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

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

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

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

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

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

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

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43 matches:

  1.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  2.    wt: 7:   7 Arithmetic and Fractions with Units/
  3.    wt: 7:   6 Fractions and Ratios/
  4.    wt: 7:   B Decimal Comparing and Subtracting Methods/
  5.    wt: 7:   A Decimal Counting and Adding Methods/
  6.    wt: 6:   11 Squares and Square Roots/
  7.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  8.    wt: 6:   9 Combinatorics Trees Tables and Products/
  9.    wt: 6:   8 Arithmetic with Signed Numbers/
  10.    wt: 6:   4 Remainder Arithmetic and Divisibility/
  11.    wt: 6:   3 Prime Factorization Skills/
  12.    wt: 6:   D Decimal Long Division Methods/
  13.    wt: 6:   C Decimal Multiplication Methods/
  14.    wt: 6:   2 Arithmetic with Decimals/
  15.    wt: 5:   5 Integers/
  16.    wt: 5:   1 Decimal Place Value/
  17.    wt: 5:   Arithmetic and Number Theory Skills/
  18.    wt: 2:   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:   4 Lines and Slopes Take 1/
  28.    wt: 1:   3 Cartesian and Polar Coordinates/
  29.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  30.    wt: 1:   B Real Numbers Extrinsic Development/
  31.    wt: 1:   A Origins of Counting and Figuring Methods/
  32.    wt: 1:   9 Proportionality Backwards and Forwards/
  33.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  34.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  35.    wt: 1:   5 Real Numbers/
  36.    wt: 1:   4 Computation Rules and Function Notation/
  37.    wt: 1:   Time Date Matters/
  38.    wt: 1:   Skills with take home value/
  39.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  40.    wt: 1:   13 Lessons on Limits and Continuity/
  41.    wt: 1:   Volume 2 Three Skills For Algebra/
  42.    wt: 1:   Work and Study Tips/
  43.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

362 matches:

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

Extended Search

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

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

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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