Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic and Pattern Based Reason to inform and amuse.

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 material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin.

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

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

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  1.    wt: 4:   Progressive Observable Motivated Mathematics Education/
  2.    wt: 4:   Mathematics Education Essays/
  3.    wt: 3:   LAMP Lean Applied Mathematics Program/
  4.    wt: 3:   9 Combinatorics Trees Tables and Products/
  5.    wt: 2:   9 Lines and Slopes Take 2 with tangent function/
  6.    wt: 2:   9 Proportionality Backwards and Forwards/
  7.    wt: 2:   2 Formula Forward Use Evaluation/
  8.    wt: 2:   8 Arithmetic with Signed Numbers/
  9.    wt: 2:   7 Arithmetic and Fractions with Units/
  10.    wt: 2:   4 Remainder Arithmetic and Divisibility/
  11.    wt: 2:   D Decimal Long Division Methods/
  12.    wt: 2:   C Decimal Multiplication Methods/
  13.    wt: 2:   B Decimal Comparing and Subtracting Methods/
  14.    wt: 2:   A Decimal Counting and Adding Methods/
  15.    wt: 2:   2 Arithmetic with Decimals/
  16.    wt: 2:   Mathematics Skill Development Framework/
  17.    wt: 1:   Archives/
  18.    wt: 1:   Direct Current Electric Circuits/
  19.    wt: 1:   8 Unifying Theme For Algebra/
  20.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  21.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  22.    wt: 1:   11 Squares and Square Roots/
  23.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  24.    wt: 1:   6 Fractions and Ratios/
  25.    wt: 1:   5 Integers/
  26.    wt: 1:   3 Prime Factorization Skills/
  27.    wt: 1:   1 Decimal Place Value/
  28.    wt: 1:   Arithmetic and Number Theory Skills/
  29.    wt: 1:   Volume 2 Three Skills For Algebra/
  30.    wt: 1:   Work and Study Tips/

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285 matches:

  1.    wt: 4:   19 Remainder Arithmetic Rule of 9 for checking sums III
  2.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  3.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  4.    wt: 3:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  5.    wt: 3:   18 Remainder Arithmetic Rule of 9 for checking sums II
  6.    wt: 3:   17 Remainder Arithmetic Rule of 9 for checking sums I
  7.    wt: 2:   Applied Maths Program14092009 POMME variant
  8.    wt: 2:   Education Reform Inconsistencies
  9.    wt: 2:   three goals for Mathematics Education
  10.    wt: 2:   formal or informal peer review
  11.    wt: 2:   Four ways to improve education reform
  12.    wt: 2:   Prequel In For A Penny In For A Pound
  13.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  14.    wt: 2:   5 Function notation for geometric transformations
  15.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  16.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  17.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  18.    wt: 2:   9 motivation for name arcsin
  19.    wt: 2:   29 secant cosecant and cotangent for acute angles
  20.    wt: 2:   26 Formulas for products of sines and cosines
  21.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  22.    wt: 2:   17E Trig Formulas for dot and cross Products
  23.    wt: 2:   17D cis formulas for sine cosines and tangent
  24.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  25.    wt: 2:   13 Trig Formulas for dot and cross Products
  26.    wt: 2:   12 cis formulas for sine cosines and tangent
  27.    wt: 2:   4 Equations for lines three forms
  28.    wt: 2:   9 Coordinates for Regions in Space
  29.    wt: 2:   Formula Usage Show Work Format
  30.    wt: 2:   1 Written work formats for developing and showing skill
  31.    wt: 2:   arithmetic videos Real Player Format
  32.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  33.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  34.    wt: 2:   16 Remainder Arithmetic Modulo 9 Example 2
  35.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  36.    wt: 2:   14 Remainder Arithmetic Modulo 9 Example
  37.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  38.    wt: 2:   9 video Prime Factorization upto 19 squared
  39.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  40.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  41.    wt: 2:   38 Formulas and derivatives for powers and roots
  42.    wt: 2:   19 Chain Rule for linear functions
  43.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  44.    wt: 2:   Postscript For Better Performance
  45.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  46.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  47.    wt: 2:   Solutions For Arithmetic Exercises
  48.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  49.    wt: 2:   G. Written work formats for developing and showing skill
  50.    wt: 1:   Appendix 2 primary school Arithmetic 01
  51.    wt: 1:   K LAMP Musings Science Education
  52.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  53.    wt: 1:   Skills Chapter 1 Arithmetic
  54.    wt: 1:   9 combinatorics probability sets
  55.    wt: 1:   2 arithmetic with signed numbers
  56.    wt: 1:   1 arithmetic with unsigned numbers
  57.    wt: 1:   three goals to set for students
  58.    wt: 1:   permissions for teachers
  59.    wt: 1:   activities for students
  60.    wt: 1:   links Education Resources online
  61.    wt: 1:   Mathematics Education Professors
  62.    wt: 1:   modern education
  63.    wt: 1:   geometric implications for algebra
  64.    wt: 1:   04 29 New Mathematics Curriculum
  65.    wt: 1:   02 21 words for teachers
  66.    wt: 1:   02 20 mathematics education references
  67.    wt: 1:   three aims for mathematics students
  68.    wt: 1:   standards for course material
  69.    wt: 1:   Education in mathematics science and technology
  70.    wt: 1:   need for a mixed mathematics curriculum
  71.    wt: 1:   education an empirical art
  72.    wt: 1:   fairness and inductive principles for instruction
  73.    wt: 1:   words for mathematics instructor
  74.    wt: 1:   chapitre 04 09 Regles accidentelles
  75.    wt: 1:   4 Energy Power Heat09
  76.    wt: 1:   C Electromotive force conventional current02
  77.    wt: 1:   B Electromotive force conventional current01
  78.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  79.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  80.    wt: 1:   24 Standards For Skill Develoment Take II
  81.    wt: 1:   24 Standards For Skill Develoment
  82.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  83.    wt: 1:   17 Math Booklets for children and young teenagers
  84.    wt: 1:   15 Counting For Parents
  85.    wt: 1:   12 Goals and Objectives For Mathematics
  86.    wt: 1:   11 Help and Defend Your Child or Teens Education
  87.    wt: 1:   10 Ends values for work study instruction
  88.    wt: 1:   9 Streaming by Student Cooperation
  89.    wt: 1:   5 Patience Please for Yourself and Your Charges
  90.    wt: 1:   4 Learning Takes Time and Effort
  91.    wt: 1:   3 Preparing for Science Studies
  92.    wt: 1:   Ages 12 to 14 Arithmetic
  93.    wt: 1:   Ages 10 to 12 Arithmetic
  94.    wt: 1:   Ages 9 to 10
  95.    wt: 1:   Ages 8 to 9
  96.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  97.    wt: 1:   19 Horizontal line rule and method
  98.    wt: 1:   9 Set theory term relation possible origins
  99.    wt: 1:   6 Set Existence Formation and Notation
  100.    wt: 1:   3 Formula or function graphing exercise
  101.    wt: 1:   Introduction Reading Guide
  102.    wt: 1:   9 quadratics physical and further context
  103.    wt: 1:   8 quadratics backward use of various formulas
  104.    wt: 1:   7 quadratic formulla derivation
  105.    wt: 1:   8 Notes for instructors or tutors
  106.    wt: 1:   12 motivation for term arctan
  107.    wt: 1:   4 possible motivation for term arccos
  108.    wt: 1:   9 Summary Degrees to Radians and back
  109.    wt: 1:   9 Head to Tail Coordinate View
  110.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  111.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  112.    wt: 1:   9 Straight Lines through Origin Equations
  113.    wt: 1:   8 Straight Lines Equation for vertical
  114.    wt: 1:   17 tangent function angle sum formulas
  115.    wt: 1:   25 tangent double angle formula Slope connection
  116.    wt: 1:   24 tangent Angle Difference Formula
  117.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  118.    wt: 1:   21 sine and cosine Half Angle Formulas
  119.    wt: 1:   20 sine and cosine Double Angle Formulas
  120.    wt: 1:   17C sine and cosine double triple angle formulas
  121.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  122.    wt: 1:   12 Graph of tangent function for one period
  123.    wt: 1:   9 Graphs of sine and cosine over one period
  124.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  125.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  126.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  127.    wt: 1:   19 N th Roots of Unity
  128.    wt: 1:   11 sine and cosine double triple angle formulas
  129.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  130.    wt: 1:   9 The complex number valued trig function cis
  131.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  132.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  133.    wt: 1:   9 Similarity of Triangles Usual Criteria
  134.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  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:   9 Pythagorean Theorem Chinese Square Proof
  141.    wt: 1:   PS H Distributive Law For Complex Numbers
  142.    wt: 1:   19 Right Triangle Similarity
  143.    wt: 1:   9 Construction of a right bisector
  144.    wt: 1:   A Modular and Remainder Arithmetic
  145.    wt: 1:   A Signed Number Arithmetic Review
  146.    wt: 1:   19 Signed Multiples of Vectors
  147.    wt: 1:   9 Division with Digits after Decimal Point
  148.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  149.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  150.    wt: 1:   6 Column Methods for Decimal Multiplication
  151.    wt: 1:   5 Distributive Law for Whole Numbers
  152.    wt: 1:   4 Commutative Law Groups Counting Form
  153.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  154.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  155.    wt: 1:   6 Compound Interest Forward and Backwards
  156.    wt: 1:   5 Triangle Area Formula Backwards
  157.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  158.    wt: 1:   3 Product Axioms Two Forms
  159.    wt: 1:   2 More and Less Than for Counts and Measures
  160.    wt: 1:   8 Coordinates for Maps and Planes
  161.    wt: 1:   3 Geometric Formulas and Function Notation
  162.    wt: 1:   1 Formulas Dependence and Function Notation
  163.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  164.    wt: 1:   9 Three Examples
  165.    wt: 1:   Using Letters for Physical Quantities
  166.    wt: 1:   13 Naming Identifying Formulas with Words
  167.    wt: 1:   9 Volume of Cone
  168.    wt: 1:   8 Compound Interest Formula Evaluation
  169.    wt: 1:   7 Compound Interest Formula Introduction
  170.    wt: 1:   5 Box Volume Formula Example
  171.    wt: 1:   4 Circle Area Formula Example
  172.    wt: 1:   3 Triangle Area Formula Example
  173.    wt: 1:   2 Another Rectangle Area Formula Example
  174.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  175.    wt: 1:   9 Sets in Probability and Statistics
  176.    wt: 1:   3 Adding Words To Arithmetic
  177.    wt: 1:   1 Three Skills For Algebra
  178.    wt: 1:   1 More and Less Than for Counts and Measures
  179.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  180.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  181.    wt: 1:   9 subtracting signed numbers
  182.    wt: 1:   4 signed coordinates for regions in space
  183.    wt: 1:   3 signed coordinates for maps and planes
  184.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  185.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  186.    wt: 1:   21 Reciprocals for Fractions and Wholes
  187.    wt: 1:   19 Dividing Fractions How TO
  188.    wt: 1:   9 Improper Fractions and Mixed Numbers
  189.    wt: 1:   11 Adding Integers Formulas and Examples
  190.    wt: 1:   10 Integer Multiplication Formulas
  191.    wt: 1:   9 Multiplying Integers
  192.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  193.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  194.    wt: 1:   23 Remainder Arithmetic Modulo 2
  195.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  196.    wt: 1:   21 Remainder Arithmetic Modulo 3
  197.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  198.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  199.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  200.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  201.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  202.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  203.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  204.    wt: 1:   5 Remainder Arithmetic Modulo 5
  205.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  206.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  207.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  208.    wt: 1:   1 Remainder Arithmetic Modulo 10
  209.    wt: 1:   19 video Prime Factorization Unique
  210.    wt: 1:   16 video Factors of 980 using prime
  211.    wt: 1:   8 video Prime Factorization upto 19
  212.    wt: 1:   3 video Primes and Composites from 9 times table
  213.    wt: 1:   Long Division forwards and backwards Example 3
  214.    wt: 1:   Long Division forwards and backwards Example 2
  215.    wt: 1:   Long Division forwards and backwards Example 1
  216.    wt: 1:   9 Why Long Division Works Take II
  217.    wt: 1:   A Elementary Basis for Multiplication Methods
  218.    wt: 1:   9 22 Minute Subtraction Review Video
  219.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  220.    wt: 1:   5 A Tip for Efficent Subtraction
  221.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  222.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  223.    wt: 1:   Exact Arithmetic Wholes and Fractions
  224.    wt: 1:   Formula Evaluation how to show work
  225.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  226.    wt: 1:   5 Conversion Arithmetic
  227.    wt: 1:   29 Chain Rule Optional Reading
  228.    wt: 1:   28 Chain Rule Preparation for a Proof
  229.    wt: 1:   22 Chain Rule for polynomials
  230.    wt: 1:   21 Chain Rule for powers
  231.    wt: 1:   20 Chain Rule for Pulley Systems
  232.    wt: 1:   10 Power rule for negative integers
  233.    wt: 1:   9 Reciprocal rule
  234.    wt: 1:   3 Motivation for Limit Definition Take 2
  235.    wt: 1:   2 Motivation for Limit Definition Take 1
  236.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  237.    wt: 1:   9 Limits Continuity and Composition
  238.    wt: 1:   3 Decimal insights for limits continuity convergence
  239.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  240.    wt: 1:   PostScript For and Against Decimal Perspectives
  241.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  242.    wt: 1:   Chapter 9 About First Courses in Calculus
  243.    wt: 1:   Fall 1983 Calculus Appetizer
  244.    wt: 1:   Foreword
  245.    wt: 1:   Postscript More on Better Performance
  246.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  247.    wt: 1:   Chapter 23. Notation For Sums
  248.    wt: 1:   Chapter 21. Third Reading Guide
  249.    wt: 1:   Chapter 19. Functions and Sets
  250.    wt: 1:   Chapter 18. Rules for Algebra
  251.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  252.    wt: 1:   Chapter 13. Second Reading Guide
  253.    wt: 1:   Chapter 12. Shorthand Usage Guide
  254.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  255.    wt: 1:   Chapter 8 Three Skills For Algebra
  256.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  257.    wt: 1:   Foreword
  258.    wt: 1:   Postscript B Mathematics Education References
  259.    wt: 1:   Chapter 9 The Two Ends
  260.    wt: 1:   Chapter 2 For and Against Mathematics
  261.    wt: 1:   Foreword
  262.    wt: 1:   Postscript C Consistency as a Tool for Reason
  263.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  264.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  265.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  266.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  267.    wt: 1:   Foreword
  268.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  269.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  270.    wt: 1:   N Mathematics Prepare for College Studies
  271.    wt: 1:   M Words to extend arithmetic
  272.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  273.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  274.    wt: 1:   Chapter 1 Arithmetic
  275.    wt: 1:   7 Games and Activities for Instruction
  276.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  277.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  278.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  279.    wt: 1:   Mathematics Education References
  280.    wt: 1:   Mathematics Education References
  281.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  282.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  283.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  284.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  285.    wt: 1:   The Math Forum and Site Content

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648 matches:

  1.    wt: 7:   arithmetic videos Real Player Format
  2.    wt: 6:   9 combinatorics probability sets
  3.    wt: 6:   Applied Maths Program14092009 POMME variant
  4.    wt: 6:   Education Reform Inconsistencies
  5.    wt: 6:   three goals for Mathematics Education
  6.    wt: 6:   formal or informal peer review
  7.    wt: 6:   Four ways to improve education reform
  8.    wt: 6:   Prequel In For A Penny In For A Pound
  9.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  10.    wt: 5:   Appendix 2 primary school Arithmetic 01
  11.    wt: 5:   2 arithmetic with signed numbers
  12.    wt: 5:   1 arithmetic with unsigned numbers
  13.    wt: 5:   three goals to set for students
  14.    wt: 5:   permissions for teachers
  15.    wt: 5:   activities for students
  16.    wt: 5:   links Education Resources online
  17.    wt: 5:   Mathematics Education Professors
  18.    wt: 5:   modern education
  19.    wt: 5:   mathematics in context
  20.    wt: 5:   Secondary One Mathematics
  21.    wt: 5:   geometric implications for algebra
  22.    wt: 5:   04 29 New Mathematics Curriculum
  23.    wt: 5:   02 21 words for teachers
  24.    wt: 5:   02 20 mathematics education references
  25.    wt: 5:   three aims for mathematics students
  26.    wt: 5:   standards for course material
  27.    wt: 5:   Education in mathematics science and technology
  28.    wt: 5:   How to be a better instructor
  29.    wt: 5:   need for a mixed mathematics curriculum
  30.    wt: 5:   education an empirical art
  31.    wt: 5:   fairness and inductive principles for instruction
  32.    wt: 5:   words for mathematics instructor
  33.    wt: 5:   25 Divisibility Tests for 2 3 5 9 10 Example
  34.    wt: 5:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  35.    wt: 5:   18 Remainder Arithmetic Rule of 9 for checking sums II
  36.    wt: 5:   17 Remainder Arithmetic Rule of 9 for checking sums I
  37.    wt: 5:   15 Remainder Arithmetic Modulo 9 Example
  38.    wt: 5:   1 Links to Online Resources Elsewhere Take 1
  39.    wt: 4:   Appendix 1 primary and preschool mathematic
  40.    wt: 4:   K LAMP Musings Science Education
  41.    wt: 4:   C LAMP Introduction Culture in Mathematics Education
  42.    wt: 4:   Skills Chapter 1 Arithmetic
  43.    wt: 4:   11 pure mathematics
  44.    wt: 4:   10 statistics
  45.    wt: 4:   8 analytic geometry etc
  46.    wt: 4:   7 logic review and decimals an odd combination
  47.    wt: 4:   6 polynomials etc
  48.    wt: 4:   5 logarithms and exponentials etc
  49.    wt: 4:   4 algebra
  50.    wt: 4:   3 Euclidean Geometry Leanly
  51.    wt: 4:   What is POMME
  52.    wt: 4:   why bother
  53.    wt: 4:   which way to go
  54.    wt: 4:   website reviews
  55.    wt: 4:   Teach the teachers plus goals
  56.    wt: 4:   Math Ed if it must be short make it lean effective
  57.    wt: 4:   site origins
  58.    wt: 4:   site eurekas
  59.    wt: 4:   About site lesson plans
  60.    wt: 4:   key notes and themes
  61.    wt: 4:   teacher certification
  62.    wt: 4:   learning takes time
  63.    wt: 4:   grouping students according to ability
  64.    wt: 4:   what should be learnt and When
  65.    wt: 4:   Postscript 2007 01 10
  66.    wt: 4:   five decades make a difference
  67.    wt: 4:   Maps Plans Drawings
  68.    wt: 4:   how letters appear
  69.    wt: 4:   Secondary Three Mathematics
  70.    wt: 4:   Secondary Two Mathematics
  71.    wt: 4:   talk the algebra talk
  72.    wt: 4:   three difficulties
  73.    wt: 4:   teaching tips
  74.    wt: 4:   What to Tell Students
  75.    wt: 4:   mathematics curriculum shifts
  76.    wt: 4:   teaching tutoring algebraic reason
  77.    wt: 4:   Lessening Algebra Difficulties
  78.    wt: 4:   the trouble with algebra
  79.    wt: 4:   05 13 OldSiteEntrancePage
  80.    wt: 4:   04 25 when to stop or suspend mathemat
  81.    wt: 4:   Operational Viewpoint to Value
  82.    wt: 4:   Theory of Knowledge
  83.    wt: 4:   mathematics instruction in general
  84.    wt: 4:   Different Kinds of Reasoning in maths
  85.    wt: 4:   three kinds of reason in mathematics
  86.    wt: 4:   cultivating intelligence
  87.    wt: 4:   Motivation and Context Problem
  88.    wt: 4:   Leaner mathematics curriculum
  89.    wt: 4:   9 Formulas for Real Exponents with Logarithms
  90.    wt: 4:   8 Straight Lines Equation for vertical
  91.    wt: 4:   musings do not puiblish real numbers
  92.    wt: 4:   9 Circle Area and Perimeter Formula Backwards Forwards
  93.    wt: 4:   1 Written work formats for developing and showing skill
  94.    wt: 4:   5 Counting with Tables Trees Product Rule Take II
  95.    wt: 4:   9 subtracting signed numbers
  96.    wt: 4:   24 Divisibility Tests for 2 3 5 9 10
  97.    wt: 4:   16 Remainder Arithmetic Modulo 9 Example 2
  98.    wt: 4:   14 Remainder Arithmetic Modulo 9 Example
  99.    wt: 4:   9 Remainder Arithmetic Divisibility by 5
  100.    wt: 4:   5 Remainder Arithmetic Modulo 5
  101.    wt: 4:   9 video Prime Factorization upto 19 squared
  102.    wt: 4:   Long Division forwards and backwards Example 1
  103.    wt: 4:   9 Why Long Division Works Take II
  104.    wt: 4:   9 22 Minute Subtraction Review Video
  105.    wt: 4:   A Related lessons in Volume 3
  106.    wt: 4:   Postscript One Sided and Intermediate Value Theorems
  107.    wt: 4:   Postscript Unifying Theme A Fourth Skill For Algebra
  108.    wt: 4:   Mathematics Education References
  109.    wt: 4:   Mathematics Education References
  110.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  111.    wt: 3:   J LAMP Introduction Extrinsic Origins
  112.    wt: 3:   I LAMP Introduction Study Habits
  113.    wt: 3:   H LAMP Introduction Instructional Concepts
  114.    wt: 3:   G LAMP Introduction Problem Solving Skills
  115.    wt: 3:   F LAMP Introduction Prerequisites
  116.    wt: 3:   E LAMP Introduction Modern Mathematics
  117.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  118.    wt: 3:   A Introduction Objectives
  119.    wt: 3:   Skills Chapter 5 Calculus
  120.    wt: 3:   Skills Chapter 4 Logic
  121.    wt: 3:   Ramblings Extrinsic numbers theory
  122.    wt: 3:   Ramblings Introduction Algebra Essay
  123.    wt: 3:   Skills Chapter 3 Algebra
  124.    wt: 3:   Skills Chapter 2 Geometry
  125.    wt: 3:   Skills Chapter 0 Introduction
  126.    wt: 3:   4 Energy Power Heat09
  127.    wt: 3:   9 Straight Lines through Origin Equations
  128.    wt: 3:   1 Straight Lines Slope Concept
  129.    wt: 3:   13 Naming Identifying Formulas with Words
  130.    wt: 3:   9 Volume of Cone
  131.    wt: 3:   8 Compound Interest Formula Evaluation
  132.    wt: 3:   7 Compound Interest Formula Introduction
  133.    wt: 3:   5 Box Volume Formula Example
  134.    wt: 3:   4 Circle Area Formula Example
  135.    wt: 3:   3 Triangle Area Formula Example
  136.    wt: 3:   2 Another Rectangle Area Formula Example
  137.    wt: 3:   4 Counting with Trees Product Rule Take I
  138.    wt: 3:   3 Counting with Tables and Trees II
  139.    wt: 3:   2 Counting with Tables and Trees I
  140.    wt: 3:   1 Counting and Counting Methods I
  141.    wt: 3:   4 signed coordinates for regions in space
  142.    wt: 3:   3 signed coordinates for maps and planes
  143.    wt: 3:   5 Reciprocals and Division for Fractions with Units
  144.    wt: 3:   C Equality for Fractions and Two Term Ratios and Fractions
  145.    wt: 3:   9 Multiplying Integers
  146.    wt: 3:   A Decimals Modular and Remainder Arithmetic
  147.    wt: 3:   27 Divisibility by 2 3 6 5 9 10 Example
  148.    wt: 3:   23 Remainder Arithmetic Modulo 2
  149.    wt: 3:   22 Remainder Arithmetic Modulo 3 more
  150.    wt: 3:   21 Remainder Arithmetic Modulo 3
  151.    wt: 3:   13 Remainder Arithmetic Modulo 5 Example
  152.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  153.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  154.    wt: 3:   10 Remainder Arithmetic Long Division by 5 Quickly
  155.    wt: 3:   8 Remainder Arithmetic Morulo 5 Examples II
  156.    wt: 3:   7 Remainder Arithmetic Modulo 5 Examples I
  157.    wt: 3:   6 Remainder Arithmetic Modulo 5 Propertie
  158.    wt: 3:   4 Remainder Arithmetic Modulo 10 in general
  159.    wt: 3:   3 Remainder Arithmetic Modulos 10 more still
  160.    wt: 3:   2 Remainder Arithmetic Modulo 10 more
  161.    wt: 3:   1 Remainder Arithmetic Modulo 10
  162.    wt: 3:   19 video Prime Factorization Unique
  163.    wt: 3:   Long Division Backwards more
  164.    wt: 3:   Long Division Backward
  165.    wt: 3:   Long Division forwards and backwards Example 3
  166.    wt: 3:   Long Division forwards and backwards Example 2
  167.    wt: 3:   C Counting Areas with Powers of Ten
  168.    wt: 3:   A Elementary Basis for Multiplication Methods
  169.    wt: 3:   Appendix 2 Three Decimal Subtraction Methods
  170.    wt: 3:   Appendix 1 Decimals Comparison Method Take II
  171.    wt: 3:   Subtraction with J Conversions Example
  172.    wt: 3:   Subtraction Another Video Lesson
  173.    wt: 3:   7 Subtraction for Decimal Fractions with Exercises
  174.    wt: 3:   5 A Tip for Efficent Subtraction
  175.    wt: 3:   Appendix 1 Counting Revisited 15 minute video
  176.    wt: 3:   9 Place Value Review Decimal form of Avogrados number included
  177.    wt: 3:   Practical Methods Ends and Values for Arithmetic
  178.    wt: 3:   38 Formulas and derivatives for powers and roots
  179.    wt: 3:   Postscript For Better Performance
  180.    wt: 3:   Appendix A. Reading Guide For Next Appendices
  181.    wt: 3:   Chapter 29 Contrapositive and Vacuously True Implications
  182.    wt: 3:   Chapter 19. Functions and Sets
  183.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  184.    wt: 3:   Chapter 9 Talking about Numbers or Quantities
  185.    wt: 3:   Solutions For Arithmetic Exercises
  186.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  187.    wt: 3:   G. Written work formats for developing and showing skill
  188.    wt: 3:   Helping the Blind in Logic and Mathematics
  189.    wt: 3:   Multiple Ways to Improve Mathematics Skill Development
  190.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  191.    wt: 3:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  192.    wt: 2:   1 Conductance Resistance Duality01
  193.    wt: 2:   H Series Circuit02
  194.    wt: 2:   C Electromotive force conventional current02
  195.    wt: 2:   B Electromotive force conventional current01
  196.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  197.    wt: 2:   9 Streaming by Student Cooperation
  198.    wt: 2:   Ages 9 to 10
  199.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  200.    wt: 2:   19 Horizontal line rule and method
  201.    wt: 2:   9 Set theory term relation possible origins
  202.    wt: 2:   5 Function notation for geometric transformations
  203.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  204.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  205.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  206.    wt: 2:   9 motivation for name arcsin
  207.    wt: 2:   8 Radian Measures of Common Angles
  208.    wt: 2:   9 Head to Tail Coordinate View
  209.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  210.    wt: 2:   C Straight Lines Slope from Coordinates
  211.    wt: 2:   B Straight Line Slope Scaling Properties More
  212.    wt: 2:   A Straight Line Slope Scaling Properties
  213.    wt: 2:   14 Straight Lines Equations General Case
  214.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  215.    wt: 2:   12 Straight Lines Graphing mx plus b
  216.    wt: 2:   11 Straight Lines Graphing y=mx
  217.    wt: 2:   10 Straight Lines through Origin Equations More
  218.    wt: 2:   7 Tangent Function is odd on this domain
  219.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  220.    wt: 2:   5 Tangent Function Graph
  221.    wt: 2:   4 Tangent Function Properties
  222.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  223.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  224.    wt: 2:   29 secant cosecant and cotangent for acute angles
  225.    wt: 2:   26 Formulas for products of sines and cosines
  226.    wt: 2:   20 sine and cosine Double Angle Formulas
  227.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  228.    wt: 2:   17E Trig Formulas for dot and cross Products
  229.    wt: 2:   17D cis formulas for sine cosines and tangent
  230.    wt: 2:   12 Graph of tangent function for one period
  231.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  232.    wt: 2:   2 Quadrant I reference Angles
  233.    wt: 2:   1 Unit Points Reflections Rotations
  234.    wt: 2:   19 N th Roots of Unity
  235.    wt: 2:   13 Trig Formulas for dot and cross Products
  236.    wt: 2:   12 cis formulas for sine cosines and tangent
  237.    wt: 2:   9 The complex number valued trig function cis
  238.    wt: 2:   9 Similarity of Triangles Usual Criteria
  239.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  240.    wt: 2:   4 Equations for lines three forms
  241.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  242.    wt: 2:   19 Right Triangle Similarity
  243.    wt: 2:   9 Construction of a right bisector
  244.    wt: 2:   A Signed Number Arithmetic Review
  245.    wt: 2:   5 Proportionality in Equivalent Fractions
  246.    wt: 2:   4 Rates Ratios and Proporitionality
  247.    wt: 2:   3 Proportionality Examples
  248.    wt: 2:   2 Algebraic View
  249.    wt: 2:   1 What is Proportionality
  250.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  251.    wt: 2:   6 Compound Interest Forward and Backwards
  252.    wt: 2:   5 Triangle Area Formula Backwards
  253.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  254.    wt: 2:   9 Coordinates for Regions in Space
  255.    wt: 2:   Simple Exercises
  256.    wt: 2:   9 Three Examples
  257.    wt: 2:   Formula Usage Show Work Format
  258.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  259.    wt: 2:   11 Volume of Sphere
  260.    wt: 2:   10 Volume of Pyramid
  261.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  262.    wt: 2:   1 More and Less Than for Counts and Measures
  263.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  264.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  265.    wt: 2:   4 LCM of 8 and 10 via Prime
  266.    wt: 2:   11 What are real lengths and numbers
  267.    wt: 2:   10 dividing signed numbers
  268.    wt: 2:   8 multiplying signed numbers
  269.    wt: 2:   7 negative and additive inverse
  270.    wt: 2:   6 adding signed numbers
  271.    wt: 2:   5 lengths and signs of numbers
  272.    wt: 2:   2 signed and unsigned numbers as coordinates
  273.    wt: 2:   7 Converting or Changing Units
  274.    wt: 2:   6 Simplification of Fractions with Units
  275.    wt: 2:   4 Fractions with Units
  276.    wt: 2:   3 Multiplying Units and Numbers
  277.    wt: 2:   2 Equality and Units
  278.    wt: 2:   1 Addition and Subtraction with Units
  279.    wt: 2:   D Three Term Ratios
  280.    wt: 2:   B Fractions and Two Term Ratios
  281.    wt: 2:   A Similarities between Fractions and Two Term Ratios
  282.    wt: 2:   21 Reciprocals for Fractions and Wholes
  283.    wt: 2:   19 Dividing Fractions How TO
  284.    wt: 2:   16 Addition Subtraction Comparision Compared
  285.    wt: 2:   15 Adding and Subtracting with Unlike Denominators
  286.    wt: 2:   9 Improper Fractions and Mixed Numbers
  287.    wt: 2:   11 Adding Integers Formulas and Examples
  288.    wt: 2:   10 Integer Multiplication Formulas
  289.    wt: 2:   26 Divisibility by 2 3 5 Example
  290.    wt: 2:   16 video Factors of 980 using prime
  291.    wt: 2:   8 video Prime Factorization upto 19
  292.    wt: 2:   3 video Primes and Composites from 9 times table
  293.    wt: 2:   Division with Counts and Length
  294.    wt: 2:   12 Why Long Division Works Take III
  295.    wt: 2:   11 Another Single Digit Divisor Example
  296.    wt: 2:   10 Division by Five Long and Short Ways
  297.    wt: 2:   8 Correcting the Mistake
  298.    wt: 2:   7 Long Divison Mistake Catching
  299.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  300.    wt: 2:   5 Long Division Include Zeroes or not
  301.    wt: 2:   4 Division with 2 Digit Divsors
  302.    wt: 2:   3 Division Single Digit Divisor Example
  303.    wt: 2:   2 Division with Single Digit Divisors
  304.    wt: 2:   1 Divsion Physical Examples
  305.    wt: 2:   D Decimal Multiplication Methods Derived
  306.    wt: 2:   B Powers of Ten
  307.    wt: 2:   6 Multiplication Commutes Order Not Important
  308.    wt: 2:   5 Decimal Fraction Multiplication
  309.    wt: 2:   4 Two and Three Digit Multipliers
  310.    wt: 2:   3 More One Digit Multipliers
  311.    wt: 2:   2 One Digit Multipliers
  312.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  313.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  314.    wt: 2:   Video Power Notation in Decimal Expansion
  315.    wt: 2:   1 Why 3 times 5 gives 15
  316.    wt: 2:   8 Subtraction with Units of Measure
  317.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  318.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  319.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  320.    wt: 2:   2 Subtraction Easy Case Examples
  321.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  322.    wt: 2:   8 What skills and work habits to require
  323.    wt: 2:   7 Adding decimal fractions using decimal point
  324.    wt: 2:   6. Counting and adding units and mixed units
  325.    wt: 2:   5. How to add decimals C. Examples
  326.    wt: 2:   4. How to add with decimals B with conversions
  327.    wt: 2:   3. How to add with decimals A sans conversions
  328.    wt: 2:   2 Decimal Counting Practices
  329.    wt: 2:   1. Explaining Addition Table
  330.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  331.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  332.    wt: 2:   Exact Arithmetic Wholes and Fractions
  333.    wt: 2:   Formula Evaluation how to show work
  334.    wt: 2:   The 12 Times Table Visually
  335.    wt: 2:   19 Chain Rule for linear functions
  336.    wt: 2:   2 Motivation for Limit Definition Take 1
  337.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  338.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  339.    wt: 2:   Chapter 9 About First Courses in Calculus
  340.    wt: 2:   Postscript More on Better Performance
  341.    wt: 2:   Chapter 23. Notation For Sums
  342.    wt: 2:   Chapter 21. Third Reading Guide
  343.    wt: 2:   Chapter 18. Rules for Algebra
  344.    wt: 2:   Chapter 13. Second Reading Guide
  345.    wt: 2:   Chapter 12. Shorthand Usage Guide
  346.    wt: 2:   Postscript What is a Variable
  347.    wt: 2:   Chapter 8 Three Skills For Algebra
  348.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  349.    wt: 2:   Foreword
  350.    wt: 2:   Chapter 9 The Two Ends
  351.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  352.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  353.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  354.    wt: 2:   S Adding words to algebra
  355.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  356.    wt: 2:   N Mathematics Prepare for College Studies
  357.    wt: 2:   M Words to extend arithmetic
  358.    wt: 2:   I. Logic and language skills
  359.    wt: 2:   Implementation Notes
  360.    wt: 2:   More Algebra and Slope based Calculus Preview
  361.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  362.    wt: 2:   Systematic Algebra Skill Development Missing Links
  363.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  364.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  365.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  366.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  367.    wt: 2:   Which Way To Go
  368.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  369.    wt: 1:   chapitre 04 09 Regles accidentelles
  370.    wt: 1:   3 Energy Power Heat08
  371.    wt: 1:   2 Energy Power Heat07
  372.    wt: 1:   1 Energy Power Heat06
  373.    wt: 1:   E Energy Power05
  374.    wt: 1:   D Energy Power04
  375.    wt: 1:   C Energy Power03
  376.    wt: 1:   B Energy Power02
  377.    wt: 1:   A Energy Power01
  378.    wt: 1:   2 Conductance Resistance Duality02
  379.    wt: 1:   F Wire Resistance Calculation04
  380.    wt: 1:   E Wire Resistance Calculation03
  381.    wt: 1:   D Wire Resistance Calculation02
  382.    wt: 1:   C Wire Resistance Calculation01
  383.    wt: 1:   B Wire Resistance Qualitative02
  384.    wt: 1:   A Wire Resistance Qualitative01
  385.    wt: 1:   3 Like resistors in parallel
  386.    wt: 1:   2 Unlike resistors in parallel01
  387.    wt: 1:   1 Like resistors in series
  388.    wt: 1:   G Series Circuit01
  389.    wt: 1:   F Unlike Resistors in Series
  390.    wt: 1:   E Kirchoffs Second Law
  391.    wt: 1:   D Kirchoff First Law
  392.    wt: 1:   A Circuit Elements
  393.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  394.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  395.    wt: 1:   24 Standards For Skill Develoment Take II
  396.    wt: 1:   24 Standards For Skill Develoment
  397.    wt: 1:   17 Math Booklets for children and young teenagers
  398.    wt: 1:   15 Counting For Parents
  399.    wt: 1:   12 Goals and Objectives For Mathematics
  400.    wt: 1:   11 Help and Defend Your Child or Teens Education
  401.    wt: 1:   10 Ends values for work study instruction
  402.    wt: 1:   5 Patience Please for Yourself and Your Charges
  403.    wt: 1:   4 Learning Takes Time and Effort
  404.    wt: 1:   3 Preparing for Science Studies
  405.    wt: 1:   Ages 12 to 14 Arithmetic
  406.    wt: 1:   Ages 10 to 12 Arithmetic
  407.    wt: 1:   Ages 8 to 9
  408.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  409.    wt: 1:   sign monoticity analysis example 4
  410.    wt: 1:   sign monoticity analysis example 3
  411.    wt: 1:   sign monoticity analysis example 2
  412.    wt: 1:   sign monoticity analysis example 1
  413.    wt: 1:   6 Set Existence Formation and Notation
  414.    wt: 1:   3 Formula or function graphing exercise
  415.    wt: 1:   Introduction Reading Guide
  416.    wt: 1:   9 quadratics physical and further context
  417.    wt: 1:   8 quadratics backward use of various formulas
  418.    wt: 1:   7 quadratic formulla derivation
  419.    wt: 1:   8 Notes for instructors or tutors
  420.    wt: 1:   12 motivation for term arctan
  421.    wt: 1:   4 possible motivation for term arccos
  422.    wt: 1:   9 Summary Degrees to Radians and back
  423.    wt: 1:   7 Radian Measures in special Triangles
  424.    wt: 1:   6 Radian Measure to Degrees
  425.    wt: 1:   5 Degrees to Radian Measure
  426.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  427.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  428.    wt: 1:   2 Radian Measure Numerical Value of one degree
  429.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  430.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  431.    wt: 1:   Straight Lines Intersection of
  432.    wt: 1:   17 tangent function angle sum formulas
  433.    wt: 1:   30 unit circle calculation of six trigonometric functions
  434.    wt: 1:   25 tangent double angle formula Slope connection
  435.    wt: 1:   24 tangent Angle Difference Formula
  436.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  437.    wt: 1:   21 sine and cosine Half Angle Formulas
  438.    wt: 1:   17C sine and cosine double triple angle formulas
  439.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  440.    wt: 1:   9 Graphs of sine and cosine over one period
  441.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  442.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  443.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  444.    wt: 1:   11 sine and cosine double triple angle formulas
  445.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  446.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  447.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  448.    wt: 1:   1 Early Concept of Like or Similar Shapes
  449.    wt: 1:   8 Mid Point Formula
  450.    wt: 1:   3 Slope product for perpendicular lines
  451.    wt: 1:   2 point slope equation for a line
  452.    wt: 1:   13 Pythagorean spatial distance formulas
  453.    wt: 1:   10 Pythagorean plane distance formula
  454.    wt: 1:   PS H Distributive Law For Complex Numbers
  455.    wt: 1:   A Modular and Remainder Arithmetic
  456.    wt: 1:   19 Signed Multiples of Vectors
  457.    wt: 1:   9 Division with Digits after Decimal Point
  458.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  459.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  460.    wt: 1:   E Long Division Methods more
  461.    wt: 1:   D Long Division Methods
  462.    wt: 1:   C Three Decimal Subtraction Methods
  463.    wt: 1:   B Decimal Comparison and Subtraction
  464.    wt: 1:   A Decimal Addition Columm Methods
  465.    wt: 1:   6 Column Methods for Decimal Multiplication
  466.    wt: 1:   5 Distributive Law for Whole Numbers
  467.    wt: 1:   4 Commutative Law Groups Counting Form
  468.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  469.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  470.    wt: 1:   3 Linear Equation Literal Solution More
  471.    wt: 1:   2 Linear Equation Literal Solution
  472.    wt: 1:   1 Changing Calculations
  473.    wt: 1:   3 Product Axioms Two Forms
  474.    wt: 1:   2 More and Less Than for Counts and Measures
  475.    wt: 1:   8 Coordinates for Maps and Planes
  476.    wt: 1:   3 Geometric Formulas and Function Notation
  477.    wt: 1:   1 Formulas Dependence and Function Notation
  478.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  479.    wt: 1:   6 Algebraic Solution Example
  480.    wt: 1:   5 Algebraic Solutions Introduction
  481.    wt: 1:   4 Four Examples Fractional Coefficients
  482.    wt: 1:   3 Four Examples
  483.    wt: 1:   2 Three Examples
  484.    wt: 1:   1 Proper Equal Sign Usage
  485.    wt: 1:   Using Letters for Physical Quantities
  486.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  487.    wt: 1:   9 Sets in Probability and Statistics
  488.    wt: 1:   3 Adding Words To Arithmetic
  489.    wt: 1:   1 Three Skills For Algebra
  490.    wt: 1:   4 Greater More Less Than Signs in General
  491.    wt: 1:   3 Comparison of Negative Numbers
  492.    wt: 1:   2 More and Less Than with Unlike Signs
  493.    wt: 1:   5 Square Roots with primes more still
  494.    wt: 1:   4 Square Roots with primes more
  495.    wt: 1:   3 Properties of Square Roots with example
  496.    wt: 1:   2 Square Roots with Prime
  497.    wt: 1:   1 Squares and Square Roots Introduction
  498.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  499.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  500.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  501.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  502.    wt: 1:   13 GCD from given Prime Factorization
  503.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  504.    wt: 1:   8 GCD from Euclidean Algorithm
  505.    wt: 1:   7 GCD and LCM from prime factorization
  506.    wt: 1:   6 GCD from Prime
  507.    wt: 1:   5 Common Divisors 60 45 via Prime
  508.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  509.    wt: 1:   2 Least Common Multiple LCM intro via list method
  510.    wt: 1:   1 Least Common Multiples LCM Introduction
  511.    wt: 1:   12 GCD 2700 288 via Prime
  512.    wt: 1:   22 Complex Compound Fractions
  513.    wt: 1:   21 Working With Signs
  514.    wt: 1:   20 Dividing Fractions the Why
  515.    wt: 1:   18 Efficient Ways to Multiply
  516.    wt: 1:   17 Efficient Ways to Add and Subtract
  517.    wt: 1:   14 Adding and Subtracting with Like Denominators
  518.    wt: 1:   13 Fraction Comparison Algebraic View
  519.    wt: 1:   12 Fraction Comparison
  520.    wt: 1:   11 Simplification an Algebraic View
  521.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  522.    wt: 1:   8 Numerals Fractionals Quantals Take II
  523.    wt: 1:   7 Numerals Fractionals Quantals
  524.    wt: 1:   6 Multiplication of Mixed Numbers
  525.    wt: 1:   6 Multiplication Algebraically Take II
  526.    wt: 1:   5 Equivalent Fractions
  527.    wt: 1:   4 Fraction Multiplication
  528.    wt: 1:   3 Unit fraction of a fraction
  529.    wt: 1:   2 Unit Fraction Multiplication
  530.    wt: 1:   1 What is a fraction Take II
  531.    wt: 1:   1 What is a fraction
  532.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  533.    wt: 1:   D Remainders Modulo 11 Pair Rule
  534.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  535.    wt: 1:   B Integer Long Division Multiple Choices
  536.    wt: 1:   A Associative Law Theorectical Note
  537.    wt: 1:   13 Subtraction with Additive Inverse
  538.    wt: 1:   12 Adding Integers More Examples
  539.    wt: 1:   8 Multiplication by Signed Numbers Integers
  540.    wt: 1:   7 Multiplication by Signs
  541.    wt: 1:   6 Multiplication by Natural Numbers
  542.    wt: 1:   5 Zero Movement and Additive Inverses
  543.    wt: 1:   4 Adding Movements wiht opposite directions
  544.    wt: 1:   3 Adding Movements with same direction
  545.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  546.    wt: 1:   1 Integers as Coordinates
  547.    wt: 1:   20 Uniqueness of Prime Factorization
  548.    wt: 1:   18 video Count Factors given Prime Factorization
  549.    wt: 1:   17 Identify and Count Factors using Primes
  550.    wt: 1:   15 video Factors of 20 using Prime Factorization
  551.    wt: 1:   14 video Factors of 24 Take II
  552.    wt: 1:   13 video Factors of 24 using prime
  553.    wt: 1:   12 LCD GCD and LCM using Primes
  554.    wt: 1:   11 Efficient Square Rule Use
  555.    wt: 1:   10 video Prime Factorization upto 23 squared
  556.    wt: 1:   7 Calculator Usage Notes and Cautions
  557.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  558.    wt: 1:   5 Prime Factorization and a Square Rule
  559.    wt: 1:   4 video Prime Factorization Introduction
  560.    wt: 1:   2 Prime and Composites less than 16
  561.    wt: 1:   1 video how Products are bigger than factor
  562.    wt: 1:   11 Place Value SI Standard International way
  563.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  564.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  565.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  566.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  567.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  568.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  569.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  570.    wt: 1:   Quick history of numbers and algebra
  571.    wt: 1:   Expression Evaluation how to show work
  572.    wt: 1:   The 20 Times Table
  573.    wt: 1:   About folder contents
  574.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  575.    wt: 1:   5 Conversion Arithmetic
  576.    wt: 1:   A Chain Rule Real Player video examples
  577.    wt: 1:   36 Cube root derivative animated
  578.    wt: 1:   29 Chain Rule Optional Reading
  579.    wt: 1:   28 Chain Rule Preparation for a Proof
  580.    wt: 1:   22 Chain Rule for polynomials
  581.    wt: 1:   21 Chain Rule for powers
  582.    wt: 1:   20 Chain Rule for Pulley Systems
  583.    wt: 1:   11 Quotient rule
  584.    wt: 1:   10 Power rule for negative integers
  585.    wt: 1:   9 Reciprocal rule
  586.    wt: 1:   3 Motivation for Limit Definition Take 2
  587.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  588.    wt: 1:   9 Limits Continuity and Composition
  589.    wt: 1:   3 Decimal insights for limits continuity convergence
  590.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  591.    wt: 1:   G.5 Motions With Bounded Velocities
  592.    wt: 1:   F.1 What Functions are Continuous
  593.    wt: 1:   PostScript For and Against Decimal Perspectives
  594.    wt: 1:   Fall 1983 Calculus Appetizer
  595.    wt: 1:   Foreword
  596.    wt: 1:   Appendix E. How To Study Mathematics and Why
  597.    wt: 1:   Appendix D. What to do in School and Why
  598.    wt: 1:   Appendix C. How to Read
  599.    wt: 1:   Appendix B. How To Learn
  600.    wt: 1:   Chapter 31 Direct and Indirect Reason
  601.    wt: 1:   Chapter 30 Truth Tables
  602.    wt: 1:   Chapter 28 Occurrence Tables
  603.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  604.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  605.    wt: 1:   Chapter 25. Mathematical Induction Examples
  606.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  607.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  608.    wt: 1:   Chapter 20. Degrees and Radians
  609.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  610.    wt: 1:   Chapter 16. Painless Theorem Proving
  611.    wt: 1:   Chapter 15. Solving Linear Equations
  612.    wt: 1:   Chapter 11. Why Shorthand
  613.    wt: 1:   Chapter 10 Describing and Changing Calculations
  614.    wt: 1:   Chapter 6 Change of Language
  615.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  616.    wt: 1:   Chapter 4 Longer Chains of Reason
  617.    wt: 1:   Chapter 3 Chains of Reason
  618.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  619.    wt: 1:   Postscript B Mathematics Education References
  620.    wt: 1:   Chapter 2 For and Against Mathematics
  621.    wt: 1:   Foreword
  622.    wt: 1:   Postscript C Consistency as a Tool for Reason
  623.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  624.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  625.    wt: 1:   Foreword
  626.    wt: 1:   R Why Learn Mathematics Skills
  627.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  628.    wt: 1:   O On Learning Mathematics and Science
  629.    wt: 1:   L Skills with take home value
  630.    wt: 1:   N Improving Marks on Tests and Finals
  631.    wt: 1:   J. More on written work and showing skill
  632.    wt: 1:   H more Routine to non routine problem solving
  633.    wt: 1:   H Jigsaw puzzles and problem solving
  634.    wt: 1:   F. The student teacher tutor feedback loop
  635.    wt: 1:   E. When and how to correct errors
  636.    wt: 1:   D. Check work a must with a caution
  637.    wt: 1:   C. Domino effect of being careful
  638.    wt: 1:   B. Domino effect of errors
  639.    wt: 1:   A. Skill has to be seen to believed
  640.    wt: 1:   How to Build Skills and Confidence
  641.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  642.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  643.    wt: 1:   Chapter 1 Arithmetic
  644.    wt: 1:   7 Games and Activities for Instruction
  645.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  646.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  647.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  648.    wt: 1:   The Math Forum and Site Content
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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