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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44 matches:

  1.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  2.    wt: 6:   11 Squares and Square Roots/
  3.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  4.    wt: 6:   9 Combinatorics Trees Tables and Products/
  5.    wt: 6:   8 Arithmetic with Signed Numbers/
  6.    wt: 6:   7 Arithmetic and Fractions with Units/
  7.    wt: 6:   6 Fractions and Ratios/
  8.    wt: 6:   4 Remainder Arithmetic and Divisibility/
  9.    wt: 6:   3 Prime Factorization Skills/
  10.    wt: 6:   B Decimal Comparing and Subtracting Methods/
  11.    wt: 6:   A Decimal Counting and Adding Methods/
  12.    wt: 5:   5 Integers/
  13.    wt: 5:   D Decimal Long Division Methods/
  14.    wt: 5:   C Decimal Multiplication Methods/
  15.    wt: 5:   2 Arithmetic with Decimals/
  16.    wt: 5:   1 Decimal Place Value/
  17.    wt: 5:   Arithmetic and Number Theory Skills/
  18.    wt: 2:   A Origins of Counting and Figuring Methods/
  19.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  20.    wt: 1:   Mathematics Skills Year by Year/
  21.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  22.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  23.    wt: 1:   12 Function Translating and Rescaling/
  24.    wt: 1:   11 Parallel Straight Lines and Transversals/
  25.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  26.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  27.    wt: 1:   7 Complex Numbers/
  28.    wt: 1:   4 Lines and Slopes Take 1/
  29.    wt: 1:   3 Cartesian and Polar Coordinates/
  30.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  31.    wt: 1:   B Real Numbers Extrinsic Development/
  32.    wt: 1:   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

339 matches:

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

Extended Search

711 matches:

  1.    wt: 9:   1 More and Less Than for Counts and Measures
  2.    wt: 8:   3 Comparison of Negative Numbers
  3.    wt: 8:   2 More and Less Than with Unlike Signs
  4.    wt: 8:   11 What are real lengths and numbers
  5.    wt: 8:   5 lengths and signs of numbers
  6.    wt: 8:   2 signed and unsigned numbers as coordinates
  7.    wt: 8:   3 Multiplying Units and Numbers
  8.    wt: 8:   C Equality for Fractions and Two Term Ratios and Fractions
  9.    wt: 8:   9 Improper Fractions and Mixed Numbers
  10.    wt: 8:   8 What skills and work habits to require
  11.    wt: 8:   6. Counting and adding units and mixed units
  12.    wt: 7:   4 Greater More Less Than Signs in General
  13.    wt: 7:   1 Squares and Square Roots Introduction
  14.    wt: 7:   17 GCD LCM of 85 and 60 via Prime
  15.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  16.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  17.    wt: 7:   9 GCD of 360 110 via Primes and Euclid Algorithm
  18.    wt: 7:   7 GCD and LCM from prime factorization
  19.    wt: 7:   4 LCM of 8 and 10 via Prime
  20.    wt: 7:   3 Counting with Tables and Trees II
  21.    wt: 7:   2 Counting with Tables and Trees I
  22.    wt: 7:   1 Counting and Counting Methods I
  23.    wt: 7:   10 dividing signed numbers
  24.    wt: 7:   9 subtracting signed numbers
  25.    wt: 7:   8 multiplying signed numbers
  26.    wt: 7:   7 negative and additive inverse
  27.    wt: 7:   6 adding signed numbers
  28.    wt: 7:   3 signed coordinates for maps and planes
  29.    wt: 7:   5 Reciprocals and Division for Fractions with Units
  30.    wt: 7:   2 Equality and Units
  31.    wt: 7:   1 Addition and Subtraction with Units
  32.    wt: 7:   B Fractions and Two Term Ratios
  33.    wt: 7:   A Similarities between Fractions and Two Term Ratios
  34.    wt: 7:   21 Reciprocals for Fractions and Wholes
  35.    wt: 7:   17 Efficient Ways to Add and Subtract
  36.    wt: 7:   15 Adding and Subtracting with Unlike Denominators
  37.    wt: 7:   14 Adding and Subtracting with Like Denominators
  38.    wt: 7:   10 Simplification of Fractions and Mixed Numerals
  39.    wt: 7:   6 Multiplication of Mixed Numbers
  40.    wt: 7:   6 Multiplication by Natural Numbers
  41.    wt: 7:   A Decimals Modular and Remainder Arithmetic
  42.    wt: 7:   17 Identify and Count Factors using Primes
  43.    wt: 7:   12 LCD GCD and LCM using Primes
  44.    wt: 7:   7 Calculator Usage Notes and Cautions
  45.    wt: 7:   6 Sieve of Eratosthenes and Square Rule
  46.    wt: 7:   5 Prime Factorization and a Square Rule
  47.    wt: 7:   3 video Primes and Composites from 9 times table
  48.    wt: 7:   2 Prime and Composites less than 16
  49.    wt: 7:   4 Subtraction with Conversions Borrows and Letter J
  50.    wt: 7:   3 Harder Cases Convert to Compare and Subtract
  51.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  52.    wt: 7:   10 Names for Big Numbers and Powers of Ten Expansion
  53.    wt: 7:   Quick history of numbers and algebra
  54.    wt: 6:   5 Square Roots with primes more still
  55.    wt: 6:   4 Square Roots with primes more
  56.    wt: 6:   3 Properties of Square Roots with example
  57.    wt: 6:   2 Square Roots with Prime
  58.    wt: 6:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  59.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  60.    wt: 6:   13 GCD from given Prime Factorization
  61.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  62.    wt: 6:   8 GCD from Euclidean Algorithm
  63.    wt: 6:   6 GCD from Prime
  64.    wt: 6:   5 Common Divisors 60 45 via Prime
  65.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  66.    wt: 6:   2 Least Common Multiple LCM intro via list method
  67.    wt: 6:   1 Least Common Multiples LCM Introduction
  68.    wt: 6:   12 GCD 2700 288 via Prime
  69.    wt: 6:   5 Counting with Tables Trees Product Rule Take II
  70.    wt: 6:   4 Counting with Trees Product Rule Take I
  71.    wt: 6:   4 signed coordinates for regions in space
  72.    wt: 6:   7 Converting or Changing Units
  73.    wt: 6:   6 Simplification of Fractions with Units
  74.    wt: 6:   4 Fractions with Units
  75.    wt: 6:   D Three Term Ratios
  76.    wt: 6:   22 Complex Compound Fractions
  77.    wt: 6:   21 Working With Signs
  78.    wt: 6:   20 Dividing Fractions the Why
  79.    wt: 6:   19 Dividing Fractions How TO
  80.    wt: 6:   18 Efficient Ways to Multiply
  81.    wt: 6:   16 Addition Subtraction Comparision Compared
  82.    wt: 6:   13 Fraction Comparison Algebraic View
  83.    wt: 6:   12 Fraction Comparison
  84.    wt: 6:   11 Simplification an Algebraic View
  85.    wt: 6:   8 Numerals Fractionals Quantals Take II
  86.    wt: 6:   7 Numerals Fractionals Quantals
  87.    wt: 6:   6 Multiplication Algebraically Take II
  88.    wt: 6:   5 Equivalent Fractions
  89.    wt: 6:   4 Fraction Multiplication
  90.    wt: 6:   3 Unit fraction of a fraction
  91.    wt: 6:   2 Unit Fraction Multiplication
  92.    wt: 6:   1 What is a fraction Take II
  93.    wt: 6:   1 What is a fraction
  94.    wt: 6:   Fraction Operations by Raising Terms A Simple Innovation
  95.    wt: 6:   11 Adding Integers Formulas and Examples
  96.    wt: 6:   8 Multiplication by Signed Numbers Integers
  97.    wt: 6:   5 Zero Movement and Additive Inverses
  98.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  99.    wt: 6:   26 Divisibility by 2 3 5 Example
  100.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  101.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  102.    wt: 6:   23 Remainder Arithmetic Modulo 2
  103.    wt: 6:   22 Remainder Arithmetic Modulo 3 more
  104.    wt: 6:   21 Remainder Arithmetic Modulo 3
  105.    wt: 6:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  106.    wt: 6:   19 Remainder Arithmetic Rule of 9 for checking sums III
  107.    wt: 6:   18 Remainder Arithmetic Rule of 9 for checking sums II
  108.    wt: 6:   17 Remainder Arithmetic Rule of 9 for checking sums I
  109.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  110.    wt: 6:   15 Remainder Arithmetic Modulo 9 Example
  111.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  112.    wt: 6:   13 Remainder Arithmetic Modulo 5 Example
  113.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  114.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  115.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  116.    wt: 6:   9 Remainder Arithmetic Divisibility by 5
  117.    wt: 6:   8 Remainder Arithmetic Morulo 5 Examples II
  118.    wt: 6:   7 Remainder Arithmetic Modulo 5 Examples I
  119.    wt: 6:   6 Remainder Arithmetic Modulo 5 Propertie
  120.    wt: 6:   5 Remainder Arithmetic Modulo 5
  121.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  122.    wt: 6:   3 Remainder Arithmetic Modulos 10 more still
  123.    wt: 6:   2 Remainder Arithmetic Modulo 10 more
  124.    wt: 6:   1 Remainder Arithmetic Modulo 10
  125.    wt: 6:   20 Uniqueness of Prime Factorization
  126.    wt: 6:   19 video Prime Factorization Unique
  127.    wt: 6:   18 video Count Factors given Prime Factorization
  128.    wt: 6:   16 video Factors of 980 using prime
  129.    wt: 6:   15 video Factors of 20 using Prime Factorization
  130.    wt: 6:   14 video Factors of 24 Take II
  131.    wt: 6:   13 video Factors of 24 using prime
  132.    wt: 6:   11 Efficient Square Rule Use
  133.    wt: 6:   10 video Prime Factorization upto 23 squared
  134.    wt: 6:   9 video Prime Factorization upto 19 squared
  135.    wt: 6:   8 video Prime Factorization upto 19
  136.    wt: 6:   4 video Prime Factorization Introduction
  137.    wt: 6:   1 video how Products are bigger than factor
  138.    wt: 6:   Division with Counts and Length
  139.    wt: 6:   Long Division forwards and backwards Example 3
  140.    wt: 6:   Long Division forwards and backwards Example 2
  141.    wt: 6:   Long Division forwards and backwards Example 1
  142.    wt: 6:   10 Division by Five Long and Short Ways
  143.    wt: 6:   4 Two and Three Digit Multipliers
  144.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  145.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  146.    wt: 6:   Subtraction with J Conversions Example
  147.    wt: 6:   Subtraction Another Video Lesson
  148.    wt: 6:   9 22 Minute Subtraction Review Video
  149.    wt: 6:   8 Subtraction with Units of Measure
  150.    wt: 6:   7 Subtraction for Decimal Fractions with Exercises
  151.    wt: 6:   6 Subtraction with Conversion Example with Exercises
  152.    wt: 6:   5 A Tip for Efficent Subtraction
  153.    wt: 6:   2 Subtraction Easy Case Examples
  154.    wt: 6:   Appendix 1 Counting Revisited 15 minute video
  155.    wt: 6:   7 Adding decimal fractions using decimal point
  156.    wt: 6:   5. How to add decimals C. Examples
  157.    wt: 6:   4. How to add with decimals B with conversions
  158.    wt: 6:   3. How to add with decimals A sans conversions
  159.    wt: 6:   2 Decimal Counting Practices
  160.    wt: 6:   1. Explaining Addition Table
  161.    wt: 6:   11 Place Value SI Standard International way
  162.    wt: 6:   9 Place Value Review Decimal form of Avogrados number included
  163.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  164.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  165.    wt: 6:   Exact Arithmetic Wholes and Fractions
  166.    wt: 6:   Practical Methods Ends and Values for Arithmetic
  167.    wt: 5:   arithmetic videos Real Player Format
  168.    wt: 5:   D Remainders Modulo 11 Pair Rule
  169.    wt: 5:   C Divisibility by 11 Integer Recognition Method
  170.    wt: 5:   B Integer Long Division Multiple Choices
  171.    wt: 5:   A Associative Law Theorectical Note
  172.    wt: 5:   13 Subtraction with Additive Inverse
  173.    wt: 5:   12 Adding Integers More Examples
  174.    wt: 5:   10 Integer Multiplication Formulas
  175.    wt: 5:   9 Multiplying Integers
  176.    wt: 5:   7 Multiplication by Signs
  177.    wt: 5:   4 Adding Movements wiht opposite directions
  178.    wt: 5:   3 Adding Movements with same direction
  179.    wt: 5:   2 Integers Multiplies of a Unit Moverment
  180.    wt: 5:   1 Integers as Coordinates
  181.    wt: 5:   Long Division Backwards more
  182.    wt: 5:   Long Division Backward
  183.    wt: 5:   12 Why Long Division Works Take III
  184.    wt: 5:   11 Another Single Digit Divisor Example
  185.    wt: 5:   9 Why Long Division Works Take II
  186.    wt: 5:   8 Correcting the Mistake
  187.    wt: 5:   7 Long Divison Mistake Catching
  188.    wt: 5:   6 Why Decimal Long Division Methods Works Take I
  189.    wt: 5:   5 Long Division Include Zeroes or not
  190.    wt: 5:   4 Division with 2 Digit Divsors
  191.    wt: 5:   3 Division Single Digit Divisor Example
  192.    wt: 5:   2 Division with Single Digit Divisors
  193.    wt: 5:   1 Divsion Physical Examples
  194.    wt: 5:   D Decimal Multiplication Methods Derived
  195.    wt: 5:   C Counting Areas with Powers of Ten
  196.    wt: 5:   B Powers of Ten
  197.    wt: 5:   A Elementary Basis for Multiplication Methods
  198.    wt: 5:   6 Multiplication Commutes Order Not Important
  199.    wt: 5:   5 Decimal Fraction Multiplication
  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:   2 Combing Counts Addition Skills and Principles
  219.    wt: 4:   1 The Counting Origins of Numbers
  220.    wt: 4:   1 Whole and Natural Numbers
  221.    wt: 4:   5 Interpreting and Drawing Maps and Plans.
  222.    wt: 4:   2 Identifying Size and Position Place and Spatial Sense
  223.    wt: 4:   1 From Number Recognition and Counting to Arithmetic B
  224.    wt: 4:   1 From Number Recognition and Counting to Arithmetic A
  225.    wt: 3:   3 Natural Logarithms and Exponentials Basic Properties
  226.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  227.    wt: 3:   11 Signed Number Addition and Addition Properties
  228.    wt: 3:   B Decimal Comparison and Subtraction
  229.    wt: 3:   5 Distributive Law for Whole Numbers
  230.    wt: 3:   3 Multiplicative Counting Skills Principles
  231.    wt: 3:   2 More and Less Than for Counts and Measures
  232.    wt: 3:   10 Real Number Lengths and Signs
  233.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  234.    wt: 3:   Chapter 16 Origins and Limitations of Rules and Patterns
  235.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  236.    wt: 3:   P Exact Arithmetic With Whole Numbers and Fractions
  237.    wt: 3:   I. Logic and language skills
  238.    wt: 3:   How to Build Skills and Confidence
  239.    wt: 3:   7 Games and Activities for Instruction
  240.    wt: 3:   4 Money Matters Saving Earning Buying Selling and Budgets
  241.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  242.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  243.    wt: 2:   Ramblings Extrinsic numbers theory
  244.    wt: 2:   2 Reading and Writing Skills
  245.    wt: 2:   Ages 12 to 14 Skills with take home value
  246.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  247.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  248.    wt: 2:   9 Set theory term relation possible origins
  249.    wt: 2:   11 Growth and Decay in Biology
  250.    wt: 2:   10 Exponential Growth and Decay Models
  251.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  252.    wt: 2:   5 Natural Logarithm Calculator Exercises
  253.    wt: 2:   9 Summary Degrees to Radians and back
  254.    wt: 2:   1 Degrees and Radians Introduction
  255.    wt: 2:   Vector and Complex Number Applet
  256.    wt: 2:   Parallel Lines and Parallel Transversals
  257.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  258.    wt: 2:   Parallel Lines and Interior Angles
  259.    wt: 2:   14 cosine even and sine and tangent are odd
  260.    wt: 2:   21 Logarithms Powers and Exponentials
  261.    wt: 2:   20 N th Roots of Complex Numbers
  262.    wt: 2:   16 References and Originality Question
  263.    wt: 2:   13 Trig Formulas for dot and cross Products
  264.    wt: 2:   12 cis formulas for sine cosines and tangent
  265.    wt: 2:   11 sine and cosine double triple angle formulas
  266.    wt: 2:   9 The complex number valued trig function cis
  267.    wt: 2:   6 Field Properties of Complex Number
  268.    wt: 2:   2 Complex Numbers made easier we hope
  269.    wt: 2:   Appetizer A Complex Number Applet
  270.    wt: 2:   10 Midpoint of [a b] and [b a]
  271.    wt: 2:   7 Exercises to test skill and concept mastery
  272.    wt: 2:   1 Numerical view of lines and their equations
  273.    wt: 2:   What is and is not here
  274.    wt: 2:   7 Complex Numbers Appetizer
  275.    wt: 2:   6 Polar Multiplication and Rotation
  276.    wt: 2:   5 Cartesian Addition and Translation
  277.    wt: 2:   4 Polar Coordinates to and from
  278.    wt: 2:   PS H Distributive Law For Complex Numbers
  279.    wt: 2:   16 Angles Subtended By Chords and Diameters
  280.    wt: 2:   6 Ruler and compass Angle Bisection
  281.    wt: 2:   1 Initial Concepts and Terms
  282.    wt: 2:   3 Lengths and Areas on Maps and Plans
  283.    wt: 2:   musings do not puiblish real numbers
  284.    wt: 2:   A Modular and Remainder Arithmetic
  285.    wt: 2:   A Signed Number Arithmetic Review
  286.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  287.    wt: 2:   22 Multiplication of Signed Numbers
  288.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  289.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  290.    wt: 2:   13 Arrows and Vectors in a Plane
  291.    wt: 2:   12 Real Numbers Line Signed Coordinates
  292.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  293.    wt: 2:   8 Division and Mulplication of Compound Fractions
  294.    wt: 2:   E Long Division Methods more
  295.    wt: 2:   D Long Division Methods
  296.    wt: 2:   C Three Decimal Subtraction Methods
  297.    wt: 2:   A Decimal Addition Columm Methods
  298.    wt: 2:   8 Column Multiplication Methods in General
  299.    wt: 2:   7 Decimals Multiplication Methods Examples
  300.    wt: 2:   6 Column Methods for Decimal Multiplication
  301.    wt: 2:   4 Commutative Law Groups Counting Form
  302.    wt: 2:   4 Rates Ratios and Proporitionality
  303.    wt: 2:   6 Equations and Systems Equivalent or Implied
  304.    wt: 2:   4 Subtraction and Division Axioms
  305.    wt: 2:   2 Addition and Multiplication Axioms
  306.    wt: 2:   4 Comparison of Negative Numbers
  307.    wt: 2:   3 More and Less Than with Unlike Signs
  308.    wt: 2:   1 Real Numbers Comparison
  309.    wt: 2:   16 Real Numbers Comparison
  310.    wt: 2:   15 Real Number Division
  311.    wt: 2:   14 Real Number Multiplication
  312.    wt: 2:   13 Real Number Subtraction
  313.    wt: 2:   12 Real Number Additive Inverses or Negatives
  314.    wt: 2:   11 Real Number Addition
  315.    wt: 2:   8 Coordinates for Maps and Planes
  316.    wt: 2:   7 Real Numbers as Line Cordinates
  317.    wt: 2:   6 Unsigned Real Numbers
  318.    wt: 2:   5 Rational Numbers More
  319.    wt: 2:   4 Rational Numbers
  320.    wt: 2:   3 Geometric Formulas and Function Notation
  321.    wt: 2:   1 Formulas Dependence and Function Notation
  322.    wt: 2:   5 Talking about Numbers and Quantities
  323.    wt: 2:   4 A Brief Story of numbers and algebra
  324.    wt: 2:   016 Numbering Occidental Calendar Days
  325.    wt: 2:   015 School and work day counting tables
  326.    wt: 2:   011 Division of Time Intervals By Numbers
  327.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  328.    wt: 2:   4 Mixing and Changing Units of Time
  329.    wt: 2:   3 Units and Lengths of Time
  330.    wt: 2:   2 Time and Date Matters in School
  331.    wt: 2:   1 Intro of Kids To Time Date Skills
  332.    wt: 2:   Example 1. Area Between x and x squared
  333.    wt: 2:   38 Formulas and derivatives for powers and roots
  334.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  335.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  336.    wt: 2:   9 Limits Continuity and Composition
  337.    wt: 2:   5 Jumps and absence of unlimited error control
  338.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  339.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  340.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  341.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  342.    wt: 2:   Appendix E. How To Study Mathematics and Why
  343.    wt: 2:   Appendix D. What to do in School and Why
  344.    wt: 2:   Chapter 31 Direct and Indirect Reason
  345.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  346.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  347.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  348.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  349.    wt: 2:   Chapter 20. Degrees and Radians
  350.    wt: 2:   Chapter 19. Functions and Sets
  351.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  352.    wt: 2:   Chapter 12. Shorthand Usage Guide
  353.    wt: 2:   Chapter 11. Why Shorthand
  354.    wt: 2:   Chapter 10 Describing and Changing Calculations
  355.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  356.    wt: 2:   Chapter 8 Three Skills For Algebra
  357.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  358.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  359.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  360.    wt: 2:   R Why Learn Mathematics Skills
  361.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  362.    wt: 2:   O On Learning Mathematics and Science
  363.    wt: 2:   L Skills with take home value
  364.    wt: 2:   N Improving Marks on Tests and Finals
  365.    wt: 2:   J. More on written work and showing skill
  366.    wt: 2:   H Jigsaw puzzles and problem solving
  367.    wt: 2:   G. Written work formats for developing and showing skill
  368.    wt: 2:   E. When and how to correct errors
  369.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  370.    wt: 1:   Appendix 1 primary and preschool mathematic
  371.    wt: 1:   J LAMP Introduction Extrinsic Origins
  372.    wt: 1:   G LAMP Introduction Problem Solving Skills
  373.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  374.    wt: 1:   Skills Chapter 5 Calculus
  375.    wt: 1:   Skills Chapter 4 Logic
  376.    wt: 1:   Skills Chapter 3 Algebra
  377.    wt: 1:   Skills Chapter 2 Geometry
  378.    wt: 1:   Skills Chapter 1 Arithmetic
  379.    wt: 1:   Skills Chapter 0 Introduction
  380.    wt: 1:   7 logic review and decimals an odd combination
  381.    wt: 1:   5 logarithms and exponentials etc
  382.    wt: 1:   2 arithmetic with signed numbers
  383.    wt: 1:   1 arithmetic with unsigned numbers
  384.    wt: 1:   site origins
  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:   8 Set view of relations and functions
  424.    wt: 1:   6 Set Existence Formation and Notation
  425.    wt: 1:   4 Function notation in and beyond mathematics
  426.    wt: 1:   9 quadratics physical and further context
  427.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  428.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  429.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  430.    wt: 1:   2 Square Root Simplification a prequel
  431.    wt: 1:   1 Calculator Starter Exercises
  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:   6 Infinite Decimals Ending in 9 repeating
  574.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  575.    wt: 1:   4 Location of Point in Decimal Addition
  576.    wt: 1:   3 Location of Point in Decimal Multiplication
  577.    wt: 1:   2 Counting Digits in Decimal Multiplication
  578.    wt: 1:   1 Fractions with Finite Decimal Expansions
  579.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  580.    wt: 1:   5 Proportionality in Equivalent Fractions
  581.    wt: 1:   3 Proportionality Examples
  582.    wt: 1:   2 Algebraic View
  583.    wt: 1:   1 What is Proportionality
  584.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  585.    wt: 1:   6 Compound Interest Forward and Backwards
  586.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  587.    wt: 1:   5 Equality in Algebra
  588.    wt: 1:   3 Product Axioms Two Forms
  589.    wt: 1:   1 Equivalent Computation Rules
  590.    wt: 1:   5 Greater More Less Than Signs in General
  591.    wt: 1:   9 Coordinates for Regions in Space
  592.    wt: 1:   3 Fractions
  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:   Skill Development Notes
  599.    wt: 1:   10 One Example
  600.    wt: 1:   9 Three Examples
  601.    wt: 1:   8 One Example
  602.    wt: 1:   7 Two Examples
  603.    wt: 1:   6 Three Examples
  604.    wt: 1:   5 Three Examples
  605.    wt: 1:   4 Two Examples
  606.    wt: 1:   3 Two Examples
  607.    wt: 1:   2 Three Examples
  608.    wt: 1:   1 Written work formats for developing and showing skill
  609.    wt: 1:   9 Sets in Probability and Statistics
  610.    wt: 1:   8 Sets of Numbers
  611.    wt: 1:   1 Three Skills For Algebra
  612.    wt: 1:   014 Counting Days with Calendars
  613.    wt: 1:   013 Travel Time Tables
  614.    wt: 1:   012 Division of Time Intervals by Time Intervals
  615.    wt: 1:   010 Repeated Addition of Time Intervals
  616.    wt: 1:   8 Addition of Time Intervals via subtotaling
  617.    wt: 1:   7 Addition of Time Intervals
  618.    wt: 1:   6 How long is a million seconds
  619.    wt: 1:   5 Conversion Arithmetic
  620.    wt: 1:   Example 2 volume of a cone
  621.    wt: 1:   Example 1 volume of a pyramid
  622.    wt: 1:   Volume of Solid by Cross Sections Lesson
  623.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  624.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  625.    wt: 1:   Example 4 with x function of y
  626.    wt: 1:   Example 3
  627.    wt: 1:   Example 2
  628.    wt: 1:   Example 1
  629.    wt: 1:   Area Between Curves Lesson Take 2
  630.    wt: 1:   Area Between Curves Lesson Take 1
  631.    wt: 1:   Summary
  632.    wt: 1:   17 Derivatives of quotients of sine and cosine
  633.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  634.    wt: 1:   15 sine and cosine derivatives 3rd step
  635.    wt: 1:   14 sine and cosine derivatives 2nd step
  636.    wt: 1:   13 sine and cosine derivatives 1st step
  637.    wt: 1:   11 Limits at infinity Three Examples
  638.    wt: 1:   10 Three one sided limits with infinite values
  639.    wt: 1:   8 Four Animated Examples
  640.    wt: 1:   7 Evaluation by immediate or delayed substitution
  641.    wt: 1:   6 Continuity at a point
  642.    wt: 1:   4 Numerical properties
  643.    wt: 1:   3 Decimal insights for limits continuity convergence
  644.    wt: 1:   2 Algebraic codification
  645.    wt: 1:   1 Numerical introduction
  646.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  647.    wt: 1:   PostScript For and Against Decimal Perspectives
  648.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  649.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  650.    wt: 1:   Chapter 22 Complex Numbers
  651.    wt: 1:   Chapter 12. Units and Slopes
  652.    wt: 1:   Chapter 10 Slopes and Units
  653.    wt: 1:   Chapter 7 Slopes and Velocity
  654.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  655.    wt: 1:   Chapter 2. Slopes and Ski Trails
  656.    wt: 1:   Postscript More on Better Performance
  657.    wt: 1:   Postscript For Better Performance
  658.    wt: 1:   Appendix C. How to Read
  659.    wt: 1:   Appendix B. How To Learn
  660.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  661.    wt: 1:   Chapter 30 Truth Tables
  662.    wt: 1:   Chapter 28 Occurrence Tables
  663.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  664.    wt: 1:   Chapter 25. Mathematical Induction Examples
  665.    wt: 1:   Chapter 23. Notation For Sums
  666.    wt: 1:   Chapter 21. Third Reading Guide
  667.    wt: 1:   Chapter 18. Rules for Algebra
  668.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  669.    wt: 1:   Chapter 16. Painless Theorem Proving
  670.    wt: 1:   Chapter 15. Solving Linear Equations
  671.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  672.    wt: 1:   Chapter 13. Second Reading Guide
  673.    wt: 1:   Postscript What is a Variable
  674.    wt: 1:   Solutions For Arithmetic Exercises
  675.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  676.    wt: 1:   Chapter 6 Change of Language
  677.    wt: 1:   Chapter 4 Longer Chains of Reason
  678.    wt: 1:   Chapter 3 Chains of Reason
  679.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  680.    wt: 1:   Foreword
  681.    wt: 1:   Chapter 2 For and Against Mathematics
  682.    wt: 1:   Postscript B More on Story Telling and Reason
  683.    wt: 1:   Chapter 24 Direct and Indirect Reason
  684.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  685.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  686.    wt: 1:   Chapter 18 Sense and Knowledge
  687.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  688.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  689.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  690.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  691.    wt: 1:   S Adding words to algebra
  692.    wt: 1:   N Mathematics Prepare for College Studies
  693.    wt: 1:   M Words to extend arithmetic
  694.    wt: 1:   H more Routine to non routine problem solving
  695.    wt: 1:   F. The student teacher tutor feedback loop
  696.    wt: 1:   D. Check work a must with a caution
  697.    wt: 1:   C. Domino effect of being careful
  698.    wt: 1:   B. Domino effect of errors
  699.    wt: 1:   A. Skill has to be seen to believed
  700.    wt: 1:   Chapter 8 Skipped Topics and Why
  701.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  702.    wt: 1:   Chapter 6 More Algebra and Geometry
  703.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  704.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  705.    wt: 1:   Helping the Blind in Logic and Mathematics
  706.    wt: 1:   More Algebra and Slope based Calculus Preview
  707.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  708.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  709.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  710.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  711.    wt: 1:   The Math Forum and Site Content

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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