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.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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

Web Page Search

86 matches:

  1.    wt: 3:   19 Chain Rule for linear functions
  2.    wt: 2:   3 Two Chain Rule Method Exercises
  3.    wt: 2:   1 Chain Rule in Reverse Integration Method
  4.    wt: 2:   A Chain Rule Real Player video examples
  5.    wt: 2:   33 Chain Rule Real Player video examples
  6.    wt: 2:   30Chain Rule A Proof
  7.    wt: 2:   29 Chain Rule Optional Reading
  8.    wt: 2:   28 Chain Rule Preparation for a Proof
  9.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  10.    wt: 2:   26 Chain Rule Recognising outer inner functions
  11.    wt: 2:   25 Chain Rule Animated Examples Continued
  12.    wt: 2:   24 Chain Rule Animated Examples
  13.    wt: 2:   23 Chain Rule in general
  14.    wt: 2:   22 Chain Rule for polynomials
  15.    wt: 2:   21 Chain Rule for powers
  16.    wt: 2:   20 Chain Rule for Pulley Systems
  17.    wt: 2:   18 Chain Rule Introduction
  18.    wt: 2:   6 Power rule from product rule
  19.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  20.    wt: 2:   Chapter 3 Algebra Starter Lessons
  21.    wt: 1:   Skills Chapter 5 Calculus
  22.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  23.    wt: 1:   chapitre 06 00 Chaines de la raison
  24.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  25.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  26.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  27.    wt: 1:   19 Horizontal line rule and method
  28.    wt: 1:   18 Vertical Line Rule and Method
  29.    wt: 1:   1 Calculator Starter Exercises
  30.    wt: 1:   7 Links Lessons Elsewhere
  31.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  32.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  33.    wt: 1:   4 Polynomials Long division linear divisor
  34.    wt: 1:   12 Links Lessons elsewhere
  35.    wt: 1:   6 Intersection of lines by solving linear systems
  36.    wt: 1:   6 Ruler and compass Angle Bisection
  37.    wt: 1:   A Measurement with Ruler Proper Use
  38.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  39.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  40.    wt: 1:   3 Linear Equation Literal Solution More
  41.    wt: 1:   2 Linear Equation Literal Solution
  42.    wt: 1:   1 Equivalent Computation Rules
  43.    wt: 1:   2 Computation Rules Evaluation
  44.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  45.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  46.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  47.    wt: 1:   4 Counting with Trees Product Rule Take I
  48.    wt: 1:   D Remainders Modulo 11 Pair Rule
  49.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  50.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  51.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  52.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  53.    wt: 1:   11 Efficient Square Rule Use
  54.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  55.    wt: 1:   5 Prime Factorization and a Square Rule
  56.    wt: 1:   A Related lessons in Volume 3
  57.    wt: 1:   12 Quotient rule examples
  58.    wt: 1:   11 Quotient rule
  59.    wt: 1:   10 Power rule for negative integers
  60.    wt: 1:   9 Reciprocal rule
  61.    wt: 1:   5 Product Rule
  62.    wt: 1:   4 Sum Rule
  63.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  64.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  65.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  66.    wt: 1:   Chapter 17. Area Approximation
  67.    wt: 1:   Chapter 16. Velocity Approximation
  68.    wt: 1:   Chapter 15. Slope Approximation
  69.    wt: 1:   Chapter 9 About First Courses in Calculus
  70.    wt: 1:   Fall 1983 Calculus Appetizer
  71.    wt: 1:   Chapter 18. Rules for Algebra
  72.    wt: 1:   Chapter 15. Solving Linear Equations
  73.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  74.    wt: 1:   Chapter 4 Longer Chains of Reason
  75.    wt: 1:   Chapter 3 Chains of Reason
  76.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  77.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  78.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  79.    wt: 1:   Chapter 7 Longer Chains of Reason
  80.    wt: 1:   Chapter 6 Chains of Reason
  81.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  82.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  83.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  84.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  85.    wt: 1:   More Algebra and Slope based Calculus Preview
  86.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

326 matches:

  1.    wt: 8:   19 Chain Rule for linear functions
  2.    wt: 7:   3 Two Chain Rule Method Exercises
  3.    wt: 7:   1 Chain Rule in Reverse Integration Method
  4.    wt: 7:   A Chain Rule Real Player video examples
  5.    wt: 7:   33 Chain Rule Real Player video examples
  6.    wt: 7:   30Chain Rule A Proof
  7.    wt: 7:   29 Chain Rule Optional Reading
  8.    wt: 7:   28 Chain Rule Preparation for a Proof
  9.    wt: 7:   27 Chain Rule sinusoidal outer inner functions EGS
  10.    wt: 7:   26 Chain Rule Recognising outer inner functions
  11.    wt: 7:   25 Chain Rule Animated Examples Continued
  12.    wt: 7:   24 Chain Rule Animated Examples
  13.    wt: 7:   23 Chain Rule in general
  14.    wt: 7:   22 Chain Rule for polynomials
  15.    wt: 7:   21 Chain Rule for powers
  16.    wt: 7:   20 Chain Rule for Pulley Systems
  17.    wt: 7:   18 Chain Rule Introduction
  18.    wt: 7:   6 Power rule from product rule
  19.    wt: 6:   A Related lessons in Volume 3
  20.    wt: 6:   12 Quotient rule examples
  21.    wt: 6:   11 Quotient rule
  22.    wt: 6:   10 Power rule for negative integers
  23.    wt: 6:   9 Reciprocal rule
  24.    wt: 6:   5 Product Rule
  25.    wt: 6:   4 Sum Rule
  26.    wt: 5:   Example 2 volume of a cone
  27.    wt: 5:   Example 1 volume of a pyramid
  28.    wt: 5:   Volume of Solid by Cross Sections Lesson
  29.    wt: 5:   Example 1. Area Between x and x squared
  30.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  31.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  32.    wt: 5:   Example 4 with x function of y
  33.    wt: 5:   Example 3
  34.    wt: 5:   Example 2
  35.    wt: 5:   Example 1
  36.    wt: 5:   Area Between Curves Lesson Take 2
  37.    wt: 5:   Area Between Curves Lesson Take 1
  38.    wt: 5:   Summary
  39.    wt: 5:   A Related Material in Volume 3
  40.    wt: 5:   5 Area Under Curve Exercise
  41.    wt: 5:   4 Definite Integrals Evaluation Exercises
  42.    wt: 5:   2 Indefinite Integrals Exercises
  43.    wt: 5:   4 Second derivative test exercise example
  44.    wt: 5:   3 Second derivative test
  45.    wt: 5:   2 Second derivative test prequel
  46.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  47.    wt: 5:   38 Formulas and derivatives for powers and roots
  48.    wt: 5:   36 Cube root derivative animated
  49.    wt: 5:   34 Derivative of exponential function
  50.    wt: 5:   31 Derivatives of inverse functions
  51.    wt: 5:   17 Derivatives of quotients of sine and cosine
  52.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  53.    wt: 5:   15 sine and cosine derivatives 3rd step
  54.    wt: 5:   14 sine and cosine derivatives 2nd step
  55.    wt: 5:   13 sine and cosine derivatives 1st step
  56.    wt: 5:   8 Differentiation of polynomials
  57.    wt: 5:   7 Animated Differentiation Examples
  58.    wt: 5:   3 Motivation for Limit Definition Take 2
  59.    wt: 5:   2 Motivation for Limit Definition Take 1
  60.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  61.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  62.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  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:   5 Jumps and absence of unlimited error control
  70.    wt: 5:   4 Numerical properties
  71.    wt: 5:   3 Decimal insights for limits continuity convergence
  72.    wt: 5:   2 Algebraic codification
  73.    wt: 5:   1 Numerical introduction
  74.    wt: 4:   2 Computation Rules Evaluation
  75.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  76.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  77.    wt: 3:   3 Linear Equation Literal Solution More
  78.    wt: 3:   2 Linear Equation Literal Solution
  79.    wt: 3:   1 Equivalent Computation Rules
  80.    wt: 3:   5 Independent versus Dependent Variables
  81.    wt: 3:   4 Changing Letters
  82.    wt: 3:   3 Geometric Formulas and Function Notation
  83.    wt: 3:   1 Formulas Dependence and Function Notation
  84.    wt: 3:   More Exercises
  85.    wt: 3:   Simple Exercises
  86.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  87.    wt: 3:   4 GE III Animated Examples
  88.    wt: 3:   3 Gaussian Elimination 3 unknowns first example
  89.    wt: 3:   3 GE III Equation Addition and Multiplication
  90.    wt: 3:   2 GE II Comparison
  91.    wt: 3:   1 GE Substitution four examples
  92.    wt: 3:   4 Solving a triangular system exercise
  93.    wt: 3:   3 Solving triangular system example
  94.    wt: 3:   2 Essentially one exercises three with solution
  95.    wt: 3:   1 Essentially One Unknown
  96.    wt: 3:   6 Algebraic Solution Example
  97.    wt: 3:   5 Algebraic Solutions Introduction
  98.    wt: 3:   4 Four Examples Fractional Coefficients
  99.    wt: 3:   3 Four Examples
  100.    wt: 3:   2 Three Examples
  101.    wt: 3:   1 Proper Equal Sign Usage
  102.    wt: 3:   Skill Development Notes
  103.    wt: 3:   10 One Example
  104.    wt: 3:   9 Three Examples
  105.    wt: 3:   8 One Example
  106.    wt: 3:   7 Two Examples
  107.    wt: 3:   6 Three Examples
  108.    wt: 3:   5 Three Examples
  109.    wt: 3:   4 Two Examples
  110.    wt: 3:   3 Two Examples
  111.    wt: 3:   2 Three Examples
  112.    wt: 3:   Using Letters for Physical Quantities
  113.    wt: 3:   Formula Usage Show Work Format
  114.    wt: 2:   musings do not puiblish real numbers
  115.    wt: 2:   A Modular and Remainder Arithmetic
  116.    wt: 2:   A Signed Number Arithmetic Review
  117.    wt: 2:   26 More Less Greater Than Comparison
  118.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  119.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  120.    wt: 2:   23 Distributive Law Two Derivations
  121.    wt: 2:   22 Multiplication of Signed Numbers
  122.    wt: 2:   21 Addition of Multiples of a Single Vector
  123.    wt: 2:   19 Signed Multiples of Vectors
  124.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  125.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  126.    wt: 2:   15 Head to Tails in place Addition Associative
  127.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  128.    wt: 2:   13 Arrows and Vectors in a Plane
  129.    wt: 2:   12 Real Numbers Line Signed Coordinates
  130.    wt: 2:   11 Signed Number Addition and Addition Properties
  131.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  132.    wt: 2:   9 Division with Digits after Decimal Point
  133.    wt: 2:   8 Division and Mulplication of Compound Fractions
  134.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  135.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  136.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  137.    wt: 2:   4 Location of Point in Decimal Addition
  138.    wt: 2:   3 Location of Point in Decimal Multiplication
  139.    wt: 2:   2 Counting Digits in Decimal Multiplication
  140.    wt: 2:   1 Fractions with Finite Decimal Expansions
  141.    wt: 2:   E Long Division Methods more
  142.    wt: 2:   D Long Division Methods
  143.    wt: 2:   C Three Decimal Subtraction Methods
  144.    wt: 2:   B Decimal Comparison and Subtraction
  145.    wt: 2:   A Decimal Addition Columm Methods
  146.    wt: 2:   8 Column Multiplication Methods in General
  147.    wt: 2:   7 Decimals Multiplication Methods Examples
  148.    wt: 2:   6 Column Methods for Decimal Multiplication
  149.    wt: 2:   5 Distributive Law for Whole Numbers
  150.    wt: 2:   4 Commutative Law Groups Counting Form
  151.    wt: 2:   3 Multiplicative Counting Skills Principles
  152.    wt: 2:   2 Combing Counts Addition Skills and Principles
  153.    wt: 2:   1 The Counting Origins of Numbers
  154.    wt: 2:   5 Areas of Rectangles Revisited
  155.    wt: 2:   4 Fraction Operations Axiomatic Development
  156.    wt: 2:   3 Inequalities Algebraically
  157.    wt: 2:   2 Fraction Operations Physical Development
  158.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  159.    wt: 2:   5 Proportionality in Equivalent Fractions
  160.    wt: 2:   4 Rates Ratios and Proporitionality
  161.    wt: 2:   3 Proportionality Examples
  162.    wt: 2:   2 Algebraic View
  163.    wt: 2:   1 What is Proportionality
  164.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  165.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  166.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  167.    wt: 2:   6 Compound Interest Forward and Backwards
  168.    wt: 2:   5 Triangle Area Formula Backwards
  169.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  170.    wt: 2:   1 Changing Calculations
  171.    wt: 2:   6 Equations and Systems Equivalent or Implied
  172.    wt: 2:   5 Equality in Algebra
  173.    wt: 2:   4 Subtraction and Division Axioms
  174.    wt: 2:   3 Product Axioms Two Forms
  175.    wt: 2:   2 Addition and Multiplication Axioms
  176.    wt: 2:   5 Greater More Less Than Signs in General
  177.    wt: 2:   4 Comparison of Negative Numbers
  178.    wt: 2:   3 More and Less Than with Unlike Signs
  179.    wt: 2:   2 More and Less Than for Counts and Measures
  180.    wt: 2:   1 Real Numbers Comparison
  181.    wt: 2:   16 Real Numbers Comparison
  182.    wt: 2:   15 Real Number Division
  183.    wt: 2:   14 Real Number Multiplication
  184.    wt: 2:   13 Real Number Subtraction
  185.    wt: 2:   12 Real Number Additive Inverses or Negatives
  186.    wt: 2:   11 Real Number Addition
  187.    wt: 2:   10 Real Number Lengths and Signs
  188.    wt: 2:   9 Coordinates for Regions in Space
  189.    wt: 2:   8 Coordinates for Maps and Planes
  190.    wt: 2:   7 Real Numbers as Line Cordinates
  191.    wt: 2:   6 Unsigned Real Numbers
  192.    wt: 2:   5 Rational Numbers More
  193.    wt: 2:   4 Rational Numbers
  194.    wt: 2:   3 Fractions
  195.    wt: 2:   2 Integers
  196.    wt: 2:   1 Whole and Natural Numbers
  197.    wt: 2:   13 Naming Identifying Formulas with Words
  198.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  199.    wt: 2:   11 Volume of Sphere
  200.    wt: 2:   10 Volume of Pyramid
  201.    wt: 2:   9 Volume of Cone
  202.    wt: 2:   8 Compound Interest Formula Evaluation
  203.    wt: 2:   7 Compound Interest Formula Introduction
  204.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  205.    wt: 2:   5 Box Volume Formula Example
  206.    wt: 2:   4 Circle Area Formula Example
  207.    wt: 2:   3 Triangle Area Formula Example
  208.    wt: 2:   2 Another Rectangle Area Formula Example
  209.    wt: 2:   1 Written work formats for developing and showing skill
  210.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  211.    wt: 2:   9 Sets in Probability and Statistics
  212.    wt: 2:   8 Sets of Numbers
  213.    wt: 2:   7 Cautious or Safe Set Construction
  214.    wt: 2:   6 Power Set Notation
  215.    wt: 2:   5 Product Builder Notation
  216.    wt: 2:   4 Subset Builder Notation
  217.    wt: 2:   3 Counting with Sets etc
  218.    wt: 2:   2 Venn Diagrams
  219.    wt: 2:   1 Finite Sets
  220.    wt: 2:   6 Three Notions of What is a Variable
  221.    wt: 2:   5 Talking about Numbers and Quantities
  222.    wt: 2:   4 A Brief Story of numbers and algebra
  223.    wt: 2:   3 Adding Words To Arithmetic
  224.    wt: 2:   2 What is a Variable
  225.    wt: 2:   1 Three Skills For Algebra
  226.    wt: 2:   About Folder Contents
  227.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  228.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  229.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  230.    wt: 2:   Chapter 17. Area Approximation
  231.    wt: 2:   Chapter 16. Velocity Approximation
  232.    wt: 2:   Chapter 15. Slope Approximation
  233.    wt: 2:   Chapter 9 About First Courses in Calculus
  234.    wt: 2:   Fall 1983 Calculus Appetizer
  235.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  236.    wt: 2:   Chapter 3 Algebra Starter Lessons
  237.    wt: 1:   Skills Chapter 5 Calculus
  238.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  239.    wt: 1:   chapitre 06 00 Chaines de la raison
  240.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  241.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  242.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  243.    wt: 1:   19 Horizontal line rule and method
  244.    wt: 1:   18 Vertical Line Rule and Method
  245.    wt: 1:   1 Calculator Starter Exercises
  246.    wt: 1:   7 Links Lessons Elsewhere
  247.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  248.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  249.    wt: 1:   4 Polynomials Long division linear divisor
  250.    wt: 1:   12 Links Lessons elsewhere
  251.    wt: 1:   6 Intersection of lines by solving linear systems
  252.    wt: 1:   6 Ruler and compass Angle Bisection
  253.    wt: 1:   A Measurement with Ruler Proper Use
  254.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  255.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  256.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  257.    wt: 1:   4 Counting with Trees Product Rule Take I
  258.    wt: 1:   D Remainders Modulo 11 Pair Rule
  259.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  260.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  261.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  262.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  263.    wt: 1:   11 Efficient Square Rule Use
  264.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  265.    wt: 1:   5 Prime Factorization and a Square Rule
  266.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  267.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  268.    wt: 1:   G.5 Motions With Bounded Velocities
  269.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  270.    wt: 1:   G.3 Constant Difference Theorem Proof
  271.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  272.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  273.    wt: 1:   F.5b Extreme Value Theorem
  274.    wt: 1:   F.5a Equicontinuity Theorems
  275.    wt: 1:   F.4 Finite Covering Theorem
  276.    wt: 1:   F.3 Intermediate Value Theorem
  277.    wt: 1:   F.2 Closed Range Theorem
  278.    wt: 1:   F.1 What Functions are Continuous
  279.    wt: 1:   E2 Algebraic Properties of Limits
  280.    wt: 1:   E1 Error Control Inequalities
  281.    wt: 1:   D2 Limits of Monotone Sequences
  282.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  283.    wt: 1:   C Triangle Inequalities
  284.    wt: 1:   B3 Bolzano Weierstrass Theorem
  285.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  286.    wt: 1:   PostScript For and Against Decimal Perspectives
  287.    wt: 1:   A1. Introduction
  288.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  289.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  290.    wt: 1:   Chapter 23 Links To Trigonometry
  291.    wt: 1:   Chapter 22 Complex Numbers
  292.    wt: 1:   Chapter 21 Arrow Addition
  293.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  294.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  295.    wt: 1:   Chapter 18. Slopes Areas Integration
  296.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  297.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  298.    wt: 1:   Chapter 13. Acceleration
  299.    wt: 1:   Chapter 12. Units and Slopes
  300.    wt: 1:   Chapter 11. Graphing Slope versus Position
  301.    wt: 1:   Chapter 10 Slopes and Units
  302.    wt: 1:   Chapter 8. Slope Interpretation
  303.    wt: 1:   Chapter 7 Slopes and Velocity
  304.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  305.    wt: 1:   Chapter 5. Slope Sign Tests
  306.    wt: 1:   Chapter 4. More Slope Sign Analysis
  307.    wt: 1:   Chapter 3. Slope Sign Analysis
  308.    wt: 1:   Chapter 2. Slopes and Ski Trails
  309.    wt: 1:   Chapter 1.Introduction
  310.    wt: 1:   Foreword
  311.    wt: 1:   Chapter 18. Rules for Algebra
  312.    wt: 1:   Chapter 15. Solving Linear Equations
  313.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  314.    wt: 1:   Chapter 4 Longer Chains of Reason
  315.    wt: 1:   Chapter 3 Chains of Reason
  316.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  317.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  318.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  319.    wt: 1:   Chapter 7 Longer Chains of Reason
  320.    wt: 1:   Chapter 6 Chains of Reason
  321.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  322.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  323.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  324.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  325.    wt: 1:   More Algebra and Slope based Calculus Preview
  326.    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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