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

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

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

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

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

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

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

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44 matches:

  1.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  2.    wt: 7:   5 Integers/
  3.    wt: 6:   11 Squares and Square Roots/
  4.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  5.    wt: 6:   9 Combinatorics Trees Tables and Products/
  6.    wt: 6:   8 Arithmetic with Signed Numbers/
  7.    wt: 6:   7 Arithmetic and Fractions with Units/
  8.    wt: 6:   6 Fractions and Ratios/
  9.    wt: 6:   4 Remainder Arithmetic and Divisibility/
  10.    wt: 6:   3 Prime Factorization Skills/
  11.    wt: 6:   B Decimal Comparing and Subtracting Methods/
  12.    wt: 6:   A Decimal Counting and Adding Methods/
  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:   PreSchool and Primary Mathematics or Quantitative Skills/
  19.    wt: 1:   Mathematics Skills Year by Year/
  20.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  21.    wt: 1:   12 Function Translating and Rescaling/
  22.    wt: 1:   11 Parallel Straight Lines and Transversals/
  23.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  24.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  25.    wt: 1:   7 Complex Numbers/
  26.    wt: 1:   5 What is Similarity/
  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:   Step 1 Stick diagram and fractions/
  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

342 matches:

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

Extended Search

716 matches:

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

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

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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