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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  1.    wt: 4:   Mathematics Education Essays/
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  6.    wt: 1:   9 Proportionality Backwards and Forwards/
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188 matches:

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

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922 matches:

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