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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7 matches:

  1.    wt: 2:   Parent Center/
  2.    wt: 2:   2 Formula Forward Use Evaluation/
  3.    wt: 1:   9 Proportionality Backwards and Forwards/
  4.    wt: 1:   8 Unifying Theme For Algebra/
  5.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  6.    wt: 1:   9 Combinatorics Trees Tables and Products/
  7.    wt: 1:   Volume 2 Three Skills For Algebra/

Web Page Search

189 matches:

  1.    wt: 2:   formal or informal peer review
  2.    wt: 2:   Prequel In For A Penny In For A Pound
  3.    wt: 2:   15 Counting For Parents
  4.    wt: 2:   14 Multiplication and Times Tables
  5.    wt: 2:   5 Function notation for geometric transformations
  6.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  7.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  8.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  9.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  10.    wt: 2:   26 Formulas for products of sines and cosines
  11.    wt: 2:   17E Trig Formulas for dot and cross Products
  12.    wt: 2:   17D cis formulas for sine cosines and tangent
  13.    wt: 2:   13 Trig Formulas for dot and cross Products
  14.    wt: 2:   12 cis formulas for sine cosines and tangent
  15.    wt: 2:   4 Equations for lines three forms
  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:   3 video Primes and Composites from 9 times table
  20.    wt: 2:   The 20 Times Table
  21.    wt: 2:   The 12 Times Table Visually
  22.    wt: 2:   38 Formulas and derivatives for powers and roots
  23.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  24.    wt: 2:   Postscript For Better Performance
  25.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  26.    wt: 2:   G. Written work formats for developing and showing skill
  27.    wt: 1:   three goals to set for students
  28.    wt: 1:   permissions for teachers
  29.    wt: 1:   activities for students
  30.    wt: 1:   Education Reform Inconsistencies
  31.    wt: 1:   geometric implications for algebra
  32.    wt: 1:   three goals for Mathematics Education
  33.    wt: 1:   02 21 words for teachers
  34.    wt: 1:   three aims for mathematics students
  35.    wt: 1:   standards for course material
  36.    wt: 1:   Four ways to improve education reform
  37.    wt: 1:   need for a mixed mathematics curriculum
  38.    wt: 1:   fairness and inductive principles for instruction
  39.    wt: 1:   words for mathematics instructor
  40.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  41.    wt: 1:   C Electromotive force conventional current02
  42.    wt: 1:   B Electromotive force conventional current01
  43.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  44.    wt: 1:   24 Standards For Skill Develoment Take II
  45.    wt: 1:   24 Standards For Skill Develoment
  46.    wt: 1:   22 Student Centered Highschool Mathematics
  47.    wt: 1:   17 Math Booklets for children and young teenagers
  48.    wt: 1:   13 Addition and Addition Tables
  49.    wt: 1:   12 Goals and Objectives For Mathematics
  50.    wt: 1:   10 Ends values for work study instruction
  51.    wt: 1:   5 Patience Please for Yourself and Your Charges
  52.    wt: 1:   4 Learning Takes Time and Effort
  53.    wt: 1:   3 Preparing for Science Studies
  54.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  55.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  56.    wt: 1:   6 Set Existence Formation and Notation
  57.    wt: 1:   3 Formula or function graphing exercise
  58.    wt: 1:   8 quadratics backward use of various formulas
  59.    wt: 1:   7 quadratic formulla derivation
  60.    wt: 1:   8 Notes for instructors or tutors
  61.    wt: 1:   12 motivation for term arctan
  62.    wt: 1:   9 motivation for name arcsin
  63.    wt: 1:   4 possible motivation for term arccos
  64.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  65.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  66.    wt: 1:   8 Straight Lines Equation for vertical
  67.    wt: 1:   17 tangent function angle sum formulas
  68.    wt: 1:   29 secant cosecant and cotangent for acute angles
  69.    wt: 1:   25 tangent double angle formula Slope connection
  70.    wt: 1:   24 tangent Angle Difference Formula
  71.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  72.    wt: 1:   21 sine and cosine Half Angle Formulas
  73.    wt: 1:   20 sine and cosine Double Angle Formulas
  74.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  75.    wt: 1:   17C sine and cosine double triple angle formulas
  76.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  77.    wt: 1:   12 Graph of tangent function for one period
  78.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  79.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  80.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  81.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  82.    wt: 1:   11 sine and cosine double triple angle formulas
  83.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  84.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  85.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  86.    wt: 1:   8 Mid Point Formula
  87.    wt: 1:   3 Slope product for perpendicular lines
  88.    wt: 1:   2 point slope equation for a line
  89.    wt: 1:   13 Pythagorean spatial distance formulas
  90.    wt: 1:   10 Pythagorean plane distance formula
  91.    wt: 1:   PS H Distributive Law For Complex Numbers
  92.    wt: 1:   6 Column Methods for Decimal Multiplication
  93.    wt: 1:   5 Distributive Law for Whole Numbers
  94.    wt: 1:   4 Commutative Law Groups Counting Form
  95.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  96.    wt: 1:   6 Compound Interest Forward and Backwards
  97.    wt: 1:   5 Triangle Area Formula Backwards
  98.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  99.    wt: 1:   3 Product Axioms Two Forms
  100.    wt: 1:   2 More and Less Than for Counts and Measures
  101.    wt: 1:   9 Coordinates for Regions in Space
  102.    wt: 1:   8 Coordinates for Maps and Planes
  103.    wt: 1:   3 Geometric Formulas and Function Notation
  104.    wt: 1:   1 Formulas Dependence and Function Notation
  105.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  106.    wt: 1:   Using Letters for Physical Quantities
  107.    wt: 1:   13 Naming Identifying Formulas with Words
  108.    wt: 1:   8 Compound Interest Formula Evaluation
  109.    wt: 1:   7 Compound Interest Formula Introduction
  110.    wt: 1:   5 Box Volume Formula Example
  111.    wt: 1:   4 Circle Area Formula Example
  112.    wt: 1:   3 Triangle Area Formula Example
  113.    wt: 1:   2 Another Rectangle Area Formula Example
  114.    wt: 1:   1 Three Skills For Algebra
  115.    wt: 1:   arithmetic videos Real Player Format
  116.    wt: 1:   1 More and Less Than for Counts and Measures
  117.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  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:   A Elementary Basis for Multiplication Methods
  137.    wt: 1:   1 Why 3 times 5 gives 15
  138.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  139.    wt: 1:   5 A Tip for Efficent Subtraction
  140.    wt: 1:   1. Explaining Addition Table
  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:   015 School and work day counting tables
  147.    wt: 1:   013 Travel Time Tables
  148.    wt: 1:   28 Chain Rule Preparation for a Proof
  149.    wt: 1:   22 Chain Rule for polynomials
  150.    wt: 1:   21 Chain Rule for powers
  151.    wt: 1:   20 Chain Rule for Pulley Systems
  152.    wt: 1:   19 Chain Rule for linear functions
  153.    wt: 1:   10 Power rule for negative integers
  154.    wt: 1:   3 Motivation for Limit Definition Take 2
  155.    wt: 1:   2 Motivation for Limit Definition Take 1
  156.    wt: 1:   3 Decimal insights for limits continuity convergence
  157.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  158.    wt: 1:   PostScript For and Against Decimal Perspectives
  159.    wt: 1:   Foreword
  160.    wt: 1:   Postscript More on Better Performance
  161.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  162.    wt: 1:   Chapter 30 Truth Tables
  163.    wt: 1:   Chapter 28 Occurrence Tables
  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 23 Truth Tables
  176.    wt: 1:   Chapter 21 Occurrence Tables
  177.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  178.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  179.    wt: 1:   Foreword
  180.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  181.    wt: 1:   N Mathematics Prepare for College Studies
  182.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  183.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  184.    wt: 1:   7 Games and Activities for Instruction
  185.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  186.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  187.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  188.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  189.    wt: 1:   The Math Forum and Site Content

Extended Search

257 matches:

  1.    wt: 4:   15 Counting For Parents
  2.    wt: 4:   14 Multiplication and Times Tables
  3.    wt: 4:   1 Written work formats for developing and showing skill
  4.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  5.    wt: 3:   24 Standards For Skill Develoment Take II
  6.    wt: 3:   24 Standards For Skill Develoment
  7.    wt: 3:   22 Student Centered Highschool Mathematics
  8.    wt: 3:   17 Math Booklets for children and young teenagers
  9.    wt: 3:   13 Addition and Addition Tables
  10.    wt: 3:   12 Goals and Objectives For Mathematics
  11.    wt: 3:   10 Ends values for work study instruction
  12.    wt: 3:   5 Patience Please for Yourself and Your Charges
  13.    wt: 3:   4 Learning Takes Time and Effort
  14.    wt: 3:   3 Preparing for Science Studies
  15.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  16.    wt: 3:   13 Naming Identifying Formulas with Words
  17.    wt: 3:   8 Compound Interest Formula Evaluation
  18.    wt: 3:   7 Compound Interest Formula Introduction
  19.    wt: 3:   5 Box Volume Formula Example
  20.    wt: 3:   4 Circle Area Formula Example
  21.    wt: 3:   3 Triangle Area Formula Example
  22.    wt: 3:   2 Another Rectangle Area Formula Example
  23.    wt: 3:   Postscript For Better Performance
  24.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  25.    wt: 2:   formal or informal peer review
  26.    wt: 2:   Prequel In For A Penny In For A Pound
  27.    wt: 2:   Home Tutoring and Home Schooling
  28.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  29.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  30.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  31.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  32.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  33.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  34.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  35.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  36.    wt: 2:   18 Primary School Mathematics
  37.    wt: 2:   16 Secondary Mathematics Tips
  38.    wt: 2:   11 Help and Defend Your Child or Teens Education
  39.    wt: 2:   9 Streaming by Student Cooperation
  40.    wt: 2:   8 The Effect of Negative Remarks
  41.    wt: 2:   7 Student Motivation
  42.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  43.    wt: 2:   2 Reading and Writing Skills
  44.    wt: 2:   1 Speaking Skills
  45.    wt: 2:   5 Function notation for geometric transformations
  46.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  47.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  48.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  49.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  50.    wt: 2:   26 Formulas for products of sines and cosines
  51.    wt: 2:   17E Trig Formulas for dot and cross Products
  52.    wt: 2:   17D cis formulas for sine cosines and tangent
  53.    wt: 2:   13 Trig Formulas for dot and cross Products
  54.    wt: 2:   12 cis formulas for sine cosines and tangent
  55.    wt: 2:   4 Equations for lines three forms
  56.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  57.    wt: 2:   6 Compound Interest Forward and Backwards
  58.    wt: 2:   5 Triangle Area Formula Backwards
  59.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  60.    wt: 2:   Formula Usage Show Work Format
  61.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  62.    wt: 2:   11 Volume of Sphere
  63.    wt: 2:   10 Volume of Pyramid
  64.    wt: 2:   9 Volume of Cone
  65.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  66.    wt: 2:   5 Counting with Tables Trees Product Rule Take II
  67.    wt: 2:   3 Counting with Tables and Trees II
  68.    wt: 2:   2 Counting with Tables and Trees I
  69.    wt: 2:   3 video Primes and Composites from 9 times table
  70.    wt: 2:   The 20 Times Table
  71.    wt: 2:   The 12 Times Table Visually
  72.    wt: 2:   38 Formulas and derivatives for powers and roots
  73.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  74.    wt: 2:   Postscript More on Better Performance
  75.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  76.    wt: 2:   Chapter 30 Truth Tables
  77.    wt: 2:   Chapter 28 Occurrence Tables
  78.    wt: 2:   Chapter 23. Notation For Sums
  79.    wt: 2:   Chapter 18. Rules for Algebra
  80.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  81.    wt: 2:   Chapter 8 Three Skills For Algebra
  82.    wt: 2:   Solutions For Arithmetic Exercises
  83.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  84.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  85.    wt: 2:   Foreword
  86.    wt: 2:   G. Written work formats for developing and showing skill
  87.    wt: 1:   three goals to set for students
  88.    wt: 1:   permissions for teachers
  89.    wt: 1:   activities for students
  90.    wt: 1:   Education Reform Inconsistencies
  91.    wt: 1:   geometric implications for algebra
  92.    wt: 1:   three goals for Mathematics Education
  93.    wt: 1:   02 21 words for teachers
  94.    wt: 1:   three aims for mathematics students
  95.    wt: 1:   standards for course material
  96.    wt: 1:   Four ways to improve education reform
  97.    wt: 1:   need for a mixed mathematics curriculum
  98.    wt: 1:   fairness and inductive principles for instruction
  99.    wt: 1:   words for mathematics instructor
  100.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  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:   6 Column Methods for Decimal Multiplication
  142.    wt: 1:   5 Distributive Law for Whole Numbers
  143.    wt: 1:   4 Commutative Law Groups Counting Form
  144.    wt: 1:   5 Proportionality in Equivalent Fractions
  145.    wt: 1:   4 Rates Ratios and Proporitionality
  146.    wt: 1:   3 Proportionality Examples
  147.    wt: 1:   2 Algebraic View
  148.    wt: 1:   1 What is Proportionality
  149.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  150.    wt: 1:   3 Linear Equation Literal Solution More
  151.    wt: 1:   2 Linear Equation Literal Solution
  152.    wt: 1:   1 Changing Calculations
  153.    wt: 1:   3 Product Axioms Two Forms
  154.    wt: 1:   2 More and Less Than for Counts and Measures
  155.    wt: 1:   9 Coordinates for Regions in Space
  156.    wt: 1:   8 Coordinates for Maps and Planes
  157.    wt: 1:   3 Geometric Formulas and Function Notation
  158.    wt: 1:   1 Formulas Dependence and Function Notation
  159.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  160.    wt: 1:   6 Algebraic Solution Example
  161.    wt: 1:   5 Algebraic Solutions Introduction
  162.    wt: 1:   4 Four Examples Fractional Coefficients
  163.    wt: 1:   3 Four Examples
  164.    wt: 1:   2 Three Examples
  165.    wt: 1:   1 Proper Equal Sign Usage
  166.    wt: 1:   Using Letters for Physical Quantities
  167.    wt: 1:   1 Three Skills For Algebra
  168.    wt: 1:   arithmetic videos Real Player Format
  169.    wt: 1:   1 More and Less Than for Counts and Measures
  170.    wt: 1:   4 Counting with Trees Product Rule Take I
  171.    wt: 1:   1 Counting and Counting Methods I
  172.    wt: 1:   4 signed coordinates for regions in space
  173.    wt: 1:   3 signed coordinates for maps and planes
  174.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  175.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  176.    wt: 1:   21 Reciprocals for Fractions and Wholes
  177.    wt: 1:   11 Adding Integers Formulas and Examples
  178.    wt: 1:   10 Integer Multiplication Formulas
  179.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  180.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  181.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  182.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  183.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  184.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  185.    wt: 1:   Long Division forwards and backwards Example 3
  186.    wt: 1:   Long Division forwards and backwards Example 2
  187.    wt: 1:   Long Division forwards and backwards Example 1
  188.    wt: 1:   A Elementary Basis for Multiplication Methods
  189.    wt: 1:   1 Why 3 times 5 gives 15
  190.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  191.    wt: 1:   5 A Tip for Efficent Subtraction
  192.    wt: 1:   1. Explaining Addition Table
  193.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  194.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  195.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  196.    wt: 1:   Formula Evaluation how to show work
  197.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  198.    wt: 1:   015 School and work day counting tables
  199.    wt: 1:   013 Travel Time Tables
  200.    wt: 1:   28 Chain Rule Preparation for a Proof
  201.    wt: 1:   22 Chain Rule for polynomials
  202.    wt: 1:   21 Chain Rule for powers
  203.    wt: 1:   20 Chain Rule for Pulley Systems
  204.    wt: 1:   19 Chain Rule for linear functions
  205.    wt: 1:   10 Power rule for negative integers
  206.    wt: 1:   3 Motivation for Limit Definition Take 2
  207.    wt: 1:   2 Motivation for Limit Definition Take 1
  208.    wt: 1:   3 Decimal insights for limits continuity convergence
  209.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  210.    wt: 1:   PostScript For and Against Decimal Perspectives
  211.    wt: 1:   Foreword
  212.    wt: 1:   Appendix E. How To Study Mathematics and Why
  213.    wt: 1:   Appendix D. What to do in School and Why
  214.    wt: 1:   Appendix C. How to Read
  215.    wt: 1:   Appendix B. How To Learn
  216.    wt: 1:   Chapter 31 Direct and Indirect Reason
  217.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  218.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  219.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  220.    wt: 1:   Chapter 25. Mathematical Induction Examples
  221.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  222.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  223.    wt: 1:   Chapter 21. Third Reading Guide
  224.    wt: 1:   Chapter 20. Degrees and Radians
  225.    wt: 1:   Chapter 19. Functions and Sets
  226.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  227.    wt: 1:   Chapter 16. Painless Theorem Proving
  228.    wt: 1:   Chapter 15. Solving Linear Equations
  229.    wt: 1:   Chapter 13. Second Reading Guide
  230.    wt: 1:   Chapter 12. Shorthand Usage Guide
  231.    wt: 1:   Chapter 11. Why Shorthand
  232.    wt: 1:   Chapter 10 Describing and Changing Calculations
  233.    wt: 1:   Postscript What is a Variable
  234.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  235.    wt: 1:   Chapter 6 Change of Language
  236.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  237.    wt: 1:   Chapter 4 Longer Chains of Reason
  238.    wt: 1:   Chapter 3 Chains of Reason
  239.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  240.    wt: 1:   Chapter 2 For and Against Mathematics
  241.    wt: 1:   Foreword
  242.    wt: 1:   Postscript C Consistency as a Tool for Reason
  243.    wt: 1:   Chapter 23 Truth Tables
  244.    wt: 1:   Chapter 21 Occurrence Tables
  245.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  246.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  247.    wt: 1:   Foreword
  248.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  249.    wt: 1:   N Mathematics Prepare for College Studies
  250.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  251.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  252.    wt: 1:   7 Games and Activities for Instruction
  253.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  254.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  255.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  256.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  257.    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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