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

213 matches:

  1.    wt: 3:   13 Addition and Addition Tables
  2.    wt: 2:   formal or informal peer review
  3.    wt: 2:   Prequel In For A Penny In For A Pound
  4.    wt: 2:   15 Counting For Parents
  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:   11 Signed Number Addition and Addition Properties
  17.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  18.    wt: 2:   Formula Usage Show Work Format
  19.    wt: 2:   1 Written work formats for developing and showing skill
  20.    wt: 2:   1. Explaining Addition Table
  21.    wt: 2:   38 Formulas and derivatives for powers and roots
  22.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  23.    wt: 2:   Postscript For Better Performance
  24.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  25.    wt: 2:   G. Written work formats for developing and showing skill
  26.    wt: 1:   three goals to set for students
  27.    wt: 1:   permissions for teachers
  28.    wt: 1:   activities for students
  29.    wt: 1:   Education Reform Inconsistencies
  30.    wt: 1:   geometric implications for algebra
  31.    wt: 1:   three goals for Mathematics Education
  32.    wt: 1:   02 21 words for teachers
  33.    wt: 1:   three aims for mathematics students
  34.    wt: 1:   standards for course material
  35.    wt: 1:   Four ways to improve education reform
  36.    wt: 1:   need for a mixed mathematics curriculum
  37.    wt: 1:   fairness and inductive principles for instruction
  38.    wt: 1:   words for mathematics instructor
  39.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  40.    wt: 1:   C Electromotive force conventional current02
  41.    wt: 1:   B Electromotive force conventional current01
  42.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  43.    wt: 1:   24 Standards For Skill Develoment Take II
  44.    wt: 1:   24 Standards For Skill Develoment
  45.    wt: 1:   22 Student Centered Highschool Mathematics
  46.    wt: 1:   17 Math Booklets for children and young teenagers
  47.    wt: 1:   14 Multiplication and Times Tables
  48.    wt: 1:   12 Goals and Objectives For Mathematics
  49.    wt: 1:   10 Ends values for work study instruction
  50.    wt: 1:   5 Patience Please for Yourself and Your Charges
  51.    wt: 1:   4 Learning Takes Time and Effort
  52.    wt: 1:   3 Preparing for Science Studies
  53.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  54.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  55.    wt: 1:   6 Set Existence Formation and Notation
  56.    wt: 1:   3 Formula or function graphing exercise
  57.    wt: 1:   8 quadratics backward use of various formulas
  58.    wt: 1:   7 quadratic formulla derivation
  59.    wt: 1:   8 Notes for instructors or tutors
  60.    wt: 1:   3 Polynomials Multiplication Addition
  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:   10 Parallelogram Addition Method
  65.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  66.    wt: 1:   5 Head To Tail Arrow Addition
  67.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  68.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  69.    wt: 1:   8 Straight Lines Equation for vertical
  70.    wt: 1:   17 tangent function angle sum formulas
  71.    wt: 1:   29 secant cosecant and cotangent for acute angles
  72.    wt: 1:   25 tangent double angle formula Slope connection
  73.    wt: 1:   24 tangent Angle Difference Formula
  74.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  75.    wt: 1:   21 sine and cosine Half Angle Formulas
  76.    wt: 1:   20 sine and cosine Double Angle Formulas
  77.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  78.    wt: 1:   17C sine and cosine double triple angle formulas
  79.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  80.    wt: 1:   12 Graph of tangent function for one period
  81.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  82.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  83.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  84.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  85.    wt: 1:   11 sine and cosine double triple angle formulas
  86.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  87.    wt: 1:   3 Addition Properties
  88.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  89.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  90.    wt: 1:   8 Mid Point Formula
  91.    wt: 1:   3 Slope product for perpendicular lines
  92.    wt: 1:   2 point slope equation for a line
  93.    wt: 1:   13 Pythagorean spatial distance formulas
  94.    wt: 1:   10 Pythagorean plane distance formula
  95.    wt: 1:   5 Cartesian Addition and Translation
  96.    wt: 1:   PS H Distributive Law For Complex Numbers
  97.    wt: 1:   PS G Rotation Distributes over Addition
  98.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  99.    wt: 1:   PS D Addition with Cartesian Coordinates
  100.    wt: 1:   21 Addition of Multiples of a Single Vector
  101.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  102.    wt: 1:   15 Head to Tails in place Addition Associative
  103.    wt: 1:   4 Location of Point in Decimal Addition
  104.    wt: 1:   A Decimal Addition Columm Methods
  105.    wt: 1:   6 Column Methods for Decimal Multiplication
  106.    wt: 1:   5 Distributive Law for Whole Numbers
  107.    wt: 1:   4 Commutative Law Groups Counting Form
  108.    wt: 1:   2 Combing Counts Addition Skills and Principles
  109.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  110.    wt: 1:   6 Compound Interest Forward and Backwards
  111.    wt: 1:   5 Triangle Area Formula Backwards
  112.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  113.    wt: 1:   3 Product Axioms Two Forms
  114.    wt: 1:   2 Addition and Multiplication Axioms
  115.    wt: 1:   2 More and Less Than for Counts and Measures
  116.    wt: 1:   11 Real Number Addition
  117.    wt: 1:   9 Coordinates for Regions in Space
  118.    wt: 1:   8 Coordinates for Maps and Planes
  119.    wt: 1:   3 Geometric Formulas and Function Notation
  120.    wt: 1:   1 Formulas Dependence and Function Notation
  121.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  122.    wt: 1:   3 GE III Equation Addition and Multiplication
  123.    wt: 1:   Using Letters for Physical Quantities
  124.    wt: 1:   13 Naming Identifying Formulas with Words
  125.    wt: 1:   8 Compound Interest Formula Evaluation
  126.    wt: 1:   7 Compound Interest Formula Introduction
  127.    wt: 1:   5 Box Volume Formula Example
  128.    wt: 1:   4 Circle Area Formula Example
  129.    wt: 1:   3 Triangle Area Formula Example
  130.    wt: 1:   2 Another Rectangle Area Formula Example
  131.    wt: 1:   1 Three Skills For Algebra
  132.    wt: 1:   arithmetic videos Real Player Format
  133.    wt: 1:   1 More and Less Than for Counts and Measures
  134.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  135.    wt: 1:   3 Counting with Tables and Trees II
  136.    wt: 1:   2 Counting with Tables and Trees I
  137.    wt: 1:   4 signed coordinates for regions in space
  138.    wt: 1:   3 signed coordinates for maps and planes
  139.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  140.    wt: 1:   1 Addition and Subtraction with Units
  141.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  142.    wt: 1:   21 Reciprocals for Fractions and Wholes
  143.    wt: 1:   16 Addition Subtraction Comparision Compared
  144.    wt: 1:   11 Adding Integers Formulas and Examples
  145.    wt: 1:   10 Integer Multiplication Formulas
  146.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  147.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  148.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  149.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  150.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  151.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  152.    wt: 1:   3 video Primes and Composites from 9 times table
  153.    wt: 1:   Long Division forwards and backwards Example 3
  154.    wt: 1:   Long Division forwards and backwards Example 2
  155.    wt: 1:   Long Division forwards and backwards Example 1
  156.    wt: 1:   A Elementary Basis for Multiplication Methods
  157.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  158.    wt: 1:   5 A Tip for Efficent Subtraction
  159.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  160.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  161.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  162.    wt: 1:   Formula Evaluation how to show work
  163.    wt: 1:   The 20 Times Table
  164.    wt: 1:   The 12 Times Table Visually
  165.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  166.    wt: 1:   015 School and work day counting tables
  167.    wt: 1:   013 Travel Time Tables
  168.    wt: 1:   010 Repeated Addition of Time Intervals
  169.    wt: 1:   8 Addition of Time Intervals via subtotaling
  170.    wt: 1:   7 Addition of Time Intervals
  171.    wt: 1:   28 Chain Rule Preparation for a Proof
  172.    wt: 1:   22 Chain Rule for polynomials
  173.    wt: 1:   21 Chain Rule for powers
  174.    wt: 1:   20 Chain Rule for Pulley Systems
  175.    wt: 1:   19 Chain Rule for linear functions
  176.    wt: 1:   10 Power rule for negative integers
  177.    wt: 1:   3 Motivation for Limit Definition Take 2
  178.    wt: 1:   2 Motivation for Limit Definition Take 1
  179.    wt: 1:   3 Decimal insights for limits continuity convergence
  180.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  181.    wt: 1:   PostScript For and Against Decimal Perspectives
  182.    wt: 1:   Chapter 21 Arrow Addition
  183.    wt: 1:   Foreword
  184.    wt: 1:   Postscript More on Better Performance
  185.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  186.    wt: 1:   Chapter 30 Truth Tables
  187.    wt: 1:   Chapter 28 Occurrence Tables
  188.    wt: 1:   Chapter 23. Notation For Sums
  189.    wt: 1:   Chapter 18. Rules for Algebra
  190.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  191.    wt: 1:   Chapter 8 Three Skills For Algebra
  192.    wt: 1:   Solutions For Arithmetic Exercises
  193.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  194.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  195.    wt: 1:   Foreword
  196.    wt: 1:   Chapter 2 For and Against Mathematics
  197.    wt: 1:   Foreword
  198.    wt: 1:   Postscript C Consistency as a Tool for Reason
  199.    wt: 1:   Chapter 23 Truth Tables
  200.    wt: 1:   Chapter 21 Occurrence Tables
  201.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  202.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  203.    wt: 1:   Foreword
  204.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  205.    wt: 1:   N Mathematics Prepare for College Studies
  206.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  207.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  208.    wt: 1:   7 Games and Activities for Instruction
  209.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  210.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  211.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  212.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  213.    wt: 1:   The Math Forum and Site Content

Extended Search

281 matches:

  1.    wt: 5:   13 Addition and Addition Tables
  2.    wt: 4:   15 Counting For Parents
  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:   14 Multiplication and Times 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:   11 Signed Number Addition and Addition Properties
  57.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  58.    wt: 2:   6 Compound Interest Forward and Backwards
  59.    wt: 2:   5 Triangle Area Formula Backwards
  60.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  61.    wt: 2:   Formula Usage Show Work Format
  62.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  63.    wt: 2:   11 Volume of Sphere
  64.    wt: 2:   10 Volume of Pyramid
  65.    wt: 2:   9 Volume of Cone
  66.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  67.    wt: 2:   5 Counting with Tables Trees Product Rule Take II
  68.    wt: 2:   3 Counting with Tables and Trees II
  69.    wt: 2:   2 Counting with Tables and Trees I
  70.    wt: 2:   1. Explaining Addition Table
  71.    wt: 2:   38 Formulas and derivatives for powers and roots
  72.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  73.    wt: 2:   Postscript More on Better Performance
  74.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  75.    wt: 2:   Chapter 30 Truth Tables
  76.    wt: 2:   Chapter 28 Occurrence Tables
  77.    wt: 2:   Chapter 23. Notation For Sums
  78.    wt: 2:   Chapter 18. Rules for Algebra
  79.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  80.    wt: 2:   Chapter 8 Three Skills For Algebra
  81.    wt: 2:   Solutions For Arithmetic Exercises
  82.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  83.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  84.    wt: 2:   Foreword
  85.    wt: 2:   G. Written work formats for developing and showing skill
  86.    wt: 1:   three goals to set for students
  87.    wt: 1:   permissions for teachers
  88.    wt: 1:   activities for students
  89.    wt: 1:   Education Reform Inconsistencies
  90.    wt: 1:   geometric implications for algebra
  91.    wt: 1:   three goals for Mathematics Education
  92.    wt: 1:   02 21 words for teachers
  93.    wt: 1:   three aims for mathematics students
  94.    wt: 1:   standards for course material
  95.    wt: 1:   Four ways to improve education reform
  96.    wt: 1:   need for a mixed mathematics curriculum
  97.    wt: 1:   fairness and inductive principles for instruction
  98.    wt: 1:   words for mathematics instructor
  99.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  100.    wt: 1:   C Electromotive force conventional current02
  101.    wt: 1:   B Electromotive force conventional current01
  102.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  103.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  104.    wt: 1:   6 Set Existence Formation and Notation
  105.    wt: 1:   3 Formula or function graphing exercise
  106.    wt: 1:   8 quadratics backward use of various formulas
  107.    wt: 1:   7 quadratic formulla derivation
  108.    wt: 1:   8 Notes for instructors or tutors
  109.    wt: 1:   3 Polynomials Multiplication Addition
  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:   10 Parallelogram Addition Method
  114.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  115.    wt: 1:   5 Head To Tail Arrow Addition
  116.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  117.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  118.    wt: 1:   8 Straight Lines Equation for vertical
  119.    wt: 1:   17 tangent function angle sum formulas
  120.    wt: 1:   29 secant cosecant and cotangent for acute angles
  121.    wt: 1:   25 tangent double angle formula Slope connection
  122.    wt: 1:   24 tangent Angle Difference Formula
  123.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  124.    wt: 1:   21 sine and cosine Half Angle Formulas
  125.    wt: 1:   20 sine and cosine Double Angle Formulas
  126.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  127.    wt: 1:   17C sine and cosine double triple angle formulas
  128.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  129.    wt: 1:   12 Graph of tangent function for one period
  130.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  131.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  132.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  133.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  134.    wt: 1:   11 sine and cosine double triple angle formulas
  135.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  136.    wt: 1:   3 Addition Properties
  137.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  138.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  139.    wt: 1:   8 Mid Point Formula
  140.    wt: 1:   3 Slope product for perpendicular lines
  141.    wt: 1:   2 point slope equation for a line
  142.    wt: 1:   13 Pythagorean spatial distance formulas
  143.    wt: 1:   10 Pythagorean plane distance formula
  144.    wt: 1:   5 Cartesian Addition and Translation
  145.    wt: 1:   PS H Distributive Law For Complex Numbers
  146.    wt: 1:   PS G Rotation Distributes over Addition
  147.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  148.    wt: 1:   PS D Addition with Cartesian Coordinates
  149.    wt: 1:   21 Addition of Multiples of a Single Vector
  150.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  151.    wt: 1:   15 Head to Tails in place Addition Associative
  152.    wt: 1:   4 Location of Point in Decimal Addition
  153.    wt: 1:   A Decimal Addition Columm Methods
  154.    wt: 1:   6 Column Methods for Decimal Multiplication
  155.    wt: 1:   5 Distributive Law for Whole Numbers
  156.    wt: 1:   4 Commutative Law Groups Counting Form
  157.    wt: 1:   2 Combing Counts Addition Skills and Principles
  158.    wt: 1:   5 Proportionality in Equivalent Fractions
  159.    wt: 1:   4 Rates Ratios and Proporitionality
  160.    wt: 1:   3 Proportionality Examples
  161.    wt: 1:   2 Algebraic View
  162.    wt: 1:   1 What is Proportionality
  163.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  164.    wt: 1:   3 Linear Equation Literal Solution More
  165.    wt: 1:   2 Linear Equation Literal Solution
  166.    wt: 1:   1 Changing Calculations
  167.    wt: 1:   3 Product Axioms Two Forms
  168.    wt: 1:   2 Addition and Multiplication Axioms
  169.    wt: 1:   2 More and Less Than for Counts and Measures
  170.    wt: 1:   11 Real Number Addition
  171.    wt: 1:   9 Coordinates for Regions in Space
  172.    wt: 1:   8 Coordinates for Maps and Planes
  173.    wt: 1:   3 Geometric Formulas and Function Notation
  174.    wt: 1:   1 Formulas Dependence and Function Notation
  175.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  176.    wt: 1:   3 GE III Equation Addition and Multiplication
  177.    wt: 1:   6 Algebraic Solution Example
  178.    wt: 1:   5 Algebraic Solutions Introduction
  179.    wt: 1:   4 Four Examples Fractional Coefficients
  180.    wt: 1:   3 Four Examples
  181.    wt: 1:   2 Three Examples
  182.    wt: 1:   1 Proper Equal Sign Usage
  183.    wt: 1:   Using Letters for Physical Quantities
  184.    wt: 1:   1 Three Skills For Algebra
  185.    wt: 1:   arithmetic videos Real Player Format
  186.    wt: 1:   1 More and Less Than for Counts and Measures
  187.    wt: 1:   4 Counting with Trees Product Rule Take I
  188.    wt: 1:   1 Counting and Counting Methods I
  189.    wt: 1:   4 signed coordinates for regions in space
  190.    wt: 1:   3 signed coordinates for maps and planes
  191.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  192.    wt: 1:   1 Addition and Subtraction with Units
  193.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  194.    wt: 1:   21 Reciprocals for Fractions and Wholes
  195.    wt: 1:   16 Addition Subtraction Comparision Compared
  196.    wt: 1:   11 Adding Integers Formulas and Examples
  197.    wt: 1:   10 Integer Multiplication Formulas
  198.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  199.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  200.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  201.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  202.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  203.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  204.    wt: 1:   3 video Primes and Composites from 9 times table
  205.    wt: 1:   Long Division forwards and backwards Example 3
  206.    wt: 1:   Long Division forwards and backwards Example 2
  207.    wt: 1:   Long Division forwards and backwards Example 1
  208.    wt: 1:   A Elementary Basis for Multiplication Methods
  209.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  210.    wt: 1:   5 A Tip for Efficent Subtraction
  211.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  212.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  213.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  214.    wt: 1:   Formula Evaluation how to show work
  215.    wt: 1:   The 20 Times Table
  216.    wt: 1:   The 12 Times Table Visually
  217.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  218.    wt: 1:   015 School and work day counting tables
  219.    wt: 1:   013 Travel Time Tables
  220.    wt: 1:   010 Repeated Addition of Time Intervals
  221.    wt: 1:   8 Addition of Time Intervals via subtotaling
  222.    wt: 1:   7 Addition of Time Intervals
  223.    wt: 1:   28 Chain Rule Preparation for a Proof
  224.    wt: 1:   22 Chain Rule for polynomials
  225.    wt: 1:   21 Chain Rule for powers
  226.    wt: 1:   20 Chain Rule for Pulley Systems
  227.    wt: 1:   19 Chain Rule for linear functions
  228.    wt: 1:   10 Power rule for negative integers
  229.    wt: 1:   3 Motivation for Limit Definition Take 2
  230.    wt: 1:   2 Motivation for Limit Definition Take 1
  231.    wt: 1:   3 Decimal insights for limits continuity convergence
  232.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  233.    wt: 1:   PostScript For and Against Decimal Perspectives
  234.    wt: 1:   Chapter 21 Arrow Addition
  235.    wt: 1:   Foreword
  236.    wt: 1:   Appendix E. How To Study Mathematics and Why
  237.    wt: 1:   Appendix D. What to do in School and Why
  238.    wt: 1:   Appendix C. How to Read
  239.    wt: 1:   Appendix B. How To Learn
  240.    wt: 1:   Chapter 31 Direct and Indirect Reason
  241.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  242.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  243.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  244.    wt: 1:   Chapter 25. Mathematical Induction Examples
  245.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  246.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  247.    wt: 1:   Chapter 21. Third Reading Guide
  248.    wt: 1:   Chapter 20. Degrees and Radians
  249.    wt: 1:   Chapter 19. Functions and Sets
  250.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  251.    wt: 1:   Chapter 16. Painless Theorem Proving
  252.    wt: 1:   Chapter 15. Solving Linear Equations
  253.    wt: 1:   Chapter 13. Second Reading Guide
  254.    wt: 1:   Chapter 12. Shorthand Usage Guide
  255.    wt: 1:   Chapter 11. Why Shorthand
  256.    wt: 1:   Chapter 10 Describing and Changing Calculations
  257.    wt: 1:   Postscript What is a Variable
  258.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  259.    wt: 1:   Chapter 6 Change of Language
  260.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  261.    wt: 1:   Chapter 4 Longer Chains of Reason
  262.    wt: 1:   Chapter 3 Chains of Reason
  263.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  264.    wt: 1:   Chapter 2 For and Against Mathematics
  265.    wt: 1:   Foreword
  266.    wt: 1:   Postscript C Consistency as a Tool for Reason
  267.    wt: 1:   Chapter 23 Truth Tables
  268.    wt: 1:   Chapter 21 Occurrence Tables
  269.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  270.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  271.    wt: 1:   Foreword
  272.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  273.    wt: 1:   N Mathematics Prepare for College Studies
  274.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  275.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  276.    wt: 1:   7 Games and Activities for Instruction
  277.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  278.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  279.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  280.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  281.    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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