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

Logic mastery strengthens comprehension and improve home, work & study habits.
Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits

Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles
Forewords + leading chapters give original reasons, still valid, for site content & growth.

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

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

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

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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:   Step 1 Stick diagram and fractions/
  19.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  20.    wt: 1:   Mathematics Skills Year by Year/
  21.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  22.    wt: 1:   12 Function Translating and Rescaling/
  23.    wt: 1:   11 Parallel Straight Lines and Transversals/
  24.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  25.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  26.    wt: 1:   7 Complex Numbers/
  27.    wt: 1:   6 Trigonometry first steps/
  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:   B Real Numbers Extrinsic Development/
  32.    wt: 1:   A Origins of Counting and Figuring Methods/
  33.    wt: 1:   9 Proportionality Backwards and Forwards/
  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

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

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicylce?

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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