Appetizers and Lessons for Mathematics & Reason Français: 26 pages
A 1100+ page site with math-free logic chapters and wordy algebra chapters.
For comprehension, study site chapters and steps. Go beyond rote learning.

Logic mastery strengthens comprehension and so improves home, work & study abilities .
 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 14+: 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.

Site Review: Mathphobics, this site may ease your fears of the subject, perhaps even help you njoy it. ... unintimidating, sometimes funny and very clear. ... . Read all. Continue with Volume 2, Three Skill for Algebra.

Site Review. Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation ... Read all. See site books as well.

Teachers & Tutors: Site material uniquely explains common troubles in terms of steps too large or missing. Plus, 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.

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45 matches:

  1.    wt: 9:   6 Fractions and Ratios/
  2.    wt: 8:   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:   C Decimal Multiplication Methods/
  11.    wt: 6:   B Decimal Comparing and Subtracting Methods/
  12.    wt: 6:   A Decimal Counting and Adding Methods/
  13.    wt: 5:   5 Integers/
  14.    wt: 5:   D Decimal Long Division 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:   Step 1 Stick diagram and fractions/
  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:   10 Examples of Algebraic Reasoning/
  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:   Volume 1 Elements of Reason/
  44.    wt: 1:   Work and Study Tips/
  45.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

481 matches:

  1.    wt: 5:   C Equality for Fractions and Two Term Ratios and Fractions
  2.    wt: 3:   27 Logarithmic use of products of sines and cosines
  3.    wt: 3:   22 Multiplication of Signed Numbers
  4.    wt: 3:   8 Division and Mulplication of Compound Fractions
  5.    wt: 3:   4 A Brief Story of numbers and algebra
  6.    wt: 3:   5 lengths and signs of numbers
  7.    wt: 3:   B Fractions and Two Term Ratios
  8.    wt: 3:   A Similarities between Fractions and Two Term Ratios
  9.    wt: 3:   10 Simplification of Fractions and Mixed Numerals
  10.    wt: 3:   9 Improper Fractions and Mixed Numbers
  11.    wt: 3:   10 Names for Big Numbers and Powers of Ten Expansion
  12.    wt: 3:   Quick history of numbers and algebra
  13.    wt: 3:   17 Derivatives of quotients of sine and cosine
  14.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  15.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  16.    wt: 3:   Chapter 16 Origins and Limitations of Rules and Patterns
  17.    wt: 3:   Chapter 12 Islands and Divisions of Knowledge
  18.    wt: 3:   P Exact Arithmetic With Whole Numbers and Fractions
  19.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  20.    wt: 2:   Ramblings Extrinsic numbers theory
  21.    wt: 2:   Theory of Knowledge
  22.    wt: 2:   27 Graduated Correction and Penalties for Young Offenders
  23.    wt: 2:   14 Multiplication and Times Tables
  24.    wt: 2:   2 Reading and Writing Skills
  25.    wt: 2:   8 Set view of relations and functions
  26.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  27.    wt: 2:   4 Resultant of a Sum of Movements
  28.    wt: 2:   Vector and Complex Number Applet
  29.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  30.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  31.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  32.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  33.    wt: 2:   26 Formulas for products of sines and cosines
  34.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  35.    wt: 2:   14 cosine even and sine and tangent are odd
  36.    wt: 2:   10 Graphs of sines and cosines many periods
  37.    wt: 2:   9 Graphs of sine and cosine over one period
  38.    wt: 2:   7 period of sine and cosine
  39.    wt: 2:   20 N th Roots of Complex Numbers
  40.    wt: 2:   6 Field Properties of Complex Number
  41.    wt: 2:   5 An Easy Proof of the Distributive Law
  42.    wt: 2:   5 Trigonometric Ratios For Tangent and Special Triangles
  43.    wt: 2:   3 Trigonometric Ratios sine and cosine
  44.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  45.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  46.    wt: 2:   8 Similarity of Triangles and Polygons
  47.    wt: 2:   5 Similarity of Circles Squares and Rectangles
  48.    wt: 2:   10 Midpoint of [a b] and [b a]
  49.    wt: 2:   1 Numerical view of lines and their equations
  50.    wt: 2:   6 Polar Multiplication and Rotation
  51.    wt: 2:   3 Lengths and Areas on Maps and Plans
  52.    wt: 2:   21 Addition of Multiples of a Single Vector
  53.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  54.    wt: 2:   11 Signed Number Addition and Addition Properties
  55.    wt: 2:   3 Location of Point in Decimal Multiplication
  56.    wt: 2:   2 Combing Counts Addition Skills and Principles
  57.    wt: 2:   1 The Counting Origins of Numbers
  58.    wt: 2:   4 Rates Ratios and Proporitionality
  59.    wt: 2:   2 Addition and Multiplication Axioms
  60.    wt: 2:   4 Comparison of Negative Numbers
  61.    wt: 2:   2 More and Less Than for Counts and Measures
  62.    wt: 2:   14 Real Number Multiplication
  63.    wt: 2:   10 Real Number Lengths and Signs
  64.    wt: 2:   1 Whole and Natural Numbers
  65.    wt: 2:   3 GE III Equation Addition and Multiplication
  66.    wt: 2:   8 Sets of Numbers
  67.    wt: 2:   5 Talking about Numbers and Quantities
  68.    wt: 2:   3 Comparison of Negative Numbers
  69.    wt: 2:   1 More and Less Than for Counts and Measures
  70.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  71.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  72.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  73.    wt: 2:   4 LCM of 8 and 10 via Prime
  74.    wt: 2:   11 What are real lengths and numbers
  75.    wt: 2:   2 signed and unsigned numbers as coordinates
  76.    wt: 2:   6 Simplification of Fractions with Units
  77.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  78.    wt: 2:   3 Multiplying Units and Numbers
  79.    wt: 2:   21 Reciprocals for Fractions and Wholes
  80.    wt: 2:   8 Multiplication by Signed Numbers Integers
  81.    wt: 2:   6 Multiplication by Natural Numbers
  82.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  83.    wt: 2:   8 What skills and work habits to require
  84.    wt: 2:   6. Counting and adding units and mixed units
  85.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  86.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  87.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  88.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  89.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  90.    wt: 2:   Exact Arithmetic Wholes and Fractions
  91.    wt: 2:   011 Division of Time Intervals By Numbers
  92.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  93.    wt: 2:   4 Mixing and Changing Units of Time
  94.    wt: 2:   3 Units and Lengths of Time
  95.    wt: 2:   1 Intro of Kids To Time Date Skills
  96.    wt: 2:   38 Formulas and derivatives for powers and roots
  97.    wt: 2:   5 Jumps and absence of unlimited error control
  98.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  99.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  100.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  101.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  102.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  103.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  104.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  105.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  106.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  107.    wt: 2:   I. Logic and language skills
  108.    wt: 2:   How to Build Skills and Confidence
  109.    wt: 1:   Appendix 1 primary and preschool mathematic
  110.    wt: 1:   G LAMP Introduction Problem Solving Skills
  111.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  112.    wt: 1:   Skills Chapter 5 Calculus
  113.    wt: 1:   Skills Chapter 4 Logic
  114.    wt: 1:   Skills Chapter 3 Algebra
  115.    wt: 1:   Skills Chapter 2 Geometry
  116.    wt: 1:   Skills Chapter 1 Arithmetic
  117.    wt: 1:   Skills Chapter 0 Introduction
  118.    wt: 1:   7 logic review and decimals an odd combination
  119.    wt: 1:   5 logarithms and exponentials etc
  120.    wt: 1:   2 arithmetic with signed numbers
  121.    wt: 1:   1 arithmetic with unsigned numbers
  122.    wt: 1:   key notes and themes
  123.    wt: 1:   Mathematics Education Professors
  124.    wt: 1:   what should be learnt and When
  125.    wt: 1:   standards for course material
  126.    wt: 1:   Education in mathematics science and technology
  127.    wt: 1:   Different Kinds of Reasoning in maths
  128.    wt: 1:   three kinds of reason in mathematics
  129.    wt: 1:   Motivation and Context Problem
  130.    wt: 1:   fairness and inductive principles for instruction
  131.    wt: 1:   E Kirchoffs Second Law
  132.    wt: 1:   D Kirchoff First Law
  133.    wt: 1:   Home Tutoring and Home Schooling
  134.    wt: 1:   24 Standards For Skill Develoment Take II
  135.    wt: 1:   24 Standards For Skill Develoment
  136.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  137.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  138.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  139.    wt: 1:   17 Math Booklets for children and young teenagers
  140.    wt: 1:   13 Addition and Addition Tables
  141.    wt: 1:   12 Goals and Objectives For Mathematics
  142.    wt: 1:   11 Help and Defend Your Child or Teens Education
  143.    wt: 1:   8 The Effect of Negative Remarks
  144.    wt: 1:   5 Patience Please for Yourself and Your Charges
  145.    wt: 1:   4 Learning Takes Time and Effort
  146.    wt: 1:   1 Speaking Skills
  147.    wt: 1:   Ages 12 to 14 Skills with take home value
  148.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  149.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  150.    wt: 1:   Objectives for Mathematics and Logic Language Skill Development
  151.    wt: 1:   26 Function definitions done and coming
  152.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  153.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  154.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  155.    wt: 1:   19 Horizontal line rule and method
  156.    wt: 1:   18 Vertical Line Rule and Method
  157.    wt: 1:   17 Function maxima minima and their location
  158.    wt: 1:   15 Sign analysis of functions
  159.    wt: 1:   11 Function Domain Range Source and Targets
  160.    wt: 1:   9 Set theory term relation possible origins
  161.    wt: 1:   6 Set Existence Formation and Notation
  162.    wt: 1:   4 Function notation in and beyond mathematics
  163.    wt: 1:   2 Algebraic use of function notation
  164.    wt: 1:   1 Geometric Introduction of Function Notation
  165.    wt: 1:   9 quadratics physical and further context
  166.    wt: 1:   8 quadratics backward use of various formulas
  167.    wt: 1:   6 quadratics numerical approach
  168.    wt: 1:   4 quadratics difference of two squares
  169.    wt: 1:   11 Growth and Decay in Biology
  170.    wt: 1:   10 Exponential Growth and Decay Models
  171.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  172.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  173.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  174.    wt: 1:   3 Polynomials Multiplication Addition
  175.    wt: 1:   2 Column Multiplication Method
  176.    wt: 1:   16 cotangent function Definition Graph and Inverse
  177.    wt: 1:   15 cosecant function Definition Graph and Inverse
  178.    wt: 1:   14 secant function Definition Graph and Inverse
  179.    wt: 1:   13 cosecant function Definition Graph and Inverse
  180.    wt: 1:   11 arctan left inverse of tangent Graph
  181.    wt: 1:   10 arctan left inverse of tangent Definition
  182.    wt: 1:   8 arcsin left inverse of sine Graph
  183.    wt: 1:   7 arcsin left inverse of sine Definition
  184.    wt: 1:   6 Graph of arccos function
  185.    wt: 1:   3 Left Inverse of cosine arccos definition
  186.    wt: 1:   9 Summary Degrees to Radians and back
  187.    wt: 1:   8 Radian Measures of Common Angles
  188.    wt: 1:   2 Radian Measure Numerical Value of one degree
  189.    wt: 1:   1 Degrees and Radians Introduction
  190.    wt: 1:   A Global Time and Navigation
  191.    wt: 1:   15 Dot and Cross Product
  192.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  193.    wt: 1:   Parallel Lines and Parallel Transversals
  194.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  195.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  196.    wt: 1:   Parallel Lines and Interior Angles
  197.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  198.    wt: 1:   Straight Lines Intersection of
  199.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  200.    wt: 1:   32 seven rows of pascals triangle
  201.    wt: 1:   30 unit circle calculation of six trigonometric functions
  202.    wt: 1:   29 secant cosecant and cotangent for acute angles
  203.    wt: 1:   28 Expressing products of sines cosines as sums
  204.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  205.    wt: 1:   21 sine and cosine Half Angle Formulas
  206.    wt: 1:   20 sine and cosine Double Angle Formulas
  207.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  208.    wt: 1:   18 sum of sinusoidal waves as a single wave
  209.    wt: 1:   17F Law of cosines
  210.    wt: 1:   17E Trig Formulas for dot and cross Products
  211.    wt: 1:   17D cis formulas for sine cosines and tangent
  212.    wt: 1:   17C sine and cosine double triple angle formulas
  213.    wt: 1:   17A The complex number valued trig function cis
  214.    wt: 1:   13 Graph of tangent function many periods
  215.    wt: 1:   12 Graph of tangent function for one period
  216.    wt: 1:   8 period of tangent function
  217.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  218.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  219.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  220.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  221.    wt: 1:   Unit Circle Development of Trigonometry
  222.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  223.    wt: 1:   21 Logarithms Powers and Exponentials
  224.    wt: 1:   19 N th Roots of Unity
  225.    wt: 1:   18 Sixth Roots of Unity
  226.    wt: 1:   17 Cube Roots of unity
  227.    wt: 1:   16 References and Originality Question
  228.    wt: 1:   14 Law of cosines
  229.    wt: 1:   13 Trig Formulas for dot and cross Products
  230.    wt: 1:   12 cis formulas for sine cosines and tangent
  231.    wt: 1:   11 sine and cosine double triple angle formulas
  232.    wt: 1:   9 The complex number valued trig function cis
  233.    wt: 1:   8 Unit Circle Development of Trigonometry
  234.    wt: 1:   4 Multiplication Properties
  235.    wt: 1:   2 Complex Numbers made easier we hope
  236.    wt: 1:   Appetizer A Complex Number Applet
  237.    wt: 1:   7 Trignometric Ratios Unit Circle
  238.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  239.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  240.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  241.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  242.    wt: 1:   9 Similarity of Triangles Usual Criteria
  243.    wt: 1:   1 Early Concept of Like or Similar Shapes
  244.    wt: 1:   7 Exercises to test skill and concept mastery
  245.    wt: 1:   6 Intersection of lines by solving linear systems
  246.    wt: 1:   5 Algebraic View of Slopes
  247.    wt: 1:   What is and is not here
  248.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  249.    wt: 1:   7 Complex Numbers Appetizer
  250.    wt: 1:   5 Cartesian Addition and Translation
  251.    wt: 1:   4 Polar Coordinates to and from
  252.    wt: 1:   PS H Distributive Law For Complex Numbers
  253.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  254.    wt: 1:   PS E Multiplication with Polar Coordinates
  255.    wt: 1:   17 Right Bisectors of Triangle Sides
  256.    wt: 1:   16 Angles Subtended By Chords and Diameters
  257.    wt: 1:   9 Construction of a right bisector
  258.    wt: 1:   6 Ruler and compass Angle Bisection
  259.    wt: 1:   3 Isometry of Triangles Congruence
  260.    wt: 1:   1 Initial Concepts and Terms
  261.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  262.    wt: 1:   musings do not puiblish real numbers
  263.    wt: 1:   A Modular and Remainder Arithmetic
  264.    wt: 1:   A Signed Number Arithmetic Review
  265.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  266.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  267.    wt: 1:   19 Signed Multiples of Vectors
  268.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  269.    wt: 1:   13 Arrows and Vectors in a Plane
  270.    wt: 1:   12 Real Numbers Line Signed Coordinates
  271.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  272.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  273.    wt: 1:   4 Location of Point in Decimal Addition
  274.    wt: 1:   2 Counting Digits in Decimal Multiplication
  275.    wt: 1:   1 Fractions with Finite Decimal Expansions
  276.    wt: 1:   B Decimal Comparison and Subtraction
  277.    wt: 1:   8 Column Multiplication Methods in General
  278.    wt: 1:   7 Decimals Multiplication Methods Examples
  279.    wt: 1:   6 Column Methods for Decimal Multiplication
  280.    wt: 1:   5 Distributive Law for Whole Numbers
  281.    wt: 1:   3 Multiplicative Counting Skills Principles
  282.    wt: 1:   5 Areas of Rectangles Revisited
  283.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  284.    wt: 1:   5 Proportionality in Equivalent Fractions
  285.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  286.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  287.    wt: 1:   6 Compound Interest Forward and Backwards
  288.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  289.    wt: 1:   6 Equations and Systems Equivalent or Implied
  290.    wt: 1:   4 Subtraction and Division Axioms
  291.    wt: 1:   3 More and Less Than with Unlike Signs
  292.    wt: 1:   1 Real Numbers Comparison
  293.    wt: 1:   16 Real Numbers Comparison
  294.    wt: 1:   15 Real Number Division
  295.    wt: 1:   13 Real Number Subtraction
  296.    wt: 1:   12 Real Number Additive Inverses or Negatives
  297.    wt: 1:   11 Real Number Addition
  298.    wt: 1:   8 Coordinates for Maps and Planes
  299.    wt: 1:   7 Real Numbers as Line Cordinates
  300.    wt: 1:   6 Unsigned Real Numbers
  301.    wt: 1:   5 Rational Numbers More
  302.    wt: 1:   4 Rational Numbers
  303.    wt: 1:   3 Fractions
  304.    wt: 1:   3 Geometric Formulas and Function Notation
  305.    wt: 1:   1 Formulas Dependence and Function Notation
  306.    wt: 1:   11 Volume of Sphere
  307.    wt: 1:   10 Volume of Pyramid
  308.    wt: 1:   9 Volume of Cone
  309.    wt: 1:   2 Another Rectangle Area Formula Example
  310.    wt: 1:   1 Written work formats for developing and showing skill
  311.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  312.    wt: 1:   9 Sets in Probability and Statistics
  313.    wt: 1:   6 Three Notions of What is a Variable
  314.    wt: 1:   1 Three Skills For Algebra
  315.    wt: 1:   2 More and Less Than with Unlike Signs
  316.    wt: 1:   3 Properties of Square Roots with example
  317.    wt: 1:   1 Squares and Square Roots Introduction
  318.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  319.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  320.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  321.    wt: 1:   7 GCD and LCM from prime factorization
  322.    wt: 1:   3 Counting with Tables and Trees II
  323.    wt: 1:   2 Counting with Tables and Trees I
  324.    wt: 1:   1 Counting and Counting Methods I
  325.    wt: 1:   10 dividing signed numbers
  326.    wt: 1:   9 subtracting signed numbers
  327.    wt: 1:   8 multiplying signed numbers
  328.    wt: 1:   7 negative and additive inverse
  329.    wt: 1:   6 adding signed numbers
  330.    wt: 1:   3 signed coordinates for maps and planes
  331.    wt: 1:   4 Fractions with Units
  332.    wt: 1:   2 Equality and Units
  333.    wt: 1:   1 Addition and Subtraction with Units
  334.    wt: 1:   D Three Term Ratios
  335.    wt: 1:   22 Complex Compound Fractions
  336.    wt: 1:   20 Dividing Fractions the Why
  337.    wt: 1:   19 Dividing Fractions How TO
  338.    wt: 1:   17 Efficient Ways to Add and Subtract
  339.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  340.    wt: 1:   14 Adding and Subtracting with Like Denominators
  341.    wt: 1:   6 Multiplication Algebraically Take II
  342.    wt: 1:   5 Equivalent Fractions
  343.    wt: 1:   4 Fraction Multiplication
  344.    wt: 1:   3 Unit fraction of a fraction
  345.    wt: 1:   2 Unit Fraction Multiplication
  346.    wt: 1:   11 Adding Integers Formulas and Examples
  347.    wt: 1:   10 Integer Multiplication Formulas
  348.    wt: 1:   7 Multiplication by Signs
  349.    wt: 1:   5 Zero Movement and Additive Inverses
  350.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  351.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  352.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  353.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  354.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  355.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  356.    wt: 1:   20 Uniqueness of Prime Factorization
  357.    wt: 1:   17 Identify and Count Factors using Primes
  358.    wt: 1:   16 video Factors of 980 using prime
  359.    wt: 1:   15 video Factors of 20 using Prime Factorization
  360.    wt: 1:   14 video Factors of 24 Take II
  361.    wt: 1:   13 video Factors of 24 using prime
  362.    wt: 1:   12 LCD GCD and LCM using Primes
  363.    wt: 1:   7 Calculator Usage Notes and Cautions
  364.    wt: 1:   5 Prime Factorization and a Square Rule
  365.    wt: 1:   3 video Primes and Composites from 9 times table
  366.    wt: 1:   2 Prime and Composites less than 16
  367.    wt: 1:   Division with Counts and Length
  368.    wt: 1:   Long Division forwards and backwards Example 3
  369.    wt: 1:   Long Division forwards and backwards Example 2
  370.    wt: 1:   Long Division forwards and backwards Example 1
  371.    wt: 1:   11 Another Single Digit Divisor Example
  372.    wt: 1:   10 Division by Five Long and Short Ways
  373.    wt: 1:   D Decimal Multiplication Methods Derived
  374.    wt: 1:   C Counting Areas with Powers of Ten
  375.    wt: 1:   B Powers of Ten
  376.    wt: 1:   A Elementary Basis for Multiplication Methods
  377.    wt: 1:   6 Multiplication Commutes Order Not Important
  378.    wt: 1:   5 Decimal Fraction Multiplication
  379.    wt: 1:   4 Two and Three Digit Multipliers
  380.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  381.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  382.    wt: 1:   Subtraction Another Video Lesson
  383.    wt: 1:   8 Subtraction with Units of Measure
  384.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  385.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  386.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  387.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  388.    wt: 1:   7 Adding decimal fractions using decimal point
  389.    wt: 1:   11 Place Value SI Standard International way
  390.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  391.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  392.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  393.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  394.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  395.    wt: 1:   016 Numbering Occidental Calendar Days
  396.    wt: 1:   015 School and work day counting tables
  397.    wt: 1:   012 Division of Time Intervals by Time Intervals
  398.    wt: 1:   010 Repeated Addition of Time Intervals
  399.    wt: 1:   8 Addition of Time Intervals via subtotaling
  400.    wt: 1:   7 Addition of Time Intervals
  401.    wt: 1:   2 Time and Date Matters in School
  402.    wt: 1:   Example 2 volume of a cone
  403.    wt: 1:   Example 1 volume of a pyramid
  404.    wt: 1:   Volume of Solid by Cross Sections Lesson
  405.    wt: 1:   Example 1. Area Between x and x squared
  406.    wt: 1:   Example 4 with x function of y
  407.    wt: 1:   34 Derivative of exponential function
  408.    wt: 1:   31 Derivatives of inverse functions
  409.    wt: 1:   30Chain Rule A Proof
  410.    wt: 1:   28 Chain Rule Preparation for a Proof
  411.    wt: 1:   15 sine and cosine derivatives 3rd step
  412.    wt: 1:   14 sine and cosine derivatives 2nd step
  413.    wt: 1:   13 sine and cosine derivatives 1st step
  414.    wt: 1:   8 Differentiation of polynomials
  415.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  416.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  417.    wt: 1:   9 Limits Continuity and Composition
  418.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  419.    wt: 1:   .H1 First Fundamental Theorem of Calculus
  420.    wt: 1:   G.3 Constant Difference Theorem Proof
  421.    wt: 1:   E2 Algebraic Properties of Limits
  422.    wt: 1:   D2 Limits of Monotone Sequences
  423.    wt: 1:   PostScript For and Against Decimal Perspectives
  424.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  425.    wt: 1:   Chapter 22 Complex Numbers
  426.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  427.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  428.    wt: 1:   Chapter 12. Units and Slopes
  429.    wt: 1:   Chapter 10 Slopes and Units
  430.    wt: 1:   Chapter 7 Slopes and Velocity
  431.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  432.    wt: 1:   Chapter 2. Slopes and Ski Trails
  433.    wt: 1:   Appendix E. How To Study Mathematics and Why
  434.    wt: 1:   Appendix D. What to do in School and Why
  435.    wt: 1:   Chapter 31 Direct and Indirect Reason
  436.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  437.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  438.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  439.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  440.    wt: 1:   Chapter 20. Degrees and Radians
  441.    wt: 1:   Chapter 19. Functions and Sets
  442.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  443.    wt: 1:   Chapter 12. Shorthand Usage Guide
  444.    wt: 1:   Chapter 11. Why Shorthand
  445.    wt: 1:   Chapter 10 Describing and Changing Calculations
  446.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  447.    wt: 1:   Chapter 8 Three Skills For Algebra
  448.    wt: 1:   Chapter 6 Change of Language
  449.    wt: 1:   Chapter 4 Longer Chains of Reason
  450.    wt: 1:   Chapter 3 Chains of Reason
  451.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  452.    wt: 1:   Chapter 7 Two Treatments of Geometry
  453.    wt: 1:   Chapter 2 For and Against Mathematics
  454.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  455.    wt: 1:   Postscript B More on Story Telling and Reason
  456.    wt: 1:   Chapter 24 Direct and Indirect Reason
  457.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  458.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  459.    wt: 1:   Chapter 18 Sense and Knowledge
  460.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  461.    wt: 1:   Chapter 8 Change of Language
  462.    wt: 1:   Chapter 7 Longer Chains of Reason
  463.    wt: 1:   Chapter 6 Chains of Reason
  464.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  465.    wt: 1:   R Why Learn Mathematics Skills
  466.    wt: 1:   O On Learning Mathematics and Science
  467.    wt: 1:   L Skills with take home value
  468.    wt: 1:   N Improving Marks on Tests and Finals
  469.    wt: 1:   J. More on written work and showing skill
  470.    wt: 1:   H Jigsaw puzzles and problem solving
  471.    wt: 1:   G. Written work formats for developing and showing skill
  472.    wt: 1:   E. When and how to correct errors
  473.    wt: 1:   C. Domino effect of being careful
  474.    wt: 1:   B. Domino effect of errors
  475.    wt: 1:   Helping the Blind in Logic and Mathematics
  476.    wt: 1:   More Algebra and Slope based Calculus Preview
  477.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  478.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  479.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  480.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  481.    wt: 1:   Montreal Basic and Advanced Mathematics Tutoring

Extended Search

762 matches:

  1.    wt: 9:   2 More and Less Than with Unlike Signs
  2.    wt: 9:   5 lengths and signs of numbers
  3.    wt: 9:   6 Simplification of Fractions with Units
  4.    wt: 9:   5 Reciprocals and Division for Fractions with Units
  5.    wt: 9:   3 Multiplying Units and Numbers
  6.    wt: 9:   21 Working With Signs
  7.    wt: 9:   18 Efficient Ways to Multiply
  8.    wt: 9:   16 Addition Subtraction Comparision Compared
  9.    wt: 9:   13 Fraction Comparison Algebraic View
  10.    wt: 9:   12 Fraction Comparison
  11.    wt: 9:   11 Simplification an Algebraic View
  12.    wt: 9:   8 Numerals Fractionals Quantals Take II
  13.    wt: 9:   7 Numerals Fractionals Quantals
  14.    wt: 9:   1 What is a fraction Take II
  15.    wt: 9:   1 What is a fraction
  16.    wt: 9:   6 Sieve of Eratosthenes and Square Rule
  17.    wt: 8:   4 Greater More Less Than Signs in General
  18.    wt: 8:   17 GCD LCM of 85 and 60 via Prime
  19.    wt: 8:   16 GCD and LCM of 650 225 via Prime
  20.    wt: 8:   9 GCD of 360 110 via Primes and Euclid Algorithm
  21.    wt: 8:   4 LCM of 8 and 10 via Prime
  22.    wt: 8:   11 What are real lengths and numbers
  23.    wt: 8:   2 signed and unsigned numbers as coordinates
  24.    wt: 8:   4 Fractions with Units
  25.    wt: 8:   2 Equality and Units
  26.    wt: 8:   1 Addition and Subtraction with Units
  27.    wt: 8:   6 Multiplication by Natural Numbers
  28.    wt: 8:   6 Multiplication Commutes Order Not Important
  29.    wt: 8:   8 What skills and work habits to require
  30.    wt: 8:   6. Counting and adding units and mixed units
  31.    wt: 8:   10 Names for Big Numbers and Powers of Ten Expansion
  32.    wt: 8:   Quick history of numbers and algebra
  33.    wt: 7:   3 Properties of Square Roots with example
  34.    wt: 7:   1 Squares and Square Roots Introduction
  35.    wt: 7:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  36.    wt: 7:   14 GCD of 650 110 via Primes LCM via Product Rule
  37.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  38.    wt: 7:   7 GCD and LCM from prime factorization
  39.    wt: 7:   3 Counting with Tables and Trees II
  40.    wt: 7:   2 Counting with Tables and Trees I
  41.    wt: 7:   1 Counting and Counting Methods I
  42.    wt: 7:   10 dividing signed numbers
  43.    wt: 7:   9 subtracting signed numbers
  44.    wt: 7:   8 multiplying signed numbers
  45.    wt: 7:   7 negative and additive inverse
  46.    wt: 7:   6 adding signed numbers
  47.    wt: 7:   3 signed coordinates for maps and planes
  48.    wt: 7:   7 Converting or Changing Units
  49.    wt: 7:   8 Multiplication by Signed Numbers Integers
  50.    wt: 7:   A Decimals Modular and Remainder Arithmetic
  51.    wt: 7:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  52.    wt: 7:   19 Remainder Arithmetic Rule of 9 for checking sums III
  53.    wt: 7:   18 Remainder Arithmetic Rule of 9 for checking sums II
  54.    wt: 7:   17 Remainder Arithmetic Rule of 9 for checking sums I
  55.    wt: 7:   20 Uniqueness of Prime Factorization
  56.    wt: 7:   17 Identify and Count Factors using Primes
  57.    wt: 7:   16 video Factors of 980 using prime
  58.    wt: 7:   15 video Factors of 20 using Prime Factorization
  59.    wt: 7:   14 video Factors of 24 Take II
  60.    wt: 7:   13 video Factors of 24 using prime
  61.    wt: 7:   12 LCD GCD and LCM using Primes
  62.    wt: 7:   7 Calculator Usage Notes and Cautions
  63.    wt: 7:   5 Prime Factorization and a Square Rule
  64.    wt: 7:   3 video Primes and Composites from 9 times table
  65.    wt: 7:   2 Prime and Composites less than 16
  66.    wt: 7:   D Decimal Multiplication Methods Derived
  67.    wt: 7:   C Counting Areas with Powers of Ten
  68.    wt: 7:   B Powers of Ten
  69.    wt: 7:   A Elementary Basis for Multiplication Methods
  70.    wt: 7:   5 Decimal Fraction Multiplication
  71.    wt: 7:   4 Two and Three Digit Multipliers
  72.    wt: 7:   Video Decimal Multiplication Geometric View Example 2
  73.    wt: 7:   Video Decimal Multiplication Geometric View Example 2
  74.    wt: 7:   Subtraction Another Video Lesson
  75.    wt: 7:   8 Subtraction with Units of Measure
  76.    wt: 7:   7 Subtraction for Decimal Fractions with Exercises
  77.    wt: 7:   6 Subtraction with Conversion Example with Exercises
  78.    wt: 7:   4 Subtraction with Conversions Borrows and Letter J
  79.    wt: 7:   3 Harder Cases Convert to Compare and Subtract
  80.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  81.    wt: 7:   7 Adding decimal fractions using decimal point
  82.    wt: 7:   9 Place Value Review Decimal form of Avogrados number included
  83.    wt: 7:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  84.    wt: 7:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  85.    wt: 7:   5 More on Groups of 3 Place Value in Decimal Fractions
  86.    wt: 7:   4 Groups of 3 Place Value in Decimal Fractions
  87.    wt: 7:   Exact Arithmetic Wholes and Fractions
  88.    wt: 6:   5 Square Roots with primes more still
  89.    wt: 6:   4 Square Roots with primes more
  90.    wt: 6:   2 Square Roots with Prime
  91.    wt: 6:   13 GCD from given Prime Factorization
  92.    wt: 6:   11 GCD 2700 288 via Euclid Algorithm
  93.    wt: 6:   8 GCD from Euclidean Algorithm
  94.    wt: 6:   6 GCD from Prime
  95.    wt: 6:   5 Common Divisors 60 45 via Prime
  96.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  97.    wt: 6:   2 Least Common Multiple LCM intro via list method
  98.    wt: 6:   1 Least Common Multiples LCM Introduction
  99.    wt: 6:   12 GCD 2700 288 via Prime
  100.    wt: 6:   5 Counting with Tables Trees Product Rule Take II
  101.    wt: 6:   4 Counting with Trees Product Rule Take I
  102.    wt: 6:   4 signed coordinates for regions in space
  103.    wt: 6:   11 Adding Integers Formulas and Examples
  104.    wt: 6:   10 Integer Multiplication Formulas
  105.    wt: 6:   7 Multiplication by Signs
  106.    wt: 6:   5 Zero Movement and Additive Inverses
  107.    wt: 6:   2 Integers Multiplies of a Unit Moverment
  108.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  109.    wt: 6:   26 Divisibility by 2 3 5 Example
  110.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  111.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  112.    wt: 6:   23 Remainder Arithmetic Modulo 2
  113.    wt: 6:   22 Remainder Arithmetic Modulo 3 more
  114.    wt: 6:   21 Remainder Arithmetic Modulo 3
  115.    wt: 6:   16 Remainder Arithmetic Modulo 9 Example 2
  116.    wt: 6:   15 Remainder Arithmetic Modulo 9 Example
  117.    wt: 6:   14 Remainder Arithmetic Modulo 9 Example
  118.    wt: 6:   13 Remainder Arithmetic Modulo 5 Example
  119.    wt: 6:   12 Remainder Arithmetic Modulo 10 Example
  120.    wt: 6:   11 Remainder Arithmetic Long Division by 5 Quickly more
  121.    wt: 6:   10 Remainder Arithmetic Long Division by 5 Quickly
  122.    wt: 6:   9 Remainder Arithmetic Divisibility by 5
  123.    wt: 6:   8 Remainder Arithmetic Morulo 5 Examples II
  124.    wt: 6:   7 Remainder Arithmetic Modulo 5 Examples I
  125.    wt: 6:   6 Remainder Arithmetic Modulo 5 Propertie
  126.    wt: 6:   5 Remainder Arithmetic Modulo 5
  127.    wt: 6:   4 Remainder Arithmetic Modulo 10 in general
  128.    wt: 6:   3 Remainder Arithmetic Modulos 10 more still
  129.    wt: 6:   2 Remainder Arithmetic Modulo 10 more
  130.    wt: 6:   1 Remainder Arithmetic Modulo 10
  131.    wt: 6:   19 video Prime Factorization Unique
  132.    wt: 6:   18 video Count Factors given Prime Factorization
  133.    wt: 6:   11 Efficient Square Rule Use
  134.    wt: 6:   10 video Prime Factorization upto 23 squared
  135.    wt: 6:   9 video Prime Factorization upto 19 squared
  136.    wt: 6:   8 video Prime Factorization upto 19
  137.    wt: 6:   4 video Prime Factorization Introduction
  138.    wt: 6:   1 video how Products are bigger than factor
  139.    wt: 6:   Division with Counts and Length
  140.    wt: 6:   Long Division forwards and backwards Example 3
  141.    wt: 6:   Long Division forwards and backwards Example 2
  142.    wt: 6:   Long Division forwards and backwards Example 1
  143.    wt: 6:   11 Another Single Digit Divisor Example
  144.    wt: 6:   10 Division by Five Long and Short Ways
  145.    wt: 6:   6 Why Decimal Long Division Methods Works Take I
  146.    wt: 6:   3 More One Digit Multipliers
  147.    wt: 6:   2 One Digit Multipliers
  148.    wt: 6:   Video Power Notation in Decimal Expansion
  149.    wt: 6:   1 Why 3 times 5 gives 15
  150.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  151.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  152.    wt: 6:   Subtraction with J Conversions Example
  153.    wt: 6:   9 22 Minute Subtraction Review Video
  154.    wt: 6:   5 A Tip for Efficent Subtraction
  155.    wt: 6:   2 Subtraction Easy Case Examples
  156.    wt: 6:   Appendix 1 Counting Revisited 15 minute video
  157.    wt: 6:   5. How to add decimals C. Examples
  158.    wt: 6:   4. How to add with decimals B with conversions
  159.    wt: 6:   3. How to add with decimals A sans conversions
  160.    wt: 6:   2 Decimal Counting Practices
  161.    wt: 6:   1. Explaining Addition Table
  162.    wt: 6:   11 Place Value SI Standard International way
  163.    wt: 6:   8 Review Lesson 1 2 4 and 6 All in One
  164.    wt: 6:   3 More on Groups of 3 Multi Digit Place Value
  165.    wt: 6:   2 Groups of Three Place Value for Multidigit Decimals
  166.    wt: 6:   1 Place Value in Three Digit Whole Numbers
  167.    wt: 6:   Practical Methods Ends and Values for Arithmetic
  168.    wt: 5:   arithmetic videos Real Player Format
  169.    wt: 5:   D Remainders Modulo 11 Pair Rule
  170.    wt: 5:   C Divisibility by 11 Integer Recognition Method
  171.    wt: 5:   B Integer Long Division Multiple Choices
  172.    wt: 5:   A Associative Law Theorectical Note
  173.    wt: 5:   13 Subtraction with Additive Inverse
  174.    wt: 5:   12 Adding Integers More Examples
  175.    wt: 5:   9 Multiplying Integers
  176.    wt: 5:   4 Adding Movements wiht opposite directions
  177.    wt: 5:   3 Adding Movements with same direction
  178.    wt: 5:   1 Integers as Coordinates
  179.    wt: 5:   Long Division Backwards more
  180.    wt: 5:   Long Division Backward
  181.    wt: 5:   12 Why Long Division Works Take III
  182.    wt: 5:   9 Why Long Division Works Take II
  183.    wt: 5:   8 Correcting the Mistake
  184.    wt: 5:   7 Long Divison Mistake Catching
  185.    wt: 5:   5 Long Division Include Zeroes or not
  186.    wt: 5:   4 Division with 2 Digit Divsors
  187.    wt: 5:   3 Division Single Digit Divisor Example
  188.    wt: 5:   2 Division with Single Digit Divisors
  189.    wt: 5:   1 Divsion Physical Examples
  190.    wt: 5:   Formula Evaluation how to show work
  191.    wt: 5:   Expression Evaluation how to show work
  192.    wt: 5:   The 20 Times Table
  193.    wt: 5:   The 12 Times Table Visually
  194.    wt: 5:   About folder contents
  195.    wt: 4:   6 Field Properties of Complex Number
  196.    wt: 4:   6 Polar Multiplication and Rotation
  197.    wt: 4:   22 Multiplication of Signed Numbers
  198.    wt: 4:   8 Division and Mulplication of Compound Fractions
  199.    wt: 4:   6 Column Methods for Decimal Multiplication
  200.    wt: 4:   2 Combing Counts Addition Skills and Principles
  201.    wt: 4:   1 The Counting Origins of Numbers
  202.    wt: 4:   Chapter 5 Islands and Divisions of Knowledge
  203.    wt: 4:   P Exact Arithmetic With Whole Numbers and Fractions
  204.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  205.    wt: 3:   27 Logarithmic use of products of sines and cosines
  206.    wt: 3:   20 N th Roots of Complex Numbers
  207.    wt: 3:   5 An Easy Proof of the Distributive Law
  208.    wt: 3:   5 Trigonometric Ratios For Tangent and Special Triangles
  209.    wt: 3:   3 Trigonometric Ratios sine and cosine
  210.    wt: 3:   2 Similar Triangles Equality of Corresponding Side Ratios
  211.    wt: 3:   10 Midpoint of [a b] and [b a]
  212.    wt: 3:   6 Intersection of lines by solving linear systems
  213.    wt: 3:   1 Numerical view of lines and their equations
  214.    wt: 3:   6 Ruler and compass Angle Bisection
  215.    wt: 3:   21 Addition of Multiples of a Single Vector
  216.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  217.    wt: 3:   11 Signed Number Addition and Addition Properties
  218.    wt: 3:   3 Location of Point in Decimal Multiplication
  219.    wt: 3:   B Decimal Comparison and Subtraction
  220.    wt: 3:   8 Column Multiplication Methods in General
  221.    wt: 3:   7 Decimals Multiplication Methods Examples
  222.    wt: 3:   5 Distributive Law for Whole Numbers
  223.    wt: 3:   3 Multiplicative Counting Skills Principles
  224.    wt: 3:   4 Rates Ratios and Proporitionality
  225.    wt: 3:   2 Addition and Multiplication Axioms
  226.    wt: 3:   4 Comparison of Negative Numbers
  227.    wt: 3:   2 More and Less Than for Counts and Measures
  228.    wt: 3:   14 Real Number Multiplication
  229.    wt: 3:   10 Real Number Lengths and Signs
  230.    wt: 3:   1 Whole and Natural Numbers
  231.    wt: 3:   6 Three Examples
  232.    wt: 3:   4 A Brief Story of numbers and algebra
  233.    wt: 3:   011 Division of Time Intervals By Numbers
  234.    wt: 3:   9 Comparison and Subtraction of Time Intervals
  235.    wt: 3:   4 Mixing and Changing Units of Time
  236.    wt: 3:   3 Units and Lengths of Time
  237.    wt: 3:   1 Intro of Kids To Time Date Skills
  238.    wt: 3:   17 Derivatives of quotients of sine and cosine
  239.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  240.    wt: 3:   5 Jumps and absence of unlimited error control
  241.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  242.    wt: 3:   Chapter 16 Origins and Limitations of Rules and Patterns
  243.    wt: 3:   Chapter 12 Islands and Divisions of Knowledge
  244.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  245.    wt: 3:   Q How Logic and Proofs extend Show Work Practices
  246.    wt: 3:   I. Logic and language skills
  247.    wt: 3:   How to Build Skills and Confidence
  248.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  249.    wt: 2:   Ramblings Extrinsic numbers theory
  250.    wt: 2:   Theory of Knowledge
  251.    wt: 2:   27 Graduated Correction and Penalties for Young Offenders
  252.    wt: 2:   14 Multiplication and Times Tables
  253.    wt: 2:   2 Reading and Writing Skills
  254.    wt: 2:   Ages 12 to 14 Skills with take home value
  255.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  256.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  257.    wt: 2:   Objectives for Mathematics and Logic Language Skill Development
  258.    wt: 2:   8 Set view of relations and functions
  259.    wt: 2:   9 Summary Degrees to Radians and back
  260.    wt: 2:   8 Radian Measures of Common Angles
  261.    wt: 2:   2 Radian Measure Numerical Value of one degree
  262.    wt: 2:   1 Degrees and Radians Introduction
  263.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  264.    wt: 2:   4 Resultant of a Sum of Movements
  265.    wt: 2:   Vector and Complex Number Applet
  266.    wt: 2:   Parallel Lines and Parallel Transversals
  267.    wt: 2:   Proportionality of Line Segments From Parallel Transversals
  268.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  269.    wt: 2:   Parallel Lines and Interior Angles
  270.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  271.    wt: 2:   Straight Lines Intersection of
  272.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  273.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  274.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  275.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  276.    wt: 2:   26 Formulas for products of sines and cosines
  277.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  278.    wt: 2:   14 cosine even and sine and tangent are odd
  279.    wt: 2:   10 Graphs of sines and cosines many periods
  280.    wt: 2:   9 Graphs of sine and cosine over one period
  281.    wt: 2:   7 period of sine and cosine
  282.    wt: 2:   21 Logarithms Powers and Exponentials
  283.    wt: 2:   19 N th Roots of Unity
  284.    wt: 2:   18 Sixth Roots of Unity
  285.    wt: 2:   17 Cube Roots of unity
  286.    wt: 2:   16 References and Originality Question
  287.    wt: 2:   14 Law of cosines
  288.    wt: 2:   13 Trig Formulas for dot and cross Products
  289.    wt: 2:   12 cis formulas for sine cosines and tangent
  290.    wt: 2:   11 sine and cosine double triple angle formulas
  291.    wt: 2:   9 The complex number valued trig function cis
  292.    wt: 2:   8 Unit Circle Development of Trigonometry
  293.    wt: 2:   4 Multiplication Properties
  294.    wt: 2:   2 Complex Numbers made easier we hope
  295.    wt: 2:   Appetizer A Complex Number Applet
  296.    wt: 2:   7 Trignometric Ratios Unit Circle
  297.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  298.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  299.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  300.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  301.    wt: 2:   8 Similarity of Triangles and Polygons
  302.    wt: 2:   5 Similarity of Circles Squares and Rectangles
  303.    wt: 2:   7 Exercises to test skill and concept mastery
  304.    wt: 2:   5 Algebraic View of Slopes
  305.    wt: 2:   What is and is not here
  306.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  307.    wt: 2:   7 Complex Numbers Appetizer
  308.    wt: 2:   5 Cartesian Addition and Translation
  309.    wt: 2:   4 Polar Coordinates to and from
  310.    wt: 2:   PS H Distributive Law For Complex Numbers
  311.    wt: 2:   PS F Scalar Multiplication Distributes over Addition
  312.    wt: 2:   PS E Multiplication with Polar Coordinates
  313.    wt: 2:   17 Right Bisectors of Triangle Sides
  314.    wt: 2:   16 Angles Subtended By Chords and Diameters
  315.    wt: 2:   9 Construction of a right bisector
  316.    wt: 2:   3 Isometry of Triangles Congruence
  317.    wt: 2:   1 Initial Concepts and Terms
  318.    wt: 2:   3 Lengths and Areas on Maps and Plans
  319.    wt: 2:   musings do not puiblish real numbers
  320.    wt: 2:   A Modular and Remainder Arithmetic
  321.    wt: 2:   A Signed Number Arithmetic Review
  322.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  323.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  324.    wt: 2:   19 Signed Multiples of Vectors
  325.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  326.    wt: 2:   13 Arrows and Vectors in a Plane
  327.    wt: 2:   12 Real Numbers Line Signed Coordinates
  328.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  329.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  330.    wt: 2:   4 Location of Point in Decimal Addition
  331.    wt: 2:   2 Counting Digits in Decimal Multiplication
  332.    wt: 2:   1 Fractions with Finite Decimal Expansions
  333.    wt: 2:   E Long Division Methods more
  334.    wt: 2:   D Long Division Methods
  335.    wt: 2:   C Three Decimal Subtraction Methods
  336.    wt: 2:   A Decimal Addition Columm Methods
  337.    wt: 2:   4 Commutative Law Groups Counting Form
  338.    wt: 2:   5 Areas of Rectangles Revisited
  339.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  340.    wt: 2:   5 Proportionality in Equivalent Fractions
  341.    wt: 2:   6 Equations and Systems Equivalent or Implied
  342.    wt: 2:   4 Subtraction and Division Axioms
  343.    wt: 2:   3 More and Less Than with Unlike Signs
  344.    wt: 2:   1 Real Numbers Comparison
  345.    wt: 2:   16 Real Numbers Comparison
  346.    wt: 2:   15 Real Number Division
  347.    wt: 2:   13 Real Number Subtraction
  348.    wt: 2:   12 Real Number Additive Inverses or Negatives
  349.    wt: 2:   11 Real Number Addition
  350.    wt: 2:   8 Coordinates for Maps and Planes
  351.    wt: 2:   7 Real Numbers as Line Cordinates
  352.    wt: 2:   6 Unsigned Real Numbers
  353.    wt: 2:   5 Rational Numbers More
  354.    wt: 2:   4 Rational Numbers
  355.    wt: 2:   3 Fractions
  356.    wt: 2:   3 Geometric Formulas and Function Notation
  357.    wt: 2:   1 Formulas Dependence and Function Notation
  358.    wt: 2:   3 GE III Equation Addition and Multiplication
  359.    wt: 2:   Skill Development Notes
  360.    wt: 2:   10 One Example
  361.    wt: 2:   9 Three Examples
  362.    wt: 2:   8 One Example
  363.    wt: 2:   7 Two Examples
  364.    wt: 2:   5 Three Examples
  365.    wt: 2:   4 Two Examples
  366.    wt: 2:   3 Two Examples
  367.    wt: 2:   2 Three Examples
  368.    wt: 2:   8 Sets of Numbers
  369.    wt: 2:   5 Talking about Numbers and Quantities
  370.    wt: 2:   016 Numbering Occidental Calendar Days
  371.    wt: 2:   015 School and work day counting tables
  372.    wt: 2:   012 Division of Time Intervals by Time Intervals
  373.    wt: 2:   010 Repeated Addition of Time Intervals
  374.    wt: 2:   8 Addition of Time Intervals via subtotaling
  375.    wt: 2:   7 Addition of Time Intervals
  376.    wt: 2:   2 Time and Date Matters in School
  377.    wt: 2:   Example 2 volume of a cone
  378.    wt: 2:   Example 1 volume of a pyramid
  379.    wt: 2:   Volume of Solid by Cross Sections Lesson
  380.    wt: 2:   Example 1. Area Between x and x squared
  381.    wt: 2:   Example 4 with x function of y
  382.    wt: 2:   38 Formulas and derivatives for powers and roots
  383.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  384.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  385.    wt: 2:   9 Limits Continuity and Composition
  386.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  387.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  388.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  389.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  390.    wt: 2:   Appendix E. How To Study Mathematics and Why
  391.    wt: 2:   Appendix D. What to do in School and Why
  392.    wt: 2:   Chapter 31 Direct and Indirect Reason
  393.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  394.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  395.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  396.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  397.    wt: 2:   Chapter 20. Degrees and Radians
  398.    wt: 2:   Chapter 19. Functions and Sets
  399.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  400.    wt: 2:   Chapter 12. Shorthand Usage Guide
  401.    wt: 2:   Chapter 11. Why Shorthand
  402.    wt: 2:   Chapter 10 Describing and Changing Calculations
  403.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  404.    wt: 2:   Chapter 8 Three Skills For Algebra
  405.    wt: 2:   Chapter 6 Change of Language
  406.    wt: 2:   Chapter 4 Longer Chains of Reason
  407.    wt: 2:   Chapter 3 Chains of Reason
  408.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  409.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  410.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  411.    wt: 2:   R Why Learn Mathematics Skills
  412.    wt: 2:   O On Learning Mathematics and Science
  413.    wt: 2:   L Skills with take home value
  414.    wt: 2:   N Improving Marks on Tests and Finals
  415.    wt: 2:   J. More on written work and showing skill
  416.    wt: 2:   H Jigsaw puzzles and problem solving
  417.    wt: 2:   G. Written work formats for developing and showing skill
  418.    wt: 2:   E. When and how to correct errors
  419.    wt: 2:   C. Domino effect of being careful
  420.    wt: 2:   B. Domino effect of errors
  421.    wt: 1:   Appendix 1 primary and preschool mathematic
  422.    wt: 1:   G LAMP Introduction Problem Solving Skills
  423.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  424.    wt: 1:   Skills Chapter 5 Calculus
  425.    wt: 1:   Skills Chapter 4 Logic
  426.    wt: 1:   Skills Chapter 3 Algebra
  427.    wt: 1:   Skills Chapter 2 Geometry
  428.    wt: 1:   Skills Chapter 1 Arithmetic
  429.    wt: 1:   Skills Chapter 0 Introduction
  430.    wt: 1:   7 logic review and decimals an odd combination
  431.    wt: 1:   5 logarithms and exponentials etc
  432.    wt: 1:   2 arithmetic with signed numbers
  433.    wt: 1:   1 arithmetic with unsigned numbers
  434.    wt: 1:   key notes and themes
  435.    wt: 1:   Mathematics Education Professors
  436.    wt: 1:   what should be learnt and When
  437.    wt: 1:   standards for course material
  438.    wt: 1:   Education in mathematics science and technology
  439.    wt: 1:   Different Kinds of Reasoning in maths
  440.    wt: 1:   three kinds of reason in mathematics
  441.    wt: 1:   Motivation and Context Problem
  442.    wt: 1:   fairness and inductive principles for instruction
  443.    wt: 1:   E Kirchoffs Second Law
  444.    wt: 1:   D Kirchoff First Law
  445.    wt: 1:   Home Tutoring and Home Schooling
  446.    wt: 1:   24 Standards For Skill Develoment Take II
  447.    wt: 1:   24 Standards For Skill Develoment
  448.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  449.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  450.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  451.    wt: 1:   17 Math Booklets for children and young teenagers
  452.    wt: 1:   13 Addition and Addition Tables
  453.    wt: 1:   12 Goals and Objectives For Mathematics
  454.    wt: 1:   11 Help and Defend Your Child or Teens Education
  455.    wt: 1:   8 The Effect of Negative Remarks
  456.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  457.    wt: 1:   5 Patience Please for Yourself and Your Charges
  458.    wt: 1:   4 Learning Takes Time and Effort
  459.    wt: 1:   1 Speaking Skills
  460.    wt: 1:   Ages 12 to 14 Geometry
  461.    wt: 1:   Ages 12 to 14 Arithmetic
  462.    wt: 1:   Ages 10 to 12 Geometry
  463.    wt: 1:   Ages 10 to 12 Arithmetic
  464.    wt: 1:   Ages 9 to 10
  465.    wt: 1:   Ages 8 to 9
  466.    wt: 1:   Ages 7 to 8
  467.    wt: 1:   Ages 6 to 7
  468.    wt: 1:   Ages 4 plus to 5 plus
  469.    wt: 1:   Ages 3 plus to 4 plus
  470.    wt: 1:   26 Function definitions done and coming
  471.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  472.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  473.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  474.    wt: 1:   19 Horizontal line rule and method
  475.    wt: 1:   18 Vertical Line Rule and Method
  476.    wt: 1:   17 Function maxima minima and their location
  477.    wt: 1:   15 Sign analysis of functions
  478.    wt: 1:   11 Function Domain Range Source and Targets
  479.    wt: 1:   9 Set theory term relation possible origins
  480.    wt: 1:   6 Set Existence Formation and Notation
  481.    wt: 1:   4 Function notation in and beyond mathematics
  482.    wt: 1:   2 Algebraic use of function notation
  483.    wt: 1:   1 Geometric Introduction of Function Notation
  484.    wt: 1:   9 quadratics physical and further context
  485.    wt: 1:   8 quadratics backward use of various formulas
  486.    wt: 1:   6 quadratics numerical approach
  487.    wt: 1:   4 quadratics difference of two squares
  488.    wt: 1:   11 Growth and Decay in Biology
  489.    wt: 1:   10 Exponential Growth and Decay Models
  490.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  491.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  492.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  493.    wt: 1:   3 Polynomials Multiplication Addition
  494.    wt: 1:   2 Column Multiplication Method
  495.    wt: 1:   16 cotangent function Definition Graph and Inverse
  496.    wt: 1:   15 cosecant function Definition Graph and Inverse
  497.    wt: 1:   14 secant function Definition Graph and Inverse
  498.    wt: 1:   13 cosecant function Definition Graph and Inverse
  499.    wt: 1:   11 arctan left inverse of tangent Graph
  500.    wt: 1:   10 arctan left inverse of tangent Definition
  501.    wt: 1:   8 arcsin left inverse of sine Graph
  502.    wt: 1:   7 arcsin left inverse of sine Definition
  503.    wt: 1:   6 Graph of arccos function
  504.    wt: 1:   3 Left Inverse of cosine arccos definition
  505.    wt: 1:   7 Radian Measures in special Triangles
  506.    wt: 1:   6 Radian Measure to Degrees
  507.    wt: 1:   5 Degrees to Radian Measure
  508.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  509.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  510.    wt: 1:   A Global Time and Navigation
  511.    wt: 1:   15 Dot and Cross Product
  512.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  513.    wt: 1:   4 graphing y=Asin(x c)
  514.    wt: 1:   3 graphing y=f(x c) plus K
  515.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  516.    wt: 1:   1 graphing y=f(x a)
  517.    wt: 1:   Triangle Angles Sum To 180 Degrees
  518.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  519.    wt: 1:   Straight Lines ASA Intersection Study More
  520.    wt: 1:   Straight Lines ASA Intersection Study
  521.    wt: 1:   Straight Lines Instersection Solving Equations
  522.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  523.    wt: 1:   C Straight Lines Slope from Coordinates
  524.    wt: 1:   B Straight Line Slope Scaling Properties More
  525.    wt: 1:   A Straight Line Slope Scaling Properties
  526.    wt: 1:   14 Straight Lines Equations General Case
  527.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  528.    wt: 1:   12 Straight Lines Graphing mx plus b
  529.    wt: 1:   11 Straight Lines Graphing y=mx
  530.    wt: 1:   10 Straight Lines through Origin Equations More
  531.    wt: 1:   9 Straight Lines through Origin Equations
  532.    wt: 1:   8 Straight Lines Equation for vertical
  533.    wt: 1:   7 Tangent Function is odd on this domain
  534.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  535.    wt: 1:   5 Tangent Function Graph
  536.    wt: 1:   4 Tangent Function Properties
  537.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  538.    wt: 1:   1 Straight Lines Slope Concept
  539.    wt: 1:   32 seven rows of pascals triangle
  540.    wt: 1:   30 unit circle calculation of six trigonometric functions
  541.    wt: 1:   29 secant cosecant and cotangent for acute angles
  542.    wt: 1:   28 Expressing products of sines cosines as sums
  543.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  544.    wt: 1:   21 sine and cosine Half Angle Formulas
  545.    wt: 1:   20 sine and cosine Double Angle Formulas
  546.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  547.    wt: 1:   18 sum of sinusoidal waves as a single wave
  548.    wt: 1:   17F Law of cosines
  549.    wt: 1:   17E Trig Formulas for dot and cross Products
  550.    wt: 1:   17D cis formulas for sine cosines and tangent
  551.    wt: 1:   17C sine and cosine double triple angle formulas
  552.    wt: 1:   17A The complex number valued trig function cis
  553.    wt: 1:   13 Graph of tangent function many periods
  554.    wt: 1:   12 Graph of tangent function for one period
  555.    wt: 1:   8 period of tangent function
  556.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  557.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  558.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  559.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  560.    wt: 1:   Unit Circle Development of Trigonometry
  561.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  562.    wt: 1:   15 Pythagorean Theorem Converse
  563.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  564.    wt: 1:   7 Second Way to Calculate Products
  565.    wt: 1:   3 Addition Properties
  566.    wt: 1:   1 Rectangular Polar Coordinates Review
  567.    wt: 1:   8 Triangles Cascade Problem Solving
  568.    wt: 1:   1 Angle Measurement with Degrees
  569.    wt: 1:   Why Trigonometry the whyslopes view
  570.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  571.    wt: 1:   9 Similarity of Triangles Usual Criteria
  572.    wt: 1:   1 Early Concept of Like or Similar Shapes
  573.    wt: 1:   Four Simple Exercises
  574.    wt: 1:   12 Links Lessons elsewhere
  575.    wt: 1:   11 A Partial Summary
  576.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  577.    wt: 1:   8 Mid Point Formula
  578.    wt: 1:   4 Equations for lines three forms
  579.    wt: 1:   3 Slope product for perpendicular lines
  580.    wt: 1:   2 point slope equation for a line
  581.    wt: 1:   13 Pythagorean spatial distance formulas
  582.    wt: 1:   12 Spatial Coordinates
  583.    wt: 1:   11 Triangle Inequality
  584.    wt: 1:   10 Pythagorean plane distance formula
  585.    wt: 1:   8 Distance Between Points on a Line
  586.    wt: 1:   3 Rectangular Coordinates Review
  587.    wt: 1:   2 Cartesian Coordinates with signs
  588.    wt: 1:   1 Cartesian Coordinates sans signs
  589.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  590.    wt: 1:   PS G Rotation Distributes over Addition
  591.    wt: 1:   PS D Addition with Cartesian Coordinates
  592.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  593.    wt: 1:   PS B Parallelogram Construction Methods
  594.    wt: 1:   PS A Kite Construction Methods
  595.    wt: 1:   21 Parallelograms
  596.    wt: 1:   19 Right Triangle Similarity
  597.    wt: 1:   18 Triangle Similarity Take 1
  598.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  599.    wt: 1:   14 Parallel Lines Postulate
  600.    wt: 1:   13 Angle Side Angle Failure
  601.    wt: 1:   12 Side Angle Side Failure
  602.    wt: 1:   11 Triangle Construction Fails
  603.    wt: 1:   10 Dropping a perpendicular to line
  604.    wt: 1:   8 Isoceles Triangles
  605.    wt: 1:   7 Angle Side Angle
  606.    wt: 1:   5 Side Angle Side
  607.    wt: 1:   4 Side Side Side
  608.    wt: 1:   2 Correspondence between Triangles
  609.    wt: 1:   Short Course on Euclidean Geometry
  610.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  611.    wt: 1:   26 More Less Greater Than Comparison
  612.    wt: 1:   23 Distributive Law Two Derivations
  613.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  614.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  615.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  616.    wt: 1:   15 Head to Tails in place Addition Associative
  617.    wt: 1:   9 Division with Digits after Decimal Point
  618.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  619.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  620.    wt: 1:   4 Fraction Operations Axiomatic Development
  621.    wt: 1:   3 Inequalities Algebraically
  622.    wt: 1:   2 Fraction Operations Physical Development
  623.    wt: 1:   3 Proportionality Examples
  624.    wt: 1:   2 Algebraic View
  625.    wt: 1:   1 What is Proportionality
  626.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  627.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  628.    wt: 1:   6 Compound Interest Forward and Backwards
  629.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  630.    wt: 1:   5 Equality in Algebra
  631.    wt: 1:   3 Product Axioms Two Forms
  632.    wt: 1:   1 Equivalent Computation Rules
  633.    wt: 1:   5 Greater More Less Than Signs in General
  634.    wt: 1:   9 Coordinates for Regions in Space
  635.    wt: 1:   2 Integers
  636.    wt: 1:   5 Independent versus Dependent Variables
  637.    wt: 1:   4 Changing Letters
  638.    wt: 1:   2 Computation Rules Evaluation
  639.    wt: 1:   6 Algebraic Solution Example
  640.    wt: 1:   11 Volume of Sphere
  641.    wt: 1:   10 Volume of Pyramid
  642.    wt: 1:   9 Volume of Cone
  643.    wt: 1:   2 Another Rectangle Area Formula Example
  644.    wt: 1:   1 Written work formats for developing and showing skill
  645.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  646.    wt: 1:   9 Sets in Probability and Statistics
  647.    wt: 1:   6 Three Notions of What is a Variable
  648.    wt: 1:   1 Three Skills For Algebra
  649.    wt: 1:   014 Counting Days with Calendars
  650.    wt: 1:   013 Travel Time Tables
  651.    wt: 1:   6 How long is a million seconds
  652.    wt: 1:   5 Conversion Arithmetic
  653.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  654.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  655.    wt: 1:   Example 3
  656.    wt: 1:   Example 2
  657.    wt: 1:   Example 1
  658.    wt: 1:   Area Between Curves Lesson Take 2
  659.    wt: 1:   Area Between Curves Lesson Take 1
  660.    wt: 1:   Summary
  661.    wt: 1:   34 Derivative of exponential function
  662.    wt: 1:   31 Derivatives of inverse functions
  663.    wt: 1:   30Chain Rule A Proof
  664.    wt: 1:   28 Chain Rule Preparation for a Proof
  665.    wt: 1:   15 sine and cosine derivatives 3rd step
  666.    wt: 1:   14 sine and cosine derivatives 2nd step
  667.    wt: 1:   13 sine and cosine derivatives 1st step
  668.    wt: 1:   8 Differentiation of polynomials
  669.    wt: 1:   11 Limits at infinity Three Examples
  670.    wt: 1:   10 Three one sided limits with infinite values
  671.    wt: 1:   8 Four Animated Examples
  672.    wt: 1:   7 Evaluation by immediate or delayed substitution
  673.    wt: 1:   6 Continuity at a point
  674.    wt: 1:   4 Numerical properties
  675.    wt: 1:   3 Decimal insights for limits continuity convergence
  676.    wt: 1:   2 Algebraic codification
  677.    wt: 1:   1 Numerical introduction
  678.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  679.    wt: 1:   .H1 First Fundamental Theorem of Calculus
  680.    wt: 1:   G.3 Constant Difference Theorem Proof
  681.    wt: 1:   E2 Algebraic Properties of Limits
  682.    wt: 1:   D2 Limits of Monotone Sequences
  683.    wt: 1:   PostScript For and Against Decimal Perspectives
  684.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  685.    wt: 1:   Chapter 22 Complex Numbers
  686.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  687.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  688.    wt: 1:   Chapter 12. Units and Slopes
  689.    wt: 1:   Chapter 10 Slopes and Units
  690.    wt: 1:   Chapter 7 Slopes and Velocity
  691.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  692.    wt: 1:   Chapter 2. Slopes and Ski Trails
  693.    wt: 1:   Postscript More on Better Performance
  694.    wt: 1:   Postscript For Better Performance
  695.    wt: 1:   Appendix C. How to Read
  696.    wt: 1:   Appendix B. How To Learn
  697.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  698.    wt: 1:   Chapter 30 Truth Tables
  699.    wt: 1:   Chapter 28 Occurrence Tables
  700.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  701.    wt: 1:   Chapter 25. Mathematical Induction Examples
  702.    wt: 1:   Chapter 25. Mathematical Induction Examples
  703.    wt: 1:   Chapter 23. Notation For Sums
  704.    wt: 1:   Chapter 21. Third Reading Guide
  705.    wt: 1:   Chapter 18. Rules for Algebra
  706.    wt: 1:   Chapter 16. Painless Theorem Proving
  707.    wt: 1:   Chapter 15. Solving Linear Equations
  708.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  709.    wt: 1:   Chapter 13. Second Reading Guide
  710.    wt: 1:   Postscript What is a Variable
  711.    wt: 1:   Solutions For Arithmetic Exercises
  712.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  713.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  714.    wt: 1:   Foreword
  715.    wt: 1:   Chapter 7 Two Treatments of Geometry
  716.    wt: 1:   Chapter 2 For and Against Mathematics
  717.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  718.    wt: 1:   Postscript B More on Story Telling and Reason
  719.    wt: 1:   Chapter 24 Direct and Indirect Reason
  720.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  721.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  722.    wt: 1:   Chapter 18 Sense and Knowledge
  723.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  724.    wt: 1:   Chapter 8 Change of Language
  725.    wt: 1:   Chapter 7 Longer Chains of Reason
  726.    wt: 1:   Chapter 6 Chains of Reason
  727.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  728.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  729.    wt: 1:   S Adding words to algebra
  730.    wt: 1:   N Mathematics Prepare for College Studies
  731.    wt: 1:   M Words to extend arithmetic
  732.    wt: 1:   H more Routine to non routine problem solving
  733.    wt: 1:   F. The student teacher tutor feedback loop
  734.    wt: 1:   D. Check work a must with a caution
  735.    wt: 1:   A. Skill has to be seen to believed
  736.    wt: 1:   Helping the Blind in Logic and Mathematics
  737.    wt: 1:   More Algebra and Slope based Calculus Preview
  738.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  739.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  740.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  741.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  742.    wt: 1:   Montreal Basic and Advanced Mathematics Tutoring
  743.    wt: 14:   C Equality for Fractions and Two Term Ratios and Fractions
  744.    wt: 12:   B Fractions and Two Term Ratios
  745.    wt: 12:   A Similarities between Fractions and Two Term Ratios
  746.    wt: 12:   10 Simplification of Fractions and Mixed Numerals
  747.    wt: 12:   9 Improper Fractions and Mixed Numbers
  748.    wt: 11:   21 Reciprocals for Fractions and Wholes
  749.    wt: 10:   3 Comparison of Negative Numbers
  750.    wt: 10:   1 More and Less Than for Counts and Measures
  751.    wt: 10:   D Three Term Ratios
  752.    wt: 10:   22 Complex Compound Fractions
  753.    wt: 10:   20 Dividing Fractions the Why
  754.    wt: 10:   19 Dividing Fractions How TO
  755.    wt: 10:   17 Efficient Ways to Add and Subtract
  756.    wt: 10:   15 Adding and Subtracting with Unlike Denominators
  757.    wt: 10:   14 Adding and Subtracting with Like Denominators
  758.    wt: 10:   6 Multiplication Algebraically Take II
  759.    wt: 10:   5 Equivalent Fractions
  760.    wt: 10:   4 Fraction Multiplication
  761.    wt: 10:   3 Unit fraction of a fraction
  762.    wt: 10:   2 Unit Fraction Multiplication

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Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills.

Mathematics Skills For Ages 3 to 14

Skills with take home value

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

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Logic-Reason for all
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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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