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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28 matches:

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

Web Page Search

63 matches:

  1.    wt: 2:   Chapter 15. Slope Approximation
  2.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  3.    wt: 2:   Chapter 3 Algebra Starter Lessons
  4.    wt: 2:   More Algebra and Slope based Calculus Preview
  5.    wt: 1:   Skills Chapter 5 Calculus
  6.    wt: 1:   chapitre 04 08 Limitations et benefices
  7.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  8.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  9.    wt: 1:   1 Calculator Starter Exercises
  10.    wt: 1:   7 Links Lessons Elsewhere
  11.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  12.    wt: 1:   C Straight Lines Slope from Coordinates
  13.    wt: 1:   B Straight Line Slope Scaling Properties More
  14.    wt: 1:   A Straight Line Slope Scaling Properties
  15.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  16.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  17.    wt: 1:   1 Straight Lines Slope Concept
  18.    wt: 1:   25 tangent double angle formula Slope connection
  19.    wt: 1:   Why Trigonometry the whyslopes view
  20.    wt: 1:   12 Links Lessons elsewhere
  21.    wt: 1:   5 Algebraic View of Slopes
  22.    wt: 1:   3 Slope product for perpendicular lines
  23.    wt: 1:   2 point slope equation for a line
  24.    wt: 1:   A Related lessons in Volume 3
  25.    wt: 1:   3 Motivation for Limit Definition Take 2
  26.    wt: 1:   2 Motivation for Limit Definition Take 1
  27.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  28.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  29.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  30.    wt: 1:   11 Limits at infinity Three Examples
  31.    wt: 1:   10 Three one sided limits with infinite values
  32.    wt: 1:   9 Limits Continuity and Composition
  33.    wt: 1:   5 Jumps and absence of unlimited error control
  34.    wt: 1:   3 Decimal insights for limits continuity convergence
  35.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  36.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  37.    wt: 1:   E2 Algebraic Properties of Limits
  38.    wt: 1:   D2 Limits of Monotone Sequences
  39.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  40.    wt: 1:   Chapter 18. Slopes Areas Integration
  41.    wt: 1:   Chapter 17. Area Approximation
  42.    wt: 1:   Chapter 16. Velocity Approximation
  43.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  44.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  45.    wt: 1:   Chapter 12. Units and Slopes
  46.    wt: 1:   Chapter 11. Graphing Slope versus Position
  47.    wt: 1:   Chapter 10 Slopes and Units
  48.    wt: 1:   Chapter 9 About First Courses in Calculus
  49.    wt: 1:   Chapter 8. Slope Interpretation
  50.    wt: 1:   Chapter 7 Slopes and Velocity
  51.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  52.    wt: 1:   Chapter 5. Slope Sign Tests
  53.    wt: 1:   Chapter 4. More Slope Sign Analysis
  54.    wt: 1:   Chapter 3. Slope Sign Analysis
  55.    wt: 1:   Chapter 2. Slopes and Ski Trails
  56.    wt: 1:   Fall 1983 Calculus Appetizer
  57.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  58.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  59.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  60.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  61.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  62.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  63.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

329 matches:

  1.    wt: 7:   13 Limits with Parameters and Derivatives Take II
  2.    wt: 7:   12 Limits with Parameters and Derivatives Take I
  3.    wt: 7:   11 Limits at infinity Three Examples
  4.    wt: 7:   10 Three one sided limits with infinite values
  5.    wt: 7:   9 Limits Continuity and Composition
  6.    wt: 7:   5 Jumps and absence of unlimited error control
  7.    wt: 7:   3 Decimal insights for limits continuity convergence
  8.    wt: 6:   A Related lessons in Volume 3
  9.    wt: 6:   3 Motivation for Limit Definition Take 2
  10.    wt: 6:   2 Motivation for Limit Definition Take 1
  11.    wt: 6:   1 Fall 1983 Why Slopes Appetizer
  12.    wt: 6:   8 Four Animated Examples
  13.    wt: 6:   7 Evaluation by immediate or delayed substitution
  14.    wt: 6:   6 Continuity at a point
  15.    wt: 6:   4 Numerical properties
  16.    wt: 6:   2 Algebraic codification
  17.    wt: 6:   1 Numerical introduction
  18.    wt: 5:   Example 2 volume of a cone
  19.    wt: 5:   Example 1 volume of a pyramid
  20.    wt: 5:   Volume of Solid by Cross Sections Lesson
  21.    wt: 5:   Example 1. Area Between x and x squared
  22.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  23.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  24.    wt: 5:   Example 4 with x function of y
  25.    wt: 5:   Example 3
  26.    wt: 5:   Example 2
  27.    wt: 5:   Example 1
  28.    wt: 5:   Area Between Curves Lesson Take 2
  29.    wt: 5:   Area Between Curves Lesson Take 1
  30.    wt: 5:   Summary
  31.    wt: 5:   A Related Material in Volume 3
  32.    wt: 5:   5 Area Under Curve Exercise
  33.    wt: 5:   4 Definite Integrals Evaluation Exercises
  34.    wt: 5:   3 Two Chain Rule Method Exercises
  35.    wt: 5:   2 Indefinite Integrals Exercises
  36.    wt: 5:   1 Chain Rule in Reverse Integration Method
  37.    wt: 5:   4 Second derivative test exercise example
  38.    wt: 5:   3 Second derivative test
  39.    wt: 5:   2 Second derivative test prequel
  40.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  41.    wt: 5:   A Chain Rule Real Player video examples
  42.    wt: 5:   38 Formulas and derivatives for powers and roots
  43.    wt: 5:   36 Cube root derivative animated
  44.    wt: 5:   34 Derivative of exponential function
  45.    wt: 5:   33 Chain Rule Real Player video examples
  46.    wt: 5:   31 Derivatives of inverse functions
  47.    wt: 5:   30Chain Rule A Proof
  48.    wt: 5:   29 Chain Rule Optional Reading
  49.    wt: 5:   28 Chain Rule Preparation for a Proof
  50.    wt: 5:   27 Chain Rule sinusoidal outer inner functions EGS
  51.    wt: 5:   26 Chain Rule Recognising outer inner functions
  52.    wt: 5:   25 Chain Rule Animated Examples Continued
  53.    wt: 5:   24 Chain Rule Animated Examples
  54.    wt: 5:   23 Chain Rule in general
  55.    wt: 5:   22 Chain Rule for polynomials
  56.    wt: 5:   21 Chain Rule for powers
  57.    wt: 5:   20 Chain Rule for Pulley Systems
  58.    wt: 5:   19 Chain Rule for linear functions
  59.    wt: 5:   18 Chain Rule Introduction
  60.    wt: 5:   17 Derivatives of quotients of sine and cosine
  61.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  62.    wt: 5:   15 sine and cosine derivatives 3rd step
  63.    wt: 5:   14 sine and cosine derivatives 2nd step
  64.    wt: 5:   13 sine and cosine derivatives 1st step
  65.    wt: 5:   12 Quotient rule examples
  66.    wt: 5:   11 Quotient rule
  67.    wt: 5:   10 Power rule for negative integers
  68.    wt: 5:   9 Reciprocal rule
  69.    wt: 5:   8 Differentiation of polynomials
  70.    wt: 5:   7 Animated Differentiation Examples
  71.    wt: 5:   6 Power rule from product rule
  72.    wt: 5:   5 Product Rule
  73.    wt: 5:   4 Sum Rule
  74.    wt: 4:   Chapter 15. Slope Approximation
  75.    wt: 3:   Chapter 18. Slopes Areas Integration
  76.    wt: 3:   Chapter 17. Area Approximation
  77.    wt: 3:   Chapter 16. Velocity Approximation
  78.    wt: 3:   Chapter 15. Algebraic Evaluation of Limits
  79.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  80.    wt: 3:   Chapter 12. Units and Slopes
  81.    wt: 3:   Chapter 11. Graphing Slope versus Position
  82.    wt: 3:   Chapter 10 Slopes and Units
  83.    wt: 3:   Chapter 9 About First Courses in Calculus
  84.    wt: 3:   Chapter 8. Slope Interpretation
  85.    wt: 3:   Chapter 7 Slopes and Velocity
  86.    wt: 3:   Chapter 6. Slopes and Vertical Shifts
  87.    wt: 3:   Chapter 5. Slope Sign Tests
  88.    wt: 3:   Chapter 4. More Slope Sign Analysis
  89.    wt: 3:   Chapter 3. Slope Sign Analysis
  90.    wt: 3:   Chapter 2. Slopes and Ski Trails
  91.    wt: 3:   Fall 1983 Calculus Appetizer
  92.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  93.    wt: 2:   C Straight Lines Slope from Coordinates
  94.    wt: 2:   B Straight Line Slope Scaling Properties More
  95.    wt: 2:   A Straight Line Slope Scaling Properties
  96.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  97.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  98.    wt: 2:   1 Straight Lines Slope Concept
  99.    wt: 2:   12 Links Lessons elsewhere
  100.    wt: 2:   5 Algebraic View of Slopes
  101.    wt: 2:   3 Slope product for perpendicular lines
  102.    wt: 2:   2 point slope equation for a line
  103.    wt: 2:   musings do not puiblish real numbers
  104.    wt: 2:   A Modular and Remainder Arithmetic
  105.    wt: 2:   A Signed Number Arithmetic Review
  106.    wt: 2:   26 More Less Greater Than Comparison
  107.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  108.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  109.    wt: 2:   23 Distributive Law Two Derivations
  110.    wt: 2:   22 Multiplication of Signed Numbers
  111.    wt: 2:   21 Addition of Multiples of a Single Vector
  112.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  113.    wt: 2:   19 Signed Multiples of Vectors
  114.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  115.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  116.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  117.    wt: 2:   15 Head to Tails in place Addition Associative
  118.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  119.    wt: 2:   13 Arrows and Vectors in a Plane
  120.    wt: 2:   12 Real Numbers Line Signed Coordinates
  121.    wt: 2:   11 Signed Number Addition and Addition Properties
  122.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  123.    wt: 2:   9 Division with Digits after Decimal Point
  124.    wt: 2:   8 Division and Mulplication of Compound Fractions
  125.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  126.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  127.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  128.    wt: 2:   4 Location of Point in Decimal Addition
  129.    wt: 2:   3 Location of Point in Decimal Multiplication
  130.    wt: 2:   2 Counting Digits in Decimal Multiplication
  131.    wt: 2:   1 Fractions with Finite Decimal Expansions
  132.    wt: 2:   E Long Division Methods more
  133.    wt: 2:   D Long Division Methods
  134.    wt: 2:   C Three Decimal Subtraction Methods
  135.    wt: 2:   B Decimal Comparison and Subtraction
  136.    wt: 2:   A Decimal Addition Columm Methods
  137.    wt: 2:   8 Column Multiplication Methods in General
  138.    wt: 2:   7 Decimals Multiplication Methods Examples
  139.    wt: 2:   6 Column Methods for Decimal Multiplication
  140.    wt: 2:   5 Distributive Law for Whole Numbers
  141.    wt: 2:   4 Commutative Law Groups Counting Form
  142.    wt: 2:   3 Multiplicative Counting Skills Principles
  143.    wt: 2:   2 Combing Counts Addition Skills and Principles
  144.    wt: 2:   1 The Counting Origins of Numbers
  145.    wt: 2:   5 Areas of Rectangles Revisited
  146.    wt: 2:   4 Fraction Operations Axiomatic Development
  147.    wt: 2:   3 Inequalities Algebraically
  148.    wt: 2:   2 Fraction Operations Physical Development
  149.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  150.    wt: 2:   5 Proportionality in Equivalent Fractions
  151.    wt: 2:   4 Rates Ratios and Proporitionality
  152.    wt: 2:   3 Proportionality Examples
  153.    wt: 2:   2 Algebraic View
  154.    wt: 2:   1 What is Proportionality
  155.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  156.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  157.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  158.    wt: 2:   6 Compound Interest Forward and Backwards
  159.    wt: 2:   5 Triangle Area Formula Backwards
  160.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  161.    wt: 2:   3 Linear Equation Literal Solution More
  162.    wt: 2:   2 Linear Equation Literal Solution
  163.    wt: 2:   1 Changing Calculations
  164.    wt: 2:   6 Equations and Systems Equivalent or Implied
  165.    wt: 2:   5 Equality in Algebra
  166.    wt: 2:   4 Subtraction and Division Axioms
  167.    wt: 2:   3 Product Axioms Two Forms
  168.    wt: 2:   2 Addition and Multiplication Axioms
  169.    wt: 2:   1 Equivalent Computation Rules
  170.    wt: 2:   5 Greater More Less Than Signs in General
  171.    wt: 2:   4 Comparison of Negative Numbers
  172.    wt: 2:   3 More and Less Than with Unlike Signs
  173.    wt: 2:   2 More and Less Than for Counts and Measures
  174.    wt: 2:   1 Real Numbers Comparison
  175.    wt: 2:   16 Real Numbers Comparison
  176.    wt: 2:   15 Real Number Division
  177.    wt: 2:   14 Real Number Multiplication
  178.    wt: 2:   13 Real Number Subtraction
  179.    wt: 2:   12 Real Number Additive Inverses or Negatives
  180.    wt: 2:   11 Real Number Addition
  181.    wt: 2:   10 Real Number Lengths and Signs
  182.    wt: 2:   9 Coordinates for Regions in Space
  183.    wt: 2:   8 Coordinates for Maps and Planes
  184.    wt: 2:   7 Real Numbers as Line Cordinates
  185.    wt: 2:   6 Unsigned Real Numbers
  186.    wt: 2:   5 Rational Numbers More
  187.    wt: 2:   4 Rational Numbers
  188.    wt: 2:   3 Fractions
  189.    wt: 2:   2 Integers
  190.    wt: 2:   1 Whole and Natural Numbers
  191.    wt: 2:   5 Independent versus Dependent Variables
  192.    wt: 2:   4 Changing Letters
  193.    wt: 2:   3 Geometric Formulas and Function Notation
  194.    wt: 2:   2 Computation Rules Evaluation
  195.    wt: 2:   1 Formulas Dependence and Function Notation
  196.    wt: 2:   More Exercises
  197.    wt: 2:   Simple Exercises
  198.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  199.    wt: 2:   4 GE III Animated Examples
  200.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  201.    wt: 2:   3 GE III Equation Addition and Multiplication
  202.    wt: 2:   2 GE II Comparison
  203.    wt: 2:   1 GE Substitution four examples
  204.    wt: 2:   4 Solving a triangular system exercise
  205.    wt: 2:   3 Solving triangular system example
  206.    wt: 2:   2 Essentially one exercises three with solution
  207.    wt: 2:   1 Essentially One Unknown
  208.    wt: 2:   6 Algebraic Solution Example
  209.    wt: 2:   5 Algebraic Solutions Introduction
  210.    wt: 2:   4 Four Examples Fractional Coefficients
  211.    wt: 2:   3 Four Examples
  212.    wt: 2:   2 Three Examples
  213.    wt: 2:   1 Proper Equal Sign Usage
  214.    wt: 2:   Skill Development Notes
  215.    wt: 2:   10 One Example
  216.    wt: 2:   9 Three Examples
  217.    wt: 2:   8 One Example
  218.    wt: 2:   7 Two Examples
  219.    wt: 2:   6 Three Examples
  220.    wt: 2:   5 Three Examples
  221.    wt: 2:   4 Two Examples
  222.    wt: 2:   3 Two Examples
  223.    wt: 2:   2 Three Examples
  224.    wt: 2:   Using Letters for Physical Quantities
  225.    wt: 2:   Formula Usage Show Work Format
  226.    wt: 2:   13 Naming Identifying Formulas with Words
  227.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  228.    wt: 2:   11 Volume of Sphere
  229.    wt: 2:   10 Volume of Pyramid
  230.    wt: 2:   9 Volume of Cone
  231.    wt: 2:   8 Compound Interest Formula Evaluation
  232.    wt: 2:   7 Compound Interest Formula Introduction
  233.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  234.    wt: 2:   5 Box Volume Formula Example
  235.    wt: 2:   4 Circle Area Formula Example
  236.    wt: 2:   3 Triangle Area Formula Example
  237.    wt: 2:   2 Another Rectangle Area Formula Example
  238.    wt: 2:   1 Written work formats for developing and showing skill
  239.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  240.    wt: 2:   9 Sets in Probability and Statistics
  241.    wt: 2:   8 Sets of Numbers
  242.    wt: 2:   7 Cautious or Safe Set Construction
  243.    wt: 2:   6 Power Set Notation
  244.    wt: 2:   5 Product Builder Notation
  245.    wt: 2:   4 Subset Builder Notation
  246.    wt: 2:   3 Counting with Sets etc
  247.    wt: 2:   2 Venn Diagrams
  248.    wt: 2:   1 Finite Sets
  249.    wt: 2:   6 Three Notions of What is a Variable
  250.    wt: 2:   5 Talking about Numbers and Quantities
  251.    wt: 2:   4 A Brief Story of numbers and algebra
  252.    wt: 2:   3 Adding Words To Arithmetic
  253.    wt: 2:   2 What is a Variable
  254.    wt: 2:   1 Three Skills For Algebra
  255.    wt: 2:   About Folder Contents
  256.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  257.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  258.    wt: 2:   E2 Algebraic Properties of Limits
  259.    wt: 2:   D2 Limits of Monotone Sequences
  260.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  261.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  262.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  263.    wt: 2:   Chapter 23 Links To Trigonometry
  264.    wt: 2:   Chapter 22 Complex Numbers
  265.    wt: 2:   Chapter 21 Arrow Addition
  266.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  267.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  268.    wt: 2:   Chapter 13. Acceleration
  269.    wt: 2:   Chapter 1.Introduction
  270.    wt: 2:   Foreword
  271.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  272.    wt: 2:   Chapter 3 Algebra Starter Lessons
  273.    wt: 2:   More Algebra and Slope based Calculus Preview
  274.    wt: 1:   Skills Chapter 5 Calculus
  275.    wt: 1:   chapitre 04 08 Limitations et benefices
  276.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  277.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  278.    wt: 1:   1 Calculator Starter Exercises
  279.    wt: 1:   7 Links Lessons Elsewhere
  280.    wt: 1:   14 Straight Lines Equations General Case
  281.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  282.    wt: 1:   12 Straight Lines Graphing mx plus b
  283.    wt: 1:   11 Straight Lines Graphing y=mx
  284.    wt: 1:   10 Straight Lines through Origin Equations More
  285.    wt: 1:   9 Straight Lines through Origin Equations
  286.    wt: 1:   8 Straight Lines Equation for vertical
  287.    wt: 1:   7 Tangent Function is odd on this domain
  288.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  289.    wt: 1:   5 Tangent Function Graph
  290.    wt: 1:   4 Tangent Function Properties
  291.    wt: 1:   25 tangent double angle formula Slope connection
  292.    wt: 1:   Why Trigonometry the whyslopes view
  293.    wt: 1:   Four Simple Exercises
  294.    wt: 1:   11 A Partial Summary
  295.    wt: 1:   10 Midpoint of [a b] and [b a]
  296.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  297.    wt: 1:   8 Mid Point Formula
  298.    wt: 1:   7 Exercises to test skill and concept mastery
  299.    wt: 1:   6 Intersection of lines by solving linear systems
  300.    wt: 1:   4 Equations for lines three forms
  301.    wt: 1:   1 Numerical view of lines and their equations
  302.    wt: 1:   What is and is not here
  303.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  304.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  305.    wt: 1:   G.5 Motions With Bounded Velocities
  306.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  307.    wt: 1:   G.3 Constant Difference Theorem Proof
  308.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  309.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  310.    wt: 1:   F.5b Extreme Value Theorem
  311.    wt: 1:   F.5a Equicontinuity Theorems
  312.    wt: 1:   F.4 Finite Covering Theorem
  313.    wt: 1:   F.3 Intermediate Value Theorem
  314.    wt: 1:   F.2 Closed Range Theorem
  315.    wt: 1:   F.1 What Functions are Continuous
  316.    wt: 1:   E1 Error Control Inequalities
  317.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  318.    wt: 1:   C Triangle Inequalities
  319.    wt: 1:   B3 Bolzano Weierstrass Theorem
  320.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  321.    wt: 1:   PostScript For and Against Decimal Perspectives
  322.    wt: 1:   A1. Introduction
  323.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  324.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  325.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  326.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  327.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  328.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  329.    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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