Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

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

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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15 matches:

  1.    wt: 4:   Mathematics Education Essays/
  2.    wt: 3:   Progressive Observable Motivated Mathematics Education/
  3.    wt: 2:   LAMP Lean Applied Mathematics Program/
  4.    wt: 2:   2 Formula Forward Use Evaluation/
  5.    wt: 1:   Archives/
  6.    wt: 1:   Mathematics Skills Year by Year/
  7.    wt: 1:   9 Proportionality Backwards and Forwards/
  8.    wt: 1:   8 Unifying Theme For Algebra/
  9.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  10.    wt: 1:   Volume 2 Three Skills For Algebra/
  11.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  12.    wt: 1:   Mathematics 506 Lessons/
  13.    wt: 1:   Secondary Mathematics A Practical Approach/
  14.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  15.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

212 matches:

  1.    wt: 3:   three goals for Mathematics Education
  2.    wt: 3:   words for mathematics instructor
  3.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  4.    wt: 2:   Mathematics Education Professors
  5.    wt: 2:   Education Reform Inconsistencies
  6.    wt: 2:   02 20 mathematics education references
  7.    wt: 2:   three aims for mathematics students
  8.    wt: 2:   formal or informal peer review
  9.    wt: 2:   Education in mathematics science and technology
  10.    wt: 2:   Four ways to improve education reform
  11.    wt: 2:   need for a mixed mathematics curriculum
  12.    wt: 2:   Prequel In For A Penny In For A Pound
  13.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  14.    wt: 2:   12 Goals and Objectives For Mathematics
  15.    wt: 2:   5 Function notation for geometric transformations
  16.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  17.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  18.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  19.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  20.    wt: 2:   8 Notes for instructors or tutors
  21.    wt: 2:   26 Formulas for products of sines and cosines
  22.    wt: 2:   17E Trig Formulas for dot and cross Products
  23.    wt: 2:   17D cis formulas for sine cosines and tangent
  24.    wt: 2:   13 Trig Formulas for dot and cross Products
  25.    wt: 2:   12 cis formulas for sine cosines and tangent
  26.    wt: 2:   4 Equations for lines three forms
  27.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  28.    wt: 2:   Formula Usage Show Work Format
  29.    wt: 2:   1 Written work formats for developing and showing skill
  30.    wt: 2:   38 Formulas and derivatives for powers and roots
  31.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  32.    wt: 2:   Postscript For Better Performance
  33.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  34.    wt: 2:   Postscript B Mathematics Education References
  35.    wt: 2:   Chapter 2 For and Against Mathematics
  36.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  37.    wt: 2:   N Mathematics Prepare for College Studies
  38.    wt: 2:   G. Written work formats for developing and showing skill
  39.    wt: 2:   Mathematics Education References
  40.    wt: 2:   Mathematics Education References
  41.    wt: 1:   K LAMP Musings Science Education
  42.    wt: 1:   E LAMP Introduction Modern Mathematics
  43.    wt: 1:   11 pure mathematics
  44.    wt: 1:   three goals to set for students
  45.    wt: 1:   permissions for teachers
  46.    wt: 1:   activities for students
  47.    wt: 1:   links Education Resources online
  48.    wt: 1:   modern education
  49.    wt: 1:   mathematics in context
  50.    wt: 1:   Secondary Three Mathematics
  51.    wt: 1:   Secondary Two Mathematics
  52.    wt: 1:   Secondary One Mathematics
  53.    wt: 1:   mathematics curriculum shifts
  54.    wt: 1:   geometric implications for algebra
  55.    wt: 1:   04 29 New Mathematics Curriculum
  56.    wt: 1:   02 21 words for teachers
  57.    wt: 1:   standards for course material
  58.    wt: 1:   mathematics instruction in general
  59.    wt: 1:   three kinds of reason in mathematics
  60.    wt: 1:   How to be a better instructor
  61.    wt: 1:   Leaner mathematics curriculum
  62.    wt: 1:   education an empirical art
  63.    wt: 1:   fairness and inductive principles for instruction
  64.    wt: 1:   C Electromotive force conventional current02
  65.    wt: 1:   B Electromotive force conventional current01
  66.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  67.    wt: 1:   24 Standards For Skill Develoment Take II
  68.    wt: 1:   24 Standards For Skill Develoment
  69.    wt: 1:   22 Student Centered Highschool Mathematics
  70.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  71.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  72.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  73.    wt: 1:   18 Primary School Mathematics
  74.    wt: 1:   17 Math Booklets for children and young teenagers
  75.    wt: 1:   16 Secondary Mathematics Tips
  76.    wt: 1:   15 Counting For Parents
  77.    wt: 1:   11 Help and Defend Your Child or Teens Education
  78.    wt: 1:   10 Ends values for work study instruction
  79.    wt: 1:   5 Patience Please for Yourself and Your Charges
  80.    wt: 1:   4 Learning Takes Time and Effort
  81.    wt: 1:   3 Preparing for Science Studies
  82.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  83.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  84.    wt: 1:   6 Set Existence Formation and Notation
  85.    wt: 1:   4 Function notation in and beyond mathematics
  86.    wt: 1:   3 Formula or function graphing exercise
  87.    wt: 1:   8 quadratics backward use of various formulas
  88.    wt: 1:   7 quadratic formulla derivation
  89.    wt: 1:   12 motivation for term arctan
  90.    wt: 1:   9 motivation for name arcsin
  91.    wt: 1:   4 possible motivation for term arccos
  92.    wt: 1:   12 From Applied To Pure Mathematics
  93.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  94.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  95.    wt: 1:   8 Straight Lines Equation for vertical
  96.    wt: 1:   17 tangent function angle sum formulas
  97.    wt: 1:   29 secant cosecant and cotangent for acute angles
  98.    wt: 1:   25 tangent double angle formula Slope connection
  99.    wt: 1:   24 tangent Angle Difference Formula
  100.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  101.    wt: 1:   21 sine and cosine Half Angle Formulas
  102.    wt: 1:   20 sine and cosine Double Angle Formulas
  103.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  104.    wt: 1:   17C sine and cosine double triple angle formulas
  105.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  106.    wt: 1:   12 Graph of tangent function for one period
  107.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  108.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  109.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  110.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  111.    wt: 1:   11 sine and cosine double triple angle formulas
  112.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  113.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  114.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  115.    wt: 1:   8 Mid Point Formula
  116.    wt: 1:   3 Slope product for perpendicular lines
  117.    wt: 1:   2 point slope equation for a line
  118.    wt: 1:   13 Pythagorean spatial distance formulas
  119.    wt: 1:   10 Pythagorean plane distance formula
  120.    wt: 1:   PS H Distributive Law For Complex Numbers
  121.    wt: 1:   6 Column Methods for Decimal Multiplication
  122.    wt: 1:   5 Distributive Law for Whole Numbers
  123.    wt: 1:   4 Commutative Law Groups Counting Form
  124.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  125.    wt: 1:   6 Compound Interest Forward and Backwards
  126.    wt: 1:   5 Triangle Area Formula Backwards
  127.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  128.    wt: 1:   3 Product Axioms Two Forms
  129.    wt: 1:   2 More and Less Than for Counts and Measures
  130.    wt: 1:   9 Coordinates for Regions in Space
  131.    wt: 1:   8 Coordinates for Maps and Planes
  132.    wt: 1:   3 Geometric Formulas and Function Notation
  133.    wt: 1:   1 Formulas Dependence and Function Notation
  134.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  135.    wt: 1:   Using Letters for Physical Quantities
  136.    wt: 1:   13 Naming Identifying Formulas with Words
  137.    wt: 1:   8 Compound Interest Formula Evaluation
  138.    wt: 1:   7 Compound Interest Formula Introduction
  139.    wt: 1:   5 Box Volume Formula Example
  140.    wt: 1:   4 Circle Area Formula Example
  141.    wt: 1:   3 Triangle Area Formula Example
  142.    wt: 1:   2 Another Rectangle Area Formula Example
  143.    wt: 1:   1 Three Skills For Algebra
  144.    wt: 1:   arithmetic videos Real Player Format
  145.    wt: 1:   1 More and Less Than for Counts and Measures
  146.    wt: 1:   4 signed coordinates for regions in space
  147.    wt: 1:   3 signed coordinates for maps and planes
  148.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  149.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  150.    wt: 1:   21 Reciprocals for Fractions and Wholes
  151.    wt: 1:   11 Adding Integers Formulas and Examples
  152.    wt: 1:   10 Integer Multiplication Formulas
  153.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  154.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  155.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  156.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  157.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  158.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  159.    wt: 1:   Long Division forwards and backwards Example 3
  160.    wt: 1:   Long Division forwards and backwards Example 2
  161.    wt: 1:   Long Division forwards and backwards Example 1
  162.    wt: 1:   A Elementary Basis for Multiplication Methods
  163.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  164.    wt: 1:   5 A Tip for Efficent Subtraction
  165.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  166.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  167.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  168.    wt: 1:   Formula Evaluation how to show work
  169.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  170.    wt: 1:   28 Chain Rule Preparation for a Proof
  171.    wt: 1:   22 Chain Rule for polynomials
  172.    wt: 1:   21 Chain Rule for powers
  173.    wt: 1:   20 Chain Rule for Pulley Systems
  174.    wt: 1:   19 Chain Rule for linear functions
  175.    wt: 1:   10 Power rule for negative integers
  176.    wt: 1:   3 Motivation for Limit Definition Take 2
  177.    wt: 1:   2 Motivation for Limit Definition Take 1
  178.    wt: 1:   3 Decimal insights for limits continuity convergence
  179.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  180.    wt: 1:   PostScript For and Against Decimal Perspectives
  181.    wt: 1:   Foreword
  182.    wt: 1:   Postscript More on Better Performance
  183.    wt: 1:   Appendix E. How To Study Mathematics and Why
  184.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  185.    wt: 1:   Chapter 23. Notation For Sums
  186.    wt: 1:   Chapter 18. Rules for Algebra
  187.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  188.    wt: 1:   Chapter 8 Three Skills For Algebra
  189.    wt: 1:   Solutions For Arithmetic Exercises
  190.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  191.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  192.    wt: 1:   Foreword
  193.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  194.    wt: 1:   Foreword
  195.    wt: 1:   Postscript C Consistency as a Tool for Reason
  196.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  197.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  198.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  199.    wt: 1:   Foreword
  200.    wt: 1:   R Why Learn Mathematics Skills
  201.    wt: 1:   O On Learning Mathematics and Science
  202.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  203.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  204.    wt: 1:   7 Games and Activities for Instruction
  205.    wt: 1:   Helping the Blind in Logic and Mathematics
  206.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  207.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  208.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  209.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  210.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  211.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  212.    wt: 1:   The Math Forum and Site Content

Extended Search

937 matches:

  1.    wt: 9:   words for mathematics instructor
  2.    wt: 8:   three goals for Mathematics Education
  3.    wt: 7:   Mathematics Education Professors
  4.    wt: 7:   Education Reform Inconsistencies
  5.    wt: 7:   02 20 mathematics education references
  6.    wt: 7:   three aims for mathematics students
  7.    wt: 7:   formal or informal peer review
  8.    wt: 7:   Education in mathematics science and technology
  9.    wt: 7:   Four ways to improve education reform
  10.    wt: 7:   need for a mixed mathematics curriculum
  11.    wt: 7:   Prequel In For A Penny In For A Pound
  12.    wt: 6:   three goals to set for students
  13.    wt: 6:   permissions for teachers
  14.    wt: 6:   activities for students
  15.    wt: 6:   links Education Resources online
  16.    wt: 6:   modern education
  17.    wt: 6:   mathematics in context
  18.    wt: 6:   Secondary Three Mathematics
  19.    wt: 6:   Secondary Two Mathematics
  20.    wt: 6:   Secondary One Mathematics
  21.    wt: 6:   mathematics curriculum shifts
  22.    wt: 6:   geometric implications for algebra
  23.    wt: 6:   04 29 New Mathematics Curriculum
  24.    wt: 6:   02 21 words for teachers
  25.    wt: 6:   standards for course material
  26.    wt: 6:   mathematics instruction in general
  27.    wt: 6:   three kinds of reason in mathematics
  28.    wt: 6:   How to be a better instructor
  29.    wt: 6:   Leaner mathematics curriculum
  30.    wt: 6:   education an empirical art
  31.    wt: 6:   fairness and inductive principles for instruction
  32.    wt: 5:   C LAMP Introduction Culture in Mathematics Education
  33.    wt: 5:   11 pure mathematics
  34.    wt: 5:   why bother
  35.    wt: 5:   which way to go
  36.    wt: 5:   website reviews
  37.    wt: 5:   Teach the teachers plus goals
  38.    wt: 5:   Math Ed if it must be short make it lean effective
  39.    wt: 5:   Applied Maths Program14092009 POMME variant
  40.    wt: 5:   site origins
  41.    wt: 5:   site eurekas
  42.    wt: 5:   About site lesson plans
  43.    wt: 5:   key notes and themes
  44.    wt: 5:   teacher certification
  45.    wt: 5:   learning takes time
  46.    wt: 5:   grouping students according to ability
  47.    wt: 5:   what should be learnt and When
  48.    wt: 5:   Postscript 2007 01 10
  49.    wt: 5:   five decades make a difference
  50.    wt: 5:   Maps Plans Drawings
  51.    wt: 5:   how letters appear
  52.    wt: 5:   talk the algebra talk
  53.    wt: 5:   three difficulties
  54.    wt: 5:   teaching tips
  55.    wt: 5:   What to Tell Students
  56.    wt: 5:   teaching tutoring algebraic reason
  57.    wt: 5:   Lessening Algebra Difficulties
  58.    wt: 5:   the trouble with algebra
  59.    wt: 5:   05 13 OldSiteEntrancePage
  60.    wt: 5:   04 25 when to stop or suspend mathemat
  61.    wt: 5:   Operational Viewpoint to Value
  62.    wt: 5:   Theory of Knowledge
  63.    wt: 5:   Different Kinds of Reasoning in maths
  64.    wt: 5:   cultivating intelligence
  65.    wt: 5:   Motivation and Context Problem
  66.    wt: 4:   K LAMP Musings Science Education
  67.    wt: 4:   E LAMP Introduction Modern Mathematics
  68.    wt: 4:   10 statistics
  69.    wt: 4:   9 combinatorics probability sets
  70.    wt: 4:   8 analytic geometry etc
  71.    wt: 4:   7 logic review and decimals an odd combination
  72.    wt: 4:   6 polynomials etc
  73.    wt: 4:   5 logarithms and exponentials etc
  74.    wt: 4:   4 algebra
  75.    wt: 4:   3 Euclidean Geometry Leanly
  76.    wt: 4:   2 arithmetic with signed numbers
  77.    wt: 4:   1 arithmetic with unsigned numbers
  78.    wt: 4:   What is POMME
  79.    wt: 4:   13 Naming Identifying Formulas with Words
  80.    wt: 4:   8 Compound Interest Formula Evaluation
  81.    wt: 4:   7 Compound Interest Formula Introduction
  82.    wt: 4:   1 Written work formats for developing and showing skill
  83.    wt: 4:   Postscript For Better Performance
  84.    wt: 4:   Chapter 14. Forward and Backward Use of a Formula
  85.    wt: 4:   Postscript B Mathematics Education References
  86.    wt: 4:   Chapter 2 For and Against Mathematics
  87.    wt: 4:   Mathematics Education References
  88.    wt: 4:   Mathematics Education References
  89.    wt: 3:   Appendix 2 primary school Arithmetic 01
  90.    wt: 3:   Appendix 1 primary and preschool mathematic
  91.    wt: 3:   J LAMP Introduction Extrinsic Origins
  92.    wt: 3:   I LAMP Introduction Study Habits
  93.    wt: 3:   H LAMP Introduction Instructional Concepts
  94.    wt: 3:   G LAMP Introduction Problem Solving Skills
  95.    wt: 3:   F LAMP Introduction Prerequisites
  96.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  97.    wt: 3:   A Introduction Objectives
  98.    wt: 3:   Skills Chapter 5 Calculus
  99.    wt: 3:   Skills Chapter 4 Logic
  100.    wt: 3:   Ramblings Extrinsic numbers theory
  101.    wt: 3:   Ramblings Introduction Algebra Essay
  102.    wt: 3:   Skills Chapter 3 Algebra
  103.    wt: 3:   Skills Chapter 2 Geometry
  104.    wt: 3:   Skills Chapter 1 Arithmetic
  105.    wt: 3:   Skills Chapter 0 Introduction
  106.    wt: 3:   25 Mathematics Education Leaving A Good Impression
  107.    wt: 3:   12 Goals and Objectives For Mathematics
  108.    wt: 3:   5 Function notation for geometric transformations
  109.    wt: 3:   8 Notes for instructors or tutors
  110.    wt: 3:   26 Formulas for products of sines and cosines
  111.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  112.    wt: 3:   6 Compound Interest Forward and Backwards
  113.    wt: 3:   11 Volume of Sphere
  114.    wt: 3:   10 Volume of Pyramid
  115.    wt: 3:   9 Volume of Cone
  116.    wt: 3:   5 Box Volume Formula Example
  117.    wt: 3:   4 Circle Area Formula Example
  118.    wt: 3:   3 Triangle Area Formula Example
  119.    wt: 3:   2 Another Rectangle Area Formula Example
  120.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  121.    wt: 3:   Postscript More on Better Performance
  122.    wt: 3:   Appendix E. How To Study Mathematics and Why
  123.    wt: 3:   Appendix A. Reading Guide For Next Appendices
  124.    wt: 3:   Chapter 18. Rules for Algebra
  125.    wt: 3:   Postscript Unifying Theme A Fourth Skill For Algebra
  126.    wt: 3:   Solutions For Arithmetic Exercises
  127.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  128.    wt: 3:   Foreword
  129.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  130.    wt: 3:   Foreword
  131.    wt: 3:   N Mathematics Prepare for College Studies
  132.    wt: 3:   Chapter 4 Logic for Reading Writing and Geometry etc
  133.    wt: 3:   7 Games and Activities for Instruction
  134.    wt: 3:   Helping the Blind in Logic and Mathematics
  135.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  136.    wt: 3:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  137.    wt: 2:   C Electromotive force conventional current02
  138.    wt: 2:   B Electromotive force conventional current01
  139.    wt: 2:   27 Graduated Correction and Penalties for Young Offenders
  140.    wt: 2:   24 Standards For Skill Develoment Take II
  141.    wt: 2:   24 Standards For Skill Develoment
  142.    wt: 2:   22 Student Centered Highschool Mathematics
  143.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  144.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  145.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  146.    wt: 2:   18 Primary School Mathematics
  147.    wt: 2:   17 Math Booklets for children and young teenagers
  148.    wt: 2:   16 Secondary Mathematics Tips
  149.    wt: 2:   15 Counting For Parents
  150.    wt: 2:   11 Help and Defend Your Child or Teens Education
  151.    wt: 2:   10 Ends values for work study instruction
  152.    wt: 2:   5 Patience Please for Yourself and Your Charges
  153.    wt: 2:   4 Learning Takes Time and Effort
  154.    wt: 2:   3 Preparing for Science Studies
  155.    wt: 2:   Ages 8 to 9
  156.    wt: 2:   Ages 7 to 8
  157.    wt: 2:   Ages 6 to 7
  158.    wt: 2:   Ages 4 plus to 5 plus
  159.    wt: 2:   Ages 3 plus to 4 plus
  160.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  161.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  162.    wt: 2:   6 Set Existence Formation and Notation
  163.    wt: 2:   4 Function notation in and beyond mathematics
  164.    wt: 2:   3 Formula or function graphing exercise
  165.    wt: 2:   8 quadratics backward use of various formulas
  166.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  167.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  168.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  169.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  170.    wt: 2:   12 motivation for term arctan
  171.    wt: 2:   9 motivation for name arcsin
  172.    wt: 2:   4 possible motivation for term arccos
  173.    wt: 2:   12 From Applied To Pure Mathematics
  174.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  175.    wt: 2:   SAS Method For Isometric Or Proportional Triangle Construction
  176.    wt: 2:   8 Straight Lines Equation for vertical
  177.    wt: 2:   17 tangent function angle sum formulas
  178.    wt: 2:   29 secant cosecant and cotangent for acute angles
  179.    wt: 2:   25 tangent double angle formula Slope connection
  180.    wt: 2:   24 tangent Angle Difference Formula
  181.    wt: 2:   22 sine of 22.5 degrees via half angle formulas
  182.    wt: 2:   21 sine and cosine Half Angle Formulas
  183.    wt: 2:   20 sine and cosine Double Angle Formulas
  184.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  185.    wt: 2:   17E Trig Formulas for dot and cross Products
  186.    wt: 2:   17D cis formulas for sine cosines and tangent
  187.    wt: 2:   12 Graph of tangent function for one period
  188.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  189.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  190.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  191.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  192.    wt: 2:   13 Trig Formulas for dot and cross Products
  193.    wt: 2:   12 cis formulas for sine cosines and tangent
  194.    wt: 2:   5 Trigonometric Ratios For Tangent and Special Triangles
  195.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  196.    wt: 2:   8 Mid Point Formula
  197.    wt: 2:   4 Equations for lines three forms
  198.    wt: 2:   2 point slope equation for a line
  199.    wt: 2:   13 Pythagorean spatial distance formulas
  200.    wt: 2:   10 Pythagorean plane distance formula
  201.    wt: 2:   PS H Distributive Law For Complex Numbers
  202.    wt: 2:   6 Column Methods for Decimal Multiplication
  203.    wt: 2:   5 Distributive Law for Whole Numbers
  204.    wt: 2:   4 Commutative Law Groups Counting Form
  205.    wt: 2:   5 Proportionality in Equivalent Fractions
  206.    wt: 2:   4 Rates Ratios and Proporitionality
  207.    wt: 2:   3 Proportionality Examples
  208.    wt: 2:   2 Algebraic View
  209.    wt: 2:   1 What is Proportionality
  210.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  211.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  212.    wt: 2:   5 Triangle Area Formula Backwards
  213.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  214.    wt: 2:   3 Linear Equation Literal Solution More
  215.    wt: 2:   2 Linear Equation Literal Solution
  216.    wt: 2:   2 More and Less Than for Counts and Measures
  217.    wt: 2:   9 Coordinates for Regions in Space
  218.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  219.    wt: 2:   6 Algebraic Solution Example
  220.    wt: 2:   5 Algebraic Solutions Introduction
  221.    wt: 2:   4 Four Examples Fractional Coefficients
  222.    wt: 2:   3 Four Examples
  223.    wt: 2:   2 Three Examples
  224.    wt: 2:   Using Letters for Physical Quantities
  225.    wt: 2:   Formula Usage Show Work Format
  226.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  227.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  228.    wt: 2:   arithmetic videos Real Player Format
  229.    wt: 2:   1 More and Less Than for Counts and Measures
  230.    wt: 2:   4 signed coordinates for regions in space
  231.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  232.    wt: 2:   21 Reciprocals for Fractions and Wholes
  233.    wt: 2:   11 Adding Integers Formulas and Examples
  234.    wt: 2:   A Elementary Basis for Multiplication Methods
  235.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  236.    wt: 2:   5 A Tip for Efficent Subtraction
  237.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  238.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  239.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  240.    wt: 2:   38 Formulas and derivatives for powers and roots
  241.    wt: 2:   20 Chain Rule for Pulley Systems
  242.    wt: 2:   10 Power rule for negative integers
  243.    wt: 2:   3 Decimal insights for limits continuity convergence
  244.    wt: 2:   PostScript For and Against Decimal Perspectives
  245.    wt: 2:   Foreword
  246.    wt: 2:   Appendix D. What to do in School and Why
  247.    wt: 2:   Appendix C. How to Read
  248.    wt: 2:   Appendix B. How To Learn
  249.    wt: 2:   Chapter 31 Direct and Indirect Reason
  250.    wt: 2:   Chapter 30 Truth Tables
  251.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  252.    wt: 2:   Chapter 28 Occurrence Tables
  253.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  254.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  255.    wt: 2:   Chapter 23. Notation For Sums
  256.    wt: 2:   Chapter 21. Third Reading Guide
  257.    wt: 2:   Chapter 19. Functions and Sets
  258.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  259.    wt: 2:   Chapter 16. Painless Theorem Proving
  260.    wt: 2:   Chapter 15. Solving Linear Equations
  261.    wt: 2:   Chapter 13. Second Reading Guide
  262.    wt: 2:   Chapter 12. Shorthand Usage Guide
  263.    wt: 2:   Chapter 11. Why Shorthand
  264.    wt: 2:   Chapter 10 Describing and Changing Calculations
  265.    wt: 2:   Postscript What is a Variable
  266.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  267.    wt: 2:   Chapter 8 Three Skills For Algebra
  268.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  269.    wt: 2:   Chapter 6 Change of Language
  270.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  271.    wt: 2:   Chapter 4 Longer Chains of Reason
  272.    wt: 2:   Chapter 3 Chains of Reason
  273.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  274.    wt: 2:   Annotated Links to Material Elsehwere
  275.    wt: 2:   Postscript A Three Remarks
  276.    wt: 2:   Chapter 12 Four Phases
  277.    wt: 2:   Chapter 11 Elementary Instruction
  278.    wt: 2:   Chapter 10 Transition
  279.    wt: 2:   Chapter 9 The Two Ends
  280.    wt: 2:   Chapter 8 Modern Instruction
  281.    wt: 2:   Chapter 7 Two Treatments of Geometry
  282.    wt: 2:   Chapter 5 Four References
  283.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  284.    wt: 2:   Chapter 3 Algebra Difficulties
  285.    wt: 2:   Chapter 1 Introduction
  286.    wt: 2:   Postscript C Consistency as a Tool for Reason
  287.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  288.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  289.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  290.    wt: 2:   Foreword
  291.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  292.    wt: 2:   R Why Learn Mathematics Skills
  293.    wt: 2:   O On Learning Mathematics and Science
  294.    wt: 2:   G. Written work formats for developing and showing skill
  295.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  296.    wt: 2:   Chapter 8 Skipped Topics and Why
  297.    wt: 2:   Chapter 6 More Algebra and Geometry
  298.    wt: 2:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  299.    wt: 2:   Chapter 3 Algebra Starter Lessons
  300.    wt: 2:   Chapter 2 Why Sets
  301.    wt: 2:   Primary and Secondary Skills and Practices with Take Home Value
  302.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  303.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  304.    wt: 2:   4 Money Matters Saving Earning Buying Selling and Budgets
  305.    wt: 2:   3 Telling Tracking Time Temporal and More Place Sense
  306.    wt: 2:   2 Identifying Size and Position Place and Spatial Sense
  307.    wt: 2:   Ends Values Methods For Skill Development Framework Prequel
  308.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  309.    wt: 2:   Implementation Notes
  310.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  311.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  312.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  313.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  314.    wt: 2:   Which Way To Go
  315.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  316.    wt: 2:   The Math Forum and Site Content
  317.    wt: 1:   chapitre 12 00 les iles et division
  318.    wt: 1:   chapitre 07 01 principle D induction mathematique
  319.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  320.    wt: 1:   chapitre 06 00 Chaines de la raison
  321.    wt: 1:   chapitre 05 00 Deception
  322.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  323.    wt: 1:   chapitre 04 09 Regles accidentelles
  324.    wt: 1:   chapitre 04 08 Limitations et benefices
  325.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  326.    wt: 1:   chapitre 04 06 engagements
  327.    wt: 1:   chapitre 04 05 Implication versus suggestion
  328.    wt: 1:   chapitre 04 04 Parlons de la logique
  329.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  330.    wt: 1:   chapitre 04 02 Deuxieme enigme
  331.    wt: 1:   chapitre 04 01 Premiere enigme
  332.    wt: 1:   chapitre 04 00 Les regles d implication
  333.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  334.    wt: 1:   chapitre 02 00 La Communication des idees
  335.    wt: 1:   chapitre 01 00 Introduction
  336.    wt: 1:   liens
  337.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  338.    wt: 1:   problemes responses
  339.    wt: 1:   problemes algebre et arithmetique
  340.    wt: 1:   Trois Notions qui menent a algebre
  341.    wt: 1:   deux definitions pour variable
  342.    wt: 1:   logique deux enigme
  343.    wt: 1:   4 Energy Power Heat09
  344.    wt: 1:   3 Energy Power Heat08
  345.    wt: 1:   2 Energy Power Heat07
  346.    wt: 1:   1 Energy Power Heat06
  347.    wt: 1:   E Energy Power05
  348.    wt: 1:   D Energy Power04
  349.    wt: 1:   C Energy Power03
  350.    wt: 1:   B Energy Power02
  351.    wt: 1:   A Energy Power01
  352.    wt: 1:   2 Conductance Resistance Duality02
  353.    wt: 1:   1 Conductance Resistance Duality01
  354.    wt: 1:   F Wire Resistance Calculation04
  355.    wt: 1:   E Wire Resistance Calculation03
  356.    wt: 1:   D Wire Resistance Calculation02
  357.    wt: 1:   C Wire Resistance Calculation01
  358.    wt: 1:   B Wire Resistance Qualitative02
  359.    wt: 1:   A Wire Resistance Qualitative01
  360.    wt: 1:   3 Like resistors in parallel
  361.    wt: 1:   2 Unlike resistors in parallel01
  362.    wt: 1:   1 Like resistors in series
  363.    wt: 1:   H Series Circuit02
  364.    wt: 1:   G Series Circuit01
  365.    wt: 1:   F Unlike Resistors in Series
  366.    wt: 1:   E Kirchoffs Second Law
  367.    wt: 1:   D Kirchoff First Law
  368.    wt: 1:   A Circuit Elements
  369.    wt: 1:   Home Tutoring and Home Schooling
  370.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  371.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  372.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  373.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  374.    wt: 1:   14 Multiplication and Times Tables
  375.    wt: 1:   13 Addition and Addition Tables
  376.    wt: 1:   9 Streaming by Student Cooperation
  377.    wt: 1:   8 The Effect of Negative Remarks
  378.    wt: 1:   7 Student Motivation
  379.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  380.    wt: 1:   2 Reading and Writing Skills
  381.    wt: 1:   1 Speaking Skills
  382.    wt: 1:   Ages 12 to 14 Skills with take home value
  383.    wt: 1:   Ages 12 to 14 Geometry
  384.    wt: 1:   Ages 12 to 14 Arithmetic
  385.    wt: 1:   Ages 10 to 12 Geometry
  386.    wt: 1:   Ages 10 to 12 Arithmetic
  387.    wt: 1:   Ages 9 to 10
  388.    wt: 1:   sign monoticity analysis example 4
  389.    wt: 1:   sign monoticity analysis example 3
  390.    wt: 1:   sign monoticity analysis example 2
  391.    wt: 1:   sign monoticity analysis example 1
  392.    wt: 1:   26 Function definitions done and coming
  393.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  394.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  395.    wt: 1:   23 Inverse Functions
  396.    wt: 1:   22 Square Root function graphically
  397.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  398.    wt: 1:   20 Interchanging coordinates a reflection
  399.    wt: 1:   19 Horizontal line rule and method
  400.    wt: 1:   18 Vertical Line Rule and Method
  401.    wt: 1:   17 Function maxima minima and their location
  402.    wt: 1:   16 Increasing or decreasing on intervals
  403.    wt: 1:   15 Sign analysis of functions
  404.    wt: 1:   14 Surjections Injections Bijections
  405.    wt: 1:   13 From one to one to many to one
  406.    wt: 1:   12 Function Domain Recognition Exercises
  407.    wt: 1:   11 Function Domain Range Source and Targets
  408.    wt: 1:   10 Interval Notation
  409.    wt: 1:   9 Set theory term relation possible origins
  410.    wt: 1:   8 Set view of relations and functions
  411.    wt: 1:   7 Functions with finite domains
  412.    wt: 1:   2 Algebraic use of function notation
  413.    wt: 1:   1 Geometric Introduction of Function Notation
  414.    wt: 1:   Introduction Reading Guide
  415.    wt: 1:   10 quadratic exercises
  416.    wt: 1:   9 quadratics physical and further context
  417.    wt: 1:   7 quadratic formulla derivation
  418.    wt: 1:   6 quadratics numerical approach
  419.    wt: 1:   4 quadratics difference of two squares
  420.    wt: 1:   1 quadratics graphing exercises
  421.    wt: 1:   Quadratics in 10 steps
  422.    wt: 1:   11 Growth and Decay in Biology
  423.    wt: 1:   5 Natural Logarithm Calculator Exercises
  424.    wt: 1:   1 Calculator Starter Exercises
  425.    wt: 1:   7 Links Lessons Elsewhere
  426.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  427.    wt: 1:   4 Polynomials Long division linear divisor
  428.    wt: 1:   3 Polynomials Multiplication Addition
  429.    wt: 1:   2 Column Multiplication Method
  430.    wt: 1:   1 Polynomials Distributive Law
  431.    wt: 1:   Rewriting algebraic substitution as function substitutions
  432.    wt: 1:   16 cotangent function Definition Graph and Inverse
  433.    wt: 1:   15 cosecant function Definition Graph and Inverse
  434.    wt: 1:   14 secant function Definition Graph and Inverse
  435.    wt: 1:   13 cosecant function Definition Graph and Inverse
  436.    wt: 1:   11 arctan left inverse of tangent Graph
  437.    wt: 1:   10 arctan left inverse of tangent Definition
  438.    wt: 1:   8 arcsin left inverse of sine Graph
  439.    wt: 1:   7 arcsin left inverse of sine Definition
  440.    wt: 1:   6 Graph of arccos function
  441.    wt: 1:   5 Swapping Coordinates is a reflection
  442.    wt: 1:   3 Left Inverse of cosine arccos definition
  443.    wt: 1:   2 cosine function more properties
  444.    wt: 1:   1 cosine function properties
  445.    wt: 1:   9 Summary Degrees to Radians and back
  446.    wt: 1:   8 Radian Measures of Common Angles
  447.    wt: 1:   7 Radian Measures in special Triangles
  448.    wt: 1:   6 Radian Measure to Degrees
  449.    wt: 1:   5 Degrees to Radian Measure
  450.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  451.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  452.    wt: 1:   A Global Time and Navigation
  453.    wt: 1:   15 Dot and Cross Product
  454.    wt: 1:   13 Velocity Vectors in Physics
  455.    wt: 1:   11 Component Method
  456.    wt: 1:   10 Parallelogram Addition Method
  457.    wt: 1:   9 Head to Tail Coordinate View
  458.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  459.    wt: 1:   6 Vectors with Coordinates
  460.    wt: 1:   5 Head To Tail Arrow Addition
  461.    wt: 1:   4 Resultant of a Sum of Movements
  462.    wt: 1:   3 Navigation with Arrows or Vectors
  463.    wt: 1:   2 Signed Coordinates
  464.    wt: 1:   1 Unsigned Coordinates
  465.    wt: 1:   Vector and Complex Number Applet
  466.    wt: 1:   4 graphing y=Asin(x c)
  467.    wt: 1:   3 graphing y=f(x c) plus K
  468.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  469.    wt: 1:   1 graphing y=f(x a)
  470.    wt: 1:   Parallel Lines and Parallel Transversals
  471.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  472.    wt: 1:   Triangle Angles Sum To 180 Degrees
  473.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  474.    wt: 1:   Parallel Lines and Interior Angles
  475.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  476.    wt: 1:   Straight Lines ASA Intersection Study More
  477.    wt: 1:   Straight Lines ASA Intersection Study
  478.    wt: 1:   Straight Lines Instersection Solving Equations
  479.    wt: 1:   Straight Lines Intersection of
  480.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  481.    wt: 1:   C Straight Lines Slope from Coordinates
  482.    wt: 1:   B Straight Line Slope Scaling Properties More
  483.    wt: 1:   A Straight Line Slope Scaling Properties
  484.    wt: 1:   14 Straight Lines Equations General Case
  485.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  486.    wt: 1:   12 Straight Lines Graphing mx plus b
  487.    wt: 1:   11 Straight Lines Graphing y=mx
  488.    wt: 1:   10 Straight Lines through Origin Equations More
  489.    wt: 1:   9 Straight Lines through Origin Equations
  490.    wt: 1:   7 Tangent Function is odd on this domain
  491.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  492.    wt: 1:   5 Tangent Function Graph
  493.    wt: 1:   4 Tangent Function Properties
  494.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  495.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  496.    wt: 1:   1 Straight Lines Slope Concept
  497.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  498.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  499.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  500.    wt: 1:   32 seven rows of pascals triangle
  501.    wt: 1:   31 basic secant cosecant cotangent trig identities
  502.    wt: 1:   30 unit circle calculation of six trigonometric functions
  503.    wt: 1:   28 Expressing products of sines cosines as sums
  504.    wt: 1:   27 Logarithmic use of products of sines and cosines
  505.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  506.    wt: 1:   18 sum of sinusoidal waves as a single wave
  507.    wt: 1:   17C sine and cosine double triple angle formulas
  508.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  509.    wt: 1:   16 Right Triangle Complementary Angle Relations
  510.    wt: 1:   15 sine cosine Complementary Angle Relations
  511.    wt: 1:   14 cosine even and sine and tangent are odd
  512.    wt: 1:   13 Graph of tangent function many periods
  513.    wt: 1:   11 tangent function undefined when terminal side vertical
  514.    wt: 1:   10 Graphs of sines and cosines many periods
  515.    wt: 1:   9 Graphs of sine and cosine over one period
  516.    wt: 1:   8 period of tangent function
  517.    wt: 1:   7 period of sine and cosine
  518.    wt: 1:   2 Quadrant I reference Angles
  519.    wt: 1:   1 Unit Points Reflections Rotations
  520.    wt: 1:   Unit Circle Development of Trigonometry
  521.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  522.    wt: 1:   19 N th Roots of Unity
  523.    wt: 1:   18 Sixth Roots of Unity
  524.    wt: 1:   17 Cube Roots of unity
  525.    wt: 1:   16 References and Originality Question
  526.    wt: 1:   11 sine and cosine double triple angle formulas
  527.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  528.    wt: 1:   8 Unit Circle Development of Trigonometry
  529.    wt: 1:   6 Field Properties of Complex Number
  530.    wt: 1:   4 Multiplication Properties
  531.    wt: 1:   3 Addition Properties
  532.    wt: 1:   1 Rectangular Polar Coordinates Review
  533.    wt: 1:   Appetizer A Complex Number Applet
  534.    wt: 1:   8 Triangles Cascade Problem Solving
  535.    wt: 1:   7 Trignometric Ratios Unit Circle
  536.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  537.    wt: 1:   3 Trigonometric Ratios sine and cosine
  538.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  539.    wt: 1:   1 Angle Measurement with Degrees
  540.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  541.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  542.    wt: 1:   12 Triangles Similarity More Problems
  543.    wt: 1:   11 Triangle Similarity Missing Side Problem
  544.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  545.    wt: 1:   9 Similarity of Triangles Usual Criteria
  546.    wt: 1:   8 Similarity of Triangles and Polygons
  547.    wt: 1:   7 Translations Rotations Reflections Dilatations
  548.    wt: 1:   6 Geometric Diagrams in Class
  549.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  550.    wt: 1:   4 Similarity Definition with Coordinate
  551.    wt: 1:   3 Similarity by Design with coordinates
  552.    wt: 1:   2 Similarity By Design
  553.    wt: 1:   1 Early Concept of Like or Similar Shapes
  554.    wt: 1:   Four Simple Exercises
  555.    wt: 1:   12 Links Lessons elsewhere
  556.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  557.    wt: 1:   7 Exercises to test skill and concept mastery
  558.    wt: 1:   6 Intersection of lines by solving linear systems
  559.    wt: 1:   5 Algebraic View of Slopes
  560.    wt: 1:   3 Slope product for perpendicular lines
  561.    wt: 1:   1 Numerical view of lines and their equations
  562.    wt: 1:   What is and is not here
  563.    wt: 1:   12 Spatial Coordinates
  564.    wt: 1:   11 Triangle Inequality
  565.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  566.    wt: 1:   7 Complex Numbers Appetizer
  567.    wt: 1:   6 Polar Multiplication and Rotation
  568.    wt: 1:   5 Cartesian Addition and Translation
  569.    wt: 1:   4 Polar Coordinates to and from
  570.    wt: 1:   3 Rectangular Coordinates Review
  571.    wt: 1:   2 Cartesian Coordinates with signs
  572.    wt: 1:   1 Cartesian Coordinates sans signs
  573.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  574.    wt: 1:   PS G Rotation Distributes over Addition
  575.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  576.    wt: 1:   PS E Multiplication with Polar Coordinates
  577.    wt: 1:   PS D Addition with Cartesian Coordinates
  578.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  579.    wt: 1:   PS B Parallelogram Construction Methods
  580.    wt: 1:   PS A Kite Construction Methods
  581.    wt: 1:   21 Parallelograms
  582.    wt: 1:   19 Right Triangle Similarity
  583.    wt: 1:   18 Triangle Similarity Take 1
  584.    wt: 1:   17 Right Bisectors of Triangle Sides
  585.    wt: 1:   16 Angles Subtended By Chords and Diameters
  586.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  587.    wt: 1:   14 Parallel Lines Postulate
  588.    wt: 1:   13 Angle Side Angle Failure
  589.    wt: 1:   12 Side Angle Side Failure
  590.    wt: 1:   11 Triangle Construction Fails
  591.    wt: 1:   10 Dropping a perpendicular to line
  592.    wt: 1:   9 Construction of a right bisector
  593.    wt: 1:   8 Isoceles Triangles
  594.    wt: 1:   7 Angle Side Angle
  595.    wt: 1:   6 Ruler and compass Angle Bisection
  596.    wt: 1:   5 Side Angle Side
  597.    wt: 1:   4 Side Side Side
  598.    wt: 1:   3 Isometry of Triangles Congruence
  599.    wt: 1:   2 Correspondence between Triangles
  600.    wt: 1:   1 Initial Concepts and Terms
  601.    wt: 1:   Short Course on Euclidean Geometry
  602.    wt: 1:   A Measurement with Ruler Proper Use
  603.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  604.    wt: 1:   6 Figuring with Maps Not to Scale
  605.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  606.    wt: 1:   4 Angles on Maps Plans drawn to scale
  607.    wt: 1:   3 Lengths and Areas on Maps and Plans
  608.    wt: 1:   2 Measuring Area Directly
  609.    wt: 1:   1 Length Measurement
  610.    wt: 1:   About Folder Contents
  611.    wt: 1:   musings do not puiblish real numbers
  612.    wt: 1:   A Modular and Remainder Arithmetic
  613.    wt: 1:   A Signed Number Arithmetic Review
  614.    wt: 1:   26 More Less Greater Than Comparison
  615.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  616.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  617.    wt: 1:   23 Distributive Law Two Derivations
  618.    wt: 1:   22 Multiplication of Signed Numbers
  619.    wt: 1:   21 Addition of Multiples of a Single Vector
  620.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  621.    wt: 1:   19 Signed Multiples of Vectors
  622.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  623.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  624.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  625.    wt: 1:   15 Head to Tails in place Addition Associative
  626.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  627.    wt: 1:   13 Arrows and Vectors in a Plane
  628.    wt: 1:   12 Real Numbers Line Signed Coordinates
  629.    wt: 1:   11 Signed Number Addition and Addition Properties
  630.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  631.    wt: 1:   9 Division with Digits after Decimal Point
  632.    wt: 1:   8 Division and Mulplication of Compound Fractions
  633.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  634.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  635.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  636.    wt: 1:   4 Location of Point in Decimal Addition
  637.    wt: 1:   3 Location of Point in Decimal Multiplication
  638.    wt: 1:   2 Counting Digits in Decimal Multiplication
  639.    wt: 1:   1 Fractions with Finite Decimal Expansions
  640.    wt: 1:   E Long Division Methods more
  641.    wt: 1:   D Long Division Methods
  642.    wt: 1:   C Three Decimal Subtraction Methods
  643.    wt: 1:   B Decimal Comparison and Subtraction
  644.    wt: 1:   A Decimal Addition Columm Methods
  645.    wt: 1:   8 Column Multiplication Methods in General
  646.    wt: 1:   7 Decimals Multiplication Methods Examples
  647.    wt: 1:   3 Multiplicative Counting Skills Principles
  648.    wt: 1:   2 Combing Counts Addition Skills and Principles
  649.    wt: 1:   1 The Counting Origins of Numbers
  650.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  651.    wt: 1:   1 Changing Calculations
  652.    wt: 1:   3 Product Axioms Two Forms
  653.    wt: 1:   5 Greater More Less Than Signs in General
  654.    wt: 1:   4 Comparison of Negative Numbers
  655.    wt: 1:   3 More and Less Than with Unlike Signs
  656.    wt: 1:   12 Real Number Additive Inverses or Negatives
  657.    wt: 1:   10 Real Number Lengths and Signs
  658.    wt: 1:   8 Coordinates for Maps and Planes
  659.    wt: 1:   5 Independent versus Dependent Variables
  660.    wt: 1:   3 Geometric Formulas and Function Notation
  661.    wt: 1:   1 Formulas Dependence and Function Notation
  662.    wt: 1:   More Exercises
  663.    wt: 1:   Simple Exercises
  664.    wt: 1:   4 GE III Animated Examples
  665.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  666.    wt: 1:   3 GE III Equation Addition and Multiplication
  667.    wt: 1:   2 GE II Comparison
  668.    wt: 1:   1 GE Substitution four examples
  669.    wt: 1:   4 Solving a triangular system exercise
  670.    wt: 1:   3 Solving triangular system example
  671.    wt: 1:   2 Essentially one exercises three with solution
  672.    wt: 1:   1 Essentially One Unknown
  673.    wt: 1:   1 Proper Equal Sign Usage
  674.    wt: 1:   Skill Development Notes
  675.    wt: 1:   10 One Example
  676.    wt: 1:   9 Three Examples
  677.    wt: 1:   8 One Example
  678.    wt: 1:   7 Two Examples
  679.    wt: 1:   6 Three Examples
  680.    wt: 1:   5 Three Examples
  681.    wt: 1:   4 Two Examples
  682.    wt: 1:   3 Two Examples
  683.    wt: 1:   2 Three Examples
  684.    wt: 1:   9 Sets in Probability and Statistics
  685.    wt: 1:   7 Cautious or Safe Set Construction
  686.    wt: 1:   2 Venn Diagrams
  687.    wt: 1:   6 Three Notions of What is a Variable
  688.    wt: 1:   4 A Brief Story of numbers and algebra
  689.    wt: 1:   3 Adding Words To Arithmetic
  690.    wt: 1:   2 What is a Variable
  691.    wt: 1:   1 Three Skills For Algebra
  692.    wt: 1:   About Folder Contents
  693.    wt: 1:   4 Greater More Less Than Signs in General
  694.    wt: 1:   3 Comparison of Negative Numbers
  695.    wt: 1:   2 More and Less Than with Unlike Signs
  696.    wt: 1:   7 negative and additive inverse
  697.    wt: 1:   6 adding signed numbers
  698.    wt: 1:   5 lengths and signs of numbers
  699.    wt: 1:   3 signed coordinates for maps and planes
  700.    wt: 1:   7 Converting or Changing Units
  701.    wt: 1:   6 Simplification of Fractions with Units
  702.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  703.    wt: 1:   4 Fractions with Units
  704.    wt: 1:   3 Multiplying Units and Numbers
  705.    wt: 1:   2 Equality and Units
  706.    wt: 1:   1 Addition and Subtraction with Units
  707.    wt: 1:   D Three Term Ratios
  708.    wt: 1:   B Fractions and Two Term Ratios
  709.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  710.    wt: 1:   21 Working With Signs
  711.    wt: 1:   20 Dividing Fractions the Why
  712.    wt: 1:   19 Dividing Fractions How TO
  713.    wt: 1:   18 Efficient Ways to Multiply
  714.    wt: 1:   17 Efficient Ways to Add and Subtract
  715.    wt: 1:   16 Addition Subtraction Comparision Compared
  716.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  717.    wt: 1:   14 Adding and Subtracting with Like Denominators
  718.    wt: 1:   13 Fraction Comparison Algebraic View
  719.    wt: 1:   12 Fraction Comparison
  720.    wt: 1:   11 Simplification an Algebraic View
  721.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  722.    wt: 1:   9 Improper Fractions and Mixed Numbers
  723.    wt: 1:   8 Numerals Fractionals Quantals Take II
  724.    wt: 1:   7 Numerals Fractionals Quantals
  725.    wt: 1:   6 Multiplication Algebraically Take II
  726.    wt: 1:   5 Equivalent Fractions
  727.    wt: 1:   4 Fraction Multiplication
  728.    wt: 1:   3 Unit fraction of a fraction
  729.    wt: 1:   2 Unit Fraction Multiplication
  730.    wt: 1:   1 What is a fraction Take II
  731.    wt: 1:   1 What is a fraction
  732.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  733.    wt: 1:   B Integer Long Division Multiple Choices
  734.    wt: 1:   A Associative Law Theorectical Note
  735.    wt: 1:   12 Adding Integers More Examples
  736.    wt: 1:   10 Integer Multiplication Formulas
  737.    wt: 1:   9 Multiplying Integers
  738.    wt: 1:   8 Multiplication by Signed Numbers Integers
  739.    wt: 1:   7 Multiplication by Signs
  740.    wt: 1:   6 Multiplication by Natural Numbers
  741.    wt: 1:   5 Zero Movement and Additive Inverses
  742.    wt: 1:   4 Adding Movements wiht opposite directions
  743.    wt: 1:   3 Adding Movements with same direction
  744.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  745.    wt: 1:   1 Integers as Coordinates
  746.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  747.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  748.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  749.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  750.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  751.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  752.    wt: 1:   20 Uniqueness of Prime Factorization
  753.    wt: 1:   17 Identify and Count Factors using Primes
  754.    wt: 1:   12 LCD GCD and LCM using Primes
  755.    wt: 1:   11 Efficient Square Rule Use
  756.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  757.    wt: 1:   2 Prime and Composites less than 16
  758.    wt: 1:   Long Division forwards and backwards Example 3
  759.    wt: 1:   Long Division forwards and backwards Example 2
  760.    wt: 1:   Long Division forwards and backwards Example 1
  761.    wt: 1:   12 Why Long Division Works Take III
  762.    wt: 1:   11 Another Single Digit Divisor Example
  763.    wt: 1:   10 Division by Five Long and Short Ways
  764.    wt: 1:   9 Why Long Division Works Take II
  765.    wt: 1:   8 Correcting the Mistake
  766.    wt: 1:   7 Long Divison Mistake Catching
  767.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  768.    wt: 1:   5 Long Division Include Zeroes or not
  769.    wt: 1:   4 Division with 2 Digit Divsors
  770.    wt: 1:   3 Division Single Digit Divisor Example
  771.    wt: 1:   2 Division with Single Digit Divisors
  772.    wt: 1:   1 Divsion Physical Examples
  773.    wt: 1:   D Decimal Multiplication Methods Derived
  774.    wt: 1:   C Counting Areas with Powers of Ten
  775.    wt: 1:   B Powers of Ten
  776.    wt: 1:   6 Multiplication Commutes Order Not Important
  777.    wt: 1:   4 Two and Three Digit Multipliers
  778.    wt: 1:   3 More One Digit Multipliers
  779.    wt: 1:   2 One Digit Multipliers
  780.    wt: 1:   1 Why 3 times 5 gives 15
  781.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  782.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  783.    wt: 1:   9 22 Minute Subtraction Review Video
  784.    wt: 1:   8 Subtraction with Units of Measure
  785.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  786.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  787.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  788.    wt: 1:   2 Subtraction Easy Case Examples
  789.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  790.    wt: 1:   8 What skills and work habits to require
  791.    wt: 1:   7 Adding decimal fractions using decimal point
  792.    wt: 1:   6. Counting and adding units and mixed units
  793.    wt: 1:   5. How to add decimals C. Examples
  794.    wt: 1:   4. How to add with decimals B with conversions
  795.    wt: 1:   3. How to add with decimals A sans conversions
  796.    wt: 1:   2 Decimal Counting Practices
  797.    wt: 1:   1. Explaining Addition Table
  798.    wt: 1:   11 Place Value SI Standard International way
  799.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  800.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  801.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  802.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  803.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  804.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  805.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  806.    wt: 1:   Quick history of numbers and algebra
  807.    wt: 1:   Exact Arithmetic Wholes and Fractions
  808.    wt: 1:   Formula Evaluation how to show work
  809.    wt: 1:   The 20 Times Table
  810.    wt: 1:   The 12 Times Table Visually
  811.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  812.    wt: 1:   About folder contents
  813.    wt: 1:   016 Numbering Occidental Calendar Days
  814.    wt: 1:   015 School and work day counting tables
  815.    wt: 1:   014 Counting Days with Calendars
  816.    wt: 1:   013 Travel Time Tables
  817.    wt: 1:   012 Division of Time Intervals by Time Intervals
  818.    wt: 1:   011 Division of Time Intervals By Numbers
  819.    wt: 1:   010 Repeated Addition of Time Intervals
  820.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  821.    wt: 1:   8 Addition of Time Intervals via subtotaling
  822.    wt: 1:   7 Addition of Time Intervals
  823.    wt: 1:   5 Conversion Arithmetic
  824.    wt: 1:   4 Mixing and Changing Units of Time
  825.    wt: 1:   3 Units and Lengths of Time
  826.    wt: 1:   2 Time and Date Matters in School
  827.    wt: 1:   1 Intro of Kids To Time Date Skills
  828.    wt: 1:   A Related Material in Volume 3
  829.    wt: 1:   5 Area Under Curve Exercise
  830.    wt: 1:   A Related lessons in Volume 3
  831.    wt: 1:   3 Second derivative test
  832.    wt: 1:   2 Second derivative test prequel
  833.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  834.    wt: 1:   A Chain Rule Real Player video examples
  835.    wt: 1:   36 Cube root derivative animated
  836.    wt: 1:   33 Chain Rule Real Player video examples
  837.    wt: 1:   30Chain Rule A Proof
  838.    wt: 1:   29 Chain Rule Optional Reading
  839.    wt: 1:   28 Chain Rule Preparation for a Proof
  840.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  841.    wt: 1:   25 Chain Rule Animated Examples Continued
  842.    wt: 1:   24 Chain Rule Animated Examples
  843.    wt: 1:   22 Chain Rule for polynomials
  844.    wt: 1:   21 Chain Rule for powers
  845.    wt: 1:   19 Chain Rule for linear functions
  846.    wt: 1:   18 Chain Rule Introduction
  847.    wt: 1:   17 Derivatives of quotients of sine and cosine
  848.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  849.    wt: 1:   12 Quotient rule examples
  850.    wt: 1:   11 Quotient rule
  851.    wt: 1:   9 Reciprocal rule
  852.    wt: 1:   7 Animated Differentiation Examples
  853.    wt: 1:   6 Power rule from product rule
  854.    wt: 1:   5 Product Rule
  855.    wt: 1:   3 Motivation for Limit Definition Take 2
  856.    wt: 1:   2 Motivation for Limit Definition Take 1
  857.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  858.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  859.    wt: 1:   11 Limits at infinity Three Examples
  860.    wt: 1:   10 Three one sided limits with infinite values
  861.    wt: 1:   9 Limits Continuity and Composition
  862.    wt: 1:   8 Four Animated Examples
  863.    wt: 1:   7 Evaluation by immediate or delayed substitution
  864.    wt: 1:   2 Algebraic codification
  865.    wt: 1:   1 Numerical introduction
  866.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  867.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  868.    wt: 1:   A1. Introduction
  869.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  870.    wt: 1:   Chapter 23 Links To Trigonometry
  871.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  872.    wt: 1:   Chapter 13. Acceleration
  873.    wt: 1:   Chapter 12. Units and Slopes
  874.    wt: 1:   Chapter 11. Graphing Slope versus Position
  875.    wt: 1:   Chapter 10 Slopes and Units
  876.    wt: 1:   Chapter 9 About First Courses in Calculus
  877.    wt: 1:   Chapter 8. Slope Interpretation
  878.    wt: 1:   Chapter 7 Slopes and Velocity
  879.    wt: 1:   Chapter 5. Slope Sign Tests
  880.    wt: 1:   Chapter 3. Slope Sign Analysis
  881.    wt: 1:   Chapter 1.Introduction
  882.    wt: 1:   Fall 1983 Calculus Appetizer
  883.    wt: 1:   Chapter 25. Mathematical Induction Examples
  884.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  885.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  886.    wt: 1:   Chapter 20. Degrees and Radians
  887.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  888.    wt: 1:   Postscript B More on Story Telling and Reason
  889.    wt: 1:   Postscript A Story Telling
  890.    wt: 1:   Chapter 24 Direct and Indirect Reason
  891.    wt: 1:   Chapter 23 Truth Tables
  892.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  893.    wt: 1:   Chapter 21 Occurrence Tables
  894.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  895.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  896.    wt: 1:   Chapter 18 Sense and Knowledge
  897.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  898.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  899.    wt: 1:   Chapter 15 Objective Processes
  900.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  901.    wt: 1:   Chapter 11 Accidental Patterns
  902.    wt: 1:   Chapter 10 Responsibility
  903.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  904.    wt: 1:   Chapter 8 Change of Language
  905.    wt: 1:   Chapter 7 Longer Chains of Reason
  906.    wt: 1:   Chapter 6 Chains of Reason
  907.    wt: 1:   Chapter 5 Deception
  908.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  909.    wt: 1:   Chapter 2 Skill Development
  910.    wt: 1:   Chapter 1 Introduction
  911.    wt: 1:   Three Remarks
  912.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  913.    wt: 1:   S Adding words to algebra
  914.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  915.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  916.    wt: 1:   M Words to extend arithmetic
  917.    wt: 1:   L Skills with take home value
  918.    wt: 1:   J. More on written work and showing skill
  919.    wt: 1:   I. Logic and language skills
  920.    wt: 1:   H more Routine to non routine problem solving
  921.    wt: 1:   H Jigsaw puzzles and problem solving
  922.    wt: 1:   F. The student teacher tutor feedback loop
  923.    wt: 1:   E. When and how to correct errors
  924.    wt: 1:   D. Check work a must with a caution
  925.    wt: 1:   C. Domino effect of being careful
  926.    wt: 1:   B. Domino effect of errors
  927.    wt: 1:   A. Skill has to be seen to believed
  928.    wt: 1:   How to Build Skills and Confidence
  929.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  930.    wt: 1:   Chapter 1 Arithmetic
  931.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  932.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  933.    wt: 1:   More Algebra and Slope based Calculus Preview
  934.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  935.    wt: 1:   Systematic Algebra Skill Development Missing Links
  936.    wt: 1:   Road Safety Questions
  937.    wt: 1:   Site Reviews

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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