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

Web Page Search

97 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:   13 Addition and Addition Tables
  6.    wt: 2:   11 Signed Number Addition and Addition Properties
  7.    wt: 1:   E LAMP Introduction Modern Mathematics
  8.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  9.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  10.    wt: 1:   11 pure mathematics
  11.    wt: 1:   7 logic review and decimals an odd combination
  12.    wt: 1:   key notes and themes
  13.    wt: 1:   Mathematics Education Professors
  14.    wt: 1:   mathematics in context
  15.    wt: 1:   Secondary Three Mathematics
  16.    wt: 1:   Secondary Two Mathematics
  17.    wt: 1:   Secondary One Mathematics
  18.    wt: 1:   three goals for Mathematics Education
  19.    wt: 1:   02 20 mathematics education references
  20.    wt: 1:   three aims for mathematics students
  21.    wt: 1:   mathematics instruction in general
  22.    wt: 1:   Education in mathematics science and technology
  23.    wt: 1:   three kinds of reason in mathematics
  24.    wt: 1:   words for mathematics instructor
  25.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  26.    wt: 1:   22 Student Centered Highschool Mathematics
  27.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  28.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  29.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  30.    wt: 1:   18 Primary School Mathematics
  31.    wt: 1:   16 Secondary Mathematics Tips
  32.    wt: 1:   12 Goals and Objectives For Mathematics
  33.    wt: 1:   4 Function notation in and beyond mathematics
  34.    wt: 1:   8 Notes for instructors or tutors
  35.    wt: 1:   3 Polynomials Multiplication Addition
  36.    wt: 1:   12 From Applied To Pure Mathematics
  37.    wt: 1:   10 Parallelogram Addition Method
  38.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  39.    wt: 1:   5 Head To Tail Arrow Addition
  40.    wt: 1:   3 Addition Properties
  41.    wt: 1:   5 Cartesian Addition and Translation
  42.    wt: 1:   PS G Rotation Distributes over Addition
  43.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  44.    wt: 1:   PS D Addition with Cartesian Coordinates
  45.    wt: 1:   21 Addition of Multiples of a Single Vector
  46.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  47.    wt: 1:   15 Head to Tails in place Addition Associative
  48.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  49.    wt: 1:   4 Location of Point in Decimal Addition
  50.    wt: 1:   A Decimal Addition Columm Methods
  51.    wt: 1:   7 Decimals Multiplication Methods Examples
  52.    wt: 1:   2 Combing Counts Addition Skills and Principles
  53.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  54.    wt: 1:   2 Addition and Multiplication Axioms
  55.    wt: 1:   11 Real Number Addition
  56.    wt: 1:   3 GE III Equation Addition and Multiplication
  57.    wt: 1:   Skill Development Notes
  58.    wt: 1:   11 Volume of Sphere
  59.    wt: 1:   10 Volume of Pyramid
  60.    wt: 1:   9 Volume of Cone
  61.    wt: 1:   5 Box Volume Formula Example
  62.    wt: 1:   1 Addition and Subtraction with Units
  63.    wt: 1:   16 Addition Subtraction Comparision Compared
  64.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  65.    wt: 1:   7 Calculator Usage Notes and Cautions
  66.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  67.    wt: 1:   5. How to add decimals C. Examples
  68.    wt: 1:   4. How to add with decimals B with conversions
  69.    wt: 1:   3. How to add with decimals A sans conversions
  70.    wt: 1:   1. Explaining Addition Table
  71.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  72.    wt: 1:   010 Repeated Addition of Time Intervals
  73.    wt: 1:   8 Addition of Time Intervals via subtotaling
  74.    wt: 1:   7 Addition of Time Intervals
  75.    wt: 1:   Example 2 volume of a cone
  76.    wt: 1:   Example 1 volume of a pyramid
  77.    wt: 1:   Volume of Solid by Cross Sections Lesson
  78.    wt: 1:   A Related Material in Volume 3
  79.    wt: 1:   A Related lessons in Volume 3
  80.    wt: 1:   Chapter 21 Arrow Addition
  81.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  82.    wt: 1:   Appendix E. How To Study Mathematics and Why
  83.    wt: 1:   Postscript B Mathematics Education References
  84.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  85.    wt: 1:   Chapter 2 For and Against Mathematics
  86.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  87.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  88.    wt: 1:   R Why Learn Mathematics Skills
  89.    wt: 1:   O On Learning Mathematics and Science
  90.    wt: 1:   N Mathematics Prepare for College Studies
  91.    wt: 1:   Helping the Blind in Logic and Mathematics
  92.    wt: 1:   Mathematics Education References
  93.    wt: 1:   Mathematics Education References
  94.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  95.    wt: 1:   Implementation Notes
  96.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  97.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

421 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: 3:   mathematics curriculum shifts
  18.    wt: 3:   04 29 New Mathematics Curriculum
  19.    wt: 3:   need for a mixed mathematics curriculum
  20.    wt: 3:   Leaner mathematics curriculum
  21.    wt: 2:   E LAMP Introduction Modern Mathematics
  22.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  23.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  24.    wt: 2:   11 pure mathematics
  25.    wt: 2:   7 logic review and decimals an odd combination
  26.    wt: 2:   key notes and themes
  27.    wt: 2:   Mathematics Education Professors
  28.    wt: 2:   mathematics in context
  29.    wt: 2:   Secondary Three Mathematics
  30.    wt: 2:   Secondary Two Mathematics
  31.    wt: 2:   Secondary One Mathematics
  32.    wt: 2:   three goals for Mathematics Education
  33.    wt: 2:   02 20 mathematics education references
  34.    wt: 2:   three aims for mathematics students
  35.    wt: 2:   mathematics instruction in general
  36.    wt: 2:   Education in mathematics science and technology
  37.    wt: 2:   three kinds of reason in mathematics
  38.    wt: 2:   words for mathematics instructor
  39.    wt: 2:   13 Addition and Addition Tables
  40.    wt: 2:   11 Signed Number Addition and Addition Properties
  41.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  42.    wt: 2:   5. How to add decimals C. Examples
  43.    wt: 2:   4. How to add with decimals B with conversions
  44.    wt: 2:   3. How to add with decimals A sans conversions
  45.    wt: 2:   1. Explaining Addition Table
  46.    wt: 2:   Example 2 volume of a cone
  47.    wt: 2:   Example 1 volume of a pyramid
  48.    wt: 2:   Volume of Solid by Cross Sections Lesson
  49.    wt: 2:   Chapter 21 Arrow Addition
  50.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  51.    wt: 2:   Appendix E. How To Study Mathematics and Why
  52.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  53.    wt: 2:   Helping the Blind in Logic and Mathematics
  54.    wt: 2:   Mathematics Education References
  55.    wt: 2:   Mathematics Education References
  56.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  57.    wt: 2:   Implementation Notes
  58.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  59.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  60.    wt: 1:   Appendix 2 primary school Arithmetic 01
  61.    wt: 1:   Appendix 1 primary and preschool mathematic
  62.    wt: 1:   K LAMP Musings Science Education
  63.    wt: 1:   J LAMP Introduction Extrinsic Origins
  64.    wt: 1:   I LAMP Introduction Study Habits
  65.    wt: 1:   H LAMP Introduction Instructional Concepts
  66.    wt: 1:   G LAMP Introduction Problem Solving Skills
  67.    wt: 1:   F LAMP Introduction Prerequisites
  68.    wt: 1:   A Introduction Objectives
  69.    wt: 1:   Skills Chapter 5 Calculus
  70.    wt: 1:   Skills Chapter 4 Logic
  71.    wt: 1:   Ramblings Extrinsic numbers theory
  72.    wt: 1:   Ramblings Introduction Algebra Essay
  73.    wt: 1:   Skills Chapter 3 Algebra
  74.    wt: 1:   Skills Chapter 2 Geometry
  75.    wt: 1:   Skills Chapter 1 Arithmetic
  76.    wt: 1:   Skills Chapter 0 Introduction
  77.    wt: 1:   10 statistics
  78.    wt: 1:   9 combinatorics probability sets
  79.    wt: 1:   8 analytic geometry etc
  80.    wt: 1:   6 polynomials etc
  81.    wt: 1:   5 logarithms and exponentials etc
  82.    wt: 1:   4 algebra
  83.    wt: 1:   3 Euclidean Geometry Leanly
  84.    wt: 1:   2 arithmetic with signed numbers
  85.    wt: 1:   1 arithmetic with unsigned numbers
  86.    wt: 1:   What is POMME
  87.    wt: 1:   why bother
  88.    wt: 1:   which way to go
  89.    wt: 1:   website reviews
  90.    wt: 1:   three goals to set for students
  91.    wt: 1:   Teach the teachers plus goals
  92.    wt: 1:   permissions for teachers
  93.    wt: 1:   Math Ed if it must be short make it lean effective
  94.    wt: 1:   Applied Maths Program14092009 POMME variant
  95.    wt: 1:   activities for students
  96.    wt: 1:   links Education Resources online
  97.    wt: 1:   site origins
  98.    wt: 1:   site eurekas
  99.    wt: 1:   About site lesson plans
  100.    wt: 1:   teacher certification
  101.    wt: 1:   modern education
  102.    wt: 1:   learning takes time
  103.    wt: 1:   grouping students according to ability
  104.    wt: 1:   what should be learnt and When
  105.    wt: 1:   Postscript 2007 01 10
  106.    wt: 1:   Education Reform Inconsistencies
  107.    wt: 1:   five decades make a difference
  108.    wt: 1:   Maps Plans Drawings
  109.    wt: 1:   how letters appear
  110.    wt: 1:   talk the algebra talk
  111.    wt: 1:   three difficulties
  112.    wt: 1:   teaching tips
  113.    wt: 1:   What to Tell Students
  114.    wt: 1:   geometric implications for algebra
  115.    wt: 1:   teaching tutoring algebraic reason
  116.    wt: 1:   Lessening Algebra Difficulties
  117.    wt: 1:   the trouble with algebra
  118.    wt: 1:   05 13 OldSiteEntrancePage
  119.    wt: 1:   04 25 when to stop or suspend mathemat
  120.    wt: 1:   02 21 words for teachers
  121.    wt: 1:   standards for course material
  122.    wt: 1:   Operational Viewpoint to Value
  123.    wt: 1:   formal or informal peer review
  124.    wt: 1:   Theory of Knowledge
  125.    wt: 1:   Different Kinds of Reasoning in maths
  126.    wt: 1:   cultivating intelligence
  127.    wt: 1:   Four ways to improve education reform
  128.    wt: 1:   How to be a better instructor
  129.    wt: 1:   Motivation and Context Problem
  130.    wt: 1:   Prequel In For A Penny In For A Pound
  131.    wt: 1:   education an empirical art
  132.    wt: 1:   fairness and inductive principles for instruction
  133.    wt: 1:   chapitre 12 00 les iles et division
  134.    wt: 1:   chapitre 07 01 principle D induction mathematique
  135.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  136.    wt: 1:   chapitre 06 00 Chaines de la raison
  137.    wt: 1:   chapitre 05 00 Deception
  138.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  139.    wt: 1:   chapitre 04 09 Regles accidentelles
  140.    wt: 1:   chapitre 04 08 Limitations et benefices
  141.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  142.    wt: 1:   chapitre 04 06 engagements
  143.    wt: 1:   chapitre 04 05 Implication versus suggestion
  144.    wt: 1:   chapitre 04 04 Parlons de la logique
  145.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  146.    wt: 1:   chapitre 04 02 Deuxieme enigme
  147.    wt: 1:   chapitre 04 01 Premiere enigme
  148.    wt: 1:   chapitre 04 00 Les regles d implication
  149.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  150.    wt: 1:   chapitre 02 00 La Communication des idees
  151.    wt: 1:   chapitre 01 00 Introduction
  152.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  153.    wt: 1:   22 Student Centered Highschool Mathematics
  154.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  155.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  156.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  157.    wt: 1:   18 Primary School Mathematics
  158.    wt: 1:   16 Secondary Mathematics Tips
  159.    wt: 1:   12 Goals and Objectives For Mathematics
  160.    wt: 1:   Ages 12 to 14 Skills with take home value
  161.    wt: 1:   Ages 12 to 14 Geometry
  162.    wt: 1:   Ages 12 to 14 Arithmetic
  163.    wt: 1:   Ages 10 to 12 Geometry
  164.    wt: 1:   Ages 10 to 12 Arithmetic
  165.    wt: 1:   Ages 9 to 10
  166.    wt: 1:   Ages 8 to 9
  167.    wt: 1:   Ages 7 to 8
  168.    wt: 1:   Ages 6 to 7
  169.    wt: 1:   Ages 4 plus to 5 plus
  170.    wt: 1:   Ages 3 plus to 4 plus
  171.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  172.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  173.    wt: 1:   4 Function notation in and beyond mathematics
  174.    wt: 1:   8 Notes for instructors or tutors
  175.    wt: 1:   3 Polynomials Multiplication Addition
  176.    wt: 1:   12 From Applied To Pure Mathematics
  177.    wt: 1:   10 Parallelogram Addition Method
  178.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  179.    wt: 1:   5 Head To Tail Arrow Addition
  180.    wt: 1:   3 Addition Properties
  181.    wt: 1:   5 Cartesian Addition and Translation
  182.    wt: 1:   PS G Rotation Distributes over Addition
  183.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  184.    wt: 1:   PS D Addition with Cartesian Coordinates
  185.    wt: 1:   21 Addition of Multiples of a Single Vector
  186.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  187.    wt: 1:   15 Head to Tails in place Addition Associative
  188.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  189.    wt: 1:   4 Location of Point in Decimal Addition
  190.    wt: 1:   A Decimal Addition Columm Methods
  191.    wt: 1:   7 Decimals Multiplication Methods Examples
  192.    wt: 1:   2 Combing Counts Addition Skills and Principles
  193.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  194.    wt: 1:   2 Addition and Multiplication Axioms
  195.    wt: 1:   11 Real Number Addition
  196.    wt: 1:   3 GE III Equation Addition and Multiplication
  197.    wt: 1:   Skill Development Notes
  198.    wt: 1:   11 Volume of Sphere
  199.    wt: 1:   10 Volume of Pyramid
  200.    wt: 1:   9 Volume of Cone
  201.    wt: 1:   5 Box Volume Formula Example
  202.    wt: 1:   1 Addition and Subtraction with Units
  203.    wt: 1:   16 Addition Subtraction Comparision Compared
  204.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  205.    wt: 1:   7 Calculator Usage Notes and Cautions
  206.    wt: 1:   Long Division Backwards more
  207.    wt: 1:   Long Division Backward
  208.    wt: 1:   Division with Counts and Length
  209.    wt: 1:   Long Division forwards and backwards Example 3
  210.    wt: 1:   Long Division forwards and backwards Example 2
  211.    wt: 1:   Long Division forwards and backwards Example 1
  212.    wt: 1:   12 Why Long Division Works Take III
  213.    wt: 1:   11 Another Single Digit Divisor Example
  214.    wt: 1:   10 Division by Five Long and Short Ways
  215.    wt: 1:   9 Why Long Division Works Take II
  216.    wt: 1:   8 Correcting the Mistake
  217.    wt: 1:   7 Long Divison Mistake Catching
  218.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  219.    wt: 1:   5 Long Division Include Zeroes or not
  220.    wt: 1:   4 Division with 2 Digit Divsors
  221.    wt: 1:   3 Division Single Digit Divisor Example
  222.    wt: 1:   2 Division with Single Digit Divisors
  223.    wt: 1:   1 Divsion Physical Examples
  224.    wt: 1:   D Decimal Multiplication Methods Derived
  225.    wt: 1:   C Counting Areas with Powers of Ten
  226.    wt: 1:   B Powers of Ten
  227.    wt: 1:   A Elementary Basis for Multiplication Methods
  228.    wt: 1:   6 Multiplication Commutes Order Not Important
  229.    wt: 1:   5 Decimal Fraction Multiplication
  230.    wt: 1:   4 Two and Three Digit Multipliers
  231.    wt: 1:   3 More One Digit Multipliers
  232.    wt: 1:   2 One Digit Multipliers
  233.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  234.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  235.    wt: 1:   Video Power Notation in Decimal Expansion
  236.    wt: 1:   1 Why 3 times 5 gives 15
  237.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  238.    wt: 1:   Subtraction with J Conversions Example
  239.    wt: 1:   Subtraction Another Video Lesson
  240.    wt: 1:   9 22 Minute Subtraction Review Video
  241.    wt: 1:   8 Subtraction with Units of Measure
  242.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  243.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  244.    wt: 1:   5 A Tip for Efficent Subtraction
  245.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  246.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  247.    wt: 1:   2 Subtraction Easy Case Examples
  248.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  249.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  250.    wt: 1:   8 What skills and work habits to require
  251.    wt: 1:   7 Adding decimal fractions using decimal point
  252.    wt: 1:   6. Counting and adding units and mixed units
  253.    wt: 1:   2 Decimal Counting Practices
  254.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  255.    wt: 1:   010 Repeated Addition of Time Intervals
  256.    wt: 1:   8 Addition of Time Intervals via subtotaling
  257.    wt: 1:   7 Addition of Time Intervals
  258.    wt: 1:   Example 1. Area Between x and x squared
  259.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  260.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  261.    wt: 1:   Example 4 with x function of y
  262.    wt: 1:   Example 3
  263.    wt: 1:   Example 2
  264.    wt: 1:   Example 1
  265.    wt: 1:   Area Between Curves Lesson Take 2
  266.    wt: 1:   Area Between Curves Lesson Take 1
  267.    wt: 1:   Summary
  268.    wt: 1:   A Related Material in Volume 3
  269.    wt: 1:   A Related lessons in Volume 3
  270.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  271.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  272.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  273.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  274.    wt: 1:   G.5 Motions With Bounded Velocities
  275.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  276.    wt: 1:   G.3 Constant Difference Theorem Proof
  277.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  278.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  279.    wt: 1:   F.5b Extreme Value Theorem
  280.    wt: 1:   F.5a Equicontinuity Theorems
  281.    wt: 1:   F.4 Finite Covering Theorem
  282.    wt: 1:   F.3 Intermediate Value Theorem
  283.    wt: 1:   F.2 Closed Range Theorem
  284.    wt: 1:   F.1 What Functions are Continuous
  285.    wt: 1:   E2 Algebraic Properties of Limits
  286.    wt: 1:   E1 Error Control Inequalities
  287.    wt: 1:   D2 Limits of Monotone Sequences
  288.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  289.    wt: 1:   C Triangle Inequalities
  290.    wt: 1:   B3 Bolzano Weierstrass Theorem
  291.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  292.    wt: 1:   PostScript For and Against Decimal Perspectives
  293.    wt: 1:   A1. Introduction
  294.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  295.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  296.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  297.    wt: 1:   Chapter 23 Links To Trigonometry
  298.    wt: 1:   Chapter 22 Complex Numbers
  299.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  300.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  301.    wt: 1:   Chapter 18. Slopes Areas Integration
  302.    wt: 1:   Chapter 17. Area Approximation
  303.    wt: 1:   Chapter 16. Velocity Approximation
  304.    wt: 1:   Chapter 15. Slope Approximation
  305.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  306.    wt: 1:   Chapter 13. Acceleration
  307.    wt: 1:   Chapter 12. Units and Slopes
  308.    wt: 1:   Chapter 11. Graphing Slope versus Position
  309.    wt: 1:   Chapter 10 Slopes and Units
  310.    wt: 1:   Chapter 9 About First Courses in Calculus
  311.    wt: 1:   Chapter 8. Slope Interpretation
  312.    wt: 1:   Chapter 7 Slopes and Velocity
  313.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  314.    wt: 1:   Chapter 5. Slope Sign Tests
  315.    wt: 1:   Chapter 4. More Slope Sign Analysis
  316.    wt: 1:   Chapter 3. Slope Sign Analysis
  317.    wt: 1:   Chapter 2. Slopes and Ski Trails
  318.    wt: 1:   Chapter 1.Introduction
  319.    wt: 1:   Fall 1983 Calculus Appetizer
  320.    wt: 1:   Foreword
  321.    wt: 1:   Postscript More on Better Performance
  322.    wt: 1:   Postscript For Better Performance
  323.    wt: 1:   Appendix D. What to do in School and Why
  324.    wt: 1:   Appendix C. How to Read
  325.    wt: 1:   Appendix B. How To Learn
  326.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  327.    wt: 1:   Chapter 31 Direct and Indirect Reason
  328.    wt: 1:   Chapter 30 Truth Tables
  329.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  330.    wt: 1:   Chapter 28 Occurrence Tables
  331.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  332.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  333.    wt: 1:   Chapter 25. Mathematical Induction Examples
  334.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  335.    wt: 1:   Chapter 23. Notation For Sums
  336.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  337.    wt: 1:   Chapter 21. Third Reading Guide
  338.    wt: 1:   Chapter 20. Degrees and Radians
  339.    wt: 1:   Chapter 19. Functions and Sets
  340.    wt: 1:   Chapter 18. Rules for Algebra
  341.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  342.    wt: 1:   Chapter 16. Painless Theorem Proving
  343.    wt: 1:   Chapter 15. Solving Linear Equations
  344.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  345.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  346.    wt: 1:   Chapter 13. Second Reading Guide
  347.    wt: 1:   Chapter 12. Shorthand Usage Guide
  348.    wt: 1:   Chapter 11. Why Shorthand
  349.    wt: 1:   Chapter 10 Describing and Changing Calculations
  350.    wt: 1:   Postscript What is a Variable
  351.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  352.    wt: 1:   Chapter 8 Three Skills For Algebra
  353.    wt: 1:   Solutions For Arithmetic Exercises
  354.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  355.    wt: 1:   Chapter 6 Change of Language
  356.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  357.    wt: 1:   Chapter 4 Longer Chains of Reason
  358.    wt: 1:   Chapter 3 Chains of Reason
  359.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  360.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  361.    wt: 1:   Foreword
  362.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  363.    wt: 1:   Postscript C Consistency as a Tool for Reason
  364.    wt: 1:   Postscript B More on Story Telling and Reason
  365.    wt: 1:   Postscript A Story Telling
  366.    wt: 1:   Chapter 24 Direct and Indirect Reason
  367.    wt: 1:   Chapter 23 Truth Tables
  368.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  369.    wt: 1:   Chapter 21 Occurrence Tables
  370.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  371.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  372.    wt: 1:   Chapter 18 Sense and Knowledge
  373.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  374.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  375.    wt: 1:   Chapter 15 Objective Processes
  376.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  377.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  378.    wt: 1:   Chapter 11 Accidental Patterns
  379.    wt: 1:   Chapter 10 Responsibility
  380.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  381.    wt: 1:   Chapter 8 Change of Language
  382.    wt: 1:   Chapter 7 Longer Chains of Reason
  383.    wt: 1:   Chapter 6 Chains of Reason
  384.    wt: 1:   Chapter 5 Deception
  385.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  386.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  387.    wt: 1:   Chapter 2 Skill Development
  388.    wt: 1:   Chapter 1 Introduction
  389.    wt: 1:   Three Remarks
  390.    wt: 1:   Foreword
  391.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  392.    wt: 1:   R Why Learn Mathematics Skills
  393.    wt: 1:   O On Learning Mathematics and Science
  394.    wt: 1:   N Mathematics Prepare for College Studies
  395.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  396.    wt: 1:   Chapter 8 Skipped Topics and Why
  397.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  398.    wt: 1:   Chapter 6 More Algebra and Geometry
  399.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  400.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  401.    wt: 1:   Chapter 3 Algebra Starter Lessons
  402.    wt: 1:   Chapter 2 Why Sets
  403.    wt: 1:   Chapter 1 Arithmetic
  404.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  405.    wt: 1:   7 Games and Activities for Instruction
  406.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  407.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  408.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  409.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  410.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  411.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  412.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  413.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  414.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  415.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  416.    wt: 1:   More Algebra and Slope based Calculus Preview
  417.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  418.    wt: 1:   Systematic Algebra Skill Development Missing Links
  419.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  420.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  421.    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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