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 Proportionality Backwards and Forwards/
  5.    wt: 3:   8 Unifying Theme For Algebra/
  6.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  7.    wt: 3:   2 Formula Forward Use Evaluation/
  8.    wt: 2:   9 Lines and Slopes Take 2 with tangent function/
  9.    wt: 2:   10 Examples of Algebraic Reasoning/
  10.    wt: 2:   9 Combinatorics Trees Tables and Products/
  11.    wt: 2:   Volume 2 Three Skills For Algebra/
  12.    wt: 2:   Mathematics Skill Development Framework/
  13.    wt: 1:   Archives/
  14.    wt: 1:   Direct Current Electric Circuits/
  15.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  16.    wt: 1:   4 Functions/
  17.    wt: 1:   3 Quadratics Geometrically/
  18.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  19.    wt: 1:   1 Five Polynomial Operations/
  20.    wt: 1:   More Algebra/
  21.    wt: 1:   B Real Numbers Extrinsic Development/
  22.    wt: 1:   A Origins of Counting and Figuring Methods/
  23.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  24.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  25.    wt: 1:   5 Real Numbers/
  26.    wt: 1:   4 Computation Rules and Function Notation/
  27.    wt: 1:   Step 4 Gaussian Elimination/
  28.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  29.    wt: 1:   Step 1 Stick diagram and fractions/
  30.    wt: 1:   3 Solving Linear Equations/
  31.    wt: 1:   1 Working With Sets/
  32.    wt: 1:   Algebra Starter Lessons/
  33.    wt: 1:   Work and Study Tips/

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278 matches:

  1.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  2.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  3.    wt: 3:   19 Remainder Arithmetic Rule of 9 for checking sums III
  4.    wt: 2:   Applied Maths Program14092009 POMME variant
  5.    wt: 2:   Education Reform Inconsistencies
  6.    wt: 2:   geometric implications for algebra
  7.    wt: 2:   three goals for Mathematics Education
  8.    wt: 2:   formal or informal peer review
  9.    wt: 2:   Four ways to improve education reform
  10.    wt: 2:   Prequel In For A Penny In For A Pound
  11.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  12.    wt: 2:   5 Function notation for geometric transformations
  13.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  14.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  15.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  16.    wt: 2:   9 motivation for name arcsin
  17.    wt: 2:   29 secant cosecant and cotangent for acute angles
  18.    wt: 2:   26 Formulas for products of sines and cosines
  19.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  20.    wt: 2:   17E Trig Formulas for dot and cross Products
  21.    wt: 2:   17D cis formulas for sine cosines and tangent
  22.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  23.    wt: 2:   13 Trig Formulas for dot and cross Products
  24.    wt: 2:   12 cis formulas for sine cosines and tangent
  25.    wt: 2:   4 Equations for lines three forms
  26.    wt: 2:   9 Coordinates for Regions in Space
  27.    wt: 2:   Formula Usage Show Work Format
  28.    wt: 2:   1 Written work formats for developing and showing skill
  29.    wt: 2:   1 Three Skills For Algebra
  30.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  31.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  32.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  33.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  34.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  35.    wt: 2:   9 video Prime Factorization upto 19 squared
  36.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  37.    wt: 2:   38 Formulas and derivatives for powers and roots
  38.    wt: 2:   19 Chain Rule for linear functions
  39.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  40.    wt: 2:   Postscript For Better Performance
  41.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  42.    wt: 2:   Chapter 18. Rules for Algebra
  43.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  44.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  45.    wt: 2:   Chapter 8 Three Skills For Algebra
  46.    wt: 2:   G. Written work formats for developing and showing skill
  47.    wt: 1:   K LAMP Musings Science Education
  48.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  49.    wt: 1:   Ramblings Introduction Algebra Essay
  50.    wt: 1:   Skills Chapter 3 Algebra
  51.    wt: 1:   9 combinatorics probability sets
  52.    wt: 1:   4 algebra
  53.    wt: 1:   three goals to set for students
  54.    wt: 1:   permissions for teachers
  55.    wt: 1:   activities for students
  56.    wt: 1:   links Education Resources online
  57.    wt: 1:   Mathematics Education Professors
  58.    wt: 1:   modern education
  59.    wt: 1:   talk the algebra talk
  60.    wt: 1:   teaching tutoring algebraic reason
  61.    wt: 1:   Lessening Algebra Difficulties
  62.    wt: 1:   the trouble with algebra
  63.    wt: 1:   04 29 New Mathematics Curriculum
  64.    wt: 1:   02 21 words for teachers
  65.    wt: 1:   02 20 mathematics education references
  66.    wt: 1:   three aims for mathematics students
  67.    wt: 1:   standards for course material
  68.    wt: 1:   Education in mathematics science and technology
  69.    wt: 1:   need for a mixed mathematics curriculum
  70.    wt: 1:   education an empirical art
  71.    wt: 1:   fairness and inductive principles for instruction
  72.    wt: 1:   words for mathematics instructor
  73.    wt: 1:   chapitre 04 09 Regles accidentelles
  74.    wt: 1:   4 Energy Power Heat09
  75.    wt: 1:   C Electromotive force conventional current02
  76.    wt: 1:   B Electromotive force conventional current01
  77.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  78.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  79.    wt: 1:   24 Standards For Skill Develoment Take II
  80.    wt: 1:   24 Standards For Skill Develoment
  81.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  82.    wt: 1:   17 Math Booklets for children and young teenagers
  83.    wt: 1:   15 Counting For Parents
  84.    wt: 1:   12 Goals and Objectives For Mathematics
  85.    wt: 1:   11 Help and Defend Your Child or Teens Education
  86.    wt: 1:   10 Ends values for work study instruction
  87.    wt: 1:   9 Streaming by Student Cooperation
  88.    wt: 1:   5 Patience Please for Yourself and Your Charges
  89.    wt: 1:   4 Learning Takes Time and Effort
  90.    wt: 1:   3 Preparing for Science Studies
  91.    wt: 1:   Ages 9 to 10
  92.    wt: 1:   Ages 8 to 9
  93.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  94.    wt: 1:   19 Horizontal line rule and method
  95.    wt: 1:   9 Set theory term relation possible origins
  96.    wt: 1:   6 Set Existence Formation and Notation
  97.    wt: 1:   3 Formula or function graphing exercise
  98.    wt: 1:   2 Algebraic use of function notation
  99.    wt: 1:   Introduction Reading Guide
  100.    wt: 1:   9 quadratics physical and further context
  101.    wt: 1:   8 quadratics backward use of various formulas
  102.    wt: 1:   7 quadratic formulla derivation
  103.    wt: 1:   8 Notes for instructors or tutors
  104.    wt: 1:   Rewriting algebraic substitution as function substitutions
  105.    wt: 1:   12 motivation for term arctan
  106.    wt: 1:   4 possible motivation for term arccos
  107.    wt: 1:   9 Summary Degrees to Radians and back
  108.    wt: 1:   9 Head to Tail Coordinate View
  109.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  110.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  111.    wt: 1:   9 Straight Lines through Origin Equations
  112.    wt: 1:   8 Straight Lines Equation for vertical
  113.    wt: 1:   17 tangent function angle sum formulas
  114.    wt: 1:   25 tangent double angle formula Slope connection
  115.    wt: 1:   24 tangent Angle Difference Formula
  116.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  117.    wt: 1:   21 sine and cosine Half Angle Formulas
  118.    wt: 1:   20 sine and cosine Double Angle Formulas
  119.    wt: 1:   17C sine and cosine double triple angle formulas
  120.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  121.    wt: 1:   12 Graph of tangent function for one period
  122.    wt: 1:   9 Graphs of sine and cosine over one period
  123.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  124.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  125.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  126.    wt: 1:   19 N th Roots of Unity
  127.    wt: 1:   11 sine and cosine double triple angle formulas
  128.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  129.    wt: 1:   9 The complex number valued trig function cis
  130.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  131.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  132.    wt: 1:   9 Similarity of Triangles Usual Criteria
  133.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  134.    wt: 1:   8 Mid Point Formula
  135.    wt: 1:   5 Algebraic View of Slopes
  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:   19 Signed Multiples of Vectors
  145.    wt: 1:   9 Division with Digits after Decimal Point
  146.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  147.    wt: 1:   6 Column Methods for Decimal Multiplication
  148.    wt: 1:   5 Distributive Law for Whole Numbers
  149.    wt: 1:   4 Commutative Law Groups Counting Form
  150.    wt: 1:   3 Inequalities Algebraically
  151.    wt: 1:   2 Algebraic View
  152.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  153.    wt: 1:   6 Compound Interest Forward and Backwards
  154.    wt: 1:   5 Triangle Area Formula Backwards
  155.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  156.    wt: 1:   5 Equality in Algebra
  157.    wt: 1:   3 Product Axioms Two Forms
  158.    wt: 1:   2 More and Less Than for Counts and Measures
  159.    wt: 1:   8 Coordinates for Maps and Planes
  160.    wt: 1:   3 Geometric Formulas and Function Notation
  161.    wt: 1:   1 Formulas Dependence and Function Notation
  162.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  163.    wt: 1:   6 Algebraic Solution Example
  164.    wt: 1:   5 Algebraic Solutions Introduction
  165.    wt: 1:   9 Three Examples
  166.    wt: 1:   Using Letters for Physical Quantities
  167.    wt: 1:   13 Naming Identifying Formulas with Words
  168.    wt: 1:   9 Volume of Cone
  169.    wt: 1:   8 Compound Interest Formula Evaluation
  170.    wt: 1:   7 Compound Interest Formula Introduction
  171.    wt: 1:   5 Box Volume Formula Example
  172.    wt: 1:   4 Circle Area Formula Example
  173.    wt: 1:   3 Triangle Area Formula Example
  174.    wt: 1:   2 Another Rectangle Area Formula Example
  175.    wt: 1:   9 Sets in Probability and Statistics
  176.    wt: 1:   4 A Brief Story of numbers and algebra
  177.    wt: 1:   arithmetic videos Real Player Format
  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:   13 Fraction Comparison Algebraic View
  189.    wt: 1:   11 Simplification an Algebraic View
  190.    wt: 1:   9 Improper Fractions and Mixed Numbers
  191.    wt: 1:   6 Multiplication Algebraically Take II
  192.    wt: 1:   11 Adding Integers Formulas and Examples
  193.    wt: 1:   10 Integer Multiplication Formulas
  194.    wt: 1:   9 Multiplying Integers
  195.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  196.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  197.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  198.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  199.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  200.    wt: 1:   19 video Prime Factorization Unique
  201.    wt: 1:   16 video Factors of 980 using prime
  202.    wt: 1:   8 video Prime Factorization upto 19
  203.    wt: 1:   3 video Primes and Composites from 9 times table
  204.    wt: 1:   Long Division forwards and backwards Example 3
  205.    wt: 1:   Long Division forwards and backwards Example 2
  206.    wt: 1:   Long Division forwards and backwards Example 1
  207.    wt: 1:   9 Why Long Division Works Take II
  208.    wt: 1:   A Elementary Basis for Multiplication Methods
  209.    wt: 1:   9 22 Minute Subtraction Review Video
  210.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  211.    wt: 1:   5 A Tip for Efficent Subtraction
  212.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  213.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  214.    wt: 1:   Quick history of numbers and algebra
  215.    wt: 1:   Formula Evaluation how to show work
  216.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  217.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  218.    wt: 1:   29 Chain Rule Optional Reading
  219.    wt: 1:   28 Chain Rule Preparation for a Proof
  220.    wt: 1:   22 Chain Rule for polynomials
  221.    wt: 1:   21 Chain Rule for powers
  222.    wt: 1:   20 Chain Rule for Pulley Systems
  223.    wt: 1:   10 Power rule for negative integers
  224.    wt: 1:   9 Reciprocal rule
  225.    wt: 1:   3 Motivation for Limit Definition Take 2
  226.    wt: 1:   2 Motivation for Limit Definition Take 1
  227.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  228.    wt: 1:   9 Limits Continuity and Composition
  229.    wt: 1:   3 Decimal insights for limits continuity convergence
  230.    wt: 1:   2 Algebraic codification
  231.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  232.    wt: 1:   E2 Algebraic Properties of Limits
  233.    wt: 1:   PostScript For and Against Decimal Perspectives
  234.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  235.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  236.    wt: 1:   Chapter 9 About First Courses in Calculus
  237.    wt: 1:   Fall 1983 Calculus Appetizer
  238.    wt: 1:   Foreword
  239.    wt: 1:   Postscript More on Better Performance
  240.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  241.    wt: 1:   Chapter 23. Notation For Sums
  242.    wt: 1:   Chapter 21. Third Reading Guide
  243.    wt: 1:   Chapter 19. Functions and Sets
  244.    wt: 1:   Chapter 13. Second Reading Guide
  245.    wt: 1:   Chapter 12. Shorthand Usage Guide
  246.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  247.    wt: 1:   Solutions For Arithmetic Exercises
  248.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  249.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  250.    wt: 1:   Foreword
  251.    wt: 1:   Postscript B Mathematics Education References
  252.    wt: 1:   Chapter 9 The Two Ends
  253.    wt: 1:   Chapter 3 Algebra Difficulties
  254.    wt: 1:   Chapter 2 For and Against Mathematics
  255.    wt: 1:   Foreword
  256.    wt: 1:   Postscript C Consistency as a Tool for Reason
  257.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  258.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  259.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  260.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  261.    wt: 1:   Foreword
  262.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  263.    wt: 1:   S Adding words to algebra
  264.    wt: 1:   N Mathematics Prepare for College Studies
  265.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  266.    wt: 1:   Chapter 6 More Algebra and Geometry
  267.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  268.    wt: 1:   Chapter 3 Algebra Starter Lessons
  269.    wt: 1:   7 Games and Activities for Instruction
  270.    wt: 1:   Mathematics Education References
  271.    wt: 1:   Mathematics Education References
  272.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  273.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  274.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  275.    wt: 1:   More Algebra and Slope based Calculus Preview
  276.    wt: 1:   Systematic Algebra Skill Development Missing Links
  277.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  278.    wt: 1:   The Math Forum and Site Content

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  1.    wt: 6:   9 combinatorics probability sets
  2.    wt: 6:   Applied Maths Program14092009 POMME variant
  3.    wt: 6:   Education Reform Inconsistencies
  4.    wt: 6:   geometric implications for algebra
  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:   9 Circle Area and Perimeter Formula Backwards Forwards
  10.    wt: 6:   Postscript Unifying Theme A Fourth Skill For Algebra
  11.    wt: 5:   4 algebra
  12.    wt: 5:   three goals to set for students
  13.    wt: 5:   permissions for teachers
  14.    wt: 5:   activities for students
  15.    wt: 5:   links Education Resources online
  16.    wt: 5:   Mathematics Education Professors
  17.    wt: 5:   modern education
  18.    wt: 5:   mathematics in context
  19.    wt: 5:   Secondary One Mathematics
  20.    wt: 5:   talk the algebra talk
  21.    wt: 5:   teaching tutoring algebraic reason
  22.    wt: 5:   Lessening Algebra Difficulties
  23.    wt: 5:   the trouble with algebra
  24.    wt: 5:   04 29 New Mathematics Curriculum
  25.    wt: 5:   02 21 words for teachers
  26.    wt: 5:   02 20 mathematics education references
  27.    wt: 5:   three aims for mathematics students
  28.    wt: 5:   standards for course material
  29.    wt: 5:   Education in mathematics science and technology
  30.    wt: 5:   How to be a better instructor
  31.    wt: 5:   need for a mixed mathematics curriculum
  32.    wt: 5:   education an empirical art
  33.    wt: 5:   fairness and inductive principles for instruction
  34.    wt: 5:   words for mathematics instructor
  35.    wt: 5:   9 Formulas for Real Exponents with Logarithms
  36.    wt: 5:   musings do not puiblish real numbers
  37.    wt: 5:   1 Written work formats for developing and showing skill
  38.    wt: 5:   arithmetic videos Real Player Format
  39.    wt: 5:   1 Links to Online Resources Elsewhere Take 1
  40.    wt: 4:   Appendix 2 primary school Arithmetic 01
  41.    wt: 4:   Appendix 1 primary and preschool mathematic
  42.    wt: 4:   K LAMP Musings Science Education
  43.    wt: 4:   C LAMP Introduction Culture in Mathematics Education
  44.    wt: 4:   Ramblings Introduction Algebra Essay
  45.    wt: 4:   Skills Chapter 3 Algebra
  46.    wt: 4:   11 pure mathematics
  47.    wt: 4:   10 statistics
  48.    wt: 4:   8 analytic geometry etc
  49.    wt: 4:   7 logic review and decimals an odd combination
  50.    wt: 4:   6 polynomials etc
  51.    wt: 4:   5 logarithms and exponentials etc
  52.    wt: 4:   3 Euclidean Geometry Leanly
  53.    wt: 4:   2 arithmetic with signed numbers
  54.    wt: 4:   1 arithmetic with unsigned numbers
  55.    wt: 4:   What is POMME
  56.    wt: 4:   why bother
  57.    wt: 4:   which way to go
  58.    wt: 4:   website reviews
  59.    wt: 4:   Teach the teachers plus goals
  60.    wt: 4:   Math Ed if it must be short make it lean effective
  61.    wt: 4:   site origins
  62.    wt: 4:   site eurekas
  63.    wt: 4:   About site lesson plans
  64.    wt: 4:   key notes and themes
  65.    wt: 4:   teacher certification
  66.    wt: 4:   learning takes time
  67.    wt: 4:   grouping students according to ability
  68.    wt: 4:   what should be learnt and When
  69.    wt: 4:   Postscript 2007 01 10
  70.    wt: 4:   five decades make a difference
  71.    wt: 4:   Maps Plans Drawings
  72.    wt: 4:   how letters appear
  73.    wt: 4:   Secondary Three Mathematics
  74.    wt: 4:   Secondary Two Mathematics
  75.    wt: 4:   three difficulties
  76.    wt: 4:   teaching tips
  77.    wt: 4:   What to Tell Students
  78.    wt: 4:   mathematics curriculum shifts
  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:   8 Straight Lines Equation for vertical
  90.    wt: 4:   2 Algebraic View
  91.    wt: 4:   8 Pythagorean Relation Forwards Backwards
  92.    wt: 4:   6 Compound Interest Forward and Backwards
  93.    wt: 4:   5 Triangle Area Formula Backwards
  94.    wt: 4:   4 Rectangle Area and Like Formulas Backwards
  95.    wt: 4:   6 Algebraic Solution Example
  96.    wt: 4:   5 Algebraic Solutions Introduction
  97.    wt: 4:   13 Naming Identifying Formulas with Words
  98.    wt: 4:   9 Volume of Cone
  99.    wt: 4:   8 Compound Interest Formula Evaluation
  100.    wt: 4:   7 Compound Interest Formula Introduction
  101.    wt: 4:   5 Box Volume Formula Example
  102.    wt: 4:   4 Circle Area Formula Example
  103.    wt: 4:   3 Triangle Area Formula Example
  104.    wt: 4:   2 Another Rectangle Area Formula Example
  105.    wt: 4:   A Related lessons in Volume 3
  106.    wt: 4:   Postscript One Sided and Intermediate Value Theorems
  107.    wt: 4:   Postscript For Better Performance
  108.    wt: 4:   Appendix A. Reading Guide For Next Appendices
  109.    wt: 4:   Chapter 29 Contrapositive and Vacuously True Implications
  110.    wt: 4:   Chapter 19. Functions and Sets
  111.    wt: 4:   Chapter 18. Rules for Algebra
  112.    wt: 4:   Chapter 14. Forward and Backward Use of a Formula
  113.    wt: 4:   Chapter 9 Talking about Numbers or Quantities
  114.    wt: 4:   Chapter 8 Three Skills For Algebra
  115.    wt: 4:   Mathematics Education References
  116.    wt: 4:   Mathematics Education References
  117.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  118.    wt: 3:   J LAMP Introduction Extrinsic Origins
  119.    wt: 3:   I LAMP Introduction Study Habits
  120.    wt: 3:   H LAMP Introduction Instructional Concepts
  121.    wt: 3:   G LAMP Introduction Problem Solving Skills
  122.    wt: 3:   F LAMP Introduction Prerequisites
  123.    wt: 3:   E LAMP Introduction Modern Mathematics
  124.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  125.    wt: 3:   A Introduction Objectives
  126.    wt: 3:   Skills Chapter 5 Calculus
  127.    wt: 3:   Skills Chapter 4 Logic
  128.    wt: 3:   Ramblings Extrinsic numbers theory
  129.    wt: 3:   Skills Chapter 2 Geometry
  130.    wt: 3:   Skills Chapter 1 Arithmetic
  131.    wt: 3:   Skills Chapter 0 Introduction
  132.    wt: 3:   4 Energy Power Heat09
  133.    wt: 3:   19 Horizontal line rule and method
  134.    wt: 3:   9 Set theory term relation possible origins
  135.    wt: 3:   5 Function notation for geometric transformations
  136.    wt: 3:   8 Formulas for Fractional Exponents with Logarithms
  137.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  138.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  139.    wt: 3:   9 Straight Lines through Origin Equations
  140.    wt: 3:   1 Straight Lines Slope Concept
  141.    wt: 3:   3 Inequalities Algebraically
  142.    wt: 3:   5 Proportionality in Equivalent Fractions
  143.    wt: 3:   4 Rates Ratios and Proporitionality
  144.    wt: 3:   3 Proportionality Examples
  145.    wt: 3:   1 What is Proportionality
  146.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  147.    wt: 3:   3 Linear Equation Literal Solution More
  148.    wt: 3:   2 Linear Equation Literal Solution
  149.    wt: 3:   1 Changing Calculations
  150.    wt: 3:   9 Coordinates for Regions in Space
  151.    wt: 3:   Simple Exercises
  152.    wt: 3:   4 Four Examples Fractional Coefficients
  153.    wt: 3:   3 Four Examples
  154.    wt: 3:   2 Three Examples
  155.    wt: 3:   1 Proper Equal Sign Usage
  156.    wt: 3:   9 Three Examples
  157.    wt: 3:   Formula Usage Show Work Format
  158.    wt: 3:   12 Cone Cylinder Sphere Lesson Idea
  159.    wt: 3:   11 Volume of Sphere
  160.    wt: 3:   10 Volume of Pyramid
  161.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  162.    wt: 3:   1 Three Skills For Algebra
  163.    wt: 3:   5 Counting with Tables Trees Product Rule Take II
  164.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  165.    wt: 3:   19 Remainder Arithmetic Rule of 9 for checking sums III
  166.    wt: 3:   9 video Prime Factorization upto 19 squared
  167.    wt: 3:   38 Formulas and derivatives for powers and roots
  168.    wt: 3:   Postscript More on Better Performance
  169.    wt: 3:   Chapter 23. Notation For Sums
  170.    wt: 3:   Chapter 21. Third Reading Guide
  171.    wt: 3:   Chapter 13. Second Reading Guide
  172.    wt: 3:   Chapter 12. Shorthand Usage Guide
  173.    wt: 3:   Postscript What is a Variable
  174.    wt: 3:   Solutions For Arithmetic Exercises
  175.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  176.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  177.    wt: 3:   Foreword
  178.    wt: 3:   S Adding words to algebra
  179.    wt: 3:   G. Written work formats for developing and showing skill
  180.    wt: 3:   Helping the Blind in Logic and Mathematics
  181.    wt: 3:   Multiple Ways to Improve Mathematics Skill Development
  182.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  183.    wt: 3:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  184.    wt: 3:   More Algebra and Slope based Calculus Preview
  185.    wt: 3:   Systematic Algebra Skill Development Missing Links
  186.    wt: 2:   1 Conductance Resistance Duality01
  187.    wt: 2:   H Series Circuit02
  188.    wt: 2:   C Electromotive force conventional current02
  189.    wt: 2:   B Electromotive force conventional current01
  190.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  191.    wt: 2:   9 Streaming by Student Cooperation
  192.    wt: 2:   Ages 9 to 10
  193.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  194.    wt: 2:   sign monoticity analysis example 4
  195.    wt: 2:   sign monoticity analysis example 3
  196.    wt: 2:   sign monoticity analysis example 2
  197.    wt: 2:   sign monoticity analysis example 1
  198.    wt: 2:   6 Set Existence Formation and Notation
  199.    wt: 2:   3 Formula or function graphing exercise
  200.    wt: 2:   2 Algebraic use of function notation
  201.    wt: 2:   Introduction Reading Guide
  202.    wt: 2:   9 quadratics physical and further context
  203.    wt: 2:   8 quadratics backward use of various formulas
  204.    wt: 2:   7 quadratic formulla derivation
  205.    wt: 2:   8 Notes for instructors or tutors
  206.    wt: 2:   Rewriting algebraic substitution as function substitutions
  207.    wt: 2:   9 motivation for name arcsin
  208.    wt: 2:   8 Radian Measures of Common Angles
  209.    wt: 2:   9 Head to Tail Coordinate View
  210.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  211.    wt: 2:   C Straight Lines Slope from Coordinates
  212.    wt: 2:   B Straight Line Slope Scaling Properties More
  213.    wt: 2:   A Straight Line Slope Scaling Properties
  214.    wt: 2:   14 Straight Lines Equations General Case
  215.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  216.    wt: 2:   12 Straight Lines Graphing mx plus b
  217.    wt: 2:   11 Straight Lines Graphing y=mx
  218.    wt: 2:   10 Straight Lines through Origin Equations More
  219.    wt: 2:   7 Tangent Function is odd on this domain
  220.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  221.    wt: 2:   5 Tangent Function Graph
  222.    wt: 2:   4 Tangent Function Properties
  223.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  224.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  225.    wt: 2:   29 secant cosecant and cotangent for acute angles
  226.    wt: 2:   26 Formulas for products of sines and cosines
  227.    wt: 2:   20 sine and cosine Double Angle Formulas
  228.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  229.    wt: 2:   17E Trig Formulas for dot and cross Products
  230.    wt: 2:   17D cis formulas for sine cosines and tangent
  231.    wt: 2:   12 Graph of tangent function for one period
  232.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  233.    wt: 2:   2 Quadrant I reference Angles
  234.    wt: 2:   1 Unit Points Reflections Rotations
  235.    wt: 2:   19 N th Roots of Unity
  236.    wt: 2:   13 Trig Formulas for dot and cross Products
  237.    wt: 2:   12 cis formulas for sine cosines and tangent
  238.    wt: 2:   9 The complex number valued trig function cis
  239.    wt: 2:   9 Similarity of Triangles Usual Criteria
  240.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  241.    wt: 2:   4 Equations for lines three forms
  242.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  243.    wt: 2:   19 Right Triangle Similarity
  244.    wt: 2:   9 Construction of a right bisector
  245.    wt: 2:   A Signed Number Arithmetic Review
  246.    wt: 2:   19 Signed Multiples of Vectors
  247.    wt: 2:   9 Division with Digits after Decimal Point
  248.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  249.    wt: 2:   E Long Division Methods more
  250.    wt: 2:   D Long Division Methods
  251.    wt: 2:   C Three Decimal Subtraction Methods
  252.    wt: 2:   B Decimal Comparison and Subtraction
  253.    wt: 2:   A Decimal Addition Columm Methods
  254.    wt: 2:   6 Column Methods for Decimal Multiplication
  255.    wt: 2:   5 Distributive Law for Whole Numbers
  256.    wt: 2:   4 Commutative Law Groups Counting Form
  257.    wt: 2:   5 Areas of Rectangles Revisited
  258.    wt: 2:   4 Fraction Operations Axiomatic Development
  259.    wt: 2:   2 Fraction Operations Physical Development
  260.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  261.    wt: 2:   5 Equality in Algebra
  262.    wt: 2:   3 Product Axioms Two Forms
  263.    wt: 2:   2 More and Less Than for Counts and Measures
  264.    wt: 2:   8 Coordinates for Maps and Planes
  265.    wt: 2:   3 Geometric Formulas and Function Notation
  266.    wt: 2:   1 Formulas Dependence and Function Notation
  267.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  268.    wt: 2:   Using Letters for Physical Quantities
  269.    wt: 2:   9 Sets in Probability and Statistics
  270.    wt: 2:   4 A Brief Story of numbers and algebra
  271.    wt: 2:   4 Counting with Trees Product Rule Take I
  272.    wt: 2:   3 Counting with Tables and Trees II
  273.    wt: 2:   2 Counting with Tables and Trees I
  274.    wt: 2:   1 Counting and Counting Methods I
  275.    wt: 2:   9 subtracting signed numbers
  276.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  277.    wt: 2:   9 Multiplying Integers
  278.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  279.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  280.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  281.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  282.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  283.    wt: 2:   19 video Prime Factorization Unique
  284.    wt: 2:   Long Division forwards and backwards Example 1
  285.    wt: 2:   9 Why Long Division Works Take II
  286.    wt: 2:   9 22 Minute Subtraction Review Video
  287.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  288.    wt: 2:   19 Chain Rule for linear functions
  289.    wt: 2:   2 Motivation for Limit Definition Take 1
  290.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  291.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  292.    wt: 2:   Chapter 9 About First Courses in Calculus
  293.    wt: 2:   Appendix E. How To Study Mathematics and Why
  294.    wt: 2:   Appendix D. What to do in School and Why
  295.    wt: 2:   Appendix C. How to Read
  296.    wt: 2:   Appendix B. How To Learn
  297.    wt: 2:   Chapter 31 Direct and Indirect Reason
  298.    wt: 2:   Chapter 30 Truth Tables
  299.    wt: 2:   Chapter 28 Occurrence Tables
  300.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  301.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  302.    wt: 2:   Chapter 25. Mathematical Induction Examples
  303.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  304.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  305.    wt: 2:   Chapter 20. Degrees and Radians
  306.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  307.    wt: 2:   Chapter 16. Painless Theorem Proving
  308.    wt: 2:   Chapter 15. Solving Linear Equations
  309.    wt: 2:   Chapter 11. Why Shorthand
  310.    wt: 2:   Chapter 10 Describing and Changing Calculations
  311.    wt: 2:   Chapter 6 Change of Language
  312.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  313.    wt: 2:   Chapter 4 Longer Chains of Reason
  314.    wt: 2:   Chapter 3 Chains of Reason
  315.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  316.    wt: 2:   Chapter 9 The Two Ends
  317.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  318.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  319.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  320.    wt: 2:   N Mathematics Prepare for College Studies
  321.    wt: 2:   I. Logic and language skills
  322.    wt: 2:   Implementation Notes
  323.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  324.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  325.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  326.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  327.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  328.    wt: 2:   Which Way To Go
  329.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  330.    wt: 1:   chapitre 04 09 Regles accidentelles
  331.    wt: 1:   3 Energy Power Heat08
  332.    wt: 1:   2 Energy Power Heat07
  333.    wt: 1:   1 Energy Power Heat06
  334.    wt: 1:   E Energy Power05
  335.    wt: 1:   D Energy Power04
  336.    wt: 1:   C Energy Power03
  337.    wt: 1:   B Energy Power02
  338.    wt: 1:   A Energy Power01
  339.    wt: 1:   2 Conductance Resistance Duality02
  340.    wt: 1:   F Wire Resistance Calculation04
  341.    wt: 1:   E Wire Resistance Calculation03
  342.    wt: 1:   D Wire Resistance Calculation02
  343.    wt: 1:   C Wire Resistance Calculation01
  344.    wt: 1:   B Wire Resistance Qualitative02
  345.    wt: 1:   A Wire Resistance Qualitative01
  346.    wt: 1:   3 Like resistors in parallel
  347.    wt: 1:   2 Unlike resistors in parallel01
  348.    wt: 1:   1 Like resistors in series
  349.    wt: 1:   G Series Circuit01
  350.    wt: 1:   F Unlike Resistors in Series
  351.    wt: 1:   E Kirchoffs Second Law
  352.    wt: 1:   D Kirchoff First Law
  353.    wt: 1:   A Circuit Elements
  354.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  355.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  356.    wt: 1:   24 Standards For Skill Develoment Take II
  357.    wt: 1:   24 Standards For Skill Develoment
  358.    wt: 1:   17 Math Booklets for children and young teenagers
  359.    wt: 1:   15 Counting For Parents
  360.    wt: 1:   12 Goals and Objectives For Mathematics
  361.    wt: 1:   11 Help and Defend Your Child or Teens Education
  362.    wt: 1:   10 Ends values for work study instruction
  363.    wt: 1:   5 Patience Please for Yourself and Your Charges
  364.    wt: 1:   4 Learning Takes Time and Effort
  365.    wt: 1:   3 Preparing for Science Studies
  366.    wt: 1:   Ages 8 to 9
  367.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  368.    wt: 1:   26 Function definitions done and coming
  369.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  370.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  371.    wt: 1:   23 Inverse Functions
  372.    wt: 1:   22 Square Root function graphically
  373.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  374.    wt: 1:   20 Interchanging coordinates a reflection
  375.    wt: 1:   18 Vertical Line Rule and Method
  376.    wt: 1:   17 Function maxima minima and their location
  377.    wt: 1:   16 Increasing or decreasing on intervals
  378.    wt: 1:   15 Sign analysis of functions
  379.    wt: 1:   14 Surjections Injections Bijections
  380.    wt: 1:   13 From one to one to many to one
  381.    wt: 1:   12 Function Domain Recognition Exercises
  382.    wt: 1:   11 Function Domain Range Source and Targets
  383.    wt: 1:   10 Interval Notation
  384.    wt: 1:   8 Set view of relations and functions
  385.    wt: 1:   7 Functions with finite domains
  386.    wt: 1:   4 Function notation in and beyond mathematics
  387.    wt: 1:   1 Geometric Introduction of Function Notation
  388.    wt: 1:   A Quadratics Summary
  389.    wt: 1:   10 quadratic exercises
  390.    wt: 1:   6 quadratics numerical approach
  391.    wt: 1:   5 quadratics completing the square
  392.    wt: 1:   4 quadratics difference of two squares
  393.    wt: 1:   3 quadratics factoring by inspection
  394.    wt: 1:   2 quadratics graphing in general
  395.    wt: 1:   1 quadratics graphing exercises
  396.    wt: 1:   Quadratics in 10 steps
  397.    wt: 1:   11 Growth and Decay in Biology
  398.    wt: 1:   10 Exponential Growth and Decay Models
  399.    wt: 1:   5 Natural Logarithm Calculator Exercises
  400.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  401.    wt: 1:   2 Square Root Simplification a prequel
  402.    wt: 1:   1 Calculator Starter Exercises
  403.    wt: 1:   7 Links Lessons Elsewhere
  404.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  405.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  406.    wt: 1:   4 Polynomials Long division linear divisor
  407.    wt: 1:   3 Polynomials Multiplication Addition
  408.    wt: 1:   2 Column Multiplication Method
  409.    wt: 1:   1 Polynomials Distributive Law
  410.    wt: 1:   12 motivation for term arctan
  411.    wt: 1:   4 possible motivation for term arccos
  412.    wt: 1:   9 Summary Degrees to Radians and back
  413.    wt: 1:   7 Radian Measures in special Triangles
  414.    wt: 1:   6 Radian Measure to Degrees
  415.    wt: 1:   5 Degrees to Radian Measure
  416.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  417.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  418.    wt: 1:   2 Radian Measure Numerical Value of one degree
  419.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  420.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  421.    wt: 1:   Straight Lines Intersection of
  422.    wt: 1:   17 tangent function angle sum formulas
  423.    wt: 1:   30 unit circle calculation of six trigonometric functions
  424.    wt: 1:   25 tangent double angle formula Slope connection
  425.    wt: 1:   24 tangent Angle Difference Formula
  426.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  427.    wt: 1:   21 sine and cosine Half Angle Formulas
  428.    wt: 1:   17C sine and cosine double triple angle formulas
  429.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  430.    wt: 1:   9 Graphs of sine and cosine over one period
  431.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  432.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  433.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  434.    wt: 1:   11 sine and cosine double triple angle formulas
  435.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  436.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  437.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  438.    wt: 1:   1 Early Concept of Like or Similar Shapes
  439.    wt: 1:   8 Mid Point Formula
  440.    wt: 1:   5 Algebraic View of Slopes
  441.    wt: 1:   3 Slope product for perpendicular lines
  442.    wt: 1:   2 point slope equation for a line
  443.    wt: 1:   13 Pythagorean spatial distance formulas
  444.    wt: 1:   10 Pythagorean plane distance formula
  445.    wt: 1:   PS H Distributive Law For Complex Numbers
  446.    wt: 1:   A Modular and Remainder Arithmetic
  447.    wt: 1:   26 More Less Greater Than Comparison
  448.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  449.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  450.    wt: 1:   23 Distributive Law Two Derivations
  451.    wt: 1:   22 Multiplication of Signed Numbers
  452.    wt: 1:   21 Addition of Multiples of a Single Vector
  453.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  454.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  455.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  456.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  457.    wt: 1:   15 Head to Tails in place Addition Associative
  458.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  459.    wt: 1:   13 Arrows and Vectors in a Plane
  460.    wt: 1:   12 Real Numbers Line Signed Coordinates
  461.    wt: 1:   11 Signed Number Addition and Addition Properties
  462.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  463.    wt: 1:   8 Division and Mulplication of Compound Fractions
  464.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  465.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  466.    wt: 1:   4 Location of Point in Decimal Addition
  467.    wt: 1:   3 Location of Point in Decimal Multiplication
  468.    wt: 1:   2 Counting Digits in Decimal Multiplication
  469.    wt: 1:   1 Fractions with Finite Decimal Expansions
  470.    wt: 1:   8 Column Multiplication Methods in General
  471.    wt: 1:   7 Decimals Multiplication Methods Examples
  472.    wt: 1:   3 Multiplicative Counting Skills Principles
  473.    wt: 1:   2 Combing Counts Addition Skills and Principles
  474.    wt: 1:   1 The Counting Origins of Numbers
  475.    wt: 1:   6 Equations and Systems Equivalent or Implied
  476.    wt: 1:   4 Subtraction and Division Axioms
  477.    wt: 1:   2 Addition and Multiplication Axioms
  478.    wt: 1:   1 Equivalent Computation Rules
  479.    wt: 1:   5 Greater More Less Than Signs in General
  480.    wt: 1:   4 Comparison of Negative Numbers
  481.    wt: 1:   3 More and Less Than with Unlike Signs
  482.    wt: 1:   1 Real Numbers Comparison
  483.    wt: 1:   16 Real Numbers Comparison
  484.    wt: 1:   15 Real Number Division
  485.    wt: 1:   14 Real Number Multiplication
  486.    wt: 1:   13 Real Number Subtraction
  487.    wt: 1:   12 Real Number Additive Inverses or Negatives
  488.    wt: 1:   11 Real Number Addition
  489.    wt: 1:   10 Real Number Lengths and Signs
  490.    wt: 1:   7 Real Numbers as Line Cordinates
  491.    wt: 1:   6 Unsigned Real Numbers
  492.    wt: 1:   5 Rational Numbers More
  493.    wt: 1:   4 Rational Numbers
  494.    wt: 1:   3 Fractions
  495.    wt: 1:   2 Integers
  496.    wt: 1:   1 Whole and Natural Numbers
  497.    wt: 1:   5 Independent versus Dependent Variables
  498.    wt: 1:   4 Changing Letters
  499.    wt: 1:   2 Computation Rules Evaluation
  500.    wt: 1:   More Exercises
  501.    wt: 1:   4 GE III Animated Examples
  502.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  503.    wt: 1:   3 GE III Equation Addition and Multiplication
  504.    wt: 1:   2 GE II Comparison
  505.    wt: 1:   1 GE Substitution four examples
  506.    wt: 1:   4 Solving a triangular system exercise
  507.    wt: 1:   3 Solving triangular system example
  508.    wt: 1:   2 Essentially one exercises three with solution
  509.    wt: 1:   1 Essentially One Unknown
  510.    wt: 1:   Skill Development Notes
  511.    wt: 1:   10 One Example
  512.    wt: 1:   8 One Example
  513.    wt: 1:   7 Two Examples
  514.    wt: 1:   6 Three Examples
  515.    wt: 1:   5 Three Examples
  516.    wt: 1:   4 Two Examples
  517.    wt: 1:   3 Two Examples
  518.    wt: 1:   2 Three Examples
  519.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  520.    wt: 1:   8 Sets of Numbers
  521.    wt: 1:   7 Cautious or Safe Set Construction
  522.    wt: 1:   6 Power Set Notation
  523.    wt: 1:   5 Product Builder Notation
  524.    wt: 1:   4 Subset Builder Notation
  525.    wt: 1:   3 Counting with Sets etc
  526.    wt: 1:   2 Venn Diagrams
  527.    wt: 1:   1 Finite Sets
  528.    wt: 1:   6 Three Notions of What is a Variable
  529.    wt: 1:   5 Talking about Numbers and Quantities
  530.    wt: 1:   3 Adding Words To Arithmetic
  531.    wt: 1:   2 What is a Variable
  532.    wt: 1:   About Folder Contents
  533.    wt: 1:   1 More and Less Than for Counts and Measures
  534.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  535.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  536.    wt: 1:   4 LCM of 8 and 10 via Prime
  537.    wt: 1:   4 signed coordinates for regions in space
  538.    wt: 1:   3 signed coordinates for maps and planes
  539.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  540.    wt: 1:   D Three Term Ratios
  541.    wt: 1:   B Fractions and Two Term Ratios
  542.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  543.    wt: 1:   21 Reciprocals for Fractions and Wholes
  544.    wt: 1:   19 Dividing Fractions How TO
  545.    wt: 1:   16 Addition Subtraction Comparision Compared
  546.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  547.    wt: 1:   13 Fraction Comparison Algebraic View
  548.    wt: 1:   11 Simplification an Algebraic View
  549.    wt: 1:   9 Improper Fractions and Mixed Numbers
  550.    wt: 1:   6 Multiplication Algebraically Take II
  551.    wt: 1:   11 Adding Integers Formulas and Examples
  552.    wt: 1:   10 Integer Multiplication Formulas
  553.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  554.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  555.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  556.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  557.    wt: 1:   5 Remainder Arithmetic Modulo 5
  558.    wt: 1:   16 video Factors of 980 using prime
  559.    wt: 1:   8 video Prime Factorization upto 19
  560.    wt: 1:   3 video Primes and Composites from 9 times table
  561.    wt: 1:   Long Division Backwards more
  562.    wt: 1:   Long Division Backward
  563.    wt: 1:   Long Division forwards and backwards Example 3
  564.    wt: 1:   Long Division forwards and backwards Example 2
  565.    wt: 1:   C Counting Areas with Powers of Ten
  566.    wt: 1:   A Elementary Basis for Multiplication Methods
  567.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  568.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  569.    wt: 1:   Subtraction with J Conversions Example
  570.    wt: 1:   Subtraction Another Video Lesson
  571.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  572.    wt: 1:   5 A Tip for Efficent Subtraction
  573.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  574.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  575.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  576.    wt: 1:   Quick history of numbers and algebra
  577.    wt: 1:   Formula Evaluation how to show work
  578.    wt: 1:   The 12 Times Table Visually
  579.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  580.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  581.    wt: 1:   A Chain Rule Real Player video examples
  582.    wt: 1:   36 Cube root derivative animated
  583.    wt: 1:   29 Chain Rule Optional Reading
  584.    wt: 1:   28 Chain Rule Preparation for a Proof
  585.    wt: 1:   22 Chain Rule for polynomials
  586.    wt: 1:   21 Chain Rule for powers
  587.    wt: 1:   20 Chain Rule for Pulley Systems
  588.    wt: 1:   11 Quotient rule
  589.    wt: 1:   10 Power rule for negative integers
  590.    wt: 1:   9 Reciprocal rule
  591.    wt: 1:   3 Motivation for Limit Definition Take 2
  592.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  593.    wt: 1:   9 Limits Continuity and Composition
  594.    wt: 1:   3 Decimal insights for limits continuity convergence
  595.    wt: 1:   2 Algebraic codification
  596.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  597.    wt: 1:   G.5 Motions With Bounded Velocities
  598.    wt: 1:   F.1 What Functions are Continuous
  599.    wt: 1:   E2 Algebraic Properties of Limits
  600.    wt: 1:   PostScript For and Against Decimal Perspectives
  601.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  602.    wt: 1:   Fall 1983 Calculus Appetizer
  603.    wt: 1:   Foreword
  604.    wt: 1:   Postscript B Mathematics Education References
  605.    wt: 1:   Chapter 3 Algebra Difficulties
  606.    wt: 1:   Chapter 2 For and Against Mathematics
  607.    wt: 1:   Foreword
  608.    wt: 1:   Postscript C Consistency as a Tool for Reason
  609.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  610.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  611.    wt: 1:   Foreword
  612.    wt: 1:   R Why Learn Mathematics Skills
  613.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  614.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  615.    wt: 1:   O On Learning Mathematics and Science
  616.    wt: 1:   M Words to extend arithmetic
  617.    wt: 1:   L Skills with take home value
  618.    wt: 1:   N Improving Marks on Tests and Finals
  619.    wt: 1:   J. More on written work and showing skill
  620.    wt: 1:   H more Routine to non routine problem solving
  621.    wt: 1:   H Jigsaw puzzles and problem solving
  622.    wt: 1:   F. The student teacher tutor feedback loop
  623.    wt: 1:   E. When and how to correct errors
  624.    wt: 1:   D. Check work a must with a caution
  625.    wt: 1:   C. Domino effect of being careful
  626.    wt: 1:   B. Domino effect of errors
  627.    wt: 1:   A. Skill has to be seen to believed
  628.    wt: 1:   How to Build Skills and Confidence
  629.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  630.    wt: 1:   Chapter 6 More Algebra and Geometry
  631.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  632.    wt: 1:   Chapter 3 Algebra Starter Lessons
  633.    wt: 1:   7 Games and Activities for Instruction
  634.    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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