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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21 matches:

  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 2:   7 Complex Numbers/
  3.    wt: 1:   LAMP Lean Applied Mathematics Program/
  4.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  5.    wt: 1:   Mathematics Education Essays/
  6.    wt: 1:   Volume 1A Regles et modeles/
  7.    wt: 1:   Mathematics Skills Year by Year/
  8.    wt: 1:   B Real Numbers Extrinsic Development/
  9.    wt: 1:   5 Real Numbers/
  10.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  11.    wt: 1:   8 Arithmetic with Signed Numbers/
  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

112 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:   20 N th Roots of Complex Numbers
  6.    wt: 2:   2 Complex Numbers made easier we hope
  7.    wt: 2:   7 Complex Numbers Appetizer
  8.    wt: 2:   PS H Distributive Law For Complex Numbers
  9.    wt: 2:   Chapter 22 Complex Numbers
  10.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  11.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  12.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  13.    wt: 1:   E LAMP Introduction Modern Mathematics
  14.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  15.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  16.    wt: 1:   Ramblings Extrinsic numbers theory
  17.    wt: 1:   11 pure mathematics
  18.    wt: 1:   2 arithmetic with signed numbers
  19.    wt: 1:   1 arithmetic with unsigned numbers
  20.    wt: 1:   key notes and themes
  21.    wt: 1:   Mathematics Education Professors
  22.    wt: 1:   mathematics in context
  23.    wt: 1:   Secondary Three Mathematics
  24.    wt: 1:   Secondary Two Mathematics
  25.    wt: 1:   Secondary One Mathematics
  26.    wt: 1:   three goals for Mathematics Education
  27.    wt: 1:   02 20 mathematics education references
  28.    wt: 1:   three aims for mathematics students
  29.    wt: 1:   mathematics instruction in general
  30.    wt: 1:   Education in mathematics science and technology
  31.    wt: 1:   three kinds of reason in mathematics
  32.    wt: 1:   words for mathematics instructor
  33.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  34.    wt: 1:   22 Student Centered Highschool Mathematics
  35.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  36.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  37.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  38.    wt: 1:   18 Primary School Mathematics
  39.    wt: 1:   16 Secondary Mathematics Tips
  40.    wt: 1:   12 Goals and Objectives For Mathematics
  41.    wt: 1:   4 Function notation in and beyond mathematics
  42.    wt: 1:   8 Notes for instructors or tutors
  43.    wt: 1:   12 From Applied To Pure Mathematics
  44.    wt: 1:   Vector and Complex Number Applet
  45.    wt: 1:   17A The complex number valued trig function cis
  46.    wt: 1:   9 The complex number valued trig function cis
  47.    wt: 1:   6 Field Properties of Complex Number
  48.    wt: 1:   Appetizer A Complex Number Applet
  49.    wt: 1:   musings do not puiblish real numbers
  50.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  51.    wt: 1:   22 Multiplication of Signed Numbers
  52.    wt: 1:   12 Real Numbers Line Signed Coordinates
  53.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  54.    wt: 1:   5 Distributive Law for Whole Numbers
  55.    wt: 1:   1 The Counting Origins of Numbers
  56.    wt: 1:   4 Comparison of Negative Numbers
  57.    wt: 1:   1 Real Numbers Comparison
  58.    wt: 1:   16 Real Numbers Comparison
  59.    wt: 1:   7 Real Numbers as Line Cordinates
  60.    wt: 1:   6 Unsigned Real Numbers
  61.    wt: 1:   5 Rational Numbers More
  62.    wt: 1:   4 Rational Numbers
  63.    wt: 1:   1 Whole and Natural Numbers
  64.    wt: 1:   Skill Development Notes
  65.    wt: 1:   11 Volume of Sphere
  66.    wt: 1:   10 Volume of Pyramid
  67.    wt: 1:   9 Volume of Cone
  68.    wt: 1:   5 Box Volume Formula Example
  69.    wt: 1:   8 Sets of Numbers
  70.    wt: 1:   5 Talking about Numbers and Quantities
  71.    wt: 1:   4 A Brief Story of numbers and algebra
  72.    wt: 1:   3 Comparison of Negative Numbers
  73.    wt: 1:   11 What are real lengths and numbers
  74.    wt: 1:   10 dividing signed numbers
  75.    wt: 1:   9 subtracting signed numbers
  76.    wt: 1:   8 multiplying signed numbers
  77.    wt: 1:   6 adding signed numbers
  78.    wt: 1:   5 lengths and signs of numbers
  79.    wt: 1:   2 signed and unsigned numbers as coordinates
  80.    wt: 1:   3 Multiplying Units and Numbers
  81.    wt: 1:   22 Complex Compound Fractions
  82.    wt: 1:   9 Improper Fractions and Mixed Numbers
  83.    wt: 1:   6 Multiplication of Mixed Numbers
  84.    wt: 1:   8 Multiplication by Signed Numbers Integers
  85.    wt: 1:   6 Multiplication by Natural Numbers
  86.    wt: 1:   7 Calculator Usage Notes and Cautions
  87.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  88.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  89.    wt: 1:   Quick history of numbers and algebra
  90.    wt: 1:   011 Division of Time Intervals By Numbers
  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:   Appendix E. How To Study Mathematics and Why
  97.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  98.    wt: 1:   Postscript B Mathematics Education References
  99.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  100.    wt: 1:   Chapter 2 For and Against Mathematics
  101.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  102.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  103.    wt: 1:   R Why Learn Mathematics Skills
  104.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  105.    wt: 1:   O On Learning Mathematics and Science
  106.    wt: 1:   N Mathematics Prepare for College Studies
  107.    wt: 1:   Helping the Blind in Logic and Mathematics
  108.    wt: 1:   Mathematics Education References
  109.    wt: 1:   Mathematics Education References
  110.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  111.    wt: 1:   Implementation Notes
  112.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

441 matches:

  1.    wt: 8:   Chapter 4 Complex Numbers and Why Slopes
  2.    wt: 7:   Postscript B Mathematics Education References
  3.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  4.    wt: 7:   Chapter 2 For and Against Mathematics
  5.    wt: 6:   Annotated Links to Material Elsehwere
  6.    wt: 6:   Postscript A Three Remarks
  7.    wt: 6:   Chapter 12 Four Phases
  8.    wt: 6:   Chapter 11 Elementary Instruction
  9.    wt: 6:   Chapter 10 Transition
  10.    wt: 6:   Chapter 9 The Two Ends
  11.    wt: 6:   Chapter 8 Modern Instruction
  12.    wt: 6:   Chapter 7 Two Treatments of Geometry
  13.    wt: 6:   Chapter 5 Four References
  14.    wt: 6:   Chapter 3 Algebra Difficulties
  15.    wt: 6:   Chapter 1 Introduction
  16.    wt: 6:   Foreword
  17.    wt: 4:   20 N th Roots of Complex Numbers
  18.    wt: 4:   2 Complex Numbers made easier we hope
  19.    wt: 3:   mathematics curriculum shifts
  20.    wt: 3:   04 29 New Mathematics Curriculum
  21.    wt: 3:   need for a mixed mathematics curriculum
  22.    wt: 3:   Leaner mathematics curriculum
  23.    wt: 3:   9 The complex number valued trig function cis
  24.    wt: 3:   6 Field Properties of Complex Number
  25.    wt: 3:   Appetizer A Complex Number Applet
  26.    wt: 3:   Chapter 22 Complex Numbers
  27.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  28.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  29.    wt: 2:   E LAMP Introduction Modern Mathematics
  30.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  31.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  32.    wt: 2:   Ramblings Extrinsic numbers theory
  33.    wt: 2:   11 pure mathematics
  34.    wt: 2:   2 arithmetic with signed numbers
  35.    wt: 2:   1 arithmetic with unsigned numbers
  36.    wt: 2:   key notes and themes
  37.    wt: 2:   Mathematics Education Professors
  38.    wt: 2:   mathematics in context
  39.    wt: 2:   Secondary Three Mathematics
  40.    wt: 2:   Secondary Two Mathematics
  41.    wt: 2:   Secondary One Mathematics
  42.    wt: 2:   three goals for Mathematics Education
  43.    wt: 2:   02 20 mathematics education references
  44.    wt: 2:   three aims for mathematics students
  45.    wt: 2:   mathematics instruction in general
  46.    wt: 2:   Education in mathematics science and technology
  47.    wt: 2:   three kinds of reason in mathematics
  48.    wt: 2:   words for mathematics instructor
  49.    wt: 2:   21 Logarithms Powers and Exponentials
  50.    wt: 2:   19 N th Roots of Unity
  51.    wt: 2:   18 Sixth Roots of Unity
  52.    wt: 2:   17 Cube Roots of unity
  53.    wt: 2:   16 References and Originality Question
  54.    wt: 2:   15 Pythagorean Theorem Converse
  55.    wt: 2:   14 Law of cosines
  56.    wt: 2:   13 Trig Formulas for dot and cross Products
  57.    wt: 2:   12 cis formulas for sine cosines and tangent
  58.    wt: 2:   11 sine and cosine double triple angle formulas
  59.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  60.    wt: 2:   8 Unit Circle Development of Trigonometry
  61.    wt: 2:   7 Second Way to Calculate Products
  62.    wt: 2:   5 An Easy Proof of the Distributive Law
  63.    wt: 2:   4 Multiplication Properties
  64.    wt: 2:   3 Addition Properties
  65.    wt: 2:   1 Rectangular Polar Coordinates Review
  66.    wt: 2:   7 Complex Numbers Appetizer
  67.    wt: 2:   PS H Distributive Law For Complex Numbers
  68.    wt: 2:   musings do not puiblish real numbers
  69.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  70.    wt: 2:   22 Multiplication of Signed Numbers
  71.    wt: 2:   12 Real Numbers Line Signed Coordinates
  72.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  73.    wt: 2:   16 Real Numbers Comparison
  74.    wt: 2:   7 Real Numbers as Line Cordinates
  75.    wt: 2:   6 Unsigned Real Numbers
  76.    wt: 2:   5 Rational Numbers More
  77.    wt: 2:   4 Rational Numbers
  78.    wt: 2:   1 Whole and Natural Numbers
  79.    wt: 2:   3 Comparison of Negative Numbers
  80.    wt: 2:   11 What are real lengths and numbers
  81.    wt: 2:   10 dividing signed numbers
  82.    wt: 2:   9 subtracting signed numbers
  83.    wt: 2:   8 multiplying signed numbers
  84.    wt: 2:   6 adding signed numbers
  85.    wt: 2:   5 lengths and signs of numbers
  86.    wt: 2:   2 signed and unsigned numbers as coordinates
  87.    wt: 2:   Example 2 volume of a cone
  88.    wt: 2:   Example 1 volume of a pyramid
  89.    wt: 2:   Volume of Solid by Cross Sections Lesson
  90.    wt: 2:   Appendix E. How To Study Mathematics and Why
  91.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  92.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  93.    wt: 2:   Helping the Blind in Logic and Mathematics
  94.    wt: 2:   Mathematics Education References
  95.    wt: 2:   Mathematics Education References
  96.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  97.    wt: 2:   Implementation Notes
  98.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  99.    wt: 1:   Appendix 2 primary school Arithmetic 01
  100.    wt: 1:   Appendix 1 primary and preschool mathematic
  101.    wt: 1:   K LAMP Musings Science Education
  102.    wt: 1:   J LAMP Introduction Extrinsic Origins
  103.    wt: 1:   I LAMP Introduction Study Habits
  104.    wt: 1:   H LAMP Introduction Instructional Concepts
  105.    wt: 1:   G LAMP Introduction Problem Solving Skills
  106.    wt: 1:   F LAMP Introduction Prerequisites
  107.    wt: 1:   A Introduction Objectives
  108.    wt: 1:   Skills Chapter 5 Calculus
  109.    wt: 1:   Skills Chapter 4 Logic
  110.    wt: 1:   Ramblings Introduction Algebra Essay
  111.    wt: 1:   Skills Chapter 3 Algebra
  112.    wt: 1:   Skills Chapter 2 Geometry
  113.    wt: 1:   Skills Chapter 1 Arithmetic
  114.    wt: 1:   Skills Chapter 0 Introduction
  115.    wt: 1:   10 statistics
  116.    wt: 1:   9 combinatorics probability sets
  117.    wt: 1:   8 analytic geometry etc
  118.    wt: 1:   7 logic review and decimals an odd combination
  119.    wt: 1:   6 polynomials etc
  120.    wt: 1:   5 logarithms and exponentials etc
  121.    wt: 1:   4 algebra
  122.    wt: 1:   3 Euclidean Geometry Leanly
  123.    wt: 1:   What is POMME
  124.    wt: 1:   why bother
  125.    wt: 1:   which way to go
  126.    wt: 1:   website reviews
  127.    wt: 1:   three goals to set for students
  128.    wt: 1:   Teach the teachers plus goals
  129.    wt: 1:   permissions for teachers
  130.    wt: 1:   Math Ed if it must be short make it lean effective
  131.    wt: 1:   Applied Maths Program14092009 POMME variant
  132.    wt: 1:   activities for students
  133.    wt: 1:   links Education Resources online
  134.    wt: 1:   site origins
  135.    wt: 1:   site eurekas
  136.    wt: 1:   About site lesson plans
  137.    wt: 1:   teacher certification
  138.    wt: 1:   modern education
  139.    wt: 1:   learning takes time
  140.    wt: 1:   grouping students according to ability
  141.    wt: 1:   what should be learnt and When
  142.    wt: 1:   Postscript 2007 01 10
  143.    wt: 1:   Education Reform Inconsistencies
  144.    wt: 1:   five decades make a difference
  145.    wt: 1:   Maps Plans Drawings
  146.    wt: 1:   how letters appear
  147.    wt: 1:   talk the algebra talk
  148.    wt: 1:   three difficulties
  149.    wt: 1:   teaching tips
  150.    wt: 1:   What to Tell Students
  151.    wt: 1:   geometric implications for algebra
  152.    wt: 1:   teaching tutoring algebraic reason
  153.    wt: 1:   Lessening Algebra Difficulties
  154.    wt: 1:   the trouble with algebra
  155.    wt: 1:   05 13 OldSiteEntrancePage
  156.    wt: 1:   04 25 when to stop or suspend mathemat
  157.    wt: 1:   02 21 words for teachers
  158.    wt: 1:   standards for course material
  159.    wt: 1:   Operational Viewpoint to Value
  160.    wt: 1:   formal or informal peer review
  161.    wt: 1:   Theory of Knowledge
  162.    wt: 1:   Different Kinds of Reasoning in maths
  163.    wt: 1:   cultivating intelligence
  164.    wt: 1:   Four ways to improve education reform
  165.    wt: 1:   How to be a better instructor
  166.    wt: 1:   Motivation and Context Problem
  167.    wt: 1:   Prequel In For A Penny In For A Pound
  168.    wt: 1:   education an empirical art
  169.    wt: 1:   fairness and inductive principles for instruction
  170.    wt: 1:   chapitre 12 00 les iles et division
  171.    wt: 1:   chapitre 07 01 principle D induction mathematique
  172.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  173.    wt: 1:   chapitre 06 00 Chaines de la raison
  174.    wt: 1:   chapitre 05 00 Deception
  175.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  176.    wt: 1:   chapitre 04 09 Regles accidentelles
  177.    wt: 1:   chapitre 04 08 Limitations et benefices
  178.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  179.    wt: 1:   chapitre 04 06 engagements
  180.    wt: 1:   chapitre 04 05 Implication versus suggestion
  181.    wt: 1:   chapitre 04 04 Parlons de la logique
  182.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  183.    wt: 1:   chapitre 04 02 Deuxieme enigme
  184.    wt: 1:   chapitre 04 01 Premiere enigme
  185.    wt: 1:   chapitre 04 00 Les regles d implication
  186.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  187.    wt: 1:   chapitre 02 00 La Communication des idees
  188.    wt: 1:   chapitre 01 00 Introduction
  189.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  190.    wt: 1:   22 Student Centered Highschool Mathematics
  191.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  192.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  193.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  194.    wt: 1:   18 Primary School Mathematics
  195.    wt: 1:   16 Secondary Mathematics Tips
  196.    wt: 1:   12 Goals and Objectives For Mathematics
  197.    wt: 1:   Ages 12 to 14 Skills with take home value
  198.    wt: 1:   Ages 12 to 14 Geometry
  199.    wt: 1:   Ages 12 to 14 Arithmetic
  200.    wt: 1:   Ages 10 to 12 Geometry
  201.    wt: 1:   Ages 10 to 12 Arithmetic
  202.    wt: 1:   Ages 9 to 10
  203.    wt: 1:   Ages 8 to 9
  204.    wt: 1:   Ages 7 to 8
  205.    wt: 1:   Ages 6 to 7
  206.    wt: 1:   Ages 4 plus to 5 plus
  207.    wt: 1:   Ages 3 plus to 4 plus
  208.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  209.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  210.    wt: 1:   4 Function notation in and beyond mathematics
  211.    wt: 1:   8 Notes for instructors or tutors
  212.    wt: 1:   12 From Applied To Pure Mathematics
  213.    wt: 1:   Vector and Complex Number Applet
  214.    wt: 1:   17A The complex number valued trig function cis
  215.    wt: 1:   A Modular and Remainder Arithmetic
  216.    wt: 1:   A Signed Number Arithmetic Review
  217.    wt: 1:   26 More Less Greater Than Comparison
  218.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  219.    wt: 1:   23 Distributive Law Two Derivations
  220.    wt: 1:   21 Addition of Multiples of a Single Vector
  221.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  222.    wt: 1:   19 Signed Multiples of Vectors
  223.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  224.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  225.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  226.    wt: 1:   15 Head to Tails in place Addition Associative
  227.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  228.    wt: 1:   13 Arrows and Vectors in a Plane
  229.    wt: 1:   11 Signed Number Addition and Addition Properties
  230.    wt: 1:   9 Division with Digits after Decimal Point
  231.    wt: 1:   8 Division and Mulplication of Compound Fractions
  232.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  233.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  234.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  235.    wt: 1:   4 Location of Point in Decimal Addition
  236.    wt: 1:   3 Location of Point in Decimal Multiplication
  237.    wt: 1:   2 Counting Digits in Decimal Multiplication
  238.    wt: 1:   1 Fractions with Finite Decimal Expansions
  239.    wt: 1:   5 Distributive Law for Whole Numbers
  240.    wt: 1:   1 The Counting Origins of Numbers
  241.    wt: 1:   4 Comparison of Negative Numbers
  242.    wt: 1:   1 Real Numbers Comparison
  243.    wt: 1:   15 Real Number Division
  244.    wt: 1:   14 Real Number Multiplication
  245.    wt: 1:   13 Real Number Subtraction
  246.    wt: 1:   12 Real Number Additive Inverses or Negatives
  247.    wt: 1:   11 Real Number Addition
  248.    wt: 1:   10 Real Number Lengths and Signs
  249.    wt: 1:   9 Coordinates for Regions in Space
  250.    wt: 1:   8 Coordinates for Maps and Planes
  251.    wt: 1:   3 Fractions
  252.    wt: 1:   2 Integers
  253.    wt: 1:   Skill Development Notes
  254.    wt: 1:   11 Volume of Sphere
  255.    wt: 1:   10 Volume of Pyramid
  256.    wt: 1:   9 Volume of Cone
  257.    wt: 1:   5 Box Volume Formula Example
  258.    wt: 1:   8 Sets of Numbers
  259.    wt: 1:   5 Talking about Numbers and Quantities
  260.    wt: 1:   4 A Brief Story of numbers and algebra
  261.    wt: 1:   4 Greater More Less Than Signs in General
  262.    wt: 1:   2 More and Less Than with Unlike Signs
  263.    wt: 1:   1 More and Less Than for Counts and Measures
  264.    wt: 1:   7 negative and additive inverse
  265.    wt: 1:   4 signed coordinates for regions in space
  266.    wt: 1:   3 signed coordinates for maps and planes
  267.    wt: 1:   3 Multiplying Units and Numbers
  268.    wt: 1:   22 Complex Compound Fractions
  269.    wt: 1:   9 Improper Fractions and Mixed Numbers
  270.    wt: 1:   6 Multiplication of Mixed Numbers
  271.    wt: 1:   8 Multiplication by Signed Numbers Integers
  272.    wt: 1:   6 Multiplication by Natural Numbers
  273.    wt: 1:   7 Calculator Usage Notes and Cautions
  274.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  275.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  276.    wt: 1:   Quick history of numbers and algebra
  277.    wt: 1:   011 Division of Time Intervals By Numbers
  278.    wt: 1:   Example 1. Area Between x and x squared
  279.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  280.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  281.    wt: 1:   Example 4 with x function of y
  282.    wt: 1:   Example 3
  283.    wt: 1:   Example 2
  284.    wt: 1:   Example 1
  285.    wt: 1:   Area Between Curves Lesson Take 2
  286.    wt: 1:   Area Between Curves Lesson Take 1
  287.    wt: 1:   Summary
  288.    wt: 1:   A Related Material in Volume 3
  289.    wt: 1:   A Related lessons in Volume 3
  290.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  291.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  292.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  293.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  294.    wt: 1:   G.5 Motions With Bounded Velocities
  295.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  296.    wt: 1:   G.3 Constant Difference Theorem Proof
  297.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  298.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  299.    wt: 1:   F.5b Extreme Value Theorem
  300.    wt: 1:   F.5a Equicontinuity Theorems
  301.    wt: 1:   F.4 Finite Covering Theorem
  302.    wt: 1:   F.3 Intermediate Value Theorem
  303.    wt: 1:   F.2 Closed Range Theorem
  304.    wt: 1:   F.1 What Functions are Continuous
  305.    wt: 1:   E2 Algebraic Properties of Limits
  306.    wt: 1:   E1 Error Control Inequalities
  307.    wt: 1:   D2 Limits of Monotone Sequences
  308.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  309.    wt: 1:   C Triangle Inequalities
  310.    wt: 1:   B3 Bolzano Weierstrass Theorem
  311.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  312.    wt: 1:   PostScript For and Against Decimal Perspectives
  313.    wt: 1:   A1. Introduction
  314.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  315.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  316.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  317.    wt: 1:   Chapter 23 Links To Trigonometry
  318.    wt: 1:   Chapter 21 Arrow Addition
  319.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  320.    wt: 1:   Chapter 18. Slopes Areas Integration
  321.    wt: 1:   Chapter 17. Area Approximation
  322.    wt: 1:   Chapter 16. Velocity Approximation
  323.    wt: 1:   Chapter 15. Slope Approximation
  324.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  325.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  326.    wt: 1:   Chapter 13. Acceleration
  327.    wt: 1:   Chapter 12. Units and Slopes
  328.    wt: 1:   Chapter 11. Graphing Slope versus Position
  329.    wt: 1:   Chapter 10 Slopes and Units
  330.    wt: 1:   Chapter 9 About First Courses in Calculus
  331.    wt: 1:   Chapter 8. Slope Interpretation
  332.    wt: 1:   Chapter 7 Slopes and Velocity
  333.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  334.    wt: 1:   Chapter 5. Slope Sign Tests
  335.    wt: 1:   Chapter 4. More Slope Sign Analysis
  336.    wt: 1:   Chapter 3. Slope Sign Analysis
  337.    wt: 1:   Chapter 2. Slopes and Ski Trails
  338.    wt: 1:   Chapter 1.Introduction
  339.    wt: 1:   Fall 1983 Calculus Appetizer
  340.    wt: 1:   Foreword
  341.    wt: 1:   Postscript More on Better Performance
  342.    wt: 1:   Postscript For Better Performance
  343.    wt: 1:   Appendix D. What to do in School and Why
  344.    wt: 1:   Appendix C. How to Read
  345.    wt: 1:   Appendix B. How To Learn
  346.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  347.    wt: 1:   Chapter 31 Direct and Indirect Reason
  348.    wt: 1:   Chapter 30 Truth Tables
  349.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  350.    wt: 1:   Chapter 28 Occurrence Tables
  351.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  352.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  353.    wt: 1:   Chapter 25. Mathematical Induction Examples
  354.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  355.    wt: 1:   Chapter 23. Notation For Sums
  356.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  357.    wt: 1:   Chapter 21. Third Reading Guide
  358.    wt: 1:   Chapter 20. Degrees and Radians
  359.    wt: 1:   Chapter 19. Functions and Sets
  360.    wt: 1:   Chapter 18. Rules for Algebra
  361.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  362.    wt: 1:   Chapter 16. Painless Theorem Proving
  363.    wt: 1:   Chapter 15. Solving Linear Equations
  364.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  365.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  366.    wt: 1:   Chapter 13. Second Reading Guide
  367.    wt: 1:   Chapter 12. Shorthand Usage Guide
  368.    wt: 1:   Chapter 11. Why Shorthand
  369.    wt: 1:   Chapter 10 Describing and Changing Calculations
  370.    wt: 1:   Postscript What is a Variable
  371.    wt: 1:   Chapter 8 Three Skills For Algebra
  372.    wt: 1:   Solutions For Arithmetic Exercises
  373.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  374.    wt: 1:   Chapter 6 Change of Language
  375.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  376.    wt: 1:   Chapter 4 Longer Chains of Reason
  377.    wt: 1:   Chapter 3 Chains of Reason
  378.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  379.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  380.    wt: 1:   Foreword
  381.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  382.    wt: 1:   Postscript C Consistency as a Tool for Reason
  383.    wt: 1:   Postscript B More on Story Telling and Reason
  384.    wt: 1:   Postscript A Story Telling
  385.    wt: 1:   Chapter 24 Direct and Indirect Reason
  386.    wt: 1:   Chapter 23 Truth Tables
  387.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  388.    wt: 1:   Chapter 21 Occurrence Tables
  389.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  390.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  391.    wt: 1:   Chapter 18 Sense and Knowledge
  392.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  393.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  394.    wt: 1:   Chapter 15 Objective Processes
  395.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  396.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  397.    wt: 1:   Chapter 11 Accidental Patterns
  398.    wt: 1:   Chapter 10 Responsibility
  399.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  400.    wt: 1:   Chapter 8 Change of Language
  401.    wt: 1:   Chapter 7 Longer Chains of Reason
  402.    wt: 1:   Chapter 6 Chains of Reason
  403.    wt: 1:   Chapter 5 Deception
  404.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  405.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  406.    wt: 1:   Chapter 2 Skill Development
  407.    wt: 1:   Chapter 1 Introduction
  408.    wt: 1:   Three Remarks
  409.    wt: 1:   Foreword
  410.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  411.    wt: 1:   R Why Learn Mathematics Skills
  412.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  413.    wt: 1:   O On Learning Mathematics and Science
  414.    wt: 1:   N Mathematics Prepare for College Studies
  415.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  416.    wt: 1:   Chapter 8 Skipped Topics and Why
  417.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  418.    wt: 1:   Chapter 6 More Algebra and Geometry
  419.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  420.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  421.    wt: 1:   Chapter 3 Algebra Starter Lessons
  422.    wt: 1:   Chapter 2 Why Sets
  423.    wt: 1:   Chapter 1 Arithmetic
  424.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  425.    wt: 1:   7 Games and Activities for Instruction
  426.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  427.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  428.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  429.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  430.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  431.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  432.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  433.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  434.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  435.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  436.    wt: 1:   More Algebra and Slope based Calculus Preview
  437.    wt: 1:   Systematic Algebra Skill Development Missing Links
  438.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  439.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  440.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  441.    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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