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: 7:   12 Comparison of Unsigned and Signed Numbers/
  3.    wt: 7:   8 Arithmetic with Signed Numbers/
  4.    wt: 7:   7 Arithmetic and Fractions with Units/
  5.    wt: 7:   B Decimal Comparing and Subtracting Methods/
  6.    wt: 7:   A Decimal Counting and Adding Methods/
  7.    wt: 6:   11 Squares and Square Roots/
  8.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  9.    wt: 6:   9 Combinatorics Trees Tables and Products/
  10.    wt: 6:   6 Fractions and Ratios/
  11.    wt: 6:   3 Prime Factorization Skills/
  12.    wt: 6:   D Decimal Long Division Methods/
  13.    wt: 6:   C Decimal Multiplication Methods/
  14.    wt: 6:   2 Arithmetic with Decimals/
  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

377 matches:

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

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
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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