Tips
  35.    wt: 1:   12 Goals and Objectives For Mathematics
  36.    wt: 1:   4 Function notation in and beyond mathematics
  37.    wt: 1:   8 Notes for instructors or tutors
  38.    wt: 1:   12 From Applied To Pure Mathematics
  39.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  40.    wt: 1:   9 Division with Digits after Decimal Point
  41.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  42.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  43.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  44.    wt: 1:   4 Location of Point in Decimal Addition
  45.    wt: 1:   3 Location of Point in Decimal Multiplication
  46.    wt: 1:   2 Counting Digits in Decimal Multiplication
  47.    wt: 1:   1 Fractions with Finite Decimal Expansions
  48.    wt: 1:   A Decimal Addition Columm Methods
  49.    wt: 1:   7 Decimals Multiplication Methods Examples
  50.    wt: 1:   6 Column Methods for Decimal Multiplication
  51.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  52.    wt: 1:   4 Subtraction and Division Axioms
  53.    wt: 1:   13 Real Number Subtraction
  54.    wt: 1:   Skill Development Notes
  55.    wt: 1:   11 Volume of Sphere
  56.    wt: 1:   10 Volume of Pyramid
  57.    wt: 1:   9 Volume of Cone
  58.    wt: 1:   5 Box Volume Formula Example
  59.    wt: 1:   1 Addition and Subtraction with Units
  60.    wt: 1:   16 Addition Subtraction Comparision Compared
  61.    wt: 1:   13 Subtraction with Additive Inverse
  62.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  63.    wt: 1:   7 Calculator Usage Notes and Cautions
  64.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  65.    wt: 1:   D Decimal Multiplication Methods Derived
  66.    wt: 1:   5 Decimal Fraction Multiplication
  67.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  68.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  69.    wt: 1:   Video Power Notation in Decimal Expansion
  70.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  71.    wt: 1:   Subtraction with J Conversions Example
  72.    wt: 1:   Subtraction Another Video Lesson
  73.    wt: 1:   9 22 Minute Subtraction Review Video
  74.    wt: 1:   8 Subtraction with Units of Measure
  75.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  76.    wt: 1:   5 A Tip for Efficent Subtraction
  77.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  78.    wt: 1:   2 Subtraction Easy Case Examples
  79.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  80.    wt: 1:   5. How to add decimals C. Examples
  81.    wt: 1:   4. How to add with decimals B with conversions
  82.    wt: 1:   3. How to add with decimals A sans conversions
  83.    wt: 1:   2 Decimal Counting Practices
  84.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  85.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  86.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  87.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  88.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  89.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  90.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  91.    wt: 1:   Example 2 volume of a cone
  92.    wt: 1:   Example 1 volume of a pyramid
  93.    wt: 1:   Volume of Solid by Cross Sections Lesson
  94.    wt: 1:   A Related Material in Volume 3
  95.    wt: 1:   A Related lessons in Volume 3
  96.    wt: 1:   3 Decimal insights for limits continuity convergence
  97.    wt: 1:   PostScript For and Against Decimal Perspectives
  98.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  99.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  100.    wt: 1:   Appendix E. How To Study Mathematics and Why
  101.    wt: 1:   Postscript B Mathematics Education References
  102.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  103.    wt: 1:   Chapter 2 For and Against Mathematics
  104.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  105.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  106.    wt: 1:   R Why Learn Mathematics Skills
  107.    wt: 1:   O On Learning Mathematics and Science
  108.    wt: 1:   N Mathematics Prepare for College Studies
  109.    wt: 1:   Helping the Blind in Logic and Mathematics
  110.    wt: 1:   Mathematics Education References
  111.    wt: 1:   Mathematics Education References
  112.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  113.    wt: 1:   Implementation Notes
  114.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  115.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

425 matches:

  1.    wt: 7:   Postscript B Mathematics Education References
  2.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  3.    wt: 7:   Chapter 2 For and Against Mathematics
  4.    wt: 6:   Annotated Links to Material Elsehwere
  5.    wt: 6:   Postscript A Three Remarks
  6.    wt: 6:   Chapter 12 Four Phases
  7.    wt: 6:   Chapter 11 Elementary Instruction
  8.    wt: 6:   Chapter 10 Transition
  9.    wt: 6:   Chapter 9 The Two Ends
  10.    wt: 6:   Chapter 8 Modern Instruction
  11.    wt: 6:   Chapter 7 Two Treatments of Geometry
  12.    wt: 6:   Chapter 5 Four References
  13.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  14.    wt: 6:   Chapter 3 Algebra Difficulties
  15.    wt: 6:   Chapter 1 Introduction
  16.    wt: 6:   Foreword
  17.    wt: 4:   Appendix 2 Three Decimal Subtraction Methods
  18.    wt: 4:   7 Subtraction for Decimal Fractions with Exercises
  19.    wt: 4:   7 Adding decimal fractions using decimal point
  20.    wt: 3:   mathematics curriculum shifts
  21.    wt: 3:   04 29 New Mathematics Curriculum
  22.    wt: 3:   need for a mixed mathematics curriculum
  23.    wt: 3:   Leaner mathematics curriculum
  24.    wt: 3:   6 Why Decimal Long Division Methods Works Take I
  25.    wt: 3:   D Decimal Multiplication Methods Derived
  26.    wt: 3:   5 Decimal Fraction Multiplication
  27.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  28.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  29.    wt: 3:   Video Power Notation in Decimal Expansion
  30.    wt: 3:   Appendix 1 Decimals Comparison Method Take II
  31.    wt: 3:   Subtraction with J Conversions Example
  32.    wt: 3:   Subtraction Another Video Lesson
  33.    wt: 3:   9 22 Minute Subtraction Review Video
  34.    wt: 3:   8 Subtraction with Units of Measure
  35.    wt: 3:   6 Subtraction with Conversion Example with Exercises
  36.    wt: 3:   5 A Tip for Efficent Subtraction
  37.    wt: 3:   4 Subtraction with Conversions Borrows and Letter J
  38.    wt: 3:   2 Subtraction Easy Case Examples
  39.    wt: 3:   1 Comparison and Subtraction Easy Direct Cases
  40.    wt: 3:   5. How to add decimals C. Examples
  41.    wt: 3:   4. How to add with decimals B with conversions
  42.    wt: 3:   3. How to add with decimals A sans conversions
  43.    wt: 3:   2 Decimal Counting Practices
  44.    wt: 2:   E LAMP Introduction Modern Mathematics
  45.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  46.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  47.    wt: 2:   11 pure mathematics
  48.    wt: 2:   7 logic review and decimals an odd combination
  49.    wt: 2:   key notes and themes
  50.    wt: 2:   Mathematics Education Professors
  51.    wt: 2:   mathematics in context
  52.    wt: 2:   Secondary Three Mathematics
  53.    wt: 2:   Secondary Two Mathematics
  54.    wt: 2:   Secondary One Mathematics
  55.    wt: 2:   three goals for Mathematics Education
  56.    wt: 2:   02 20 mathematics education references
  57.    wt: 2:   three aims for mathematics students
  58.    wt: 2:   mathematics instruction in general
  59.    wt: 2:   Education in mathematics science and technology
  60.    wt: 2:   three kinds of reason in mathematics
  61.    wt: 2:   words for mathematics instructor
  62.    wt: 2:   C Three Decimal Subtraction Methods
  63.    wt: 2:   B Decimal Comparison and Subtraction
  64.    wt: 2:   Long Division Backwards more
  65.    wt: 2:   Long Division Backward
  66.    wt: 2:   Division with Counts and Length
  67.    wt: 2:   Long Division forwards and backwards Example 3
  68.    wt: 2:   Long Division forwards and backwards Example 2
  69.    wt: 2:   Long Division forwards and backwards Example 1
  70.    wt: 2:   12 Why Long Division Works Take III
  71.    wt: 2:   11 Another Single Digit Divisor Example
  72.    wt: 2:   10 Division by Five Long and Short Ways
  73.    wt: 2:   9 Why Long Division Works Take II
  74.    wt: 2:   8 Correcting the Mistake
  75.    wt: 2:   7 Long Divison Mistake Catching
  76.    wt: 2:   5 Long Division Include Zeroes or not
  77.    wt: 2:   4 Division with 2 Digit Divsors
  78.    wt: 2:   3 Division Single Digit Divisor Example
  79.    wt: 2:   2 Division with Single Digit Divisors
  80.    wt: 2:   1 Divsion Physical Examples
  81.    wt: 2:   C Counting Areas with Powers of Ten
  82.    wt: 2:   B Powers of Ten
  83.    wt: 2:   A Elementary Basis for Multiplication Methods
  84.    wt: 2:   6 Multiplication Commutes Order Not Important
  85.    wt: 2:   4 Two and Three Digit Multipliers
  86.    wt: 2:   3 More One Digit Multipliers
  87.    wt: 2:   2 One Digit Multipliers
  88.    wt: 2:   1 Why 3 times 5 gives 15
  89.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  90.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  91.    wt: 2:   8 What skills and work habits to require
  92.    wt: 2:   6. Counting and adding units and mixed units
  93.    wt: 2:   1. Explaining Addition Table
  94.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  95.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  96.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  97.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  98.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  99.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  100.    wt: 2:   Example 2 volume of a cone
  101.    wt: 2:   Example 1 volume of a pyramid
  102.    wt: 2:   Volume of Solid by Cross Sections Lesson
  103.    wt: 2:   PostScript For and Against Decimal Perspectives
  104.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  105.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  106.    wt: 2:   Appendix E. How To Study Mathematics and Why
  107.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  108.    wt: 2:   Helping the Blind in Logic and Mathematics
  109.    wt: 2:   Mathematics Education References
  110.    wt: 2:   Mathematics Education References
  111.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  112.    wt: 2:   Implementation Notes
  113.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  114.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  115.    wt: 1:   Appendix 2 primary school Arithmetic 01
  116.    wt: 1:   Appendix 1 primary and preschool mathematic
  117.    wt: 1:   K LAMP Musings Science Education
  118.    wt: 1:   J LAMP Introduction Extrinsic Origins
  119.    wt: 1:   I LAMP Introduction Study Habits
  120.    wt: 1:   H LAMP Introduction Instructional Concepts
  121.    wt: 1:   G LAMP Introduction Problem Solving Skills
  122.    wt: 1:   F LAMP Introduction Prerequisites
  123.    wt: 1:   A Introduction Objectives
  124.    wt: 1:   Skills Chapter 5 Calculus
  125.    wt: 1:   Skills Chapter 4 Logic
  126.    wt: 1:   Ramblings Extrinsic numbers theory
  127.    wt: 1:   Ramblings Introduction Algebra Essay
  128.    wt: 1:   Skills Chapter 3 Algebra
  129.    wt: 1:   Skills Chapter 2 Geometry
  130.    wt: 1:   Skills Chapter 1 Arithmetic
  131.    wt: 1:   Skills Chapter 0 Introduction
  132.    wt: 1:   10 statistics
  133.    wt: 1:   9 combinatorics probability sets
  134.    wt: 1:   8 analytic geometry etc
  135.    wt: 1:   6 polynomials etc
  136.    wt: 1:   5 logarithms and exponentials etc
  137.    wt: 1:   4 algebra
  138.    wt: 1:   3 Euclidean Geometry Leanly
  139.    wt: 1:   2 arithmetic with signed numbers
  140.    wt: 1:   1 arithmetic with unsigned numbers
  141.    wt: 1:   What is POMME
  142.    wt: 1:   why bother
  143.    wt: 1:   which way to go
  144.    wt: 1:   website reviews
  145.    wt: 1:   three goals to set for students
  146.    wt: 1:   Teach the teachers plus goals
  147.    wt: 1:   permissions for teachers
  148.    wt: 1:   Math Ed if it must be short make it lean effective
  149.    wt: 1:   Applied Maths Program14092009 POMME variant
  150.    wt: 1:   activities for students
  151.    wt: 1:   links Education Resources online
  152.    wt: 1:   site origins
  153.    wt: 1:   site eurekas
  154.    wt: 1:   About site lesson plans
  155.    wt: 1:   teacher certification
  156.    wt: 1:   modern education
  157.    wt: 1:   learning takes time
  158.    wt: 1:   grouping students according to ability
  159.    wt: 1:   what should be learnt and When
  160.    wt: 1:   Postscript 2007 01 10
  161.    wt: 1:   Education Reform Inconsistencies
  162.    wt: 1:   five decades make a difference
  163.    wt: 1:   Maps Plans Drawings
  164.    wt: 1:   how letters appear
  165.    wt: 1:   talk the algebra talk
  166.    wt: 1:   three difficulties
  167.    wt: 1:   teaching tips
  168.    wt: 1:   What to Tell Students
  169.    wt: 1:   geometric implications for algebra
  170.    wt: 1:   teaching tutoring algebraic reason
  171.    wt: 1:   Lessening Algebra Difficulties
  172.    wt: 1:   the trouble with algebra
  173.    wt: 1:   05 13 OldSiteEntrancePage
  174.    wt: 1:   04 25 when to stop or suspend mathemat
  175.    wt: 1:   02 21 words for teachers
  176.    wt: 1:   standards for course material
  177.    wt: 1:   Operational Viewpoint to Value
  178.    wt: 1:   formal or informal peer review
  179.    wt: 1:   Theory of Knowledge
  180.    wt: 1:   Different Kinds of Reasoning in maths
  181.    wt: 1:   cultivating intelligence
  182.    wt: 1:   Four ways to improve education reform
  183.    wt: 1:   How to be a better instructor
  184.    wt: 1:   Motivation and Context Problem
  185.    wt: 1:   Prequel In For A Penny In For A Pound
  186.    wt: 1:   education an empirical art
  187.    wt: 1:   fairness and inductive principles for instruction
  188.    wt: 1:   chapitre 12 00 les iles et division
  189.    wt: 1:   chapitre 07 01 principle D induction mathematique
  190.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  191.    wt: 1:   chapitre 06 00 Chaines de la raison
  192.    wt: 1:   chapitre 05 00 Deception
  193.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  194.    wt: 1:   chapitre 04 09 Regles accidentelles
  195.    wt: 1:   chapitre 04 08 Limitations et benefices
  196.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  197.    wt: 1:   chapitre 04 06 engagements
  198.    wt: 1:   chapitre 04 05 Implication versus suggestion
  199.    wt: 1:   chapitre 04 04 Parlons de la logique
  200.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  201.    wt: 1:   chapitre 04 02 Deuxieme enigme
  202.    wt: 1:   chapitre 04 01 Premiere enigme
  203.    wt: 1:   chapitre 04 00 Les regles d implication
  204.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  205.    wt: 1:   chapitre 02 00 La Communication des idees
  206.    wt: 1:   chapitre 01 00 Introduction
  207.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  208.    wt: 1:   22 Student Centered Highschool Mathematics
  209.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  210.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  211.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  212.    wt: 1:   18 Primary School Mathematics
  213.    wt: 1:   16 Secondary Mathematics Tips
  214.    wt: 1:   12 Goals and Objectives For Mathematics
  215.    wt: 1:   Ages 12 to 14 Skills with take home value
  216.    wt: 1:   Ages 12 to 14 Geometry
  217.    wt: 1:   Ages 12 to 14 Arithmetic
  218.    wt: 1:   Ages 10 to 12 Geometry
  219.    wt: 1:   Ages 10 to 12 Arithmetic
  220.    wt: 1:   Ages 9 to 10
  221.    wt: 1:   Ages 8 to 9
  222.    wt: 1:   Ages 7 to 8
  223.    wt: 1:   Ages 6 to 7
  224.    wt: 1:   Ages 4 plus to 5 plus
  225.    wt: 1:   Ages 3 plus to 4 plus
  226.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  227.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  228.    wt: 1:   4 Function notation in and beyond mathematics
  229.    wt: 1:   8 Notes for instructors or tutors
  230.    wt: 1:   12 From Applied To Pure Mathematics
  231.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  232.    wt: 1:   9 Division with Digits after Decimal Point
  233.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  234.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  235.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  236.    wt: 1:   4 Location of Point in Decimal Addition
  237.    wt: 1:   3 Location of Point in Decimal Multiplication
  238.    wt: 1:   2 Counting Digits in Decimal Multiplication
  239.    wt: 1:   1 Fractions with Finite Decimal Expansions
  240.    wt: 1:   A Decimal Addition Columm Methods
  241.    wt: 1:   7 Decimals Multiplication Methods Examples
  242.    wt: 1:   6 Column Methods for Decimal Multiplication
  243.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  244.    wt: 1:   4 Subtraction and Division Axioms
  245.    wt: 1:   13 Real Number Subtraction
  246.    wt: 1:   Skill Development Notes
  247.    wt: 1:   11 Volume of Sphere
  248.    wt: 1:   10 Volume of Pyramid
  249.    wt: 1:   9 Volume of Cone
  250.    wt: 1:   5 Box Volume Formula Example
  251.    wt: 1:   1 Addition and Subtraction with Units
  252.    wt: 1:   16 Addition Subtraction Comparision Compared
  253.    wt: 1:   13 Subtraction with Additive Inverse
  254.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  255.    wt: 1:   7 Calculator Usage Notes and Cautions
  256.    wt: 1:   11 Place Value SI Standard International way
  257.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  258.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  259.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  260.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  261.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  262.    wt: 1:   Example 1. Area Between x and x squared
  263.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  264.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  265.    wt: 1:   Example 4 with x function of y
  266.    wt: 1:   Example 3
  267.    wt: 1:   Example 2
  268.    wt: 1:   Example 1
  269.    wt: 1:   Area Between Curves Lesson Take 2
  270.    wt: 1:   Area Between Curves Lesson Take 1
  271.    wt: 1:   Summary
  272.    wt: 1:   A Related Material in Volume 3
  273.    wt: 1:   A Related lessons in Volume 3
  274.    wt: 1:   3 Decimal insights for limits continuity convergence
  275.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  276.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  277.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  278.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  279.    wt: 1:   G.5 Motions With Bounded Velocities
  280.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  281.    wt: 1:   G.3 Constant Difference Theorem Proof
  282.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  283.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  284.    wt: 1:   F.5b Extreme Value Theorem
  285.    wt: 1:   F.5a Equicontinuity Theorems
  286.    wt: 1:   F.4 Finite Covering Theorem
  287.    wt: 1:   F.3 Intermediate Value Theorem
  288.    wt: 1:   F.2 Closed Range Theorem
  289.    wt: 1:   F.1 What Functions are Continuous
  290.    wt: 1:   E2 Algebraic Properties of Limits
  291.    wt: 1:   E1 Error Control Inequalities
  292.    wt: 1:   D2 Limits of Monotone Sequences
  293.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  294.    wt: 1:   C Triangle Inequalities
  295.    wt: 1:   B3 Bolzano Weierstrass Theorem
  296.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  297.    wt: 1:   A1. Introduction
  298.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  299.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  300.    wt: 1:   Chapter 23 Links To Trigonometry
  301.    wt: 1:   Chapter 22 Complex Numbers
  302.    wt: 1:   Chapter 21 Arrow Addition
  303.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  304.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  305.    wt: 1:   Chapter 18. Slopes Areas Integration
  306.    wt: 1:   Chapter 17. Area Approximation
  307.    wt: 1:   Chapter 16. Velocity Approximation
  308.    wt: 1:   Chapter 15. Slope Approximation
  309.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  310.    wt: 1:   Chapter 13. Acceleration
  311.    wt: 1:   Chapter 12. Units and Slopes
  312.    wt: 1:   Chapter 11. Graphing Slope versus Position
  313.    wt: 1:   Chapter 10 Slopes and Units
  314.    wt: 1:   Chapter 9 About First Courses in Calculus
  315.    wt: 1:   Chapter 8. Slope Interpretation
  316.    wt: 1:   Chapter 7 Slopes and Velocity
  317.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  318.    wt: 1:   Chapter 5. Slope Sign Tests
  319.    wt: 1:   Chapter 4. More Slope Sign Analysis
  320.    wt: 1:   Chapter 3. Slope Sign Analysis
  321.    wt: 1:   Chapter 2. Slopes and Ski Trails
  322.    wt: 1:   Chapter 1.Introduction
  323.    wt: 1:   Fall 1983 Calculus Appetizer
  324.    wt: 1:   Foreword
  325.    wt: 1:   Postscript More on Better Performance
  326.    wt: 1:   Postscript For Better Performance
  327.    wt: 1:   Appendix D. What to do in School and Why
  328.    wt: 1:   Appendix C. How to Read
  329.    wt: 1:   Appendix B. How To Learn
  330.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  331.    wt: 1:   Chapter 31 Direct and Indirect Reason
  332.    wt: 1:   Chapter 30 Truth Tables
  333.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  334.    wt: 1:   Chapter 28 Occurrence Tables
  335.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  336.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  337.    wt: 1:   Chapter 25. Mathematical Induction Examples
  338.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  339.    wt: 1:   Chapter 23. Notation For Sums
  340.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  341.    wt: 1:   Chapter 21. Third Reading Guide
  342.    wt: 1:   Chapter 20. Degrees and Radians
  343.    wt: 1:   Chapter 19. Functions and Sets
  344.    wt: 1:   Chapter 18. Rules for Algebra
  345.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  346.    wt: 1:   Chapter 16. Painless Theorem Proving
  347.    wt: 1:   Chapter 15. Solving Linear Equations
  348.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  349.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  350.    wt: 1:   Chapter 13. Second Reading Guide
  351.    wt: 1:   Chapter 12. Shorthand Usage Guide
  352.    wt: 1:   Chapter 11. Why Shorthand
  353.    wt: 1:   Chapter 10 Describing and Changing Calculations
  354.    wt: 1:   Postscript What is a Variable
  355.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  356.    wt: 1:   Chapter 8 Three Skills For Algebra
  357.    wt: 1:   Solutions For Arithmetic Exercises
  358.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  359.    wt: 1:   Chapter 6 Change of Language
  360.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  361.    wt: 1:   Chapter 4 Longer Chains of Reason
  362.    wt: 1:   Chapter 3 Chains of Reason
  363.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  364.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  365.    wt: 1:   Foreword
  366.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  367.    wt: 1:   Postscript C Consistency as a Tool for Reason
  368.    wt: 1:   Postscript B More on Story Telling and Reason
  369.    wt: 1:   Postscript A Story Telling
  370.    wt: 1:   Chapter 24 Direct and Indirect Reason
  371.    wt: 1:   Chapter 23 Truth Tables
  372.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  373.    wt: 1:   Chapter 21 Occurrence Tables
  374.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  375.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  376.    wt: 1:   Chapter 18 Sense and Knowledge
  377.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  378.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  379.    wt: 1:   Chapter 15 Objective Processes
  380.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  381.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  382.    wt: 1:   Chapter 11 Accidental Patterns
  383.    wt: 1:   Chapter 10 Responsibility
  384.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  385.    wt: 1:   Chapter 8 Change of Language
  386.    wt: 1:   Chapter 7 Longer Chains of Reason
  387.    wt: 1:   Chapter 6 Chains of Reason
  388.    wt: 1:   Chapter 5 Deception
  389.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  390.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  391.    wt: 1:   Chapter 2 Skill Development
  392.    wt: 1:   Chapter 1 Introduction
  393.    wt: 1:   Three Remarks
  394.    wt: 1:   Foreword
  395.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  396.    wt: 1:   R Why Learn Mathematics Skills
  397.    wt: 1:   O On Learning Mathematics and Science
  398.    wt: 1:   N Mathematics Prepare for College Studies
  399.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  400.    wt: 1:   Chapter 8 Skipped Topics and Why
  401.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  402.    wt: 1:   Chapter 6 More Algebra and Geometry
  403.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  404.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  405.    wt: 1:   Chapter 3 Algebra Starter Lessons
  406.    wt: 1:   Chapter 2 Why Sets
  407.    wt: 1:   Chapter 1 Arithmetic
  408.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  409.    wt: 1:   7 Games and Activities for Instruction
  410.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  411.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  412.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  413.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  414.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  415.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  416.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  417.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  418.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  419.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  420.    wt: 1:   More Algebra and Slope based Calculus Preview
  421.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  422.    wt: 1:   Systematic Algebra Skill Development Missing Links
  423.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  424.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  425.    wt: 1:   Which Way To Go

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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