Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers in school and out. See site volumes.

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

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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44 matches:

  1.    wt: 9:   6 Fractions and Ratios/
  2.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  3.    wt: 7:   7 Arithmetic and Fractions with Units/
  4.    wt: 6:   11 Squares and Square Roots/
  5.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  6.    wt: 6:   9 Combinatorics Trees Tables and Products/
  7.    wt: 6:   8 Arithmetic with Signed Numbers/
  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:   9 Proportionality Backwards and Forwards/
  19.    wt: 2:   Step 1 Stick diagram and fractions/
  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:   6 Trigonometry first steps/
  29.    wt: 1:   4 Lines and Slopes Take 1/
  30.    wt: 1:   3 Cartesian and Polar Coordinates/
  31.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  32.    wt: 1:   B Real Numbers Extrinsic Development/
  33.    wt: 1:   A Origins of Counting and Figuring Methods/
  34.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  35.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  36.    wt: 1:   5 Real Numbers/
  37.    wt: 1:   4 Computation Rules and Function Notation/
  38.    wt: 1:   Time Date Matters/
  39.    wt: 1:   Skills with take home value/
  40.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  41.    wt: 1:   13 Lessons on Limits and Continuity/
  42.    wt: 1:   Volume 2 Three Skills For Algebra/
  43.    wt: 1:   Work and Study Tips/
  44.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

360 matches:

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

Extended Search

712 matches:

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

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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