Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic and Pattern Based Reason to inform and amuse.

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 material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin.

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 focus on skills with actual or potential local 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: 4:   Progressive Observable Motivated Mathematics Education/
  2.    wt: 4:   Mathematics Education Essays/
  3.    wt: 2:   4 Lessons on Using Derivatives/
  4.    wt: 2:   38 Lessons on Calculating Derivatives/
  5.    wt: 1:   LAMP Lean Applied Mathematics Program/
  6.    wt: 1:   Archives/
  7.    wt: 1:   1 Five Polynomial Operations/
  8.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  9.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  10.    wt: 1:   D Decimal Long Division Methods/
  11.    wt: 1:   Secondary Mathematics A Practical Approach/
  12.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/

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146 matches:

  1.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  2.    wt: 2:   4 Polynomials Long division linear divisor
  3.    wt: 2:   23 Distributive Law Two Derivations
  4.    wt: 2:   12 Real Number Additive Inverses or Negatives
  5.    wt: 2:   7 negative and additive inverse
  6.    wt: 2:   10 Division by Five Long and Short Ways
  7.    wt: 2:   4 Division with 2 Digit Divsors
  8.    wt: 2:   3 Division Single Digit Divisor Example
  9.    wt: 2:   2 Division with Single Digit Divisors
  10.    wt: 2:   4 Second derivative test exercise example
  11.    wt: 2:   3 Second derivative test
  12.    wt: 2:   2 Second derivative test prequel
  13.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  14.    wt: 2:   38 Formulas and derivatives for powers and roots
  15.    wt: 2:   36 Cube root derivative animated
  16.    wt: 2:   34 Derivative of exponential function
  17.    wt: 2:   31 Derivatives of inverse functions
  18.    wt: 2:   17 Derivatives of quotients of sine and cosine
  19.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  20.    wt: 2:   15 sine and cosine derivatives 3rd step
  21.    wt: 2:   14 sine and cosine derivatives 2nd step
  22.    wt: 2:   13 sine and cosine derivatives 1st step
  23.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  24.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  25.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  26.    wt: 1:   K LAMP Musings Science Education
  27.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  28.    wt: 1:   A Introduction Objectives
  29.    wt: 1:   Math Ed if it must be short make it lean effective
  30.    wt: 1:   Applied Maths Program14092009 POMME variant
  31.    wt: 1:   activities for students
  32.    wt: 1:   links Education Resources online
  33.    wt: 1:   Mathematics Education Professors
  34.    wt: 1:   modern education
  35.    wt: 1:   Education Reform Inconsistencies
  36.    wt: 1:   five decades make a difference
  37.    wt: 1:   Secondary Three Mathematics
  38.    wt: 1:   Secondary Two Mathematics
  39.    wt: 1:   Secondary One Mathematics
  40.    wt: 1:   three goals for Mathematics Education
  41.    wt: 1:   02 20 mathematics education references
  42.    wt: 1:   Education in mathematics science and technology
  43.    wt: 1:   Different Kinds of Reasoning in maths
  44.    wt: 1:   cultivating intelligence
  45.    wt: 1:   Four ways to improve education reform
  46.    wt: 1:   Motivation and Context Problem
  47.    wt: 1:   education an empirical art
  48.    wt: 1:   fairness and inductive principles for instruction
  49.    wt: 1:   chapitre 12 00 les iles et division
  50.    wt: 1:   B Wire Resistance Qualitative02
  51.    wt: 1:   A Wire Resistance Qualitative01
  52.    wt: 1:   C Electromotive force conventional current02
  53.    wt: 1:   B Electromotive force conventional current01
  54.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  55.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  56.    wt: 1:   16 Secondary Mathematics Tips
  57.    wt: 1:   12 Goals and Objectives For Mathematics
  58.    wt: 1:   11 Help and Defend Your Child or Teens Education
  59.    wt: 1:   8 The Effect of Negative Remarks
  60.    wt: 1:   7 Student Motivation
  61.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  62.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  63.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  64.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  65.    wt: 1:   7 quadratic formulla derivation
  66.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  67.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  68.    wt: 1:   1 Polynomials Distributive Law
  69.    wt: 1:   12 motivation for term arctan
  70.    wt: 1:   9 motivation for name arcsin
  71.    wt: 1:   4 possible motivation for term arccos
  72.    wt: 1:   5 An Easy Proof of the Distributive Law
  73.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  74.    wt: 1:   PS H Distributive Law For Complex Numbers
  75.    wt: 1:   15 Head to Tails in place Addition Associative
  76.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  77.    wt: 1:   9 Division with Digits after Decimal Point
  78.    wt: 1:   8 Division and Mulplication of Compound Fractions
  79.    wt: 1:   E Long Division Methods more
  80.    wt: 1:   D Long Division Methods
  81.    wt: 1:   5 Distributive Law for Whole Numbers
  82.    wt: 1:   4 Commutative Law Groups Counting Form
  83.    wt: 1:   3 Multiplicative Counting Skills Principles
  84.    wt: 1:   5 Proportionality in Equivalent Fractions
  85.    wt: 1:   6 Equations and Systems Equivalent or Implied
  86.    wt: 1:   4 Subtraction and Division Axioms
  87.    wt: 1:   1 Equivalent Computation Rules
  88.    wt: 1:   4 Comparison of Negative Numbers
  89.    wt: 1:   15 Real Number Division
  90.    wt: 1:   3 Comparison of Negative Numbers
  91.    wt: 1:   13 GCD from given Prime Factorization
  92.    wt: 1:   5 Common Divisors 60 45 via Prime
  93.    wt: 1:   10 dividing signed numbers
  94.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  95.    wt: 1:   20 Dividing Fractions the Why
  96.    wt: 1:   19 Dividing Fractions How TO
  97.    wt: 1:   5 Equivalent Fractions
  98.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  99.    wt: 1:   B Integer Long Division Multiple Choices
  100.    wt: 1:   A Associative Law Theorectical Note
  101.    wt: 1:   13 Subtraction with Additive Inverse
  102.    wt: 1:   5 Zero Movement and Additive Inverses
  103.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  104.    wt: 1:   26 Divisibility by 2 3 5 Example
  105.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  106.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  107.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  108.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  109.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  110.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  111.    wt: 1:   18 video Count Factors given Prime Factorization
  112.    wt: 1:   Long Division Backwards more
  113.    wt: 1:   Long Division Backward
  114.    wt: 1:   Division with Counts and Length
  115.    wt: 1:   Long Division forwards and backwards Example 3
  116.    wt: 1:   Long Division forwards and backwards Example 2
  117.    wt: 1:   Long Division forwards and backwards Example 1
  118.    wt: 1:   12 Why Long Division Works Take III
  119.    wt: 1:   11 Another Single Digit Divisor Example
  120.    wt: 1:   9 Why Long Division Works Take II
  121.    wt: 1:   7 Long Divison Mistake Catching
  122.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  123.    wt: 1:   5 Long Division Include Zeroes or not
  124.    wt: 1:   1 Divsion Physical Examples
  125.    wt: 1:   D Decimal Multiplication Methods Derived
  126.    wt: 1:   1 Why 3 times 5 gives 15
  127.    wt: 1:   012 Division of Time Intervals by Time Intervals
  128.    wt: 1:   011 Division of Time Intervals By Numbers
  129.    wt: 1:   10 Power rule for negative integers
  130.    wt: 1:   3 Motivation for Limit Definition Take 2
  131.    wt: 1:   2 Motivation for Limit Definition Take 1
  132.    wt: 1:   PostScript For and Against Decimal Perspectives
  133.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  134.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  135.    wt: 1:   Postscript B Mathematics Education References
  136.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  137.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  138.    wt: 1:   Chapter 15 Objective Processes
  139.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  140.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  141.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  142.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  143.    wt: 1:   7 Games and Activities for Instruction
  144.    wt: 1:   Mathematics Education References
  145.    wt: 1:   Mathematics Education References
  146.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

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287 matches:

  1.    wt: 5:   Math Ed if it must be short make it lean effective
  2.    wt: 5:   Applied Maths Program14092009 POMME variant
  3.    wt: 5:   activities for students
  4.    wt: 5:   links Education Resources online
  5.    wt: 5:   Mathematics Education Professors
  6.    wt: 5:   modern education
  7.    wt: 5:   Education Reform Inconsistencies
  8.    wt: 5:   five decades make a difference
  9.    wt: 5:   Secondary Three Mathematics
  10.    wt: 5:   Secondary Two Mathematics
  11.    wt: 5:   Secondary One Mathematics
  12.    wt: 5:   three goals for Mathematics Education
  13.    wt: 5:   02 20 mathematics education references
  14.    wt: 5:   Education in mathematics science and technology
  15.    wt: 5:   Different Kinds of Reasoning in maths
  16.    wt: 5:   cultivating intelligence
  17.    wt: 5:   Four ways to improve education reform
  18.    wt: 5:   Motivation and Context Problem
  19.    wt: 5:   education an empirical art
  20.    wt: 5:   fairness and inductive principles for instruction
  21.    wt: 4:   11 pure mathematics
  22.    wt: 4:   10 statistics
  23.    wt: 4:   9 combinatorics probability sets
  24.    wt: 4:   8 analytic geometry etc
  25.    wt: 4:   7 logic review and decimals an odd combination
  26.    wt: 4:   6 polynomials etc
  27.    wt: 4:   5 logarithms and exponentials etc
  28.    wt: 4:   4 algebra
  29.    wt: 4:   3 Euclidean Geometry Leanly
  30.    wt: 4:   2 arithmetic with signed numbers
  31.    wt: 4:   1 arithmetic with unsigned numbers
  32.    wt: 4:   What is POMME
  33.    wt: 4:   why bother
  34.    wt: 4:   which way to go
  35.    wt: 4:   website reviews
  36.    wt: 4:   three goals to set for students
  37.    wt: 4:   Teach the teachers plus goals
  38.    wt: 4:   permissions for teachers
  39.    wt: 4:   site origins
  40.    wt: 4:   site eurekas
  41.    wt: 4:   About site lesson plans
  42.    wt: 4:   key notes and themes
  43.    wt: 4:   teacher certification
  44.    wt: 4:   learning takes time
  45.    wt: 4:   grouping students according to ability
  46.    wt: 4:   what should be learnt and When
  47.    wt: 4:   mathematics in context
  48.    wt: 4:   Postscript 2007 01 10
  49.    wt: 4:   Maps Plans Drawings
  50.    wt: 4:   how letters appear
  51.    wt: 4:   talk the algebra talk
  52.    wt: 4:   three difficulties
  53.    wt: 4:   teaching tips
  54.    wt: 4:   What to Tell Students
  55.    wt: 4:   mathematics curriculum shifts
  56.    wt: 4:   geometric implications for algebra
  57.    wt: 4:   teaching tutoring algebraic reason
  58.    wt: 4:   Lessening Algebra Difficulties
  59.    wt: 4:   the trouble with algebra
  60.    wt: 4:   05 13 OldSiteEntrancePage
  61.    wt: 4:   04 29 New Mathematics Curriculum
  62.    wt: 4:   04 25 when to stop or suspend mathemat
  63.    wt: 4:   02 21 words for teachers
  64.    wt: 4:   three aims for mathematics students
  65.    wt: 4:   standards for course material
  66.    wt: 4:   Operational Viewpoint to Value
  67.    wt: 4:   formal or informal peer review
  68.    wt: 4:   Theory of Knowledge
  69.    wt: 4:   mathematics instruction in general
  70.    wt: 4:   three kinds of reason in mathematics
  71.    wt: 4:   How to be a better instructor
  72.    wt: 4:   need for a mixed mathematics curriculum
  73.    wt: 4:   Leaner mathematics curriculum
  74.    wt: 4:   Prequel In For A Penny In For A Pound
  75.    wt: 4:   words for mathematics instructor
  76.    wt: 4:   4 Second derivative test exercise example
  77.    wt: 4:   3 Second derivative test
  78.    wt: 4:   2 Second derivative test prequel
  79.    wt: 4:   1 Two cubic sketching exercises with 1st derivative
  80.    wt: 4:   38 Formulas and derivatives for powers and roots
  81.    wt: 4:   36 Cube root derivative animated
  82.    wt: 4:   34 Derivative of exponential function
  83.    wt: 4:   31 Derivatives of inverse functions
  84.    wt: 4:   17 Derivatives of quotients of sine and cosine
  85.    wt: 4:   16 Derivatives of reciprocals of sine and cosine
  86.    wt: 4:   15 sine and cosine derivatives 3rd step
  87.    wt: 4:   14 sine and cosine derivatives 2nd step
  88.    wt: 4:   13 sine and cosine derivatives 1st step
  89.    wt: 3:   5 Polynomials Long division Nonlinear divisor
  90.    wt: 3:   4 Polynomials Long division linear divisor
  91.    wt: 3:   10 Division by Five Long and Short Ways
  92.    wt: 3:   4 Division with 2 Digit Divsors
  93.    wt: 3:   3 Division Single Digit Divisor Example
  94.    wt: 3:   2 Division with Single Digit Divisors
  95.    wt: 3:   10 Power rule for negative integers
  96.    wt: 3:   3 Motivation for Limit Definition Take 2
  97.    wt: 3:   2 Motivation for Limit Definition Take 1
  98.    wt: 2:   K LAMP Musings Science Education
  99.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  100.    wt: 2:   A Introduction Objectives
  101.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  102.    wt: 2:   1 Polynomials Distributive Law
  103.    wt: 2:   23 Distributive Law Two Derivations
  104.    wt: 2:   6 Equations and Systems Equivalent or Implied
  105.    wt: 2:   4 Subtraction and Division Axioms
  106.    wt: 2:   1 Equivalent Computation Rules
  107.    wt: 2:   12 Real Number Additive Inverses or Negatives
  108.    wt: 2:   7 negative and additive inverse
  109.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  110.    wt: 2:   26 Divisibility by 2 3 5 Example
  111.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  112.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  113.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  114.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  115.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  116.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  117.    wt: 2:   Long Division Backwards more
  118.    wt: 2:   Long Division Backward
  119.    wt: 2:   Division with Counts and Length
  120.    wt: 2:   Long Division forwards and backwards Example 3
  121.    wt: 2:   Long Division forwards and backwards Example 2
  122.    wt: 2:   Long Division forwards and backwards Example 1
  123.    wt: 2:   12 Why Long Division Works Take III
  124.    wt: 2:   11 Another Single Digit Divisor Example
  125.    wt: 2:   9 Why Long Division Works Take II
  126.    wt: 2:   7 Long Divison Mistake Catching
  127.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  128.    wt: 2:   5 Long Division Include Zeroes or not
  129.    wt: 2:   1 Divsion Physical Examples
  130.    wt: 2:   A Related lessons in Volume 3
  131.    wt: 2:   A Chain Rule Real Player video examples
  132.    wt: 2:   33 Chain Rule Real Player video examples
  133.    wt: 2:   30Chain Rule A Proof
  134.    wt: 2:   29 Chain Rule Optional Reading
  135.    wt: 2:   28 Chain Rule Preparation for a Proof
  136.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  137.    wt: 2:   26 Chain Rule Recognising outer inner functions
  138.    wt: 2:   25 Chain Rule Animated Examples Continued
  139.    wt: 2:   24 Chain Rule Animated Examples
  140.    wt: 2:   23 Chain Rule in general
  141.    wt: 2:   22 Chain Rule for polynomials
  142.    wt: 2:   21 Chain Rule for powers
  143.    wt: 2:   20 Chain Rule for Pulley Systems
  144.    wt: 2:   19 Chain Rule for linear functions
  145.    wt: 2:   18 Chain Rule Introduction
  146.    wt: 2:   12 Quotient rule examples
  147.    wt: 2:   11 Quotient rule
  148.    wt: 2:   9 Reciprocal rule
  149.    wt: 2:   8 Differentiation of polynomials
  150.    wt: 2:   7 Animated Differentiation Examples
  151.    wt: 2:   6 Power rule from product rule
  152.    wt: 2:   5 Product Rule
  153.    wt: 2:   4 Sum Rule
  154.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  155.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  156.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  157.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  158.    wt: 2:   Primary and Secondary Skills and Practices with Take Home Value
  159.    wt: 2:   7 Games and Activities for Instruction
  160.    wt: 1:   Appendix 2 primary school Arithmetic 01
  161.    wt: 1:   Appendix 1 primary and preschool mathematic
  162.    wt: 1:   J LAMP Introduction Extrinsic Origins
  163.    wt: 1:   I LAMP Introduction Study Habits
  164.    wt: 1:   H LAMP Introduction Instructional Concepts
  165.    wt: 1:   G LAMP Introduction Problem Solving Skills
  166.    wt: 1:   F LAMP Introduction Prerequisites
  167.    wt: 1:   E LAMP Introduction Modern Mathematics
  168.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  169.    wt: 1:   Skills Chapter 5 Calculus
  170.    wt: 1:   Skills Chapter 4 Logic
  171.    wt: 1:   Ramblings Extrinsic numbers theory
  172.    wt: 1:   Ramblings Introduction Algebra Essay
  173.    wt: 1:   Skills Chapter 3 Algebra
  174.    wt: 1:   Skills Chapter 2 Geometry
  175.    wt: 1:   Skills Chapter 1 Arithmetic
  176.    wt: 1:   Skills Chapter 0 Introduction
  177.    wt: 1:   chapitre 12 00 les iles et division
  178.    wt: 1:   B Wire Resistance Qualitative02
  179.    wt: 1:   A Wire Resistance Qualitative01
  180.    wt: 1:   C Electromotive force conventional current02
  181.    wt: 1:   B Electromotive force conventional current01
  182.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  183.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  184.    wt: 1:   16 Secondary Mathematics Tips
  185.    wt: 1:   12 Goals and Objectives For Mathematics
  186.    wt: 1:   11 Help and Defend Your Child or Teens Education
  187.    wt: 1:   8 The Effect of Negative Remarks
  188.    wt: 1:   7 Student Motivation
  189.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  190.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  191.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  192.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  193.    wt: 1:   7 quadratic formulla derivation
  194.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  195.    wt: 1:   8 Notes for instructors or tutors
  196.    wt: 1:   7 Links Lessons Elsewhere
  197.    wt: 1:   3 Polynomials Multiplication Addition
  198.    wt: 1:   2 Column Multiplication Method
  199.    wt: 1:   12 motivation for term arctan
  200.    wt: 1:   9 motivation for name arcsin
  201.    wt: 1:   4 possible motivation for term arccos
  202.    wt: 1:   5 An Easy Proof of the Distributive Law
  203.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  204.    wt: 1:   PS H Distributive Law For Complex Numbers
  205.    wt: 1:   15 Head to Tails in place Addition Associative
  206.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  207.    wt: 1:   9 Division with Digits after Decimal Point
  208.    wt: 1:   8 Division and Mulplication of Compound Fractions
  209.    wt: 1:   E Long Division Methods more
  210.    wt: 1:   D Long Division Methods
  211.    wt: 1:   5 Distributive Law for Whole Numbers
  212.    wt: 1:   4 Commutative Law Groups Counting Form
  213.    wt: 1:   3 Multiplicative Counting Skills Principles
  214.    wt: 1:   5 Proportionality in Equivalent Fractions
  215.    wt: 1:   5 Equality in Algebra
  216.    wt: 1:   3 Product Axioms Two Forms
  217.    wt: 1:   2 Addition and Multiplication Axioms
  218.    wt: 1:   4 Comparison of Negative Numbers
  219.    wt: 1:   15 Real Number Division
  220.    wt: 1:   3 Comparison of Negative Numbers
  221.    wt: 1:   13 GCD from given Prime Factorization
  222.    wt: 1:   5 Common Divisors 60 45 via Prime
  223.    wt: 1:   10 dividing signed numbers
  224.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  225.    wt: 1:   20 Dividing Fractions the Why
  226.    wt: 1:   19 Dividing Fractions How TO
  227.    wt: 1:   5 Equivalent Fractions
  228.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  229.    wt: 1:   B Integer Long Division Multiple Choices
  230.    wt: 1:   A Associative Law Theorectical Note
  231.    wt: 1:   13 Subtraction with Additive Inverse
  232.    wt: 1:   5 Zero Movement and Additive Inverses
  233.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  234.    wt: 1:   23 Remainder Arithmetic Modulo 2
  235.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  236.    wt: 1:   21 Remainder Arithmetic Modulo 3
  237.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  238.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  239.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  240.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  241.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  242.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  243.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  244.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  245.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  246.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  247.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  248.    wt: 1:   5 Remainder Arithmetic Modulo 5
  249.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  250.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  251.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  252.    wt: 1:   1 Remainder Arithmetic Modulo 10
  253.    wt: 1:   18 video Count Factors given Prime Factorization
  254.    wt: 1:   8 Correcting the Mistake
  255.    wt: 1:   D Decimal Multiplication Methods Derived
  256.    wt: 1:   1 Why 3 times 5 gives 15
  257.    wt: 1:   012 Division of Time Intervals by Time Intervals
  258.    wt: 1:   011 Division of Time Intervals By Numbers
  259.    wt: 1:   PostScript For and Against Decimal Perspectives
  260.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  261.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  262.    wt: 1:   Postscript B Mathematics Education References
  263.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  264.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  265.    wt: 1:   Chapter 15 Objective Processes
  266.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  267.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  268.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  269.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  270.    wt: 1:   Chapter 8 Skipped Topics and Why
  271.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  272.    wt: 1:   Chapter 6 More Algebra and Geometry
  273.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  274.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  275.    wt: 1:   Chapter 3 Algebra Starter Lessons
  276.    wt: 1:   Chapter 2 Why Sets
  277.    wt: 1:   Chapter 1 Arithmetic
  278.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  279.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  280.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  281.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  282.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  283.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  284.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  285.    wt: 1:   Mathematics Education References
  286.    wt: 1:   Mathematics Education References
  287.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
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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