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Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
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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
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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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29 matches:

  1.    wt: 5:   12 Webvideo Lessons on Area and Volume Calculation/
  2.    wt: 5:   5 Lessons on Integration/
  3.    wt: 5:   4 Lessons on Using Derivatives/
  4.    wt: 5:   38 Lessons on Calculating Derivatives/
  5.    wt: 5:   13 Lessons on Limits and Continuity/
  6.    wt: 4:   B Real Numbers Extrinsic Development/
  7.    wt: 4:   5 Real Numbers/
  8.    wt: 4:   70 Calculus Starter Lessons/
  9.    wt: 2:   A Origins of Counting and Figuring Methods/
  10.    wt: 2:   10 Examples of Algebraic Reasoning/
  11.    wt: 2:   9 Proportionality Backwards and Forwards/
  12.    wt: 2:   8 Unifying Theme For Algebra/
  13.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  14.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  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:   7 Complex Numbers/
  25.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  26.    wt: 1:   8 Arithmetic with Signed Numbers/
  27.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  28.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  29.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

78 matches:

  1.    wt: 2:   musings do not puiblish real numbers
  2.    wt: 2:   12 Real Numbers Line Signed Coordinates
  3.    wt: 2:   1 Real Numbers Comparison
  4.    wt: 2:   16 Real Numbers Comparison
  5.    wt: 2:   7 Real Numbers as Line Cordinates
  6.    wt: 2:   6 Unsigned Real Numbers
  7.    wt: 2:   11 What are real lengths and numbers
  8.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  9.    wt: 2:   Chapter 3 Algebra Starter Lessons
  10.    wt: 1:   Skills Chapter 5 Calculus
  11.    wt: 1:   Ramblings Extrinsic numbers theory
  12.    wt: 1:   2 arithmetic with signed numbers
  13.    wt: 1:   1 arithmetic with unsigned numbers
  14.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  15.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  16.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  17.    wt: 1:   1 Calculator Starter Exercises
  18.    wt: 1:   7 Links Lessons Elsewhere
  19.    wt: 1:   20 N th Roots of Complex Numbers
  20.    wt: 1:   2 Complex Numbers made easier we hope
  21.    wt: 1:   12 Links Lessons elsewhere
  22.    wt: 1:   7 Complex Numbers Appetizer
  23.    wt: 1:   PS H Distributive Law For Complex Numbers
  24.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  25.    wt: 1:   22 Multiplication of Signed Numbers
  26.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  27.    wt: 1:   5 Distributive Law for Whole Numbers
  28.    wt: 1:   1 The Counting Origins of Numbers
  29.    wt: 1:   4 Comparison of Negative Numbers
  30.    wt: 1:   15 Real Number Division
  31.    wt: 1:   14 Real Number Multiplication
  32.    wt: 1:   13 Real Number Subtraction
  33.    wt: 1:   12 Real Number Additive Inverses or Negatives
  34.    wt: 1:   11 Real Number Addition
  35.    wt: 1:   10 Real Number Lengths and Signs
  36.    wt: 1:   5 Rational Numbers More
  37.    wt: 1:   4 Rational Numbers
  38.    wt: 1:   1 Whole and Natural Numbers
  39.    wt: 1:   8 Sets of Numbers
  40.    wt: 1:   5 Talking about Numbers and Quantities
  41.    wt: 1:   4 A Brief Story of numbers and algebra
  42.    wt: 1:   arithmetic videos Real Player Format
  43.    wt: 1:   3 Comparison of Negative Numbers
  44.    wt: 1:   10 dividing signed numbers
  45.    wt: 1:   9 subtracting signed numbers
  46.    wt: 1:   8 multiplying signed numbers
  47.    wt: 1:   6 adding signed numbers
  48.    wt: 1:   5 lengths and signs of numbers
  49.    wt: 1:   2 signed and unsigned numbers as coordinates
  50.    wt: 1:   3 Multiplying Units and Numbers
  51.    wt: 1:   9 Improper Fractions and Mixed Numbers
  52.    wt: 1:   6 Multiplication of Mixed Numbers
  53.    wt: 1:   8 Multiplication by Signed Numbers Integers
  54.    wt: 1:   6 Multiplication by Natural Numbers
  55.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  56.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  57.    wt: 1:   Quick history of numbers and algebra
  58.    wt: 1:   011 Division of Time Intervals By Numbers
  59.    wt: 1:   A Related lessons in Volume 3
  60.    wt: 1:   A Chain Rule Real Player video examples
  61.    wt: 1:   33 Chain Rule Real Player video examples
  62.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  63.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  64.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  65.    wt: 1:   Chapter 22 Complex Numbers
  66.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  67.    wt: 1:   Chapter 9 About First Courses in Calculus
  68.    wt: 1:   Fall 1983 Calculus Appetizer
  69.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  70.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  71.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  72.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  73.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  74.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  75.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  76.    wt: 1:   More Algebra and Slope based Calculus Preview
  77.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  78.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

349 matches:

  1.    wt: 6:   musings do not puiblish real numbers
  2.    wt: 6:   12 Real Numbers Line Signed Coordinates
  3.    wt: 6:   16 Real Numbers Comparison
  4.    wt: 6:   7 Real Numbers as Line Cordinates
  5.    wt: 6:   6 Unsigned Real Numbers
  6.    wt: 6:   A Related lessons in Volume 3
  7.    wt: 6:   A Chain Rule Real Player video examples
  8.    wt: 6:   33 Chain Rule Real Player video examples
  9.    wt: 5:   24 Signed Numbers Arithmmetic Properties
  10.    wt: 5:   22 Multiplication of Signed Numbers
  11.    wt: 5:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  12.    wt: 5:   15 Real Number Division
  13.    wt: 5:   14 Real Number Multiplication
  14.    wt: 5:   13 Real Number Subtraction
  15.    wt: 5:   12 Real Number Additive Inverses or Negatives
  16.    wt: 5:   11 Real Number Addition
  17.    wt: 5:   10 Real Number Lengths and Signs
  18.    wt: 5:   5 Rational Numbers More
  19.    wt: 5:   4 Rational Numbers
  20.    wt: 5:   1 Whole and Natural Numbers
  21.    wt: 5:   Example 2 volume of a cone
  22.    wt: 5:   Example 1 volume of a pyramid
  23.    wt: 5:   Volume of Solid by Cross Sections Lesson
  24.    wt: 5:   Example 1. Area Between x and x squared
  25.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  26.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  27.    wt: 5:   Example 4 with x function of y
  28.    wt: 5:   Example 3
  29.    wt: 5:   Example 2
  30.    wt: 5:   Example 1
  31.    wt: 5:   Area Between Curves Lesson Take 2
  32.    wt: 5:   Area Between Curves Lesson Take 1
  33.    wt: 5:   Summary
  34.    wt: 5:   A Related Material in Volume 3
  35.    wt: 5:   5 Area Under Curve Exercise
  36.    wt: 5:   4 Definite Integrals Evaluation Exercises
  37.    wt: 5:   3 Two Chain Rule Method Exercises
  38.    wt: 5:   2 Indefinite Integrals Exercises
  39.    wt: 5:   1 Chain Rule in Reverse Integration Method
  40.    wt: 5:   4 Second derivative test exercise example
  41.    wt: 5:   3 Second derivative test
  42.    wt: 5:   2 Second derivative test prequel
  43.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  44.    wt: 5:   38 Formulas and derivatives for powers and roots
  45.    wt: 5:   36 Cube root derivative animated
  46.    wt: 5:   34 Derivative of exponential function
  47.    wt: 5:   31 Derivatives of inverse functions
  48.    wt: 5:   30Chain Rule A Proof
  49.    wt: 5:   29 Chain Rule Optional Reading
  50.    wt: 5:   28 Chain Rule Preparation for a Proof
  51.    wt: 5:   27 Chain Rule sinusoidal outer inner functions EGS
  52.    wt: 5:   26 Chain Rule Recognising outer inner functions
  53.    wt: 5:   25 Chain Rule Animated Examples Continued
  54.    wt: 5:   24 Chain Rule Animated Examples
  55.    wt: 5:   23 Chain Rule in general
  56.    wt: 5:   22 Chain Rule for polynomials
  57.    wt: 5:   21 Chain Rule for powers
  58.    wt: 5:   20 Chain Rule for Pulley Systems
  59.    wt: 5:   19 Chain Rule for linear functions
  60.    wt: 5:   18 Chain Rule Introduction
  61.    wt: 5:   17 Derivatives of quotients of sine and cosine
  62.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  63.    wt: 5:   15 sine and cosine derivatives 3rd step
  64.    wt: 5:   14 sine and cosine derivatives 2nd step
  65.    wt: 5:   13 sine and cosine derivatives 1st step
  66.    wt: 5:   12 Quotient rule examples
  67.    wt: 5:   11 Quotient rule
  68.    wt: 5:   10 Power rule for negative integers
  69.    wt: 5:   9 Reciprocal rule
  70.    wt: 5:   8 Differentiation of polynomials
  71.    wt: 5:   7 Animated Differentiation Examples
  72.    wt: 5:   6 Power rule from product rule
  73.    wt: 5:   5 Product Rule
  74.    wt: 5:   4 Sum Rule
  75.    wt: 5:   3 Motivation for Limit Definition Take 2
  76.    wt: 5:   2 Motivation for Limit Definition Take 1
  77.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  78.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  79.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  80.    wt: 5:   11 Limits at infinity Three Examples
  81.    wt: 5:   10 Three one sided limits with infinite values
  82.    wt: 5:   9 Limits Continuity and Composition
  83.    wt: 5:   8 Four Animated Examples
  84.    wt: 5:   7 Evaluation by immediate or delayed substitution
  85.    wt: 5:   6 Continuity at a point
  86.    wt: 5:   5 Jumps and absence of unlimited error control
  87.    wt: 5:   4 Numerical properties
  88.    wt: 5:   3 Decimal insights for limits continuity convergence
  89.    wt: 5:   2 Algebraic codification
  90.    wt: 5:   1 Numerical introduction
  91.    wt: 4:   A Modular and Remainder Arithmetic
  92.    wt: 4:   A Signed Number Arithmetic Review
  93.    wt: 4:   26 More Less Greater Than Comparison
  94.    wt: 4:   25 Mid way Convergence to Axiomatic Approach
  95.    wt: 4:   23 Distributive Law Two Derivations
  96.    wt: 4:   21 Addition of Multiples of a Single Vector
  97.    wt: 4:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  98.    wt: 4:   19 Signed Multiples of Vectors
  99.    wt: 4:   18 Geometrically Why Vector Addition Commutes
  100.    wt: 4:   17 Arrows Rotate to Reverse with Length Unchanged
  101.    wt: 4:   16 Collinear Horizontal Arrows Vectors
  102.    wt: 4:   15 Head to Tails in place Addition Associative
  103.    wt: 4:   14 Vector Head to Tail Sums and Resultants
  104.    wt: 4:   13 Arrows and Vectors in a Plane
  105.    wt: 4:   11 Signed Number Addition and Addition Properties
  106.    wt: 4:   9 Division with Digits after Decimal Point
  107.    wt: 4:   8 Division and Mulplication of Compound Fractions
  108.    wt: 4:   7 Arithmetic with Infinite Decimal Expansions
  109.    wt: 4:   6 Infinite Decimals Ending in 9 repeating
  110.    wt: 4:   5 Fractions with Infinite Decimal Expansions
  111.    wt: 4:   4 Location of Point in Decimal Addition
  112.    wt: 4:   3 Location of Point in Decimal Multiplication
  113.    wt: 4:   2 Counting Digits in Decimal Multiplication
  114.    wt: 4:   1 Fractions with Finite Decimal Expansions
  115.    wt: 4:   1 Real Numbers Comparison
  116.    wt: 4:   9 Coordinates for Regions in Space
  117.    wt: 4:   8 Coordinates for Maps and Planes
  118.    wt: 4:   3 Fractions
  119.    wt: 4:   2 Integers
  120.    wt: 3:   5 Distributive Law for Whole Numbers
  121.    wt: 3:   1 The Counting Origins of Numbers
  122.    wt: 3:   4 Comparison of Negative Numbers
  123.    wt: 3:   8 Sets of Numbers
  124.    wt: 3:   5 Talking about Numbers and Quantities
  125.    wt: 3:   4 A Brief Story of numbers and algebra
  126.    wt: 3:   11 What are real lengths and numbers
  127.    wt: 2:   20 N th Roots of Complex Numbers
  128.    wt: 2:   2 Complex Numbers made easier we hope
  129.    wt: 2:   E Long Division Methods more
  130.    wt: 2:   D Long Division Methods
  131.    wt: 2:   C Three Decimal Subtraction Methods
  132.    wt: 2:   B Decimal Comparison and Subtraction
  133.    wt: 2:   A Decimal Addition Columm Methods
  134.    wt: 2:   8 Column Multiplication Methods in General
  135.    wt: 2:   7 Decimals Multiplication Methods Examples
  136.    wt: 2:   6 Column Methods for Decimal Multiplication
  137.    wt: 2:   4 Commutative Law Groups Counting Form
  138.    wt: 2:   3 Multiplicative Counting Skills Principles
  139.    wt: 2:   2 Combing Counts Addition Skills and Principles
  140.    wt: 2:   5 Areas of Rectangles Revisited
  141.    wt: 2:   4 Fraction Operations Axiomatic Development
  142.    wt: 2:   3 Inequalities Algebraically
  143.    wt: 2:   2 Fraction Operations Physical Development
  144.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  145.    wt: 2:   5 Proportionality in Equivalent Fractions
  146.    wt: 2:   4 Rates Ratios and Proporitionality
  147.    wt: 2:   3 Proportionality Examples
  148.    wt: 2:   2 Algebraic View
  149.    wt: 2:   1 What is Proportionality
  150.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  151.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  152.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  153.    wt: 2:   6 Compound Interest Forward and Backwards
  154.    wt: 2:   5 Triangle Area Formula Backwards
  155.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  156.    wt: 2:   3 Linear Equation Literal Solution More
  157.    wt: 2:   2 Linear Equation Literal Solution
  158.    wt: 2:   1 Changing Calculations
  159.    wt: 2:   6 Equations and Systems Equivalent or Implied
  160.    wt: 2:   5 Equality in Algebra
  161.    wt: 2:   4 Subtraction and Division Axioms
  162.    wt: 2:   3 Product Axioms Two Forms
  163.    wt: 2:   2 Addition and Multiplication Axioms
  164.    wt: 2:   1 Equivalent Computation Rules
  165.    wt: 2:   5 Greater More Less Than Signs in General
  166.    wt: 2:   3 More and Less Than with Unlike Signs
  167.    wt: 2:   2 More and Less Than for Counts and Measures
  168.    wt: 2:   5 Independent versus Dependent Variables
  169.    wt: 2:   4 Changing Letters
  170.    wt: 2:   3 Geometric Formulas and Function Notation
  171.    wt: 2:   2 Computation Rules Evaluation
  172.    wt: 2:   1 Formulas Dependence and Function Notation
  173.    wt: 2:   More Exercises
  174.    wt: 2:   Simple Exercises
  175.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  176.    wt: 2:   4 GE III Animated Examples
  177.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  178.    wt: 2:   3 GE III Equation Addition and Multiplication
  179.    wt: 2:   2 GE II Comparison
  180.    wt: 2:   1 GE Substitution four examples
  181.    wt: 2:   4 Solving a triangular system exercise
  182.    wt: 2:   3 Solving triangular system example
  183.    wt: 2:   2 Essentially one exercises three with solution
  184.    wt: 2:   1 Essentially One Unknown
  185.    wt: 2:   6 Algebraic Solution Example
  186.    wt: 2:   5 Algebraic Solutions Introduction
  187.    wt: 2:   4 Four Examples Fractional Coefficients
  188.    wt: 2:   3 Four Examples
  189.    wt: 2:   2 Three Examples
  190.    wt: 2:   1 Proper Equal Sign Usage
  191.    wt: 2:   Skill Development Notes
  192.    wt: 2:   10 One Example
  193.    wt: 2:   9 Three Examples
  194.    wt: 2:   8 One Example
  195.    wt: 2:   7 Two Examples
  196.    wt: 2:   6 Three Examples
  197.    wt: 2:   5 Three Examples
  198.    wt: 2:   4 Two Examples
  199.    wt: 2:   3 Two Examples
  200.    wt: 2:   2 Three Examples
  201.    wt: 2:   Using Letters for Physical Quantities
  202.    wt: 2:   Formula Usage Show Work Format
  203.    wt: 2:   13 Naming Identifying Formulas with Words
  204.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  205.    wt: 2:   11 Volume of Sphere
  206.    wt: 2:   10 Volume of Pyramid
  207.    wt: 2:   9 Volume of Cone
  208.    wt: 2:   8 Compound Interest Formula Evaluation
  209.    wt: 2:   7 Compound Interest Formula Introduction
  210.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  211.    wt: 2:   5 Box Volume Formula Example
  212.    wt: 2:   4 Circle Area Formula Example
  213.    wt: 2:   3 Triangle Area Formula Example
  214.    wt: 2:   2 Another Rectangle Area Formula Example
  215.    wt: 2:   1 Written work formats for developing and showing skill
  216.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  217.    wt: 2:   9 Sets in Probability and Statistics
  218.    wt: 2:   7 Cautious or Safe Set Construction
  219.    wt: 2:   6 Power Set Notation
  220.    wt: 2:   5 Product Builder Notation
  221.    wt: 2:   4 Subset Builder Notation
  222.    wt: 2:   3 Counting with Sets etc
  223.    wt: 2:   2 Venn Diagrams
  224.    wt: 2:   1 Finite Sets
  225.    wt: 2:   6 Three Notions of What is a Variable
  226.    wt: 2:   3 Adding Words To Arithmetic
  227.    wt: 2:   2 What is a Variable
  228.    wt: 2:   1 Three Skills For Algebra
  229.    wt: 2:   About Folder Contents
  230.    wt: 2:   3 Comparison of Negative Numbers
  231.    wt: 2:   10 dividing signed numbers
  232.    wt: 2:   9 subtracting signed numbers
  233.    wt: 2:   8 multiplying signed numbers
  234.    wt: 2:   6 adding signed numbers
  235.    wt: 2:   5 lengths and signs of numbers
  236.    wt: 2:   2 signed and unsigned numbers as coordinates
  237.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  238.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  239.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  240.    wt: 2:   Chapter 22 Complex Numbers
  241.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  242.    wt: 2:   Chapter 9 About First Courses in Calculus
  243.    wt: 2:   Fall 1983 Calculus Appetizer
  244.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  245.    wt: 2:   Chapter 3 Algebra Starter Lessons
  246.    wt: 1:   Skills Chapter 5 Calculus
  247.    wt: 1:   Ramblings Extrinsic numbers theory
  248.    wt: 1:   2 arithmetic with signed numbers
  249.    wt: 1:   1 arithmetic with unsigned numbers
  250.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  251.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  252.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  253.    wt: 1:   1 Calculator Starter Exercises
  254.    wt: 1:   7 Links Lessons Elsewhere
  255.    wt: 1:   21 Logarithms Powers and Exponentials
  256.    wt: 1:   19 N th Roots of Unity
  257.    wt: 1:   18 Sixth Roots of Unity
  258.    wt: 1:   17 Cube Roots of unity
  259.    wt: 1:   16 References and Originality Question
  260.    wt: 1:   15 Pythagorean Theorem Converse
  261.    wt: 1:   14 Law of cosines
  262.    wt: 1:   13 Trig Formulas for dot and cross Products
  263.    wt: 1:   12 cis formulas for sine cosines and tangent
  264.    wt: 1:   11 sine and cosine double triple angle formulas
  265.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  266.    wt: 1:   9 The complex number valued trig function cis
  267.    wt: 1:   8 Unit Circle Development of Trigonometry
  268.    wt: 1:   7 Second Way to Calculate Products
  269.    wt: 1:   6 Field Properties of Complex Number
  270.    wt: 1:   5 An Easy Proof of the Distributive Law
  271.    wt: 1:   4 Multiplication Properties
  272.    wt: 1:   3 Addition Properties
  273.    wt: 1:   1 Rectangular Polar Coordinates Review
  274.    wt: 1:   Appetizer A Complex Number Applet
  275.    wt: 1:   12 Links Lessons elsewhere
  276.    wt: 1:   7 Complex Numbers Appetizer
  277.    wt: 1:   PS H Distributive Law For Complex Numbers
  278.    wt: 1:   arithmetic videos Real Player Format
  279.    wt: 1:   4 Greater More Less Than Signs in General
  280.    wt: 1:   2 More and Less Than with Unlike Signs
  281.    wt: 1:   1 More and Less Than for Counts and Measures
  282.    wt: 1:   7 negative and additive inverse
  283.    wt: 1:   4 signed coordinates for regions in space
  284.    wt: 1:   3 signed coordinates for maps and planes
  285.    wt: 1:   3 Multiplying Units and Numbers
  286.    wt: 1:   9 Improper Fractions and Mixed Numbers
  287.    wt: 1:   6 Multiplication of Mixed Numbers
  288.    wt: 1:   8 Multiplication by Signed Numbers Integers
  289.    wt: 1:   6 Multiplication by Natural Numbers
  290.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  291.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  292.    wt: 1:   Quick history of numbers and algebra
  293.    wt: 1:   011 Division of Time Intervals By Numbers
  294.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  295.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  296.    wt: 1:   G.5 Motions With Bounded Velocities
  297.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  298.    wt: 1:   G.3 Constant Difference Theorem Proof
  299.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  300.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  301.    wt: 1:   F.5b Extreme Value Theorem
  302.    wt: 1:   F.5a Equicontinuity Theorems
  303.    wt: 1:   F.4 Finite Covering Theorem
  304.    wt: 1:   F.3 Intermediate Value Theorem
  305.    wt: 1:   F.2 Closed Range Theorem
  306.    wt: 1:   F.1 What Functions are Continuous
  307.    wt: 1:   E2 Algebraic Properties of Limits
  308.    wt: 1:   E1 Error Control Inequalities
  309.    wt: 1:   D2 Limits of Monotone Sequences
  310.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  311.    wt: 1:   C Triangle Inequalities
  312.    wt: 1:   B3 Bolzano Weierstrass Theorem
  313.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  314.    wt: 1:   PostScript For and Against Decimal Perspectives
  315.    wt: 1:   A1. Introduction
  316.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  317.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  318.    wt: 1:   Chapter 23 Links To Trigonometry
  319.    wt: 1:   Chapter 21 Arrow Addition
  320.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  321.    wt: 1:   Chapter 18. Slopes Areas Integration
  322.    wt: 1:   Chapter 17. Area Approximation
  323.    wt: 1:   Chapter 16. Velocity Approximation
  324.    wt: 1:   Chapter 15. Slope Approximation
  325.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  326.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  327.    wt: 1:   Chapter 13. Acceleration
  328.    wt: 1:   Chapter 12. Units and Slopes
  329.    wt: 1:   Chapter 11. Graphing Slope versus Position
  330.    wt: 1:   Chapter 10 Slopes and Units
  331.    wt: 1:   Chapter 8. Slope Interpretation
  332.    wt: 1:   Chapter 7 Slopes and Velocity
  333.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  334.    wt: 1:   Chapter 5. Slope Sign Tests
  335.    wt: 1:   Chapter 4. More Slope Sign Analysis
  336.    wt: 1:   Chapter 3. Slope Sign Analysis
  337.    wt: 1:   Chapter 2. Slopes and Ski Trails
  338.    wt: 1:   Chapter 1.Introduction
  339.    wt: 1:   Foreword
  340.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  341.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  342.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  343.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  344.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  345.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  346.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  347.    wt: 1:   More Algebra and Slope based Calculus Preview
  348.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  349.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

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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