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

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

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

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

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

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

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30 matches:

  1.    wt: 6:   4 Lessons on Using Derivatives/
  2.    wt: 6:   38 Lessons on Calculating Derivatives/
  3.    wt: 5:   12 Webvideo Lessons on Area and Volume Calculation/
  4.    wt: 5:   5 Lessons on Integration/
  5.    wt: 5:   13 Lessons on Limits and Continuity/
  6.    wt: 4:   70 Calculus Starter Lessons/
  7.    wt: 3:   A Origins of Counting and Figuring Methods/
  8.    wt: 3:   10 Examples of Algebraic Reasoning/
  9.    wt: 2:   B Real Numbers Extrinsic Development/
  10.    wt: 2:   9 Proportionality Backwards and Forwards/
  11.    wt: 2:   8 Unifying Theme For Algebra/
  12.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  13.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  14.    wt: 2:   5 Real Numbers/
  15.    wt: 2:   4 Computation Rules and Function Notation/
  16.    wt: 2:   Step 4 Gaussian Elimination/
  17.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  18.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  19.    wt: 2:   Step 1 Stick diagram and fractions/
  20.    wt: 2:   3 Solving Linear Equations/
  21.    wt: 2:   2 Formula Forward Use Evaluation/
  22.    wt: 2:   1 Working With Sets/
  23.    wt: 2:   Algebra Starter Lessons/
  24.    wt: 1:   4 Functions/
  25.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  26.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  27.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  28.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  29.    wt: 1:   Volume 1 Elements of Reason/
  30.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

217 matches:

  1.    wt: 4:   31 Derivatives of inverse functions
  2.    wt: 3:   17 Derivatives of quotients of sine and cosine
  3.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  4.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  5.    wt: 2:   23 Inverse Functions
  6.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  7.    wt: 2:   15 Sign analysis of functions
  8.    wt: 2:   8 Set view of relations and functions
  9.    wt: 2:   11 arctan left inverse of tangent Graph
  10.    wt: 2:   10 arctan left inverse of tangent Definition
  11.    wt: 2:   8 arcsin left inverse of sine Graph
  12.    wt: 2:   7 arcsin left inverse of sine Definition
  13.    wt: 2:   3 Left Inverse of cosine arccos definition
  14.    wt: 2:   4 Resultant of a Sum of Movements
  15.    wt: 2:   30 unit circle calculation of six trigonometric functions
  16.    wt: 2:   27 Logarithmic use of products of sines and cosines
  17.    wt: 2:   5 An Easy Proof of the Distributive Law
  18.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  19.    wt: 2:   21 Addition of Multiples of a Single Vector
  20.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  21.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  22.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  23.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  24.    wt: 2:   Chapter 3 Algebra Starter Lessons
  25.    wt: 1:   Skills Chapter 5 Calculus
  26.    wt: 1:   Mathematics Education Professors
  27.    wt: 1:   Theory of Knowledge
  28.    wt: 1:   Different Kinds of Reasoning in maths
  29.    wt: 1:   three kinds of reason in mathematics
  30.    wt: 1:   E Kirchoffs Second Law
  31.    wt: 1:   D Kirchoff First Law
  32.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  33.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  34.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  35.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  36.    wt: 1:   8 The Effect of Negative Remarks
  37.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  38.    wt: 1:   7 Functions with finite domains
  39.    wt: 1:   2 Algebraic use of function notation
  40.    wt: 1:   1 Geometric Introduction of Function Notation
  41.    wt: 1:   8 quadratics backward use of various formulas
  42.    wt: 1:   4 quadratics difference of two squares
  43.    wt: 1:   1 Calculator Starter Exercises
  44.    wt: 1:   7 Links Lessons Elsewhere
  45.    wt: 1:   16 cotangent function Definition Graph and Inverse
  46.    wt: 1:   15 cosecant function Definition Graph and Inverse
  47.    wt: 1:   14 secant function Definition Graph and Inverse
  48.    wt: 1:   13 cosecant function Definition Graph and Inverse
  49.    wt: 1:   6 Graph of arccos function
  50.    wt: 1:   8 Radian Measures of Common Angles
  51.    wt: 1:   2 Radian Measure Numerical Value of one degree
  52.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  53.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  54.    wt: 1:   Straight Lines Intersection of
  55.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  56.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  57.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  58.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  59.    wt: 1:   32 seven rows of pascals triangle
  60.    wt: 1:   28 Expressing products of sines cosines as sums
  61.    wt: 1:   26 Formulas for products of sines and cosines
  62.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  63.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  64.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  65.    wt: 1:   18 sum of sinusoidal waves as a single wave
  66.    wt: 1:   17F Law of cosines
  67.    wt: 1:   13 Graph of tangent function many periods
  68.    wt: 1:   12 Graph of tangent function for one period
  69.    wt: 1:   10 Graphs of sines and cosines many periods
  70.    wt: 1:   9 Graphs of sine and cosine over one period
  71.    wt: 1:   8 period of tangent function
  72.    wt: 1:   7 period of sine and cosine
  73.    wt: 1:   Unit Circle Development of Trigonometry
  74.    wt: 1:   20 N th Roots of Complex Numbers
  75.    wt: 1:   19 N th Roots of Unity
  76.    wt: 1:   18 Sixth Roots of Unity
  77.    wt: 1:   17 Cube Roots of unity
  78.    wt: 1:   14 Law of cosines
  79.    wt: 1:   8 Unit Circle Development of Trigonometry
  80.    wt: 1:   6 Field Properties of Complex Number
  81.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  82.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  83.    wt: 1:   9 Similarity of Triangles Usual Criteria
  84.    wt: 1:   8 Similarity of Triangles and Polygons
  85.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  86.    wt: 1:   1 Early Concept of Like or Similar Shapes
  87.    wt: 1:   12 Links Lessons elsewhere
  88.    wt: 1:   10 Midpoint of [a b] and [b a]
  89.    wt: 1:   6 Intersection of lines by solving linear systems
  90.    wt: 1:   5 Algebraic View of Slopes
  91.    wt: 1:   1 Numerical view of lines and their equations
  92.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  93.    wt: 1:   17 Right Bisectors of Triangle Sides
  94.    wt: 1:   9 Construction of a right bisector
  95.    wt: 1:   3 Isometry of Triangles Congruence
  96.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  97.    wt: 1:   22 Multiplication of Signed Numbers
  98.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  99.    wt: 1:   19 Signed Multiples of Vectors
  100.    wt: 1:   8 Division and Mulplication of Compound Fractions
  101.    wt: 1:   4 Location of Point in Decimal Addition
  102.    wt: 1:   3 Location of Point in Decimal Multiplication
  103.    wt: 1:   1 The Counting Origins of Numbers
  104.    wt: 1:   5 Areas of Rectangles Revisited
  105.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  106.    wt: 1:   4 Comparison of Negative Numbers
  107.    wt: 1:   12 Real Number Additive Inverses or Negatives
  108.    wt: 1:   11 Volume of Sphere
  109.    wt: 1:   10 Volume of Pyramid
  110.    wt: 1:   9 Volume of Cone
  111.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  112.    wt: 1:   8 Sets of Numbers
  113.    wt: 1:   6 Three Notions of What is a Variable
  114.    wt: 1:   4 A Brief Story of numbers and algebra
  115.    wt: 1:   3 Comparison of Negative Numbers
  116.    wt: 1:   3 Properties of Square Roots with example
  117.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  118.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  119.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  120.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  121.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  122.    wt: 1:   4 LCM of 8 and 10 via Prime
  123.    wt: 1:   7 negative and additive inverse
  124.    wt: 1:   5 lengths and signs of numbers
  125.    wt: 1:   6 Simplification of Fractions with Units
  126.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  127.    wt: 1:   6 Multiplication of Mixed Numbers
  128.    wt: 1:   3 Unit fraction of a fraction
  129.    wt: 1:   13 Subtraction with Additive Inverse
  130.    wt: 1:   5 Zero Movement and Additive Inverses
  131.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  132.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  133.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  134.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  135.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  136.    wt: 1:   20 Uniqueness of Prime Factorization
  137.    wt: 1:   16 video Factors of 980 using prime
  138.    wt: 1:   15 video Factors of 20 using Prime Factorization
  139.    wt: 1:   14 video Factors of 24 Take II
  140.    wt: 1:   13 video Factors of 24 using prime
  141.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  142.    wt: 1:   C Counting Areas with Powers of Ten
  143.    wt: 1:   B Powers of Ten
  144.    wt: 1:   8 Subtraction with Units of Measure
  145.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  146.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  147.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  148.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  149.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  150.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  151.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  152.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  153.    wt: 1:   Quick history of numbers and algebra
  154.    wt: 1:   012 Division of Time Intervals by Time Intervals
  155.    wt: 1:   011 Division of Time Intervals By Numbers
  156.    wt: 1:   010 Repeated Addition of Time Intervals
  157.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  158.    wt: 1:   8 Addition of Time Intervals via subtotaling
  159.    wt: 1:   7 Addition of Time Intervals
  160.    wt: 1:   4 Mixing and Changing Units of Time
  161.    wt: 1:   3 Units and Lengths of Time
  162.    wt: 1:   1 Intro of Kids To Time Date Skills
  163.    wt: 1:   Example 2 volume of a cone
  164.    wt: 1:   Example 1 volume of a pyramid
  165.    wt: 1:   Volume of Solid by Cross Sections Lesson
  166.    wt: 1:   Example 4 with x function of y
  167.    wt: 1:   A Related lessons in Volume 3
  168.    wt: 1:   38 Formulas and derivatives for powers and roots
  169.    wt: 1:   34 Derivative of exponential function
  170.    wt: 1:   30Chain Rule A Proof
  171.    wt: 1:   28 Chain Rule Preparation for a Proof
  172.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  173.    wt: 1:   26 Chain Rule Recognising outer inner functions
  174.    wt: 1:   19 Chain Rule for linear functions
  175.    wt: 1:   15 sine and cosine derivatives 3rd step
  176.    wt: 1:   14 sine and cosine derivatives 2nd step
  177.    wt: 1:   13 sine and cosine derivatives 1st step
  178.    wt: 1:   8 Differentiation of polynomials
  179.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  180.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  181.    wt: 1:   5 Jumps and absence of unlimited error control
  182.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  183.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  184.    wt: 1:   G.3 Constant Difference Theorem Proof
  185.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  186.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  187.    wt: 1:   F.1 What Functions are Continuous
  188.    wt: 1:   E2 Algebraic Properties of Limits
  189.    wt: 1:   D2 Limits of Monotone Sequences
  190.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  191.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  192.    wt: 1:   Chapter 9 About First Courses in Calculus
  193.    wt: 1:   Fall 1983 Calculus Appetizer
  194.    wt: 1:   Chapter 19. Functions and Sets
  195.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  196.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  197.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  198.    wt: 1:   Chapter 6 Change of Language
  199.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  200.    wt: 1:   Chapter 4 Longer Chains of Reason
  201.    wt: 1:   Chapter 3 Chains of Reason
  202.    wt: 1:   Chapter 7 Two Treatments of Geometry
  203.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  204.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  205.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  206.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  207.    wt: 1:   Chapter 8 Change of Language
  208.    wt: 1:   Chapter 7 Longer Chains of Reason
  209.    wt: 1:   Chapter 6 Chains of Reason
  210.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  211.    wt: 1:   C. Domino effect of being careful
  212.    wt: 1:   B. Domino effect of errors
  213.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  214.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  215.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  216.    wt: 1:   More Algebra and Slope based Calculus Preview
  217.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

468 matches:

  1.    wt: 9:   17 Derivatives of quotients of sine and cosine
  2.    wt: 9:   16 Derivatives of reciprocals of sine and cosine
  3.    wt: 7:   A Related lessons in Volume 3
  4.    wt: 7:   38 Formulas and derivatives for powers and roots
  5.    wt: 7:   34 Derivative of exponential function
  6.    wt: 7:   30Chain Rule A Proof
  7.    wt: 7:   28 Chain Rule Preparation for a Proof
  8.    wt: 7:   27 Chain Rule sinusoidal outer inner functions EGS
  9.    wt: 7:   26 Chain Rule Recognising outer inner functions
  10.    wt: 7:   19 Chain Rule for linear functions
  11.    wt: 7:   15 sine and cosine derivatives 3rd step
  12.    wt: 7:   14 sine and cosine derivatives 2nd step
  13.    wt: 7:   13 sine and cosine derivatives 1st step
  14.    wt: 7:   8 Differentiation of polynomials
  15.    wt: 6:   Example 2 volume of a cone
  16.    wt: 6:   Example 1 volume of a pyramid
  17.    wt: 6:   Volume of Solid by Cross Sections Lesson
  18.    wt: 6:   Example 4 with x function of y
  19.    wt: 6:   4 Second derivative test exercise example
  20.    wt: 6:   3 Second derivative test
  21.    wt: 6:   2 Second derivative test prequel
  22.    wt: 6:   1 Two cubic sketching exercises with 1st derivative
  23.    wt: 6:   A Chain Rule Real Player video examples
  24.    wt: 6:   36 Cube root derivative animated
  25.    wt: 6:   33 Chain Rule Real Player video examples
  26.    wt: 6:   29 Chain Rule Optional Reading
  27.    wt: 6:   25 Chain Rule Animated Examples Continued
  28.    wt: 6:   24 Chain Rule Animated Examples
  29.    wt: 6:   23 Chain Rule in general
  30.    wt: 6:   22 Chain Rule for polynomials
  31.    wt: 6:   21 Chain Rule for powers
  32.    wt: 6:   20 Chain Rule for Pulley Systems
  33.    wt: 6:   18 Chain Rule Introduction
  34.    wt: 6:   12 Quotient rule examples
  35.    wt: 6:   11 Quotient rule
  36.    wt: 6:   10 Power rule for negative integers
  37.    wt: 6:   9 Reciprocal rule
  38.    wt: 6:   7 Animated Differentiation Examples
  39.    wt: 6:   6 Power rule from product rule
  40.    wt: 6:   5 Product Rule
  41.    wt: 6:   4 Sum Rule
  42.    wt: 6:   3 Motivation for Limit Definition Take 2
  43.    wt: 6:   2 Motivation for Limit Definition Take 1
  44.    wt: 6:   1 Fall 1983 Why Slopes Appetizer
  45.    wt: 6:   13 Limits with Parameters and Derivatives Take II
  46.    wt: 6:   12 Limits with Parameters and Derivatives Take I
  47.    wt: 6:   5 Jumps and absence of unlimited error control
  48.    wt: 5:   Example 1. Area Between x and x squared
  49.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  50.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  51.    wt: 5:   Example 3
  52.    wt: 5:   Example 2
  53.    wt: 5:   Example 1
  54.    wt: 5:   Area Between Curves Lesson Take 2
  55.    wt: 5:   Area Between Curves Lesson Take 1
  56.    wt: 5:   Summary
  57.    wt: 5:   A Related Material in Volume 3
  58.    wt: 5:   5 Area Under Curve Exercise
  59.    wt: 5:   4 Definite Integrals Evaluation Exercises
  60.    wt: 5:   3 Two Chain Rule Method Exercises
  61.    wt: 5:   2 Indefinite Integrals Exercises
  62.    wt: 5:   1 Chain Rule in Reverse Integration Method
  63.    wt: 5:   11 Limits at infinity Three Examples
  64.    wt: 5:   10 Three one sided limits with infinite values
  65.    wt: 5:   9 Limits Continuity and Composition
  66.    wt: 5:   8 Four Animated Examples
  67.    wt: 5:   7 Evaluation by immediate or delayed substitution
  68.    wt: 5:   6 Continuity at a point
  69.    wt: 5:   4 Numerical properties
  70.    wt: 5:   3 Decimal insights for limits continuity convergence
  71.    wt: 5:   2 Algebraic codification
  72.    wt: 5:   1 Numerical introduction
  73.    wt: 4:   21 Addition of Multiples of a Single Vector
  74.    wt: 4:   1 The Counting Origins of Numbers
  75.    wt: 4:   5 Areas of Rectangles Revisited
  76.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  77.    wt: 3:   23 Inverse Functions
  78.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  79.    wt: 3:   15 Sign analysis of functions
  80.    wt: 3:   8 Set view of relations and functions
  81.    wt: 3:   11 arctan left inverse of tangent Graph
  82.    wt: 3:   10 arctan left inverse of tangent Definition
  83.    wt: 3:   8 arcsin left inverse of sine Graph
  84.    wt: 3:   7 arcsin left inverse of sine Definition
  85.    wt: 3:   3 Left Inverse of cosine arccos definition
  86.    wt: 3:   22 Multiplication of Signed Numbers
  87.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  88.    wt: 3:   19 Signed Multiples of Vectors
  89.    wt: 3:   8 Division and Mulplication of Compound Fractions
  90.    wt: 3:   4 Location of Point in Decimal Addition
  91.    wt: 3:   3 Location of Point in Decimal Multiplication
  92.    wt: 3:   E Long Division Methods more
  93.    wt: 3:   D Long Division Methods
  94.    wt: 3:   C Three Decimal Subtraction Methods
  95.    wt: 3:   B Decimal Comparison and Subtraction
  96.    wt: 3:   A Decimal Addition Columm Methods
  97.    wt: 3:   8 Column Multiplication Methods in General
  98.    wt: 3:   7 Decimals Multiplication Methods Examples
  99.    wt: 3:   6 Column Methods for Decimal Multiplication
  100.    wt: 3:   5 Distributive Law for Whole Numbers
  101.    wt: 3:   4 Commutative Law Groups Counting Form
  102.    wt: 3:   3 Multiplicative Counting Skills Principles
  103.    wt: 3:   2 Combing Counts Addition Skills and Principles
  104.    wt: 3:   4 Fraction Operations Axiomatic Development
  105.    wt: 3:   3 Inequalities Algebraically
  106.    wt: 3:   2 Fraction Operations Physical Development
  107.    wt: 3:   1 Decimals Modular and Remainder Arithmetic
  108.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  109.    wt: 3:   4 Comparison of Negative Numbers
  110.    wt: 3:   12 Real Number Additive Inverses or Negatives
  111.    wt: 3:   11 Volume of Sphere
  112.    wt: 3:   10 Volume of Pyramid
  113.    wt: 3:   9 Volume of Cone
  114.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  115.    wt: 3:   8 Sets of Numbers
  116.    wt: 3:   6 Three Notions of What is a Variable
  117.    wt: 3:   4 A Brief Story of numbers and algebra
  118.    wt: 3:   G.1 First Fundamental Theorem of Calculus
  119.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  120.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  121.    wt: 2:   7 Functions with finite domains
  122.    wt: 2:   2 Algebraic use of function notation
  123.    wt: 2:   1 Geometric Introduction of Function Notation
  124.    wt: 2:   16 cotangent function Definition Graph and Inverse
  125.    wt: 2:   15 cosecant function Definition Graph and Inverse
  126.    wt: 2:   14 secant function Definition Graph and Inverse
  127.    wt: 2:   13 cosecant function Definition Graph and Inverse
  128.    wt: 2:   6 Graph of arccos function
  129.    wt: 2:   4 Resultant of a Sum of Movements
  130.    wt: 2:   30 unit circle calculation of six trigonometric functions
  131.    wt: 2:   27 Logarithmic use of products of sines and cosines
  132.    wt: 2:   5 An Easy Proof of the Distributive Law
  133.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  134.    wt: 2:   musings do not puiblish real numbers
  135.    wt: 2:   A Modular and Remainder Arithmetic
  136.    wt: 2:   A Signed Number Arithmetic Review
  137.    wt: 2:   26 More Less Greater Than Comparison
  138.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  139.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  140.    wt: 2:   23 Distributive Law Two Derivations
  141.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  142.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  143.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  144.    wt: 2:   15 Head to Tails in place Addition Associative
  145.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  146.    wt: 2:   13 Arrows and Vectors in a Plane
  147.    wt: 2:   12 Real Numbers Line Signed Coordinates
  148.    wt: 2:   11 Signed Number Addition and Addition Properties
  149.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  150.    wt: 2:   9 Division with Digits after Decimal Point
  151.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  152.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  153.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  154.    wt: 2:   2 Counting Digits in Decimal Multiplication
  155.    wt: 2:   1 Fractions with Finite Decimal Expansions
  156.    wt: 2:   5 Proportionality in Equivalent Fractions
  157.    wt: 2:   4 Rates Ratios and Proporitionality
  158.    wt: 2:   3 Proportionality Examples
  159.    wt: 2:   2 Algebraic View
  160.    wt: 2:   1 What is Proportionality
  161.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  162.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  163.    wt: 2:   6 Compound Interest Forward and Backwards
  164.    wt: 2:   5 Triangle Area Formula Backwards
  165.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  166.    wt: 2:   3 Linear Equation Literal Solution More
  167.    wt: 2:   2 Linear Equation Literal Solution
  168.    wt: 2:   1 Changing Calculations
  169.    wt: 2:   6 Equations and Systems Equivalent or Implied
  170.    wt: 2:   5 Equality in Algebra
  171.    wt: 2:   4 Subtraction and Division Axioms
  172.    wt: 2:   3 Product Axioms Two Forms
  173.    wt: 2:   2 Addition and Multiplication Axioms
  174.    wt: 2:   1 Equivalent Computation Rules
  175.    wt: 2:   5 Greater More Less Than Signs in General
  176.    wt: 2:   3 More and Less Than with Unlike Signs
  177.    wt: 2:   2 More and Less Than for Counts and Measures
  178.    wt: 2:   1 Real Numbers Comparison
  179.    wt: 2:   16 Real Numbers Comparison
  180.    wt: 2:   15 Real Number Division
  181.    wt: 2:   14 Real Number Multiplication
  182.    wt: 2:   13 Real Number Subtraction
  183.    wt: 2:   11 Real Number Addition
  184.    wt: 2:   10 Real Number Lengths and Signs
  185.    wt: 2:   9 Coordinates for Regions in Space
  186.    wt: 2:   8 Coordinates for Maps and Planes
  187.    wt: 2:   7 Real Numbers as Line Cordinates
  188.    wt: 2:   6 Unsigned Real Numbers
  189.    wt: 2:   5 Rational Numbers More
  190.    wt: 2:   4 Rational Numbers
  191.    wt: 2:   3 Fractions
  192.    wt: 2:   2 Integers
  193.    wt: 2:   1 Whole and Natural Numbers
  194.    wt: 2:   5 Independent versus Dependent Variables
  195.    wt: 2:   4 Changing Letters
  196.    wt: 2:   3 Geometric Formulas and Function Notation
  197.    wt: 2:   2 Computation Rules Evaluation
  198.    wt: 2:   1 Formulas Dependence and Function Notation
  199.    wt: 2:   More Exercises
  200.    wt: 2:   Simple Exercises
  201.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  202.    wt: 2:   4 GE III Animated Examples
  203.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  204.    wt: 2:   3 GE III Equation Addition and Multiplication
  205.    wt: 2:   2 GE II Comparison
  206.    wt: 2:   1 GE Substitution four examples
  207.    wt: 2:   4 Solving a triangular system exercise
  208.    wt: 2:   3 Solving triangular system example
  209.    wt: 2:   2 Essentially one exercises three with solution
  210.    wt: 2:   1 Essentially One Unknown
  211.    wt: 2:   6 Algebraic Solution Example
  212.    wt: 2:   5 Algebraic Solutions Introduction
  213.    wt: 2:   4 Four Examples Fractional Coefficients
  214.    wt: 2:   3 Four Examples
  215.    wt: 2:   2 Three Examples
  216.    wt: 2:   1 Proper Equal Sign Usage
  217.    wt: 2:   Skill Development Notes
  218.    wt: 2:   10 One Example
  219.    wt: 2:   9 Three Examples
  220.    wt: 2:   8 One Example
  221.    wt: 2:   7 Two Examples
  222.    wt: 2:   6 Three Examples
  223.    wt: 2:   5 Three Examples
  224.    wt: 2:   4 Two Examples
  225.    wt: 2:   3 Two Examples
  226.    wt: 2:   2 Three Examples
  227.    wt: 2:   Using Letters for Physical Quantities
  228.    wt: 2:   Formula Usage Show Work Format
  229.    wt: 2:   13 Naming Identifying Formulas with Words
  230.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  231.    wt: 2:   8 Compound Interest Formula Evaluation
  232.    wt: 2:   7 Compound Interest Formula Introduction
  233.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  234.    wt: 2:   5 Box Volume Formula Example
  235.    wt: 2:   4 Circle Area Formula Example
  236.    wt: 2:   3 Triangle Area Formula Example
  237.    wt: 2:   2 Another Rectangle Area Formula Example
  238.    wt: 2:   1 Written work formats for developing and showing skill
  239.    wt: 2:   9 Sets in Probability and Statistics
  240.    wt: 2:   7 Cautious or Safe Set Construction
  241.    wt: 2:   6 Power Set Notation
  242.    wt: 2:   5 Product Builder Notation
  243.    wt: 2:   4 Subset Builder Notation
  244.    wt: 2:   3 Counting with Sets etc
  245.    wt: 2:   2 Venn Diagrams
  246.    wt: 2:   1 Finite Sets
  247.    wt: 2:   5 Talking about Numbers and Quantities
  248.    wt: 2:   3 Adding Words To Arithmetic
  249.    wt: 2:   2 What is a Variable
  250.    wt: 2:   1 Three Skills For Algebra
  251.    wt: 2:   About Folder Contents
  252.    wt: 2:   3 Comparison of Negative Numbers
  253.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  254.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  255.    wt: 2:   G.3 Constant Difference Theorem Proof
  256.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  257.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  258.    wt: 2:   F.1 What Functions are Continuous
  259.    wt: 2:   E2 Algebraic Properties of Limits
  260.    wt: 2:   D2 Limits of Monotone Sequences
  261.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  262.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  263.    wt: 2:   Chapter 9 About First Courses in Calculus
  264.    wt: 2:   Fall 1983 Calculus Appetizer
  265.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  266.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  267.    wt: 2:   Chapter 3 Algebra Starter Lessons
  268.    wt: 1:   Skills Chapter 5 Calculus
  269.    wt: 1:   Mathematics Education Professors
  270.    wt: 1:   Theory of Knowledge
  271.    wt: 1:   Different Kinds of Reasoning in maths
  272.    wt: 1:   three kinds of reason in mathematics
  273.    wt: 1:   E Kirchoffs Second Law
  274.    wt: 1:   D Kirchoff First Law
  275.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  276.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  277.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  278.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  279.    wt: 1:   8 The Effect of Negative Remarks
  280.    wt: 1:   26 Function definitions done and coming
  281.    wt: 1:   22 Square Root function graphically
  282.    wt: 1:   20 Interchanging coordinates a reflection
  283.    wt: 1:   19 Horizontal line rule and method
  284.    wt: 1:   18 Vertical Line Rule and Method
  285.    wt: 1:   17 Function maxima minima and their location
  286.    wt: 1:   16 Increasing or decreasing on intervals
  287.    wt: 1:   14 Surjections Injections Bijections
  288.    wt: 1:   13 From one to one to many to one
  289.    wt: 1:   12 Function Domain Recognition Exercises
  290.    wt: 1:   11 Function Domain Range Source and Targets
  291.    wt: 1:   10 Interval Notation
  292.    wt: 1:   9 Set theory term relation possible origins
  293.    wt: 1:   6 Set Existence Formation and Notation
  294.    wt: 1:   5 Function notation for geometric transformations
  295.    wt: 1:   4 Function notation in and beyond mathematics
  296.    wt: 1:   3 Formula or function graphing exercise
  297.    wt: 1:   Introduction Reading Guide
  298.    wt: 1:   8 quadratics backward use of various formulas
  299.    wt: 1:   4 quadratics difference of two squares
  300.    wt: 1:   1 Calculator Starter Exercises
  301.    wt: 1:   7 Links Lessons Elsewhere
  302.    wt: 1:   12 motivation for term arctan
  303.    wt: 1:   9 motivation for name arcsin
  304.    wt: 1:   5 Swapping Coordinates is a reflection
  305.    wt: 1:   4 possible motivation for term arccos
  306.    wt: 1:   2 cosine function more properties
  307.    wt: 1:   1 cosine function properties
  308.    wt: 1:   8 Radian Measures of Common Angles
  309.    wt: 1:   2 Radian Measure Numerical Value of one degree
  310.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  311.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  312.    wt: 1:   Straight Lines Intersection of
  313.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  314.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  315.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  316.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  317.    wt: 1:   32 seven rows of pascals triangle
  318.    wt: 1:   28 Expressing products of sines cosines as sums
  319.    wt: 1:   26 Formulas for products of sines and cosines
  320.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  321.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  322.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  323.    wt: 1:   18 sum of sinusoidal waves as a single wave
  324.    wt: 1:   17F Law of cosines
  325.    wt: 1:   13 Graph of tangent function many periods
  326.    wt: 1:   12 Graph of tangent function for one period
  327.    wt: 1:   10 Graphs of sines and cosines many periods
  328.    wt: 1:   9 Graphs of sine and cosine over one period
  329.    wt: 1:   8 period of tangent function
  330.    wt: 1:   7 period of sine and cosine
  331.    wt: 1:   Unit Circle Development of Trigonometry
  332.    wt: 1:   20 N th Roots of Complex Numbers
  333.    wt: 1:   19 N th Roots of Unity
  334.    wt: 1:   18 Sixth Roots of Unity
  335.    wt: 1:   17 Cube Roots of unity
  336.    wt: 1:   14 Law of cosines
  337.    wt: 1:   8 Unit Circle Development of Trigonometry
  338.    wt: 1:   6 Field Properties of Complex Number
  339.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  340.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  341.    wt: 1:   9 Similarity of Triangles Usual Criteria
  342.    wt: 1:   8 Similarity of Triangles and Polygons
  343.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  344.    wt: 1:   1 Early Concept of Like or Similar Shapes
  345.    wt: 1:   12 Links Lessons elsewhere
  346.    wt: 1:   10 Midpoint of [a b] and [b a]
  347.    wt: 1:   6 Intersection of lines by solving linear systems
  348.    wt: 1:   5 Algebraic View of Slopes
  349.    wt: 1:   1 Numerical view of lines and their equations
  350.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  351.    wt: 1:   17 Right Bisectors of Triangle Sides
  352.    wt: 1:   9 Construction of a right bisector
  353.    wt: 1:   3 Isometry of Triangles Congruence
  354.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  355.    wt: 1:   4 Greater More Less Than Signs in General
  356.    wt: 1:   2 More and Less Than with Unlike Signs
  357.    wt: 1:   1 More and Less Than for Counts and Measures
  358.    wt: 1:   3 Properties of Square Roots with example
  359.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  360.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  361.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  362.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  363.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  364.    wt: 1:   4 LCM of 8 and 10 via Prime
  365.    wt: 1:   7 negative and additive inverse
  366.    wt: 1:   5 lengths and signs of numbers
  367.    wt: 1:   6 Simplification of Fractions with Units
  368.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  369.    wt: 1:   6 Multiplication of Mixed Numbers
  370.    wt: 1:   3 Unit fraction of a fraction
  371.    wt: 1:   13 Subtraction with Additive Inverse
  372.    wt: 1:   5 Zero Movement and Additive Inverses
  373.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  374.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  375.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  376.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  377.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  378.    wt: 1:   20 Uniqueness of Prime Factorization
  379.    wt: 1:   16 video Factors of 980 using prime
  380.    wt: 1:   15 video Factors of 20 using Prime Factorization
  381.    wt: 1:   14 video Factors of 24 Take II
  382.    wt: 1:   13 video Factors of 24 using prime
  383.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  384.    wt: 1:   C Counting Areas with Powers of Ten
  385.    wt: 1:   B Powers of Ten
  386.    wt: 1:   8 Subtraction with Units of Measure
  387.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  388.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  389.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  390.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  391.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  392.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  393.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  394.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  395.    wt: 1:   Quick history of numbers and algebra
  396.    wt: 1:   012 Division of Time Intervals by Time Intervals
  397.    wt: 1:   011 Division of Time Intervals By Numbers
  398.    wt: 1:   010 Repeated Addition of Time Intervals
  399.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  400.    wt: 1:   8 Addition of Time Intervals via subtotaling
  401.    wt: 1:   7 Addition of Time Intervals
  402.    wt: 1:   4 Mixing and Changing Units of Time
  403.    wt: 1:   3 Units and Lengths of Time
  404.    wt: 1:   1 Intro of Kids To Time Date Skills
  405.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  406.    wt: 1:   G.5 Motions With Bounded Velocities
  407.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  408.    wt: 1:   F.5b Extreme Value Theorem
  409.    wt: 1:   F.5a Equicontinuity Theorems
  410.    wt: 1:   F.4 Finite Covering Theorem
  411.    wt: 1:   F.3 Intermediate Value Theorem
  412.    wt: 1:   F.2 Closed Range Theorem
  413.    wt: 1:   E1 Error Control Inequalities
  414.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  415.    wt: 1:   C Triangle Inequalities
  416.    wt: 1:   B3 Bolzano Weierstrass Theorem
  417.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  418.    wt: 1:   PostScript For and Against Decimal Perspectives
  419.    wt: 1:   A1. Introduction
  420.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  421.    wt: 1:   Chapter 23 Links To Trigonometry
  422.    wt: 1:   Chapter 22 Complex Numbers
  423.    wt: 1:   Chapter 21 Arrow Addition
  424.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  425.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  426.    wt: 1:   Chapter 18. Slopes Areas Integration
  427.    wt: 1:   Chapter 17. Area Approximation
  428.    wt: 1:   Chapter 16. Velocity Approximation
  429.    wt: 1:   Chapter 15. Slope Approximation
  430.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  431.    wt: 1:   Chapter 13. Acceleration
  432.    wt: 1:   Chapter 12. Units and Slopes
  433.    wt: 1:   Chapter 11. Graphing Slope versus Position
  434.    wt: 1:   Chapter 10 Slopes and Units
  435.    wt: 1:   Chapter 8. Slope Interpretation
  436.    wt: 1:   Chapter 7 Slopes and Velocity
  437.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  438.    wt: 1:   Chapter 5. Slope Sign Tests
  439.    wt: 1:   Chapter 4. More Slope Sign Analysis
  440.    wt: 1:   Chapter 3. Slope Sign Analysis
  441.    wt: 1:   Chapter 2. Slopes and Ski Trails
  442.    wt: 1:   Chapter 1.Introduction
  443.    wt: 1:   Foreword
  444.    wt: 1:   Chapter 19. Functions and Sets
  445.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  446.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  447.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  448.    wt: 1:   Chapter 6 Change of Language
  449.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  450.    wt: 1:   Chapter 4 Longer Chains of Reason
  451.    wt: 1:   Chapter 3 Chains of Reason
  452.    wt: 1:   Chapter 7 Two Treatments of Geometry
  453.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  454.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  455.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  456.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  457.    wt: 1:   Chapter 8 Change of Language
  458.    wt: 1:   Chapter 7 Longer Chains of Reason
  459.    wt: 1:   Chapter 6 Chains of Reason
  460.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  461.    wt: 1:   C. Domino effect of being careful
  462.    wt: 1:   B. Domino effect of errors
  463.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  464.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  465.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  466.    wt: 1:   More Algebra and Slope based Calculus Preview
  467.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  468.    wt: 10:   31 Derivatives of inverse functions

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

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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