Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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8 matches:

  1.    wt: 2:   Parent Center/
  2.    wt: 2:   2 Formula Forward Use Evaluation/
  3.    wt: 1:   A Origins of Counting and Figuring Methods/
  4.    wt: 1:   9 Proportionality Backwards and Forwards/
  5.    wt: 1:   8 Unifying Theme For Algebra/
  6.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  7.    wt: 1:   A Decimal Counting and Adding Methods/
  8.    wt: 1:   Volume 2 Three Skills For Algebra/

Web Page Search

190 matches:

  1.    wt: 3:   15 Counting For Parents
  2.    wt: 2:   formal or informal peer review
  3.    wt: 2:   Prequel In For A Penny In For A Pound
  4.    wt: 2:   5 Function notation for geometric transformations
  5.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  6.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  7.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  8.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  9.    wt: 2:   26 Formulas for products of sines and cosines
  10.    wt: 2:   17E Trig Formulas for dot and cross Products
  11.    wt: 2:   17D cis formulas for sine cosines and tangent
  12.    wt: 2:   13 Trig Formulas for dot and cross Products
  13.    wt: 2:   12 cis formulas for sine cosines and tangent
  14.    wt: 2:   4 Equations for lines three forms
  15.    wt: 2:   4 Commutative Law Groups Counting Form
  16.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  17.    wt: 2:   Formula Usage Show Work Format
  18.    wt: 2:   1 Written work formats for developing and showing skill
  19.    wt: 2:   1 Counting and Counting Methods I
  20.    wt: 2:   38 Formulas and derivatives for powers and roots
  21.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  22.    wt: 2:   Postscript For Better Performance
  23.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  24.    wt: 2:   G. Written work formats for developing and showing skill
  25.    wt: 1:   three goals to set for students
  26.    wt: 1:   permissions for teachers
  27.    wt: 1:   activities for students
  28.    wt: 1:   Education Reform Inconsistencies
  29.    wt: 1:   geometric implications for algebra
  30.    wt: 1:   three goals for Mathematics Education
  31.    wt: 1:   02 21 words for teachers
  32.    wt: 1:   three aims for mathematics students
  33.    wt: 1:   standards for course material
  34.    wt: 1:   Four ways to improve education reform
  35.    wt: 1:   need for a mixed mathematics curriculum
  36.    wt: 1:   fairness and inductive principles for instruction
  37.    wt: 1:   words for mathematics instructor
  38.    wt: 1:   C Electromotive force conventional current02
  39.    wt: 1:   B Electromotive force conventional current01
  40.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  41.    wt: 1:   24 Standards For Skill Develoment Take II
  42.    wt: 1:   24 Standards For Skill Develoment
  43.    wt: 1:   22 Student Centered Highschool Mathematics
  44.    wt: 1:   17 Math Booklets for children and young teenagers
  45.    wt: 1:   12 Goals and Objectives For Mathematics
  46.    wt: 1:   10 Ends values for work study instruction
  47.    wt: 1:   5 Patience Please for Yourself and Your Charges
  48.    wt: 1:   4 Learning Takes Time and Effort
  49.    wt: 1:   3 Preparing for Science Studies
  50.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  51.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  52.    wt: 1:   6 Set Existence Formation and Notation
  53.    wt: 1:   3 Formula or function graphing exercise
  54.    wt: 1:   8 quadratics backward use of various formulas
  55.    wt: 1:   7 quadratic formulla derivation
  56.    wt: 1:   8 Notes for instructors or tutors
  57.    wt: 1:   12 motivation for term arctan
  58.    wt: 1:   9 motivation for name arcsin
  59.    wt: 1:   4 possible motivation for term arccos
  60.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  61.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  62.    wt: 1:   8 Straight Lines Equation for vertical
  63.    wt: 1:   17 tangent function angle sum formulas
  64.    wt: 1:   29 secant cosecant and cotangent for acute angles
  65.    wt: 1:   25 tangent double angle formula Slope connection
  66.    wt: 1:   24 tangent Angle Difference Formula
  67.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  68.    wt: 1:   21 sine and cosine Half Angle Formulas
  69.    wt: 1:   20 sine and cosine Double Angle Formulas
  70.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  71.    wt: 1:   17C sine and cosine double triple angle formulas
  72.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  73.    wt: 1:   12 Graph of tangent function for one period
  74.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  75.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  76.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  77.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  78.    wt: 1:   11 sine and cosine double triple angle formulas
  79.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  80.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  81.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  82.    wt: 1:   8 Mid Point Formula
  83.    wt: 1:   3 Slope product for perpendicular lines
  84.    wt: 1:   2 point slope equation for a line
  85.    wt: 1:   13 Pythagorean spatial distance formulas
  86.    wt: 1:   10 Pythagorean plane distance formula
  87.    wt: 1:   PS H Distributive Law For Complex Numbers
  88.    wt: 1:   2 Counting Digits in Decimal Multiplication
  89.    wt: 1:   6 Column Methods for Decimal Multiplication
  90.    wt: 1:   5 Distributive Law for Whole Numbers
  91.    wt: 1:   3 Multiplicative Counting Skills Principles
  92.    wt: 1:   1 The Counting Origins of Numbers
  93.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  94.    wt: 1:   6 Compound Interest Forward and Backwards
  95.    wt: 1:   5 Triangle Area Formula Backwards
  96.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  97.    wt: 1:   3 Product Axioms Two Forms
  98.    wt: 1:   2 More and Less Than for Counts and Measures
  99.    wt: 1:   9 Coordinates for Regions in Space
  100.    wt: 1:   8 Coordinates for Maps and Planes
  101.    wt: 1:   3 Geometric Formulas and Function Notation
  102.    wt: 1:   1 Formulas Dependence and Function Notation
  103.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  104.    wt: 1:   Using Letters for Physical Quantities
  105.    wt: 1:   13 Naming Identifying Formulas with Words
  106.    wt: 1:   8 Compound Interest Formula Evaluation
  107.    wt: 1:   7 Compound Interest Formula Introduction
  108.    wt: 1:   5 Box Volume Formula Example
  109.    wt: 1:   4 Circle Area Formula Example
  110.    wt: 1:   3 Triangle Area Formula Example
  111.    wt: 1:   2 Another Rectangle Area Formula Example
  112.    wt: 1:   3 Counting with Sets etc
  113.    wt: 1:   1 Three Skills For Algebra
  114.    wt: 1:   arithmetic videos Real Player Format
  115.    wt: 1:   1 More and Less Than for Counts and Measures
  116.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  117.    wt: 1:   4 Counting with Trees Product Rule Take I
  118.    wt: 1:   3 Counting with Tables and Trees II
  119.    wt: 1:   2 Counting with Tables and Trees I
  120.    wt: 1:   4 signed coordinates for regions in space
  121.    wt: 1:   3 signed coordinates for maps and planes
  122.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  123.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  124.    wt: 1:   21 Reciprocals for Fractions and Wholes
  125.    wt: 1:   11 Adding Integers Formulas and Examples
  126.    wt: 1:   10 Integer Multiplication Formulas
  127.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  128.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  129.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  130.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  131.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  132.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  133.    wt: 1:   Long Division forwards and backwards Example 3
  134.    wt: 1:   Long Division forwards and backwards Example 2
  135.    wt: 1:   Long Division forwards and backwards Example 1
  136.    wt: 1:   C Counting Areas with Powers of Ten
  137.    wt: 1:   A Elementary Basis for Multiplication Methods
  138.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  139.    wt: 1:   5 A Tip for Efficent Subtraction
  140.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  141.    wt: 1:   6. Counting and adding units and mixed units
  142.    wt: 1:   2 Decimal Counting Practices
  143.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  144.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  145.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  146.    wt: 1:   Formula Evaluation how to show work
  147.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  148.    wt: 1:   015 School and work day counting tables
  149.    wt: 1:   014 Counting Days with Calendars
  150.    wt: 1:   28 Chain Rule Preparation for a Proof
  151.    wt: 1:   22 Chain Rule for polynomials
  152.    wt: 1:   21 Chain Rule for powers
  153.    wt: 1:   20 Chain Rule for Pulley Systems
  154.    wt: 1:   19 Chain Rule for linear functions
  155.    wt: 1:   10 Power rule for negative integers
  156.    wt: 1:   3 Motivation for Limit Definition Take 2
  157.    wt: 1:   2 Motivation for Limit Definition Take 1
  158.    wt: 1:   3 Decimal insights for limits continuity convergence
  159.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  160.    wt: 1:   PostScript For and Against Decimal Perspectives
  161.    wt: 1:   Foreword
  162.    wt: 1:   Postscript More on Better Performance
  163.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  164.    wt: 1:   Chapter 23. Notation For Sums
  165.    wt: 1:   Chapter 18. Rules for Algebra
  166.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  167.    wt: 1:   Chapter 8 Three Skills For Algebra
  168.    wt: 1:   Solutions For Arithmetic Exercises
  169.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  170.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  171.    wt: 1:   Foreword
  172.    wt: 1:   Chapter 2 For and Against Mathematics
  173.    wt: 1:   Foreword
  174.    wt: 1:   Postscript C Consistency as a Tool for Reason
  175.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  176.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  177.    wt: 1:   Foreword
  178.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  179.    wt: 1:   N Mathematics Prepare for College Studies
  180.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  181.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  182.    wt: 1:   7 Games and Activities for Instruction
  183.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  184.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  185.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  186.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  187.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  188.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  189.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  190.    wt: 1:   The Math Forum and Site Content

Extended Search

274 matches:

  1.    wt: 5:   15 Counting For Parents
  2.    wt: 4:   1 Written work formats for developing and showing skill
  3.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  4.    wt: 3:   24 Standards For Skill Develoment Take II
  5.    wt: 3:   24 Standards For Skill Develoment
  6.    wt: 3:   22 Student Centered Highschool Mathematics
  7.    wt: 3:   17 Math Booklets for children and young teenagers
  8.    wt: 3:   12 Goals and Objectives For Mathematics
  9.    wt: 3:   10 Ends values for work study instruction
  10.    wt: 3:   5 Patience Please for Yourself and Your Charges
  11.    wt: 3:   4 Learning Takes Time and Effort
  12.    wt: 3:   3 Preparing for Science Studies
  13.    wt: 3:   4 Commutative Law Groups Counting Form
  14.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  15.    wt: 3:   13 Naming Identifying Formulas with Words
  16.    wt: 3:   8 Compound Interest Formula Evaluation
  17.    wt: 3:   7 Compound Interest Formula Introduction
  18.    wt: 3:   5 Box Volume Formula Example
  19.    wt: 3:   4 Circle Area Formula Example
  20.    wt: 3:   3 Triangle Area Formula Example
  21.    wt: 3:   2 Another Rectangle Area Formula Example
  22.    wt: 3:   Postscript For Better Performance
  23.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  24.    wt: 2:   formal or informal peer review
  25.    wt: 2:   Prequel In For A Penny In For A Pound
  26.    wt: 2:   Home Tutoring and Home Schooling
  27.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  28.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  29.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  30.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  31.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  32.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  33.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  34.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  35.    wt: 2:   18 Primary School Mathematics
  36.    wt: 2:   16 Secondary Mathematics Tips
  37.    wt: 2:   14 Multiplication and Times Tables
  38.    wt: 2:   13 Addition and Addition Tables
  39.    wt: 2:   11 Help and Defend Your Child or Teens Education
  40.    wt: 2:   9 Streaming by Student Cooperation
  41.    wt: 2:   8 The Effect of Negative Remarks
  42.    wt: 2:   7 Student Motivation
  43.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  44.    wt: 2:   2 Reading and Writing Skills
  45.    wt: 2:   1 Speaking Skills
  46.    wt: 2:   5 Function notation for geometric transformations
  47.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  48.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  49.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  50.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  51.    wt: 2:   26 Formulas for products of sines and cosines
  52.    wt: 2:   17E Trig Formulas for dot and cross Products
  53.    wt: 2:   17D cis formulas for sine cosines and tangent
  54.    wt: 2:   13 Trig Formulas for dot and cross Products
  55.    wt: 2:   12 cis formulas for sine cosines and tangent
  56.    wt: 2:   4 Equations for lines three forms
  57.    wt: 2:   6 Column Methods for Decimal Multiplication
  58.    wt: 2:   5 Distributive Law for Whole Numbers
  59.    wt: 2:   3 Multiplicative Counting Skills Principles
  60.    wt: 2:   1 The Counting Origins of Numbers
  61.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  62.    wt: 2:   6 Compound Interest Forward and Backwards
  63.    wt: 2:   5 Triangle Area Formula Backwards
  64.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  65.    wt: 2:   Formula Usage Show Work Format
  66.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  67.    wt: 2:   11 Volume of Sphere
  68.    wt: 2:   10 Volume of Pyramid
  69.    wt: 2:   9 Volume of Cone
  70.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  71.    wt: 2:   1 Counting and Counting Methods I
  72.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  73.    wt: 2:   6. Counting and adding units and mixed units
  74.    wt: 2:   2 Decimal Counting Practices
  75.    wt: 2:   38 Formulas and derivatives for powers and roots
  76.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  77.    wt: 2:   Postscript More on Better Performance
  78.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  79.    wt: 2:   Chapter 23. Notation For Sums
  80.    wt: 2:   Chapter 18. Rules for Algebra
  81.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  82.    wt: 2:   Chapter 8 Three Skills For Algebra
  83.    wt: 2:   Solutions For Arithmetic Exercises
  84.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  85.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  86.    wt: 2:   Foreword
  87.    wt: 2:   G. Written work formats for developing and showing skill
  88.    wt: 1:   three goals to set for students
  89.    wt: 1:   permissions for teachers
  90.    wt: 1:   activities for students
  91.    wt: 1:   Education Reform Inconsistencies
  92.    wt: 1:   geometric implications for algebra
  93.    wt: 1:   three goals for Mathematics Education
  94.    wt: 1:   02 21 words for teachers
  95.    wt: 1:   three aims for mathematics students
  96.    wt: 1:   standards for course material
  97.    wt: 1:   Four ways to improve education reform
  98.    wt: 1:   need for a mixed mathematics curriculum
  99.    wt: 1:   fairness and inductive principles for instruction
  100.    wt: 1:   words for mathematics instructor
  101.    wt: 1:   C Electromotive force conventional current02
  102.    wt: 1:   B Electromotive force conventional current01
  103.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  104.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  105.    wt: 1:   6 Set Existence Formation and Notation
  106.    wt: 1:   3 Formula or function graphing exercise
  107.    wt: 1:   8 quadratics backward use of various formulas
  108.    wt: 1:   7 quadratic formulla derivation
  109.    wt: 1:   8 Notes for instructors or tutors
  110.    wt: 1:   12 motivation for term arctan
  111.    wt: 1:   9 motivation for name arcsin
  112.    wt: 1:   4 possible motivation for term arccos
  113.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  114.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  115.    wt: 1:   8 Straight Lines Equation for vertical
  116.    wt: 1:   17 tangent function angle sum formulas
  117.    wt: 1:   29 secant cosecant and cotangent for acute angles
  118.    wt: 1:   25 tangent double angle formula Slope connection
  119.    wt: 1:   24 tangent Angle Difference Formula
  120.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  121.    wt: 1:   21 sine and cosine Half Angle Formulas
  122.    wt: 1:   20 sine and cosine Double Angle Formulas
  123.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  124.    wt: 1:   17C sine and cosine double triple angle formulas
  125.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  126.    wt: 1:   12 Graph of tangent function for one period
  127.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  128.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  129.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  130.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  131.    wt: 1:   11 sine and cosine double triple angle formulas
  132.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  133.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  134.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  135.    wt: 1:   8 Mid Point Formula
  136.    wt: 1:   3 Slope product for perpendicular lines
  137.    wt: 1:   2 point slope equation for a line
  138.    wt: 1:   13 Pythagorean spatial distance formulas
  139.    wt: 1:   10 Pythagorean plane distance formula
  140.    wt: 1:   PS H Distributive Law For Complex Numbers
  141.    wt: 1:   2 Counting Digits in Decimal Multiplication
  142.    wt: 1:   E Long Division Methods more
  143.    wt: 1:   D Long Division Methods
  144.    wt: 1:   C Three Decimal Subtraction Methods
  145.    wt: 1:   B Decimal Comparison and Subtraction
  146.    wt: 1:   A Decimal Addition Columm Methods
  147.    wt: 1:   8 Column Multiplication Methods in General
  148.    wt: 1:   7 Decimals Multiplication Methods Examples
  149.    wt: 1:   2 Combing Counts Addition Skills and Principles
  150.    wt: 1:   5 Proportionality in Equivalent Fractions
  151.    wt: 1:   4 Rates Ratios and Proporitionality
  152.    wt: 1:   3 Proportionality Examples
  153.    wt: 1:   2 Algebraic View
  154.    wt: 1:   1 What is Proportionality
  155.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  156.    wt: 1:   3 Linear Equation Literal Solution More
  157.    wt: 1:   2 Linear Equation Literal Solution
  158.    wt: 1:   1 Changing Calculations
  159.    wt: 1:   3 Product Axioms Two Forms
  160.    wt: 1:   2 More and Less Than for Counts and Measures
  161.    wt: 1:   9 Coordinates for Regions in Space
  162.    wt: 1:   8 Coordinates for Maps and Planes
  163.    wt: 1:   3 Geometric Formulas and Function Notation
  164.    wt: 1:   1 Formulas Dependence and Function Notation
  165.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  166.    wt: 1:   6 Algebraic Solution Example
  167.    wt: 1:   5 Algebraic Solutions Introduction
  168.    wt: 1:   4 Four Examples Fractional Coefficients
  169.    wt: 1:   3 Four Examples
  170.    wt: 1:   2 Three Examples
  171.    wt: 1:   1 Proper Equal Sign Usage
  172.    wt: 1:   Using Letters for Physical Quantities
  173.    wt: 1:   3 Counting with Sets etc
  174.    wt: 1:   1 Three Skills For Algebra
  175.    wt: 1:   arithmetic videos Real Player Format
  176.    wt: 1:   1 More and Less Than for Counts and Measures
  177.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  178.    wt: 1:   4 Counting with Trees Product Rule Take I
  179.    wt: 1:   3 Counting with Tables and Trees II
  180.    wt: 1:   2 Counting with Tables and Trees I
  181.    wt: 1:   4 signed coordinates for regions in space
  182.    wt: 1:   3 signed coordinates for maps and planes
  183.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  184.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  185.    wt: 1:   21 Reciprocals for Fractions and Wholes
  186.    wt: 1:   11 Adding Integers Formulas and Examples
  187.    wt: 1:   10 Integer Multiplication Formulas
  188.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  189.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  190.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  191.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  192.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  193.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  194.    wt: 1:   Long Division forwards and backwards Example 3
  195.    wt: 1:   Long Division forwards and backwards Example 2
  196.    wt: 1:   Long Division forwards and backwards Example 1
  197.    wt: 1:   C Counting Areas with Powers of Ten
  198.    wt: 1:   A Elementary Basis for Multiplication Methods
  199.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  200.    wt: 1:   5 A Tip for Efficent Subtraction
  201.    wt: 1:   8 What skills and work habits to require
  202.    wt: 1:   7 Adding decimal fractions using decimal point
  203.    wt: 1:   5. How to add decimals C. Examples
  204.    wt: 1:   4. How to add with decimals B with conversions
  205.    wt: 1:   3. How to add with decimals A sans conversions
  206.    wt: 1:   1. Explaining Addition Table
  207.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  208.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  209.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  210.    wt: 1:   Formula Evaluation how to show work
  211.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  212.    wt: 1:   015 School and work day counting tables
  213.    wt: 1:   014 Counting Days with Calendars
  214.    wt: 1:   28 Chain Rule Preparation for a Proof
  215.    wt: 1:   22 Chain Rule for polynomials
  216.    wt: 1:   21 Chain Rule for powers
  217.    wt: 1:   20 Chain Rule for Pulley Systems
  218.    wt: 1:   19 Chain Rule for linear functions
  219.    wt: 1:   10 Power rule for negative integers
  220.    wt: 1:   3 Motivation for Limit Definition Take 2
  221.    wt: 1:   2 Motivation for Limit Definition Take 1
  222.    wt: 1:   3 Decimal insights for limits continuity convergence
  223.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  224.    wt: 1:   PostScript For and Against Decimal Perspectives
  225.    wt: 1:   Foreword
  226.    wt: 1:   Appendix E. How To Study Mathematics and Why
  227.    wt: 1:   Appendix D. What to do in School and Why
  228.    wt: 1:   Appendix C. How to Read
  229.    wt: 1:   Appendix B. How To Learn
  230.    wt: 1:   Chapter 31 Direct and Indirect Reason
  231.    wt: 1:   Chapter 30 Truth Tables
  232.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  233.    wt: 1:   Chapter 28 Occurrence Tables
  234.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  235.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  236.    wt: 1:   Chapter 25. Mathematical Induction Examples
  237.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  238.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  239.    wt: 1:   Chapter 21. Third Reading Guide
  240.    wt: 1:   Chapter 20. Degrees and Radians
  241.    wt: 1:   Chapter 19. Functions and Sets
  242.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  243.    wt: 1:   Chapter 16. Painless Theorem Proving
  244.    wt: 1:   Chapter 15. Solving Linear Equations
  245.    wt: 1:   Chapter 13. Second Reading Guide
  246.    wt: 1:   Chapter 12. Shorthand Usage Guide
  247.    wt: 1:   Chapter 11. Why Shorthand
  248.    wt: 1:   Chapter 10 Describing and Changing Calculations
  249.    wt: 1:   Postscript What is a Variable
  250.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  251.    wt: 1:   Chapter 6 Change of Language
  252.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  253.    wt: 1:   Chapter 4 Longer Chains of Reason
  254.    wt: 1:   Chapter 3 Chains of Reason
  255.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  256.    wt: 1:   Chapter 2 For and Against Mathematics
  257.    wt: 1:   Foreword
  258.    wt: 1:   Postscript C Consistency as a Tool for Reason
  259.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  260.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  261.    wt: 1:   Foreword
  262.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  263.    wt: 1:   N Mathematics Prepare for College Studies
  264.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  265.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  266.    wt: 1:   7 Games and Activities for Instruction
  267.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  268.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  269.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  270.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  271.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  272.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  273.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  274.    wt: 1:   The Math Forum and Site Content

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

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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