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.

Home << Search

[1] [2] [3] [4]

Key Word Search

Folder Search

27 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:   4 Computation Rules and Function Notation/
  8.    wt: 2:   B Real Numbers Extrinsic Development/
  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:   5 Real Numbers/
  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:   2 Natural Logarithms Exponentials Powers Roots/
  25.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  26.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  27.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

90 matches:

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

Extended Search

335 matches:

  1.    wt: 9:   21 Chain Rule for powers
  2.    wt: 8:   A Chain Rule Real Player video examples
  3.    wt: 8:   38 Formulas and derivatives for powers and roots
  4.    wt: 8:   33 Chain Rule Real Player video examples
  5.    wt: 8:   30Chain Rule A Proof
  6.    wt: 8:   29 Chain Rule Optional Reading
  7.    wt: 8:   28 Chain Rule Preparation for a Proof
  8.    wt: 8:   27 Chain Rule sinusoidal outer inner functions EGS
  9.    wt: 8:   26 Chain Rule Recognising outer inner functions
  10.    wt: 8:   25 Chain Rule Animated Examples Continued
  11.    wt: 8:   24 Chain Rule Animated Examples
  12.    wt: 8:   23 Chain Rule in general
  13.    wt: 8:   22 Chain Rule for polynomials
  14.    wt: 8:   20 Chain Rule for Pulley Systems
  15.    wt: 8:   19 Chain Rule for linear functions
  16.    wt: 8:   18 Chain Rule Introduction
  17.    wt: 8:   6 Power rule from product rule
  18.    wt: 7:   3 Two Chain Rule Method Exercises
  19.    wt: 7:   1 Chain Rule in Reverse Integration Method
  20.    wt: 7:   A Related lessons in Volume 3
  21.    wt: 7:   31 Derivatives of inverse functions
  22.    wt: 7:   17 Derivatives of quotients of sine and cosine
  23.    wt: 7:   16 Derivatives of reciprocals of sine and cosine
  24.    wt: 7:   15 sine and cosine derivatives 3rd step
  25.    wt: 7:   14 sine and cosine derivatives 2nd step
  26.    wt: 7:   13 sine and cosine derivatives 1st step
  27.    wt: 7:   12 Quotient rule examples
  28.    wt: 7:   11 Quotient rule
  29.    wt: 7:   10 Power rule for negative integers
  30.    wt: 7:   9 Reciprocal rule
  31.    wt: 7:   5 Product Rule
  32.    wt: 7:   4 Sum Rule
  33.    wt: 6:   4 Second derivative test exercise example
  34.    wt: 6:   3 Second derivative test
  35.    wt: 6:   2 Second derivative test prequel
  36.    wt: 6:   1 Two cubic sketching exercises with 1st derivative
  37.    wt: 6:   36 Cube root derivative animated
  38.    wt: 6:   34 Derivative of exponential function
  39.    wt: 6:   8 Differentiation of polynomials
  40.    wt: 6:   7 Animated Differentiation Examples
  41.    wt: 6:   3 Motivation for Limit Definition Take 2
  42.    wt: 6:   2 Motivation for Limit Definition Take 1
  43.    wt: 6:   1 Fall 1983 Why Slopes Appetizer
  44.    wt: 6:   13 Limits with Parameters and Derivatives Take II
  45.    wt: 6:   12 Limits with Parameters and Derivatives Take I
  46.    wt: 5:   Example 2 volume of a cone
  47.    wt: 5:   Example 1 volume of a pyramid
  48.    wt: 5:   Volume of Solid by Cross Sections Lesson
  49.    wt: 5:   Example 1. Area Between x and x squared
  50.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  51.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  52.    wt: 5:   Example 4 with x function of y
  53.    wt: 5:   Example 3
  54.    wt: 5:   Example 2
  55.    wt: 5:   Example 1
  56.    wt: 5:   Area Between Curves Lesson Take 2
  57.    wt: 5:   Area Between Curves Lesson Take 1
  58.    wt: 5:   Summary
  59.    wt: 5:   A Related Material in Volume 3
  60.    wt: 5:   5 Area Under Curve Exercise
  61.    wt: 5:   4 Definite Integrals Evaluation Exercises
  62.    wt: 5:   2 Indefinite Integrals Exercises
  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:   1 Equivalent Computation Rules
  76.    wt: 3:   5 Independent versus Dependent Variables
  77.    wt: 3:   4 Changing Letters
  78.    wt: 3:   3 Geometric Formulas and Function Notation
  79.    wt: 3:   1 Formulas Dependence and Function Notation
  80.    wt: 2:   1 Calculator Starter Exercises
  81.    wt: 2:   musings do not puiblish real numbers
  82.    wt: 2:   A Modular and Remainder Arithmetic
  83.    wt: 2:   A Signed Number Arithmetic Review
  84.    wt: 2:   26 More Less Greater Than Comparison
  85.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  86.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  87.    wt: 2:   23 Distributive Law Two Derivations
  88.    wt: 2:   22 Multiplication of Signed Numbers
  89.    wt: 2:   21 Addition of Multiples of a Single Vector
  90.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  91.    wt: 2:   19 Signed Multiples of Vectors
  92.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  93.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  94.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  95.    wt: 2:   15 Head to Tails in place Addition Associative
  96.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  97.    wt: 2:   13 Arrows and Vectors in a Plane
  98.    wt: 2:   12 Real Numbers Line Signed Coordinates
  99.    wt: 2:   11 Signed Number Addition and Addition Properties
  100.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  101.    wt: 2:   9 Division with Digits after Decimal Point
  102.    wt: 2:   8 Division and Mulplication of Compound Fractions
  103.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  104.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  105.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  106.    wt: 2:   4 Location of Point in Decimal Addition
  107.    wt: 2:   3 Location of Point in Decimal Multiplication
  108.    wt: 2:   2 Counting Digits in Decimal Multiplication
  109.    wt: 2:   1 Fractions with Finite Decimal Expansions
  110.    wt: 2:   E Long Division Methods more
  111.    wt: 2:   D Long Division Methods
  112.    wt: 2:   C Three Decimal Subtraction Methods
  113.    wt: 2:   B Decimal Comparison and Subtraction
  114.    wt: 2:   A Decimal Addition Columm Methods
  115.    wt: 2:   8 Column Multiplication Methods in General
  116.    wt: 2:   7 Decimals Multiplication Methods Examples
  117.    wt: 2:   6 Column Methods for Decimal Multiplication
  118.    wt: 2:   5 Distributive Law for Whole Numbers
  119.    wt: 2:   4 Commutative Law Groups Counting Form
  120.    wt: 2:   3 Multiplicative Counting Skills Principles
  121.    wt: 2:   2 Combing Counts Addition Skills and Principles
  122.    wt: 2:   1 The Counting Origins of Numbers
  123.    wt: 2:   5 Areas of Rectangles Revisited
  124.    wt: 2:   4 Fraction Operations Axiomatic Development
  125.    wt: 2:   3 Inequalities Algebraically
  126.    wt: 2:   2 Fraction Operations Physical Development
  127.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  128.    wt: 2:   5 Proportionality in Equivalent Fractions
  129.    wt: 2:   4 Rates Ratios and Proporitionality
  130.    wt: 2:   3 Proportionality Examples
  131.    wt: 2:   2 Algebraic View
  132.    wt: 2:   1 What is Proportionality
  133.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  134.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  135.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  136.    wt: 2:   6 Compound Interest Forward and Backwards
  137.    wt: 2:   5 Triangle Area Formula Backwards
  138.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  139.    wt: 2:   3 Linear Equation Literal Solution More
  140.    wt: 2:   2 Linear Equation Literal Solution
  141.    wt: 2:   1 Changing Calculations
  142.    wt: 2:   6 Equations and Systems Equivalent or Implied
  143.    wt: 2:   5 Equality in Algebra
  144.    wt: 2:   4 Subtraction and Division Axioms
  145.    wt: 2:   3 Product Axioms Two Forms
  146.    wt: 2:   2 Addition and Multiplication Axioms
  147.    wt: 2:   5 Greater More Less Than Signs in General
  148.    wt: 2:   4 Comparison of Negative Numbers
  149.    wt: 2:   3 More and Less Than with Unlike Signs
  150.    wt: 2:   2 More and Less Than for Counts and Measures
  151.    wt: 2:   1 Real Numbers Comparison
  152.    wt: 2:   16 Real Numbers Comparison
  153.    wt: 2:   15 Real Number Division
  154.    wt: 2:   14 Real Number Multiplication
  155.    wt: 2:   13 Real Number Subtraction
  156.    wt: 2:   12 Real Number Additive Inverses or Negatives
  157.    wt: 2:   11 Real Number Addition
  158.    wt: 2:   10 Real Number Lengths and Signs
  159.    wt: 2:   9 Coordinates for Regions in Space
  160.    wt: 2:   8 Coordinates for Maps and Planes
  161.    wt: 2:   7 Real Numbers as Line Cordinates
  162.    wt: 2:   6 Unsigned Real Numbers
  163.    wt: 2:   5 Rational Numbers More
  164.    wt: 2:   4 Rational Numbers
  165.    wt: 2:   3 Fractions
  166.    wt: 2:   2 Integers
  167.    wt: 2:   1 Whole and Natural Numbers
  168.    wt: 2:   More Exercises
  169.    wt: 2:   Simple Exercises
  170.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  171.    wt: 2:   4 GE III Animated Examples
  172.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  173.    wt: 2:   3 GE III Equation Addition and Multiplication
  174.    wt: 2:   2 GE II Comparison
  175.    wt: 2:   1 GE Substitution four examples
  176.    wt: 2:   4 Solving a triangular system exercise
  177.    wt: 2:   3 Solving triangular system example
  178.    wt: 2:   2 Essentially one exercises three with solution
  179.    wt: 2:   1 Essentially One Unknown
  180.    wt: 2:   6 Algebraic Solution Example
  181.    wt: 2:   5 Algebraic Solutions Introduction
  182.    wt: 2:   4 Four Examples Fractional Coefficients
  183.    wt: 2:   3 Four Examples
  184.    wt: 2:   2 Three Examples
  185.    wt: 2:   1 Proper Equal Sign Usage
  186.    wt: 2:   Skill Development Notes
  187.    wt: 2:   10 One Example
  188.    wt: 2:   9 Three Examples
  189.    wt: 2:   8 One Example
  190.    wt: 2:   7 Two Examples
  191.    wt: 2:   6 Three Examples
  192.    wt: 2:   5 Three Examples
  193.    wt: 2:   4 Two Examples
  194.    wt: 2:   3 Two Examples
  195.    wt: 2:   2 Three Examples
  196.    wt: 2:   Using Letters for Physical Quantities
  197.    wt: 2:   Formula Usage Show Work Format
  198.    wt: 2:   13 Naming Identifying Formulas with Words
  199.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  200.    wt: 2:   11 Volume of Sphere
  201.    wt: 2:   10 Volume of Pyramid
  202.    wt: 2:   9 Volume of Cone
  203.    wt: 2:   8 Compound Interest Formula Evaluation
  204.    wt: 2:   7 Compound Interest Formula Introduction
  205.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  206.    wt: 2:   5 Box Volume Formula Example
  207.    wt: 2:   4 Circle Area Formula Example
  208.    wt: 2:   3 Triangle Area Formula Example
  209.    wt: 2:   2 Another Rectangle Area Formula Example
  210.    wt: 2:   1 Written work formats for developing and showing skill
  211.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  212.    wt: 2:   9 Sets in Probability and Statistics
  213.    wt: 2:   8 Sets of Numbers
  214.    wt: 2:   7 Cautious or Safe Set Construction
  215.    wt: 2:   6 Power Set Notation
  216.    wt: 2:   5 Product Builder Notation
  217.    wt: 2:   4 Subset Builder Notation
  218.    wt: 2:   3 Counting with Sets etc
  219.    wt: 2:   2 Venn Diagrams
  220.    wt: 2:   1 Finite Sets
  221.    wt: 2:   6 Three Notions of What is a Variable
  222.    wt: 2:   5 Talking about Numbers and Quantities
  223.    wt: 2:   4 A Brief Story of numbers and algebra
  224.    wt: 2:   3 Adding Words To Arithmetic
  225.    wt: 2:   2 What is a Variable
  226.    wt: 2:   1 Three Skills For Algebra
  227.    wt: 2:   About Folder Contents
  228.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  229.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  230.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  231.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  232.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  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:   11 Growth and Decay in Biology
  246.    wt: 1:   10 Exponential Growth and Decay Models
  247.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  248.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  249.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  250.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  251.    wt: 1:   5 Natural Logarithm Calculator Exercises
  252.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  253.    wt: 1:   2 Square Root Simplification a prequel
  254.    wt: 1:   7 Links Lessons Elsewhere
  255.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  256.    wt: 1:   21 Logarithms Powers and Exponentials
  257.    wt: 1:   12 Links Lessons elsewhere
  258.    wt: 1:   6 Ruler and compass Angle Bisection
  259.    wt: 1:   A Measurement with Ruler Proper Use
  260.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  261.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  262.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  263.    wt: 1:   4 Counting with Trees Product Rule Take I
  264.    wt: 1:   D Remainders Modulo 11 Pair Rule
  265.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  266.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  267.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  268.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  269.    wt: 1:   11 Efficient Square Rule Use
  270.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  271.    wt: 1:   5 Prime Factorization and a Square Rule
  272.    wt: 1:   C Counting Areas with Powers of Ten
  273.    wt: 1:   B Powers of Ten
  274.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  275.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  276.    wt: 1:   G.5 Motions With Bounded Velocities
  277.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  278.    wt: 1:   G.3 Constant Difference Theorem Proof
  279.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  280.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  281.    wt: 1:   F.5b Extreme Value Theorem
  282.    wt: 1:   F.5a Equicontinuity Theorems
  283.    wt: 1:   F.4 Finite Covering Theorem
  284.    wt: 1:   F.3 Intermediate Value Theorem
  285.    wt: 1:   F.2 Closed Range Theorem
  286.    wt: 1:   F.1 What Functions are Continuous
  287.    wt: 1:   E2 Algebraic Properties of Limits
  288.    wt: 1:   E1 Error Control Inequalities
  289.    wt: 1:   D2 Limits of Monotone Sequences
  290.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  291.    wt: 1:   C Triangle Inequalities
  292.    wt: 1:   B3 Bolzano Weierstrass Theorem
  293.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  294.    wt: 1:   PostScript For and Against Decimal Perspectives
  295.    wt: 1:   A1. Introduction
  296.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  297.    wt: 1:   Chapter 23 Links To Trigonometry
  298.    wt: 1:   Chapter 22 Complex Numbers
  299.    wt: 1:   Chapter 21 Arrow Addition
  300.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  301.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  302.    wt: 1:   Chapter 18. Slopes Areas Integration
  303.    wt: 1:   Chapter 17. Area Approximation
  304.    wt: 1:   Chapter 16. Velocity Approximation
  305.    wt: 1:   Chapter 15. Slope Approximation
  306.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  307.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  308.    wt: 1:   Chapter 13. Acceleration
  309.    wt: 1:   Chapter 12. Units and Slopes
  310.    wt: 1:   Chapter 11. Graphing Slope versus Position
  311.    wt: 1:   Chapter 10 Slopes and Units
  312.    wt: 1:   Chapter 8. Slope Interpretation
  313.    wt: 1:   Chapter 7 Slopes and Velocity
  314.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  315.    wt: 1:   Chapter 5. Slope Sign Tests
  316.    wt: 1:   Chapter 4. More Slope Sign Analysis
  317.    wt: 1:   Chapter 3. Slope Sign Analysis
  318.    wt: 1:   Chapter 2. Slopes and Ski Trails
  319.    wt: 1:   Chapter 1.Introduction
  320.    wt: 1:   Foreword
  321.    wt: 1:   Chapter 18. Rules for Algebra
  322.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  323.    wt: 1:   Chapter 4 Longer Chains of Reason
  324.    wt: 1:   Chapter 3 Chains of Reason
  325.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  326.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  327.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  328.    wt: 1:   Chapter 7 Longer Chains of Reason
  329.    wt: 1:   Chapter 6 Chains of Reason
  330.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  331.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  332.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  333.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  334.    wt: 1:   More Algebra and Slope based Calculus Preview
  335.    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.

Return to Page Top

Home << Search

[1] [2] [3] [4]

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

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.