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

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

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

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

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

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

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

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54 matches:

  1.    wt: 6:   Step 2 Algebraic solutions for one unknown/
  2.    wt: 6:   2 Formula Forward Use Evaluation/
  3.    wt: 6:   12 Comparison of Unsigned and Signed Numbers/
  4.    wt: 6:   Volume 2 Three Skills For Algebra/
  5.    wt: 4:   10 Examples of Algebraic Reasoning/
  6.    wt: 4:   8 Unifying Theme For Algebra/
  7.    wt: 4:   B Decimal Comparing and Subtracting Methods/
  8.    wt: 3:   2 Natural Logarithms Exponentials Powers Roots/
  9.    wt: 3:   A Origins of Counting and Figuring Methods/
  10.    wt: 3:   9 Proportionality Backwards and Forwards/
  11.    wt: 3:   6 More Less Greater Than Inequalities and Comparison/
  12.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  13.    wt: 3:   D Decimal Long Division Methods/
  14.    wt: 3:   C Decimal Multiplication Methods/
  15.    wt: 3:   A Decimal Counting and Adding Methods/
  16.    wt: 3:   2 Arithmetic with Decimals/
  17.    wt: 2:   5 Factored Polynomial Sign Analysis Examples/
  18.    wt: 2:   12 Function Translating and Rescaling/
  19.    wt: 2:   2 Euclidean Geometry Constructions Theory extras/
  20.    wt: 2:   B Real Numbers Extrinsic Development/
  21.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  22.    wt: 2:   5 Real Numbers/
  23.    wt: 2:   4 Computation Rules and Function Notation/
  24.    wt: 2:   Step 4 Gaussian Elimination/
  25.    wt: 2:   Step 1 Stick diagram and fractions/
  26.    wt: 2:   3 Solving Linear Equations/
  27.    wt: 2:   1 Working With Sets/
  28.    wt: 2:   Algebra Starter Lessons/
  29.    wt: 2:   8 Arithmetic with Signed Numbers/
  30.    wt: 2:   3 Prime Factorization Skills/
  31.    wt: 2:   Volume 1 Elements of Reason/
  32.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  33.    wt: 1:   Mathematics Skills Year by Year/
  34.    wt: 1:   4 Functions/
  35.    wt: 1:   3 Quadratics Geometrically/
  36.    wt: 1:   1 Five Polynomial Operations/
  37.    wt: 1:   More Algebra/
  38.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  39.    wt: 1:   11 Squares and Square Roots/
  40.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  41.    wt: 1:   9 Combinatorics Trees Tables and Products/
  42.    wt: 1:   7 Arithmetic and Fractions with Units/
  43.    wt: 1:   6 Fractions and Ratios/
  44.    wt: 1:   5 Integers/
  45.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  46.    wt: 1:   1 Decimal Place Value/
  47.    wt: 1:   Arithmetic and Number Theory Skills/
  48.    wt: 1:   Time Date Matters/
  49.    wt: 1:   Skills with take home value/
  50.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  51.    wt: 1:   38 Lessons on Calculating Derivatives/
  52.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  53.    wt: 1:   Volume 1A Pattern Based Reason/
  54.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/

Web Page Search

591 matches:

  1.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  2.    wt: 4:   2 Algebraic use of function notation
  3.    wt: 4:   27 Logarithmic use of products of sines and cosines
  4.    wt: 4:   26 Formulas for products of sines and cosines
  5.    wt: 4:   23 sine and cosine of 180 plus 22.5 degrees
  6.    wt: 4:   22 Multiplication of Signed Numbers
  7.    wt: 4:   1 Three Skills For Algebra
  8.    wt: 4:   2 Groups of Three Place Value for Multidigit Decimals
  9.    wt: 4:   E2 Algebraic Properties of Limits
  10.    wt: 4:   Chapter 14. Forward and Backward Use of a Formula
  11.    wt: 4:   Chapter 8 Three Skills For Algebra
  12.    wt: 3:   02 21 words for teachers
  13.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  14.    wt: 3:   8 quadratics backward use of various formulas
  15.    wt: 3:   12 Graph of tangent function for one period
  16.    wt: 3:   12 cis formulas for sine cosines and tangent
  17.    wt: 3:   2 Similar Triangles Equality of Corresponding Side Ratios
  18.    wt: 3:   4 Equations for lines three forms
  19.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  20.    wt: 3:   21 Addition of Multiples of a Single Vector
  21.    wt: 3:   1 Proper Equal Sign Usage
  22.    wt: 3:   16 GCD and LCM of 650 225 via Prime
  23.    wt: 3:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  24.    wt: 3:   12 GCD 2700 288 via Prime
  25.    wt: 3:   2 signed and unsigned numbers as coordinates
  26.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  27.    wt: 3:   24 Divisibility Tests for 2 3 5 9 10
  28.    wt: 3:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  29.    wt: 3:   28 Chain Rule Preparation for a Proof
  30.    wt: 3:   22 Chain Rule for polynomials
  31.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  32.    wt: 3:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  33.    wt: 2:   Skills Chapter 3 Algebra
  34.    wt: 2:   Skills Chapter 2 Geometry
  35.    wt: 2:   2 arithmetic with signed numbers
  36.    wt: 2:   three goals to set for students
  37.    wt: 2:   geometric implications for algebra
  38.    wt: 2:   three goals for Mathematics Education
  39.    wt: 2:   02 20 mathematics education references
  40.    wt: 2:   three aims for mathematics students
  41.    wt: 2:   formal or informal peer review
  42.    wt: 2:   three kinds of reason in mathematics
  43.    wt: 2:   Prequel In For A Penny In For A Pound
  44.    wt: 2:   2 Conductance Resistance Duality02
  45.    wt: 2:   C Electromotive force conventional current02
  46.    wt: 2:   24 Standards For Skill Develoment Take II
  47.    wt: 2:   24 Standards For Skill Develoment
  48.    wt: 2:   22 Student Centered Highschool Mathematics
  49.    wt: 2:   12 Goals and Objectives For Mathematics
  50.    wt: 2:   2 Reading and Writing Skills
  51.    wt: 2:   Ages 12 to 14 Skills with take home value
  52.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  53.    wt: 2:   sign monoticity analysis example 2
  54.    wt: 2:   22 Square Root function graphically
  55.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  56.    wt: 2:   15 Sign analysis of functions
  57.    wt: 2:   5 Function notation for geometric transformations
  58.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  59.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  60.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  61.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  62.    wt: 2:   12 motivation for term arctan
  63.    wt: 2:   2 cosine function more properties
  64.    wt: 2:   2 Radian Measure Numerical Value of one degree
  65.    wt: 2:   4 Resultant of a Sum of Movements
  66.    wt: 2:   2 Signed Coordinates
  67.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  68.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  69.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  70.    wt: 2:   32 seven rows of pascals triangle
  71.    wt: 2:   29 secant cosecant and cotangent for acute angles
  72.    wt: 2:   28 Expressing products of sines cosines as sums
  73.    wt: 2:   25 tangent double angle formula Slope connection
  74.    wt: 2:   24 tangent Angle Difference Formula
  75.    wt: 2:   21 sine and cosine Half Angle Formulas
  76.    wt: 2:   20 sine and cosine Double Angle Formulas
  77.    wt: 2:   17E Trig Formulas for dot and cross Products
  78.    wt: 2:   17D cis formulas for sine cosines and tangent
  79.    wt: 2:   20 N th Roots of Complex Numbers
  80.    wt: 2:   13 Trig Formulas for dot and cross Products
  81.    wt: 2:   6 Field Properties of Complex Number
  82.    wt: 2:   5 An Easy Proof of the Distributive Law
  83.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  84.    wt: 2:   2 Similarity By Design
  85.    wt: 2:   5 Algebraic View of Slopes
  86.    wt: 2:   2 point slope equation for a line
  87.    wt: 2:   2 Cartesian Coordinates with signs
  88.    wt: 2:   A Measurement with Ruler Proper Use
  89.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  90.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  91.    wt: 2:   19 Signed Multiples of Vectors
  92.    wt: 2:   12 Real Numbers Line Signed Coordinates
  93.    wt: 2:   11 Signed Number Addition and Addition Properties
  94.    wt: 2:   2 Combing Counts Addition Skills and Principles
  95.    wt: 2:   3 Inequalities Algebraically
  96.    wt: 2:   2 Algebraic View
  97.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  98.    wt: 2:   5 Equality in Algebra
  99.    wt: 2:   2 More and Less Than for Counts and Measures
  100.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  101.    wt: 2:   2 Essentially one exercises three with solution
  102.    wt: 2:   2 Three Examples
  103.    wt: 2:   2 Three Examples
  104.    wt: 2:   Formula Usage Show Work Format
  105.    wt: 2:   2 Another Rectangle Area Formula Example
  106.    wt: 2:   1 Written work formats for developing and showing skill
  107.    wt: 2:   6 Three Notions of What is a Variable
  108.    wt: 2:   4 A Brief Story of numbers and algebra
  109.    wt: 2:   2 More and Less Than with Unlike Signs
  110.    wt: 2:   3 Properties of Square Roots with example
  111.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  112.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  113.    wt: 2:   5 lengths and signs of numbers
  114.    wt: 2:   4 signed coordinates for regions in space
  115.    wt: 2:   3 signed coordinates for maps and planes
  116.    wt: 2:   2 Equality and Units
  117.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  118.    wt: 2:   22 Complex Compound Fractions
  119.    wt: 2:   21 Working With Signs
  120.    wt: 2:   21 Reciprocals for Fractions and Wholes
  121.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  122.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  123.    wt: 2:   26 Divisibility by 2 3 5 Example
  124.    wt: 2:   23 Remainder Arithmetic Modulo 2
  125.    wt: 2:   22 Remainder Arithmetic Modulo 3 more
  126.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  127.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  128.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  129.    wt: 2:   20 Uniqueness of Prime Factorization
  130.    wt: 2:   15 video Factors of 20 using Prime Factorization
  131.    wt: 2:   14 video Factors of 24 Take II
  132.    wt: 2:   13 video Factors of 24 using prime
  133.    wt: 2:   Long Division forwards and backwards Example 2
  134.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  135.    wt: 2:   9 22 Minute Subtraction Review Video
  136.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  137.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  138.    wt: 2:   Quick history of numbers and algebra
  139.    wt: 2:   012 Division of Time Intervals by Time Intervals
  140.    wt: 2:   1 Intro of Kids To Time Date Skills
  141.    wt: 2:   Example 2 volume of a cone
  142.    wt: 2:   38 Formulas and derivatives for powers and roots
  143.    wt: 2:   21 Chain Rule for powers
  144.    wt: 2:   20 Chain Rule for Pulley Systems
  145.    wt: 2:   17 Derivatives of quotients of sine and cosine
  146.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  147.    wt: 2:   3 Motivation for Limit Definition Take 2
  148.    wt: 2:   2 Motivation for Limit Definition Take 1
  149.    wt: 2:   2 Algebraic codification
  150.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  151.    wt: 2:   D2 Limits of Monotone Sequences
  152.    wt: 2:   Chapter 22 Complex Numbers
  153.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  154.    wt: 2:   Postscript For Better Performance
  155.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  156.    wt: 2:   Chapter 23. Notation For Sums
  157.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  158.    wt: 2:   Chapter 18. Rules for Algebra
  159.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  160.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  161.    wt: 2:   Chapter 2 For and Against Mathematics
  162.    wt: 2:   Chapter 22 Contrapositive and Vacuously True Implications
  163.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  164.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  165.    wt: 2:   G. Written work formats for developing and showing skill
  166.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  167.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  168.    wt: 1:   Appendix 2 primary school Arithmetic 01
  169.    wt: 1:   G LAMP Introduction Problem Solving Skills
  170.    wt: 1:   Skills Chapter 5 Calculus
  171.    wt: 1:   Skills Chapter 4 Logic
  172.    wt: 1:   Ramblings Introduction Algebra Essay
  173.    wt: 1:   Skills Chapter 1 Arithmetic
  174.    wt: 1:   Skills Chapter 0 Introduction
  175.    wt: 1:   4 algebra
  176.    wt: 1:   1 arithmetic with unsigned numbers
  177.    wt: 1:   permissions for teachers
  178.    wt: 1:   Applied Maths Program14092009 POMME variant
  179.    wt: 1:   activities for students
  180.    wt: 1:   Mathematics Education Professors
  181.    wt: 1:   Postscript 2007 01 10
  182.    wt: 1:   Education Reform Inconsistencies
  183.    wt: 1:   Secondary Three Mathematics
  184.    wt: 1:   talk the algebra talk
  185.    wt: 1:   three difficulties
  186.    wt: 1:   teaching tutoring algebraic reason
  187.    wt: 1:   Lessening Algebra Difficulties
  188.    wt: 1:   the trouble with algebra
  189.    wt: 1:   04 29 New Mathematics Curriculum
  190.    wt: 1:   04 25 when to stop or suspend mathemat
  191.    wt: 1:   standards for course material
  192.    wt: 1:   Theory of Knowledge
  193.    wt: 1:   Different Kinds of Reasoning in maths
  194.    wt: 1:   Four ways to improve education reform
  195.    wt: 1:   need for a mixed mathematics curriculum
  196.    wt: 1:   fairness and inductive principles for instruction
  197.    wt: 1:   words for mathematics instructor
  198.    wt: 1:   chapitre 12 00 les iles et division
  199.    wt: 1:   chapitre 04 02 Deuxieme enigme
  200.    wt: 1:   chapitre 02 00 La Communication des idees
  201.    wt: 1:   2 Energy Power Heat07
  202.    wt: 1:   B Energy Power02
  203.    wt: 1:   D Wire Resistance Calculation02
  204.    wt: 1:   B Wire Resistance Qualitative02
  205.    wt: 1:   2 Unlike resistors in parallel01
  206.    wt: 1:   H Series Circuit02
  207.    wt: 1:   E Kirchoffs Second Law
  208.    wt: 1:   D Kirchoff First Law
  209.    wt: 1:   B Electromotive force conventional current01
  210.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  211.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  212.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  213.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  214.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  215.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  216.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  217.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  218.    wt: 1:   17 Math Booklets for children and young teenagers
  219.    wt: 1:   15 Counting For Parents
  220.    wt: 1:   10 Ends values for work study instruction
  221.    wt: 1:   8 The Effect of Negative Remarks
  222.    wt: 1:   5 Patience Please for Yourself and Your Charges
  223.    wt: 1:   4 Learning Takes Time and Effort
  224.    wt: 1:   3 Preparing for Science Studies
  225.    wt: 1:   1 Speaking Skills
  226.    wt: 1:   Ages 12 to 14 Geometry
  227.    wt: 1:   Ages 12 to 14 Arithmetic
  228.    wt: 1:   Ages 10 to 12 Geometry
  229.    wt: 1:   Ages 10 to 12 Arithmetic
  230.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  231.    wt: 1:   sign monoticity analysis example 4
  232.    wt: 1:   sign monoticity analysis example 3
  233.    wt: 1:   sign monoticity analysis example 1
  234.    wt: 1:   26 Function definitions done and coming
  235.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  236.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  237.    wt: 1:   23 Inverse Functions
  238.    wt: 1:   20 Interchanging coordinates a reflection
  239.    wt: 1:   12 Function Domain Recognition Exercises
  240.    wt: 1:   8 Set view of relations and functions
  241.    wt: 1:   6 Set Existence Formation and Notation
  242.    wt: 1:   3 Formula or function graphing exercise
  243.    wt: 1:   1 Geometric Introduction of Function Notation
  244.    wt: 1:   7 quadratic formulla derivation
  245.    wt: 1:   4 quadratics difference of two squares
  246.    wt: 1:   2 quadratics graphing in general
  247.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  248.    wt: 1:   2 Square Root Simplification a prequel
  249.    wt: 1:   8 Notes for instructors or tutors
  250.    wt: 1:   2 Column Multiplication Method
  251.    wt: 1:   Rewriting algebraic substitution as function substitutions
  252.    wt: 1:   11 arctan left inverse of tangent Graph
  253.    wt: 1:   10 arctan left inverse of tangent Definition
  254.    wt: 1:   9 motivation for name arcsin
  255.    wt: 1:   8 arcsin left inverse of sine Graph
  256.    wt: 1:   7 arcsin left inverse of sine Definition
  257.    wt: 1:   6 Graph of arccos function
  258.    wt: 1:   4 possible motivation for term arccos
  259.    wt: 1:   3 Left Inverse of cosine arccos definition
  260.    wt: 1:   1 cosine function properties
  261.    wt: 1:   8 Radian Measures of Common Angles
  262.    wt: 1:   12 From Applied To Pure Mathematics
  263.    wt: 1:   1 Unsigned Coordinates
  264.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  265.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  266.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  267.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  268.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  269.    wt: 1:   Straight Lines Intersection of
  270.    wt: 1:   B Straight Line Slope Scaling Properties More
  271.    wt: 1:   A Straight Line Slope Scaling Properties
  272.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  273.    wt: 1:   12 Straight Lines Graphing mx plus b
  274.    wt: 1:   8 Straight Lines Equation for vertical
  275.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  276.    wt: 1:   4 Tangent Function Properties
  277.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  278.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  279.    wt: 1:   17 tangent function angle sum formulas
  280.    wt: 1:   30 unit circle calculation of six trigonometric functions
  281.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  282.    wt: 1:   18 sum of sinusoidal waves as a single wave
  283.    wt: 1:   17F Law of cosines
  284.    wt: 1:   17C sine and cosine double triple angle formulas
  285.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  286.    wt: 1:   13 Graph of tangent function many periods
  287.    wt: 1:   10 Graphs of sines and cosines many periods
  288.    wt: 1:   9 Graphs of sine and cosine over one period
  289.    wt: 1:   8 period of tangent function
  290.    wt: 1:   7 period of sine and cosine
  291.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  292.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  293.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  294.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  295.    wt: 1:   2 Quadrant I reference Angles
  296.    wt: 1:   Unit Circle Development of Trigonometry
  297.    wt: 1:   21 Logarithms Powers and Exponentials
  298.    wt: 1:   19 N th Roots of Unity
  299.    wt: 1:   18 Sixth Roots of Unity
  300.    wt: 1:   17 Cube Roots of unity
  301.    wt: 1:   14 Law of cosines
  302.    wt: 1:   11 sine and cosine double triple angle formulas
  303.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  304.    wt: 1:   8 Unit Circle Development of Trigonometry
  305.    wt: 1:   4 Multiplication Properties
  306.    wt: 1:   3 Addition Properties
  307.    wt: 1:   2 Complex Numbers made easier we hope
  308.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  309.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  310.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  311.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  312.    wt: 1:   12 Triangles Similarity More Problems
  313.    wt: 1:   9 Similarity of Triangles Usual Criteria
  314.    wt: 1:   8 Similarity of Triangles and Polygons
  315.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  316.    wt: 1:   3 Similarity by Design with coordinates
  317.    wt: 1:   1 Early Concept of Like or Similar Shapes
  318.    wt: 1:   12 Links Lessons elsewhere
  319.    wt: 1:   10 Midpoint of [a b] and [b a]
  320.    wt: 1:   8 Mid Point Formula
  321.    wt: 1:   6 Intersection of lines by solving linear systems
  322.    wt: 1:   3 Slope product for perpendicular lines
  323.    wt: 1:   1 Numerical view of lines and their equations
  324.    wt: 1:   13 Pythagorean spatial distance formulas
  325.    wt: 1:   12 Spatial Coordinates
  326.    wt: 1:   11 Triangle Inequality
  327.    wt: 1:   10 Pythagorean plane distance formula
  328.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  329.    wt: 1:   1 Cartesian Coordinates sans signs
  330.    wt: 1:   PS H Distributive Law For Complex Numbers
  331.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  332.    wt: 1:   21 Parallelograms
  333.    wt: 1:   17 Right Bisectors of Triangle Sides
  334.    wt: 1:   12 Side Angle Side Failure
  335.    wt: 1:   9 Construction of a right bisector
  336.    wt: 1:   3 Isometry of Triangles Congruence
  337.    wt: 1:   2 Correspondence between Triangles
  338.    wt: 1:   2 Measuring Area Directly
  339.    wt: 1:   A Signed Number Arithmetic Review
  340.    wt: 1:   26 More Less Greater Than Comparison
  341.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  342.    wt: 1:   23 Distributive Law Two Derivations
  343.    wt: 1:   8 Division and Mulplication of Compound Fractions
  344.    wt: 1:   4 Location of Point in Decimal Addition
  345.    wt: 1:   3 Location of Point in Decimal Multiplication
  346.    wt: 1:   2 Counting Digits in Decimal Multiplication
  347.    wt: 1:   C Three Decimal Subtraction Methods
  348.    wt: 1:   6 Column Methods for Decimal Multiplication
  349.    wt: 1:   5 Distributive Law for Whole Numbers
  350.    wt: 1:   4 Commutative Law Groups Counting Form
  351.    wt: 1:   3 Multiplicative Counting Skills Principles
  352.    wt: 1:   1 The Counting Origins of Numbers
  353.    wt: 1:   5 Areas of Rectangles Revisited
  354.    wt: 1:   2 Fraction Operations Physical Development
  355.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  356.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  357.    wt: 1:   6 Compound Interest Forward and Backwards
  358.    wt: 1:   5 Triangle Area Formula Backwards
  359.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  360.    wt: 1:   2 Linear Equation Literal Solution
  361.    wt: 1:   3 Product Axioms Two Forms
  362.    wt: 1:   2 Addition and Multiplication Axioms
  363.    wt: 1:   5 Greater More Less Than Signs in General
  364.    wt: 1:   4 Comparison of Negative Numbers
  365.    wt: 1:   3 More and Less Than with Unlike Signs
  366.    wt: 1:   12 Real Number Additive Inverses or Negatives
  367.    wt: 1:   10 Real Number Lengths and Signs
  368.    wt: 1:   9 Coordinates for Regions in Space
  369.    wt: 1:   8 Coordinates for Maps and Planes
  370.    wt: 1:   6 Unsigned Real Numbers
  371.    wt: 1:   2 Integers
  372.    wt: 1:   3 Geometric Formulas and Function Notation
  373.    wt: 1:   2 Computation Rules Evaluation
  374.    wt: 1:   1 Formulas Dependence and Function Notation
  375.    wt: 1:   2 GE II Comparison
  376.    wt: 1:   6 Algebraic Solution Example
  377.    wt: 1:   5 Algebraic Solutions Introduction
  378.    wt: 1:   9 Three Examples
  379.    wt: 1:   6 Three Examples
  380.    wt: 1:   5 Three Examples
  381.    wt: 1:   Using Letters for Physical Quantities
  382.    wt: 1:   13 Naming Identifying Formulas with Words
  383.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  384.    wt: 1:   11 Volume of Sphere
  385.    wt: 1:   10 Volume of Pyramid
  386.    wt: 1:   9 Volume of Cone
  387.    wt: 1:   8 Compound Interest Formula Evaluation
  388.    wt: 1:   7 Compound Interest Formula Introduction
  389.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  390.    wt: 1:   5 Box Volume Formula Example
  391.    wt: 1:   4 Circle Area Formula Example
  392.    wt: 1:   3 Triangle Area Formula Example
  393.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  394.    wt: 1:   8 Sets of Numbers
  395.    wt: 1:   2 Venn Diagrams
  396.    wt: 1:   2 What is a Variable
  397.    wt: 1:   arithmetic videos Real Player Format
  398.    wt: 1:   4 Greater More Less Than Signs in General
  399.    wt: 1:   3 Comparison of Negative Numbers
  400.    wt: 1:   1 More and Less Than for Counts and Measures
  401.    wt: 1:   2 Square Roots with Prime
  402.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  403.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  404.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  405.    wt: 1:   4 LCM of 8 and 10 via Prime
  406.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  407.    wt: 1:   2 Least Common Multiple LCM intro via list method
  408.    wt: 1:   2 Counting with Tables and Trees I
  409.    wt: 1:   10 dividing signed numbers
  410.    wt: 1:   9 subtracting signed numbers
  411.    wt: 1:   8 multiplying signed numbers
  412.    wt: 1:   6 adding signed numbers
  413.    wt: 1:   6 Simplification of Fractions with Units
  414.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  415.    wt: 1:   D Three Term Ratios
  416.    wt: 1:   20 Dividing Fractions the Why
  417.    wt: 1:   13 Fraction Comparison Algebraic View
  418.    wt: 1:   12 Fraction Comparison
  419.    wt: 1:   11 Simplification an Algebraic View
  420.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  421.    wt: 1:   9 Improper Fractions and Mixed Numbers
  422.    wt: 1:   6 Multiplication of Mixed Numbers
  423.    wt: 1:   6 Multiplication Algebraically Take II
  424.    wt: 1:   3 Unit fraction of a fraction
  425.    wt: 1:   2 Unit Fraction Multiplication
  426.    wt: 1:   12 Adding Integers More Examples
  427.    wt: 1:   11 Adding Integers Formulas and Examples
  428.    wt: 1:   10 Integer Multiplication Formulas
  429.    wt: 1:   8 Multiplication by Signed Numbers Integers
  430.    wt: 1:   7 Multiplication by Signs
  431.    wt: 1:   21 Remainder Arithmetic Modulo 3
  432.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  433.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  434.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  435.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  436.    wt: 1:   16 video Factors of 980 using prime
  437.    wt: 1:   12 LCD GCD and LCM using Primes
  438.    wt: 1:   11 Efficient Square Rule Use
  439.    wt: 1:   10 video Prime Factorization upto 23 squared
  440.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  441.    wt: 1:   2 Prime and Composites less than 16
  442.    wt: 1:   Long Division forwards and backwards Example 3
  443.    wt: 1:   Long Division forwards and backwards Example 1
  444.    wt: 1:   12 Why Long Division Works Take III
  445.    wt: 1:   4 Division with 2 Digit Divsors
  446.    wt: 1:   2 Division with Single Digit Divisors
  447.    wt: 1:   C Counting Areas with Powers of Ten
  448.    wt: 1:   B Powers of Ten
  449.    wt: 1:   A Elementary Basis for Multiplication Methods
  450.    wt: 1:   4 Two and Three Digit Multipliers
  451.    wt: 1:   2 One Digit Multipliers
  452.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  453.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  454.    wt: 1:   8 Subtraction with Units of Measure
  455.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  456.    wt: 1:   5 A Tip for Efficent Subtraction
  457.    wt: 1:   2 Subtraction Easy Case Examples
  458.    wt: 1:   8 What skills and work habits to require
  459.    wt: 1:   2 Decimal Counting Practices
  460.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  461.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  462.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  463.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  464.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  465.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  466.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  467.    wt: 1:   Formula Evaluation how to show work
  468.    wt: 1:   The 20 Times Table
  469.    wt: 1:   The 12 Times Table Visually
  470.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  471.    wt: 1:   011 Division of Time Intervals By Numbers
  472.    wt: 1:   010 Repeated Addition of Time Intervals
  473.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  474.    wt: 1:   8 Addition of Time Intervals via subtotaling
  475.    wt: 1:   7 Addition of Time Intervals
  476.    wt: 1:   4 Mixing and Changing Units of Time
  477.    wt: 1:   3 Units and Lengths of Time
  478.    wt: 1:   2 Time and Date Matters in School
  479.    wt: 1:   Example 1 volume of a pyramid
  480.    wt: 1:   Volume of Solid by Cross Sections Lesson
  481.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  482.    wt: 1:   Example 4 with x function of y
  483.    wt: 1:   Example 2
  484.    wt: 1:   Area Between Curves Lesson Take 2
  485.    wt: 1:   2 Indefinite Integrals Exercises
  486.    wt: 1:   2 Second derivative test prequel
  487.    wt: 1:   34 Derivative of exponential function
  488.    wt: 1:   31 Derivatives of inverse functions
  489.    wt: 1:   30Chain Rule A Proof
  490.    wt: 1:   29 Chain Rule Optional Reading
  491.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  492.    wt: 1:   26 Chain Rule Recognising outer inner functions
  493.    wt: 1:   25 Chain Rule Animated Examples Continued
  494.    wt: 1:   24 Chain Rule Animated Examples
  495.    wt: 1:   23 Chain Rule in general
  496.    wt: 1:   19 Chain Rule for linear functions
  497.    wt: 1:   14 sine and cosine derivatives 2nd step
  498.    wt: 1:   12 Quotient rule examples
  499.    wt: 1:   10 Power rule for negative integers
  500.    wt: 1:   8 Differentiation of polynomials
  501.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  502.    wt: 1:   11 Limits at infinity Three Examples
  503.    wt: 1:   10 Three one sided limits with infinite values
  504.    wt: 1:   5 Jumps and absence of unlimited error control
  505.    wt: 1:   4 Numerical properties
  506.    wt: 1:   3 Decimal insights for limits continuity convergence
  507.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  508.    wt: 1:   G.3 Constant Difference Theorem Proof
  509.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  510.    wt: 1:   F.2 Closed Range Theorem
  511.    wt: 1:   E1 Error Control Inequalities
  512.    wt: 1:   C Triangle Inequalities
  513.    wt: 1:   PostScript For and Against Decimal Perspectives
  514.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  515.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  516.    wt: 1:   Chapter 23 Links To Trigonometry
  517.    wt: 1:   Chapter 21 Arrow Addition
  518.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  519.    wt: 1:   Chapter 12. Units and Slopes
  520.    wt: 1:   Chapter 5. Slope Sign Tests
  521.    wt: 1:   Chapter 4. More Slope Sign Analysis
  522.    wt: 1:   Chapter 3. Slope Sign Analysis
  523.    wt: 1:   Chapter 2. Slopes and Ski Trails
  524.    wt: 1:   Foreword
  525.    wt: 1:   Postscript More on Better Performance
  526.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  527.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  528.    wt: 1:   Chapter 28 Occurrence Tables
  529.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  530.    wt: 1:   Chapter 25. Mathematical Induction Examples
  531.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  532.    wt: 1:   Chapter 21. Third Reading Guide
  533.    wt: 1:   Chapter 20. Degrees and Radians
  534.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  535.    wt: 1:   Chapter 12. Shorthand Usage Guide
  536.    wt: 1:   Solutions For Arithmetic Exercises
  537.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  538.    wt: 1:   Chapter 6 Change of Language
  539.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  540.    wt: 1:   Chapter 4 Longer Chains of Reason
  541.    wt: 1:   Chapter 3 Chains of Reason
  542.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  543.    wt: 1:   Foreword
  544.    wt: 1:   Postscript A Three Remarks
  545.    wt: 1:   Chapter 12 Four Phases
  546.    wt: 1:   Chapter 7 Two Treatments of Geometry
  547.    wt: 1:   Chapter 3 Algebra Difficulties
  548.    wt: 1:   Foreword
  549.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  550.    wt: 1:   Postscript C Consistency as a Tool for Reason
  551.    wt: 1:   Chapter 24 Direct and Indirect Reason
  552.    wt: 1:   Chapter 23 Truth Tables
  553.    wt: 1:   Chapter 21 Occurrence Tables
  554.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  555.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  556.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  557.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  558.    wt: 1:   Chapter 8 Change of Language
  559.    wt: 1:   Chapter 7 Longer Chains of Reason
  560.    wt: 1:   Chapter 6 Chains of Reason
  561.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  562.    wt: 1:   Chapter 2 Skill Development
  563.    wt: 1:   Three Remarks
  564.    wt: 1:   Foreword
  565.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  566.    wt: 1:   S Adding words to algebra
  567.    wt: 1:   R Why Learn Mathematics Skills
  568.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  569.    wt: 1:   N Mathematics Prepare for College Studies
  570.    wt: 1:   L Skills with take home value
  571.    wt: 1:   I. Logic and language skills
  572.    wt: 1:   C. Domino effect of being careful
  573.    wt: 1:   B. Domino effect of errors
  574.    wt: 1:   How to Build Skills and Confidence
  575.    wt: 1:   Chapter 6 More Algebra and Geometry
  576.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  577.    wt: 1:   Chapter 3 Algebra Starter Lessons
  578.    wt: 1:   Chapter 2 Why Sets
  579.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  580.    wt: 1:   7 Games and Activities for Instruction
  581.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  582.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  583.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  584.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  585.    wt: 1:   More Algebra and Slope based Calculus Preview
  586.    wt: 1:   Systematic Algebra Skill Development Missing Links
  587.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  588.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  589.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  590.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  591.    wt: 1:   The Math Forum and Site Content

Extended Search

948 matches:

  1.    wt: 9:   2 Three Examples
  2.    wt: 9:   1 Proper Equal Sign Usage
  3.    wt: 9:   2 More and Less Than with Unlike Signs
  4.    wt: 9:   Chapter 26 What is in chapters 27 to 31
  5.    wt: 9:   Chapter 23. Notation For Sums
  6.    wt: 9:   Chapter 2 Implication Rules Forwards and Backwards
  7.    wt: 8:   2 Another Rectangle Area Formula Example
  8.    wt: 8:   1 Written work formats for developing and showing skill
  9.    wt: 8:   Postscript For Better Performance
  10.    wt: 8:   Chapter 29 Contrapositive and Vacuously True Implications
  11.    wt: 8:   Chapter 28 Occurrence Tables
  12.    wt: 8:   Chapter 27 Shorthand Symbols as Pronouns
  13.    wt: 8:   Chapter 25. Mathematical Induction Examples
  14.    wt: 8:   Chapter 24. Personal Investment and Pension EGS
  15.    wt: 8:   Chapter 21. Third Reading Guide
  16.    wt: 8:   Chapter 20. Degrees and Radians
  17.    wt: 8:   Chapter 18. Rules for Algebra
  18.    wt: 8:   Postscript Unifying Theme A Fourth Skill For Algebra
  19.    wt: 8:   Chapter 12. Shorthand Usage Guide
  20.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  21.    wt: 7:   6 Algebraic Solution Example
  22.    wt: 7:   5 Algebraic Solutions Introduction
  23.    wt: 7:   13 Naming Identifying Formulas with Words
  24.    wt: 7:   12 Cone Cylinder Sphere Lesson Idea
  25.    wt: 7:   11 Volume of Sphere
  26.    wt: 7:   10 Volume of Pyramid
  27.    wt: 7:   9 Volume of Cone
  28.    wt: 7:   8 Compound Interest Formula Evaluation
  29.    wt: 7:   7 Compound Interest Formula Introduction
  30.    wt: 7:   6 Pythagorean Hypotenuse Calculation Example
  31.    wt: 7:   5 Box Volume Formula Example
  32.    wt: 7:   4 Circle Area Formula Example
  33.    wt: 7:   3 Triangle Area Formula Example
  34.    wt: 7:   4 Greater More Less Than Signs in General
  35.    wt: 7:   3 Comparison of Negative Numbers
  36.    wt: 7:   1 More and Less Than for Counts and Measures
  37.    wt: 7:   Postscript More on Better Performance
  38.    wt: 7:   Appendix B. How To Learn
  39.    wt: 7:   Appendix A. Reading Guide For Next Appendices
  40.    wt: 7:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  41.    wt: 7:   Solutions For Arithmetic Exercises
  42.    wt: 7:   Chapter 7 Prep for Calculus Arithmetic Exercises
  43.    wt: 7:   Chapter 6 Change of Language
  44.    wt: 7:   Chapter 5 Islands and Divisions of Knowledge
  45.    wt: 7:   Chapter 4 Longer Chains of Reason
  46.    wt: 7:   Chapter 3 Chains of Reason
  47.    wt: 7:   Chapter 1 Introduction to Chapters 2 to 6
  48.    wt: 7:   Foreword
  49.    wt: 6:   2 Algebraic use of function notation
  50.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  51.    wt: 6:   22 Multiplication of Signed Numbers
  52.    wt: 6:   21 Addition of Multiples of a Single Vector
  53.    wt: 6:   2 Combing Counts Addition Skills and Principles
  54.    wt: 6:   3 Inequalities Algebraically
  55.    wt: 6:   2 Algebraic View
  56.    wt: 6:   9 Circle Area and Perimeter Formula Backwards Forwards
  57.    wt: 6:   2 Essentially one exercises three with solution
  58.    wt: 6:   4 Four Examples Fractional Coefficients
  59.    wt: 6:   3 Four Examples
  60.    wt: 6:   1 Three Skills For Algebra
  61.    wt: 6:   2 signed and unsigned numbers as coordinates
  62.    wt: 6:   Long Division forwards and backwards Example 2
  63.    wt: 6:   Appendix 2 Three Decimal Subtraction Methods
  64.    wt: 6:   9 22 Minute Subtraction Review Video
  65.    wt: 6:   2 Subtraction Easy Case Examples
  66.    wt: 6:   2 Groups of Three Place Value for Multidigit Decimals
  67.    wt: 6:   Appendix E. How To Study Mathematics and Why
  68.    wt: 6:   Appendix D. What to do in School and Why
  69.    wt: 6:   Appendix C. How to Read
  70.    wt: 6:   Chapter 31 Direct and Indirect Reason
  71.    wt: 6:   Chapter 30 Truth Tables
  72.    wt: 6:   Chapter 19. Functions and Sets
  73.    wt: 6:   Chapter 16. Painless Theorem Proving
  74.    wt: 6:   Chapter 15. Solving Linear Equations
  75.    wt: 6:   Chapter 13. Second Reading Guide
  76.    wt: 6:   Chapter 11. Why Shorthand
  77.    wt: 6:   Chapter 10 Describing and Changing Calculations
  78.    wt: 6:   Postscript What is a Variable
  79.    wt: 6:   Chapter 9 Talking about Numbers or Quantities
  80.    wt: 5:   sign monoticity analysis example 2
  81.    wt: 5:   22 Square Root function graphically
  82.    wt: 5:   9 Formulas for Real Exponents with Logarithms
  83.    wt: 5:   8 Formulas for Fractional Exponents with Logarithms
  84.    wt: 5:   7 Formulas for Roots with Logarithms Derivation
  85.    wt: 5:   6 Formulas for Even and Odd Roots with Logarithms
  86.    wt: 5:   2 Square Root Simplification a prequel
  87.    wt: 5:   27 Logarithmic use of products of sines and cosines
  88.    wt: 5:   26 Formulas for products of sines and cosines
  89.    wt: 5:   24 Signed Numbers Arithmmetic Properties
  90.    wt: 5:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  91.    wt: 5:   19 Signed Multiples of Vectors
  92.    wt: 5:   12 Real Numbers Line Signed Coordinates
  93.    wt: 5:   11 Signed Number Addition and Addition Properties
  94.    wt: 5:   5 Areas of Rectangles Revisited
  95.    wt: 5:   2 Fraction Operations Physical Development
  96.    wt: 5:   8 Pythagorean Relation Forwards Backwards
  97.    wt: 5:   7 Pythagorean Theorem Chinese Square Proof
  98.    wt: 5:   6 Compound Interest Forward and Backwards
  99.    wt: 5:   5 Triangle Area Formula Backwards
  100.    wt: 5:   4 Rectangle Area and Like Formulas Backwards
  101.    wt: 5:   2 Linear Equation Literal Solution
  102.    wt: 5:   2 More and Less Than for Counts and Measures
  103.    wt: 5:   2 Three Examples
  104.    wt: 5:   16 GCD and LCM of 650 225 via Prime
  105.    wt: 5:   3 signed coordinates for maps and planes
  106.    wt: 5:   20 Uniqueness of Prime Factorization
  107.    wt: 5:   Long Division forwards and backwards Example 3
  108.    wt: 5:   12 Why Long Division Works Take III
  109.    wt: 5:   2 Division with Single Digit Divisors
  110.    wt: 5:   2 One Digit Multipliers
  111.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  112.    wt: 5:   Video Decimal Multiplication Geometric View Example 2
  113.    wt: 5:   Video Power Notation in Decimal Expansion
  114.    wt: 5:   8 Subtraction with Units of Measure
  115.    wt: 5:   7 Subtraction for Decimal Fractions with Exercises
  116.    wt: 5:   5 A Tip for Efficent Subtraction
  117.    wt: 5:   2 Decimal Counting Practices
  118.    wt: 5:   Chapter 22 Contrapositive and Vacuously True Implications
  119.    wt: 4:   2 arithmetic with signed numbers
  120.    wt: 4:   three goals for Mathematics Education
  121.    wt: 4:   02 21 words for teachers
  122.    wt: 4:   27 Graduated Correction and Penalties for Young Offenders
  123.    wt: 4:   22 Student Centered Highschool Mathematics
  124.    wt: 4:   Ages 12 to 14 Skills with take home value
  125.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  126.    wt: 4:   8 quadratics backward use of various formulas
  127.    wt: 4:   3 Natural Logarithms and Exponentials Basic Properties
  128.    wt: 4:   12 cis formulas for sine cosines and tangent
  129.    wt: 4:   2 Similar Triangles Equality of Corresponding Side Ratios
  130.    wt: 4:   PS H Distributive Law For Complex Numbers
  131.    wt: 4:   PS C Similarity Use Recognize it in Trigonometry
  132.    wt: 4:   PS B Parallelogram Construction Methods
  133.    wt: 4:   21 Parallelograms
  134.    wt: 4:   12 Side Angle Side Failure
  135.    wt: 4:   2 Correspondence between Triangles
  136.    wt: 4:   C Three Decimal Subtraction Methods
  137.    wt: 4:   6 Column Methods for Decimal Multiplication
  138.    wt: 4:   5 Distributive Law for Whole Numbers
  139.    wt: 4:   4 Commutative Law Groups Counting Form
  140.    wt: 4:   3 Multiplicative Counting Skills Principles
  141.    wt: 4:   1 The Counting Origins of Numbers
  142.    wt: 4:   4 Fraction Operations Axiomatic Development
  143.    wt: 4:   1 Decimals Modular and Remainder Arithmetic
  144.    wt: 4:   3 Linear Equation Literal Solution More
  145.    wt: 4:   1 Changing Calculations
  146.    wt: 4:   5 Equality in Algebra
  147.    wt: 4:   5 Greater More Less Than Signs in General
  148.    wt: 4:   4 Comparison of Negative Numbers
  149.    wt: 4:   3 More and Less Than with Unlike Signs
  150.    wt: 4:   12 Real Number Additive Inverses or Negatives
  151.    wt: 4:   10 Real Number Lengths and Signs
  152.    wt: 4:   5 Gaussian Elimination for 3 unknowns 2nd example
  153.    wt: 4:   2 GE II Comparison
  154.    wt: 4:   Formula Usage Show Work Format
  155.    wt: 4:   6 Three Notions of What is a Variable
  156.    wt: 4:   4 A Brief Story of numbers and algebra
  157.    wt: 4:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  158.    wt: 4:   12 GCD 2700 288 via Prime
  159.    wt: 4:   5 lengths and signs of numbers
  160.    wt: 4:   4 signed coordinates for regions in space
  161.    wt: 4:   22 Complex Compound Fractions
  162.    wt: 4:   21 Working With Signs
  163.    wt: 4:   21 Reciprocals for Fractions and Wholes
  164.    wt: 4:   2 Integers Multiplies of a Unit Moverment
  165.    wt: 4:   27 Divisibility by 2 3 6 5 9 10 Example
  166.    wt: 4:   25 Divisibility Tests for 2 3 5 9 10 Example
  167.    wt: 4:   24 Divisibility Tests for 2 3 5 9 10
  168.    wt: 4:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  169.    wt: 4:   18 Remainder Arithmetic Rule of 9 for checking sums II
  170.    wt: 4:   15 video Factors of 20 using Prime Factorization
  171.    wt: 4:   14 video Factors of 24 Take II
  172.    wt: 4:   13 video Factors of 24 using prime
  173.    wt: 4:   12 LCD GCD and LCM using Primes
  174.    wt: 4:   2 Prime and Composites less than 16
  175.    wt: 4:   Long Division Backwards more
  176.    wt: 4:   Long Division Backward
  177.    wt: 4:   Long Division forwards and backwards Example 1
  178.    wt: 4:   4 Division with 2 Digit Divsors
  179.    wt: 4:   C Counting Areas with Powers of Ten
  180.    wt: 4:   B Powers of Ten
  181.    wt: 4:   A Elementary Basis for Multiplication Methods
  182.    wt: 4:   4 Two and Three Digit Multipliers
  183.    wt: 4:   Appendix 1 Decimals Comparison Method Take II
  184.    wt: 4:   Subtraction with J Conversions Example
  185.    wt: 4:   Subtraction Another Video Lesson
  186.    wt: 4:   6 Subtraction with Conversion Example with Exercises
  187.    wt: 4:   4 Subtraction with Conversions Borrows and Letter J
  188.    wt: 4:   3 Harder Cases Convert to Compare and Subtract
  189.    wt: 4:   1 Comparison and Subtraction Easy Direct Cases
  190.    wt: 4:   8 What skills and work habits to require
  191.    wt: 4:   28 Chain Rule Preparation for a Proof
  192.    wt: 4:   22 Chain Rule for polynomials
  193.    wt: 4:   21 Chain Rule for powers
  194.    wt: 4:   16 Derivatives of reciprocals of sine and cosine
  195.    wt: 4:   G.2 Lipshitz Conditions Integration Calculus Reform
  196.    wt: 4:   E2 Algebraic Properties of Limits
  197.    wt: 4:   Chapter 22 Complex Numbers
  198.    wt: 4:   Chapter 2 For and Against Mathematics
  199.    wt: 4:   Chapter 12 Islands and Divisions of Knowledge
  200.    wt: 4:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  201.    wt: 3:   Skills Chapter 2 Geometry
  202.    wt: 3:   geometric implications for algebra
  203.    wt: 3:   Lessening Algebra Difficulties
  204.    wt: 3:   the trouble with algebra
  205.    wt: 3:   02 20 mathematics education references
  206.    wt: 3:   three aims for mathematics students
  207.    wt: 3:   three kinds of reason in mathematics
  208.    wt: 3:   Prequel In For A Penny In For A Pound
  209.    wt: 3:   B Energy Power02
  210.    wt: 3:   2 Conductance Resistance Duality02
  211.    wt: 3:   24 Standards For Skill Develoment Take II
  212.    wt: 3:   24 Standards For Skill Develoment
  213.    wt: 3:   12 Goals and Objectives For Mathematics
  214.    wt: 3:   2 Reading and Writing Skills
  215.    wt: 3:   Ages 12 to 14 Geometry
  216.    wt: 3:   Ages 12 to 14 Arithmetic
  217.    wt: 3:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  218.    wt: 3:   sign monoticity analysis example 4
  219.    wt: 3:   sign monoticity analysis example 3
  220.    wt: 3:   sign monoticity analysis example 1
  221.    wt: 3:   26 Function definitions done and coming
  222.    wt: 3:   25 Absolute Value greatest integer and saw tooth functions
  223.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  224.    wt: 3:   23 Inverse Functions
  225.    wt: 3:   20 Interchanging coordinates a reflection
  226.    wt: 3:   15 Sign analysis of functions
  227.    wt: 3:   12 Function Domain Recognition Exercises
  228.    wt: 3:   5 Function notation for geometric transformations
  229.    wt: 3:   11 Growth and Decay in Biology
  230.    wt: 3:   10 Exponential Growth and Decay Models
  231.    wt: 3:   5 Natural Logarithm Calculator Exercises
  232.    wt: 3:   1 Calculator Starter Exercises
  233.    wt: 3:   12 motivation for term arctan
  234.    wt: 3:   2 Signed Coordinates
  235.    wt: 3:   2 Graphing y=Af(x) Vertical Scaling
  236.    wt: 3:   B Straight Line Slope Scaling Properties More
  237.    wt: 3:   A Straight Line Slope Scaling Properties
  238.    wt: 3:   8 Straight Lines Equation for vertical
  239.    wt: 3:   6 Tangent Function Inclination Angle Take 2
  240.    wt: 3:   4 Tangent Function Properties
  241.    wt: 3:   3 Straight Lines Slope as Tangent of Inclination Angle
  242.    wt: 3:   2 Straight Lines Slopes As Rise Over Run
  243.    wt: 3:   33 sines and cosines of 2A 3A 4A 5A
  244.    wt: 3:   29 secant cosecant and cotangent for acute angles
  245.    wt: 3:   28 Expressing products of sines cosines as sums
  246.    wt: 3:   25 tangent double angle formula Slope connection
  247.    wt: 3:   24 tangent Angle Difference Formula
  248.    wt: 3:   21 sine and cosine Half Angle Formulas
  249.    wt: 3:   12 Graph of tangent function for one period
  250.    wt: 3:   20 N th Roots of Complex Numbers
  251.    wt: 3:   2 Similarity By Design
  252.    wt: 3:   4 Equations for lines three forms
  253.    wt: 3:   2 point slope equation for a line
  254.    wt: 3:   2 Cartesian Coordinates with signs
  255.    wt: 3:   PS G Rotation Distributes over Addition
  256.    wt: 3:   PS F Scalar Multiplication Distributes over Addition
  257.    wt: 3:   PS E Multiplication with Polar Coordinates
  258.    wt: 3:   PS D Addition with Cartesian Coordinates
  259.    wt: 3:   PS A Kite Construction Methods
  260.    wt: 3:   17 Right Bisectors of Triangle Sides
  261.    wt: 3:   9 Construction of a right bisector
  262.    wt: 3:   3 Isometry of Triangles Congruence
  263.    wt: 3:   A Signed Number Arithmetic Review
  264.    wt: 3:   26 More Less Greater Than Comparison
  265.    wt: 3:   25 Mid way Convergence to Axiomatic Approach
  266.    wt: 3:   23 Distributive Law Two Derivations
  267.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  268.    wt: 3:   17 Arrows Rotate to Reverse with Length Unchanged
  269.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  270.    wt: 3:   15 Head to Tails in place Addition Associative
  271.    wt: 3:   14 Vector Head to Tail Sums and Resultants
  272.    wt: 3:   13 Arrows and Vectors in a Plane
  273.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  274.    wt: 3:   8 Division and Mulplication of Compound Fractions
  275.    wt: 3:   4 Location of Point in Decimal Addition
  276.    wt: 3:   3 Location of Point in Decimal Multiplication
  277.    wt: 3:   2 Counting Digits in Decimal Multiplication
  278.    wt: 3:   E Long Division Methods more
  279.    wt: 3:   D Long Division Methods
  280.    wt: 3:   B Decimal Comparison and Subtraction
  281.    wt: 3:   A Decimal Addition Columm Methods
  282.    wt: 3:   8 Column Multiplication Methods in General
  283.    wt: 3:   7 Decimals Multiplication Methods Examples
  284.    wt: 3:   5 Proportionality in Equivalent Fractions
  285.    wt: 3:   4 Rates Ratios and Proporitionality
  286.    wt: 3:   3 Proportionality Examples
  287.    wt: 3:   1 What is Proportionality
  288.    wt: 3:   3 Product Axioms Two Forms
  289.    wt: 3:   2 Addition and Multiplication Axioms
  290.    wt: 3:   1 Real Numbers Comparison
  291.    wt: 3:   16 Real Numbers Comparison
  292.    wt: 3:   15 Real Number Division
  293.    wt: 3:   14 Real Number Multiplication
  294.    wt: 3:   13 Real Number Subtraction
  295.    wt: 3:   11 Real Number Addition
  296.    wt: 3:   9 Coordinates for Regions in Space
  297.    wt: 3:   8 Coordinates for Maps and Planes
  298.    wt: 3:   6 Unsigned Real Numbers
  299.    wt: 3:   2 Integers
  300.    wt: 3:   3 Geometric Formulas and Function Notation
  301.    wt: 3:   2 Computation Rules Evaluation
  302.    wt: 3:   1 Formulas Dependence and Function Notation
  303.    wt: 3:   4 Solving a triangular system exercise
  304.    wt: 3:   3 Solving triangular system example
  305.    wt: 3:   1 Essentially One Unknown
  306.    wt: 3:   9 Three Examples
  307.    wt: 3:   6 Three Examples
  308.    wt: 3:   5 Three Examples
  309.    wt: 3:   Using Letters for Physical Quantities
  310.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  311.    wt: 3:   8 Sets of Numbers
  312.    wt: 3:   2 Venn Diagrams
  313.    wt: 3:   2 What is a Variable
  314.    wt: 3:   3 Properties of Square Roots with example
  315.    wt: 3:   11 GCD 2700 288 via Euclid Algorithm
  316.    wt: 3:   10 Euclid Algorithm with 129 125 and with 45 14
  317.    wt: 3:   10 dividing signed numbers
  318.    wt: 3:   9 subtracting signed numbers
  319.    wt: 3:   8 multiplying signed numbers
  320.    wt: 3:   6 adding signed numbers
  321.    wt: 3:   2 Equality and Units
  322.    wt: 3:   C Equality for Fractions and Two Term Ratios and Fractions
  323.    wt: 3:   20 Dividing Fractions the Why
  324.    wt: 3:   2 Unit Fraction Multiplication
  325.    wt: 3:   12 Adding Integers More Examples
  326.    wt: 3:   26 Divisibility by 2 3 5 Example
  327.    wt: 3:   23 Remainder Arithmetic Modulo 2
  328.    wt: 3:   22 Remainder Arithmetic Modulo 3 more
  329.    wt: 3:   19 Remainder Arithmetic Rule of 9 for checking sums III
  330.    wt: 3:   17 Remainder Arithmetic Rule of 9 for checking sums I
  331.    wt: 3:   2 Remainder Arithmetic Modulo 10 more
  332.    wt: 3:   16 video Factors of 980 using prime
  333.    wt: 3:   11 Efficient Square Rule Use
  334.    wt: 3:   10 video Prime Factorization upto 23 squared
  335.    wt: 3:   6 Sieve of Eratosthenes and Square Rule
  336.    wt: 3:   Division with Counts and Length
  337.    wt: 3:   11 Another Single Digit Divisor Example
  338.    wt: 3:   10 Division by Five Long and Short Ways
  339.    wt: 3:   9 Why Long Division Works Take II
  340.    wt: 3:   8 Correcting the Mistake
  341.    wt: 3:   7 Long Divison Mistake Catching
  342.    wt: 3:   6 Why Decimal Long Division Methods Works Take I
  343.    wt: 3:   5 Long Division Include Zeroes or not
  344.    wt: 3:   3 Division Single Digit Divisor Example
  345.    wt: 3:   1 Divsion Physical Examples
  346.    wt: 3:   D Decimal Multiplication Methods Derived
  347.    wt: 3:   6 Multiplication Commutes Order Not Important
  348.    wt: 3:   5 Decimal Fraction Multiplication
  349.    wt: 3:   3 More One Digit Multipliers
  350.    wt: 3:   1 Why 3 times 5 gives 15
  351.    wt: 3:   Appendix 1 Counting Revisited 15 minute video
  352.    wt: 3:   7 Adding decimal fractions using decimal point
  353.    wt: 3:   6. Counting and adding units and mixed units
  354.    wt: 3:   5. How to add decimals C. Examples
  355.    wt: 3:   4. How to add with decimals B with conversions
  356.    wt: 3:   3. How to add with decimals A sans conversions
  357.    wt: 3:   1. Explaining Addition Table
  358.    wt: 3:   10 Names for Big Numbers and Powers of Ten Expansion
  359.    wt: 3:   9 Place Value Review Decimal form of Avogrados number included
  360.    wt: 3:   Quick history of numbers and algebra
  361.    wt: 3:   The 20 Times Table
  362.    wt: 3:   012 Division of Time Intervals by Time Intervals
  363.    wt: 3:   1 Intro of Kids To Time Date Skills
  364.    wt: 3:   Example 2 volume of a cone
  365.    wt: 3:   38 Formulas and derivatives for powers and roots
  366.    wt: 3:   30Chain Rule A Proof
  367.    wt: 3:   20 Chain Rule for Pulley Systems
  368.    wt: 3:   17 Derivatives of quotients of sine and cosine
  369.    wt: 3:   10 Power rule for negative integers
  370.    wt: 3:   8 Differentiation of polynomials
  371.    wt: 3:   4 Sum Rule
  372.    wt: 3:   3 Motivation for Limit Definition Take 2
  373.    wt: 3:   2 Motivation for Limit Definition Take 1
  374.    wt: 3:   2 Algebraic codification
  375.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  376.    wt: 3:   Chapter 12 Four Phases
  377.    wt: 3:   Postscript D Reflections on Law of the Excluded Middle
  378.    wt: 3:   Postscript C Consistency as a Tool for Reason
  379.    wt: 3:   Chapter 24 Direct and Indirect Reason
  380.    wt: 3:   Chapter 23 Truth Tables
  381.    wt: 3:   Chapter 21 Occurrence Tables
  382.    wt: 3:   Chapter 20 Shorthand Symbols as Pronouns
  383.    wt: 3:   Chapter 19 What is in chapters 20 to 24
  384.    wt: 3:   Chapter 2 Skill Development
  385.    wt: 3:   Three Remarks
  386.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  387.    wt: 3:   2 Identifying Size and Position Place and Spatial Sense
  388.    wt: 2:   Skills Chapter 3 Algebra
  389.    wt: 2:   4 algebra
  390.    wt: 2:   1 arithmetic with unsigned numbers
  391.    wt: 2:   three goals to set for students
  392.    wt: 2:   Applied Maths Program14092009 POMME variant
  393.    wt: 2:   Secondary Three Mathematics
  394.    wt: 2:   talk the algebra talk
  395.    wt: 2:   three difficulties
  396.    wt: 2:   teaching tutoring algebraic reason
  397.    wt: 2:   04 29 New Mathematics Curriculum
  398.    wt: 2:   04 25 when to stop or suspend mathemat
  399.    wt: 2:   formal or informal peer review
  400.    wt: 2:   fairness and inductive principles for instruction
  401.    wt: 2:   2 Energy Power Heat07
  402.    wt: 2:   C Electromotive force conventional current02
  403.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  404.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  405.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  406.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  407.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  408.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  409.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  410.    wt: 2:   Ages 10 to 12 Geometry
  411.    wt: 2:   Ages 10 to 12 Arithmetic
  412.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  413.    wt: 2:   8 Set view of relations and functions
  414.    wt: 2:   6 Set Existence Formation and Notation
  415.    wt: 2:   3 Formula or function graphing exercise
  416.    wt: 2:   1 Geometric Introduction of Function Notation
  417.    wt: 2:   7 quadratic formulla derivation
  418.    wt: 2:   4 quadratics difference of two squares
  419.    wt: 2:   2 quadratics graphing in general
  420.    wt: 2:   8 Notes for instructors or tutors
  421.    wt: 2:   2 Column Multiplication Method
  422.    wt: 2:   Rewriting algebraic substitution as function substitutions
  423.    wt: 2:   11 arctan left inverse of tangent Graph
  424.    wt: 2:   10 arctan left inverse of tangent Definition
  425.    wt: 2:   2 cosine function more properties
  426.    wt: 2:   2 Radian Measure Numerical Value of one degree
  427.    wt: 2:   12 From Applied To Pure Mathematics
  428.    wt: 2:   4 Resultant of a Sum of Movements
  429.    wt: 2:   4 graphing y=Asin(x c)
  430.    wt: 2:   3 graphing y=f(x c) plus K
  431.    wt: 2:   1 graphing y=f(x a)
  432.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  433.    wt: 2:   C Straight Lines Slope from Coordinates
  434.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  435.    wt: 2:   12 Straight Lines Graphing mx plus b
  436.    wt: 2:   11 Straight Lines Graphing y=mx
  437.    wt: 2:   7 Tangent Function is odd on this domain
  438.    wt: 2:   5 Tangent Function Graph
  439.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  440.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  441.    wt: 2:   32 seven rows of pascals triangle
  442.    wt: 2:   30 unit circle calculation of six trigonometric functions
  443.    wt: 2:   20 sine and cosine Double Angle Formulas
  444.    wt: 2:   17E Trig Formulas for dot and cross Products
  445.    wt: 2:   17D cis formulas for sine cosines and tangent
  446.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  447.    wt: 2:   21 Logarithms Powers and Exponentials
  448.    wt: 2:   13 Trig Formulas for dot and cross Products
  449.    wt: 2:   6 Field Properties of Complex Number
  450.    wt: 2:   5 An Easy Proof of the Distributive Law
  451.    wt: 2:   2 Complex Numbers made easier we hope
  452.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  453.    wt: 2:   5 Trigonometric Ratios For Tangent and Special Triangles
  454.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  455.    wt: 2:   12 Triangles Similarity More Problems
  456.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  457.    wt: 2:   12 Links Lessons elsewhere
  458.    wt: 2:   5 Algebraic View of Slopes
  459.    wt: 2:   12 Spatial Coordinates
  460.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  461.    wt: 2:   19 Right Triangle Similarity
  462.    wt: 2:   18 Triangle Similarity Take 1
  463.    wt: 2:   16 Angles Subtended By Chords and Diameters
  464.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  465.    wt: 2:   14 Parallel Lines Postulate
  466.    wt: 2:   13 Angle Side Angle Failure
  467.    wt: 2:   11 Triangle Construction Fails
  468.    wt: 2:   10 Dropping a perpendicular to line
  469.    wt: 2:   8 Isoceles Triangles
  470.    wt: 2:   7 Angle Side Angle
  471.    wt: 2:   6 Ruler and compass Angle Bisection
  472.    wt: 2:   5 Side Angle Side
  473.    wt: 2:   4 Side Side Side
  474.    wt: 2:   1 Initial Concepts and Terms
  475.    wt: 2:   Short Course on Euclidean Geometry
  476.    wt: 2:   A Measurement with Ruler Proper Use
  477.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  478.    wt: 2:   musings do not puiblish real numbers
  479.    wt: 2:   A Modular and Remainder Arithmetic
  480.    wt: 2:   9 Division with Digits after Decimal Point
  481.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  482.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  483.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  484.    wt: 2:   1 Fractions with Finite Decimal Expansions
  485.    wt: 2:   6 Equations and Systems Equivalent or Implied
  486.    wt: 2:   4 Subtraction and Division Axioms
  487.    wt: 2:   1 Equivalent Computation Rules
  488.    wt: 2:   7 Real Numbers as Line Cordinates
  489.    wt: 2:   5 Rational Numbers More
  490.    wt: 2:   4 Rational Numbers
  491.    wt: 2:   3 Fractions
  492.    wt: 2:   1 Whole and Natural Numbers
  493.    wt: 2:   5 Independent versus Dependent Variables
  494.    wt: 2:   4 Changing Letters
  495.    wt: 2:   More Exercises
  496.    wt: 2:   Simple Exercises
  497.    wt: 2:   4 GE III Animated Examples
  498.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  499.    wt: 2:   3 GE III Equation Addition and Multiplication
  500.    wt: 2:   1 GE Substitution four examples
  501.    wt: 2:   Skill Development Notes
  502.    wt: 2:   10 One Example
  503.    wt: 2:   8 One Example
  504.    wt: 2:   7 Two Examples
  505.    wt: 2:   4 Two Examples
  506.    wt: 2:   3 Two Examples
  507.    wt: 2:   9 Sets in Probability and Statistics
  508.    wt: 2:   7 Cautious or Safe Set Construction
  509.    wt: 2:   6 Power Set Notation
  510.    wt: 2:   5 Product Builder Notation
  511.    wt: 2:   4 Subset Builder Notation
  512.    wt: 2:   3 Counting with Sets etc
  513.    wt: 2:   1 Finite Sets
  514.    wt: 2:   5 Talking about Numbers and Quantities
  515.    wt: 2:   3 Adding Words To Arithmetic
  516.    wt: 2:   About Folder Contents
  517.    wt: 2:   arithmetic videos Real Player Format
  518.    wt: 2:   2 Square Roots with Prime
  519.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  520.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  521.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  522.    wt: 2:   8 GCD from Euclidean Algorithm
  523.    wt: 2:   4 LCM of 8 and 10 via Prime
  524.    wt: 2:   LCM 60 45 Avoid List Method Use Prime
  525.    wt: 2:   2 Least Common Multiple LCM intro via list method
  526.    wt: 2:   2 Counting with Tables and Trees I
  527.    wt: 2:   11 What are real lengths and numbers
  528.    wt: 2:   7 negative and additive inverse
  529.    wt: 2:   6 Simplification of Fractions with Units
  530.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  531.    wt: 2:   D Three Term Ratios
  532.    wt: 2:   19 Dividing Fractions How TO
  533.    wt: 2:   13 Fraction Comparison Algebraic View
  534.    wt: 2:   12 Fraction Comparison
  535.    wt: 2:   11 Simplification an Algebraic View
  536.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  537.    wt: 2:   9 Improper Fractions and Mixed Numbers
  538.    wt: 2:   6 Multiplication of Mixed Numbers
  539.    wt: 2:   6 Multiplication Algebraically Take II
  540.    wt: 2:   3 Unit fraction of a fraction
  541.    wt: 2:   13 Subtraction with Additive Inverse
  542.    wt: 2:   11 Adding Integers Formulas and Examples
  543.    wt: 2:   10 Integer Multiplication Formulas
  544.    wt: 2:   8 Multiplication by Signed Numbers Integers
  545.    wt: 2:   7 Multiplication by Signs
  546.    wt: 2:   21 Remainder Arithmetic Modulo 3
  547.    wt: 2:   16 Remainder Arithmetic Modulo 9 Example 2
  548.    wt: 2:   12 Remainder Arithmetic Modulo 10 Example
  549.    wt: 2:   8 Remainder Arithmetic Morulo 5 Examples II
  550.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  551.    wt: 2:   5 Remainder Arithmetic Modulo 5
  552.    wt: 2:   4 Remainder Arithmetic Modulo 10 in general
  553.    wt: 2:   3 Remainder Arithmetic Modulos 10 more still
  554.    wt: 2:   1 Remainder Arithmetic Modulo 10
  555.    wt: 2:   19 video Prime Factorization Unique
  556.    wt: 2:   18 video Count Factors given Prime Factorization
  557.    wt: 2:   17 Identify and Count Factors using Primes
  558.    wt: 2:   9 video Prime Factorization upto 19 squared
  559.    wt: 2:   8 video Prime Factorization upto 19
  560.    wt: 2:   7 Calculator Usage Notes and Cautions
  561.    wt: 2:   5 Prime Factorization and a Square Rule
  562.    wt: 2:   4 video Prime Factorization Introduction
  563.    wt: 2:   3 video Primes and Composites from 9 times table
  564.    wt: 2:   1 video how Products are bigger than factor
  565.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  566.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  567.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  568.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  569.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  570.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  571.    wt: 2:   1 Place Value in Three Digit Whole Numbers
  572.    wt: 2:   Formula Evaluation how to show work
  573.    wt: 2:   The 12 Times Table Visually
  574.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  575.    wt: 2:   011 Division of Time Intervals By Numbers
  576.    wt: 2:   010 Repeated Addition of Time Intervals
  577.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  578.    wt: 2:   8 Addition of Time Intervals via subtotaling
  579.    wt: 2:   7 Addition of Time Intervals
  580.    wt: 2:   4 Mixing and Changing Units of Time
  581.    wt: 2:   3 Units and Lengths of Time
  582.    wt: 2:   2 Time and Date Matters in School
  583.    wt: 2:   Example 1 volume of a pyramid
  584.    wt: 2:   Volume of Solid by Cross Sections Lesson
  585.    wt: 2:   Example 1. Area Between x and x squared
  586.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  587.    wt: 2:   Example 4 with x function of y
  588.    wt: 2:   Example 3
  589.    wt: 2:   Example 2
  590.    wt: 2:   Area Between Curves Lesson Take 2
  591.    wt: 2:   A Chain Rule Real Player video examples
  592.    wt: 2:   34 Derivative of exponential function
  593.    wt: 2:   31 Derivatives of inverse functions
  594.    wt: 2:   29 Chain Rule Optional Reading
  595.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  596.    wt: 2:   26 Chain Rule Recognising outer inner functions
  597.    wt: 2:   25 Chain Rule Animated Examples Continued
  598.    wt: 2:   24 Chain Rule Animated Examples
  599.    wt: 2:   23 Chain Rule in general
  600.    wt: 2:   19 Chain Rule for linear functions
  601.    wt: 2:   14 sine and cosine derivatives 2nd step
  602.    wt: 2:   12 Quotient rule examples
  603.    wt: 2:   11 Quotient rule
  604.    wt: 2:   9 Reciprocal rule
  605.    wt: 2:   7 Animated Differentiation Examples
  606.    wt: 2:   6 Power rule from product rule
  607.    wt: 2:   5 Product Rule
  608.    wt: 2:   11 Limits at infinity Three Examples
  609.    wt: 2:   3 Decimal insights for limits continuity convergence
  610.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  611.    wt: 2:   D2 Limits of Monotone Sequences
  612.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  613.    wt: 2:   Chapter 23 Links To Trigonometry
  614.    wt: 2:   Chapter 21 Arrow Addition
  615.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  616.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  617.    wt: 2:   Chapter 12. Units and Slopes
  618.    wt: 2:   Chapter 2. Slopes and Ski Trails
  619.    wt: 2:   Postscript A Three Remarks
  620.    wt: 2:   Chapter 7 Two Treatments of Geometry
  621.    wt: 2:   Chapter 3 Algebra Difficulties
  622.    wt: 2:   Foreword
  623.    wt: 2:   Postscript B More on Story Telling and Reason
  624.    wt: 2:   Postscript A Story Telling
  625.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  626.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  627.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  628.    wt: 2:   Chapter 8 Change of Language
  629.    wt: 2:   Chapter 7 Longer Chains of Reason
  630.    wt: 2:   Chapter 6 Chains of Reason
  631.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  632.    wt: 2:   Foreword
  633.    wt: 2:   L Skills with take home value
  634.    wt: 2:   G. Written work formats for developing and showing skill
  635.    wt: 2:   B. Domino effect of errors
  636.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  637.    wt: 2:   Chapter 2 Why Sets
  638.    wt: 2:   Primary and Secondary Skills and Practices with Take Home Value
  639.    wt: 2:   7 Games and Activities for Instruction
  640.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  641.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  642.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  643.    wt: 1:   Appendix 2 primary school Arithmetic 01
  644.    wt: 1:   G LAMP Introduction Problem Solving Skills
  645.    wt: 1:   Skills Chapter 5 Calculus
  646.    wt: 1:   Skills Chapter 4 Logic
  647.    wt: 1:   Ramblings Introduction Algebra Essay
  648.    wt: 1:   Skills Chapter 1 Arithmetic
  649.    wt: 1:   Skills Chapter 0 Introduction
  650.    wt: 1:   11 pure mathematics
  651.    wt: 1:   10 statistics
  652.    wt: 1:   9 combinatorics probability sets
  653.    wt: 1:   8 analytic geometry etc
  654.    wt: 1:   7 logic review and decimals an odd combination
  655.    wt: 1:   6 polynomials etc
  656.    wt: 1:   5 logarithms and exponentials etc
  657.    wt: 1:   3 Euclidean Geometry Leanly
  658.    wt: 1:   What is POMME
  659.    wt: 1:   why bother
  660.    wt: 1:   permissions for teachers
  661.    wt: 1:   activities for students
  662.    wt: 1:   About site lesson plans
  663.    wt: 1:   Mathematics Education Professors
  664.    wt: 1:   learning takes time
  665.    wt: 1:   Postscript 2007 01 10
  666.    wt: 1:   Education Reform Inconsistencies
  667.    wt: 1:   Maps Plans Drawings
  668.    wt: 1:   how letters appear
  669.    wt: 1:   Secondary Two Mathematics
  670.    wt: 1:   Secondary One Mathematics
  671.    wt: 1:   teaching tips
  672.    wt: 1:   What to Tell Students
  673.    wt: 1:   mathematics curriculum shifts
  674.    wt: 1:   05 13 OldSiteEntrancePage
  675.    wt: 1:   standards for course material
  676.    wt: 1:   Theory of Knowledge
  677.    wt: 1:   Different Kinds of Reasoning in maths
  678.    wt: 1:   Four ways to improve education reform
  679.    wt: 1:   need for a mixed mathematics curriculum
  680.    wt: 1:   education an empirical art
  681.    wt: 1:   words for mathematics instructor
  682.    wt: 1:   chapitre 12 00 les iles et division
  683.    wt: 1:   chapitre 04 02 Deuxieme enigme
  684.    wt: 1:   chapitre 02 00 La Communication des idees
  685.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  686.    wt: 1:   4 Energy Power Heat09
  687.    wt: 1:   3 Energy Power Heat08
  688.    wt: 1:   1 Energy Power Heat06
  689.    wt: 1:   E Energy Power05
  690.    wt: 1:   D Energy Power04
  691.    wt: 1:   C Energy Power03
  692.    wt: 1:   A Energy Power01
  693.    wt: 1:   D Wire Resistance Calculation02
  694.    wt: 1:   B Wire Resistance Qualitative02
  695.    wt: 1:   3 Like resistors in parallel
  696.    wt: 1:   2 Unlike resistors in parallel01
  697.    wt: 1:   H Series Circuit02
  698.    wt: 1:   E Kirchoffs Second Law
  699.    wt: 1:   D Kirchoff First Law
  700.    wt: 1:   B Electromotive force conventional current01
  701.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  702.    wt: 1:   17 Math Booklets for children and young teenagers
  703.    wt: 1:   15 Counting For Parents
  704.    wt: 1:   10 Ends values for work study instruction
  705.    wt: 1:   8 The Effect of Negative Remarks
  706.    wt: 1:   5 Patience Please for Yourself and Your Charges
  707.    wt: 1:   4 Learning Takes Time and Effort
  708.    wt: 1:   3 Preparing for Science Studies
  709.    wt: 1:   1 Speaking Skills
  710.    wt: 1:   Ages 9 to 10
  711.    wt: 1:   Ages 8 to 9
  712.    wt: 1:   Ages 7 to 8
  713.    wt: 1:   Ages 6 to 7
  714.    wt: 1:   Ages 4 plus to 5 plus
  715.    wt: 1:   Ages 3 plus to 4 plus
  716.    wt: 1:   19 Horizontal line rule and method
  717.    wt: 1:   18 Vertical Line Rule and Method
  718.    wt: 1:   17 Function maxima minima and their location
  719.    wt: 1:   16 Increasing or decreasing on intervals
  720.    wt: 1:   14 Surjections Injections Bijections
  721.    wt: 1:   13 From one to one to many to one
  722.    wt: 1:   11 Function Domain Range Source and Targets
  723.    wt: 1:   10 Interval Notation
  724.    wt: 1:   9 Set theory term relation possible origins
  725.    wt: 1:   7 Functions with finite domains
  726.    wt: 1:   4 Function notation in and beyond mathematics
  727.    wt: 1:   Introduction Reading Guide
  728.    wt: 1:   A Quadratics Summary
  729.    wt: 1:   10 quadratic exercises
  730.    wt: 1:   9 quadratics physical and further context
  731.    wt: 1:   6 quadratics numerical approach
  732.    wt: 1:   5 quadratics completing the square
  733.    wt: 1:   3 quadratics factoring by inspection
  734.    wt: 1:   1 quadratics graphing exercises
  735.    wt: 1:   Quadratics in 10 steps
  736.    wt: 1:   7 Links Lessons Elsewhere
  737.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  738.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  739.    wt: 1:   4 Polynomials Long division linear divisor
  740.    wt: 1:   3 Polynomials Multiplication Addition
  741.    wt: 1:   1 Polynomials Distributive Law
  742.    wt: 1:   16 cotangent function Definition Graph and Inverse
  743.    wt: 1:   15 cosecant function Definition Graph and Inverse
  744.    wt: 1:   14 secant function Definition Graph and Inverse
  745.    wt: 1:   13 cosecant function Definition Graph and Inverse
  746.    wt: 1:   9 motivation for name arcsin
  747.    wt: 1:   8 arcsin left inverse of sine Graph
  748.    wt: 1:   7 arcsin left inverse of sine Definition
  749.    wt: 1:   6 Graph of arccos function
  750.    wt: 1:   4 possible motivation for term arccos
  751.    wt: 1:   3 Left Inverse of cosine arccos definition
  752.    wt: 1:   1 cosine function properties
  753.    wt: 1:   9 Summary Degrees to Radians and back
  754.    wt: 1:   8 Radian Measures of Common Angles
  755.    wt: 1:   1 Unsigned Coordinates
  756.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  757.    wt: 1:   Parallel Lines and Interior Angles
  758.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  759.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  760.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  761.    wt: 1:   Straight Lines ASA Intersection Study More
  762.    wt: 1:   Straight Lines Intersection of
  763.    wt: 1:   14 Straight Lines Equations General Case
  764.    wt: 1:   10 Straight Lines through Origin Equations More
  765.    wt: 1:   9 Straight Lines through Origin Equations
  766.    wt: 1:   1 Straight Lines Slope Concept
  767.    wt: 1:   17 tangent function angle sum formulas
  768.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  769.    wt: 1:   18 sum of sinusoidal waves as a single wave
  770.    wt: 1:   17F Law of cosines
  771.    wt: 1:   17C sine and cosine double triple angle formulas
  772.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  773.    wt: 1:   13 Graph of tangent function many periods
  774.    wt: 1:   10 Graphs of sines and cosines many periods
  775.    wt: 1:   9 Graphs of sine and cosine over one period
  776.    wt: 1:   8 period of tangent function
  777.    wt: 1:   7 period of sine and cosine
  778.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  779.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  780.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  781.    wt: 1:   2 Quadrant I reference Angles
  782.    wt: 1:   Unit Circle Development of Trigonometry
  783.    wt: 1:   19 N th Roots of Unity
  784.    wt: 1:   18 Sixth Roots of Unity
  785.    wt: 1:   17 Cube Roots of unity
  786.    wt: 1:   14 Law of cosines
  787.    wt: 1:   11 sine and cosine double triple angle formulas
  788.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  789.    wt: 1:   8 Unit Circle Development of Trigonometry
  790.    wt: 1:   4 Multiplication Properties
  791.    wt: 1:   3 Addition Properties
  792.    wt: 1:   8 Triangles Cascade Problem Solving
  793.    wt: 1:   7 Trignometric Ratios Unit Circle
  794.    wt: 1:   3 Trigonometric Ratios sine and cosine
  795.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  796.    wt: 1:   9 Similarity of Triangles Usual Criteria
  797.    wt: 1:   8 Similarity of Triangles and Polygons
  798.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  799.    wt: 1:   4 Similarity Definition with Coordinate
  800.    wt: 1:   3 Similarity by Design with coordinates
  801.    wt: 1:   1 Early Concept of Like or Similar Shapes
  802.    wt: 1:   10 Midpoint of [a b] and [b a]
  803.    wt: 1:   8 Mid Point Formula
  804.    wt: 1:   6 Intersection of lines by solving linear systems
  805.    wt: 1:   3 Slope product for perpendicular lines
  806.    wt: 1:   1 Numerical view of lines and their equations
  807.    wt: 1:   13 Pythagorean spatial distance formulas
  808.    wt: 1:   11 Triangle Inequality
  809.    wt: 1:   10 Pythagorean plane distance formula
  810.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  811.    wt: 1:   1 Cartesian Coordinates sans signs
  812.    wt: 1:   2 Measuring Area Directly
  813.    wt: 1:   5 Square Roots with primes more still
  814.    wt: 1:   4 Square Roots with primes more
  815.    wt: 1:   1 Squares and Square Roots Introduction
  816.    wt: 1:   13 GCD from given Prime Factorization
  817.    wt: 1:   7 GCD and LCM from prime factorization
  818.    wt: 1:   6 GCD from Prime
  819.    wt: 1:   5 Common Divisors 60 45 via Prime
  820.    wt: 1:   1 Least Common Multiples LCM Introduction
  821.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  822.    wt: 1:   4 Counting with Trees Product Rule Take I
  823.    wt: 1:   3 Counting with Tables and Trees II
  824.    wt: 1:   1 Counting and Counting Methods I
  825.    wt: 1:   7 Converting or Changing Units
  826.    wt: 1:   4 Fractions with Units
  827.    wt: 1:   3 Multiplying Units and Numbers
  828.    wt: 1:   1 Addition and Subtraction with Units
  829.    wt: 1:   B Fractions and Two Term Ratios
  830.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  831.    wt: 1:   18 Efficient Ways to Multiply
  832.    wt: 1:   17 Efficient Ways to Add and Subtract
  833.    wt: 1:   16 Addition Subtraction Comparision Compared
  834.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  835.    wt: 1:   14 Adding and Subtracting with Like Denominators
  836.    wt: 1:   8 Numerals Fractionals Quantals Take II
  837.    wt: 1:   7 Numerals Fractionals Quantals
  838.    wt: 1:   5 Equivalent Fractions
  839.    wt: 1:   4 Fraction Multiplication
  840.    wt: 1:   1 What is a fraction Take II
  841.    wt: 1:   1 What is a fraction
  842.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  843.    wt: 1:   D Remainders Modulo 11 Pair Rule
  844.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  845.    wt: 1:   B Integer Long Division Multiple Choices
  846.    wt: 1:   A Associative Law Theorectical Note
  847.    wt: 1:   9 Multiplying Integers
  848.    wt: 1:   6 Multiplication by Natural Numbers
  849.    wt: 1:   5 Zero Movement and Additive Inverses
  850.    wt: 1:   4 Adding Movements wiht opposite directions
  851.    wt: 1:   3 Adding Movements with same direction
  852.    wt: 1:   1 Integers as Coordinates
  853.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  854.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  855.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  856.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  857.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  858.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  859.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  860.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  861.    wt: 1:   11 Place Value SI Standard International way
  862.    wt: 1:   Exact Arithmetic Wholes and Fractions
  863.    wt: 1:   Expression Evaluation how to show work
  864.    wt: 1:   About folder contents
  865.    wt: 1:   016 Numbering Occidental Calendar Days
  866.    wt: 1:   015 School and work day counting tables
  867.    wt: 1:   014 Counting Days with Calendars
  868.    wt: 1:   013 Travel Time Tables
  869.    wt: 1:   6 How long is a million seconds
  870.    wt: 1:   5 Conversion Arithmetic
  871.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  872.    wt: 1:   Example 1
  873.    wt: 1:   Area Between Curves Lesson Take 1
  874.    wt: 1:   Summary
  875.    wt: 1:   2 Indefinite Integrals Exercises
  876.    wt: 1:   1 Chain Rule in Reverse Integration Method
  877.    wt: 1:   2 Second derivative test prequel
  878.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  879.    wt: 1:   36 Cube root derivative animated
  880.    wt: 1:   33 Chain Rule Real Player video examples
  881.    wt: 1:   18 Chain Rule Introduction
  882.    wt: 1:   15 sine and cosine derivatives 3rd step
  883.    wt: 1:   13 sine and cosine derivatives 1st step
  884.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  885.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  886.    wt: 1:   10 Three one sided limits with infinite values
  887.    wt: 1:   5 Jumps and absence of unlimited error control
  888.    wt: 1:   4 Numerical properties
  889.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  890.    wt: 1:   G.3 Constant Difference Theorem Proof
  891.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  892.    wt: 1:   F.4 Finite Covering Theorem
  893.    wt: 1:   F.2 Closed Range Theorem
  894.    wt: 1:   E1 Error Control Inequalities
  895.    wt: 1:   C Triangle Inequalities
  896.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  897.    wt: 1:   PostScript For and Against Decimal Perspectives
  898.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  899.    wt: 1:   Chapter 5. Slope Sign Tests
  900.    wt: 1:   Chapter 4. More Slope Sign Analysis
  901.    wt: 1:   Chapter 3. Slope Sign Analysis
  902.    wt: 1:   Fall 1983 Calculus Appetizer
  903.    wt: 1:   Foreword
  904.    wt: 1:   Annotated Links to Material Elsehwere
  905.    wt: 1:   Postscript B Mathematics Education References
  906.    wt: 1:   Chapter 11 Elementary Instruction
  907.    wt: 1:   Chapter 10 Transition
  908.    wt: 1:   Chapter 9 The Two Ends
  909.    wt: 1:   Chapter 8 Modern Instruction
  910.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  911.    wt: 1:   Chapter 5 Four References
  912.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  913.    wt: 1:   Chapter 1 Introduction
  914.    wt: 1:   Chapter 18 Sense and Knowledge
  915.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  916.    wt: 1:   Chapter 15 Objective Processes
  917.    wt: 1:   Chapter 11 Accidental Patterns
  918.    wt: 1:   Chapter 10 Responsibility
  919.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  920.    wt: 1:   Chapter 5 Deception
  921.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  922.    wt: 1:   Chapter 1 Introduction
  923.    wt: 1:   S Adding words to algebra
  924.    wt: 1:   R Why Learn Mathematics Skills
  925.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  926.    wt: 1:   N Mathematics Prepare for College Studies
  927.    wt: 1:   I. Logic and language skills
  928.    wt: 1:   C. Domino effect of being careful
  929.    wt: 1:   How to Build Skills and Confidence
  930.    wt: 1:   Chapter 6 More Algebra and Geometry
  931.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  932.    wt: 1:   Chapter 3 Algebra Starter Lessons
  933.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  934.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  935.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  936.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  937.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  938.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  939.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  940.    wt: 1:   More Algebra and Slope based Calculus Preview
  941.    wt: 1:   Systematic Algebra Skill Development Missing Links
  942.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  943.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  944.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  945.    wt: 1:   The Math Forum and Site Content
  946.    wt: 10:   Chapter 22. Geometric Sums and Sequences
  947.    wt: 10:   Chapter 14. Forward and Backward Use of a Formula
  948.    wt: 10:   Chapter 8 Three Skills For Algebra

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

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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