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 Lines and Slopes Take 2 with tangent function/
  5.    wt: 2:   2 Euclidean Geometry Constructions Theory extras/
  6.    wt: 2:   9 Proportionality Backwards and Forwards/
  7.    wt: 2:   2 Formula Forward Use Evaluation/
  8.    wt: 2:   9 Combinatorics Trees Tables and Products/
  9.    wt: 2:   Mathematics Skill Development Framework/
  10.    wt: 1:   Archives/
  11.    wt: 1:   Direct Current Electric Circuits/
  12.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  13.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  14.    wt: 1:   13 Vectors/
  15.    wt: 1:   12 Function Translating and Rescaling/
  16.    wt: 1:   11 Parallel Straight Lines and Transversals/
  17.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  18.    wt: 1:   8 Unit Circle Trigonometry/
  19.    wt: 1:   7 Complex Numbers/
  20.    wt: 1:   6 Trigonometry first steps/
  21.    wt: 1:   5 What is Similarity/
  22.    wt: 1:   4 Lines and Slopes Take 1/
  23.    wt: 1:   3 Cartesian and Polar Coordinates/
  24.    wt: 1:   1 Maps Plans Measurement/
  25.    wt: 1:   Geometry maps plans trigonometry vectors/
  26.    wt: 1:   8 Unifying Theme For Algebra/
  27.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  28.    wt: 1:   Volume 2 Three Skills For Algebra/
  29.    wt: 1:   Work and Study Tips/

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