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 Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

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:   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/

Web Page Search

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

Extended Search

642 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:   9 Formulas for Real Exponents with Logarithms
  31.    wt: 4:   9 Straight Lines through Origin Equations
  32.    wt: 4:   1 Straight Lines Slope Concept
  33.    wt: 4:   19 Right Triangle Similarity
  34.    wt: 4:   9 Construction of a right bisector
  35.    wt: 4:   musings do not puiblish real numbers
  36.    wt: 4:   9 Circle Area and Perimeter Formula Backwards Forwards
  37.    wt: 4:   1 Written work formats for developing and showing skill
  38.    wt: 4:   A Related lessons in Volume 3
  39.    wt: 4:   Postscript One Sided and Intermediate Value Theorems
  40.    wt: 4:   Postscript Unifying Theme A Fourth Skill For Algebra
  41.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  42.    wt: 3:   K LAMP Musings Science Education
  43.    wt: 3:   J LAMP Introduction Extrinsic Origins
  44.    wt: 3:   I LAMP Introduction Study Habits
  45.    wt: 3:   H LAMP Introduction Instructional Concepts
  46.    wt: 3:   G LAMP Introduction Problem Solving Skills
  47.    wt: 3:   F LAMP Introduction Prerequisites
  48.    wt: 3:   E LAMP Introduction Modern Mathematics
  49.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  50.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  51.    wt: 3:   A Introduction Objectives
  52.    wt: 3:   Skills Chapter 5 Calculus
  53.    wt: 3:   Skills Chapter 4 Logic
  54.    wt: 3:   Ramblings Extrinsic numbers theory
  55.    wt: 3:   Ramblings Introduction Algebra Essay
  56.    wt: 3:   Skills Chapter 3 Algebra
  57.    wt: 3:   Skills Chapter 1 Arithmetic
  58.    wt: 3:   Skills Chapter 0 Introduction
  59.    wt: 3:   11 pure mathematics
  60.    wt: 3:   10 statistics
  61.    wt: 3:   7 logic review and decimals an odd combination
  62.    wt: 3:   6 polynomials etc
  63.    wt: 3:   5 logarithms and exponentials etc
  64.    wt: 3:   4 algebra
  65.    wt: 3:   2 arithmetic with signed numbers
  66.    wt: 3:   1 arithmetic with unsigned numbers
  67.    wt: 3:   What is POMME
  68.    wt: 3:   why bother
  69.    wt: 3:   which way to go
  70.    wt: 3:   website reviews
  71.    wt: 3:   Teach the teachers plus goals
  72.    wt: 3:   Math Ed if it must be short make it lean effective
  73.    wt: 3:   links Education Resources online
  74.    wt: 3:   site origins
  75.    wt: 3:   site eurekas
  76.    wt: 3:   About site lesson plans
  77.    wt: 3:   key notes and themes
  78.    wt: 3:   Mathematics Education Professors
  79.    wt: 3:   teacher certification
  80.    wt: 3:   modern education
  81.    wt: 3:   learning takes time
  82.    wt: 3:   grouping students according to ability
  83.    wt: 3:   what should be learnt and When
  84.    wt: 3:   Postscript 2007 01 10
  85.    wt: 3:   five decades make a difference
  86.    wt: 3:   Maps Plans Drawings
  87.    wt: 3:   how letters appear
  88.    wt: 3:   Secondary Three Mathematics
  89.    wt: 3:   Secondary Two Mathematics
  90.    wt: 3:   talk the algebra talk
  91.    wt: 3:   three difficulties
  92.    wt: 3:   teaching tips
  93.    wt: 3:   What to Tell Students
  94.    wt: 3:   mathematics curriculum shifts
  95.    wt: 3:   teaching tutoring algebraic reason
  96.    wt: 3:   Lessening Algebra Difficulties
  97.    wt: 3:   the trouble with algebra
  98.    wt: 3:   05 13 OldSiteEntrancePage
  99.    wt: 3:   04 25 when to stop or suspend mathemat
  100.    wt: 3:   02 20 mathematics education references
  101.    wt: 3:   Operational Viewpoint to Value
  102.    wt: 3:   Theory of Knowledge
  103.    wt: 3:   mathematics instruction in general
  104.    wt: 3:   Education in mathematics science and technology
  105.    wt: 3:   Different Kinds of Reasoning in maths
  106.    wt: 3:   three kinds of reason in mathematics
  107.    wt: 3:   cultivating intelligence
  108.    wt: 3:   Motivation and Context Problem
  109.    wt: 3:   Leaner mathematics curriculum
  110.    wt: 3:   education an empirical art
  111.    wt: 3:   4 Energy Power Heat09
  112.    wt: 3:   9 motivation for name arcsin
  113.    wt: 3:   8 Radian Measures of Common Angles
  114.    wt: 3:   9 Head to Tail Coordinate View
  115.    wt: 3:   D Straight Lines Slope from Coordinates Examples
  116.    wt: 3:   C Straight Lines Slope from Coordinates
  117.    wt: 3:   B Straight Line Slope Scaling Properties More
  118.    wt: 3:   A Straight Line Slope Scaling Properties
  119.    wt: 3:   14 Straight Lines Equations General Case
  120.    wt: 3:   13 Straight Lines Finding Equations from 2 points
  121.    wt: 3:   12 Straight Lines Graphing mx plus b
  122.    wt: 3:   11 Straight Lines Graphing y=mx
  123.    wt: 3:   10 Straight Lines through Origin Equations More
  124.    wt: 3:   7 Tangent Function is odd on this domain
  125.    wt: 3:   6 Tangent Function Inclination Angle Take 2
  126.    wt: 3:   5 Tangent Function Graph
  127.    wt: 3:   4 Tangent Function Properties
  128.    wt: 3:   3 Straight Lines Slope as Tangent of Inclination Angle
  129.    wt: 3:   2 Straight Lines Slopes As Rise Over Run
  130.    wt: 3:   29 secant cosecant and cotangent for acute angles
  131.    wt: 3:   26 Formulas for products of sines and cosines
  132.    wt: 3:   20 sine and cosine Double Angle Formulas
  133.    wt: 3:   19 Pythagorean Identity For sine and cosine functions
  134.    wt: 3:   17E Trig Formulas for dot and cross Products
  135.    wt: 3:   17D cis formulas for sine cosines and tangent
  136.    wt: 3:   12 Graph of tangent function for one period
  137.    wt: 3:   3 sines and cosines for reference angle 90 degrees
  138.    wt: 3:   2 Quadrant I reference Angles
  139.    wt: 3:   1 Unit Points Reflections Rotations
  140.    wt: 3:   19 N th Roots of Unity
  141.    wt: 3:   13 Trig Formulas for dot and cross Products
  142.    wt: 3:   12 cis formulas for sine cosines and tangent
  143.    wt: 3:   9 The complex number valued trig function cis
  144.    wt: 3:   9 Similarity of Triangles Usual Criteria
  145.    wt: 3:   9 Midpoint Coordinates Half Endpoint Sum
  146.    wt: 3:   4 Equations for lines three forms
  147.    wt: 3:   9 Pythagorean Theorem Chinese Square Proof
  148.    wt: 3:   Euclidean Geometry Elsewhere LINKS
  149.    wt: 3:   PS H Distributive Law For Complex Numbers
  150.    wt: 3:   Short Course on Euclidean Geometry
  151.    wt: 3:   13 Naming Identifying Formulas with Words
  152.    wt: 3:   9 Volume of Cone
  153.    wt: 3:   8 Compound Interest Formula Evaluation
  154.    wt: 3:   7 Compound Interest Formula Introduction
  155.    wt: 3:   5 Box Volume Formula Example
  156.    wt: 3:   4 Circle Area Formula Example
  157.    wt: 3:   3 Triangle Area Formula Example
  158.    wt: 3:   2 Another Rectangle Area Formula Example
  159.    wt: 3:   5 Counting with Tables Trees Product Rule Take II
  160.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  161.    wt: 3:   19 Remainder Arithmetic Rule of 9 for checking sums III
  162.    wt: 3:   9 video Prime Factorization upto 19 squared
  163.    wt: 3:   38 Formulas and derivatives for powers and roots
  164.    wt: 3:   Postscript For Better Performance
  165.    wt: 3:   Appendix A. Reading Guide For Next Appendices
  166.    wt: 3:   Chapter 29 Contrapositive and Vacuously True Implications
  167.    wt: 3:   Chapter 19. Functions and Sets
  168.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  169.    wt: 3:   Chapter 9 Talking about Numbers or Quantities
  170.    wt: 3:   G. Written work formats for developing and showing skill
  171.    wt: 3:   Helping the Blind in Logic and Mathematics
  172.    wt: 3:   Mathematics Education References
  173.    wt: 3:   Mathematics Education References
  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:   24 Standards For Skill Develoment Take II
  345.    wt: 1:   24 Standards For Skill Develoment
  346.    wt: 1:   17 Math Booklets for children and young teenagers
  347.    wt: 1:   15 Counting For Parents
  348.    wt: 1:   12 Goals and Objectives For Mathematics
  349.    wt: 1:   10 Ends values for work study instruction
  350.    wt: 1:   5 Patience Please for Yourself and Your Charges
  351.    wt: 1:   4 Learning Takes Time and Effort
  352.    wt: 1:   3 Preparing for Science Studies
  353.    wt: 1:   Ages 12 to 14 Geometry
  354.    wt: 1:   Ages 10 to 12 Geometry
  355.    wt: 1:   Ages 8 to 9
  356.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  357.    wt: 1:   sign monoticity analysis example 4
  358.    wt: 1:   sign monoticity analysis example 3
  359.    wt: 1:   sign monoticity analysis example 2
  360.    wt: 1:   sign monoticity analysis example 1
  361.    wt: 1:   6 Set Existence Formation and Notation
  362.    wt: 1:   3 Formula or function graphing exercise
  363.    wt: 1:   Introduction Reading Guide
  364.    wt: 1:   9 quadratics physical and further context
  365.    wt: 1:   8 quadratics backward use of various formulas
  366.    wt: 1:   7 quadratic formulla derivation
  367.    wt: 1:   8 Notes for instructors or tutors
  368.    wt: 1:   16 cotangent function Definition Graph and Inverse
  369.    wt: 1:   15 cosecant function Definition Graph and Inverse
  370.    wt: 1:   14 secant function Definition Graph and Inverse
  371.    wt: 1:   13 cosecant function Definition Graph and Inverse
  372.    wt: 1:   11 arctan left inverse of tangent Graph
  373.    wt: 1:   10 arctan left inverse of tangent Definition
  374.    wt: 1:   8 arcsin left inverse of sine Graph
  375.    wt: 1:   7 arcsin left inverse of sine Definition
  376.    wt: 1:   6 Graph of arccos function
  377.    wt: 1:   5 Swapping Coordinates is a reflection
  378.    wt: 1:   3 Left Inverse of cosine arccos definition
  379.    wt: 1:   2 cosine function more properties
  380.    wt: 1:   1 cosine function properties
  381.    wt: 1:   1 Degrees and Radians Introduction
  382.    wt: 1:   A Global Time and Navigation
  383.    wt: 1:   15 Dot and Cross Product
  384.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  385.    wt: 1:   13 Velocity Vectors in Physics
  386.    wt: 1:   12 From Applied To Pure Mathematics
  387.    wt: 1:   11 Component Method
  388.    wt: 1:   10 Parallelogram Addition Method
  389.    wt: 1:   8 Parallel Vectors
  390.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  391.    wt: 1:   6 Vectors with Coordinates
  392.    wt: 1:   5 Head To Tail Arrow Addition
  393.    wt: 1:   4 Resultant of a Sum of Movements
  394.    wt: 1:   3 Navigation with Arrows or Vectors
  395.    wt: 1:   2 Signed Coordinates
  396.    wt: 1:   1 Unsigned Coordinates
  397.    wt: 1:   Vector and Complex Number Applet
  398.    wt: 1:   4 graphing y=Asin(x c)
  399.    wt: 1:   3 graphing y=f(x c) plus K
  400.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  401.    wt: 1:   1 graphing y=f(x a)
  402.    wt: 1:   Parallel Lines and Parallel Transversals
  403.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  404.    wt: 1:   Triangle Angles Sum To 180 Degrees
  405.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  406.    wt: 1:   Parallel Lines and Interior Angles
  407.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  408.    wt: 1:   Straight Lines ASA Intersection Study More
  409.    wt: 1:   Straight Lines ASA Intersection Study
  410.    wt: 1:   Straight Lines Instersection Solving Equations
  411.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  412.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  413.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  414.    wt: 1:   32 seven rows of pascals triangle
  415.    wt: 1:   31 basic secant cosecant cotangent trig identities
  416.    wt: 1:   28 Expressing products of sines cosines as sums
  417.    wt: 1:   27 Logarithmic use of products of sines and cosines
  418.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  419.    wt: 1:   18 sum of sinusoidal waves as a single wave
  420.    wt: 1:   17G Pythagorean Theorem Converse
  421.    wt: 1:   17F Law of cosines
  422.    wt: 1:   17A The complex number valued trig function cis
  423.    wt: 1:   16 Right Triangle Complementary Angle Relations
  424.    wt: 1:   15 sine cosine Complementary Angle Relations
  425.    wt: 1:   14 cosine even and sine and tangent are odd
  426.    wt: 1:   13 Graph of tangent function many periods
  427.    wt: 1:   11 tangent function undefined when terminal side vertical
  428.    wt: 1:   10 Graphs of sines and cosines many periods
  429.    wt: 1:   8 period of tangent function
  430.    wt: 1:   7 period of sine and cosine
  431.    wt: 1:   Unit Circle Development of Trigonometry
  432.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  433.    wt: 1:   21 Logarithms Powers and Exponentials
  434.    wt: 1:   20 N th Roots of Complex Numbers
  435.    wt: 1:   18 Sixth Roots of Unity
  436.    wt: 1:   17 Cube Roots of unity
  437.    wt: 1:   16 References and Originality Question
  438.    wt: 1:   15 Pythagorean Theorem Converse
  439.    wt: 1:   14 Law of cosines
  440.    wt: 1:   8 Unit Circle Development of Trigonometry
  441.    wt: 1:   7 Second Way to Calculate Products
  442.    wt: 1:   6 Field Properties of Complex Number
  443.    wt: 1:   5 An Easy Proof of the Distributive Law
  444.    wt: 1:   4 Multiplication Properties
  445.    wt: 1:   3 Addition Properties
  446.    wt: 1:   2 Complex Numbers made easier we hope
  447.    wt: 1:   1 Rectangular Polar Coordinates Review
  448.    wt: 1:   Appetizer A Complex Number Applet
  449.    wt: 1:   8 Triangles Cascade Problem Solving
  450.    wt: 1:   7 Trignometric Ratios Unit Circle
  451.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  452.    wt: 1:   3 Trigonometric Ratios sine and cosine
  453.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  454.    wt: 1:   1 Angle Measurement with Degrees
  455.    wt: 1:   Why Trigonometry the whyslopes view
  456.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  457.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  458.    wt: 1:   12 Triangles Similarity More Problems
  459.    wt: 1:   11 Triangle Similarity Missing Side Problem
  460.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  461.    wt: 1:   8 Similarity of Triangles and Polygons
  462.    wt: 1:   7 Translations Rotations Reflections Dilatations
  463.    wt: 1:   6 Geometric Diagrams in Class
  464.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  465.    wt: 1:   4 Similarity Definition with Coordinate
  466.    wt: 1:   3 Similarity by Design with coordinates
  467.    wt: 1:   2 Similarity By Design
  468.    wt: 1:   Four Simple Exercises
  469.    wt: 1:   12 Links Lessons elsewhere
  470.    wt: 1:   11 A Partial Summary
  471.    wt: 1:   10 Midpoint of [a b] and [b a]
  472.    wt: 1:   7 Exercises to test skill and concept mastery
  473.    wt: 1:   6 Intersection of lines by solving linear systems
  474.    wt: 1:   5 Algebraic View of Slopes
  475.    wt: 1:   1 Numerical view of lines and their equations
  476.    wt: 1:   What is and is not here
  477.    wt: 1:   12 Spatial Coordinates
  478.    wt: 1:   11 Triangle Inequality
  479.    wt: 1:   8 Distance Between Points on a Line
  480.    wt: 1:   7 Complex Numbers Appetizer
  481.    wt: 1:   6 Polar Multiplication and Rotation
  482.    wt: 1:   5 Cartesian Addition and Translation
  483.    wt: 1:   4 Polar Coordinates to and from
  484.    wt: 1:   3 Rectangular Coordinates Review
  485.    wt: 1:   2 Cartesian Coordinates with signs
  486.    wt: 1:   1 Cartesian Coordinates sans signs
  487.    wt: 1:   A Measurement with Ruler Proper Use
  488.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  489.    wt: 1:   6 Figuring with Maps Not to Scale
  490.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  491.    wt: 1:   4 Angles on Maps Plans drawn to scale
  492.    wt: 1:   3 Lengths and Areas on Maps and Plans
  493.    wt: 1:   2 Measuring Area Directly
  494.    wt: 1:   1 Length Measurement
  495.    wt: 1:   About Folder Contents
  496.    wt: 1:   A Signed Number Arithmetic Review
  497.    wt: 1:   19 Signed Multiples of Vectors
  498.    wt: 1:   9 Division with Digits after Decimal Point
  499.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  500.    wt: 1:   E Long Division Methods more
  501.    wt: 1:   D Long Division Methods
  502.    wt: 1:   C Three Decimal Subtraction Methods
  503.    wt: 1:   B Decimal Comparison and Subtraction
  504.    wt: 1:   A Decimal Addition Columm Methods
  505.    wt: 1:   6 Column Methods for Decimal Multiplication
  506.    wt: 1:   5 Distributive Law for Whole Numbers
  507.    wt: 1:   4 Commutative Law Groups Counting Form
  508.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  509.    wt: 1:   3 Linear Equation Literal Solution More
  510.    wt: 1:   2 Linear Equation Literal Solution
  511.    wt: 1:   1 Changing Calculations
  512.    wt: 1:   3 Product Axioms Two Forms
  513.    wt: 1:   2 More and Less Than for Counts and Measures
  514.    wt: 1:   8 Coordinates for Maps and Planes
  515.    wt: 1:   3 Geometric Formulas and Function Notation
  516.    wt: 1:   1 Formulas Dependence and Function Notation
  517.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  518.    wt: 1:   6 Algebraic Solution Example
  519.    wt: 1:   5 Algebraic Solutions Introduction
  520.    wt: 1:   4 Four Examples Fractional Coefficients
  521.    wt: 1:   3 Four Examples
  522.    wt: 1:   2 Three Examples
  523.    wt: 1:   1 Proper Equal Sign Usage
  524.    wt: 1:   Using Letters for Physical Quantities
  525.    wt: 1:   9 Sets in Probability and Statistics
  526.    wt: 1:   1 Three Skills For Algebra
  527.    wt: 1:   1 More and Less Than for Counts and Measures
  528.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  529.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  530.    wt: 1:   4 LCM of 8 and 10 via Prime
  531.    wt: 1:   4 signed coordinates for regions in space
  532.    wt: 1:   3 signed coordinates for maps and planes
  533.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  534.    wt: 1:   D Three Term Ratios
  535.    wt: 1:   B Fractions and Two Term Ratios
  536.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  537.    wt: 1:   21 Reciprocals for Fractions and Wholes
  538.    wt: 1:   19 Dividing Fractions How TO
  539.    wt: 1:   16 Addition Subtraction Comparision Compared
  540.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  541.    wt: 1:   9 Improper Fractions and Mixed Numbers
  542.    wt: 1:   11 Adding Integers Formulas and Examples
  543.    wt: 1:   10 Integer Multiplication Formulas
  544.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  545.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  546.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  547.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  548.    wt: 1:   5 Remainder Arithmetic Modulo 5
  549.    wt: 1:   16 video Factors of 980 using prime
  550.    wt: 1:   8 video Prime Factorization upto 19
  551.    wt: 1:   3 video Primes and Composites from 9 times table
  552.    wt: 1:   Long Division Backwards more
  553.    wt: 1:   Long Division Backward
  554.    wt: 1:   Long Division forwards and backwards Example 3
  555.    wt: 1:   Long Division forwards and backwards Example 2
  556.    wt: 1:   C Counting Areas with Powers of Ten
  557.    wt: 1:   A Elementary Basis for Multiplication Methods
  558.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  559.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  560.    wt: 1:   Subtraction with J Conversions Example
  561.    wt: 1:   Subtraction Another Video Lesson
  562.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  563.    wt: 1:   5 A Tip for Efficent Subtraction
  564.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  565.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  566.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  567.    wt: 1:   Formula Evaluation how to show work
  568.    wt: 1:   The 12 Times Table Visually
  569.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  570.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  571.    wt: 1:   A Chain Rule Real Player video examples
  572.    wt: 1:   36 Cube root derivative animated
  573.    wt: 1:   29 Chain Rule Optional Reading
  574.    wt: 1:   28 Chain Rule Preparation for a Proof
  575.    wt: 1:   22 Chain Rule for polynomials
  576.    wt: 1:   21 Chain Rule for powers
  577.    wt: 1:   20 Chain Rule for Pulley Systems
  578.    wt: 1:   11 Quotient rule
  579.    wt: 1:   10 Power rule for negative integers
  580.    wt: 1:   9 Reciprocal rule
  581.    wt: 1:   3 Motivation for Limit Definition Take 2
  582.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  583.    wt: 1:   9 Limits Continuity and Composition
  584.    wt: 1:   3 Decimal insights for limits continuity convergence
  585.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  586.    wt: 1:   G.5 Motions With Bounded Velocities
  587.    wt: 1:   F.1 What Functions are Continuous
  588.    wt: 1:   PostScript For and Against Decimal Perspectives
  589.    wt: 1:   Fall 1983 Calculus Appetizer
  590.    wt: 1:   Foreword
  591.    wt: 1:   Appendix E. How To Study Mathematics and Why
  592.    wt: 1:   Appendix D. What to do in School and Why
  593.    wt: 1:   Appendix C. How to Read
  594.    wt: 1:   Appendix B. How To Learn
  595.    wt: 1:   Chapter 31 Direct and Indirect Reason
  596.    wt: 1:   Chapter 30 Truth Tables
  597.    wt: 1:   Chapter 28 Occurrence Tables
  598.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  599.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  600.    wt: 1:   Chapter 25. Mathematical Induction Examples
  601.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  602.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  603.    wt: 1:   Chapter 20. Degrees and Radians
  604.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  605.    wt: 1:   Chapter 16. Painless Theorem Proving
  606.    wt: 1:   Chapter 15. Solving Linear Equations
  607.    wt: 1:   Chapter 11. Why Shorthand
  608.    wt: 1:   Chapter 10 Describing and Changing Calculations
  609.    wt: 1:   Chapter 6 Change of Language
  610.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  611.    wt: 1:   Chapter 4 Longer Chains of Reason
  612.    wt: 1:   Chapter 3 Chains of Reason
  613.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  614.    wt: 1:   Chapter 7 Two Treatments of Geometry
  615.    wt: 1:   Chapter 2 For and Against Mathematics
  616.    wt: 1:   Foreword
  617.    wt: 1:   Postscript C Consistency as a Tool for Reason
  618.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  619.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  620.    wt: 1:   Foreword
  621.    wt: 1:   R Why Learn Mathematics Skills
  622.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  623.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  624.    wt: 1:   O On Learning Mathematics and Science
  625.    wt: 1:   M Words to extend arithmetic
  626.    wt: 1:   L Skills with take home value
  627.    wt: 1:   N Improving Marks on Tests and Finals
  628.    wt: 1:   J. More on written work and showing skill
  629.    wt: 1:   H more Routine to non routine problem solving
  630.    wt: 1:   H Jigsaw puzzles and problem solving
  631.    wt: 1:   F. The student teacher tutor feedback loop
  632.    wt: 1:   E. When and how to correct errors
  633.    wt: 1:   D. Check work a must with a caution
  634.    wt: 1:   C. Domino effect of being careful
  635.    wt: 1:   B. Domino effect of errors
  636.    wt: 1:   A. Skill has to be seen to believed
  637.    wt: 1:   How to Build Skills and Confidence
  638.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  639.    wt: 1:   Chapter 6 More Algebra and Geometry
  640.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  641.    wt: 1:   7 Games and Activities for Instruction
  642.    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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