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

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

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

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

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

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

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

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

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273 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:   22 Student Centered Highschool Mathematics
  74.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  75.    wt: 1:   17 Math Booklets for children and young teenagers
  76.    wt: 1:   15 Counting For Parents
  77.    wt: 1:   12 Goals and Objectives For Mathematics
  78.    wt: 1:   10 Ends values for work study instruction
  79.    wt: 1:   9 Streaming by Student Cooperation
  80.    wt: 1:   5 Patience Please for Yourself and Your Charges
  81.    wt: 1:   4 Learning Takes Time and Effort
  82.    wt: 1:   3 Preparing for Science Studies
  83.    wt: 1:   Ages 12 to 14 Arithmetic
  84.    wt: 1:   Ages 10 to 12 Arithmetic
  85.    wt: 1:   Ages 9 to 10
  86.    wt: 1:   Ages 8 to 9
  87.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  88.    wt: 1:   19 Horizontal line rule and method
  89.    wt: 1:   9 Set theory term relation possible origins
  90.    wt: 1:   6 Set Existence Formation and Notation
  91.    wt: 1:   3 Formula or function graphing exercise
  92.    wt: 1:   Introduction Reading Guide
  93.    wt: 1:   9 quadratics physical and further context
  94.    wt: 1:   8 quadratics backward use of various formulas
  95.    wt: 1:   7 quadratic formulla derivation
  96.    wt: 1:   8 Notes for instructors or tutors
  97.    wt: 1:   12 motivation for term arctan
  98.    wt: 1:   4 possible motivation for term arccos
  99.    wt: 1:   9 Summary Degrees to Radians and back
  100.    wt: 1:   9 Head to Tail Coordinate View
  101.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  102.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  103.    wt: 1:   9 Straight Lines through Origin Equations
  104.    wt: 1:   8 Straight Lines Equation for vertical
  105.    wt: 1:   17 tangent function angle sum formulas
  106.    wt: 1:   25 tangent double angle formula Slope connection
  107.    wt: 1:   24 tangent Angle Difference Formula
  108.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  109.    wt: 1:   21 sine and cosine Half Angle Formulas
  110.    wt: 1:   20 sine and cosine Double Angle Formulas
  111.    wt: 1:   17C sine and cosine double triple angle formulas
  112.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  113.    wt: 1:   12 Graph of tangent function for one period
  114.    wt: 1:   9 Graphs of sine and cosine over one period
  115.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  116.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  117.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  118.    wt: 1:   19 N th Roots of Unity
  119.    wt: 1:   11 sine and cosine double triple angle formulas
  120.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  121.    wt: 1:   9 The complex number valued trig function cis
  122.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  123.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  124.    wt: 1:   9 Similarity of Triangles Usual Criteria
  125.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  126.    wt: 1:   8 Mid Point Formula
  127.    wt: 1:   3 Slope product for perpendicular lines
  128.    wt: 1:   2 point slope equation for a line
  129.    wt: 1:   13 Pythagorean spatial distance formulas
  130.    wt: 1:   10 Pythagorean plane distance formula
  131.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  132.    wt: 1:   PS H Distributive Law For Complex Numbers
  133.    wt: 1:   19 Right Triangle Similarity
  134.    wt: 1:   9 Construction of a right bisector
  135.    wt: 1:   A Modular and Remainder Arithmetic
  136.    wt: 1:   A Signed Number Arithmetic Review
  137.    wt: 1:   19 Signed Multiples of Vectors
  138.    wt: 1:   9 Division with Digits after Decimal Point
  139.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  140.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  141.    wt: 1:   6 Column Methods for Decimal Multiplication
  142.    wt: 1:   5 Distributive Law for Whole Numbers
  143.    wt: 1:   4 Commutative Law Groups Counting Form
  144.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  145.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  146.    wt: 1:   6 Compound Interest Forward and Backwards
  147.    wt: 1:   5 Triangle Area Formula Backwards
  148.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  149.    wt: 1:   3 Product Axioms Two Forms
  150.    wt: 1:   2 More and Less Than for Counts and Measures
  151.    wt: 1:   8 Coordinates for Maps and Planes
  152.    wt: 1:   3 Geometric Formulas and Function Notation
  153.    wt: 1:   1 Formulas Dependence and Function Notation
  154.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  155.    wt: 1:   9 Three Examples
  156.    wt: 1:   Using Letters for Physical Quantities
  157.    wt: 1:   13 Naming Identifying Formulas with Words
  158.    wt: 1:   9 Volume of Cone
  159.    wt: 1:   8 Compound Interest Formula Evaluation
  160.    wt: 1:   7 Compound Interest Formula Introduction
  161.    wt: 1:   5 Box Volume Formula Example
  162.    wt: 1:   4 Circle Area Formula Example
  163.    wt: 1:   3 Triangle Area Formula Example
  164.    wt: 1:   2 Another Rectangle Area Formula Example
  165.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  166.    wt: 1:   9 Sets in Probability and Statistics
  167.    wt: 1:   3 Adding Words To Arithmetic
  168.    wt: 1:   1 Three Skills For Algebra
  169.    wt: 1:   1 More and Less Than for Counts and Measures
  170.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  171.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  172.    wt: 1:   9 subtracting signed numbers
  173.    wt: 1:   4 signed coordinates for regions in space
  174.    wt: 1:   3 signed coordinates for maps and planes
  175.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  176.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  177.    wt: 1:   21 Reciprocals for Fractions and Wholes
  178.    wt: 1:   19 Dividing Fractions How TO
  179.    wt: 1:   9 Improper Fractions and Mixed Numbers
  180.    wt: 1:   11 Adding Integers Formulas and Examples
  181.    wt: 1:   10 Integer Multiplication Formulas
  182.    wt: 1:   9 Multiplying Integers
  183.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  184.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  185.    wt: 1:   23 Remainder Arithmetic Modulo 2
  186.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  187.    wt: 1:   21 Remainder Arithmetic Modulo 3
  188.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  189.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  190.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  191.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  192.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  193.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  194.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  195.    wt: 1:   5 Remainder Arithmetic Modulo 5
  196.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  197.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  198.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  199.    wt: 1:   1 Remainder Arithmetic Modulo 10
  200.    wt: 1:   19 video Prime Factorization Unique
  201.    wt: 1:   16 video Factors of 980 using prime
  202.    wt: 1:   8 video Prime Factorization upto 19
  203.    wt: 1:   3 video Primes and Composites from 9 times table
  204.    wt: 1:   Long Division forwards and backwards Example 3
  205.    wt: 1:   Long Division forwards and backwards Example 2
  206.    wt: 1:   Long Division forwards and backwards Example 1
  207.    wt: 1:   9 Why Long Division Works Take II
  208.    wt: 1:   A Elementary Basis for Multiplication Methods
  209.    wt: 1:   9 22 Minute Subtraction Review Video
  210.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  211.    wt: 1:   5 A Tip for Efficent Subtraction
  212.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  213.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  214.    wt: 1:   Exact Arithmetic Wholes and Fractions
  215.    wt: 1:   Formula Evaluation how to show work
  216.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  217.    wt: 1:   5 Conversion Arithmetic
  218.    wt: 1:   29 Chain Rule Optional Reading
  219.    wt: 1:   28 Chain Rule Preparation for a Proof
  220.    wt: 1:   22 Chain Rule for polynomials
  221.    wt: 1:   21 Chain Rule for powers
  222.    wt: 1:   20 Chain Rule for Pulley Systems
  223.    wt: 1:   10 Power rule for negative integers
  224.    wt: 1:   9 Reciprocal rule
  225.    wt: 1:   3 Motivation for Limit Definition Take 2
  226.    wt: 1:   2 Motivation for Limit Definition Take 1
  227.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  228.    wt: 1:   9 Limits Continuity and Composition
  229.    wt: 1:   3 Decimal insights for limits continuity convergence
  230.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  231.    wt: 1:   PostScript For and Against Decimal Perspectives
  232.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  233.    wt: 1:   Chapter 9 About First Courses in Calculus
  234.    wt: 1:   Fall 1983 Calculus Appetizer
  235.    wt: 1:   Foreword
  236.    wt: 1:   Postscript More on Better Performance
  237.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  238.    wt: 1:   Chapter 23. Notation For Sums
  239.    wt: 1:   Chapter 21. Third Reading Guide
  240.    wt: 1:   Chapter 19. Functions and Sets
  241.    wt: 1:   Chapter 18. Rules for Algebra
  242.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  243.    wt: 1:   Chapter 13. Second Reading Guide
  244.    wt: 1:   Chapter 12. Shorthand Usage Guide
  245.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  246.    wt: 1:   Chapter 8 Three Skills For Algebra
  247.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  248.    wt: 1:   Foreword
  249.    wt: 1:   Chapter 9 The Two Ends
  250.    wt: 1:   Chapter 2 For and Against Mathematics
  251.    wt: 1:   Foreword
  252.    wt: 1:   Postscript C Consistency as a Tool for Reason
  253.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  254.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  255.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  256.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  257.    wt: 1:   Foreword
  258.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  259.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  260.    wt: 1:   N Mathematics Prepare for College Studies
  261.    wt: 1:   M Words to extend arithmetic
  262.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  263.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  264.    wt: 1:   Chapter 1 Arithmetic
  265.    wt: 1:   7 Games and Activities for Instruction
  266.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  267.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  268.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  269.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  270.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  271.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  272.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  273.    wt: 1:   The Math Forum and Site Content

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  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:   19 Extending the Oral Dimension of Mathematics
  36.    wt: 4:   9 Streaming by Student Cooperation
  37.    wt: 4:   9 Formulas for Real Exponents with Logarithms
  38.    wt: 4:   8 Straight Lines Equation for vertical
  39.    wt: 4:   musings do not puiblish real numbers
  40.    wt: 4:   9 Circle Area and Perimeter Formula Backwards Forwards
  41.    wt: 4:   1 Written work formats for developing and showing skill
  42.    wt: 4:   5 Counting with Tables Trees Product Rule Take II
  43.    wt: 4:   9 subtracting signed numbers
  44.    wt: 4:   24 Divisibility Tests for 2 3 5 9 10
  45.    wt: 4:   16 Remainder Arithmetic Modulo 9 Example 2
  46.    wt: 4:   14 Remainder Arithmetic Modulo 9 Example
  47.    wt: 4:   9 Remainder Arithmetic Divisibility by 5
  48.    wt: 4:   5 Remainder Arithmetic Modulo 5
  49.    wt: 4:   9 video Prime Factorization upto 19 squared
  50.    wt: 4:   Long Division forwards and backwards Example 1
  51.    wt: 4:   9 Why Long Division Works Take II
  52.    wt: 4:   9 22 Minute Subtraction Review Video
  53.    wt: 4:   A Related lessons in Volume 3
  54.    wt: 4:   Postscript One Sided and Intermediate Value Theorems
  55.    wt: 4:   Postscript Unifying Theme A Fourth Skill For Algebra
  56.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  57.    wt: 3:   K LAMP Musings Science Education
  58.    wt: 3:   J LAMP Introduction Extrinsic Origins
  59.    wt: 3:   I LAMP Introduction Study Habits
  60.    wt: 3:   H LAMP Introduction Instructional Concepts
  61.    wt: 3:   G LAMP Introduction Problem Solving Skills
  62.    wt: 3:   F LAMP Introduction Prerequisites
  63.    wt: 3:   E LAMP Introduction Modern Mathematics
  64.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  65.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  66.    wt: 3:   A Introduction Objectives
  67.    wt: 3:   Skills Chapter 5 Calculus
  68.    wt: 3:   Skills Chapter 4 Logic
  69.    wt: 3:   Ramblings Extrinsic numbers theory
  70.    wt: 3:   Ramblings Introduction Algebra Essay
  71.    wt: 3:   Skills Chapter 3 Algebra
  72.    wt: 3:   Skills Chapter 2 Geometry
  73.    wt: 3:   Skills Chapter 0 Introduction
  74.    wt: 3:   11 pure mathematics
  75.    wt: 3:   10 statistics
  76.    wt: 3:   8 analytic geometry etc
  77.    wt: 3:   7 logic review and decimals an odd combination
  78.    wt: 3:   6 polynomials etc
  79.    wt: 3:   5 logarithms and exponentials etc
  80.    wt: 3:   4 algebra
  81.    wt: 3:   3 Euclidean Geometry Leanly
  82.    wt: 3:   What is POMME
  83.    wt: 3:   why bother
  84.    wt: 3:   which way to go
  85.    wt: 3:   website reviews
  86.    wt: 3:   Teach the teachers plus goals
  87.    wt: 3:   Math Ed if it must be short make it lean effective
  88.    wt: 3:   links Education Resources online
  89.    wt: 3:   site origins
  90.    wt: 3:   site eurekas
  91.    wt: 3:   About site lesson plans
  92.    wt: 3:   key notes and themes
  93.    wt: 3:   Mathematics Education Professors
  94.    wt: 3:   teacher certification
  95.    wt: 3:   modern education
  96.    wt: 3:   learning takes time
  97.    wt: 3:   grouping students according to ability
  98.    wt: 3:   what should be learnt and When
  99.    wt: 3:   Postscript 2007 01 10
  100.    wt: 3:   five decades make a difference
  101.    wt: 3:   Maps Plans Drawings
  102.    wt: 3:   how letters appear
  103.    wt: 3:   Secondary Three Mathematics
  104.    wt: 3:   Secondary Two Mathematics
  105.    wt: 3:   talk the algebra talk
  106.    wt: 3:   three difficulties
  107.    wt: 3:   teaching tips
  108.    wt: 3:   What to Tell Students
  109.    wt: 3:   mathematics curriculum shifts
  110.    wt: 3:   teaching tutoring algebraic reason
  111.    wt: 3:   Lessening Algebra Difficulties
  112.    wt: 3:   the trouble with algebra
  113.    wt: 3:   05 13 OldSiteEntrancePage
  114.    wt: 3:   04 25 when to stop or suspend mathemat
  115.    wt: 3:   02 20 mathematics education references
  116.    wt: 3:   Operational Viewpoint to Value
  117.    wt: 3:   Theory of Knowledge
  118.    wt: 3:   mathematics instruction in general
  119.    wt: 3:   Education in mathematics science and technology
  120.    wt: 3:   Different Kinds of Reasoning in maths
  121.    wt: 3:   three kinds of reason in mathematics
  122.    wt: 3:   cultivating intelligence
  123.    wt: 3:   Motivation and Context Problem
  124.    wt: 3:   Leaner mathematics curriculum
  125.    wt: 3:   education an empirical art
  126.    wt: 3:   4 Energy Power Heat09
  127.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  128.    wt: 3:   24 Standards For Skill Develoment Take II
  129.    wt: 3:   24 Standards For Skill Develoment
  130.    wt: 3:   22 Student Centered Highschool Mathematics
  131.    wt: 3:   17 Math Booklets for children and young teenagers
  132.    wt: 3:   15 Counting For Parents
  133.    wt: 3:   12 Goals and Objectives For Mathematics
  134.    wt: 3:   10 Ends values for work study instruction
  135.    wt: 3:   5 Patience Please for Yourself and Your Charges
  136.    wt: 3:   4 Learning Takes Time and Effort
  137.    wt: 3:   3 Preparing for Science Studies
  138.    wt: 3:   9 Straight Lines through Origin Equations
  139.    wt: 3:   1 Straight Lines Slope Concept
  140.    wt: 3:   13 Naming Identifying Formulas with Words
  141.    wt: 3:   9 Volume of Cone
  142.    wt: 3:   8 Compound Interest Formula Evaluation
  143.    wt: 3:   7 Compound Interest Formula Introduction
  144.    wt: 3:   5 Box Volume Formula Example
  145.    wt: 3:   4 Circle Area Formula Example
  146.    wt: 3:   3 Triangle Area Formula Example
  147.    wt: 3:   2 Another Rectangle Area Formula Example
  148.    wt: 3:   4 Counting with Trees Product Rule Take I
  149.    wt: 3:   3 Counting with Tables and Trees II
  150.    wt: 3:   2 Counting with Tables and Trees I
  151.    wt: 3:   1 Counting and Counting Methods I
  152.    wt: 3:   4 signed coordinates for regions in space
  153.    wt: 3:   3 signed coordinates for maps and planes
  154.    wt: 3:   5 Reciprocals and Division for Fractions with Units
  155.    wt: 3:   C Equality for Fractions and Two Term Ratios and Fractions
  156.    wt: 3:   9 Multiplying Integers
  157.    wt: 3:   A Decimals Modular and Remainder Arithmetic
  158.    wt: 3:   27 Divisibility by 2 3 6 5 9 10 Example
  159.    wt: 3:   23 Remainder Arithmetic Modulo 2
  160.    wt: 3:   22 Remainder Arithmetic Modulo 3 more
  161.    wt: 3:   21 Remainder Arithmetic Modulo 3
  162.    wt: 3:   13 Remainder Arithmetic Modulo 5 Example
  163.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  164.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  165.    wt: 3:   10 Remainder Arithmetic Long Division by 5 Quickly
  166.    wt: 3:   8 Remainder Arithmetic Morulo 5 Examples II
  167.    wt: 3:   7 Remainder Arithmetic Modulo 5 Examples I
  168.    wt: 3:   6 Remainder Arithmetic Modulo 5 Propertie
  169.    wt: 3:   4 Remainder Arithmetic Modulo 10 in general
  170.    wt: 3:   3 Remainder Arithmetic Modulos 10 more still
  171.    wt: 3:   2 Remainder Arithmetic Modulo 10 more
  172.    wt: 3:   1 Remainder Arithmetic Modulo 10
  173.    wt: 3:   19 video Prime Factorization Unique
  174.    wt: 3:   Long Division Backwards more
  175.    wt: 3:   Long Division Backward
  176.    wt: 3:   Long Division forwards and backwards Example 3
  177.    wt: 3:   Long Division forwards and backwards Example 2
  178.    wt: 3:   C Counting Areas with Powers of Ten
  179.    wt: 3:   A Elementary Basis for Multiplication Methods
  180.    wt: 3:   Appendix 2 Three Decimal Subtraction Methods
  181.    wt: 3:   Appendix 1 Decimals Comparison Method Take II
  182.    wt: 3:   Subtraction with J Conversions Example
  183.    wt: 3:   Subtraction Another Video Lesson
  184.    wt: 3:   7 Subtraction for Decimal Fractions with Exercises
  185.    wt: 3:   5 A Tip for Efficent Subtraction
  186.    wt: 3:   Appendix 1 Counting Revisited 15 minute video
  187.    wt: 3:   9 Place Value Review Decimal form of Avogrados number included
  188.    wt: 3:   Practical Methods Ends and Values for Arithmetic
  189.    wt: 3:   38 Formulas and derivatives for powers and roots
  190.    wt: 3:   Postscript For Better Performance
  191.    wt: 3:   Appendix A. Reading Guide For Next Appendices
  192.    wt: 3:   Chapter 29 Contrapositive and Vacuously True Implications
  193.    wt: 3:   Chapter 19. Functions and Sets
  194.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  195.    wt: 3:   Chapter 9 Talking about Numbers or Quantities
  196.    wt: 3:   Solutions For Arithmetic Exercises
  197.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  198.    wt: 3:   G. Written work formats for developing and showing skill
  199.    wt: 3:   Helping the Blind in Logic and Mathematics
  200.    wt: 3:   Mathematics Education References
  201.    wt: 3:   Mathematics Education References
  202.    wt: 3:   Multiple Ways to Improve Mathematics Skill Development
  203.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  204.    wt: 3:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  205.    wt: 2:   1 Conductance Resistance Duality01
  206.    wt: 2:   H Series Circuit02
  207.    wt: 2:   C Electromotive force conventional current02
  208.    wt: 2:   B Electromotive force conventional current01
  209.    wt: 2:   Home Tutoring and Home Schooling
  210.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  211.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  212.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  213.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  214.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  215.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  216.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  217.    wt: 2:   18 Primary School Mathematics
  218.    wt: 2:   16 Secondary Mathematics Tips
  219.    wt: 2:   14 Multiplication and Times Tables
  220.    wt: 2:   13 Addition and Addition Tables
  221.    wt: 2:   11 Help and Defend Your Child or Teens Education
  222.    wt: 2:   8 The Effect of Negative Remarks
  223.    wt: 2:   7 Student Motivation
  224.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  225.    wt: 2:   2 Reading and Writing Skills
  226.    wt: 2:   1 Speaking Skills
  227.    wt: 2:   Ages 9 to 10
  228.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  229.    wt: 2:   19 Horizontal line rule and method
  230.    wt: 2:   9 Set theory term relation possible origins
  231.    wt: 2:   5 Function notation for geometric transformations
  232.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  233.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  234.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  235.    wt: 2:   9 motivation for name arcsin
  236.    wt: 2:   8 Radian Measures of Common Angles
  237.    wt: 2:   9 Head to Tail Coordinate View
  238.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  239.    wt: 2:   C Straight Lines Slope from Coordinates
  240.    wt: 2:   B Straight Line Slope Scaling Properties More
  241.    wt: 2:   A Straight Line Slope Scaling Properties
  242.    wt: 2:   14 Straight Lines Equations General Case
  243.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  244.    wt: 2:   12 Straight Lines Graphing mx plus b
  245.    wt: 2:   11 Straight Lines Graphing y=mx
  246.    wt: 2:   10 Straight Lines through Origin Equations More
  247.    wt: 2:   7 Tangent Function is odd on this domain
  248.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  249.    wt: 2:   5 Tangent Function Graph
  250.    wt: 2:   4 Tangent Function Properties
  251.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  252.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  253.    wt: 2:   29 secant cosecant and cotangent for acute angles
  254.    wt: 2:   26 Formulas for products of sines and cosines
  255.    wt: 2:   20 sine and cosine Double Angle Formulas
  256.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  257.    wt: 2:   17E Trig Formulas for dot and cross Products
  258.    wt: 2:   17D cis formulas for sine cosines and tangent
  259.    wt: 2:   12 Graph of tangent function for one period
  260.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  261.    wt: 2:   2 Quadrant I reference Angles
  262.    wt: 2:   1 Unit Points Reflections Rotations
  263.    wt: 2:   19 N th Roots of Unity
  264.    wt: 2:   13 Trig Formulas for dot and cross Products
  265.    wt: 2:   12 cis formulas for sine cosines and tangent
  266.    wt: 2:   9 The complex number valued trig function cis
  267.    wt: 2:   9 Similarity of Triangles Usual Criteria
  268.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  269.    wt: 2:   4 Equations for lines three forms
  270.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  271.    wt: 2:   19 Right Triangle Similarity
  272.    wt: 2:   9 Construction of a right bisector
  273.    wt: 2:   A Signed Number Arithmetic Review
  274.    wt: 2:   5 Proportionality in Equivalent Fractions
  275.    wt: 2:   4 Rates Ratios and Proporitionality
  276.    wt: 2:   3 Proportionality Examples
  277.    wt: 2:   2 Algebraic View
  278.    wt: 2:   1 What is Proportionality
  279.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  280.    wt: 2:   6 Compound Interest Forward and Backwards
  281.    wt: 2:   5 Triangle Area Formula Backwards
  282.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  283.    wt: 2:   9 Coordinates for Regions in Space
  284.    wt: 2:   Simple Exercises
  285.    wt: 2:   9 Three Examples
  286.    wt: 2:   Formula Usage Show Work Format
  287.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  288.    wt: 2:   11 Volume of Sphere
  289.    wt: 2:   10 Volume of Pyramid
  290.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  291.    wt: 2:   1 More and Less Than for Counts and Measures
  292.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  293.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  294.    wt: 2:   4 LCM of 8 and 10 via Prime
  295.    wt: 2:   11 What are real lengths and numbers
  296.    wt: 2:   10 dividing signed numbers
  297.    wt: 2:   8 multiplying signed numbers
  298.    wt: 2:   7 negative and additive inverse
  299.    wt: 2:   6 adding signed numbers
  300.    wt: 2:   5 lengths and signs of numbers
  301.    wt: 2:   2 signed and unsigned numbers as coordinates
  302.    wt: 2:   7 Converting or Changing Units
  303.    wt: 2:   6 Simplification of Fractions with Units
  304.    wt: 2:   4 Fractions with Units
  305.    wt: 2:   3 Multiplying Units and Numbers
  306.    wt: 2:   2 Equality and Units
  307.    wt: 2:   1 Addition and Subtraction with Units
  308.    wt: 2:   D Three Term Ratios
  309.    wt: 2:   B Fractions and Two Term Ratios
  310.    wt: 2:   A Similarities between Fractions and Two Term Ratios
  311.    wt: 2:   21 Reciprocals for Fractions and Wholes
  312.    wt: 2:   19 Dividing Fractions How TO
  313.    wt: 2:   16 Addition Subtraction Comparision Compared
  314.    wt: 2:   15 Adding and Subtracting with Unlike Denominators
  315.    wt: 2:   9 Improper Fractions and Mixed Numbers
  316.    wt: 2:   11 Adding Integers Formulas and Examples
  317.    wt: 2:   10 Integer Multiplication Formulas
  318.    wt: 2:   26 Divisibility by 2 3 5 Example
  319.    wt: 2:   16 video Factors of 980 using prime
  320.    wt: 2:   8 video Prime Factorization upto 19
  321.    wt: 2:   3 video Primes and Composites from 9 times table
  322.    wt: 2:   Division with Counts and Length
  323.    wt: 2:   12 Why Long Division Works Take III
  324.    wt: 2:   11 Another Single Digit Divisor Example
  325.    wt: 2:   10 Division by Five Long and Short Ways
  326.    wt: 2:   8 Correcting the Mistake
  327.    wt: 2:   7 Long Divison Mistake Catching
  328.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  329.    wt: 2:   5 Long Division Include Zeroes or not
  330.    wt: 2:   4 Division with 2 Digit Divsors
  331.    wt: 2:   3 Division Single Digit Divisor Example
  332.    wt: 2:   2 Division with Single Digit Divisors
  333.    wt: 2:   1 Divsion Physical Examples
  334.    wt: 2:   D Decimal Multiplication Methods Derived
  335.    wt: 2:   B Powers of Ten
  336.    wt: 2:   6 Multiplication Commutes Order Not Important
  337.    wt: 2:   5 Decimal Fraction Multiplication
  338.    wt: 2:   4 Two and Three Digit Multipliers
  339.    wt: 2:   3 More One Digit Multipliers
  340.    wt: 2:   2 One Digit Multipliers
  341.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  342.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  343.    wt: 2:   Video Power Notation in Decimal Expansion
  344.    wt: 2:   1 Why 3 times 5 gives 15
  345.    wt: 2:   8 Subtraction with Units of Measure
  346.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  347.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  348.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  349.    wt: 2:   2 Subtraction Easy Case Examples
  350.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  351.    wt: 2:   8 What skills and work habits to require
  352.    wt: 2:   7 Adding decimal fractions using decimal point
  353.    wt: 2:   6. Counting and adding units and mixed units
  354.    wt: 2:   5. How to add decimals C. Examples
  355.    wt: 2:   4. How to add with decimals B with conversions
  356.    wt: 2:   3. How to add with decimals A sans conversions
  357.    wt: 2:   2 Decimal Counting Practices
  358.    wt: 2:   1. Explaining Addition Table
  359.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  360.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  361.    wt: 2:   Exact Arithmetic Wholes and Fractions
  362.    wt: 2:   Formula Evaluation how to show work
  363.    wt: 2:   The 12 Times Table Visually
  364.    wt: 2:   19 Chain Rule for linear functions
  365.    wt: 2:   2 Motivation for Limit Definition Take 1
  366.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  367.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  368.    wt: 2:   Chapter 9 About First Courses in Calculus
  369.    wt: 2:   Postscript More on Better Performance
  370.    wt: 2:   Chapter 23. Notation For Sums
  371.    wt: 2:   Chapter 21. Third Reading Guide
  372.    wt: 2:   Chapter 18. Rules for Algebra
  373.    wt: 2:   Chapter 13. Second Reading Guide
  374.    wt: 2:   Chapter 12. Shorthand Usage Guide
  375.    wt: 2:   Postscript What is a Variable
  376.    wt: 2:   Chapter 8 Three Skills For Algebra
  377.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  378.    wt: 2:   Foreword
  379.    wt: 2:   Chapter 9 The Two Ends
  380.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  381.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  382.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  383.    wt: 2:   S Adding words to algebra
  384.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  385.    wt: 2:   N Mathematics Prepare for College Studies
  386.    wt: 2:   M Words to extend arithmetic
  387.    wt: 2:   I. Logic and language skills
  388.    wt: 2:   Implementation Notes
  389.    wt: 2:   More Algebra and Slope based Calculus Preview
  390.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  391.    wt: 2:   Systematic Algebra Skill Development Missing Links
  392.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  393.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  394.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  395.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  396.    wt: 2:   Which Way To Go
  397.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  398.    wt: 1:   chapitre 04 09 Regles accidentelles
  399.    wt: 1:   3 Energy Power Heat08
  400.    wt: 1:   2 Energy Power Heat07
  401.    wt: 1:   1 Energy Power Heat06
  402.    wt: 1:   E Energy Power05
  403.    wt: 1:   D Energy Power04
  404.    wt: 1:   C Energy Power03
  405.    wt: 1:   B Energy Power02
  406.    wt: 1:   A Energy Power01
  407.    wt: 1:   2 Conductance Resistance Duality02
  408.    wt: 1:   F Wire Resistance Calculation04
  409.    wt: 1:   E Wire Resistance Calculation03
  410.    wt: 1:   D Wire Resistance Calculation02
  411.    wt: 1:   C Wire Resistance Calculation01
  412.    wt: 1:   B Wire Resistance Qualitative02
  413.    wt: 1:   A Wire Resistance Qualitative01
  414.    wt: 1:   3 Like resistors in parallel
  415.    wt: 1:   2 Unlike resistors in parallel01
  416.    wt: 1:   1 Like resistors in series
  417.    wt: 1:   G Series Circuit01
  418.    wt: 1:   F Unlike Resistors in Series
  419.    wt: 1:   E Kirchoffs Second Law
  420.    wt: 1:   D Kirchoff First Law
  421.    wt: 1:   A Circuit Elements
  422.    wt: 1:   Ages 12 to 14 Arithmetic
  423.    wt: 1:   Ages 10 to 12 Arithmetic
  424.    wt: 1:   Ages 8 to 9
  425.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  426.    wt: 1:   sign monoticity analysis example 4
  427.    wt: 1:   sign monoticity analysis example 3
  428.    wt: 1:   sign monoticity analysis example 2
  429.    wt: 1:   sign monoticity analysis example 1
  430.    wt: 1:   6 Set Existence Formation and Notation
  431.    wt: 1:   3 Formula or function graphing exercise
  432.    wt: 1:   Introduction Reading Guide
  433.    wt: 1:   9 quadratics physical and further context
  434.    wt: 1:   8 quadratics backward use of various formulas
  435.    wt: 1:   7 quadratic formulla derivation
  436.    wt: 1:   8 Notes for instructors or tutors
  437.    wt: 1:   12 motivation for term arctan
  438.    wt: 1:   4 possible motivation for term arccos
  439.    wt: 1:   9 Summary Degrees to Radians and back
  440.    wt: 1:   7 Radian Measures in special Triangles
  441.    wt: 1:   6 Radian Measure to Degrees
  442.    wt: 1:   5 Degrees to Radian Measure
  443.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  444.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  445.    wt: 1:   2 Radian Measure Numerical Value of one degree
  446.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  447.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  448.    wt: 1:   Straight Lines Intersection of
  449.    wt: 1:   17 tangent function angle sum formulas
  450.    wt: 1:   30 unit circle calculation of six trigonometric functions
  451.    wt: 1:   25 tangent double angle formula Slope connection
  452.    wt: 1:   24 tangent Angle Difference Formula
  453.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  454.    wt: 1:   21 sine and cosine Half Angle Formulas
  455.    wt: 1:   17C sine and cosine double triple angle formulas
  456.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  457.    wt: 1:   9 Graphs of sine and cosine over one period
  458.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  459.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  460.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  461.    wt: 1:   11 sine and cosine double triple angle formulas
  462.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  463.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  464.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  465.    wt: 1:   1 Early Concept of Like or Similar Shapes
  466.    wt: 1:   8 Mid Point Formula
  467.    wt: 1:   3 Slope product for perpendicular lines
  468.    wt: 1:   2 point slope equation for a line
  469.    wt: 1:   13 Pythagorean spatial distance formulas
  470.    wt: 1:   10 Pythagorean plane distance formula
  471.    wt: 1:   PS H Distributive Law For Complex Numbers
  472.    wt: 1:   A Modular and Remainder Arithmetic
  473.    wt: 1:   19 Signed Multiples of Vectors
  474.    wt: 1:   9 Division with Digits after Decimal Point
  475.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  476.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  477.    wt: 1:   E Long Division Methods more
  478.    wt: 1:   D Long Division Methods
  479.    wt: 1:   C Three Decimal Subtraction Methods
  480.    wt: 1:   B Decimal Comparison and Subtraction
  481.    wt: 1:   A Decimal Addition Columm Methods
  482.    wt: 1:   6 Column Methods for Decimal Multiplication
  483.    wt: 1:   5 Distributive Law for Whole Numbers
  484.    wt: 1:   4 Commutative Law Groups Counting Form
  485.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  486.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  487.    wt: 1:   3 Linear Equation Literal Solution More
  488.    wt: 1:   2 Linear Equation Literal Solution
  489.    wt: 1:   1 Changing Calculations
  490.    wt: 1:   3 Product Axioms Two Forms
  491.    wt: 1:   2 More and Less Than for Counts and Measures
  492.    wt: 1:   8 Coordinates for Maps and Planes
  493.    wt: 1:   3 Geometric Formulas and Function Notation
  494.    wt: 1:   1 Formulas Dependence and Function Notation
  495.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  496.    wt: 1:   6 Algebraic Solution Example
  497.    wt: 1:   5 Algebraic Solutions Introduction
  498.    wt: 1:   4 Four Examples Fractional Coefficients
  499.    wt: 1:   3 Four Examples
  500.    wt: 1:   2 Three Examples
  501.    wt: 1:   1 Proper Equal Sign Usage
  502.    wt: 1:   Using Letters for Physical Quantities
  503.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  504.    wt: 1:   9 Sets in Probability and Statistics
  505.    wt: 1:   3 Adding Words To Arithmetic
  506.    wt: 1:   1 Three Skills For Algebra
  507.    wt: 1:   4 Greater More Less Than Signs in General
  508.    wt: 1:   3 Comparison of Negative Numbers
  509.    wt: 1:   2 More and Less Than with Unlike Signs
  510.    wt: 1:   5 Square Roots with primes more still
  511.    wt: 1:   4 Square Roots with primes more
  512.    wt: 1:   3 Properties of Square Roots with example
  513.    wt: 1:   2 Square Roots with Prime
  514.    wt: 1:   1 Squares and Square Roots Introduction
  515.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  516.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  517.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  518.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  519.    wt: 1:   13 GCD from given Prime Factorization
  520.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  521.    wt: 1:   8 GCD from Euclidean Algorithm
  522.    wt: 1:   7 GCD and LCM from prime factorization
  523.    wt: 1:   6 GCD from Prime
  524.    wt: 1:   5 Common Divisors 60 45 via Prime
  525.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  526.    wt: 1:   2 Least Common Multiple LCM intro via list method
  527.    wt: 1:   1 Least Common Multiples LCM Introduction
  528.    wt: 1:   12 GCD 2700 288 via Prime
  529.    wt: 1:   22 Complex Compound Fractions
  530.    wt: 1:   21 Working With Signs
  531.    wt: 1:   20 Dividing Fractions the Why
  532.    wt: 1:   18 Efficient Ways to Multiply
  533.    wt: 1:   17 Efficient Ways to Add and Subtract
  534.    wt: 1:   14 Adding and Subtracting with Like Denominators
  535.    wt: 1:   13 Fraction Comparison Algebraic View
  536.    wt: 1:   12 Fraction Comparison
  537.    wt: 1:   11 Simplification an Algebraic View
  538.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  539.    wt: 1:   8 Numerals Fractionals Quantals Take II
  540.    wt: 1:   7 Numerals Fractionals Quantals
  541.    wt: 1:   6 Multiplication of Mixed Numbers
  542.    wt: 1:   6 Multiplication Algebraically Take II
  543.    wt: 1:   5 Equivalent Fractions
  544.    wt: 1:   4 Fraction Multiplication
  545.    wt: 1:   3 Unit fraction of a fraction
  546.    wt: 1:   2 Unit Fraction Multiplication
  547.    wt: 1:   1 What is a fraction Take II
  548.    wt: 1:   1 What is a fraction
  549.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  550.    wt: 1:   D Remainders Modulo 11 Pair Rule
  551.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  552.    wt: 1:   B Integer Long Division Multiple Choices
  553.    wt: 1:   A Associative Law Theorectical Note
  554.    wt: 1:   13 Subtraction with Additive Inverse
  555.    wt: 1:   12 Adding Integers More Examples
  556.    wt: 1:   8 Multiplication by Signed Numbers Integers
  557.    wt: 1:   7 Multiplication by Signs
  558.    wt: 1:   6 Multiplication by Natural Numbers
  559.    wt: 1:   5 Zero Movement and Additive Inverses
  560.    wt: 1:   4 Adding Movements wiht opposite directions
  561.    wt: 1:   3 Adding Movements with same direction
  562.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  563.    wt: 1:   1 Integers as Coordinates
  564.    wt: 1:   20 Uniqueness of Prime Factorization
  565.    wt: 1:   18 video Count Factors given Prime Factorization
  566.    wt: 1:   17 Identify and Count Factors using Primes
  567.    wt: 1:   15 video Factors of 20 using Prime Factorization
  568.    wt: 1:   14 video Factors of 24 Take II
  569.    wt: 1:   13 video Factors of 24 using prime
  570.    wt: 1:   12 LCD GCD and LCM using Primes
  571.    wt: 1:   11 Efficient Square Rule Use
  572.    wt: 1:   10 video Prime Factorization upto 23 squared
  573.    wt: 1:   7 Calculator Usage Notes and Cautions
  574.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  575.    wt: 1:   5 Prime Factorization and a Square Rule
  576.    wt: 1:   4 video Prime Factorization Introduction
  577.    wt: 1:   2 Prime and Composites less than 16
  578.    wt: 1:   1 video how Products are bigger than factor
  579.    wt: 1:   11 Place Value SI Standard International way
  580.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  581.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  582.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  583.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  584.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  585.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  586.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  587.    wt: 1:   Quick history of numbers and algebra
  588.    wt: 1:   Expression Evaluation how to show work
  589.    wt: 1:   The 20 Times Table
  590.    wt: 1:   About folder contents
  591.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  592.    wt: 1:   5 Conversion Arithmetic
  593.    wt: 1:   A Chain Rule Real Player video examples
  594.    wt: 1:   36 Cube root derivative animated
  595.    wt: 1:   29 Chain Rule Optional Reading
  596.    wt: 1:   28 Chain Rule Preparation for a Proof
  597.    wt: 1:   22 Chain Rule for polynomials
  598.    wt: 1:   21 Chain Rule for powers
  599.    wt: 1:   20 Chain Rule for Pulley Systems
  600.    wt: 1:   11 Quotient rule
  601.    wt: 1:   10 Power rule for negative integers
  602.    wt: 1:   9 Reciprocal rule
  603.    wt: 1:   3 Motivation for Limit Definition Take 2
  604.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  605.    wt: 1:   9 Limits Continuity and Composition
  606.    wt: 1:   3 Decimal insights for limits continuity convergence
  607.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  608.    wt: 1:   G.5 Motions With Bounded Velocities
  609.    wt: 1:   F.1 What Functions are Continuous
  610.    wt: 1:   PostScript For and Against Decimal Perspectives
  611.    wt: 1:   Fall 1983 Calculus Appetizer
  612.    wt: 1:   Foreword
  613.    wt: 1:   Appendix E. How To Study Mathematics and Why
  614.    wt: 1:   Appendix D. What to do in School and Why
  615.    wt: 1:   Appendix C. How to Read
  616.    wt: 1:   Appendix B. How To Learn
  617.    wt: 1:   Chapter 31 Direct and Indirect Reason
  618.    wt: 1:   Chapter 30 Truth Tables
  619.    wt: 1:   Chapter 28 Occurrence Tables
  620.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  621.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  622.    wt: 1:   Chapter 25. Mathematical Induction Examples
  623.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  624.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  625.    wt: 1:   Chapter 20. Degrees and Radians
  626.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  627.    wt: 1:   Chapter 16. Painless Theorem Proving
  628.    wt: 1:   Chapter 15. Solving Linear Equations
  629.    wt: 1:   Chapter 11. Why Shorthand
  630.    wt: 1:   Chapter 10 Describing and Changing Calculations
  631.    wt: 1:   Chapter 6 Change of Language
  632.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  633.    wt: 1:   Chapter 4 Longer Chains of Reason
  634.    wt: 1:   Chapter 3 Chains of Reason
  635.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  636.    wt: 1:   Chapter 2 For and Against Mathematics
  637.    wt: 1:   Foreword
  638.    wt: 1:   Postscript C Consistency as a Tool for Reason
  639.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  640.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  641.    wt: 1:   Foreword
  642.    wt: 1:   R Why Learn Mathematics Skills
  643.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  644.    wt: 1:   O On Learning Mathematics and Science
  645.    wt: 1:   L Skills with take home value
  646.    wt: 1:   N Improving Marks on Tests and Finals
  647.    wt: 1:   J. More on written work and showing skill
  648.    wt: 1:   H more Routine to non routine problem solving
  649.    wt: 1:   H Jigsaw puzzles and problem solving
  650.    wt: 1:   F. The student teacher tutor feedback loop
  651.    wt: 1:   E. When and how to correct errors
  652.    wt: 1:   D. Check work a must with a caution
  653.    wt: 1:   C. Domino effect of being careful
  654.    wt: 1:   B. Domino effect of errors
  655.    wt: 1:   A. Skill has to be seen to believed
  656.    wt: 1:   How to Build Skills and Confidence
  657.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  658.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  659.    wt: 1:   Chapter 1 Arithmetic
  660.    wt: 1:   7 Games and Activities for Instruction
  661.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  662.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  663.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  664.    wt: 1:   The Math Forum and Site Content

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

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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