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: 3:   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

193 matches:

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

Extended Search

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

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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