Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

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

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.

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11 matches:

  1.    wt: 6:   Volume 1A Pattern Based Reason/
  2.    wt: 4:   Volume 1 Elements of Reason/
  3.    wt: 2:   Volume 1A Regles et modeles/
  4.    wt: 2:   10 Examples of Algebraic Reasoning/
  5.    wt: 1:   A Origins of Counting and Figuring Methods/
  6.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  7.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  8.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  9.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  10.    wt: 1:   Volume 2 Three Skills For Algebra/
  11.    wt: 1:   Volume 1B Mathematics Curriculum Notes/

Web Page Search

188 matches:

  1.    wt: 2:   Different Kinds of Reasoning in maths
  2.    wt: 2:   three kinds of reason in mathematics
  3.    wt: 2:   4 Resultant of a Sum of Movements
  4.    wt: 2:   27 Logarithmic use of products of sines and cosines
  5.    wt: 2:   5 An Easy Proof of the Distributive Law
  6.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  7.    wt: 2:   21 Addition of Multiples of a Single Vector
  8.    wt: 2:   11 Volume of Sphere
  9.    wt: 2:   10 Volume of Pyramid
  10.    wt: 2:   9 Volume of Cone
  11.    wt: 2:   Example 2 volume of a cone
  12.    wt: 2:   Example 1 volume of a pyramid
  13.    wt: 2:   Volume of Solid by Cross Sections Lesson
  14.    wt: 2:   17 Derivatives of quotients of sine and cosine
  15.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  16.    wt: 2:   Chapter 4 Longer Chains of Reason
  17.    wt: 2:   Chapter 3 Chains of Reason
  18.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  19.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  20.    wt: 2:   Chapter 7 Longer Chains of Reason
  21.    wt: 2:   Chapter 6 Chains of Reason
  22.    wt: 1:   Mathematics Education Professors
  23.    wt: 1:   teaching tutoring algebraic reason
  24.    wt: 1:   Theory of Knowledge
  25.    wt: 1:   E Kirchoffs Second Law
  26.    wt: 1:   D Kirchoff First Law
  27.    wt: 1:   A Circuit Elements
  28.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  29.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  30.    wt: 1:   8 The Effect of Negative Remarks
  31.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  32.    wt: 1:   15 Sign analysis of functions
  33.    wt: 1:   8 Set view of relations and functions
  34.    wt: 1:   2 Algebraic use of function notation
  35.    wt: 1:   1 Geometric Introduction of Function Notation
  36.    wt: 1:   8 quadratics backward use of various formulas
  37.    wt: 1:   4 quadratics difference of two squares
  38.    wt: 1:   11 arctan left inverse of tangent Graph
  39.    wt: 1:   10 arctan left inverse of tangent Definition
  40.    wt: 1:   8 arcsin left inverse of sine Graph
  41.    wt: 1:   7 arcsin left inverse of sine Definition
  42.    wt: 1:   6 Graph of arccos function
  43.    wt: 1:   3 Left Inverse of cosine arccos definition
  44.    wt: 1:   8 Radian Measures of Common Angles
  45.    wt: 1:   2 Radian Measure Numerical Value of one degree
  46.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  47.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  48.    wt: 1:   Straight Lines Intersection of
  49.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  50.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  51.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  52.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  53.    wt: 1:   32 seven rows of pascals triangle
  54.    wt: 1:   30 unit circle calculation of six trigonometric functions
  55.    wt: 1:   28 Expressing products of sines cosines as sums
  56.    wt: 1:   26 Formulas for products of sines and cosines
  57.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  58.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  59.    wt: 1:   18 sum of sinusoidal waves as a single wave
  60.    wt: 1:   17F Law of cosines
  61.    wt: 1:   13 Graph of tangent function many periods
  62.    wt: 1:   12 Graph of tangent function for one period
  63.    wt: 1:   10 Graphs of sines and cosines many periods
  64.    wt: 1:   9 Graphs of sine and cosine over one period
  65.    wt: 1:   8 period of tangent function
  66.    wt: 1:   7 period of sine and cosine
  67.    wt: 1:   Unit Circle Development of Trigonometry
  68.    wt: 1:   20 N th Roots of Complex Numbers
  69.    wt: 1:   19 N th Roots of Unity
  70.    wt: 1:   18 Sixth Roots of Unity
  71.    wt: 1:   17 Cube Roots of unity
  72.    wt: 1:   14 Law of cosines
  73.    wt: 1:   8 Unit Circle Development of Trigonometry
  74.    wt: 1:   6 Field Properties of Complex Number
  75.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  76.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  77.    wt: 1:   9 Similarity of Triangles Usual Criteria
  78.    wt: 1:   8 Similarity of Triangles and Polygons
  79.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  80.    wt: 1:   1 Early Concept of Like or Similar Shapes
  81.    wt: 1:   10 Midpoint of [a b] and [b a]
  82.    wt: 1:   6 Intersection of lines by solving linear systems
  83.    wt: 1:   5 Algebraic View of Slopes
  84.    wt: 1:   1 Numerical view of lines and their equations
  85.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  86.    wt: 1:   17 Right Bisectors of Triangle Sides
  87.    wt: 1:   9 Construction of a right bisector
  88.    wt: 1:   3 Isometry of Triangles Congruence
  89.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  90.    wt: 1:   22 Multiplication of Signed Numbers
  91.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  92.    wt: 1:   19 Signed Multiples of Vectors
  93.    wt: 1:   8 Division and Mulplication of Compound Fractions
  94.    wt: 1:   4 Location of Point in Decimal Addition
  95.    wt: 1:   3 Location of Point in Decimal Multiplication
  96.    wt: 1:   1 The Counting Origins of Numbers
  97.    wt: 1:   5 Areas of Rectangles Revisited
  98.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  99.    wt: 1:   4 Comparison of Negative Numbers
  100.    wt: 1:   5 Box Volume Formula Example
  101.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  102.    wt: 1:   8 Sets of Numbers
  103.    wt: 1:   6 Three Notions of What is a Variable
  104.    wt: 1:   4 A Brief Story of numbers and algebra
  105.    wt: 1:   3 Comparison of Negative Numbers
  106.    wt: 1:   3 Properties of Square Roots with example
  107.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  108.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  109.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  110.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  111.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  112.    wt: 1:   4 LCM of 8 and 10 via Prime
  113.    wt: 1:   5 lengths and signs of numbers
  114.    wt: 1:   6 Simplification of Fractions with Units
  115.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  116.    wt: 1:   6 Multiplication of Mixed Numbers
  117.    wt: 1:   3 Unit fraction of a fraction
  118.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  119.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  120.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  121.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  122.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  123.    wt: 1:   20 Uniqueness of Prime Factorization
  124.    wt: 1:   16 video Factors of 980 using prime
  125.    wt: 1:   15 video Factors of 20 using Prime Factorization
  126.    wt: 1:   14 video Factors of 24 Take II
  127.    wt: 1:   13 video Factors of 24 using prime
  128.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  129.    wt: 1:   C Counting Areas with Powers of Ten
  130.    wt: 1:   B Powers of Ten
  131.    wt: 1:   8 Subtraction with Units of Measure
  132.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  133.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  134.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  135.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  136.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  137.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  138.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  139.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  140.    wt: 1:   Quick history of numbers and algebra
  141.    wt: 1:   012 Division of Time Intervals by Time Intervals
  142.    wt: 1:   011 Division of Time Intervals By Numbers
  143.    wt: 1:   010 Repeated Addition of Time Intervals
  144.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  145.    wt: 1:   8 Addition of Time Intervals via subtotaling
  146.    wt: 1:   7 Addition of Time Intervals
  147.    wt: 1:   4 Mixing and Changing Units of Time
  148.    wt: 1:   3 Units and Lengths of Time
  149.    wt: 1:   1 Intro of Kids To Time Date Skills
  150.    wt: 1:   Example 4 with x function of y
  151.    wt: 1:   A Related Material in Volume 3
  152.    wt: 1:   A Related lessons in Volume 3
  153.    wt: 1:   34 Derivative of exponential function
  154.    wt: 1:   31 Derivatives of inverse functions
  155.    wt: 1:   30Chain Rule A Proof
  156.    wt: 1:   28 Chain Rule Preparation for a Proof
  157.    wt: 1:   8 Differentiation of polynomials
  158.    wt: 1:   5 Jumps and absence of unlimited error control
  159.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  160.    wt: 1:   G.3 Constant Difference Theorem Proof
  161.    wt: 1:   E2 Algebraic Properties of Limits
  162.    wt: 1:   D2 Limits of Monotone Sequences
  163.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  164.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  165.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  166.    wt: 1:   Chapter 31 Direct and Indirect Reason
  167.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  168.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  169.    wt: 1:   Chapter 6 Change of Language
  170.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  171.    wt: 1:   Chapter 7 Two Treatments of Geometry
  172.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  173.    wt: 1:   Postscript C Consistency as a Tool for Reason
  174.    wt: 1:   Postscript B More on Story Telling and Reason
  175.    wt: 1:   Chapter 24 Direct and Indirect Reason
  176.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  177.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  178.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  179.    wt: 1:   Chapter 11 Accidental Patterns
  180.    wt: 1:   Chapter 8 Change of Language
  181.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  182.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  183.    wt: 1:   C. Domino effect of being careful
  184.    wt: 1:   B. Domino effect of errors
  185.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  186.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  187.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  188.    wt: 1:   More Algebra and Slope based Calculus Preview

Extended Search

348 matches:

  1.    wt: 8:   Chapter 16 Origins and Limitations of Rules and Patterns
  2.    wt: 8:   Chapter 7 Longer Chains of Reason
  3.    wt: 8:   Chapter 6 Chains of Reason
  4.    wt: 7:   Postscript D Reflections on Law of the Excluded Middle
  5.    wt: 7:   Postscript C Consistency as a Tool for Reason
  6.    wt: 7:   Postscript B More on Story Telling and Reason
  7.    wt: 7:   Chapter 24 Direct and Indirect Reason
  8.    wt: 7:   Chapter 14 Deductive and Empirical Views of Mathematics
  9.    wt: 7:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  10.    wt: 7:   Chapter 12 Islands and Divisions of Knowledge
  11.    wt: 7:   Chapter 11 Accidental Patterns
  12.    wt: 7:   Chapter 8 Change of Language
  13.    wt: 6:   Postscript A Story Telling
  14.    wt: 6:   Chapter 23 Truth Tables
  15.    wt: 6:   Chapter 22 Contrapositive and Vacuously True Implications
  16.    wt: 6:   Chapter 21 Occurrence Tables
  17.    wt: 6:   Chapter 20 Shorthand Symbols as Pronouns
  18.    wt: 6:   Chapter 19 What is in chapters 20 to 24
  19.    wt: 6:   Chapter 18 Sense and Knowledge
  20.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  21.    wt: 6:   Chapter 15 Objective Processes
  22.    wt: 6:   Chapter 10 Responsibility
  23.    wt: 6:   Chapter 9 What is in Chapters 10 to 18
  24.    wt: 6:   Chapter 5 Deception
  25.    wt: 6:   Chapter 4 Implication Rules Forwards and Backwards
  26.    wt: 6:   Chapter 3 What is in chapters 4 to 8
  27.    wt: 6:   Chapter 2 Skill Development
  28.    wt: 6:   Chapter 1 Introduction
  29.    wt: 6:   Three Remarks
  30.    wt: 6:   Foreword
  31.    wt: 3:   5 Areas of Rectangles Revisited
  32.    wt: 3:   Example 2 volume of a cone
  33.    wt: 3:   Example 1 volume of a pyramid
  34.    wt: 3:   Volume of Solid by Cross Sections Lesson
  35.    wt: 3:   Chapter 4 Longer Chains of Reason
  36.    wt: 3:   Chapter 3 Chains of Reason
  37.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  38.    wt: 2:   Different Kinds of Reasoning in maths
  39.    wt: 2:   three kinds of reason in mathematics
  40.    wt: 2:   chapitre 12 00 les iles et division
  41.    wt: 2:   chapitre 07 01 principle D induction mathematique
  42.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  43.    wt: 2:   chapitre 06 00 Chaines de la raison
  44.    wt: 2:   chapitre 05 00 Deception
  45.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  46.    wt: 2:   chapitre 04 09 Regles accidentelles
  47.    wt: 2:   chapitre 04 08 Limitations et benefices
  48.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  49.    wt: 2:   chapitre 04 06 engagements
  50.    wt: 2:   chapitre 04 05 Implication versus suggestion
  51.    wt: 2:   chapitre 04 04 Parlons de la logique
  52.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  53.    wt: 2:   chapitre 04 02 Deuxieme enigme
  54.    wt: 2:   chapitre 04 01 Premiere enigme
  55.    wt: 2:   chapitre 04 00 Les regles d implication
  56.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  57.    wt: 2:   chapitre 02 00 La Communication des idees
  58.    wt: 2:   chapitre 01 00 Introduction
  59.    wt: 2:   4 Resultant of a Sum of Movements
  60.    wt: 2:   27 Logarithmic use of products of sines and cosines
  61.    wt: 2:   5 An Easy Proof of the Distributive Law
  62.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  63.    wt: 2:   21 Addition of Multiples of a Single Vector
  64.    wt: 2:   1 The Counting Origins of Numbers
  65.    wt: 2:   4 Fraction Operations Axiomatic Development
  66.    wt: 2:   3 Inequalities Algebraically
  67.    wt: 2:   2 Fraction Operations Physical Development
  68.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  69.    wt: 2:   11 Volume of Sphere
  70.    wt: 2:   10 Volume of Pyramid
  71.    wt: 2:   9 Volume of Cone
  72.    wt: 2:   3 Comparison of Negative Numbers
  73.    wt: 2:   Example 4 with x function of y
  74.    wt: 2:   Area Between Curves Lesson Take 2
  75.    wt: 2:   A Related Material in Volume 3
  76.    wt: 2:   17 Derivatives of quotients of sine and cosine
  77.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  78.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  79.    wt: 2:   G.3 Constant Difference Theorem Proof
  80.    wt: 2:   E2 Algebraic Properties of Limits
  81.    wt: 2:   D2 Limits of Monotone Sequences
  82.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  83.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  84.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  85.    wt: 2:   Chapter 31 Direct and Indirect Reason
  86.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  87.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  88.    wt: 2:   Chapter 6 Change of Language
  89.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  90.    wt: 2:   Chapter 7 Two Treatments of Geometry
  91.    wt: 1:   Mathematics Education Professors
  92.    wt: 1:   teaching tutoring algebraic reason
  93.    wt: 1:   Theory of Knowledge
  94.    wt: 1:   E Kirchoffs Second Law
  95.    wt: 1:   D Kirchoff First Law
  96.    wt: 1:   A Circuit Elements
  97.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  98.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  99.    wt: 1:   8 The Effect of Negative Remarks
  100.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  101.    wt: 1:   15 Sign analysis of functions
  102.    wt: 1:   8 Set view of relations and functions
  103.    wt: 1:   2 Algebraic use of function notation
  104.    wt: 1:   1 Geometric Introduction of Function Notation
  105.    wt: 1:   8 quadratics backward use of various formulas
  106.    wt: 1:   4 quadratics difference of two squares
  107.    wt: 1:   11 arctan left inverse of tangent Graph
  108.    wt: 1:   10 arctan left inverse of tangent Definition
  109.    wt: 1:   8 arcsin left inverse of sine Graph
  110.    wt: 1:   7 arcsin left inverse of sine Definition
  111.    wt: 1:   6 Graph of arccos function
  112.    wt: 1:   3 Left Inverse of cosine arccos definition
  113.    wt: 1:   8 Radian Measures of Common Angles
  114.    wt: 1:   2 Radian Measure Numerical Value of one degree
  115.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  116.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  117.    wt: 1:   Straight Lines Intersection of
  118.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  119.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  120.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  121.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  122.    wt: 1:   32 seven rows of pascals triangle
  123.    wt: 1:   30 unit circle calculation of six trigonometric functions
  124.    wt: 1:   28 Expressing products of sines cosines as sums
  125.    wt: 1:   26 Formulas for products of sines and cosines
  126.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  127.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  128.    wt: 1:   18 sum of sinusoidal waves as a single wave
  129.    wt: 1:   17F Law of cosines
  130.    wt: 1:   13 Graph of tangent function many periods
  131.    wt: 1:   12 Graph of tangent function for one period
  132.    wt: 1:   10 Graphs of sines and cosines many periods
  133.    wt: 1:   9 Graphs of sine and cosine over one period
  134.    wt: 1:   8 period of tangent function
  135.    wt: 1:   7 period of sine and cosine
  136.    wt: 1:   Unit Circle Development of Trigonometry
  137.    wt: 1:   20 N th Roots of Complex Numbers
  138.    wt: 1:   19 N th Roots of Unity
  139.    wt: 1:   18 Sixth Roots of Unity
  140.    wt: 1:   17 Cube Roots of unity
  141.    wt: 1:   14 Law of cosines
  142.    wt: 1:   8 Unit Circle Development of Trigonometry
  143.    wt: 1:   6 Field Properties of Complex Number
  144.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  145.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  146.    wt: 1:   9 Similarity of Triangles Usual Criteria
  147.    wt: 1:   8 Similarity of Triangles and Polygons
  148.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  149.    wt: 1:   1 Early Concept of Like or Similar Shapes
  150.    wt: 1:   10 Midpoint of [a b] and [b a]
  151.    wt: 1:   6 Intersection of lines by solving linear systems
  152.    wt: 1:   5 Algebraic View of Slopes
  153.    wt: 1:   1 Numerical view of lines and their equations
  154.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  155.    wt: 1:   17 Right Bisectors of Triangle Sides
  156.    wt: 1:   9 Construction of a right bisector
  157.    wt: 1:   3 Isometry of Triangles Congruence
  158.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  159.    wt: 1:   22 Multiplication of Signed Numbers
  160.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  161.    wt: 1:   19 Signed Multiples of Vectors
  162.    wt: 1:   8 Division and Mulplication of Compound Fractions
  163.    wt: 1:   4 Location of Point in Decimal Addition
  164.    wt: 1:   3 Location of Point in Decimal Multiplication
  165.    wt: 1:   E Long Division Methods more
  166.    wt: 1:   D Long Division Methods
  167.    wt: 1:   C Three Decimal Subtraction Methods
  168.    wt: 1:   B Decimal Comparison and Subtraction
  169.    wt: 1:   A Decimal Addition Columm Methods
  170.    wt: 1:   8 Column Multiplication Methods in General
  171.    wt: 1:   7 Decimals Multiplication Methods Examples
  172.    wt: 1:   6 Column Methods for Decimal Multiplication
  173.    wt: 1:   5 Distributive Law for Whole Numbers
  174.    wt: 1:   4 Commutative Law Groups Counting Form
  175.    wt: 1:   3 Multiplicative Counting Skills Principles
  176.    wt: 1:   2 Combing Counts Addition Skills and Principles
  177.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  178.    wt: 1:   4 Comparison of Negative Numbers
  179.    wt: 1:   5 Box Volume Formula Example
  180.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  181.    wt: 1:   8 Sets of Numbers
  182.    wt: 1:   6 Three Notions of What is a Variable
  183.    wt: 1:   4 A Brief Story of numbers and algebra
  184.    wt: 1:   4 Greater More Less Than Signs in General
  185.    wt: 1:   2 More and Less Than with Unlike Signs
  186.    wt: 1:   1 More and Less Than for Counts and Measures
  187.    wt: 1:   3 Properties of Square Roots with example
  188.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  189.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  190.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  191.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  192.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  193.    wt: 1:   4 LCM of 8 and 10 via Prime
  194.    wt: 1:   5 lengths and signs of numbers
  195.    wt: 1:   6 Simplification of Fractions with Units
  196.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  197.    wt: 1:   6 Multiplication of Mixed Numbers
  198.    wt: 1:   3 Unit fraction of a fraction
  199.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  200.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  201.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  202.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  203.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  204.    wt: 1:   20 Uniqueness of Prime Factorization
  205.    wt: 1:   16 video Factors of 980 using prime
  206.    wt: 1:   15 video Factors of 20 using Prime Factorization
  207.    wt: 1:   14 video Factors of 24 Take II
  208.    wt: 1:   13 video Factors of 24 using prime
  209.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  210.    wt: 1:   C Counting Areas with Powers of Ten
  211.    wt: 1:   B Powers of Ten
  212.    wt: 1:   8 Subtraction with Units of Measure
  213.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  214.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  215.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  216.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  217.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  218.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  219.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  220.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  221.    wt: 1:   Quick history of numbers and algebra
  222.    wt: 1:   012 Division of Time Intervals by Time Intervals
  223.    wt: 1:   011 Division of Time Intervals By Numbers
  224.    wt: 1:   010 Repeated Addition of Time Intervals
  225.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  226.    wt: 1:   8 Addition of Time Intervals via subtotaling
  227.    wt: 1:   7 Addition of Time Intervals
  228.    wt: 1:   4 Mixing and Changing Units of Time
  229.    wt: 1:   3 Units and Lengths of Time
  230.    wt: 1:   1 Intro of Kids To Time Date Skills
  231.    wt: 1:   Example 1. Area Between x and x squared
  232.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  233.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  234.    wt: 1:   Example 3
  235.    wt: 1:   Example 2
  236.    wt: 1:   Example 1
  237.    wt: 1:   Area Between Curves Lesson Take 1
  238.    wt: 1:   Summary
  239.    wt: 1:   A Related lessons in Volume 3
  240.    wt: 1:   34 Derivative of exponential function
  241.    wt: 1:   31 Derivatives of inverse functions
  242.    wt: 1:   30Chain Rule A Proof
  243.    wt: 1:   28 Chain Rule Preparation for a Proof
  244.    wt: 1:   8 Differentiation of polynomials
  245.    wt: 1:   5 Jumps and absence of unlimited error control
  246.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  247.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  248.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  249.    wt: 1:   G.5 Motions With Bounded Velocities
  250.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  251.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  252.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  253.    wt: 1:   F.5b Extreme Value Theorem
  254.    wt: 1:   F.5a Equicontinuity Theorems
  255.    wt: 1:   F.4 Finite Covering Theorem
  256.    wt: 1:   F.3 Intermediate Value Theorem
  257.    wt: 1:   F.2 Closed Range Theorem
  258.    wt: 1:   F.1 What Functions are Continuous
  259.    wt: 1:   E1 Error Control Inequalities
  260.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  261.    wt: 1:   C Triangle Inequalities
  262.    wt: 1:   B3 Bolzano Weierstrass Theorem
  263.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  264.    wt: 1:   PostScript For and Against Decimal Perspectives
  265.    wt: 1:   A1. Introduction
  266.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  267.    wt: 1:   Chapter 23 Links To Trigonometry
  268.    wt: 1:   Chapter 22 Complex Numbers
  269.    wt: 1:   Chapter 21 Arrow Addition
  270.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  271.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  272.    wt: 1:   Chapter 18. Slopes Areas Integration
  273.    wt: 1:   Chapter 17. Area Approximation
  274.    wt: 1:   Chapter 16. Velocity Approximation
  275.    wt: 1:   Chapter 15. Slope Approximation
  276.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  277.    wt: 1:   Chapter 13. Acceleration
  278.    wt: 1:   Chapter 12. Units and Slopes
  279.    wt: 1:   Chapter 11. Graphing Slope versus Position
  280.    wt: 1:   Chapter 10 Slopes and Units
  281.    wt: 1:   Chapter 9 About First Courses in Calculus
  282.    wt: 1:   Chapter 8. Slope Interpretation
  283.    wt: 1:   Chapter 7 Slopes and Velocity
  284.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  285.    wt: 1:   Chapter 5. Slope Sign Tests
  286.    wt: 1:   Chapter 4. More Slope Sign Analysis
  287.    wt: 1:   Chapter 3. Slope Sign Analysis
  288.    wt: 1:   Chapter 2. Slopes and Ski Trails
  289.    wt: 1:   Chapter 1.Introduction
  290.    wt: 1:   Fall 1983 Calculus Appetizer
  291.    wt: 1:   Foreword
  292.    wt: 1:   Postscript More on Better Performance
  293.    wt: 1:   Postscript For Better Performance
  294.    wt: 1:   Appendix E. How To Study Mathematics and Why
  295.    wt: 1:   Appendix D. What to do in School and Why
  296.    wt: 1:   Appendix C. How to Read
  297.    wt: 1:   Appendix B. How To Learn
  298.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  299.    wt: 1:   Chapter 30 Truth Tables
  300.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  301.    wt: 1:   Chapter 28 Occurrence Tables
  302.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  303.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  304.    wt: 1:   Chapter 25. Mathematical Induction Examples
  305.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  306.    wt: 1:   Chapter 23. Notation For Sums
  307.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  308.    wt: 1:   Chapter 21. Third Reading Guide
  309.    wt: 1:   Chapter 20. Degrees and Radians
  310.    wt: 1:   Chapter 19. Functions and Sets
  311.    wt: 1:   Chapter 18. Rules for Algebra
  312.    wt: 1:   Chapter 16. Painless Theorem Proving
  313.    wt: 1:   Chapter 15. Solving Linear Equations
  314.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  315.    wt: 1:   Chapter 13. Second Reading Guide
  316.    wt: 1:   Chapter 12. Shorthand Usage Guide
  317.    wt: 1:   Chapter 11. Why Shorthand
  318.    wt: 1:   Chapter 10 Describing and Changing Calculations
  319.    wt: 1:   Postscript What is a Variable
  320.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  321.    wt: 1:   Chapter 8 Three Skills For Algebra
  322.    wt: 1:   Solutions For Arithmetic Exercises
  323.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  324.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  325.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  326.    wt: 1:   Foreword
  327.    wt: 1:   Annotated Links to Material Elsehwere
  328.    wt: 1:   Postscript B Mathematics Education References
  329.    wt: 1:   Postscript A Three Remarks
  330.    wt: 1:   Chapter 12 Four Phases
  331.    wt: 1:   Chapter 11 Elementary Instruction
  332.    wt: 1:   Chapter 10 Transition
  333.    wt: 1:   Chapter 9 The Two Ends
  334.    wt: 1:   Chapter 8 Modern Instruction
  335.    wt: 1:   Chapter 5 Four References
  336.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  337.    wt: 1:   Chapter 3 Algebra Difficulties
  338.    wt: 1:   Chapter 2 For and Against Mathematics
  339.    wt: 1:   Chapter 1 Introduction
  340.    wt: 1:   Foreword
  341.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  342.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  343.    wt: 1:   C. Domino effect of being careful
  344.    wt: 1:   B. Domino effect of errors
  345.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  346.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  347.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  348.    wt: 1:   More Algebra and Slope based Calculus Preview

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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