Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

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

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

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

Web Page Search

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

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661 matches:

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

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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