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 Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

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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43 matches:

  1.    wt: 8:   1 Maps Plans Measurement/
  2.    wt: 7:   10 Intersecting Straight Lines and Transversals/
  3.    wt: 7:   4 Lines and Slopes Take 1/
  4.    wt: 6:   13 Vectors/
  5.    wt: 6:   11 Parallel Straight Lines and Transversals/
  6.    wt: 6:   8 Unit Circle Trigonometry/
  7.    wt: 6:   6 Trigonometry first steps/
  8.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  9.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  10.    wt: 5:   12 Function Translating and Rescaling/
  11.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  12.    wt: 5:   7 Complex Numbers/
  13.    wt: 5:   5 What is Similarity/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 3:   10 Examples of Algebraic Reasoning/
  18.    wt: 3:   10 LCM GCD and Euclid GCD Algorithm/
  19.    wt: 2:   11 Squares and Square Roots/
  20.    wt: 2:   4 Remainder Arithmetic and Divisibility/
  21.    wt: 2:   5 Lessons on Integration/
  22.    wt: 2:   4 Lessons on Using Derivatives/
  23.    wt: 2:   13 Lessons on Limits and Continuity/
  24.    wt: 1:   Mathematics Education Essays/
  25.    wt: 1:   Volume 1A Regles et modeles/
  26.    wt: 1:   4 Functions/
  27.    wt: 1:   3 Quadratics Geometrically/
  28.    wt: 1:   1 Five Polynomial Operations/
  29.    wt: 1:   A Origins of Counting and Figuring Methods/
  30.    wt: 1:   4 Computation Rules and Function Notation/
  31.    wt: 1:   Step 4 Gaussian Elimination/
  32.    wt: 1:   Step 1 Stick diagram and fractions/
  33.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  34.    wt: 1:   D Decimal Long Division Methods/
  35.    wt: 1:   A Decimal Counting and Adding Methods/
  36.    wt: 1:   1 Decimal Place Value/
  37.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  38.    wt: 1:   38 Lessons on Calculating Derivatives/
  39.    wt: 1:   70 Calculus Starter Lessons/
  40.    wt: 1:   Volume 2 Three Skills For Algebra/
  41.    wt: 1:   Volume 1 Elements of Reason/
  42.    wt: 1:   Secondary Mathematics A Practical Approach/
  43.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/

Web Page Search

272 matches:

  1.    wt: 5:   4 quadratics difference of two squares
  2.    wt: 4:   10 Similarity of Triangles Equivalent of Two Criteria
  3.    wt: 2:   Maps Plans Drawings
  4.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  5.    wt: 2:   chapitre 04 04 Parlons de la logique
  6.    wt: 2:   8 quadratics backward use of various formulas
  7.    wt: 2:   Quadratics in 10 steps
  8.    wt: 2:   10 arctan left inverse of tangent Definition
  9.    wt: 2:   4 Resultant of a Sum of Movements
  10.    wt: 2:   27 Logarithmic use of products of sines and cosines
  11.    wt: 2:   10 Graphs of sines and cosines many periods
  12.    wt: 2:   Unit Circle Development of Trigonometry
  13.    wt: 2:   8 Unit Circle Development of Trigonometry
  14.    wt: 2:   5 An Easy Proof of the Distributive Law
  15.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  16.    wt: 2:   5 Similarity of Circles Squares and Rectangles
  17.    wt: 2:   10 Midpoint of [a b] and [b a]
  18.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  19.    wt: 2:   4 Angles on Maps Plans drawn to scale
  20.    wt: 2:   3 Lengths and Areas on Maps and Plans
  21.    wt: 2:   21 Addition of Multiples of a Single Vector
  22.    wt: 2:   19 Signed Multiples of Vectors
  23.    wt: 2:   10 Volume of Pyramid
  24.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  25.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  26.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  27.    wt: 2:   4 LCM of 8 and 10 via Prime
  28.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  29.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  30.    wt: 2:   010 Repeated Addition of Time Intervals
  31.    wt: 2:   17 Derivatives of quotients of sine and cosine
  32.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  33.    wt: 2:   G.3 Constant Difference Theorem Proof
  34.    wt: 2:   Chapter 7 Two Treatments of Geometry
  35.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  36.    wt: 1:   10 statistics
  37.    wt: 1:   About site lesson plans
  38.    wt: 1:   Mathematics Education Professors
  39.    wt: 1:   Postscript 2007 01 10
  40.    wt: 1:   five decades make a difference
  41.    wt: 1:   Secondary Two Mathematics
  42.    wt: 1:   04 29 New Mathematics Curriculum
  43.    wt: 1:   04 25 when to stop or suspend mathemat
  44.    wt: 1:   Theory of Knowledge
  45.    wt: 1:   Different Kinds of Reasoning in maths
  46.    wt: 1:   three kinds of reason in mathematics
  47.    wt: 1:   chapitre 04 09 Regles accidentelles
  48.    wt: 1:   chapitre 04 08 Limitations et benefices
  49.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  50.    wt: 1:   chapitre 04 06 engagements
  51.    wt: 1:   chapitre 04 05 Implication versus suggestion
  52.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  53.    wt: 1:   chapitre 04 02 Deuxieme enigme
  54.    wt: 1:   chapitre 04 01 Premiere enigme
  55.    wt: 1:   chapitre 04 00 Les regles d implication
  56.    wt: 1:   D Energy Power04
  57.    wt: 1:   F Wire Resistance Calculation04
  58.    wt: 1:   E Kirchoffs Second Law
  59.    wt: 1:   D Kirchoff First Law
  60.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  61.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  62.    wt: 1:   10 Ends values for work study instruction
  63.    wt: 1:   8 The Effect of Negative Remarks
  64.    wt: 1:   Ages 10 to 12 Geometry
  65.    wt: 1:   Ages 10 to 12 Arithmetic
  66.    wt: 1:   Ages 9 to 10
  67.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  68.    wt: 1:   15 Sign analysis of functions
  69.    wt: 1:   10 Interval Notation
  70.    wt: 1:   8 Set view of relations and functions
  71.    wt: 1:   2 Algebraic use of function notation
  72.    wt: 1:   1 Geometric Introduction of Function Notation
  73.    wt: 1:   A Quadratics Summary
  74.    wt: 1:   10 quadratic exercises
  75.    wt: 1:   9 quadratics physical and further context
  76.    wt: 1:   6 quadratics numerical approach
  77.    wt: 1:   5 quadratics completing the square
  78.    wt: 1:   3 quadratics factoring by inspection
  79.    wt: 1:   2 quadratics graphing in general
  80.    wt: 1:   1 quadratics graphing exercises
  81.    wt: 1:   10 Exponential Growth and Decay Models
  82.    wt: 1:   11 arctan left inverse of tangent Graph
  83.    wt: 1:   8 arcsin left inverse of sine Graph
  84.    wt: 1:   7 arcsin left inverse of sine Definition
  85.    wt: 1:   6 Graph of arccos function
  86.    wt: 1:   3 Left Inverse of cosine arccos definition
  87.    wt: 1:   8 Radian Measures of Common Angles
  88.    wt: 1:   2 Radian Measure Numerical Value of one degree
  89.    wt: 1:   13 Velocity Vectors in Physics
  90.    wt: 1:   10 Parallelogram Addition Method
  91.    wt: 1:   8 Parallel Vectors
  92.    wt: 1:   6 Vectors with Coordinates
  93.    wt: 1:   3 Navigation with Arrows or Vectors
  94.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  95.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  96.    wt: 1:   Straight Lines Intersection of
  97.    wt: 1:   10 Straight Lines through Origin Equations More
  98.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  99.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  100.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  101.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  102.    wt: 1:   32 seven rows of pascals triangle
  103.    wt: 1:   30 unit circle calculation of six trigonometric functions
  104.    wt: 1:   28 Expressing products of sines cosines as sums
  105.    wt: 1:   26 Formulas for products of sines and cosines
  106.    wt: 1:   24 tangent Angle Difference Formula
  107.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  108.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  109.    wt: 1:   18 sum of sinusoidal waves as a single wave
  110.    wt: 1:   17F Law of cosines
  111.    wt: 1:   13 Graph of tangent function many periods
  112.    wt: 1:   12 Graph of tangent function for one period
  113.    wt: 1:   9 Graphs of sine and cosine over one period
  114.    wt: 1:   8 period of tangent function
  115.    wt: 1:   7 period of sine and cosine
  116.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  117.    wt: 1:   20 N th Roots of Complex Numbers
  118.    wt: 1:   19 N th Roots of Unity
  119.    wt: 1:   18 Sixth Roots of Unity
  120.    wt: 1:   17 Cube Roots of unity
  121.    wt: 1:   14 Law of cosines
  122.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  123.    wt: 1:   6 Field Properties of Complex Number
  124.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  125.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  126.    wt: 1:   Why Trigonometry the whyslopes view
  127.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  128.    wt: 1:   9 Similarity of Triangles Usual Criteria
  129.    wt: 1:   8 Similarity of Triangles and Polygons
  130.    wt: 1:   1 Early Concept of Like or Similar Shapes
  131.    wt: 1:   6 Intersection of lines by solving linear systems
  132.    wt: 1:   5 Algebraic View of Slopes
  133.    wt: 1:   1 Numerical view of lines and their equations
  134.    wt: 1:   10 Pythagorean plane distance formula
  135.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  136.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  137.    wt: 1:   17 Right Bisectors of Triangle Sides
  138.    wt: 1:   10 Dropping a perpendicular to line
  139.    wt: 1:   9 Construction of a right bisector
  140.    wt: 1:   3 Isometry of Triangles Congruence
  141.    wt: 1:   6 Figuring with Maps Not to Scale
  142.    wt: 1:   23 Distributive Law Two Derivations
  143.    wt: 1:   22 Multiplication of Signed Numbers
  144.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  145.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  146.    wt: 1:   13 Arrows and Vectors in a Plane
  147.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  148.    wt: 1:   8 Division and Mulplication of Compound Fractions
  149.    wt: 1:   4 Location of Point in Decimal Addition
  150.    wt: 1:   3 Location of Point in Decimal Multiplication
  151.    wt: 1:   1 The Counting Origins of Numbers
  152.    wt: 1:   5 Areas of Rectangles Revisited
  153.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  154.    wt: 1:   3 Product Axioms Two Forms
  155.    wt: 1:   4 Comparison of Negative Numbers
  156.    wt: 1:   10 Real Number Lengths and Signs
  157.    wt: 1:   8 Coordinates for Maps and Planes
  158.    wt: 1:   10 One Example
  159.    wt: 1:   7 Two Examples
  160.    wt: 1:   4 Two Examples
  161.    wt: 1:   3 Two Examples
  162.    wt: 1:   11 Volume of Sphere
  163.    wt: 1:   9 Volume of Cone
  164.    wt: 1:   8 Sets of Numbers
  165.    wt: 1:   6 Three Notions of What is a Variable
  166.    wt: 1:   4 A Brief Story of numbers and algebra
  167.    wt: 1:   3 Comparison of Negative Numbers
  168.    wt: 1:   3 Properties of Square Roots with example
  169.    wt: 1:   1 Squares and Square Roots Introduction
  170.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  171.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  172.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  173.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  174.    wt: 1:   10 dividing signed numbers
  175.    wt: 1:   5 lengths and signs of numbers
  176.    wt: 1:   3 signed coordinates for maps and planes
  177.    wt: 1:   6 Simplification of Fractions with Units
  178.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  179.    wt: 1:   B Fractions and Two Term Ratios
  180.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  181.    wt: 1:   6 Multiplication of Mixed Numbers
  182.    wt: 1:   3 Unit fraction of a fraction
  183.    wt: 1:   10 Integer Multiplication Formulas
  184.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  185.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  186.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  187.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  188.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  189.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  190.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  191.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  192.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  193.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  194.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  195.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  196.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  197.    wt: 1:   1 Remainder Arithmetic Modulo 10
  198.    wt: 1:   20 Uniqueness of Prime Factorization
  199.    wt: 1:   16 video Factors of 980 using prime
  200.    wt: 1:   15 video Factors of 20 using Prime Factorization
  201.    wt: 1:   14 video Factors of 24 Take II
  202.    wt: 1:   13 video Factors of 24 using prime
  203.    wt: 1:   10 video Prime Factorization upto 23 squared
  204.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  205.    wt: 1:   10 Division by Five Long and Short Ways
  206.    wt: 1:   C Counting Areas with Powers of Ten
  207.    wt: 1:   B Powers of Ten
  208.    wt: 1:   4 Two and Three Digit Multipliers
  209.    wt: 1:   8 Subtraction with Units of Measure
  210.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  211.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  212.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  213.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  214.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  215.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  216.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  217.    wt: 1:   Quick history of numbers and algebra
  218.    wt: 1:   012 Division of Time Intervals by Time Intervals
  219.    wt: 1:   011 Division of Time Intervals By Numbers
  220.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  221.    wt: 1:   8 Addition of Time Intervals via subtotaling
  222.    wt: 1:   7 Addition of Time Intervals
  223.    wt: 1:   4 Mixing and Changing Units of Time
  224.    wt: 1:   3 Units and Lengths of Time
  225.    wt: 1:   1 Intro of Kids To Time Date Skills
  226.    wt: 1:   Example 2 volume of a cone
  227.    wt: 1:   Example 1 volume of a pyramid
  228.    wt: 1:   Volume of Solid by Cross Sections Lesson
  229.    wt: 1:   Example 4 with x function of y
  230.    wt: 1:   3 Two Chain Rule Method Exercises
  231.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  232.    wt: 1:   34 Derivative of exponential function
  233.    wt: 1:   31 Derivatives of inverse functions
  234.    wt: 1:   30Chain Rule A Proof
  235.    wt: 1:   28 Chain Rule Preparation for a Proof
  236.    wt: 1:   10 Power rule for negative integers
  237.    wt: 1:   8 Differentiation of polynomials
  238.    wt: 1:   10 Three one sided limits with infinite values
  239.    wt: 1:   5 Jumps and absence of unlimited error control
  240.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  241.    wt: 1:   E2 Algebraic Properties of Limits
  242.    wt: 1:   D2 Limits of Monotone Sequences
  243.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  244.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  245.    wt: 1:   Chapter 23 Links To Trigonometry
  246.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  247.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  248.    wt: 1:   Chapter 10 Slopes and Units
  249.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  250.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  251.    wt: 1:   Chapter 10 Describing and Changing Calculations
  252.    wt: 1:   Chapter 6 Change of Language
  253.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  254.    wt: 1:   Chapter 4 Longer Chains of Reason
  255.    wt: 1:   Chapter 3 Chains of Reason
  256.    wt: 1:   Chapter 10 Transition
  257.    wt: 1:   Chapter 9 The Two Ends
  258.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  259.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  260.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  261.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  262.    wt: 1:   Chapter 10 Responsibility
  263.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  264.    wt: 1:   Chapter 8 Change of Language
  265.    wt: 1:   Chapter 7 Longer Chains of Reason
  266.    wt: 1:   Chapter 6 Chains of Reason
  267.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  268.    wt: 1:   C. Domino effect of being careful
  269.    wt: 1:   B. Domino effect of errors
  270.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  271.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  272.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

821 matches:

  1.    wt: 9:   Analytic View of Triangle Construction or Line Instersection More
  2.    wt: 9:   10 Graphs of sines and cosines many periods
  3.    wt: 9:   4 Equations for lines three forms
  4.    wt: 9:   1 Numerical view of lines and their equations
  5.    wt: 9:   6 Figuring with Maps Not to Scale
  6.    wt: 8:   4 quadratics difference of two squares
  7.    wt: 8:   10 Parallelogram Addition Method
  8.    wt: 8:   SAS Method For Isometric Or Proportional Triangle Construction
  9.    wt: 8:   Straight Lines ASA Intersection Study More
  10.    wt: 8:   Straight Lines ASA Intersection Study
  11.    wt: 8:   Straight Lines Instersection Solving Equations
  12.    wt: 8:   Straight Lines Intersection of
  13.    wt: 8:   27 Logarithmic use of products of sines and cosines
  14.    wt: 8:   13 Graph of tangent function many periods
  15.    wt: 8:   12 Graph of tangent function for one period
  16.    wt: 8:   9 Graphs of sine and cosine over one period
  17.    wt: 8:   8 period of tangent function
  18.    wt: 8:   7 period of sine and cosine
  19.    wt: 8:   Unit Circle Development of Trigonometry
  20.    wt: 8:   6 Trigonometry Sines of Supplementary Angles
  21.    wt: 8:   4 Trigonometric Ratios For Two Special Triangles
  22.    wt: 8:   11 A Partial Summary
  23.    wt: 8:   6 Intersection of lines by solving linear systems
  24.    wt: 8:   5 Algebraic View of Slopes
  25.    wt: 8:   A Measurement with Ruler Proper Use
  26.    wt: 8:   5 Drawing to Scale Avoids Angle Distortions
  27.    wt: 8:   2 Measuring Area Directly
  28.    wt: 8:   1 Length Measurement
  29.    wt: 7:   10 arctan left inverse of tangent Definition
  30.    wt: 7:   13 Velocity Vectors in Physics
  31.    wt: 7:   11 Component Method
  32.    wt: 7:   8 Parallel Vectors
  33.    wt: 7:   6 Vectors with Coordinates
  34.    wt: 7:   5 Head To Tail Arrow Addition
  35.    wt: 7:   3 Navigation with Arrows or Vectors
  36.    wt: 7:   1 Unsigned Coordinates
  37.    wt: 7:   Proportionality of Line Segments From Parallel Transversals
  38.    wt: 7:   Construction Methods and Criteria for Isometric and Similar Triangles
  39.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  40.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  41.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  42.    wt: 7:   32 seven rows of pascals triangle
  43.    wt: 7:   30 unit circle calculation of six trigonometric functions
  44.    wt: 7:   28 Expressing products of sines cosines as sums
  45.    wt: 7:   26 Formulas for products of sines and cosines
  46.    wt: 7:   24 tangent Angle Difference Formula
  47.    wt: 7:   23 sine and cosine of 180 plus 22.5 degrees
  48.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  49.    wt: 7:   18 sum of sinusoidal waves as a single wave
  50.    wt: 7:   17F Law of cosines
  51.    wt: 7:   11 tangent function undefined when terminal side vertical
  52.    wt: 7:   6 sines and cosines for reference angle 30 degrees
  53.    wt: 7:   5 sines and cosines for reference angle 60 degrees
  54.    wt: 7:   4 sines and cosines for reference angle 45 degrees
  55.    wt: 7:   3 sines and cosines for reference angle 90 degrees
  56.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  57.    wt: 7:   10 sine cosine Angle Sum Formulas via cis
  58.    wt: 7:   8 Unit Circle Development of Trigonometry
  59.    wt: 7:   5 An Easy Proof of the Distributive Law
  60.    wt: 7:   4 Multiplication Properties
  61.    wt: 7:   2 Similar Triangles Equality of Corresponding Side Ratios
  62.    wt: 7:   1 Angle Measurement with Degrees
  63.    wt: 7:   Why Trigonometry the whyslopes view
  64.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  65.    wt: 7:   5 Similarity of Circles Squares and Rectangles
  66.    wt: 7:   1 Early Concept of Like or Similar Shapes
  67.    wt: 7:   Four Simple Exercises
  68.    wt: 7:   12 Links Lessons elsewhere
  69.    wt: 7:   9 Midpoint Coordinates Half Endpoint Sum
  70.    wt: 7:   8 Mid Point Formula
  71.    wt: 7:   7 Exercises to test skill and concept mastery
  72.    wt: 7:   3 Slope product for perpendicular lines
  73.    wt: 7:   2 point slope equation for a line
  74.    wt: 7:   What is and is not here
  75.    wt: 7:   10 Pythagorean plane distance formula
  76.    wt: 7:   4 Polar Coordinates to and from
  77.    wt: 7:   10 Dropping a perpendicular to line
  78.    wt: 7:   4 Side Side Side
  79.    wt: 6:   11 arctan left inverse of tangent Graph
  80.    wt: 6:   8 arcsin left inverse of sine Graph
  81.    wt: 6:   7 arcsin left inverse of sine Definition
  82.    wt: 6:   6 Graph of arccos function
  83.    wt: 6:   3 Left Inverse of cosine arccos definition
  84.    wt: 6:   8 Radian Measures of Common Angles
  85.    wt: 6:   2 Radian Measure Numerical Value of one degree
  86.    wt: 6:   A Global Time and Navigation
  87.    wt: 6:   15 Dot and Cross Product
  88.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  89.    wt: 6:   12 From Applied To Pure Mathematics
  90.    wt: 6:   9 Head to Tail Coordinate View
  91.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  92.    wt: 6:   2 Signed Coordinates
  93.    wt: 6:   Vector and Complex Number Applet
  94.    wt: 6:   4 graphing y=Asin(x c)
  95.    wt: 6:   Parallel Lines and Parallel Transversals
  96.    wt: 6:   Triangle Angles Sum To 180 Degrees
  97.    wt: 6:   Parallel Lines and Alternating Corresponding Angles
  98.    wt: 6:   Parallel Lines and Interior Angles
  99.    wt: 6:   10 Straight Lines through Origin Equations More
  100.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  101.    wt: 6:   17 tangent function angle sum formulas
  102.    wt: 6:   31 basic secant cosecant cotangent trig identities
  103.    wt: 6:   29 secant cosecant and cotangent for acute angles
  104.    wt: 6:   25 tangent double angle formula Slope connection
  105.    wt: 6:   21 sine and cosine Half Angle Formulas
  106.    wt: 6:   20 sine and cosine Double Angle Formulas
  107.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  108.    wt: 6:   17G Pythagorean Theorem Converse
  109.    wt: 6:   17E Trig Formulas for dot and cross Products
  110.    wt: 6:   17D cis formulas for sine cosines and tangent
  111.    wt: 6:   17C sine and cosine double triple angle formulas
  112.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  113.    wt: 6:   17A The complex number valued trig function cis
  114.    wt: 6:   16 Right Triangle Complementary Angle Relations
  115.    wt: 6:   15 sine cosine Complementary Angle Relations
  116.    wt: 6:   14 cosine even and sine and tangent are odd
  117.    wt: 6:   2 Quadrant I reference Angles
  118.    wt: 6:   1 Unit Points Reflections Rotations
  119.    wt: 6:   21 Logarithms Powers and Exponentials
  120.    wt: 6:   20 N th Roots of Complex Numbers
  121.    wt: 6:   19 N th Roots of Unity
  122.    wt: 6:   18 Sixth Roots of Unity
  123.    wt: 6:   17 Cube Roots of unity
  124.    wt: 6:   14 Law of cosines
  125.    wt: 6:   11 sine and cosine double triple angle formulas
  126.    wt: 6:   6 Field Properties of Complex Number
  127.    wt: 6:   1 Rectangular Polar Coordinates Review
  128.    wt: 6:   8 Triangles Cascade Problem Solving
  129.    wt: 6:   7 Trignometric Ratios Unit Circle
  130.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  131.    wt: 6:   3 Trigonometric Ratios sine and cosine
  132.    wt: 6:   11 Triangle Similarity Missing Side Problem
  133.    wt: 6:   9 Similarity of Triangles Usual Criteria
  134.    wt: 6:   8 Similarity of Triangles and Polygons
  135.    wt: 6:   4 Similarity Definition with Coordinate
  136.    wt: 6:   2 Similarity By Design
  137.    wt: 6:   11 Triangle Inequality
  138.    wt: 6:   9 Pythagorean Theorem Chinese Square Proof
  139.    wt: 6:   1 Cartesian Coordinates sans signs
  140.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  141.    wt: 6:   PS A Kite Construction Methods
  142.    wt: 6:   21 Parallelograms
  143.    wt: 6:   17 Right Bisectors of Triangle Sides
  144.    wt: 6:   11 Triangle Construction Fails
  145.    wt: 6:   9 Construction of a right bisector
  146.    wt: 6:   3 Isometry of Triangles Congruence
  147.    wt: 6:   1 Initial Concepts and Terms
  148.    wt: 6:   14 GCD of 650 110 via Primes LCM via Product Rule
  149.    wt: 6:   9 GCD of 360 110 via Primes and Euclid Algorithm
  150.    wt: 6:   4 LCM of 8 and 10 via Prime
  151.    wt: 5:   16 cotangent function Definition Graph and Inverse
  152.    wt: 5:   15 cosecant function Definition Graph and Inverse
  153.    wt: 5:   14 secant function Definition Graph and Inverse
  154.    wt: 5:   13 cosecant function Definition Graph and Inverse
  155.    wt: 5:   12 motivation for term arctan
  156.    wt: 5:   9 motivation for name arcsin
  157.    wt: 5:   5 Swapping Coordinates is a reflection
  158.    wt: 5:   4 possible motivation for term arccos
  159.    wt: 5:   2 cosine function more properties
  160.    wt: 5:   1 cosine function properties
  161.    wt: 5:   9 Summary Degrees to Radians and back
  162.    wt: 5:   7 Radian Measures in special Triangles
  163.    wt: 5:   6 Radian Measure to Degrees
  164.    wt: 5:   5 Degrees to Radian Measure
  165.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  166.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  167.    wt: 5:   1 Degrees and Radians Introduction
  168.    wt: 5:   3 graphing y=f(x c) plus K
  169.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  170.    wt: 5:   1 graphing y=f(x a)
  171.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  172.    wt: 5:   C Straight Lines Slope from Coordinates
  173.    wt: 5:   B Straight Line Slope Scaling Properties More
  174.    wt: 5:   A Straight Line Slope Scaling Properties
  175.    wt: 5:   14 Straight Lines Equations General Case
  176.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  177.    wt: 5:   12 Straight Lines Graphing mx plus b
  178.    wt: 5:   11 Straight Lines Graphing y=mx
  179.    wt: 5:   9 Straight Lines through Origin Equations
  180.    wt: 5:   8 Straight Lines Equation for vertical
  181.    wt: 5:   7 Tangent Function is odd on this domain
  182.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  183.    wt: 5:   5 Tangent Function Graph
  184.    wt: 5:   4 Tangent Function Properties
  185.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  186.    wt: 5:   1 Straight Lines Slope Concept
  187.    wt: 5:   16 References and Originality Question
  188.    wt: 5:   15 Pythagorean Theorem Converse
  189.    wt: 5:   13 Trig Formulas for dot and cross Products
  190.    wt: 5:   12 cis formulas for sine cosines and tangent
  191.    wt: 5:   9 The complex number valued trig function cis
  192.    wt: 5:   7 Second Way to Calculate Products
  193.    wt: 5:   3 Addition Properties
  194.    wt: 5:   2 Complex Numbers made easier we hope
  195.    wt: 5:   Appetizer A Complex Number Applet
  196.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  197.    wt: 5:   12 Triangles Similarity More Problems
  198.    wt: 5:   7 Translations Rotations Reflections Dilatations
  199.    wt: 5:   6 Geometric Diagrams in Class
  200.    wt: 5:   3 Similarity by Design with coordinates
  201.    wt: 5:   13 Pythagorean spatial distance formulas
  202.    wt: 5:   12 Spatial Coordinates
  203.    wt: 5:   8 Distance Between Points on a Line
  204.    wt: 5:   7 Complex Numbers Appetizer
  205.    wt: 5:   6 Polar Multiplication and Rotation
  206.    wt: 5:   5 Cartesian Addition and Translation
  207.    wt: 5:   3 Rectangular Coordinates Review
  208.    wt: 5:   2 Cartesian Coordinates with signs
  209.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  210.    wt: 5:   PS H Distributive Law For Complex Numbers
  211.    wt: 5:   PS G Rotation Distributes over Addition
  212.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  213.    wt: 5:   PS E Multiplication with Polar Coordinates
  214.    wt: 5:   PS D Addition with Cartesian Coordinates
  215.    wt: 5:   PS B Parallelogram Construction Methods
  216.    wt: 5:   19 Right Triangle Similarity
  217.    wt: 5:   18 Triangle Similarity Take 1
  218.    wt: 5:   16 Angles Subtended By Chords and Diameters
  219.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  220.    wt: 5:   14 Parallel Lines Postulate
  221.    wt: 5:   13 Angle Side Angle Failure
  222.    wt: 5:   12 Side Angle Side Failure
  223.    wt: 5:   8 Isoceles Triangles
  224.    wt: 5:   7 Angle Side Angle
  225.    wt: 5:   6 Ruler and compass Angle Bisection
  226.    wt: 5:   5 Side Angle Side
  227.    wt: 5:   2 Correspondence between Triangles
  228.    wt: 5:   Short Course on Euclidean Geometry
  229.    wt: 5:   About Folder Contents
  230.    wt: 5:   10 Euclid Algorithm with 129 125 and with 45 14
  231.    wt: 4:   8 quadratics backward use of various formulas
  232.    wt: 4:   5 Areas of Rectangles Revisited
  233.    wt: 4:   4 Fraction Operations Axiomatic Development
  234.    wt: 4:   4 Two Examples
  235.    wt: 4:   17 GCD LCM of 85 and 60 via Prime
  236.    wt: 4:   16 GCD and LCM of 650 225 via Prime
  237.    wt: 4:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  238.    wt: 4:   13 GCD from given Prime Factorization
  239.    wt: 4:   11 GCD 2700 288 via Euclid Algorithm
  240.    wt: 4:   8 GCD from Euclidean Algorithm
  241.    wt: 4:   7 GCD and LCM from prime factorization
  242.    wt: 4:   6 GCD from Prime
  243.    wt: 4:   1 Least Common Multiples LCM Introduction
  244.    wt: 4:   12 GCD 2700 288 via Prime
  245.    wt: 4:   25 Divisibility Tests for 2 3 5 9 10 Example
  246.    wt: 4:   24 Divisibility Tests for 2 3 5 9 10
  247.    wt: 4:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  248.    wt: 4:   19 Remainder Arithmetic Rule of 9 for checking sums III
  249.    wt: 4:   18 Remainder Arithmetic Rule of 9 for checking sums II
  250.    wt: 4:   17 Remainder Arithmetic Rule of 9 for checking sums I
  251.    wt: 4:   10 Names for Big Numbers and Powers of Ten Expansion
  252.    wt: 4:   4 Groups of 3 Place Value in Decimal Fractions
  253.    wt: 4:   10 Three one sided limits with infinite values
  254.    wt: 3:   Mathematics Education Professors
  255.    wt: 3:   Maps Plans Drawings
  256.    wt: 3:   Secondary Two Mathematics
  257.    wt: 3:   04 29 New Mathematics Curriculum
  258.    wt: 3:   04 25 when to stop or suspend mathemat
  259.    wt: 3:   Theory of Knowledge
  260.    wt: 3:   Different Kinds of Reasoning in maths
  261.    wt: 3:   three kinds of reason in mathematics
  262.    wt: 3:   cultivating intelligence
  263.    wt: 3:   chapitre 04 10 Etapes pour une meilleur raison
  264.    wt: 3:   chapitre 04 04 Parlons de la logique
  265.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  266.    wt: 3:   10 Interval Notation
  267.    wt: 3:   4 Function notation in and beyond mathematics
  268.    wt: 3:   1 Geometric Introduction of Function Notation
  269.    wt: 3:   10 quadratic exercises
  270.    wt: 3:   9 quadratics physical and further context
  271.    wt: 3:   6 quadratics numerical approach
  272.    wt: 3:   5 quadratics completing the square
  273.    wt: 3:   3 quadratics factoring by inspection
  274.    wt: 3:   2 quadratics graphing in general
  275.    wt: 3:   1 quadratics graphing exercises
  276.    wt: 3:   Quadratics in 10 steps
  277.    wt: 3:   4 Commutative Law Groups Counting Form
  278.    wt: 3:   1 The Counting Origins of Numbers
  279.    wt: 3:   3 Inequalities Algebraically
  280.    wt: 3:   2 Fraction Operations Physical Development
  281.    wt: 3:   1 Decimals Modular and Remainder Arithmetic
  282.    wt: 3:   4 Changing Letters
  283.    wt: 3:   4 GE III Animated Examples
  284.    wt: 3:   10 One Example
  285.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  286.    wt: 3:   4 A Brief Story of numbers and algebra
  287.    wt: 3:   4 Greater More Less Than Signs in General
  288.    wt: 3:   3 Properties of Square Roots with example
  289.    wt: 3:   1 Squares and Square Roots Introduction
  290.    wt: 3:   5 Common Divisors 60 45 via Prime
  291.    wt: 3:   LCM 60 45 Avoid List Method Use Prime
  292.    wt: 3:   2 Least Common Multiple LCM intro via list method
  293.    wt: 3:   10 Simplification of Fractions and Mixed Numerals
  294.    wt: 3:   27 Divisibility by 2 3 6 5 9 10 Example
  295.    wt: 3:   26 Divisibility by 2 3 5 Example
  296.    wt: 3:   23 Remainder Arithmetic Modulo 2
  297.    wt: 3:   22 Remainder Arithmetic Modulo 3 more
  298.    wt: 3:   21 Remainder Arithmetic Modulo 3
  299.    wt: 3:   16 Remainder Arithmetic Modulo 9 Example 2
  300.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  301.    wt: 3:   10 Remainder Arithmetic Long Division by 5 Quickly
  302.    wt: 3:   4 Remainder Arithmetic Modulo 10 in general
  303.    wt: 3:   3 Remainder Arithmetic Modulos 10 more still
  304.    wt: 3:   2 Remainder Arithmetic Modulo 10 more
  305.    wt: 3:   1 Remainder Arithmetic Modulo 10
  306.    wt: 3:   10 Division by Five Long and Short Ways
  307.    wt: 3:   4 Division with 2 Digit Divsors
  308.    wt: 3:   4 Two and Three Digit Multipliers
  309.    wt: 3:   010 Repeated Addition of Time Intervals
  310.    wt: 3:   Example 2 volume of a cone
  311.    wt: 3:   Area Between Crossing Curves Lesson Take 2
  312.    wt: 3:   4 Definite Integrals Evaluation Exercises
  313.    wt: 3:   3 Two Chain Rule Method Exercises
  314.    wt: 3:   2 Indefinite Integrals Exercises
  315.    wt: 3:   4 Second derivative test exercise example
  316.    wt: 3:   3 Second derivative test
  317.    wt: 3:   1 Two cubic sketching exercises with 1st derivative
  318.    wt: 3:   17 Derivatives of quotients of sine and cosine
  319.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  320.    wt: 3:   9 Limits Continuity and Composition
  321.    wt: 3:   5 Jumps and absence of unlimited error control
  322.    wt: 3:   4 Numerical properties
  323.    wt: 3:   1 Numerical introduction
  324.    wt: 3:   Chapter 10 Describing and Changing Calculations
  325.    wt: 3:   Chapter 4 Longer Chains of Reason
  326.    wt: 3:   Appendix A Calculus with Proofs for Keen or Gifted
  327.    wt: 3:   5 Interpreting and Drawing Maps and Plans.
  328.    wt: 2:   10 statistics
  329.    wt: 2:   which way to go
  330.    wt: 2:   Teach the teachers plus goals
  331.    wt: 2:   activities for students
  332.    wt: 2:   site eurekas
  333.    wt: 2:   About site lesson plans
  334.    wt: 2:   key notes and themes
  335.    wt: 2:   grouping students according to ability
  336.    wt: 2:   what should be learnt and When
  337.    wt: 2:   Postscript 2007 01 10
  338.    wt: 2:   five decades make a difference
  339.    wt: 2:   Secondary Three Mathematics
  340.    wt: 2:   geometric implications for algebra
  341.    wt: 2:   05 13 OldSiteEntrancePage
  342.    wt: 2:   02 21 words for teachers
  343.    wt: 2:   02 20 mathematics education references
  344.    wt: 2:   three aims for mathematics students
  345.    wt: 2:   standards for course material
  346.    wt: 2:   Operational Viewpoint to Value
  347.    wt: 2:   formal or informal peer review
  348.    wt: 2:   mathematics instruction in general
  349.    wt: 2:   Education in mathematics science and technology
  350.    wt: 2:   Four ways to improve education reform
  351.    wt: 2:   Leaner mathematics curriculum
  352.    wt: 2:   chapitre 04 09 Regles accidentelles
  353.    wt: 2:   chapitre 04 08 Limitations et benefices
  354.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  355.    wt: 2:   chapitre 04 06 engagements
  356.    wt: 2:   chapitre 04 05 Implication versus suggestion
  357.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  358.    wt: 2:   chapitre 04 02 Deuxieme enigme
  359.    wt: 2:   chapitre 04 01 Premiere enigme
  360.    wt: 2:   chapitre 04 00 Les regles d implication
  361.    wt: 2:   10 Ends values for work study instruction
  362.    wt: 2:   4 Learning Takes Time and Effort
  363.    wt: 2:   Ages 10 to 12 Geometry
  364.    wt: 2:   Ages 10 to 12 Arithmetic
  365.    wt: 2:   15 Sign analysis of functions
  366.    wt: 2:   11 Function Domain Range Source and Targets
  367.    wt: 2:   8 Set view of relations and functions
  368.    wt: 2:   2 Algebraic use of function notation
  369.    wt: 2:   A Quadratics Summary
  370.    wt: 2:   7 quadratic formulla derivation
  371.    wt: 2:   10 Exponential Growth and Decay Models
  372.    wt: 2:   4 Polynomials Long division linear divisor
  373.    wt: 2:   21 Addition of Multiples of a Single Vector
  374.    wt: 2:   19 Signed Multiples of Vectors
  375.    wt: 2:   8 Division and Mulplication of Compound Fractions
  376.    wt: 2:   4 Location of Point in Decimal Addition
  377.    wt: 2:   3 Location of Point in Decimal Multiplication
  378.    wt: 2:   4 Rates Ratios and Proporitionality
  379.    wt: 2:   4 Comparison of Negative Numbers
  380.    wt: 2:   8 Coordinates for Maps and Planes
  381.    wt: 2:   5 Independent versus Dependent Variables
  382.    wt: 2:   3 Geometric Formulas and Function Notation
  383.    wt: 2:   2 Computation Rules Evaluation
  384.    wt: 2:   1 Formulas Dependence and Function Notation
  385.    wt: 2:   1 GE Substitution four examples
  386.    wt: 2:   4 Solving a triangular system exercise
  387.    wt: 2:   4 Four Examples Fractional Coefficients
  388.    wt: 2:   Skill Development Notes
  389.    wt: 2:   7 Two Examples
  390.    wt: 2:   3 Two Examples
  391.    wt: 2:   10 Volume of Pyramid
  392.    wt: 2:   6 Three Notions of What is a Variable
  393.    wt: 2:   3 Comparison of Negative Numbers
  394.    wt: 2:   1 More and Less Than for Counts and Measures
  395.    wt: 2:   5 Square Roots with primes more still
  396.    wt: 2:   4 Square Roots with primes more
  397.    wt: 2:   2 Square Roots with Prime
  398.    wt: 2:   10 dividing signed numbers
  399.    wt: 2:   4 signed coordinates for regions in space
  400.    wt: 2:   6 Multiplication of Mixed Numbers
  401.    wt: 2:   3 Unit fraction of a fraction
  402.    wt: 2:   10 Integer Multiplication Formulas
  403.    wt: 2:   4 Adding Movements wiht opposite directions
  404.    wt: 2:   A Decimals Modular and Remainder Arithmetic
  405.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  406.    wt: 2:   14 Remainder Arithmetic Modulo 9 Example
  407.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  408.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  409.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  410.    wt: 2:   8 Remainder Arithmetic Morulo 5 Examples II
  411.    wt: 2:   7 Remainder Arithmetic Modulo 5 Examples I
  412.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  413.    wt: 2:   5 Remainder Arithmetic Modulo 5
  414.    wt: 2:   10 video Prime Factorization upto 23 squared
  415.    wt: 2:   4 video Prime Factorization Introduction
  416.    wt: 2:   11 Another Single Digit Divisor Example
  417.    wt: 2:   1 Divsion Physical Examples
  418.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  419.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  420.    wt: 2:   4. How to add with decimals B with conversions
  421.    wt: 2:   1. Explaining Addition Table
  422.    wt: 2:   11 Place Value SI Standard International way
  423.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  424.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  425.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  426.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  427.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  428.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  429.    wt: 2:   1 Place Value in Three Digit Whole Numbers
  430.    wt: 2:   012 Division of Time Intervals by Time Intervals
  431.    wt: 2:   011 Division of Time Intervals By Numbers
  432.    wt: 2:   4 Mixing and Changing Units of Time
  433.    wt: 2:   Example 1 volume of a pyramid
  434.    wt: 2:   Volume of Solid by Cross Sections Lesson
  435.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  436.    wt: 2:   Example 4 with x function of y
  437.    wt: 2:   Example 2
  438.    wt: 2:   Area Between Curves Lesson Take 1
  439.    wt: 2:   A Related Material in Volume 3
  440.    wt: 2:   5 Area Under Curve Exercise
  441.    wt: 2:   1 Chain Rule in Reverse Integration Method
  442.    wt: 2:   A Related lessons in Volume 3
  443.    wt: 2:   2 Second derivative test prequel
  444.    wt: 2:   38 Formulas and derivatives for powers and roots
  445.    wt: 2:   34 Derivative of exponential function
  446.    wt: 2:   31 Derivatives of inverse functions
  447.    wt: 2:   30Chain Rule A Proof
  448.    wt: 2:   29 Chain Rule Optional Reading
  449.    wt: 2:   28 Chain Rule Preparation for a Proof
  450.    wt: 2:   19 Chain Rule for linear functions
  451.    wt: 2:   14 sine and cosine derivatives 2nd step
  452.    wt: 2:   13 sine and cosine derivatives 1st step
  453.    wt: 2:   10 Power rule for negative integers
  454.    wt: 2:   8 Differentiation of polynomials
  455.    wt: 2:   4 Sum Rule
  456.    wt: 2:   3 Motivation for Limit Definition Take 2
  457.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  458.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  459.    wt: 2:   11 Limits at infinity Three Examples
  460.    wt: 2:   8 Four Animated Examples
  461.    wt: 2:   7 Evaluation by immediate or delayed substitution
  462.    wt: 2:   6 Continuity at a point
  463.    wt: 2:   3 Decimal insights for limits continuity convergence
  464.    wt: 2:   2 Algebraic codification
  465.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  466.    wt: 2:   G.3 Constant Difference Theorem Proof
  467.    wt: 2:   Chapter 10 Slopes and Units
  468.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  469.    wt: 2:   Chapter 31 Direct and Indirect Reason
  470.    wt: 2:   Chapter 21. Third Reading Guide
  471.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  472.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  473.    wt: 2:   Chapter 11. Why Shorthand
  474.    wt: 2:   Chapter 6 Change of Language
  475.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  476.    wt: 2:   Chapter 3 Chains of Reason
  477.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  478.    wt: 2:   Chapter 10 Transition
  479.    wt: 2:   Chapter 7 Two Treatments of Geometry
  480.    wt: 2:   Chapter 10 Responsibility
  481.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  482.    wt: 2:   Chapter 1 Arithmetic
  483.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  484.    wt: 2:   4 Money Matters Saving Earning Buying Selling and Budgets
  485.    wt: 2:   1 From Number Recognition and Counting to Arithmetic A
  486.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  487.    wt: 1:   Skills Chapter 1 Arithmetic
  488.    wt: 1:   Skills Chapter 0 Introduction
  489.    wt: 1:   4 algebra
  490.    wt: 1:   why bother
  491.    wt: 1:   website reviews
  492.    wt: 1:   three goals to set for students
  493.    wt: 1:   permissions for teachers
  494.    wt: 1:   Math Ed if it must be short make it lean effective
  495.    wt: 1:   Applied Maths Program14092009 POMME variant
  496.    wt: 1:   links Education Resources online
  497.    wt: 1:   site origins
  498.    wt: 1:   teacher certification
  499.    wt: 1:   modern education
  500.    wt: 1:   learning takes time
  501.    wt: 1:   mathematics in context
  502.    wt: 1:   Education Reform Inconsistencies
  503.    wt: 1:   how letters appear
  504.    wt: 1:   Secondary One Mathematics
  505.    wt: 1:   talk the algebra talk
  506.    wt: 1:   three difficulties
  507.    wt: 1:   teaching tips
  508.    wt: 1:   What to Tell Students
  509.    wt: 1:   mathematics curriculum shifts
  510.    wt: 1:   teaching tutoring algebraic reason
  511.    wt: 1:   Lessening Algebra Difficulties
  512.    wt: 1:   the trouble with algebra
  513.    wt: 1:   three goals for Mathematics Education
  514.    wt: 1:   How to be a better instructor
  515.    wt: 1:   Motivation and Context Problem
  516.    wt: 1:   need for a mixed mathematics curriculum
  517.    wt: 1:   Prequel In For A Penny In For A Pound
  518.    wt: 1:   education an empirical art
  519.    wt: 1:   fairness and inductive principles for instruction
  520.    wt: 1:   words for mathematics instructor
  521.    wt: 1:   chapitre 12 00 les iles et division
  522.    wt: 1:   chapitre 07 01 principle D induction mathematique
  523.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  524.    wt: 1:   chapitre 06 00 Chaines de la raison
  525.    wt: 1:   chapitre 05 00 Deception
  526.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  527.    wt: 1:   chapitre 02 00 La Communication des idees
  528.    wt: 1:   chapitre 01 00 Introduction
  529.    wt: 1:   problemes responses
  530.    wt: 1:   problemes algebre et arithmetique
  531.    wt: 1:   4 Energy Power Heat09
  532.    wt: 1:   D Energy Power04
  533.    wt: 1:   A Energy Power01
  534.    wt: 1:   F Wire Resistance Calculation04
  535.    wt: 1:   2 Unlike resistors in parallel01
  536.    wt: 1:   1 Like resistors in series
  537.    wt: 1:   E Kirchoffs Second Law
  538.    wt: 1:   D Kirchoff First Law
  539.    wt: 1:   C Electromotive force conventional current02
  540.    wt: 1:   A Circuit Elements
  541.    wt: 1:   Home Tutoring and Home Schooling
  542.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  543.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  544.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  545.    wt: 1:   11 Help and Defend Your Child or Teens Education
  546.    wt: 1:   8 The Effect of Negative Remarks
  547.    wt: 1:   1 Speaking Skills
  548.    wt: 1:   Ages 9 to 10
  549.    wt: 1:   Ages 4 plus to 5 plus
  550.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  551.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  552.    wt: 1:   sign monoticity analysis example 1
  553.    wt: 1:   26 Function definitions done and coming
  554.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  555.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  556.    wt: 1:   23 Inverse Functions
  557.    wt: 1:   22 Square Root function graphically
  558.    wt: 1:   20 Interchanging coordinates a reflection
  559.    wt: 1:   19 Horizontal line rule and method
  560.    wt: 1:   18 Vertical Line Rule and Method
  561.    wt: 1:   17 Function maxima minima and their location
  562.    wt: 1:   16 Increasing or decreasing on intervals
  563.    wt: 1:   14 Surjections Injections Bijections
  564.    wt: 1:   13 From one to one to many to one
  565.    wt: 1:   12 Function Domain Recognition Exercises
  566.    wt: 1:   9 Set theory term relation possible origins
  567.    wt: 1:   7 Functions with finite domains
  568.    wt: 1:   6 Set Existence Formation and Notation
  569.    wt: 1:   5 Function notation for geometric transformations
  570.    wt: 1:   3 Formula or function graphing exercise
  571.    wt: 1:   Introduction Reading Guide
  572.    wt: 1:   11 Growth and Decay in Biology
  573.    wt: 1:   1 Calculator Starter Exercises
  574.    wt: 1:   8 Notes for instructors or tutors
  575.    wt: 1:   7 Links Lessons Elsewhere
  576.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  577.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  578.    wt: 1:   3 Polynomials Multiplication Addition
  579.    wt: 1:   2 Column Multiplication Method
  580.    wt: 1:   1 Polynomials Distributive Law
  581.    wt: 1:   23 Distributive Law Two Derivations
  582.    wt: 1:   22 Multiplication of Signed Numbers
  583.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  584.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  585.    wt: 1:   13 Arrows and Vectors in a Plane
  586.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  587.    wt: 1:   9 Division with Digits after Decimal Point
  588.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  589.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  590.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  591.    wt: 1:   2 Counting Digits in Decimal Multiplication
  592.    wt: 1:   1 Fractions with Finite Decimal Expansions
  593.    wt: 1:   E Long Division Methods more
  594.    wt: 1:   D Long Division Methods
  595.    wt: 1:   C Three Decimal Subtraction Methods
  596.    wt: 1:   B Decimal Comparison and Subtraction
  597.    wt: 1:   A Decimal Addition Columm Methods
  598.    wt: 1:   8 Column Multiplication Methods in General
  599.    wt: 1:   7 Decimals Multiplication Methods Examples
  600.    wt: 1:   6 Column Methods for Decimal Multiplication
  601.    wt: 1:   5 Distributive Law for Whole Numbers
  602.    wt: 1:   3 Multiplicative Counting Skills Principles
  603.    wt: 1:   2 Combing Counts Addition Skills and Principles
  604.    wt: 1:   1 What is Proportionality
  605.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  606.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  607.    wt: 1:   4 Subtraction and Division Axioms
  608.    wt: 1:   3 Product Axioms Two Forms
  609.    wt: 1:   10 Real Number Lengths and Signs
  610.    wt: 1:   9 Coordinates for Regions in Space
  611.    wt: 1:   7 Real Numbers as Line Cordinates
  612.    wt: 1:   6 Unsigned Real Numbers
  613.    wt: 1:   4 Rational Numbers
  614.    wt: 1:   Simple Exercises
  615.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  616.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  617.    wt: 1:   3 GE III Equation Addition and Multiplication
  618.    wt: 1:   2 GE II Comparison
  619.    wt: 1:   1 Essentially One Unknown
  620.    wt: 1:   1 Proper Equal Sign Usage
  621.    wt: 1:   9 Three Examples
  622.    wt: 1:   8 One Example
  623.    wt: 1:   6 Three Examples
  624.    wt: 1:   5 Three Examples
  625.    wt: 1:   2 Three Examples
  626.    wt: 1:   11 Volume of Sphere
  627.    wt: 1:   9 Volume of Cone
  628.    wt: 1:   4 Circle Area Formula Example
  629.    wt: 1:   8 Sets of Numbers
  630.    wt: 1:   4 Subset Builder Notation
  631.    wt: 1:   5 Talking about Numbers and Quantities
  632.    wt: 1:   3 Adding Words To Arithmetic
  633.    wt: 1:   2 What is a Variable
  634.    wt: 1:   1 Three Skills For Algebra
  635.    wt: 1:   2 More and Less Than with Unlike Signs
  636.    wt: 1:   11 What are real lengths and numbers
  637.    wt: 1:   5 lengths and signs of numbers
  638.    wt: 1:   3 signed coordinates for maps and planes
  639.    wt: 1:   6 Simplification of Fractions with Units
  640.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  641.    wt: 1:   B Fractions and Two Term Ratios
  642.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  643.    wt: 1:   17 Efficient Ways to Add and Subtract
  644.    wt: 1:   16 Addition Subtraction Comparision Compared
  645.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  646.    wt: 1:   14 Adding and Subtracting with Like Denominators
  647.    wt: 1:   13 Fraction Comparison Algebraic View
  648.    wt: 1:   12 Fraction Comparison
  649.    wt: 1:   11 Simplification an Algebraic View
  650.    wt: 1:   9 Improper Fractions and Mixed Numbers
  651.    wt: 1:   8 Numerals Fractionals Quantals Take II
  652.    wt: 1:   7 Numerals Fractionals Quantals
  653.    wt: 1:   6 Multiplication Algebraically Take II
  654.    wt: 1:   5 Equivalent Fractions
  655.    wt: 1:   4 Fraction Multiplication
  656.    wt: 1:   2 Unit Fraction Multiplication
  657.    wt: 1:   1 What is a fraction Take II
  658.    wt: 1:   1 What is a fraction
  659.    wt: 1:   11 Adding Integers Formulas and Examples
  660.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  661.    wt: 1:   1 Integers as Coordinates
  662.    wt: 1:   20 Uniqueness of Prime Factorization
  663.    wt: 1:   16 video Factors of 980 using prime
  664.    wt: 1:   15 video Factors of 20 using Prime Factorization
  665.    wt: 1:   14 video Factors of 24 Take II
  666.    wt: 1:   13 video Factors of 24 using prime
  667.    wt: 1:   11 Efficient Square Rule Use
  668.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  669.    wt: 1:   1 video how Products are bigger than factor
  670.    wt: 1:   Long Division Backwards more
  671.    wt: 1:   Long Division Backward
  672.    wt: 1:   Division with Counts and Length
  673.    wt: 1:   Long Division forwards and backwards Example 3
  674.    wt: 1:   Long Division forwards and backwards Example 2
  675.    wt: 1:   Long Division forwards and backwards Example 1
  676.    wt: 1:   12 Why Long Division Works Take III
  677.    wt: 1:   9 Why Long Division Works Take II
  678.    wt: 1:   8 Correcting the Mistake
  679.    wt: 1:   7 Long Divison Mistake Catching
  680.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  681.    wt: 1:   5 Long Division Include Zeroes or not
  682.    wt: 1:   3 Division Single Digit Divisor Example
  683.    wt: 1:   2 Division with Single Digit Divisors
  684.    wt: 1:   D Decimal Multiplication Methods Derived
  685.    wt: 1:   C Counting Areas with Powers of Ten
  686.    wt: 1:   B Powers of Ten
  687.    wt: 1:   1 Why 3 times 5 gives 15
  688.    wt: 1:   8 Subtraction with Units of Measure
  689.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  690.    wt: 1:   8 What skills and work habits to require
  691.    wt: 1:   7 Adding decimal fractions using decimal point
  692.    wt: 1:   6. Counting and adding units and mixed units
  693.    wt: 1:   5. How to add decimals C. Examples
  694.    wt: 1:   3. How to add with decimals A sans conversions
  695.    wt: 1:   2 Decimal Counting Practices
  696.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  697.    wt: 1:   Quick history of numbers and algebra
  698.    wt: 1:   016 Numbering Occidental Calendar Days
  699.    wt: 1:   015 School and work day counting tables
  700.    wt: 1:   014 Counting Days with Calendars
  701.    wt: 1:   013 Travel Time Tables
  702.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  703.    wt: 1:   8 Addition of Time Intervals via subtotaling
  704.    wt: 1:   7 Addition of Time Intervals
  705.    wt: 1:   3 Units and Lengths of Time
  706.    wt: 1:   1 Intro of Kids To Time Date Skills
  707.    wt: 1:   Example 1. Area Between x and x squared
  708.    wt: 1:   Example 3
  709.    wt: 1:   Example 1
  710.    wt: 1:   Area Between Curves Lesson Take 2
  711.    wt: 1:   Summary
  712.    wt: 1:   A Chain Rule Real Player video examples
  713.    wt: 1:   36 Cube root derivative animated
  714.    wt: 1:   33 Chain Rule Real Player video examples
  715.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  716.    wt: 1:   26 Chain Rule Recognising outer inner functions
  717.    wt: 1:   25 Chain Rule Animated Examples Continued
  718.    wt: 1:   24 Chain Rule Animated Examples
  719.    wt: 1:   23 Chain Rule in general
  720.    wt: 1:   22 Chain Rule for polynomials
  721.    wt: 1:   21 Chain Rule for powers
  722.    wt: 1:   20 Chain Rule for Pulley Systems
  723.    wt: 1:   18 Chain Rule Introduction
  724.    wt: 1:   15 sine and cosine derivatives 3rd step
  725.    wt: 1:   12 Quotient rule examples
  726.    wt: 1:   11 Quotient rule
  727.    wt: 1:   9 Reciprocal rule
  728.    wt: 1:   7 Animated Differentiation Examples
  729.    wt: 1:   6 Power rule from product rule
  730.    wt: 1:   5 Product Rule
  731.    wt: 1:   2 Motivation for Limit Definition Take 1
  732.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  733.    wt: 1:   F.3 Intermediate Value Theorem
  734.    wt: 1:   F.2 Closed Range Theorem
  735.    wt: 1:   E2 Algebraic Properties of Limits
  736.    wt: 1:   D2 Limits of Monotone Sequences
  737.    wt: 1:   C Triangle Inequalities
  738.    wt: 1:   PostScript For and Against Decimal Perspectives
  739.    wt: 1:   A1. Introduction
  740.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  741.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  742.    wt: 1:   Chapter 23 Links To Trigonometry
  743.    wt: 1:   Chapter 21 Arrow Addition
  744.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  745.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  746.    wt: 1:   Chapter 11. Graphing Slope versus Position
  747.    wt: 1:   Chapter 4. More Slope Sign Analysis
  748.    wt: 1:   Chapter 1.Introduction
  749.    wt: 1:   Foreword
  750.    wt: 1:   Postscript More on Better Performance
  751.    wt: 1:   Postscript For Better Performance
  752.    wt: 1:   Appendix E. How To Study Mathematics and Why
  753.    wt: 1:   Appendix D. What to do in School and Why
  754.    wt: 1:   Appendix C. How to Read
  755.    wt: 1:   Appendix B. How To Learn
  756.    wt: 1:   Chapter 30 Truth Tables
  757.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  758.    wt: 1:   Chapter 28 Occurrence Tables
  759.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  760.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  761.    wt: 1:   Chapter 25. Mathematical Induction Examples
  762.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  763.    wt: 1:   Chapter 23. Notation For Sums
  764.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  765.    wt: 1:   Chapter 20. Degrees and Radians
  766.    wt: 1:   Chapter 19. Functions and Sets
  767.    wt: 1:   Chapter 18. Rules for Algebra
  768.    wt: 1:   Chapter 16. Painless Theorem Proving
  769.    wt: 1:   Chapter 15. Solving Linear Equations
  770.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  771.    wt: 1:   Chapter 13. Second Reading Guide
  772.    wt: 1:   Chapter 12. Shorthand Usage Guide
  773.    wt: 1:   Postscript What is a Variable
  774.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  775.    wt: 1:   Chapter 8 Three Skills For Algebra
  776.    wt: 1:   Solutions For Arithmetic Exercises
  777.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  778.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  779.    wt: 1:   Foreword
  780.    wt: 1:   Chapter 11 Elementary Instruction
  781.    wt: 1:   Chapter 9 The Two Ends
  782.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  783.    wt: 1:   Chapter 1 Introduction
  784.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  785.    wt: 1:   Chapter 21 Occurrence Tables
  786.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  787.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  788.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  789.    wt: 1:   Chapter 11 Accidental Patterns
  790.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  791.    wt: 1:   Chapter 8 Change of Language
  792.    wt: 1:   Chapter 7 Longer Chains of Reason
  793.    wt: 1:   Chapter 6 Chains of Reason
  794.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  795.    wt: 1:   Chapter 1 Introduction
  796.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  797.    wt: 1:   N Improving Marks on Tests and Finals
  798.    wt: 1:   J. More on written work and showing skill
  799.    wt: 1:   D. Check work a must with a caution
  800.    wt: 1:   C. Domino effect of being careful
  801.    wt: 1:   B. Domino effect of errors
  802.    wt: 1:   A. Skill has to be seen to believed
  803.    wt: 1:   Chapter 8 Skipped Topics and Why
  804.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  805.    wt: 1:   Chapter 6 More Algebra and Geometry
  806.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  807.    wt: 1:   Chapter 3 Algebra Starter Lessons
  808.    wt: 1:   Chapter 2 Why Sets
  809.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  810.    wt: 1:   7 Games and Activities for Instruction
  811.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  812.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  813.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  814.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  815.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  816.    wt: 11:   4 Angles on Maps Plans drawn to scale
  817.    wt: 10:   4 Resultant of a Sum of Movements
  818.    wt: 10:   10 Similarity of Triangles Equivalent of Two Criteria
  819.    wt: 10:   10 Midpoint of [a b] and [b a]
  820.    wt: 10:   8 More Use of Maps Not Drawn to Scale
  821.    wt: 10:   3 Lengths and Areas on Maps and Plans
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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