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

113 matches:

  1.    wt: 3:   2 signed and unsigned numbers as coordinates
  2.    wt: 2:   2 arithmetic with signed numbers
  3.    wt: 2:   1 arithmetic with unsigned numbers
  4.    wt: 2:   mathematics curriculum shifts
  5.    wt: 2:   04 29 New Mathematics Curriculum
  6.    wt: 2:   need for a mixed mathematics curriculum
  7.    wt: 2:   Leaner mathematics curriculum
  8.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  9.    wt: 2:   22 Multiplication of Signed Numbers
  10.    wt: 2:   12 Real Numbers Line Signed Coordinates
  11.    wt: 2:   6 Unsigned Real Numbers
  12.    wt: 2:   10 dividing signed numbers
  13.    wt: 2:   9 subtracting signed numbers
  14.    wt: 2:   8 multiplying signed numbers
  15.    wt: 2:   6 adding signed numbers
  16.    wt: 2:   8 Multiplication by Signed Numbers Integers
  17.    wt: 1:   E LAMP Introduction Modern Mathematics
  18.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  19.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  20.    wt: 1:   Ramblings Extrinsic numbers theory
  21.    wt: 1:   11 pure mathematics
  22.    wt: 1:   key notes and themes
  23.    wt: 1:   Mathematics Education Professors
  24.    wt: 1:   mathematics in context
  25.    wt: 1:   Secondary Three Mathematics
  26.    wt: 1:   Secondary Two Mathematics
  27.    wt: 1:   Secondary One Mathematics
  28.    wt: 1:   three goals for Mathematics Education
  29.    wt: 1:   02 20 mathematics education references
  30.    wt: 1:   three aims for mathematics students
  31.    wt: 1:   mathematics instruction in general
  32.    wt: 1:   Education in mathematics science and technology
  33.    wt: 1:   three kinds of reason in mathematics
  34.    wt: 1:   words for mathematics instructor
  35.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  36.    wt: 1:   22 Student Centered Highschool Mathematics
  37.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  38.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  39.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  40.    wt: 1:   18 Primary School Mathematics
  41.    wt: 1:   16 Secondary Mathematics Tips
  42.    wt: 1:   12 Goals and Objectives For Mathematics
  43.    wt: 1:   4 Function notation in and beyond mathematics
  44.    wt: 1:   8 Notes for instructors or tutors
  45.    wt: 1:   12 From Applied To Pure Mathematics
  46.    wt: 1:   2 Signed Coordinates
  47.    wt: 1:   1 Unsigned Coordinates
  48.    wt: 1:   20 N th Roots of Complex Numbers
  49.    wt: 1:   2 Complex Numbers made easier we hope
  50.    wt: 1:   7 Complex Numbers Appetizer
  51.    wt: 1:   PS H Distributive Law For Complex Numbers
  52.    wt: 1:   musings do not puiblish real numbers
  53.    wt: 1:   A Signed Number Arithmetic Review
  54.    wt: 1:   19 Signed Multiples of Vectors
  55.    wt: 1:   11 Signed Number Addition and Addition Properties
  56.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  57.    wt: 1:   5 Distributive Law for Whole Numbers
  58.    wt: 1:   1 The Counting Origins of Numbers
  59.    wt: 1:   4 Comparison of Negative Numbers
  60.    wt: 1:   1 Real Numbers Comparison
  61.    wt: 1:   16 Real Numbers Comparison
  62.    wt: 1:   7 Real Numbers as Line Cordinates
  63.    wt: 1:   5 Rational Numbers More
  64.    wt: 1:   4 Rational Numbers
  65.    wt: 1:   1 Whole and Natural Numbers
  66.    wt: 1:   Skill Development Notes
  67.    wt: 1:   11 Volume of Sphere
  68.    wt: 1:   10 Volume of Pyramid
  69.    wt: 1:   9 Volume of Cone
  70.    wt: 1:   5 Box Volume Formula Example
  71.    wt: 1:   8 Sets of Numbers
  72.    wt: 1:   5 Talking about Numbers and Quantities
  73.    wt: 1:   4 A Brief Story of numbers and algebra
  74.    wt: 1:   3 Comparison of Negative Numbers
  75.    wt: 1:   11 What are real lengths and numbers
  76.    wt: 1:   5 lengths and signs of numbers
  77.    wt: 1:   4 signed coordinates for regions in space
  78.    wt: 1:   3 signed coordinates for maps and planes
  79.    wt: 1:   3 Multiplying Units and Numbers
  80.    wt: 1:   9 Improper Fractions and Mixed Numbers
  81.    wt: 1:   6 Multiplication of Mixed Numbers
  82.    wt: 1:   6 Multiplication by Natural Numbers
  83.    wt: 1:   7 Calculator Usage Notes and Cautions
  84.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  85.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  86.    wt: 1:   Quick history of numbers and algebra
  87.    wt: 1:   011 Division of Time Intervals By Numbers
  88.    wt: 1:   Example 2 volume of a cone
  89.    wt: 1:   Example 1 volume of a pyramid
  90.    wt: 1:   Volume of Solid by Cross Sections Lesson
  91.    wt: 1:   A Related Material in Volume 3
  92.    wt: 1:   A Related lessons in Volume 3
  93.    wt: 1:   Chapter 22 Complex Numbers
  94.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  95.    wt: 1:   Appendix E. How To Study Mathematics and Why
  96.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  97.    wt: 1:   Postscript B Mathematics Education References
  98.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  99.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  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:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  113.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

440 matches:

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