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

358 matches:

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

Extended Search

713 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: 9:   6. Counting and adding units and mixed units
  20.    wt: 8:   3 Comparison of Negative Numbers
  21.    wt: 8:   2 More and Less Than with Unlike Signs
  22.    wt: 8:   11 What are real lengths and numbers
  23.    wt: 8:   5 lengths and signs of numbers
  24.    wt: 8:   2 signed and unsigned numbers as coordinates
  25.    wt: 8:   6 Simplification of Fractions with Units
  26.    wt: 8:   4 Fractions with Units
  27.    wt: 8:   2 Equality and Units
  28.    wt: 8:   1 Addition and Subtraction with Units
  29.    wt: 8:   6 Sieve of Eratosthenes and Square Rule
  30.    wt: 8:   8 What skills and work habits to require
  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:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  65.    wt: 7:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  66.    wt: 7:   Quick history of numbers and algebra
  67.    wt: 7:   Exact Arithmetic Wholes and Fractions
  68.    wt: 6:   5 Square Roots with primes more still
  69.    wt: 6:   4 Square Roots with primes more
  70.    wt: 6:   3 Properties of Square Roots with example
  71.    wt: 6:   2 Square Roots with Prime
  72.    wt: 6:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  73.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  74.    wt: 6:   13 GCD from given Prime Factorization
  75.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  76.    wt: 6:   8 GCD from Euclidean Algorithm
  77.    wt: 6:   6 GCD from Prime
  78.    wt: 6:   5 Common Divisors 60 45 via Prime
  79.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  80.    wt: 6:   2 Least Common Multiple LCM intro via list method
  81.    wt: 6:   1 Least Common Multiples LCM Introduction
  82.    wt: 6:   12 GCD 2700 288 via Prime
  83.    wt: 6:   5 Counting with Tables Trees Product Rule Take II
  84.    wt: 6:   4 Counting with Trees Product Rule Take I
  85.    wt: 6:   4 signed coordinates for regions in space
  86.    wt: 6:   11 Adding Integers Formulas and Examples
  87.    wt: 6:   8 Multiplication by Signed Numbers Integers
  88.    wt: 6:   5 Zero Movement and Additive Inverses
  89.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  90.    wt: 6:   26 Divisibility by 2 3 5 Example
  91.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  92.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  93.    wt: 6:   23 Remainder Arithmetic Modulo 2
  94.    wt: 6:   22 Remainder Arithmetic Modulo 3 more
  95.    wt: 6:   21 Remainder Arithmetic Modulo 3
  96.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  97.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  98.    wt: 6:   18 Remainder Arithmetic Rule of 9 for checking sums II
  99.    wt: 6:   17 Remainder Arithmetic Rule of 9 for checking sums I
  100.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  101.    wt: 6:   15 Remainder Arithmetic Modulo 9 Example
  102.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  103.    wt: 6:   13 Remainder Arithmetic Modulo 5 Example
  104.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  105.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  106.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  107.    wt: 6:   9 Remainder Arithmetic Divisibility by 5
  108.    wt: 6:   8 Remainder Arithmetic Morulo 5 Examples II
  109.    wt: 6:   7 Remainder Arithmetic Modulo 5 Examples I
  110.    wt: 6:   6 Remainder Arithmetic Modulo 5 Propertie
  111.    wt: 6:   5 Remainder Arithmetic Modulo 5
  112.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  113.    wt: 6:   3 Remainder Arithmetic Modulos 10 more still
  114.    wt: 6:   2 Remainder Arithmetic Modulo 10 more
  115.    wt: 6:   1 Remainder Arithmetic Modulo 10
  116.    wt: 6:   20 Uniqueness of Prime Factorization
  117.    wt: 6:   19 video Prime Factorization Unique
  118.    wt: 6:   18 video Count Factors given Prime Factorization
  119.    wt: 6:   16 video Factors of 980 using prime
  120.    wt: 6:   15 video Factors of 20 using Prime Factorization
  121.    wt: 6:   14 video Factors of 24 Take II
  122.    wt: 6:   13 video Factors of 24 using prime
  123.    wt: 6:   11 Efficient Square Rule Use
  124.    wt: 6:   10 video Prime Factorization upto 23 squared
  125.    wt: 6:   9 video Prime Factorization upto 19 squared
  126.    wt: 6:   8 video Prime Factorization upto 19
  127.    wt: 6:   4 video Prime Factorization Introduction
  128.    wt: 6:   1 video how Products are bigger than factor
  129.    wt: 6:   Division with Counts and Length
  130.    wt: 6:   Long Division forwards and backwards Example 3
  131.    wt: 6:   Long Division forwards and backwards Example 2
  132.    wt: 6:   Long Division forwards and backwards Example 1
  133.    wt: 6:   10 Division by Five Long and Short Ways
  134.    wt: 6:   6 Why Decimal Long Division Methods Works Take I
  135.    wt: 6:   6 Multiplication Commutes Order Not Important
  136.    wt: 6:   4 Two and Three Digit Multipliers
  137.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  138.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  139.    wt: 6:   Subtraction with J Conversions Example
  140.    wt: 6:   Subtraction Another Video Lesson
  141.    wt: 6:   9 22 Minute Subtraction Review Video
  142.    wt: 6:   8 Subtraction with Units of Measure
  143.    wt: 6:   5 A Tip for Efficent Subtraction
  144.    wt: 6:   2 Subtraction Easy Case Examples
  145.    wt: 6:   Appendix 1 Counting Revisited 15 minute video
  146.    wt: 6:   5. How to add decimals C. Examples
  147.    wt: 6:   4. How to add with decimals B with conversions
  148.    wt: 6:   3. How to add with decimals A sans conversions
  149.    wt: 6:   2 Decimal Counting Practices
  150.    wt: 6:   1. Explaining Addition Table
  151.    wt: 6:   11 Place Value SI Standard International way
  152.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  153.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  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:   need for a mixed mathematics curriculum
  382.    wt: 1:   fairness and inductive principles for instruction
  383.    wt: 1:   Home Tutoring and Home Schooling
  384.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  385.    wt: 1:   24 Standards For Skill Develoment Take II
  386.    wt: 1:   24 Standards For Skill Develoment
  387.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  388.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  389.    wt: 1:   17 Math Booklets for children and young teenagers
  390.    wt: 1:   14 Multiplication and Times Tables
  391.    wt: 1:   13 Addition and Addition Tables
  392.    wt: 1:   12 Goals and Objectives For Mathematics
  393.    wt: 1:   11 Help and Defend Your Child or Teens Education
  394.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  395.    wt: 1:   5 Patience Please for Yourself and Your Charges
  396.    wt: 1:   4 Learning Takes Time and Effort
  397.    wt: 1:   1 Speaking Skills
  398.    wt: 1:   Ages 12 to 14 Geometry
  399.    wt: 1:   Ages 12 to 14 Arithmetic
  400.    wt: 1:   Ages 10 to 12 Geometry
  401.    wt: 1:   Ages 10 to 12 Arithmetic
  402.    wt: 1:   Ages 9 to 10
  403.    wt: 1:   Ages 8 to 9
  404.    wt: 1:   Ages 7 to 8
  405.    wt: 1:   Ages 6 to 7
  406.    wt: 1:   Ages 4 plus to 5 plus
  407.    wt: 1:   Ages 3 plus to 4 plus
  408.    wt: 1:   26 Function definitions done and coming
  409.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  410.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  411.    wt: 1:   19 Horizontal line rule and method
  412.    wt: 1:   18 Vertical Line Rule and Method
  413.    wt: 1:   17 Function maxima minima and their location
  414.    wt: 1:   11 Function Domain Range Source and Targets
  415.    wt: 1:   9 Set theory term relation possible origins
  416.    wt: 1:   8 Set view of relations and functions
  417.    wt: 1:   6 Set Existence Formation and Notation
  418.    wt: 1:   4 Function notation in and beyond mathematics
  419.    wt: 1:   9 quadratics physical and further context
  420.    wt: 1:   11 Growth and Decay in Biology
  421.    wt: 1:   10 Exponential Growth and Decay Models
  422.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  423.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  424.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  425.    wt: 1:   16 cotangent function Definition Graph and Inverse
  426.    wt: 1:   15 cosecant function Definition Graph and Inverse
  427.    wt: 1:   14 secant function Definition Graph and Inverse
  428.    wt: 1:   13 cosecant function Definition Graph and Inverse
  429.    wt: 1:   8 Radian Measures of Common Angles
  430.    wt: 1:   7 Radian Measures in special Triangles
  431.    wt: 1:   6 Radian Measure to Degrees
  432.    wt: 1:   5 Degrees to Radian Measure
  433.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  434.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  435.    wt: 1:   2 Radian Measure Numerical Value of one degree
  436.    wt: 1:   A Global Time and Navigation
  437.    wt: 1:   15 Dot and Cross Product
  438.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  439.    wt: 1:   4 graphing y=Asin(x c)
  440.    wt: 1:   3 graphing y=f(x c) plus K
  441.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  442.    wt: 1:   1 graphing y=f(x a)
  443.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  444.    wt: 1:   Triangle Angles Sum To 180 Degrees
  445.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  446.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  447.    wt: 1:   Straight Lines ASA Intersection Study More
  448.    wt: 1:   Straight Lines ASA Intersection Study
  449.    wt: 1:   Straight Lines Instersection Solving Equations
  450.    wt: 1:   Straight Lines Intersection of
  451.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  452.    wt: 1:   C Straight Lines Slope from Coordinates
  453.    wt: 1:   B Straight Line Slope Scaling Properties More
  454.    wt: 1:   A Straight Line Slope Scaling Properties
  455.    wt: 1:   14 Straight Lines Equations General Case
  456.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  457.    wt: 1:   12 Straight Lines Graphing mx plus b
  458.    wt: 1:   11 Straight Lines Graphing y=mx
  459.    wt: 1:   10 Straight Lines through Origin Equations More
  460.    wt: 1:   9 Straight Lines through Origin Equations
  461.    wt: 1:   8 Straight Lines Equation for vertical
  462.    wt: 1:   7 Tangent Function is odd on this domain
  463.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  464.    wt: 1:   5 Tangent Function Graph
  465.    wt: 1:   4 Tangent Function Properties
  466.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  467.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  468.    wt: 1:   1 Straight Lines Slope Concept
  469.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  470.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  471.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  472.    wt: 1:   29 secant cosecant and cotangent for acute angles
  473.    wt: 1:   27 Logarithmic use of products of sines and cosines
  474.    wt: 1:   26 Formulas for products of sines and cosines
  475.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  476.    wt: 1:   21 sine and cosine Half Angle Formulas
  477.    wt: 1:   20 sine and cosine Double Angle Formulas
  478.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  479.    wt: 1:   17E Trig Formulas for dot and cross Products
  480.    wt: 1:   17D cis formulas for sine cosines and tangent
  481.    wt: 1:   17C sine and cosine double triple angle formulas
  482.    wt: 1:   17A The complex number valued trig function cis
  483.    wt: 1:   10 Graphs of sines and cosines many periods
  484.    wt: 1:   9 Graphs of sine and cosine over one period
  485.    wt: 1:   7 period of sine and cosine
  486.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  487.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  488.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  489.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  490.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  491.    wt: 1:   19 N th Roots of Unity
  492.    wt: 1:   18 Sixth Roots of Unity
  493.    wt: 1:   17 Cube Roots of unity
  494.    wt: 1:   15 Pythagorean Theorem Converse
  495.    wt: 1:   14 Law of cosines
  496.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  497.    wt: 1:   8 Unit Circle Development of Trigonometry
  498.    wt: 1:   7 Second Way to Calculate Products
  499.    wt: 1:   5 An Easy Proof of the Distributive Law
  500.    wt: 1:   4 Multiplication Properties
  501.    wt: 1:   3 Addition Properties
  502.    wt: 1:   1 Rectangular Polar Coordinates Review
  503.    wt: 1:   8 Triangles Cascade Problem Solving
  504.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  505.    wt: 1:   1 Angle Measurement with Degrees
  506.    wt: 1:   Why Trigonometry the whyslopes view
  507.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  508.    wt: 1:   8 Similarity of Triangles and Polygons
  509.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  510.    wt: 1:   Four Simple Exercises
  511.    wt: 1:   12 Links Lessons elsewhere
  512.    wt: 1:   11 A Partial Summary
  513.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  514.    wt: 1:   8 Mid Point Formula
  515.    wt: 1:   5 Algebraic View of Slopes
  516.    wt: 1:   4 Equations for lines three forms
  517.    wt: 1:   3 Slope product for perpendicular lines
  518.    wt: 1:   2 point slope equation for a line
  519.    wt: 1:   13 Pythagorean spatial distance formulas
  520.    wt: 1:   12 Spatial Coordinates
  521.    wt: 1:   11 Triangle Inequality
  522.    wt: 1:   10 Pythagorean plane distance formula
  523.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  524.    wt: 1:   8 Distance Between Points on a Line
  525.    wt: 1:   3 Rectangular Coordinates Review
  526.    wt: 1:   2 Cartesian Coordinates with signs
  527.    wt: 1:   1 Cartesian Coordinates sans signs
  528.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  529.    wt: 1:   PS G Rotation Distributes over Addition
  530.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  531.    wt: 1:   PS E Multiplication with Polar Coordinates
  532.    wt: 1:   PS D Addition with Cartesian Coordinates
  533.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  534.    wt: 1:   PS B Parallelogram Construction Methods
  535.    wt: 1:   PS A Kite Construction Methods
  536.    wt: 1:   21 Parallelograms
  537.    wt: 1:   19 Right Triangle Similarity
  538.    wt: 1:   18 Triangle Similarity Take 1
  539.    wt: 1:   17 Right Bisectors of Triangle Sides
  540.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  541.    wt: 1:   14 Parallel Lines Postulate
  542.    wt: 1:   13 Angle Side Angle Failure
  543.    wt: 1:   12 Side Angle Side Failure
  544.    wt: 1:   11 Triangle Construction Fails
  545.    wt: 1:   10 Dropping a perpendicular to line
  546.    wt: 1:   9 Construction of a right bisector
  547.    wt: 1:   8 Isoceles Triangles
  548.    wt: 1:   7 Angle Side Angle
  549.    wt: 1:   5 Side Angle Side
  550.    wt: 1:   4 Side Side Side
  551.    wt: 1:   3 Isometry of Triangles Congruence
  552.    wt: 1:   2 Correspondence between Triangles
  553.    wt: 1:   Short Course on Euclidean Geometry
  554.    wt: 1:   26 More Less Greater Than Comparison
  555.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  556.    wt: 1:   23 Distributive Law Two Derivations
  557.    wt: 1:   21 Addition of Multiples of a Single Vector
  558.    wt: 1:   19 Signed Multiples of Vectors
  559.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  560.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  561.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  562.    wt: 1:   15 Head to Tails in place Addition Associative
  563.    wt: 1:   9 Division with Digits after Decimal Point
  564.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  565.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  566.    wt: 1:   4 Location of Point in Decimal Addition
  567.    wt: 1:   3 Location of Point in Decimal Multiplication
  568.    wt: 1:   2 Counting Digits in Decimal Multiplication
  569.    wt: 1:   E Long Division Methods more
  570.    wt: 1:   D Long Division Methods
  571.    wt: 1:   C Three Decimal Subtraction Methods
  572.    wt: 1:   A Decimal Addition Columm Methods
  573.    wt: 1:   8 Column Multiplication Methods in General
  574.    wt: 1:   7 Decimals Multiplication Methods Examples
  575.    wt: 1:   4 Commutative Law Groups Counting Form
  576.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  577.    wt: 1:   3 Proportionality Examples
  578.    wt: 1:   2 Algebraic View
  579.    wt: 1:   1 What is Proportionality
  580.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  581.    wt: 1:   6 Compound Interest Forward and Backwards
  582.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  583.    wt: 1:   5 Equality in Algebra
  584.    wt: 1:   3 Product Axioms Two Forms
  585.    wt: 1:   1 Equivalent Computation Rules
  586.    wt: 1:   5 Greater More Less Than Signs in General
  587.    wt: 1:   9 Coordinates for Regions in Space
  588.    wt: 1:   2 Integers
  589.    wt: 1:   5 Independent versus Dependent Variables
  590.    wt: 1:   4 Changing Letters
  591.    wt: 1:   2 Computation Rules Evaluation
  592.    wt: 1:   3 GE III Equation Addition and Multiplication
  593.    wt: 1:   6 Algebraic Solution Example
  594.    wt: 1:   1 Written work formats for developing and showing skill
  595.    wt: 1:   9 Sets in Probability and Statistics
  596.    wt: 1:   8 Sets of Numbers
  597.    wt: 1:   1 Three Skills For Algebra
  598.    wt: 1:   014 Counting Days with Calendars
  599.    wt: 1:   013 Travel Time Tables
  600.    wt: 1:   012 Division of Time Intervals by Time Intervals
  601.    wt: 1:   010 Repeated Addition of Time Intervals
  602.    wt: 1:   8 Addition of Time Intervals via subtotaling
  603.    wt: 1:   7 Addition of Time Intervals
  604.    wt: 1:   6 How long is a million seconds
  605.    wt: 1:   5 Conversion Arithmetic
  606.    wt: 1:   Example 2 volume of a cone
  607.    wt: 1:   Example 1 volume of a pyramid
  608.    wt: 1:   Volume of Solid by Cross Sections Lesson
  609.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  610.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  611.    wt: 1:   Example 4 with x function of y
  612.    wt: 1:   Example 3
  613.    wt: 1:   Example 2
  614.    wt: 1:   Example 1
  615.    wt: 1:   Area Between Curves Lesson Take 2
  616.    wt: 1:   Area Between Curves Lesson Take 1
  617.    wt: 1:   Summary
  618.    wt: 1:   17 Derivatives of quotients of sine and cosine
  619.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  620.    wt: 1:   15 sine and cosine derivatives 3rd step
  621.    wt: 1:   14 sine and cosine derivatives 2nd step
  622.    wt: 1:   13 sine and cosine derivatives 1st step
  623.    wt: 1:   11 Limits at infinity Three Examples
  624.    wt: 1:   10 Three one sided limits with infinite values
  625.    wt: 1:   8 Four Animated Examples
  626.    wt: 1:   7 Evaluation by immediate or delayed substitution
  627.    wt: 1:   6 Continuity at a point
  628.    wt: 1:   4 Numerical properties
  629.    wt: 1:   3 Decimal insights for limits continuity convergence
  630.    wt: 1:   2 Algebraic codification
  631.    wt: 1:   1 Numerical introduction
  632.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  633.    wt: 1:   PostScript For and Against Decimal Perspectives
  634.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  635.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  636.    wt: 1:   Chapter 22 Complex Numbers
  637.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  638.    wt: 1:   Chapter 12. Units and Slopes
  639.    wt: 1:   Chapter 10 Slopes and Units
  640.    wt: 1:   Chapter 7 Slopes and Velocity
  641.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  642.    wt: 1:   Chapter 2. Slopes and Ski Trails
  643.    wt: 1:   Postscript More on Better Performance
  644.    wt: 1:   Postscript For Better Performance
  645.    wt: 1:   Appendix C. How to Read
  646.    wt: 1:   Appendix B. How To Learn
  647.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  648.    wt: 1:   Chapter 30 Truth Tables
  649.    wt: 1:   Chapter 28 Occurrence Tables
  650.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  651.    wt: 1:   Chapter 25. Mathematical Induction Examples
  652.    wt: 1:   Chapter 23. Notation For Sums
  653.    wt: 1:   Chapter 21. Third Reading Guide
  654.    wt: 1:   Chapter 18. Rules for Algebra
  655.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  656.    wt: 1:   Chapter 16. Painless Theorem Proving
  657.    wt: 1:   Chapter 15. Solving Linear Equations
  658.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  659.    wt: 1:   Chapter 13. Second Reading Guide
  660.    wt: 1:   Postscript What is a Variable
  661.    wt: 1:   Solutions For Arithmetic Exercises
  662.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  663.    wt: 1:   Chapter 6 Change of Language
  664.    wt: 1:   Chapter 4 Longer Chains of Reason
  665.    wt: 1:   Chapter 3 Chains of Reason
  666.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  667.    wt: 1:   Foreword
  668.    wt: 1:   Chapter 2 For and Against Mathematics
  669.    wt: 1:   Postscript B More on Story Telling and Reason
  670.    wt: 1:   Chapter 24 Direct and Indirect Reason
  671.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  672.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  673.    wt: 1:   Chapter 18 Sense and Knowledge
  674.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  675.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  676.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  677.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  678.    wt: 1:   S Adding words to algebra
  679.    wt: 1:   N Mathematics Prepare for College Studies
  680.    wt: 1:   M Words to extend arithmetic
  681.    wt: 1:   H more Routine to non routine problem solving
  682.    wt: 1:   F. The student teacher tutor feedback loop
  683.    wt: 1:   D. Check work a must with a caution
  684.    wt: 1:   C. Domino effect of being careful
  685.    wt: 1:   B. Domino effect of errors
  686.    wt: 1:   A. Skill has to be seen to believed
  687.    wt: 1:   Chapter 8 Skipped Topics and Why
  688.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  689.    wt: 1:   Chapter 6 More Algebra and Geometry
  690.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  691.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  692.    wt: 1:   Helping the Blind in Logic and Mathematics
  693.    wt: 1:   More Algebra and Slope based Calculus Preview
  694.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  695.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  696.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  697.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  698.    wt: 1:   The Math Forum and Site Content
  699.    wt: 14:   C Equality for Fractions and Two Term Ratios and Fractions
  700.    wt: 14:   9 Improper Fractions and Mixed Numbers
  701.    wt: 12:   B Fractions and Two Term Ratios
  702.    wt: 12:   A Similarities between Fractions and Two Term Ratios
  703.    wt: 12:   10 Simplification of Fractions and Mixed Numerals
  704.    wt: 11:   21 Reciprocals for Fractions and Wholes
  705.    wt: 11:   6 Multiplication of Mixed Numbers
  706.    wt: 10:   D Three Term Ratios
  707.    wt: 10:   22 Complex Compound Fractions
  708.    wt: 10:   20 Dividing Fractions the Why
  709.    wt: 10:   19 Dividing Fractions How TO
  710.    wt: 10:   17 Efficient Ways to Add and Subtract
  711.    wt: 10:   15 Adding and Subtracting with Unlike Denominators
  712.    wt: 10:   14 Adding and Subtracting with Like Denominators
  713.    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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