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

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272 matches:

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

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645 matches:

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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