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

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

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

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

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

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

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

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43 matches:

  1.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  2.    wt: 6:   11 Squares and Square Roots/
  3.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  4.    wt: 6:   9 Combinatorics Trees Tables and Products/
  5.    wt: 6:   8 Arithmetic with Signed Numbers/
  6.    wt: 6:   7 Arithmetic and Fractions with Units/
  7.    wt: 6:   6 Fractions and Ratios/
  8.    wt: 6:   4 Remainder Arithmetic and Divisibility/
  9.    wt: 6:   3 Prime Factorization Skills/
  10.    wt: 6:   B Decimal Comparing and Subtracting Methods/
  11.    wt: 6:   A Decimal Counting and Adding Methods/
  12.    wt: 5:   5 Integers/
  13.    wt: 5:   D Decimal Long Division Methods/
  14.    wt: 5:   C Decimal Multiplication Methods/
  15.    wt: 5:   2 Arithmetic with Decimals/
  16.    wt: 5:   1 Decimal Place Value/
  17.    wt: 5:   Arithmetic and Number Theory Skills/
  18.    wt: 2:   B Real Numbers Extrinsic Development/
  19.    wt: 2:   5 Real Numbers/
  20.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  21.    wt: 1:   Mathematics Skills Year by Year/
  22.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  23.    wt: 1:   12 Function Translating and Rescaling/
  24.    wt: 1:   11 Parallel Straight Lines and Transversals/
  25.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  26.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  27.    wt: 1:   7 Complex Numbers/
  28.    wt: 1:   4 Lines and Slopes Take 1/
  29.    wt: 1:   3 Cartesian and Polar Coordinates/
  30.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  31.    wt: 1:   A Origins of Counting and Figuring Methods/
  32.    wt: 1:   9 Proportionality Backwards and Forwards/
  33.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  34.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  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

350 matches:

  1.    wt: 3:   11 Signed Number Addition and Addition Properties
  2.    wt: 3:   10 Real Number Lengths and Signs
  3.    wt: 3:   11 What are real lengths and numbers
  4.    wt: 3:   Primary and Secondary Skills and Practices with Take Home Value
  5.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  6.    wt: 2:   Ramblings Extrinsic numbers theory
  7.    wt: 2:   2 Reading and Writing Skills
  8.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  9.    wt: 2:   Vector and Complex Number Applet
  10.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  11.    wt: 2:   14 cosine even and sine and tangent are odd
  12.    wt: 2:   6 Field Properties of Complex Number
  13.    wt: 2:   3 Lengths and Areas on Maps and Plans
  14.    wt: 2:   musings do not puiblish real numbers
  15.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  16.    wt: 2:   12 Real Numbers Line Signed Coordinates
  17.    wt: 2:   2 Combing Counts Addition Skills and Principles
  18.    wt: 2:   2 More and Less Than for Counts and Measures
  19.    wt: 2:   1 Real Numbers Comparison
  20.    wt: 2:   16 Real Numbers Comparison
  21.    wt: 2:   15 Real Number Division
  22.    wt: 2:   14 Real Number Multiplication
  23.    wt: 2:   13 Real Number Subtraction
  24.    wt: 2:   12 Real Number Additive Inverses or Negatives
  25.    wt: 2:   11 Real Number Addition
  26.    wt: 2:   7 Real Numbers as Line Cordinates
  27.    wt: 2:   6 Unsigned Real Numbers
  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:   5 lengths and signs of numbers
  33.    wt: 2:   2 signed and unsigned numbers as coordinates
  34.    wt: 2:   3 Multiplying Units and Numbers
  35.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  36.    wt: 2:   9 Improper Fractions and Mixed Numbers
  37.    wt: 2:   8 What skills and work habits to require
  38.    wt: 2:   6. Counting and adding units and mixed units
  39.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  40.    wt: 2:   Quick history of numbers and algebra
  41.    wt: 2:   38 Formulas and derivatives for powers and roots
  42.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  43.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  44.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  45.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  46.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  47.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  48.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  49.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  50.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  51.    wt: 2:   I. Logic and language skills
  52.    wt: 2:   How to Build Skills and Confidence
  53.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  54.    wt: 2:   2 Identifying Size and Position Place and Spatial Sense
  55.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  56.    wt: 2:   1 From Number Recognition and Counting to Arithmetic A
  57.    wt: 1:   Appendix 1 primary and preschool mathematic
  58.    wt: 1:   G LAMP Introduction Problem Solving Skills
  59.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  60.    wt: 1:   Skills Chapter 5 Calculus
  61.    wt: 1:   Skills Chapter 4 Logic
  62.    wt: 1:   Skills Chapter 3 Algebra
  63.    wt: 1:   Skills Chapter 2 Geometry
  64.    wt: 1:   Skills Chapter 1 Arithmetic
  65.    wt: 1:   Skills Chapter 0 Introduction
  66.    wt: 1:   7 logic review and decimals an odd combination
  67.    wt: 1:   5 logarithms and exponentials etc
  68.    wt: 1:   2 arithmetic with signed numbers
  69.    wt: 1:   1 arithmetic with unsigned numbers
  70.    wt: 1:   key notes and themes
  71.    wt: 1:   what should be learnt and When
  72.    wt: 1:   standards for course material
  73.    wt: 1:   Theory of Knowledge
  74.    wt: 1:   Education in mathematics science and technology
  75.    wt: 1:   Motivation and Context Problem
  76.    wt: 1:   fairness and inductive principles for instruction
  77.    wt: 1:   Home Tutoring and Home Schooling
  78.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  79.    wt: 1:   24 Standards For Skill Develoment Take II
  80.    wt: 1:   24 Standards For Skill Develoment
  81.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  82.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  83.    wt: 1:   17 Math Booklets for children and young teenagers
  84.    wt: 1:   14 Multiplication and Times Tables
  85.    wt: 1:   13 Addition and Addition Tables
  86.    wt: 1:   12 Goals and Objectives For Mathematics
  87.    wt: 1:   11 Help and Defend Your Child or Teens Education
  88.    wt: 1:   5 Patience Please for Yourself and Your Charges
  89.    wt: 1:   4 Learning Takes Time and Effort
  90.    wt: 1:   1 Speaking Skills
  91.    wt: 1:   Ages 12 to 14 Skills with take home value
  92.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  93.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  94.    wt: 1:   26 Function definitions done and coming
  95.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  96.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  97.    wt: 1:   19 Horizontal line rule and method
  98.    wt: 1:   18 Vertical Line Rule and Method
  99.    wt: 1:   17 Function maxima minima and their location
  100.    wt: 1:   11 Function Domain Range Source and Targets
  101.    wt: 1:   9 Set theory term relation possible origins
  102.    wt: 1:   8 Set view of relations and functions
  103.    wt: 1:   6 Set Existence Formation and Notation
  104.    wt: 1:   4 Function notation in and beyond mathematics
  105.    wt: 1:   9 quadratics physical and further context
  106.    wt: 1:   11 Growth and Decay in Biology
  107.    wt: 1:   10 Exponential Growth and Decay Models
  108.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  109.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  110.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  111.    wt: 1:   16 cotangent function Definition Graph and Inverse
  112.    wt: 1:   15 cosecant function Definition Graph and Inverse
  113.    wt: 1:   14 secant function Definition Graph and Inverse
  114.    wt: 1:   13 cosecant function Definition Graph and Inverse
  115.    wt: 1:   2 cosine function more properties
  116.    wt: 1:   1 cosine function properties
  117.    wt: 1:   9 Summary Degrees to Radians and back
  118.    wt: 1:   1 Degrees and Radians Introduction
  119.    wt: 1:   A Global Time and Navigation
  120.    wt: 1:   15 Dot and Cross Product
  121.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  122.    wt: 1:   Parallel Lines and Parallel Transversals
  123.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  124.    wt: 1:   Parallel Lines and Interior Angles
  125.    wt: 1:   B Straight Line Slope Scaling Properties More
  126.    wt: 1:   A Straight Line Slope Scaling Properties
  127.    wt: 1:   4 Tangent Function Properties
  128.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  129.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  130.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  131.    wt: 1:   29 secant cosecant and cotangent for acute angles
  132.    wt: 1:   27 Logarithmic use of products of sines and cosines
  133.    wt: 1:   26 Formulas for products of sines and cosines
  134.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  135.    wt: 1:   21 sine and cosine Half Angle Formulas
  136.    wt: 1:   20 sine and cosine Double Angle Formulas
  137.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  138.    wt: 1:   17E Trig Formulas for dot and cross Products
  139.    wt: 1:   17D cis formulas for sine cosines and tangent
  140.    wt: 1:   17C sine and cosine double triple angle formulas
  141.    wt: 1:   17A The complex number valued trig function cis
  142.    wt: 1:   10 Graphs of sines and cosines many periods
  143.    wt: 1:   9 Graphs of sine and cosine over one period
  144.    wt: 1:   7 period of sine and cosine
  145.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  146.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  147.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  148.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  149.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  150.    wt: 1:   21 Logarithms Powers and Exponentials
  151.    wt: 1:   20 N th Roots of Complex Numbers
  152.    wt: 1:   16 References and Originality Question
  153.    wt: 1:   13 Trig Formulas for dot and cross Products
  154.    wt: 1:   12 cis formulas for sine cosines and tangent
  155.    wt: 1:   11 sine and cosine double triple angle formulas
  156.    wt: 1:   9 The complex number valued trig function cis
  157.    wt: 1:   4 Multiplication Properties
  158.    wt: 1:   3 Addition Properties
  159.    wt: 1:   2 Complex Numbers made easier we hope
  160.    wt: 1:   Appetizer A Complex Number Applet
  161.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  162.    wt: 1:   3 Trigonometric Ratios sine and cosine
  163.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  164.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  165.    wt: 1:   8 Similarity of Triangles and Polygons
  166.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  167.    wt: 1:   10 Midpoint of [a b] and [b a]
  168.    wt: 1:   7 Exercises to test skill and concept mastery
  169.    wt: 1:   1 Numerical view of lines and their equations
  170.    wt: 1:   What is and is not here
  171.    wt: 1:   7 Complex Numbers Appetizer
  172.    wt: 1:   6 Polar Multiplication and Rotation
  173.    wt: 1:   5 Cartesian Addition and Translation
  174.    wt: 1:   4 Polar Coordinates to and from
  175.    wt: 1:   PS H Distributive Law For Complex Numbers
  176.    wt: 1:   16 Angles Subtended By Chords and Diameters
  177.    wt: 1:   6 Ruler and compass Angle Bisection
  178.    wt: 1:   1 Initial Concepts and Terms
  179.    wt: 1:   A Modular and Remainder Arithmetic
  180.    wt: 1:   A Signed Number Arithmetic Review
  181.    wt: 1:   22 Multiplication of Signed Numbers
  182.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  183.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  184.    wt: 1:   13 Arrows and Vectors in a Plane
  185.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  186.    wt: 1:   8 Division and Mulplication of Compound Fractions
  187.    wt: 1:   B Decimal Comparison and Subtraction
  188.    wt: 1:   5 Distributive Law for Whole Numbers
  189.    wt: 1:   3 Multiplicative Counting Skills Principles
  190.    wt: 1:   1 The Counting Origins of Numbers
  191.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  192.    wt: 1:   4 Rates Ratios and Proporitionality
  193.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  194.    wt: 1:   6 Compound Interest Forward and Backwards
  195.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  196.    wt: 1:   6 Equations and Systems Equivalent or Implied
  197.    wt: 1:   4 Subtraction and Division Axioms
  198.    wt: 1:   2 Addition and Multiplication Axioms
  199.    wt: 1:   4 Comparison of Negative Numbers
  200.    wt: 1:   3 More and Less Than with Unlike Signs
  201.    wt: 1:   8 Coordinates for Maps and Planes
  202.    wt: 1:   5 Rational Numbers More
  203.    wt: 1:   4 Rational Numbers
  204.    wt: 1:   3 Geometric Formulas and Function Notation
  205.    wt: 1:   1 Formulas Dependence and Function Notation
  206.    wt: 1:   3 GE III Equation Addition and Multiplication
  207.    wt: 1:   1 Written work formats for developing and showing skill
  208.    wt: 1:   9 Sets in Probability and Statistics
  209.    wt: 1:   8 Sets of Numbers
  210.    wt: 1:   1 Three Skills For Algebra
  211.    wt: 1:   arithmetic videos Real Player Format
  212.    wt: 1:   3 Comparison of Negative Numbers
  213.    wt: 1:   2 More and Less Than with Unlike Signs
  214.    wt: 1:   3 Properties of Square Roots with example
  215.    wt: 1:   1 Squares and Square Roots Introduction
  216.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  217.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  218.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  219.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  220.    wt: 1:   7 GCD and LCM from prime factorization
  221.    wt: 1:   4 LCM of 8 and 10 via Prime
  222.    wt: 1:   3 Counting with Tables and Trees II
  223.    wt: 1:   2 Counting with Tables and Trees I
  224.    wt: 1:   1 Counting and Counting Methods I
  225.    wt: 1:   10 dividing signed numbers
  226.    wt: 1:   9 subtracting signed numbers
  227.    wt: 1:   8 multiplying signed numbers
  228.    wt: 1:   7 negative and additive inverse
  229.    wt: 1:   6 adding signed numbers
  230.    wt: 1:   3 signed coordinates for maps and planes
  231.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  232.    wt: 1:   2 Equality and Units
  233.    wt: 1:   1 Addition and Subtraction with Units
  234.    wt: 1:   B Fractions and Two Term Ratios
  235.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  236.    wt: 1:   21 Reciprocals for Fractions and Wholes
  237.    wt: 1:   17 Efficient Ways to Add and Subtract
  238.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  239.    wt: 1:   14 Adding and Subtracting with Like Denominators
  240.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  241.    wt: 1:   6 Multiplication of Mixed Numbers
  242.    wt: 1:   11 Adding Integers Formulas and Examples
  243.    wt: 1:   8 Multiplication by Signed Numbers Integers
  244.    wt: 1:   6 Multiplication by Natural Numbers
  245.    wt: 1:   5 Zero Movement and Additive Inverses
  246.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  247.    wt: 1:   17 Identify and Count Factors using Primes
  248.    wt: 1:   12 LCD GCD and LCM using Primes
  249.    wt: 1:   7 Calculator Usage Notes and Cautions
  250.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  251.    wt: 1:   5 Prime Factorization and a Square Rule
  252.    wt: 1:   3 video Primes and Composites from 9 times table
  253.    wt: 1:   2 Prime and Composites less than 16
  254.    wt: 1:   Division with Counts and Length
  255.    wt: 1:   Long Division forwards and backwards Example 3
  256.    wt: 1:   Long Division forwards and backwards Example 2
  257.    wt: 1:   Long Division forwards and backwards Example 1
  258.    wt: 1:   10 Division by Five Long and Short Ways
  259.    wt: 1:   4 Two and Three Digit Multipliers
  260.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  261.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  262.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  263.    wt: 1:   11 Place Value SI Standard International way
  264.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  265.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  266.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  267.    wt: 1:   Exact Arithmetic Wholes and Fractions
  268.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  269.    wt: 1:   016 Numbering Occidental Calendar Days
  270.    wt: 1:   015 School and work day counting tables
  271.    wt: 1:   011 Division of Time Intervals By Numbers
  272.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  273.    wt: 1:   4 Mixing and Changing Units of Time
  274.    wt: 1:   3 Units and Lengths of Time
  275.    wt: 1:   2 Time and Date Matters in School
  276.    wt: 1:   1 Intro of Kids To Time Date Skills
  277.    wt: 1:   Example 1. Area Between x and x squared
  278.    wt: 1:   A Chain Rule Real Player video examples
  279.    wt: 1:   33 Chain Rule Real Player video examples
  280.    wt: 1:   17 Derivatives of quotients of sine and cosine
  281.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  282.    wt: 1:   15 sine and cosine derivatives 3rd step
  283.    wt: 1:   14 sine and cosine derivatives 2nd step
  284.    wt: 1:   13 sine and cosine derivatives 1st step
  285.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  286.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  287.    wt: 1:   9 Limits Continuity and Composition
  288.    wt: 1:   5 Jumps and absence of unlimited error control
  289.    wt: 1:   4 Numerical properties
  290.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  291.    wt: 1:   E2 Algebraic Properties of Limits
  292.    wt: 1:   PostScript For and Against Decimal Perspectives
  293.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  294.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  295.    wt: 1:   Chapter 22 Complex Numbers
  296.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  297.    wt: 1:   Chapter 12. Units and Slopes
  298.    wt: 1:   Chapter 10 Slopes and Units
  299.    wt: 1:   Chapter 7 Slopes and Velocity
  300.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  301.    wt: 1:   Chapter 2. Slopes and Ski Trails
  302.    wt: 1:   Appendix E. How To Study Mathematics and Why
  303.    wt: 1:   Appendix D. What to do in School and Why
  304.    wt: 1:   Chapter 31 Direct and Indirect Reason
  305.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  306.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  307.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  308.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  309.    wt: 1:   Chapter 20. Degrees and Radians
  310.    wt: 1:   Chapter 19. Functions and Sets
  311.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  312.    wt: 1:   Chapter 12. Shorthand Usage Guide
  313.    wt: 1:   Chapter 11. Why Shorthand
  314.    wt: 1:   Chapter 10 Describing and Changing Calculations
  315.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  316.    wt: 1:   Chapter 8 Three Skills For Algebra
  317.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  318.    wt: 1:   Chapter 2 For and Against Mathematics
  319.    wt: 1:   Postscript B More on Story Telling and Reason
  320.    wt: 1:   Chapter 24 Direct and Indirect Reason
  321.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  322.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  323.    wt: 1:   Chapter 18 Sense and Knowledge
  324.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  325.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  326.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  327.    wt: 1:   R Why Learn Mathematics Skills
  328.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  329.    wt: 1:   O On Learning Mathematics and Science
  330.    wt: 1:   L Skills with take home value
  331.    wt: 1:   N Improving Marks on Tests and Finals
  332.    wt: 1:   J. More on written work and showing skill
  333.    wt: 1:   H Jigsaw puzzles and problem solving
  334.    wt: 1:   G. Written work formats for developing and showing skill
  335.    wt: 1:   E. When and how to correct errors
  336.    wt: 1:   Chapter 8 Skipped Topics and Why
  337.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  338.    wt: 1:   Chapter 6 More Algebra and Geometry
  339.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  340.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  341.    wt: 1:   7 Games and Activities for Instruction
  342.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  343.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  344.    wt: 1:   Helping the Blind in Logic and Mathematics
  345.    wt: 1:   More Algebra and Slope based Calculus Preview
  346.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  347.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  348.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  349.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  350.    wt: 1:   The Math Forum and Site Content

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  1.    wt: 9:   1 More and Less Than for Counts and Measures
  2.    wt: 9:   11 What are real lengths and numbers
  3.    wt: 8:   3 Comparison of Negative Numbers
  4.    wt: 8:   2 More and Less Than with Unlike Signs
  5.    wt: 8:   5 lengths and signs of numbers
  6.    wt: 8:   2 signed and unsigned numbers as coordinates
  7.    wt: 8:   3 Multiplying Units and Numbers
  8.    wt: 8:   C Equality for Fractions and Two Term Ratios and Fractions
  9.    wt: 8:   9 Improper Fractions and Mixed Numbers
  10.    wt: 8:   8 What skills and work habits to require
  11.    wt: 8:   6. Counting and adding units and mixed units
  12.    wt: 7:   4 Greater More Less Than Signs in General
  13.    wt: 7:   3 Properties of Square Roots with example
  14.    wt: 7:   1 Squares and Square Roots Introduction
  15.    wt: 7:   17 GCD LCM of 85 and 60 via Prime
  16.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  17.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  18.    wt: 7:   9 GCD of 360 110 via Primes and Euclid Algorithm
  19.    wt: 7:   7 GCD and LCM from prime factorization
  20.    wt: 7:   4 LCM of 8 and 10 via Prime
  21.    wt: 7:   3 Counting with Tables and Trees II
  22.    wt: 7:   2 Counting with Tables and Trees I
  23.    wt: 7:   1 Counting and Counting Methods I
  24.    wt: 7:   10 dividing signed numbers
  25.    wt: 7:   9 subtracting signed numbers
  26.    wt: 7:   8 multiplying signed numbers
  27.    wt: 7:   7 negative and additive inverse
  28.    wt: 7:   6 adding signed numbers
  29.    wt: 7:   3 signed coordinates for maps and planes
  30.    wt: 7:   5 Reciprocals and Division for Fractions with Units
  31.    wt: 7:   2 Equality and Units
  32.    wt: 7:   1 Addition and Subtraction with Units
  33.    wt: 7:   B Fractions and Two Term Ratios
  34.    wt: 7:   A Similarities between Fractions and Two Term Ratios
  35.    wt: 7:   21 Reciprocals for Fractions and Wholes
  36.    wt: 7:   17 Efficient Ways to Add and Subtract
  37.    wt: 7:   15 Adding and Subtracting with Unlike Denominators
  38.    wt: 7:   14 Adding and Subtracting with Like Denominators
  39.    wt: 7:   10 Simplification of Fractions and Mixed Numerals
  40.    wt: 7:   6 Multiplication of Mixed Numbers
  41.    wt: 7:   A Decimals Modular and Remainder Arithmetic
  42.    wt: 7:   6 Remainder Arithmetic Modulo 5 Propertie
  43.    wt: 7:   17 Identify and Count Factors using Primes
  44.    wt: 7:   12 LCD GCD and LCM using Primes
  45.    wt: 7:   7 Calculator Usage Notes and Cautions
  46.    wt: 7:   6 Sieve of Eratosthenes and Square Rule
  47.    wt: 7:   5 Prime Factorization and a Square Rule
  48.    wt: 7:   3 video Primes and Composites from 9 times table
  49.    wt: 7:   2 Prime and Composites less than 16
  50.    wt: 7:   4 Subtraction with Conversions Borrows and Letter J
  51.    wt: 7:   3 Harder Cases Convert to Compare and Subtract
  52.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  53.    wt: 7:   10 Names for Big Numbers and Powers of Ten Expansion
  54.    wt: 7:   Quick history of numbers and algebra
  55.    wt: 6:   arithmetic videos Real Player Format
  56.    wt: 6:   5 Square Roots with primes more still
  57.    wt: 6:   4 Square Roots with primes more
  58.    wt: 6:   2 Square Roots with Prime
  59.    wt: 6:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  60.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  61.    wt: 6:   13 GCD from given Prime Factorization
  62.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  63.    wt: 6:   8 GCD from Euclidean Algorithm
  64.    wt: 6:   6 GCD from Prime
  65.    wt: 6:   5 Common Divisors 60 45 via Prime
  66.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  67.    wt: 6:   2 Least Common Multiple LCM intro via list method
  68.    wt: 6:   1 Least Common Multiples LCM Introduction
  69.    wt: 6:   12 GCD 2700 288 via Prime
  70.    wt: 6:   5 Counting with Tables Trees Product Rule Take II
  71.    wt: 6:   4 Counting with Trees Product Rule Take I
  72.    wt: 6:   4 signed coordinates for regions in space
  73.    wt: 6:   7 Converting or Changing Units
  74.    wt: 6:   6 Simplification of Fractions with Units
  75.    wt: 6:   4 Fractions with Units
  76.    wt: 6:   D Three Term Ratios
  77.    wt: 6:   22 Complex Compound Fractions
  78.    wt: 6:   21 Working With Signs
  79.    wt: 6:   20 Dividing Fractions the Why
  80.    wt: 6:   19 Dividing Fractions How TO
  81.    wt: 6:   18 Efficient Ways to Multiply
  82.    wt: 6:   16 Addition Subtraction Comparision Compared
  83.    wt: 6:   13 Fraction Comparison Algebraic View
  84.    wt: 6:   12 Fraction Comparison
  85.    wt: 6:   11 Simplification an Algebraic View
  86.    wt: 6:   8 Numerals Fractionals Quantals Take II
  87.    wt: 6:   7 Numerals Fractionals Quantals
  88.    wt: 6:   6 Multiplication Algebraically Take II
  89.    wt: 6:   5 Equivalent Fractions
  90.    wt: 6:   4 Fraction Multiplication
  91.    wt: 6:   3 Unit fraction of a fraction
  92.    wt: 6:   2 Unit Fraction Multiplication
  93.    wt: 6:   1 What is a fraction Take II
  94.    wt: 6:   1 What is a fraction
  95.    wt: 6:   Fraction Operations by Raising Terms A Simple Innovation
  96.    wt: 6:   11 Adding Integers Formulas and Examples
  97.    wt: 6:   8 Multiplication by Signed Numbers Integers
  98.    wt: 6:   6 Multiplication by Natural Numbers
  99.    wt: 6:   5 Zero Movement and Additive Inverses
  100.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  101.    wt: 6:   26 Divisibility by 2 3 5 Example
  102.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  103.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  104.    wt: 6:   23 Remainder Arithmetic Modulo 2
  105.    wt: 6:   22 Remainder Arithmetic Modulo 3 more
  106.    wt: 6:   21 Remainder Arithmetic Modulo 3
  107.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  108.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  109.    wt: 6:   18 Remainder Arithmetic Rule of 9 for checking sums II
  110.    wt: 6:   17 Remainder Arithmetic Rule of 9 for checking sums I
  111.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  112.    wt: 6:   15 Remainder Arithmetic Modulo 9 Example
  113.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  114.    wt: 6:   13 Remainder Arithmetic Modulo 5 Example
  115.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  116.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  117.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  118.    wt: 6:   9 Remainder Arithmetic Divisibility by 5
  119.    wt: 6:   8 Remainder Arithmetic Morulo 5 Examples II
  120.    wt: 6:   7 Remainder Arithmetic Modulo 5 Examples I
  121.    wt: 6:   5 Remainder Arithmetic Modulo 5
  122.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  123.    wt: 6:   3 Remainder Arithmetic Modulos 10 more still
  124.    wt: 6:   2 Remainder Arithmetic Modulo 10 more
  125.    wt: 6:   1 Remainder Arithmetic Modulo 10
  126.    wt: 6:   20 Uniqueness of Prime Factorization
  127.    wt: 6:   19 video Prime Factorization Unique
  128.    wt: 6:   18 video Count Factors given Prime Factorization
  129.    wt: 6:   16 video Factors of 980 using prime
  130.    wt: 6:   15 video Factors of 20 using Prime Factorization
  131.    wt: 6:   14 video Factors of 24 Take II
  132.    wt: 6:   13 video Factors of 24 using prime
  133.    wt: 6:   11 Efficient Square Rule Use
  134.    wt: 6:   10 video Prime Factorization upto 23 squared
  135.    wt: 6:   9 video Prime Factorization upto 19 squared
  136.    wt: 6:   8 video Prime Factorization upto 19
  137.    wt: 6:   4 video Prime Factorization Introduction
  138.    wt: 6:   1 video how Products are bigger than factor
  139.    wt: 6:   Division with Counts and Length
  140.    wt: 6:   Long Division forwards and backwards Example 3
  141.    wt: 6:   Long Division forwards and backwards Example 2
  142.    wt: 6:   Long Division forwards and backwards Example 1
  143.    wt: 6:   10 Division by Five Long and Short Ways
  144.    wt: 6:   4 Two and Three Digit Multipliers
  145.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  146.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  147.    wt: 6:   Subtraction with J Conversions Example
  148.    wt: 6:   Subtraction Another Video Lesson
  149.    wt: 6:   9 22 Minute Subtraction Review Video
  150.    wt: 6:   8 Subtraction with Units of Measure
  151.    wt: 6:   7 Subtraction for Decimal Fractions with Exercises
  152.    wt: 6:   6 Subtraction with Conversion Example with Exercises
  153.    wt: 6:   5 A Tip for Efficent Subtraction
  154.    wt: 6:   2 Subtraction Easy Case Examples
  155.    wt: 6:   Appendix 1 Counting Revisited 15 minute video
  156.    wt: 6:   7 Adding decimal fractions using decimal point
  157.    wt: 6:   5. How to add decimals C. Examples
  158.    wt: 6:   4. How to add with decimals B with conversions
  159.    wt: 6:   3. How to add with decimals A sans conversions
  160.    wt: 6:   2 Decimal Counting Practices
  161.    wt: 6:   1. Explaining Addition Table
  162.    wt: 6:   11 Place Value SI Standard International way
  163.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  164.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  165.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  166.    wt: 6:   Exact Arithmetic Wholes and Fractions
  167.    wt: 6:   Practical Methods Ends and Values for Arithmetic
  168.    wt: 5:   11 Signed Number Addition and Addition Properties
  169.    wt: 5:   10 Real Number Lengths and Signs
  170.    wt: 5:   D Remainders Modulo 11 Pair Rule
  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:   Long Division Backwards more
  184.    wt: 5:   Long Division Backward
  185.    wt: 5:   12 Why Long Division Works Take III
  186.    wt: 5:   11 Another Single Digit Divisor Example
  187.    wt: 5:   9 Why Long Division Works Take II
  188.    wt: 5:   8 Correcting the Mistake
  189.    wt: 5:   7 Long Divison Mistake Catching
  190.    wt: 5:   6 Why Decimal Long Division Methods Works Take I
  191.    wt: 5:   5 Long Division Include Zeroes or not
  192.    wt: 5:   4 Division with 2 Digit Divsors
  193.    wt: 5:   3 Division Single Digit Divisor Example
  194.    wt: 5:   2 Division with Single Digit Divisors
  195.    wt: 5:   1 Divsion Physical Examples
  196.    wt: 5:   D Decimal Multiplication Methods Derived
  197.    wt: 5:   C Counting Areas with Powers of Ten
  198.    wt: 5:   B Powers of Ten
  199.    wt: 5:   A Elementary Basis for Multiplication Methods
  200.    wt: 5:   6 Multiplication Commutes Order Not Important
  201.    wt: 5:   5 Decimal Fraction Multiplication
  202.    wt: 5:   3 More One Digit Multipliers
  203.    wt: 5:   2 One Digit Multipliers
  204.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  205.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  206.    wt: 5:   Video Power Notation in Decimal Expansion
  207.    wt: 5:   1 Why 3 times 5 gives 15
  208.    wt: 5:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  209.    wt: 5:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  210.    wt: 5:   5 More on Groups of 3 Place Value in Decimal Fractions
  211.    wt: 5:   4 Groups of 3 Place Value in Decimal Fractions
  212.    wt: 5:   3 More on Groups of 3 Multi Digit Place Value
  213.    wt: 5:   2 Groups of Three Place Value for Multidigit Decimals
  214.    wt: 5:   Formula Evaluation how to show work
  215.    wt: 5:   Expression Evaluation how to show work
  216.    wt: 5:   The 20 Times Table
  217.    wt: 5:   The 12 Times Table Visually
  218.    wt: 5:   About folder contents
  219.    wt: 5:   Primary and Secondary Skills and Practices with Take Home Value
  220.    wt: 4:   musings do not puiblish real numbers
  221.    wt: 4:   24 Signed Numbers Arithmmetic Properties
  222.    wt: 4:   12 Real Numbers Line Signed Coordinates
  223.    wt: 4:   16 Real Numbers Comparison
  224.    wt: 4:   15 Real Number Division
  225.    wt: 4:   14 Real Number Multiplication
  226.    wt: 4:   13 Real Number Subtraction
  227.    wt: 4:   12 Real Number Additive Inverses or Negatives
  228.    wt: 4:   11 Real Number Addition
  229.    wt: 4:   7 Real Numbers as Line Cordinates
  230.    wt: 4:   6 Unsigned Real Numbers
  231.    wt: 4:   1 Whole and Natural Numbers
  232.    wt: 4:   5 Interpreting and Drawing Maps and Plans.
  233.    wt: 4:   2 Identifying Size and Position Place and Spatial Sense
  234.    wt: 4:   1 From Number Recognition and Counting to Arithmetic B
  235.    wt: 4:   1 From Number Recognition and Counting to Arithmetic A
  236.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  237.    wt: 3:   6 Field Properties of Complex Number
  238.    wt: 3:   A Modular and Remainder Arithmetic
  239.    wt: 3:   A Signed Number Arithmetic Review
  240.    wt: 3:   22 Multiplication of Signed Numbers
  241.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  242.    wt: 3:   14 Vector Head to Tail Sums and Resultants
  243.    wt: 3:   13 Arrows and Vectors in a Plane
  244.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  245.    wt: 3:   8 Division and Mulplication of Compound Fractions
  246.    wt: 3:   2 Combing Counts Addition Skills and Principles
  247.    wt: 3:   2 More and Less Than for Counts and Measures
  248.    wt: 3:   1 Real Numbers Comparison
  249.    wt: 3:   8 Coordinates for Maps and Planes
  250.    wt: 3:   5 Rational Numbers More
  251.    wt: 3:   4 Rational Numbers
  252.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  253.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  254.    wt: 3:   P Exact Arithmetic With Whole Numbers and Fractions
  255.    wt: 3:   I. Logic and language skills
  256.    wt: 3:   How to Build Skills and Confidence
  257.    wt: 3:   7 Games and Activities for Instruction
  258.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  259.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  260.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  261.    wt: 2:   Ramblings Extrinsic numbers theory
  262.    wt: 2:   2 Reading and Writing Skills
  263.    wt: 2:   Ages 12 to 14 Skills with take home value
  264.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  265.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  266.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  267.    wt: 2:   9 Summary Degrees to Radians and back
  268.    wt: 2:   1 Degrees and Radians Introduction
  269.    wt: 2:   Vector and Complex Number Applet
  270.    wt: 2:   Parallel Lines and Parallel Transversals
  271.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  272.    wt: 2:   Parallel Lines and Interior Angles
  273.    wt: 2:   B Straight Line Slope Scaling Properties More
  274.    wt: 2:   A Straight Line Slope Scaling Properties
  275.    wt: 2:   4 Tangent Function Properties
  276.    wt: 2:   14 cosine even and sine and tangent are odd
  277.    wt: 2:   21 Logarithms Powers and Exponentials
  278.    wt: 2:   20 N th Roots of Complex Numbers
  279.    wt: 2:   16 References and Originality Question
  280.    wt: 2:   13 Trig Formulas for dot and cross Products
  281.    wt: 2:   12 cis formulas for sine cosines and tangent
  282.    wt: 2:   11 sine and cosine double triple angle formulas
  283.    wt: 2:   9 The complex number valued trig function cis
  284.    wt: 2:   4 Multiplication Properties
  285.    wt: 2:   3 Addition Properties
  286.    wt: 2:   2 Complex Numbers made easier we hope
  287.    wt: 2:   Appetizer A Complex Number Applet
  288.    wt: 2:   10 Midpoint of [a b] and [b a]
  289.    wt: 2:   7 Exercises to test skill and concept mastery
  290.    wt: 2:   1 Numerical view of lines and their equations
  291.    wt: 2:   What is and is not here
  292.    wt: 2:   7 Complex Numbers Appetizer
  293.    wt: 2:   6 Polar Multiplication and Rotation
  294.    wt: 2:   5 Cartesian Addition and Translation
  295.    wt: 2:   4 Polar Coordinates to and from
  296.    wt: 2:   PS H Distributive Law For Complex Numbers
  297.    wt: 2:   16 Angles Subtended By Chords and Diameters
  298.    wt: 2:   6 Ruler and compass Angle Bisection
  299.    wt: 2:   1 Initial Concepts and Terms
  300.    wt: 2:   3 Lengths and Areas on Maps and Plans
  301.    wt: 2:   26 More Less Greater Than Comparison
  302.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  303.    wt: 2:   23 Distributive Law Two Derivations
  304.    wt: 2:   21 Addition of Multiples of a Single Vector
  305.    wt: 2:   19 Signed Multiples of Vectors
  306.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  307.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  308.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  309.    wt: 2:   15 Head to Tails in place Addition Associative
  310.    wt: 2:   9 Division with Digits after Decimal Point
  311.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  312.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  313.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  314.    wt: 2:   4 Location of Point in Decimal Addition
  315.    wt: 2:   3 Location of Point in Decimal Multiplication
  316.    wt: 2:   2 Counting Digits in Decimal Multiplication
  317.    wt: 2:   1 Fractions with Finite Decimal Expansions
  318.    wt: 2:   B Decimal Comparison and Subtraction
  319.    wt: 2:   5 Distributive Law for Whole Numbers
  320.    wt: 2:   3 Multiplicative Counting Skills Principles
  321.    wt: 2:   1 The Counting Origins of Numbers
  322.    wt: 2:   4 Rates Ratios and Proporitionality
  323.    wt: 2:   6 Equations and Systems Equivalent or Implied
  324.    wt: 2:   4 Subtraction and Division Axioms
  325.    wt: 2:   2 Addition and Multiplication Axioms
  326.    wt: 2:   4 Comparison of Negative Numbers
  327.    wt: 2:   3 More and Less Than with Unlike Signs
  328.    wt: 2:   9 Coordinates for Regions in Space
  329.    wt: 2:   3 Fractions
  330.    wt: 2:   2 Integers
  331.    wt: 2:   3 Geometric Formulas and Function Notation
  332.    wt: 2:   1 Formulas Dependence and Function Notation
  333.    wt: 2:   5 Talking about Numbers and Quantities
  334.    wt: 2:   4 A Brief Story of numbers and algebra
  335.    wt: 2:   016 Numbering Occidental Calendar Days
  336.    wt: 2:   015 School and work day counting tables
  337.    wt: 2:   011 Division of Time Intervals By Numbers
  338.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  339.    wt: 2:   4 Mixing and Changing Units of Time
  340.    wt: 2:   3 Units and Lengths of Time
  341.    wt: 2:   2 Time and Date Matters in School
  342.    wt: 2:   1 Intro of Kids To Time Date Skills
  343.    wt: 2:   Example 1. Area Between x and x squared
  344.    wt: 2:   38 Formulas and derivatives for powers and roots
  345.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  346.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  347.    wt: 2:   9 Limits Continuity and Composition
  348.    wt: 2:   5 Jumps and absence of unlimited error control
  349.    wt: 2:   4 Numerical properties
  350.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  351.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  352.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  353.    wt: 2:   Appendix E. How To Study Mathematics and Why
  354.    wt: 2:   Appendix D. What to do in School and Why
  355.    wt: 2:   Chapter 31 Direct and Indirect Reason
  356.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  357.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  358.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  359.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  360.    wt: 2:   Chapter 20. Degrees and Radians
  361.    wt: 2:   Chapter 19. Functions and Sets
  362.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  363.    wt: 2:   Chapter 12. Shorthand Usage Guide
  364.    wt: 2:   Chapter 11. Why Shorthand
  365.    wt: 2:   Chapter 10 Describing and Changing Calculations
  366.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  367.    wt: 2:   Chapter 8 Three Skills For Algebra
  368.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  369.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  370.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  371.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  372.    wt: 2:   R Why Learn Mathematics Skills
  373.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  374.    wt: 2:   O On Learning Mathematics and Science
  375.    wt: 2:   L Skills with take home value
  376.    wt: 2:   N Improving Marks on Tests and Finals
  377.    wt: 2:   J. More on written work and showing skill
  378.    wt: 2:   H Jigsaw puzzles and problem solving
  379.    wt: 2:   G. Written work formats for developing and showing skill
  380.    wt: 2:   E. When and how to correct errors
  381.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  382.    wt: 1:   Appendix 1 primary and preschool mathematic
  383.    wt: 1:   G LAMP Introduction Problem Solving Skills
  384.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  385.    wt: 1:   Skills Chapter 5 Calculus
  386.    wt: 1:   Skills Chapter 4 Logic
  387.    wt: 1:   Skills Chapter 3 Algebra
  388.    wt: 1:   Skills Chapter 2 Geometry
  389.    wt: 1:   Skills Chapter 1 Arithmetic
  390.    wt: 1:   Skills Chapter 0 Introduction
  391.    wt: 1:   7 logic review and decimals an odd combination
  392.    wt: 1:   5 logarithms and exponentials etc
  393.    wt: 1:   2 arithmetic with signed numbers
  394.    wt: 1:   1 arithmetic with unsigned numbers
  395.    wt: 1:   key notes and themes
  396.    wt: 1:   what should be learnt and When
  397.    wt: 1:   standards for course material
  398.    wt: 1:   Theory of Knowledge
  399.    wt: 1:   Education in mathematics science and technology
  400.    wt: 1:   Motivation and Context Problem
  401.    wt: 1:   fairness and inductive principles for instruction
  402.    wt: 1:   Home Tutoring and Home Schooling
  403.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  404.    wt: 1:   24 Standards For Skill Develoment Take II
  405.    wt: 1:   24 Standards For Skill Develoment
  406.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  407.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  408.    wt: 1:   17 Math Booklets for children and young teenagers
  409.    wt: 1:   14 Multiplication and Times Tables
  410.    wt: 1:   13 Addition and Addition Tables
  411.    wt: 1:   12 Goals and Objectives For Mathematics
  412.    wt: 1:   11 Help and Defend Your Child or Teens Education
  413.    wt: 1:   5 Patience Please for Yourself and Your Charges
  414.    wt: 1:   4 Learning Takes Time and Effort
  415.    wt: 1:   1 Speaking Skills
  416.    wt: 1:   Ages 12 to 14 Geometry
  417.    wt: 1:   Ages 12 to 14 Arithmetic
  418.    wt: 1:   Ages 10 to 12 Geometry
  419.    wt: 1:   Ages 10 to 12 Arithmetic
  420.    wt: 1:   Ages 9 to 10
  421.    wt: 1:   Ages 8 to 9
  422.    wt: 1:   Ages 7 to 8
  423.    wt: 1:   Ages 6 to 7
  424.    wt: 1:   Ages 4 plus to 5 plus
  425.    wt: 1:   Ages 3 plus to 4 plus
  426.    wt: 1:   26 Function definitions done and coming
  427.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  428.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  429.    wt: 1:   19 Horizontal line rule and method
  430.    wt: 1:   18 Vertical Line Rule and Method
  431.    wt: 1:   17 Function maxima minima and their location
  432.    wt: 1:   11 Function Domain Range Source and Targets
  433.    wt: 1:   9 Set theory term relation possible origins
  434.    wt: 1:   8 Set view of relations and functions
  435.    wt: 1:   6 Set Existence Formation and Notation
  436.    wt: 1:   4 Function notation in and beyond mathematics
  437.    wt: 1:   9 quadratics physical and further context
  438.    wt: 1:   11 Growth and Decay in Biology
  439.    wt: 1:   10 Exponential Growth and Decay Models
  440.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  441.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  442.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  443.    wt: 1:   16 cotangent function Definition Graph and Inverse
  444.    wt: 1:   15 cosecant function Definition Graph and Inverse
  445.    wt: 1:   14 secant function Definition Graph and Inverse
  446.    wt: 1:   13 cosecant function Definition Graph and Inverse
  447.    wt: 1:   2 cosine function more properties
  448.    wt: 1:   1 cosine function properties
  449.    wt: 1:   8 Radian Measures of Common Angles
  450.    wt: 1:   7 Radian Measures in special Triangles
  451.    wt: 1:   6 Radian Measure to Degrees
  452.    wt: 1:   5 Degrees to Radian Measure
  453.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  454.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  455.    wt: 1:   2 Radian Measure Numerical Value of one degree
  456.    wt: 1:   A Global Time and Navigation
  457.    wt: 1:   15 Dot and Cross Product
  458.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  459.    wt: 1:   4 graphing y=Asin(x c)
  460.    wt: 1:   3 graphing y=f(x c) plus K
  461.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  462.    wt: 1:   1 graphing y=f(x a)
  463.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  464.    wt: 1:   Triangle Angles Sum To 180 Degrees
  465.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  466.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  467.    wt: 1:   Straight Lines ASA Intersection Study More
  468.    wt: 1:   Straight Lines ASA Intersection Study
  469.    wt: 1:   Straight Lines Instersection Solving Equations
  470.    wt: 1:   Straight Lines Intersection of
  471.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  472.    wt: 1:   C Straight Lines Slope from Coordinates
  473.    wt: 1:   14 Straight Lines Equations General Case
  474.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  475.    wt: 1:   12 Straight Lines Graphing mx plus b
  476.    wt: 1:   11 Straight Lines Graphing y=mx
  477.    wt: 1:   10 Straight Lines through Origin Equations More
  478.    wt: 1:   9 Straight Lines through Origin Equations
  479.    wt: 1:   8 Straight Lines Equation for vertical
  480.    wt: 1:   7 Tangent Function is odd on this domain
  481.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  482.    wt: 1:   5 Tangent Function Graph
  483.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  484.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  485.    wt: 1:   1 Straight Lines Slope Concept
  486.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  487.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  488.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  489.    wt: 1:   29 secant cosecant and cotangent for acute angles
  490.    wt: 1:   27 Logarithmic use of products of sines and cosines
  491.    wt: 1:   26 Formulas for products of sines and cosines
  492.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  493.    wt: 1:   21 sine and cosine Half Angle Formulas
  494.    wt: 1:   20 sine and cosine Double Angle Formulas
  495.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  496.    wt: 1:   17E Trig Formulas for dot and cross Products
  497.    wt: 1:   17D cis formulas for sine cosines and tangent
  498.    wt: 1:   17C sine and cosine double triple angle formulas
  499.    wt: 1:   17A The complex number valued trig function cis
  500.    wt: 1:   10 Graphs of sines and cosines many periods
  501.    wt: 1:   9 Graphs of sine and cosine over one period
  502.    wt: 1:   7 period of sine and cosine
  503.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  504.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  505.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  506.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  507.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  508.    wt: 1:   19 N th Roots of Unity
  509.    wt: 1:   18 Sixth Roots of Unity
  510.    wt: 1:   17 Cube Roots of unity
  511.    wt: 1:   15 Pythagorean Theorem Converse
  512.    wt: 1:   14 Law of cosines
  513.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  514.    wt: 1:   8 Unit Circle Development of Trigonometry
  515.    wt: 1:   7 Second Way to Calculate Products
  516.    wt: 1:   5 An Easy Proof of the Distributive Law
  517.    wt: 1:   1 Rectangular Polar Coordinates Review
  518.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  519.    wt: 1:   3 Trigonometric Ratios sine and cosine
  520.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  521.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  522.    wt: 1:   8 Similarity of Triangles and Polygons
  523.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  524.    wt: 1:   Four Simple Exercises
  525.    wt: 1:   12 Links Lessons elsewhere
  526.    wt: 1:   11 A Partial Summary
  527.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  528.    wt: 1:   8 Mid Point Formula
  529.    wt: 1:   6 Intersection of lines by solving linear systems
  530.    wt: 1:   5 Algebraic View of Slopes
  531.    wt: 1:   4 Equations for lines three forms
  532.    wt: 1:   3 Slope product for perpendicular lines
  533.    wt: 1:   2 point slope equation for a line
  534.    wt: 1:   13 Pythagorean spatial distance formulas
  535.    wt: 1:   12 Spatial Coordinates
  536.    wt: 1:   11 Triangle Inequality
  537.    wt: 1:   10 Pythagorean plane distance formula
  538.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  539.    wt: 1:   8 Distance Between Points on a Line
  540.    wt: 1:   3 Rectangular Coordinates Review
  541.    wt: 1:   2 Cartesian Coordinates with signs
  542.    wt: 1:   1 Cartesian Coordinates sans signs
  543.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  544.    wt: 1:   PS G Rotation Distributes over Addition
  545.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  546.    wt: 1:   PS E Multiplication with Polar Coordinates
  547.    wt: 1:   PS D Addition with Cartesian Coordinates
  548.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  549.    wt: 1:   PS B Parallelogram Construction Methods
  550.    wt: 1:   PS A Kite Construction Methods
  551.    wt: 1:   21 Parallelograms
  552.    wt: 1:   19 Right Triangle Similarity
  553.    wt: 1:   18 Triangle Similarity Take 1
  554.    wt: 1:   17 Right Bisectors of Triangle Sides
  555.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  556.    wt: 1:   14 Parallel Lines Postulate
  557.    wt: 1:   13 Angle Side Angle Failure
  558.    wt: 1:   12 Side Angle Side Failure
  559.    wt: 1:   11 Triangle Construction Fails
  560.    wt: 1:   10 Dropping a perpendicular to line
  561.    wt: 1:   9 Construction of a right bisector
  562.    wt: 1:   8 Isoceles Triangles
  563.    wt: 1:   7 Angle Side Angle
  564.    wt: 1:   5 Side Angle Side
  565.    wt: 1:   4 Side Side Side
  566.    wt: 1:   3 Isometry of Triangles Congruence
  567.    wt: 1:   2 Correspondence between Triangles
  568.    wt: 1:   Short Course on Euclidean Geometry
  569.    wt: 1:   E Long Division Methods more
  570.    wt: 1:   D Long Division Methods
  571.    wt: 1:   C Three Decimal Subtraction Methods
  572.    wt: 1:   A Decimal Addition Columm Methods
  573.    wt: 1:   8 Column Multiplication Methods in General
  574.    wt: 1:   7 Decimals Multiplication Methods Examples
  575.    wt: 1:   6 Column Methods for Decimal Multiplication
  576.    wt: 1:   4 Commutative Law Groups Counting Form
  577.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  578.    wt: 1:   5 Proportionality in Equivalent Fractions
  579.    wt: 1:   3 Proportionality Examples
  580.    wt: 1:   2 Algebraic View
  581.    wt: 1:   1 What is Proportionality
  582.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  583.    wt: 1:   6 Compound Interest Forward and Backwards
  584.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  585.    wt: 1:   5 Equality in Algebra
  586.    wt: 1:   3 Product Axioms Two Forms
  587.    wt: 1:   1 Equivalent Computation Rules
  588.    wt: 1:   5 Greater More Less Than Signs in General
  589.    wt: 1:   5 Independent versus Dependent Variables
  590.    wt: 1:   4 Changing Letters
  591.    wt: 1:   2 Computation Rules Evaluation
  592.    wt: 1:   3 GE III Equation Addition and Multiplication
  593.    wt: 1:   Skill Development Notes
  594.    wt: 1:   10 One Example
  595.    wt: 1:   9 Three Examples
  596.    wt: 1:   8 One Example
  597.    wt: 1:   7 Two Examples
  598.    wt: 1:   6 Three Examples
  599.    wt: 1:   5 Three Examples
  600.    wt: 1:   4 Two Examples
  601.    wt: 1:   3 Two Examples
  602.    wt: 1:   2 Three Examples
  603.    wt: 1:   1 Written work formats for developing and showing skill
  604.    wt: 1:   9 Sets in Probability and Statistics
  605.    wt: 1:   8 Sets of Numbers
  606.    wt: 1:   1 Three Skills For Algebra
  607.    wt: 1:   014 Counting Days with Calendars
  608.    wt: 1:   013 Travel Time Tables
  609.    wt: 1:   012 Division of Time Intervals by Time Intervals
  610.    wt: 1:   010 Repeated Addition of Time Intervals
  611.    wt: 1:   8 Addition of Time Intervals via subtotaling
  612.    wt: 1:   7 Addition of Time Intervals
  613.    wt: 1:   6 How long is a million seconds
  614.    wt: 1:   5 Conversion Arithmetic
  615.    wt: 1:   Example 2 volume of a cone
  616.    wt: 1:   Example 1 volume of a pyramid
  617.    wt: 1:   Volume of Solid by Cross Sections Lesson
  618.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  619.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  620.    wt: 1:   Example 4 with x function of y
  621.    wt: 1:   Example 3
  622.    wt: 1:   Example 2
  623.    wt: 1:   Example 1
  624.    wt: 1:   Area Between Curves Lesson Take 2
  625.    wt: 1:   Area Between Curves Lesson Take 1
  626.    wt: 1:   Summary
  627.    wt: 1:   A Chain Rule Real Player video examples
  628.    wt: 1:   33 Chain Rule Real Player video examples
  629.    wt: 1:   17 Derivatives of quotients of sine and cosine
  630.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  631.    wt: 1:   15 sine and cosine derivatives 3rd step
  632.    wt: 1:   14 sine and cosine derivatives 2nd step
  633.    wt: 1:   13 sine and cosine derivatives 1st step
  634.    wt: 1:   11 Limits at infinity Three Examples
  635.    wt: 1:   10 Three one sided limits with infinite values
  636.    wt: 1:   8 Four Animated Examples
  637.    wt: 1:   7 Evaluation by immediate or delayed substitution
  638.    wt: 1:   6 Continuity at a point
  639.    wt: 1:   3 Decimal insights for limits continuity convergence
  640.    wt: 1:   2 Algebraic codification
  641.    wt: 1:   1 Numerical introduction
  642.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  643.    wt: 1:   E2 Algebraic Properties of Limits
  644.    wt: 1:   PostScript For and Against Decimal Perspectives
  645.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  646.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  647.    wt: 1:   Chapter 22 Complex Numbers
  648.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  649.    wt: 1:   Chapter 12. Units and Slopes
  650.    wt: 1:   Chapter 10 Slopes and Units
  651.    wt: 1:   Chapter 7 Slopes and Velocity
  652.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  653.    wt: 1:   Chapter 2. Slopes and Ski Trails
  654.    wt: 1:   Postscript More on Better Performance
  655.    wt: 1:   Postscript For Better Performance
  656.    wt: 1:   Appendix C. How to Read
  657.    wt: 1:   Appendix B. How To Learn
  658.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  659.    wt: 1:   Chapter 30 Truth Tables
  660.    wt: 1:   Chapter 28 Occurrence Tables
  661.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  662.    wt: 1:   Chapter 25. Mathematical Induction Examples
  663.    wt: 1:   Chapter 23. Notation For Sums
  664.    wt: 1:   Chapter 21. Third Reading Guide
  665.    wt: 1:   Chapter 18. Rules for Algebra
  666.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  667.    wt: 1:   Chapter 16. Painless Theorem Proving
  668.    wt: 1:   Chapter 15. Solving Linear Equations
  669.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  670.    wt: 1:   Chapter 13. Second Reading Guide
  671.    wt: 1:   Postscript What is a Variable
  672.    wt: 1:   Solutions For Arithmetic Exercises
  673.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  674.    wt: 1:   Chapter 6 Change of Language
  675.    wt: 1:   Chapter 4 Longer Chains of Reason
  676.    wt: 1:   Chapter 3 Chains of Reason
  677.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  678.    wt: 1:   Foreword
  679.    wt: 1:   Chapter 2 For and Against Mathematics
  680.    wt: 1:   Postscript B More on Story Telling and Reason
  681.    wt: 1:   Chapter 24 Direct and Indirect Reason
  682.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  683.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  684.    wt: 1:   Chapter 18 Sense and Knowledge
  685.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  686.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  687.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  688.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  689.    wt: 1:   S Adding words to algebra
  690.    wt: 1:   N Mathematics Prepare for College Studies
  691.    wt: 1:   M Words to extend arithmetic
  692.    wt: 1:   H more Routine to non routine problem solving
  693.    wt: 1:   F. The student teacher tutor feedback loop
  694.    wt: 1:   D. Check work a must with a caution
  695.    wt: 1:   C. Domino effect of being careful
  696.    wt: 1:   B. Domino effect of errors
  697.    wt: 1:   A. Skill has to be seen to believed
  698.    wt: 1:   Chapter 8 Skipped Topics and Why
  699.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  700.    wt: 1:   Chapter 6 More Algebra and Geometry
  701.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  702.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  703.    wt: 1:   Helping the Blind in Logic and Mathematics
  704.    wt: 1:   More Algebra and Slope based Calculus Preview
  705.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  706.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  707.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  708.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  709.    wt: 1:   The Math Forum and Site Content

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

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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