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

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

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

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

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

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

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

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

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44 matches:

  1.    wt: 9:   6 Fractions and Ratios/
  2.    wt: 7:   12 Comparison of Unsigned and Signed Numbers/
  3.    wt: 7:   7 Arithmetic and Fractions with Units/
  4.    wt: 6:   11 Squares and Square Roots/
  5.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  6.    wt: 6:   9 Combinatorics Trees Tables and Products/
  7.    wt: 6:   8 Arithmetic with Signed Numbers/
  8.    wt: 6:   4 Remainder Arithmetic and Divisibility/
  9.    wt: 6:   3 Prime Factorization Skills/
  10.    wt: 6:   B Decimal Comparing and Subtracting Methods/
  11.    wt: 6:   A Decimal Counting and Adding Methods/
  12.    wt: 5:   5 Integers/
  13.    wt: 5:   D Decimal Long Division Methods/
  14.    wt: 5:   C Decimal Multiplication Methods/
  15.    wt: 5:   2 Arithmetic with Decimals/
  16.    wt: 5:   1 Decimal Place Value/
  17.    wt: 5:   Arithmetic and Number Theory Skills/
  18.    wt: 2:   Step 1 Stick diagram and fractions/
  19.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  20.    wt: 1:   Mathematics Skills Year by Year/
  21.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  22.    wt: 1:   12 Function Translating and Rescaling/
  23.    wt: 1:   11 Parallel Straight Lines and Transversals/
  24.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  25.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  26.    wt: 1:   7 Complex Numbers/
  27.    wt: 1:   6 Trigonometry first steps/
  28.    wt: 1:   4 Lines and Slopes Take 1/
  29.    wt: 1:   3 Cartesian and Polar Coordinates/
  30.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  31.    wt: 1:   B Real Numbers Extrinsic Development/
  32.    wt: 1:   A Origins of Counting and Figuring Methods/
  33.    wt: 1:   9 Proportionality Backwards and Forwards/
  34.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  35.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  36.    wt: 1:   5 Real Numbers/
  37.    wt: 1:   4 Computation Rules and Function Notation/
  38.    wt: 1:   Time Date Matters/
  39.    wt: 1:   Skills with take home value/
  40.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  41.    wt: 1:   13 Lessons on Limits and Continuity/
  42.    wt: 1:   Volume 2 Three Skills For Algebra/
  43.    wt: 1:   Work and Study Tips/
  44.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

372 matches:

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