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:   Volume 2 Three Skills For Algebra/
  3.    wt: 5:   2 Formula Forward Use Evaluation/
  4.    wt: 4:   10 Examples of Algebraic Reasoning/
  5.    wt: 4:   8 Unifying Theme For Algebra/
  6.    wt: 4:   12 Comparison of Unsigned and Signed Numbers/
  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:   Step 3 Easy systems in 2 or more unknowns/
  12.    wt: 3:   D Decimal Long Division Methods/
  13.    wt: 3:   C Decimal Multiplication Methods/
  14.    wt: 3:   A Decimal Counting and Adding Methods/
  15.    wt: 3:   2 Arithmetic with Decimals/
  16.    wt: 2:   12 Function Translating and Rescaling/
  17.    wt: 2:   2 Euclidean Geometry Constructions Theory extras/
  18.    wt: 2:   B Real Numbers Extrinsic Development/
  19.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  20.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  21.    wt: 2:   5 Real Numbers/
  22.    wt: 2:   4 Computation Rules and Function Notation/
  23.    wt: 2:   Step 4 Gaussian Elimination/
  24.    wt: 2:   Step 1 Stick diagram and fractions/
  25.    wt: 2:   3 Solving Linear Equations/
  26.    wt: 2:   1 Working With Sets/
  27.    wt: 2:   Algebra Starter Lessons/
  28.    wt: 2:   3 Prime Factorization Skills/
  29.    wt: 2:   Volume 1 Elements of Reason/
  30.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  31.    wt: 1:   Mathematics Skills Year by Year/
  32.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  33.    wt: 1:   4 Functions/
  34.    wt: 1:   3 Quadratics Geometrically/
  35.    wt: 1:   1 Five Polynomial Operations/
  36.    wt: 1:   More Algebra/
  37.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  38.    wt: 1:   11 Squares and Square Roots/
  39.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  40.    wt: 1:   9 Combinatorics Trees Tables and Products/
  41.    wt: 1:   8 Arithmetic with Signed Numbers/
  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

550 matches:

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

Extended Search

934 matches:

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