Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic
and Pattern Based Reason to inform and amuse thinkers and avid readers, studying or not. Enjoy.

Logic mastery strengthens comprehension and improve home, work & study habits.
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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

About: Site material shows how common troubles stem from steps too large or missing. Site material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin. If one site element is not to your liking, try another. Each is different. Many are unique

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus. Reform: look before you leap - plan all in detail first.

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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43 matches:

  1.    wt: 8:   4 Remainder Arithmetic and Divisibility/
  2.    wt: 8:   B Decimal Comparing and Subtracting Methods/
  3.    wt: 8:   A Decimal Counting and Adding Methods/
  4.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  5.    wt: 7:   8 Arithmetic with Signed Numbers/
  6.    wt: 7:   7 Arithmetic and Fractions with Units/
  7.    wt: 7:   D Decimal Long Division Methods/
  8.    wt: 7:   C Decimal Multiplication Methods/
  9.    wt: 7:   2 Arithmetic with Decimals/
  10.    wt: 6:   11 Squares and Square Roots/
  11.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  12.    wt: 6:   9 Combinatorics Trees Tables and Products/
  13.    wt: 6:   6 Fractions and Ratios/
  14.    wt: 6:   3 Prime Factorization Skills/
  15.    wt: 5:   5 Integers/
  16.    wt: 5:   1 Decimal Place Value/
  17.    wt: 5:   Arithmetic and Number Theory Skills/
  18.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  19.    wt: 1:   Mathematics Skills Year by Year/
  20.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  21.    wt: 1:   12 Function Translating and Rescaling/
  22.    wt: 1:   11 Parallel Straight Lines and Transversals/
  23.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  24.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  25.    wt: 1:   7 Complex Numbers/
  26.    wt: 1:   4 Lines and Slopes Take 1/
  27.    wt: 1:   3 Cartesian and Polar Coordinates/
  28.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  29.    wt: 1:   B Real Numbers Extrinsic Development/
  30.    wt: 1:   A Origins of Counting and Figuring Methods/
  31.    wt: 1:   9 Proportionality Backwards and Forwards/
  32.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  33.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  34.    wt: 1:   5 Real Numbers/
  35.    wt: 1:   4 Computation Rules and Function Notation/
  36.    wt: 1:   Step 1 Stick diagram and fractions/
  37.    wt: 1:   Time Date Matters/
  38.    wt: 1:   Skills with take home value/
  39.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  40.    wt: 1:   13 Lessons on Limits and Continuity/
  41.    wt: 1:   Volume 2 Three Skills For Algebra/
  42.    wt: 1:   Work and Study Tips/
  43.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

384 matches:

  1.    wt: 5:   1 Decimals Modular and Remainder Arithmetic
  2.    wt: 5:   A Decimals Modular and Remainder Arithmetic
  3.    wt: 4:   A Modular and Remainder Arithmetic
  4.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  5.    wt: 3:   P Exact Arithmetic With Whole Numbers and Fractions
  6.    wt: 3:   Primary and Secondary Skills and Practices with Take Home Value
  7.    wt: 3:   1 From Number Recognition and Counting to Arithmetic B
  8.    wt: 3:   1 From Number Recognition and Counting to Arithmetic A
  9.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  10.    wt: 2:   Ramblings Extrinsic numbers theory
  11.    wt: 2:   Skills Chapter 1 Arithmetic
  12.    wt: 2:   7 logic review and decimals an odd combination
  13.    wt: 2:   2 arithmetic with signed numbers
  14.    wt: 2:   1 arithmetic with unsigned numbers
  15.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  16.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  17.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  18.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  19.    wt: 2:   2 Reading and Writing Skills
  20.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  21.    wt: 2:   Vector and Complex Number Applet
  22.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  23.    wt: 2:   14 cosine even and sine and tangent are odd
  24.    wt: 2:   3 Lengths and Areas on Maps and Plans
  25.    wt: 2:   A Signed Number Arithmetic Review
  26.    wt: 2:   11 Signed Number Addition and Addition Properties
  27.    wt: 2:   2 Combing Counts Addition Skills and Principles
  28.    wt: 2:   2 More and Less Than for Counts and Measures
  29.    wt: 2:   10 Real Number Lengths and Signs
  30.    wt: 2:   1 Whole and Natural Numbers
  31.    wt: 2:   5 Talking about Numbers and Quantities
  32.    wt: 2:   4 A Brief Story of numbers and algebra
  33.    wt: 2:   1 More and Less Than for Counts and Measures
  34.    wt: 2:   11 What are real lengths and numbers
  35.    wt: 2:   5 lengths and signs of numbers
  36.    wt: 2:   2 signed and unsigned numbers as coordinates
  37.    wt: 2:   3 Multiplying Units and Numbers
  38.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  39.    wt: 2:   9 Improper Fractions and Mixed Numbers
  40.    wt: 2:   23 Remainder Arithmetic Modulo 2
  41.    wt: 2:   22 Remainder Arithmetic Modulo 3 more
  42.    wt: 2:   21 Remainder Arithmetic Modulo 3
  43.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  44.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  45.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  46.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  47.    wt: 2:   16 Remainder Arithmetic Modulo 9 Example 2
  48.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  49.    wt: 2:   14 Remainder Arithmetic Modulo 9 Example
  50.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  51.    wt: 2:   12 Remainder Arithmetic Modulo 10 Example
  52.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  53.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  54.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  55.    wt: 2:   8 Remainder Arithmetic Morulo 5 Examples II
  56.    wt: 2:   7 Remainder Arithmetic Modulo 5 Examples I
  57.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  58.    wt: 2:   5 Remainder Arithmetic Modulo 5
  59.    wt: 2:   4 Remainder Arithmetic Modulo 10 in general
  60.    wt: 2:   3 Remainder Arithmetic Modulos 10 more still
  61.    wt: 2:   2 Remainder Arithmetic Modulo 10 more
  62.    wt: 2:   1 Remainder Arithmetic Modulo 10
  63.    wt: 2:   8 What skills and work habits to require
  64.    wt: 2:   6. Counting and adding units and mixed units
  65.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  66.    wt: 2:   Quick history of numbers and algebra
  67.    wt: 2:   Exact Arithmetic Wholes and Fractions
  68.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  69.    wt: 2:   38 Formulas and derivatives for powers and roots
  70.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  71.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  72.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  73.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  74.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  75.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  76.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  77.    wt: 2:   I. Logic and language skills
  78.    wt: 2:   How to Build Skills and Confidence
  79.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  80.    wt: 2:   2 Identifying Size and Position Place and Spatial Sense
  81.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  82.    wt: 1:   Appendix 2 primary school Arithmetic 01
  83.    wt: 1:   Appendix 1 primary and preschool mathematic
  84.    wt: 1:   G LAMP Introduction Problem Solving Skills
  85.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  86.    wt: 1:   Skills Chapter 5 Calculus
  87.    wt: 1:   Skills Chapter 4 Logic
  88.    wt: 1:   Skills Chapter 3 Algebra
  89.    wt: 1:   Skills Chapter 2 Geometry
  90.    wt: 1:   Skills Chapter 0 Introduction
  91.    wt: 1:   5 logarithms and exponentials etc
  92.    wt: 1:   key notes and themes
  93.    wt: 1:   what should be learnt and When
  94.    wt: 1:   standards for course material
  95.    wt: 1:   Theory of Knowledge
  96.    wt: 1:   Education in mathematics science and technology
  97.    wt: 1:   Motivation and Context Problem
  98.    wt: 1:   fairness and inductive principles for instruction
  99.    wt: 1:   Home Tutoring and Home Schooling
  100.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  101.    wt: 1:   24 Standards For Skill Develoment Take II
  102.    wt: 1:   24 Standards For Skill Develoment
  103.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  104.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  105.    wt: 1:   17 Math Booklets for children and young teenagers
  106.    wt: 1:   14 Multiplication and Times Tables
  107.    wt: 1:   13 Addition and Addition Tables
  108.    wt: 1:   12 Goals and Objectives For Mathematics
  109.    wt: 1:   11 Help and Defend Your Child or Teens Education
  110.    wt: 1:   5 Patience Please for Yourself and Your Charges
  111.    wt: 1:   4 Learning Takes Time and Effort
  112.    wt: 1:   1 Speaking Skills
  113.    wt: 1:   Ages 12 to 14 Skills with take home value
  114.    wt: 1:   Ages 12 to 14 Arithmetic
  115.    wt: 1:   Ages 10 to 12 Arithmetic
  116.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  117.    wt: 1:   26 Function definitions done and coming
  118.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  119.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  120.    wt: 1:   19 Horizontal line rule and method
  121.    wt: 1:   18 Vertical Line Rule and Method
  122.    wt: 1:   17 Function maxima minima and their location
  123.    wt: 1:   11 Function Domain Range Source and Targets
  124.    wt: 1:   9 Set theory term relation possible origins
  125.    wt: 1:   8 Set view of relations and functions
  126.    wt: 1:   6 Set Existence Formation and Notation
  127.    wt: 1:   4 Function notation in and beyond mathematics
  128.    wt: 1:   9 quadratics physical and further context
  129.    wt: 1:   11 Growth and Decay in Biology
  130.    wt: 1:   10 Exponential Growth and Decay Models
  131.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  132.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  133.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  134.    wt: 1:   16 cotangent function Definition Graph and Inverse
  135.    wt: 1:   15 cosecant function Definition Graph and Inverse
  136.    wt: 1:   14 secant function Definition Graph and Inverse
  137.    wt: 1:   13 cosecant function Definition Graph and Inverse
  138.    wt: 1:   9 Summary Degrees to Radians and back
  139.    wt: 1:   1 Degrees and Radians Introduction
  140.    wt: 1:   A Global Time and Navigation
  141.    wt: 1:   15 Dot and Cross Product
  142.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  143.    wt: 1:   Parallel Lines and Parallel Transversals
  144.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  145.    wt: 1:   Parallel Lines and Interior Angles
  146.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  147.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  148.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  149.    wt: 1:   29 secant cosecant and cotangent for acute angles
  150.    wt: 1:   27 Logarithmic use of products of sines and cosines
  151.    wt: 1:   26 Formulas for products of sines and cosines
  152.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  153.    wt: 1:   21 sine and cosine Half Angle Formulas
  154.    wt: 1:   20 sine and cosine Double Angle Formulas
  155.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  156.    wt: 1:   17E Trig Formulas for dot and cross Products
  157.    wt: 1:   17D cis formulas for sine cosines and tangent
  158.    wt: 1:   17C sine and cosine double triple angle formulas
  159.    wt: 1:   17A The complex number valued trig function cis
  160.    wt: 1:   10 Graphs of sines and cosines many periods
  161.    wt: 1:   9 Graphs of sine and cosine over one period
  162.    wt: 1:   7 period of sine and cosine
  163.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  164.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  165.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  166.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  167.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  168.    wt: 1:   21 Logarithms Powers and Exponentials
  169.    wt: 1:   20 N th Roots of Complex Numbers
  170.    wt: 1:   16 References and Originality Question
  171.    wt: 1:   13 Trig Formulas for dot and cross Products
  172.    wt: 1:   12 cis formulas for sine cosines and tangent
  173.    wt: 1:   11 sine and cosine double triple angle formulas
  174.    wt: 1:   9 The complex number valued trig function cis
  175.    wt: 1:   6 Field Properties of Complex Number
  176.    wt: 1:   2 Complex Numbers made easier we hope
  177.    wt: 1:   Appetizer A Complex Number Applet
  178.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  179.    wt: 1:   3 Trigonometric Ratios sine and cosine
  180.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  181.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  182.    wt: 1:   8 Similarity of Triangles and Polygons
  183.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  184.    wt: 1:   10 Midpoint of [a b] and [b a]
  185.    wt: 1:   7 Exercises to test skill and concept mastery
  186.    wt: 1:   1 Numerical view of lines and their equations
  187.    wt: 1:   What is and is not here
  188.    wt: 1:   7 Complex Numbers Appetizer
  189.    wt: 1:   6 Polar Multiplication and Rotation
  190.    wt: 1:   5 Cartesian Addition and Translation
  191.    wt: 1:   4 Polar Coordinates to and from
  192.    wt: 1:   PS H Distributive Law For Complex Numbers
  193.    wt: 1:   16 Angles Subtended By Chords and Diameters
  194.    wt: 1:   6 Ruler and compass Angle Bisection
  195.    wt: 1:   1 Initial Concepts and Terms
  196.    wt: 1:   musings do not puiblish real numbers
  197.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  198.    wt: 1:   22 Multiplication of Signed Numbers
  199.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  200.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  201.    wt: 1:   13 Arrows and Vectors in a Plane
  202.    wt: 1:   12 Real Numbers Line Signed Coordinates
  203.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  204.    wt: 1:   8 Division and Mulplication of Compound Fractions
  205.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  206.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  207.    wt: 1:   B Decimal Comparison and Subtraction
  208.    wt: 1:   7 Decimals Multiplication Methods Examples
  209.    wt: 1:   5 Distributive Law for Whole Numbers
  210.    wt: 1:   3 Multiplicative Counting Skills Principles
  211.    wt: 1:   1 The Counting Origins of Numbers
  212.    wt: 1:   4 Rates Ratios and Proporitionality
  213.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  214.    wt: 1:   6 Compound Interest Forward and Backwards
  215.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  216.    wt: 1:   6 Equations and Systems Equivalent or Implied
  217.    wt: 1:   4 Subtraction and Division Axioms
  218.    wt: 1:   2 Addition and Multiplication Axioms
  219.    wt: 1:   4 Comparison of Negative Numbers
  220.    wt: 1:   3 More and Less Than with Unlike Signs
  221.    wt: 1:   1 Real Numbers Comparison
  222.    wt: 1:   16 Real Numbers Comparison
  223.    wt: 1:   15 Real Number Division
  224.    wt: 1:   14 Real Number Multiplication
  225.    wt: 1:   13 Real Number Subtraction
  226.    wt: 1:   12 Real Number Additive Inverses or Negatives
  227.    wt: 1:   11 Real Number Addition
  228.    wt: 1:   8 Coordinates for Maps and Planes
  229.    wt: 1:   7 Real Numbers as Line Cordinates
  230.    wt: 1:   6 Unsigned Real Numbers
  231.    wt: 1:   5 Rational Numbers More
  232.    wt: 1:   4 Rational Numbers
  233.    wt: 1:   3 Geometric Formulas and Function Notation
  234.    wt: 1:   1 Formulas Dependence and Function Notation
  235.    wt: 1:   3 GE III Equation Addition and Multiplication
  236.    wt: 1:   1 Written work formats for developing and showing skill
  237.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  238.    wt: 1:   9 Sets in Probability and Statistics
  239.    wt: 1:   8 Sets of Numbers
  240.    wt: 1:   3 Adding Words To Arithmetic
  241.    wt: 1:   1 Three Skills For Algebra
  242.    wt: 1:   arithmetic videos Real Player Format
  243.    wt: 1:   3 Comparison of Negative Numbers
  244.    wt: 1:   2 More and Less Than with Unlike Signs
  245.    wt: 1:   1 Squares and Square Roots Introduction
  246.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  247.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  248.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  249.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  250.    wt: 1:   7 GCD and LCM from prime factorization
  251.    wt: 1:   4 LCM of 8 and 10 via Prime
  252.    wt: 1:   3 Counting with Tables and Trees II
  253.    wt: 1:   2 Counting with Tables and Trees I
  254.    wt: 1:   1 Counting and Counting Methods I
  255.    wt: 1:   10 dividing signed numbers
  256.    wt: 1:   9 subtracting signed numbers
  257.    wt: 1:   8 multiplying signed numbers
  258.    wt: 1:   7 negative and additive inverse
  259.    wt: 1:   6 adding signed numbers
  260.    wt: 1:   3 signed coordinates for maps and planes
  261.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  262.    wt: 1:   2 Equality and Units
  263.    wt: 1:   1 Addition and Subtraction with Units
  264.    wt: 1:   B Fractions and Two Term Ratios
  265.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  266.    wt: 1:   21 Reciprocals for Fractions and Wholes
  267.    wt: 1:   17 Efficient Ways to Add and Subtract
  268.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  269.    wt: 1:   14 Adding and Subtracting with Like Denominators
  270.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  271.    wt: 1:   6 Multiplication of Mixed Numbers
  272.    wt: 1:   D Remainders Modulo 11 Pair Rule
  273.    wt: 1:   11 Adding Integers Formulas and Examples
  274.    wt: 1:   8 Multiplication by Signed Numbers Integers
  275.    wt: 1:   6 Multiplication by Natural Numbers
  276.    wt: 1:   5 Zero Movement and Additive Inverses
  277.    wt: 1:   17 Identify and Count Factors using Primes
  278.    wt: 1:   12 LCD GCD and LCM using Primes
  279.    wt: 1:   7 Calculator Usage Notes and Cautions
  280.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  281.    wt: 1:   5 Prime Factorization and a Square Rule
  282.    wt: 1:   3 video Primes and Composites from 9 times table
  283.    wt: 1:   2 Prime and Composites less than 16
  284.    wt: 1:   Division with Counts and Length
  285.    wt: 1:   Long Division forwards and backwards Example 3
  286.    wt: 1:   Long Division forwards and backwards Example 2
  287.    wt: 1:   Long Division forwards and backwards Example 1
  288.    wt: 1:   10 Division by Five Long and Short Ways
  289.    wt: 1:   4 Two and Three Digit Multipliers
  290.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  291.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  292.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  293.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  294.    wt: 1:   5. How to add decimals C. Examples
  295.    wt: 1:   4. How to add with decimals B with conversions
  296.    wt: 1:   3. How to add with decimals A sans conversions
  297.    wt: 1:   11 Place Value SI Standard International way
  298.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  299.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  300.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  301.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  302.    wt: 1:   016 Numbering Occidental Calendar Days
  303.    wt: 1:   015 School and work day counting tables
  304.    wt: 1:   011 Division of Time Intervals By Numbers
  305.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  306.    wt: 1:   5 Conversion Arithmetic
  307.    wt: 1:   4 Mixing and Changing Units of Time
  308.    wt: 1:   3 Units and Lengths of Time
  309.    wt: 1:   2 Time and Date Matters in School
  310.    wt: 1:   1 Intro of Kids To Time Date Skills
  311.    wt: 1:   Example 1. Area Between x and x squared
  312.    wt: 1:   17 Derivatives of quotients of sine and cosine
  313.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  314.    wt: 1:   15 sine and cosine derivatives 3rd step
  315.    wt: 1:   14 sine and cosine derivatives 2nd step
  316.    wt: 1:   13 sine and cosine derivatives 1st step
  317.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  318.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  319.    wt: 1:   9 Limits Continuity and Composition
  320.    wt: 1:   5 Jumps and absence of unlimited error control
  321.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  322.    wt: 1:   PostScript For and Against Decimal Perspectives
  323.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  324.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  325.    wt: 1:   Chapter 22 Complex Numbers
  326.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  327.    wt: 1:   Chapter 12. Units and Slopes
  328.    wt: 1:   Chapter 10 Slopes and Units
  329.    wt: 1:   Chapter 7 Slopes and Velocity
  330.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  331.    wt: 1:   Chapter 2. Slopes and Ski Trails
  332.    wt: 1:   Appendix E. How To Study Mathematics and Why
  333.    wt: 1:   Appendix D. What to do in School and Why
  334.    wt: 1:   Chapter 31 Direct and Indirect Reason
  335.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  336.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  337.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  338.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  339.    wt: 1:   Chapter 20. Degrees and Radians
  340.    wt: 1:   Chapter 19. Functions and Sets
  341.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  342.    wt: 1:   Chapter 12. Shorthand Usage Guide
  343.    wt: 1:   Chapter 11. Why Shorthand
  344.    wt: 1:   Chapter 10 Describing and Changing Calculations
  345.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  346.    wt: 1:   Chapter 8 Three Skills For Algebra
  347.    wt: 1:   Solutions For Arithmetic Exercises
  348.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  349.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  350.    wt: 1:   Chapter 2 For and Against Mathematics
  351.    wt: 1:   Postscript B More on Story Telling and Reason
  352.    wt: 1:   Chapter 24 Direct and Indirect Reason
  353.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  354.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  355.    wt: 1:   Chapter 18 Sense and Knowledge
  356.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  357.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  358.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  359.    wt: 1:   R Why Learn Mathematics Skills
  360.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  361.    wt: 1:   O On Learning Mathematics and Science
  362.    wt: 1:   M Words to extend arithmetic
  363.    wt: 1:   L Skills with take home value
  364.    wt: 1:   N Improving Marks on Tests and Finals
  365.    wt: 1:   J. More on written work and showing skill
  366.    wt: 1:   H Jigsaw puzzles and problem solving
  367.    wt: 1:   G. Written work formats for developing and showing skill
  368.    wt: 1:   E. When and how to correct errors
  369.    wt: 1:   Chapter 8 Skipped Topics and Why
  370.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  371.    wt: 1:   Chapter 6 More Algebra and Geometry
  372.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  373.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  374.    wt: 1:   Chapter 1 Arithmetic
  375.    wt: 1:   7 Games and Activities for Instruction
  376.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  377.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  378.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  379.    wt: 1:   Helping the Blind in Logic and Mathematics
  380.    wt: 1:   More Algebra and Slope based Calculus Preview
  381.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  382.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  383.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  384.    wt: 1:   The Math Forum and Site Content

Extended Search

711 matches:

  1.    wt: 9:   1 More and Less Than for Counts and Measures
  2.    wt: 9:   11 What are real lengths and numbers
  3.    wt: 9:   5 lengths and signs of numbers
  4.    wt: 9:   2 signed and unsigned numbers as coordinates
  5.    wt: 9:   3 Multiplying Units and Numbers
  6.    wt: 9:   Appendix 1 Decimals Comparison Method Take II
  7.    wt: 9:   4 Subtraction with Conversions Borrows and Letter J
  8.    wt: 9:   3 Harder Cases Convert to Compare and Subtract
  9.    wt: 9:   1 Comparison and Subtraction Easy Direct Cases
  10.    wt: 9:   5. How to add decimals C. Examples
  11.    wt: 9:   4. How to add with decimals B with conversions
  12.    wt: 9:   3. How to add with decimals A sans conversions
  13.    wt: 8:   3 Comparison of Negative Numbers
  14.    wt: 8:   2 More and Less Than with Unlike Signs
  15.    wt: 8:   10 dividing signed numbers
  16.    wt: 8:   9 subtracting signed numbers
  17.    wt: 8:   8 multiplying signed numbers
  18.    wt: 8:   7 negative and additive inverse
  19.    wt: 8:   6 adding signed numbers
  20.    wt: 8:   3 signed coordinates for maps and planes
  21.    wt: 8:   5 Reciprocals and Division for Fractions with Units
  22.    wt: 8:   2 Equality and Units
  23.    wt: 8:   1 Addition and Subtraction with Units
  24.    wt: 8:   C Equality for Fractions and Two Term Ratios and Fractions
  25.    wt: 8:   9 Improper Fractions and Mixed Numbers
  26.    wt: 8:   27 Divisibility by 2 3 6 5 9 10 Example
  27.    wt: 8:   26 Divisibility by 2 3 5 Example
  28.    wt: 8:   25 Divisibility Tests for 2 3 5 9 10 Example
  29.    wt: 8:   24 Divisibility Tests for 2 3 5 9 10
  30.    wt: 8:   Division with Counts and Length
  31.    wt: 8:   Long Division forwards and backwards Example 3
  32.    wt: 8:   Long Division forwards and backwards Example 2
  33.    wt: 8:   Long Division forwards and backwards Example 1
  34.    wt: 8:   10 Division by Five Long and Short Ways
  35.    wt: 8:   4 Two and Three Digit Multipliers
  36.    wt: 8:   Appendix 2 Three Decimal Subtraction Methods
  37.    wt: 8:   Subtraction with J Conversions Example
  38.    wt: 8:   Subtraction Another Video Lesson
  39.    wt: 8:   9 22 Minute Subtraction Review Video
  40.    wt: 8:   8 Subtraction with Units of Measure
  41.    wt: 8:   7 Subtraction for Decimal Fractions with Exercises
  42.    wt: 8:   6 Subtraction with Conversion Example with Exercises
  43.    wt: 8:   5 A Tip for Efficent Subtraction
  44.    wt: 8:   2 Subtraction Easy Case Examples
  45.    wt: 8:   Appendix 1 Counting Revisited 15 minute video
  46.    wt: 8:   7 Adding decimal fractions using decimal point
  47.    wt: 8:   2 Decimal Counting Practices
  48.    wt: 8:   1. Explaining Addition Table
  49.    wt: 7:   4 Greater More Less Than Signs in General
  50.    wt: 7:   1 Squares and Square Roots Introduction
  51.    wt: 7:   17 GCD LCM of 85 and 60 via Prime
  52.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  53.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  54.    wt: 7:   9 GCD of 360 110 via Primes and Euclid Algorithm
  55.    wt: 7:   7 GCD and LCM from prime factorization
  56.    wt: 7:   4 LCM of 8 and 10 via Prime
  57.    wt: 7:   3 Counting with Tables and Trees II
  58.    wt: 7:   2 Counting with Tables and Trees I
  59.    wt: 7:   1 Counting and Counting Methods I
  60.    wt: 7:   4 signed coordinates for regions in space
  61.    wt: 7:   7 Converting or Changing Units
  62.    wt: 7:   6 Simplification of Fractions with Units
  63.    wt: 7:   4 Fractions with Units
  64.    wt: 7:   B Fractions and Two Term Ratios
  65.    wt: 7:   A Similarities between Fractions and Two Term Ratios
  66.    wt: 7:   21 Reciprocals for Fractions and Wholes
  67.    wt: 7:   17 Efficient Ways to Add and Subtract
  68.    wt: 7:   15 Adding and Subtracting with Unlike Denominators
  69.    wt: 7:   14 Adding and Subtracting with Like Denominators
  70.    wt: 7:   10 Simplification of Fractions and Mixed Numerals
  71.    wt: 7:   6 Multiplication of Mixed Numbers
  72.    wt: 7:   17 Identify and Count Factors using Primes
  73.    wt: 7:   12 LCD GCD and LCM using Primes
  74.    wt: 7:   7 Calculator Usage Notes and Cautions
  75.    wt: 7:   6 Sieve of Eratosthenes and Square Rule
  76.    wt: 7:   5 Prime Factorization and a Square Rule
  77.    wt: 7:   3 video Primes and Composites from 9 times table
  78.    wt: 7:   2 Prime and Composites less than 16
  79.    wt: 7:   Long Division Backwards more
  80.    wt: 7:   Long Division Backward
  81.    wt: 7:   12 Why Long Division Works Take III
  82.    wt: 7:   11 Another Single Digit Divisor Example
  83.    wt: 7:   9 Why Long Division Works Take II
  84.    wt: 7:   8 Correcting the Mistake
  85.    wt: 7:   7 Long Divison Mistake Catching
  86.    wt: 7:   6 Why Decimal Long Division Methods Works Take I
  87.    wt: 7:   5 Long Division Include Zeroes or not
  88.    wt: 7:   4 Division with 2 Digit Divsors
  89.    wt: 7:   3 Division Single Digit Divisor Example
  90.    wt: 7:   2 Division with Single Digit Divisors
  91.    wt: 7:   1 Divsion Physical Examples
  92.    wt: 7:   D Decimal Multiplication Methods Derived
  93.    wt: 7:   C Counting Areas with Powers of Ten
  94.    wt: 7:   B Powers of Ten
  95.    wt: 7:   A Elementary Basis for Multiplication Methods
  96.    wt: 7:   6 Multiplication Commutes Order Not Important
  97.    wt: 7:   5 Decimal Fraction Multiplication
  98.    wt: 7:   3 More One Digit Multipliers
  99.    wt: 7:   2 One Digit Multipliers
  100.    wt: 7:   Video Decimal Multiplication Geometric View Example 2
  101.    wt: 7:   Video Decimal Multiplication Geometric View Example 2
  102.    wt: 7:   Video Power Notation in Decimal Expansion
  103.    wt: 7:   1 Why 3 times 5 gives 15
  104.    wt: 7:   10 Names for Big Numbers and Powers of Ten Expansion
  105.    wt: 7:   Quick history of numbers and algebra
  106.    wt: 7:   Exact Arithmetic Wholes and Fractions
  107.    wt: 7:   Practical Methods Ends and Values for Arithmetic
  108.    wt: 6:   arithmetic videos Real Player Format
  109.    wt: 6:   5 Square Roots with primes more still
  110.    wt: 6:   4 Square Roots with primes more
  111.    wt: 6:   3 Properties of Square Roots with example
  112.    wt: 6:   2 Square Roots with Prime
  113.    wt: 6:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  114.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  115.    wt: 6:   13 GCD from given Prime Factorization
  116.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  117.    wt: 6:   8 GCD from Euclidean Algorithm
  118.    wt: 6:   6 GCD from Prime
  119.    wt: 6:   5 Common Divisors 60 45 via Prime
  120.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  121.    wt: 6:   2 Least Common Multiple LCM intro via list method
  122.    wt: 6:   1 Least Common Multiples LCM Introduction
  123.    wt: 6:   12 GCD 2700 288 via Prime
  124.    wt: 6:   5 Counting with Tables Trees Product Rule Take II
  125.    wt: 6:   4 Counting with Trees Product Rule Take I
  126.    wt: 6:   D Three Term Ratios
  127.    wt: 6:   22 Complex Compound Fractions
  128.    wt: 6:   21 Working With Signs
  129.    wt: 6:   20 Dividing Fractions the Why
  130.    wt: 6:   19 Dividing Fractions How TO
  131.    wt: 6:   18 Efficient Ways to Multiply
  132.    wt: 6:   16 Addition Subtraction Comparision Compared
  133.    wt: 6:   13 Fraction Comparison Algebraic View
  134.    wt: 6:   12 Fraction Comparison
  135.    wt: 6:   11 Simplification an Algebraic View
  136.    wt: 6:   8 Numerals Fractionals Quantals Take II
  137.    wt: 6:   7 Numerals Fractionals Quantals
  138.    wt: 6:   6 Multiplication Algebraically Take II
  139.    wt: 6:   5 Equivalent Fractions
  140.    wt: 6:   4 Fraction Multiplication
  141.    wt: 6:   3 Unit fraction of a fraction
  142.    wt: 6:   2 Unit Fraction Multiplication
  143.    wt: 6:   1 What is a fraction Take II
  144.    wt: 6:   1 What is a fraction
  145.    wt: 6:   Fraction Operations by Raising Terms A Simple Innovation
  146.    wt: 6:   D Remainders Modulo 11 Pair Rule
  147.    wt: 6:   11 Adding Integers Formulas and Examples
  148.    wt: 6:   8 Multiplication by Signed Numbers Integers
  149.    wt: 6:   6 Multiplication by Natural Numbers
  150.    wt: 6:   5 Zero Movement and Additive Inverses
  151.    wt: 6:   20 Uniqueness of Prime Factorization
  152.    wt: 6:   19 video Prime Factorization Unique
  153.    wt: 6:   18 video Count Factors given Prime Factorization
  154.    wt: 6:   16 video Factors of 980 using prime
  155.    wt: 6:   15 video Factors of 20 using Prime Factorization
  156.    wt: 6:   14 video Factors of 24 Take II
  157.    wt: 6:   13 video Factors of 24 using prime
  158.    wt: 6:   11 Efficient Square Rule Use
  159.    wt: 6:   10 video Prime Factorization upto 23 squared
  160.    wt: 6:   9 video Prime Factorization upto 19 squared
  161.    wt: 6:   8 video Prime Factorization upto 19
  162.    wt: 6:   4 video Prime Factorization Introduction
  163.    wt: 6:   1 video how Products are bigger than factor
  164.    wt: 6:   11 Place Value SI Standard International way
  165.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  166.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  167.    wt: 6:   2 Groups of Three Place Value for Multidigit Decimals
  168.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  169.    wt: 5:   A Modular and Remainder Arithmetic
  170.    wt: 5:   1 Decimals Modular and Remainder Arithmetic
  171.    wt: 5:   C Divisibility by 11 Integer Recognition Method
  172.    wt: 5:   B Integer Long Division Multiple Choices
  173.    wt: 5:   A Associative Law Theorectical Note
  174.    wt: 5:   13 Subtraction with Additive Inverse
  175.    wt: 5:   12 Adding Integers More Examples
  176.    wt: 5:   10 Integer Multiplication Formulas
  177.    wt: 5:   9 Multiplying Integers
  178.    wt: 5:   7 Multiplication by Signs
  179.    wt: 5:   4 Adding Movements wiht opposite directions
  180.    wt: 5:   3 Adding Movements with same direction
  181.    wt: 5:   2 Integers Multiplies of a Unit Moverment
  182.    wt: 5:   1 Integers as Coordinates
  183.    wt: 5:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  184.    wt: 5:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  185.    wt: 5:   5 More on Groups of 3 Place Value in Decimal Fractions
  186.    wt: 5:   4 Groups of 3 Place Value in Decimal Fractions
  187.    wt: 5:   3 More on Groups of 3 Multi Digit Place Value
  188.    wt: 5:   Formula Evaluation how to show work
  189.    wt: 5:   Expression Evaluation how to show work
  190.    wt: 5:   The 20 Times Table
  191.    wt: 5:   The 12 Times Table Visually
  192.    wt: 5:   About folder contents
  193.    wt: 5:   Primary and Secondary Skills and Practices with Take Home Value
  194.    wt: 5:   1 From Number Recognition and Counting to Arithmetic B
  195.    wt: 5:   1 From Number Recognition and Counting to Arithmetic A
  196.    wt: 4:   P Exact Arithmetic With Whole Numbers and Fractions
  197.    wt: 4:   5 Interpreting and Drawing Maps and Plans.
  198.    wt: 4:   2 Identifying Size and Position Place and Spatial Sense
  199.    wt: 3:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  200.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  201.    wt: 3:   A Signed Number Arithmetic Review
  202.    wt: 3:   11 Signed Number Addition and Addition Properties
  203.    wt: 3:   2 Combing Counts Addition Skills and Principles
  204.    wt: 3:   2 More and Less Than for Counts and Measures
  205.    wt: 3:   10 Real Number Lengths and Signs
  206.    wt: 3:   1 Whole and Natural Numbers
  207.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  208.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  209.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  210.    wt: 3:   I. Logic and language skills
  211.    wt: 3:   How to Build Skills and Confidence
  212.    wt: 3:   7 Games and Activities for Instruction
  213.    wt: 3:   6 Measuring via counting or arithmetic the role of fractions
  214.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  215.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  216.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  217.    wt: 2:   Ramblings Extrinsic numbers theory
  218.    wt: 2:   Skills Chapter 1 Arithmetic
  219.    wt: 2:   7 logic review and decimals an odd combination
  220.    wt: 2:   2 arithmetic with signed numbers
  221.    wt: 2:   1 arithmetic with unsigned numbers
  222.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  223.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  224.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  225.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  226.    wt: 2:   2 Reading and Writing Skills
  227.    wt: 2:   Ages 12 to 14 Skills with take home value
  228.    wt: 2:   Ages 12 to 14 Arithmetic
  229.    wt: 2:   Ages 10 to 12 Arithmetic
  230.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  231.    wt: 2:   9 Summary Degrees to Radians and back
  232.    wt: 2:   1 Degrees and Radians Introduction
  233.    wt: 2:   Vector and Complex Number Applet
  234.    wt: 2:   Parallel Lines and Parallel Transversals
  235.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  236.    wt: 2:   Parallel Lines and Interior Angles
  237.    wt: 2:   14 cosine even and sine and tangent are odd
  238.    wt: 2:   21 Logarithms Powers and Exponentials
  239.    wt: 2:   20 N th Roots of Complex Numbers
  240.    wt: 2:   16 References and Originality Question
  241.    wt: 2:   13 Trig Formulas for dot and cross Products
  242.    wt: 2:   12 cis formulas for sine cosines and tangent
  243.    wt: 2:   11 sine and cosine double triple angle formulas
  244.    wt: 2:   9 The complex number valued trig function cis
  245.    wt: 2:   6 Field Properties of Complex Number
  246.    wt: 2:   2 Complex Numbers made easier we hope
  247.    wt: 2:   Appetizer A Complex Number Applet
  248.    wt: 2:   10 Midpoint of [a b] and [b a]
  249.    wt: 2:   7 Exercises to test skill and concept mastery
  250.    wt: 2:   1 Numerical view of lines and their equations
  251.    wt: 2:   What is and is not here
  252.    wt: 2:   7 Complex Numbers Appetizer
  253.    wt: 2:   6 Polar Multiplication and Rotation
  254.    wt: 2:   5 Cartesian Addition and Translation
  255.    wt: 2:   4 Polar Coordinates to and from
  256.    wt: 2:   PS H Distributive Law For Complex Numbers
  257.    wt: 2:   16 Angles Subtended By Chords and Diameters
  258.    wt: 2:   6 Ruler and compass Angle Bisection
  259.    wt: 2:   1 Initial Concepts and Terms
  260.    wt: 2:   3 Lengths and Areas on Maps and Plans
  261.    wt: 2:   musings do not puiblish real numbers
  262.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  263.    wt: 2:   22 Multiplication of Signed Numbers
  264.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  265.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  266.    wt: 2:   13 Arrows and Vectors in a Plane
  267.    wt: 2:   12 Real Numbers Line Signed Coordinates
  268.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  269.    wt: 2:   8 Division and Mulplication of Compound Fractions
  270.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  271.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  272.    wt: 2:   B Decimal Comparison and Subtraction
  273.    wt: 2:   7 Decimals Multiplication Methods Examples
  274.    wt: 2:   5 Distributive Law for Whole Numbers
  275.    wt: 2:   3 Multiplicative Counting Skills Principles
  276.    wt: 2:   1 The Counting Origins of Numbers
  277.    wt: 2:   4 Rates Ratios and Proporitionality
  278.    wt: 2:   6 Equations and Systems Equivalent or Implied
  279.    wt: 2:   4 Subtraction and Division Axioms
  280.    wt: 2:   2 Addition and Multiplication Axioms
  281.    wt: 2:   4 Comparison of Negative Numbers
  282.    wt: 2:   3 More and Less Than with Unlike Signs
  283.    wt: 2:   1 Real Numbers Comparison
  284.    wt: 2:   16 Real Numbers Comparison
  285.    wt: 2:   15 Real Number Division
  286.    wt: 2:   14 Real Number Multiplication
  287.    wt: 2:   13 Real Number Subtraction
  288.    wt: 2:   12 Real Number Additive Inverses or Negatives
  289.    wt: 2:   11 Real Number Addition
  290.    wt: 2:   8 Coordinates for Maps and Planes
  291.    wt: 2:   7 Real Numbers as Line Cordinates
  292.    wt: 2:   6 Unsigned Real Numbers
  293.    wt: 2:   5 Rational Numbers More
  294.    wt: 2:   4 Rational Numbers
  295.    wt: 2:   3 Geometric Formulas and Function Notation
  296.    wt: 2:   1 Formulas Dependence and Function Notation
  297.    wt: 2:   5 Talking about Numbers and Quantities
  298.    wt: 2:   4 A Brief Story of numbers and algebra
  299.    wt: 2:   016 Numbering Occidental Calendar Days
  300.    wt: 2:   015 School and work day counting tables
  301.    wt: 2:   011 Division of Time Intervals By Numbers
  302.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  303.    wt: 2:   5 Conversion Arithmetic
  304.    wt: 2:   4 Mixing and Changing Units of Time
  305.    wt: 2:   3 Units and Lengths of Time
  306.    wt: 2:   2 Time and Date Matters in School
  307.    wt: 2:   1 Intro of Kids To Time Date Skills
  308.    wt: 2:   Example 1. Area Between x and x squared
  309.    wt: 2:   38 Formulas and derivatives for powers and roots
  310.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  311.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  312.    wt: 2:   9 Limits Continuity and Composition
  313.    wt: 2:   5 Jumps and absence of unlimited error control
  314.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  315.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  316.    wt: 2:   Appendix E. How To Study Mathematics and Why
  317.    wt: 2:   Appendix D. What to do in School and Why
  318.    wt: 2:   Chapter 31 Direct and Indirect Reason
  319.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  320.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  321.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  322.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  323.    wt: 2:   Chapter 20. Degrees and Radians
  324.    wt: 2:   Chapter 19. Functions and Sets
  325.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  326.    wt: 2:   Chapter 12. Shorthand Usage Guide
  327.    wt: 2:   Chapter 11. Why Shorthand
  328.    wt: 2:   Chapter 10 Describing and Changing Calculations
  329.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  330.    wt: 2:   Chapter 8 Three Skills For Algebra
  331.    wt: 2:   Solutions For Arithmetic Exercises
  332.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  333.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  334.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  335.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  336.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  337.    wt: 2:   R Why Learn Mathematics Skills
  338.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  339.    wt: 2:   O On Learning Mathematics and Science
  340.    wt: 2:   M Words to extend arithmetic
  341.    wt: 2:   L Skills with take home value
  342.    wt: 2:   N Improving Marks on Tests and Finals
  343.    wt: 2:   J. More on written work and showing skill
  344.    wt: 2:   H Jigsaw puzzles and problem solving
  345.    wt: 2:   G. Written work formats for developing and showing skill
  346.    wt: 2:   E. When and how to correct errors
  347.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  348.    wt: 1:   Appendix 2 primary school Arithmetic 01
  349.    wt: 1:   Appendix 1 primary and preschool mathematic
  350.    wt: 1:   G LAMP Introduction Problem Solving Skills
  351.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  352.    wt: 1:   Skills Chapter 5 Calculus
  353.    wt: 1:   Skills Chapter 4 Logic
  354.    wt: 1:   Skills Chapter 3 Algebra
  355.    wt: 1:   Skills Chapter 2 Geometry
  356.    wt: 1:   Skills Chapter 0 Introduction
  357.    wt: 1:   5 logarithms and exponentials etc
  358.    wt: 1:   key notes and themes
  359.    wt: 1:   what should be learnt and When
  360.    wt: 1:   standards for course material
  361.    wt: 1:   Theory of Knowledge
  362.    wt: 1:   Education in mathematics science and technology
  363.    wt: 1:   Motivation and Context Problem
  364.    wt: 1:   fairness and inductive principles for instruction
  365.    wt: 1:   Home Tutoring and Home Schooling
  366.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  367.    wt: 1:   24 Standards For Skill Develoment Take II
  368.    wt: 1:   24 Standards For Skill Develoment
  369.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  370.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  371.    wt: 1:   17 Math Booklets for children and young teenagers
  372.    wt: 1:   14 Multiplication and Times Tables
  373.    wt: 1:   13 Addition and Addition Tables
  374.    wt: 1:   12 Goals and Objectives For Mathematics
  375.    wt: 1:   11 Help and Defend Your Child or Teens Education
  376.    wt: 1:   5 Patience Please for Yourself and Your Charges
  377.    wt: 1:   4 Learning Takes Time and Effort
  378.    wt: 1:   1 Speaking Skills
  379.    wt: 1:   Ages 12 to 14 Geometry
  380.    wt: 1:   Ages 10 to 12 Geometry
  381.    wt: 1:   Ages 9 to 10
  382.    wt: 1:   Ages 8 to 9
  383.    wt: 1:   Ages 7 to 8
  384.    wt: 1:   Ages 6 to 7
  385.    wt: 1:   Ages 4 plus to 5 plus
  386.    wt: 1:   Ages 3 plus to 4 plus
  387.    wt: 1:   26 Function definitions done and coming
  388.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  389.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  390.    wt: 1:   19 Horizontal line rule and method
  391.    wt: 1:   18 Vertical Line Rule and Method
  392.    wt: 1:   17 Function maxima minima and their location
  393.    wt: 1:   11 Function Domain Range Source and Targets
  394.    wt: 1:   9 Set theory term relation possible origins
  395.    wt: 1:   8 Set view of relations and functions
  396.    wt: 1:   6 Set Existence Formation and Notation
  397.    wt: 1:   4 Function notation in and beyond mathematics
  398.    wt: 1:   9 quadratics physical and further context
  399.    wt: 1:   11 Growth and Decay in Biology
  400.    wt: 1:   10 Exponential Growth and Decay Models
  401.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  402.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  403.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  404.    wt: 1:   16 cotangent function Definition Graph and Inverse
  405.    wt: 1:   15 cosecant function Definition Graph and Inverse
  406.    wt: 1:   14 secant function Definition Graph and Inverse
  407.    wt: 1:   13 cosecant function Definition Graph and Inverse
  408.    wt: 1:   8 Radian Measures of Common Angles
  409.    wt: 1:   7 Radian Measures in special Triangles
  410.    wt: 1:   6 Radian Measure to Degrees
  411.    wt: 1:   5 Degrees to Radian Measure
  412.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  413.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  414.    wt: 1:   2 Radian Measure Numerical Value of one degree
  415.    wt: 1:   A Global Time and Navigation
  416.    wt: 1:   15 Dot and Cross Product
  417.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  418.    wt: 1:   4 graphing y=Asin(x c)
  419.    wt: 1:   3 graphing y=f(x c) plus K
  420.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  421.    wt: 1:   1 graphing y=f(x a)
  422.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  423.    wt: 1:   Triangle Angles Sum To 180 Degrees
  424.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  425.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  426.    wt: 1:   Straight Lines ASA Intersection Study More
  427.    wt: 1:   Straight Lines ASA Intersection Study
  428.    wt: 1:   Straight Lines Instersection Solving Equations
  429.    wt: 1:   Straight Lines Intersection of
  430.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  431.    wt: 1:   C Straight Lines Slope from Coordinates
  432.    wt: 1:   B Straight Line Slope Scaling Properties More
  433.    wt: 1:   A Straight Line Slope Scaling Properties
  434.    wt: 1:   14 Straight Lines Equations General Case
  435.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  436.    wt: 1:   12 Straight Lines Graphing mx plus b
  437.    wt: 1:   11 Straight Lines Graphing y=mx
  438.    wt: 1:   10 Straight Lines through Origin Equations More
  439.    wt: 1:   9 Straight Lines through Origin Equations
  440.    wt: 1:   8 Straight Lines Equation for vertical
  441.    wt: 1:   7 Tangent Function is odd on this domain
  442.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  443.    wt: 1:   5 Tangent Function Graph
  444.    wt: 1:   4 Tangent Function Properties
  445.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  446.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  447.    wt: 1:   1 Straight Lines Slope Concept
  448.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  449.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  450.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  451.    wt: 1:   29 secant cosecant and cotangent for acute angles
  452.    wt: 1:   27 Logarithmic use of products of sines and cosines
  453.    wt: 1:   26 Formulas for products of sines and cosines
  454.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  455.    wt: 1:   21 sine and cosine Half Angle Formulas
  456.    wt: 1:   20 sine and cosine Double Angle Formulas
  457.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  458.    wt: 1:   17E Trig Formulas for dot and cross Products
  459.    wt: 1:   17D cis formulas for sine cosines and tangent
  460.    wt: 1:   17C sine and cosine double triple angle formulas
  461.    wt: 1:   17A The complex number valued trig function cis
  462.    wt: 1:   10 Graphs of sines and cosines many periods
  463.    wt: 1:   9 Graphs of sine and cosine over one period
  464.    wt: 1:   7 period of sine and cosine
  465.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  466.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  467.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  468.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  469.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  470.    wt: 1:   19 N th Roots of Unity
  471.    wt: 1:   18 Sixth Roots of Unity
  472.    wt: 1:   17 Cube Roots of unity
  473.    wt: 1:   15 Pythagorean Theorem Converse
  474.    wt: 1:   14 Law of cosines
  475.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  476.    wt: 1:   8 Unit Circle Development of Trigonometry
  477.    wt: 1:   7 Second Way to Calculate Products
  478.    wt: 1:   5 An Easy Proof of the Distributive Law
  479.    wt: 1:   4 Multiplication Properties
  480.    wt: 1:   3 Addition Properties
  481.    wt: 1:   1 Rectangular Polar Coordinates Review
  482.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  483.    wt: 1:   3 Trigonometric Ratios sine and cosine
  484.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  485.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  486.    wt: 1:   8 Similarity of Triangles and Polygons
  487.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  488.    wt: 1:   Four Simple Exercises
  489.    wt: 1:   12 Links Lessons elsewhere
  490.    wt: 1:   11 A Partial Summary
  491.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  492.    wt: 1:   8 Mid Point Formula
  493.    wt: 1:   6 Intersection of lines by solving linear systems
  494.    wt: 1:   5 Algebraic View of Slopes
  495.    wt: 1:   4 Equations for lines three forms
  496.    wt: 1:   3 Slope product for perpendicular lines
  497.    wt: 1:   2 point slope equation for a line
  498.    wt: 1:   13 Pythagorean spatial distance formulas
  499.    wt: 1:   12 Spatial Coordinates
  500.    wt: 1:   11 Triangle Inequality
  501.    wt: 1:   10 Pythagorean plane distance formula
  502.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  503.    wt: 1:   8 Distance Between Points on a Line
  504.    wt: 1:   3 Rectangular Coordinates Review
  505.    wt: 1:   2 Cartesian Coordinates with signs
  506.    wt: 1:   1 Cartesian Coordinates sans signs
  507.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  508.    wt: 1:   PS G Rotation Distributes over Addition
  509.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  510.    wt: 1:   PS E Multiplication with Polar Coordinates
  511.    wt: 1:   PS D Addition with Cartesian Coordinates
  512.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  513.    wt: 1:   PS B Parallelogram Construction Methods
  514.    wt: 1:   PS A Kite Construction Methods
  515.    wt: 1:   21 Parallelograms
  516.    wt: 1:   19 Right Triangle Similarity
  517.    wt: 1:   18 Triangle Similarity Take 1
  518.    wt: 1:   17 Right Bisectors of Triangle Sides
  519.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  520.    wt: 1:   14 Parallel Lines Postulate
  521.    wt: 1:   13 Angle Side Angle Failure
  522.    wt: 1:   12 Side Angle Side Failure
  523.    wt: 1:   11 Triangle Construction Fails
  524.    wt: 1:   10 Dropping a perpendicular to line
  525.    wt: 1:   9 Construction of a right bisector
  526.    wt: 1:   8 Isoceles Triangles
  527.    wt: 1:   7 Angle Side Angle
  528.    wt: 1:   5 Side Angle Side
  529.    wt: 1:   4 Side Side Side
  530.    wt: 1:   3 Isometry of Triangles Congruence
  531.    wt: 1:   2 Correspondence between Triangles
  532.    wt: 1:   Short Course on Euclidean Geometry
  533.    wt: 1:   26 More Less Greater Than Comparison
  534.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  535.    wt: 1:   23 Distributive Law Two Derivations
  536.    wt: 1:   21 Addition of Multiples of a Single Vector
  537.    wt: 1:   19 Signed Multiples of Vectors
  538.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  539.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  540.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  541.    wt: 1:   15 Head to Tails in place Addition Associative
  542.    wt: 1:   9 Division with Digits after Decimal Point
  543.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  544.    wt: 1:   4 Location of Point in Decimal Addition
  545.    wt: 1:   3 Location of Point in Decimal Multiplication
  546.    wt: 1:   2 Counting Digits in Decimal Multiplication
  547.    wt: 1:   1 Fractions with Finite Decimal Expansions
  548.    wt: 1:   E Long Division Methods more
  549.    wt: 1:   D Long Division Methods
  550.    wt: 1:   C Three Decimal Subtraction Methods
  551.    wt: 1:   A Decimal Addition Columm Methods
  552.    wt: 1:   8 Column Multiplication Methods in General
  553.    wt: 1:   6 Column Methods for Decimal Multiplication
  554.    wt: 1:   4 Commutative Law Groups Counting Form
  555.    wt: 1:   5 Proportionality in Equivalent Fractions
  556.    wt: 1:   3 Proportionality Examples
  557.    wt: 1:   2 Algebraic View
  558.    wt: 1:   1 What is Proportionality
  559.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  560.    wt: 1:   6 Compound Interest Forward and Backwards
  561.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  562.    wt: 1:   5 Equality in Algebra
  563.    wt: 1:   3 Product Axioms Two Forms
  564.    wt: 1:   1 Equivalent Computation Rules
  565.    wt: 1:   5 Greater More Less Than Signs in General
  566.    wt: 1:   9 Coordinates for Regions in Space
  567.    wt: 1:   3 Fractions
  568.    wt: 1:   2 Integers
  569.    wt: 1:   5 Independent versus Dependent Variables
  570.    wt: 1:   4 Changing Letters
  571.    wt: 1:   2 Computation Rules Evaluation
  572.    wt: 1:   3 GE III Equation Addition and Multiplication
  573.    wt: 1:   Skill Development Notes
  574.    wt: 1:   10 One Example
  575.    wt: 1:   9 Three Examples
  576.    wt: 1:   8 One Example
  577.    wt: 1:   7 Two Examples
  578.    wt: 1:   6 Three Examples
  579.    wt: 1:   5 Three Examples
  580.    wt: 1:   4 Two Examples
  581.    wt: 1:   3 Two Examples
  582.    wt: 1:   2 Three Examples
  583.    wt: 1:   1 Written work formats for developing and showing skill
  584.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  585.    wt: 1:   9 Sets in Probability and Statistics
  586.    wt: 1:   8 Sets of Numbers
  587.    wt: 1:   3 Adding Words To Arithmetic
  588.    wt: 1:   1 Three Skills For Algebra
  589.    wt: 1:   014 Counting Days with Calendars
  590.    wt: 1:   013 Travel Time Tables
  591.    wt: 1:   012 Division of Time Intervals by Time Intervals
  592.    wt: 1:   010 Repeated Addition of Time Intervals
  593.    wt: 1:   8 Addition of Time Intervals via subtotaling
  594.    wt: 1:   7 Addition of Time Intervals
  595.    wt: 1:   6 How long is a million seconds
  596.    wt: 1:   Example 2 volume of a cone
  597.    wt: 1:   Example 1 volume of a pyramid
  598.    wt: 1:   Volume of Solid by Cross Sections Lesson
  599.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  600.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  601.    wt: 1:   Example 4 with x function of y
  602.    wt: 1:   Example 3
  603.    wt: 1:   Example 2
  604.    wt: 1:   Example 1
  605.    wt: 1:   Area Between Curves Lesson Take 2
  606.    wt: 1:   Area Between Curves Lesson Take 1
  607.    wt: 1:   Summary
  608.    wt: 1:   17 Derivatives of quotients of sine and cosine
  609.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  610.    wt: 1:   15 sine and cosine derivatives 3rd step
  611.    wt: 1:   14 sine and cosine derivatives 2nd step
  612.    wt: 1:   13 sine and cosine derivatives 1st step
  613.    wt: 1:   11 Limits at infinity Three Examples
  614.    wt: 1:   10 Three one sided limits with infinite values
  615.    wt: 1:   8 Four Animated Examples
  616.    wt: 1:   7 Evaluation by immediate or delayed substitution
  617.    wt: 1:   6 Continuity at a point
  618.    wt: 1:   4 Numerical properties
  619.    wt: 1:   3 Decimal insights for limits continuity convergence
  620.    wt: 1:   2 Algebraic codification
  621.    wt: 1:   1 Numerical introduction
  622.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  623.    wt: 1:   PostScript For and Against Decimal Perspectives
  624.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  625.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  626.    wt: 1:   Chapter 22 Complex Numbers
  627.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  628.    wt: 1:   Chapter 12. Units and Slopes
  629.    wt: 1:   Chapter 10 Slopes and Units
  630.    wt: 1:   Chapter 7 Slopes and Velocity
  631.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  632.    wt: 1:   Chapter 2. Slopes and Ski Trails
  633.    wt: 1:   Postscript More on Better Performance
  634.    wt: 1:   Postscript For Better Performance
  635.    wt: 1:   Appendix C. How to Read
  636.    wt: 1:   Appendix B. How To Learn
  637.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  638.    wt: 1:   Chapter 30 Truth Tables
  639.    wt: 1:   Chapter 28 Occurrence Tables
  640.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  641.    wt: 1:   Chapter 25. Mathematical Induction Examples
  642.    wt: 1:   Chapter 23. Notation For Sums
  643.    wt: 1:   Chapter 21. Third Reading Guide
  644.    wt: 1:   Chapter 18. Rules for Algebra
  645.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  646.    wt: 1:   Chapter 16. Painless Theorem Proving
  647.    wt: 1:   Chapter 15. Solving Linear Equations
  648.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  649.    wt: 1:   Chapter 13. Second Reading Guide
  650.    wt: 1:   Postscript What is a Variable
  651.    wt: 1:   Chapter 6 Change of Language
  652.    wt: 1:   Chapter 4 Longer Chains of Reason
  653.    wt: 1:   Chapter 3 Chains of Reason
  654.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  655.    wt: 1:   Foreword
  656.    wt: 1:   Chapter 2 For and Against Mathematics
  657.    wt: 1:   Postscript B More on Story Telling and Reason
  658.    wt: 1:   Chapter 24 Direct and Indirect Reason
  659.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  660.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  661.    wt: 1:   Chapter 18 Sense and Knowledge
  662.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  663.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  664.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  665.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  666.    wt: 1:   S Adding words to algebra
  667.    wt: 1:   N Mathematics Prepare for College Studies
  668.    wt: 1:   H more Routine to non routine problem solving
  669.    wt: 1:   F. The student teacher tutor feedback loop
  670.    wt: 1:   D. Check work a must with a caution
  671.    wt: 1:   C. Domino effect of being careful
  672.    wt: 1:   B. Domino effect of errors
  673.    wt: 1:   A. Skill has to be seen to believed
  674.    wt: 1:   Chapter 8 Skipped Topics and Why
  675.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  676.    wt: 1:   Chapter 6 More Algebra and Geometry
  677.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  678.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  679.    wt: 1:   Chapter 1 Arithmetic
  680.    wt: 1:   Helping the Blind in Logic and Mathematics
  681.    wt: 1:   More Algebra and Slope based Calculus Preview
  682.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  683.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  684.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  685.    wt: 1:   The Math Forum and Site Content
  686.    wt: 13:   A Decimals Modular and Remainder Arithmetic
  687.    wt: 10:   23 Remainder Arithmetic Modulo 2
  688.    wt: 10:   22 Remainder Arithmetic Modulo 3 more
  689.    wt: 10:   21 Remainder Arithmetic Modulo 3
  690.    wt: 10:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  691.    wt: 10:   19 Remainder Arithmetic Rule of 9 for checking sums III
  692.    wt: 10:   18 Remainder Arithmetic Rule of 9 for checking sums II
  693.    wt: 10:   17 Remainder Arithmetic Rule of 9 for checking sums I
  694.    wt: 10:   16 Remainder Arithmetic Modulo 9 Example 2
  695.    wt: 10:   15 Remainder Arithmetic Modulo 9 Example
  696.    wt: 10:   14 Remainder Arithmetic Modulo 9 Example
  697.    wt: 10:   13 Remainder Arithmetic Modulo 5 Example
  698.    wt: 10:   12 Remainder Arithmetic Modulo 10 Example
  699.    wt: 10:   11 Remainder Arithmetic Long Division by 5 Quickly more
  700.    wt: 10:   10 Remainder Arithmetic Long Division by 5 Quickly
  701.    wt: 10:   9 Remainder Arithmetic Divisibility by 5
  702.    wt: 10:   8 Remainder Arithmetic Morulo 5 Examples II
  703.    wt: 10:   7 Remainder Arithmetic Modulo 5 Examples I
  704.    wt: 10:   6 Remainder Arithmetic Modulo 5 Propertie
  705.    wt: 10:   5 Remainder Arithmetic Modulo 5
  706.    wt: 10:   4 Remainder Arithmetic Modulo 10 in general
  707.    wt: 10:   3 Remainder Arithmetic Modulos 10 more still
  708.    wt: 10:   2 Remainder Arithmetic Modulo 10 more
  709.    wt: 10:   1 Remainder Arithmetic Modulo 10
  710.    wt: 10:   8 What skills and work habits to require
  711.    wt: 10:   6. Counting and adding units and mixed units

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 bicylce?

Death Penalty: How Texas sent an innocent man to his death - The wrong Carlos.

For home-tutoring or -schooling, or for schools or colleges with course content control: Secondary Mathematics for Ages 11+, A Practical Approach.

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
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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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