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Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
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Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

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

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

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

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

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30 matches:

  1.    wt: 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: 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:   4 Functions/
  25.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  26.    wt: 1:   12 Function Translating and Rescaling/
  27.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  28.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  29.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  30.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

90 matches:

  1.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  2.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  3.    wt: 2:   Chapter 3 Algebra Starter Lessons
  4.    wt: 1:   Skills Chapter 5 Calculus
  5.    wt: 1:   24 Standards For Skill Develoment Take II
  6.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  7.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  8.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  9.    wt: 1:   26 Function definitions done and coming
  10.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  11.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  12.    wt: 1:   23 Inverse Functions
  13.    wt: 1:   22 Square Root function graphically
  14.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  15.    wt: 1:   17 Function maxima minima and their location
  16.    wt: 1:   15 Sign analysis of functions
  17.    wt: 1:   12 Function Domain Recognition Exercises
  18.    wt: 1:   11 Function Domain Range Source and Targets
  19.    wt: 1:   8 Set view of relations and functions
  20.    wt: 1:   7 Functions with finite domains
  21.    wt: 1:   5 Function notation for geometric transformations
  22.    wt: 1:   4 Function notation in and beyond mathematics
  23.    wt: 1:   3 Formula or function graphing exercise
  24.    wt: 1:   2 Algebraic use of function notation
  25.    wt: 1:   1 Geometric Introduction of Function Notation
  26.    wt: 1:   1 Calculator Starter Exercises
  27.    wt: 1:   7 Links Lessons Elsewhere
  28.    wt: 1:   Rewriting algebraic substitution as function substitutions
  29.    wt: 1:   16 cotangent function Definition Graph and Inverse
  30.    wt: 1:   15 cosecant function Definition Graph and Inverse
  31.    wt: 1:   14 secant function Definition Graph and Inverse
  32.    wt: 1:   13 cosecant function Definition Graph and Inverse
  33.    wt: 1:   6 Graph of arccos function
  34.    wt: 1:   2 cosine function more properties
  35.    wt: 1:   1 cosine function properties
  36.    wt: 1:   7 Tangent Function is odd on this domain
  37.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  38.    wt: 1:   5 Tangent Function Graph
  39.    wt: 1:   4 Tangent Function Properties
  40.    wt: 1:   17 tangent function angle sum formulas
  41.    wt: 1:   30 unit circle calculation of six trigonometric functions
  42.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  43.    wt: 1:   17A The complex number valued trig function cis
  44.    wt: 1:   13 Graph of tangent function many periods
  45.    wt: 1:   12 Graph of tangent function for one period
  46.    wt: 1:   11 tangent function undefined when terminal side vertical
  47.    wt: 1:   8 period of tangent function
  48.    wt: 1:   9 The complex number valued trig function cis
  49.    wt: 1:   12 Links Lessons elsewhere
  50.    wt: 1:   3 Geometric Formulas and Function Notation
  51.    wt: 1:   1 Formulas Dependence and Function Notation
  52.    wt: 1:   4 GE III Animated Examples
  53.    wt: 1:   3 GE III Equation Addition and Multiplication
  54.    wt: 1:   2 GE II Comparison
  55.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  56.    wt: 1:   3 Counting with Tables and Trees II
  57.    wt: 1:   8 Numerals Fractionals Quantals Take II
  58.    wt: 1:   6 Multiplication Algebraically Take II
  59.    wt: 1:   1 What is a fraction Take II
  60.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  61.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  62.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  63.    wt: 1:   14 video Factors of 24 Take II
  64.    wt: 1:   12 Why Long Division Works Take III
  65.    wt: 1:   9 Why Long Division Works Take II
  66.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  67.    wt: 1:   Example 4 with x function of y
  68.    wt: 1:   A Related lessons in Volume 3
  69.    wt: 1:   34 Derivative of exponential function
  70.    wt: 1:   31 Derivatives of inverse functions
  71.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  72.    wt: 1:   26 Chain Rule Recognising outer inner functions
  73.    wt: 1:   19 Chain Rule for linear functions
  74.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  75.    wt: 1:   9 Limits Continuity and Composition
  76.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  77.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  78.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  79.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  80.    wt: 1:   F.1 What Functions are Continuous
  81.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  82.    wt: 1:   Chapter 9 About First Courses in Calculus
  83.    wt: 1:   Fall 1983 Calculus Appetizer
  84.    wt: 1:   Chapter 19. Functions and Sets
  85.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  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

384 matches:

  1.    wt: 6:   Example 4 with x function of y
  2.    wt: 6:   A Related lessons in Volume 3
  3.    wt: 6:   34 Derivative of exponential function
  4.    wt: 6:   31 Derivatives of inverse functions
  5.    wt: 6:   27 Chain Rule sinusoidal outer inner functions EGS
  6.    wt: 6:   26 Chain Rule Recognising outer inner functions
  7.    wt: 6:   19 Chain Rule for linear functions
  8.    wt: 6:   13 Limits with Parameters and Derivatives Take II
  9.    wt: 6:   9 Limits Continuity and Composition
  10.    wt: 5:   Example 2 volume of a cone
  11.    wt: 5:   Example 1 volume of a pyramid
  12.    wt: 5:   Volume of Solid by Cross Sections Lesson
  13.    wt: 5:   Example 1. Area Between x and x squared
  14.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  15.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  16.    wt: 5:   Example 3
  17.    wt: 5:   Example 2
  18.    wt: 5:   Example 1
  19.    wt: 5:   Area Between Curves Lesson Take 2
  20.    wt: 5:   Area Between Curves Lesson Take 1
  21.    wt: 5:   Summary
  22.    wt: 5:   A Related Material in Volume 3
  23.    wt: 5:   5 Area Under Curve Exercise
  24.    wt: 5:   4 Definite Integrals Evaluation Exercises
  25.    wt: 5:   3 Two Chain Rule Method Exercises
  26.    wt: 5:   2 Indefinite Integrals Exercises
  27.    wt: 5:   1 Chain Rule in Reverse Integration Method
  28.    wt: 5:   4 Second derivative test exercise example
  29.    wt: 5:   3 Second derivative test
  30.    wt: 5:   2 Second derivative test prequel
  31.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  32.    wt: 5:   A Chain Rule Real Player video examples
  33.    wt: 5:   38 Formulas and derivatives for powers and roots
  34.    wt: 5:   36 Cube root derivative animated
  35.    wt: 5:   33 Chain Rule Real Player video examples
  36.    wt: 5:   30Chain Rule A Proof
  37.    wt: 5:   29 Chain Rule Optional Reading
  38.    wt: 5:   28 Chain Rule Preparation for a Proof
  39.    wt: 5:   25 Chain Rule Animated Examples Continued
  40.    wt: 5:   24 Chain Rule Animated Examples
  41.    wt: 5:   23 Chain Rule in general
  42.    wt: 5:   22 Chain Rule for polynomials
  43.    wt: 5:   21 Chain Rule for powers
  44.    wt: 5:   20 Chain Rule for Pulley Systems
  45.    wt: 5:   18 Chain Rule Introduction
  46.    wt: 5:   17 Derivatives of quotients of sine and cosine
  47.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  48.    wt: 5:   15 sine and cosine derivatives 3rd step
  49.    wt: 5:   14 sine and cosine derivatives 2nd step
  50.    wt: 5:   13 sine and cosine derivatives 1st step
  51.    wt: 5:   12 Quotient rule examples
  52.    wt: 5:   11 Quotient rule
  53.    wt: 5:   10 Power rule for negative integers
  54.    wt: 5:   9 Reciprocal rule
  55.    wt: 5:   8 Differentiation of polynomials
  56.    wt: 5:   7 Animated Differentiation Examples
  57.    wt: 5:   6 Power rule from product rule
  58.    wt: 5:   5 Product Rule
  59.    wt: 5:   4 Sum Rule
  60.    wt: 5:   3 Motivation for Limit Definition Take 2
  61.    wt: 5:   2 Motivation for Limit Definition Take 1
  62.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  63.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  64.    wt: 5:   11 Limits at infinity Three Examples
  65.    wt: 5:   10 Three one sided limits with infinite values
  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:   3 Geometric Formulas and Function Notation
  75.    wt: 4:   1 Formulas Dependence and Function Notation
  76.    wt: 3:   5 Independent versus Dependent Variables
  77.    wt: 3:   4 Changing Letters
  78.    wt: 3:   2 Computation Rules Evaluation
  79.    wt: 3:   4 GE III Animated Examples
  80.    wt: 3:   3 GE III Equation Addition and Multiplication
  81.    wt: 3:   2 GE II Comparison
  82.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  83.    wt: 2:   26 Function definitions done and coming
  84.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  85.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  86.    wt: 2:   23 Inverse Functions
  87.    wt: 2:   22 Square Root function graphically
  88.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  89.    wt: 2:   17 Function maxima minima and their location
  90.    wt: 2:   15 Sign analysis of functions
  91.    wt: 2:   12 Function Domain Recognition Exercises
  92.    wt: 2:   11 Function Domain Range Source and Targets
  93.    wt: 2:   8 Set view of relations and functions
  94.    wt: 2:   7 Functions with finite domains
  95.    wt: 2:   5 Function notation for geometric transformations
  96.    wt: 2:   4 Function notation in and beyond mathematics
  97.    wt: 2:   3 Formula or function graphing exercise
  98.    wt: 2:   2 Algebraic use of function notation
  99.    wt: 2:   1 Geometric Introduction of Function Notation
  100.    wt: 2:   16 cotangent function Definition Graph and Inverse
  101.    wt: 2:   15 cosecant function Definition Graph and Inverse
  102.    wt: 2:   14 secant function Definition Graph and Inverse
  103.    wt: 2:   13 cosecant function Definition Graph and Inverse
  104.    wt: 2:   6 Graph of arccos function
  105.    wt: 2:   2 cosine function more properties
  106.    wt: 2:   1 cosine function properties
  107.    wt: 2:   7 Tangent Function is odd on this domain
  108.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  109.    wt: 2:   5 Tangent Function Graph
  110.    wt: 2:   4 Tangent Function Properties
  111.    wt: 2:   musings do not puiblish real numbers
  112.    wt: 2:   A Modular and Remainder Arithmetic
  113.    wt: 2:   A Signed Number Arithmetic Review
  114.    wt: 2:   26 More Less Greater Than Comparison
  115.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  116.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  117.    wt: 2:   23 Distributive Law Two Derivations
  118.    wt: 2:   22 Multiplication of Signed Numbers
  119.    wt: 2:   21 Addition of Multiples of a Single Vector
  120.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  121.    wt: 2:   19 Signed Multiples of Vectors
  122.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  123.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  124.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  125.    wt: 2:   15 Head to Tails in place Addition Associative
  126.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  127.    wt: 2:   13 Arrows and Vectors in a Plane
  128.    wt: 2:   12 Real Numbers Line Signed Coordinates
  129.    wt: 2:   11 Signed Number Addition and Addition Properties
  130.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  131.    wt: 2:   9 Division with Digits after Decimal Point
  132.    wt: 2:   8 Division and Mulplication of Compound Fractions
  133.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  134.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  135.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  136.    wt: 2:   4 Location of Point in Decimal Addition
  137.    wt: 2:   3 Location of Point in Decimal Multiplication
  138.    wt: 2:   2 Counting Digits in Decimal Multiplication
  139.    wt: 2:   1 Fractions with Finite Decimal Expansions
  140.    wt: 2:   E Long Division Methods more
  141.    wt: 2:   D Long Division Methods
  142.    wt: 2:   C Three Decimal Subtraction Methods
  143.    wt: 2:   B Decimal Comparison and Subtraction
  144.    wt: 2:   A Decimal Addition Columm Methods
  145.    wt: 2:   8 Column Multiplication Methods in General
  146.    wt: 2:   7 Decimals Multiplication Methods Examples
  147.    wt: 2:   6 Column Methods for Decimal Multiplication
  148.    wt: 2:   5 Distributive Law for Whole Numbers
  149.    wt: 2:   4 Commutative Law Groups Counting Form
  150.    wt: 2:   3 Multiplicative Counting Skills Principles
  151.    wt: 2:   2 Combing Counts Addition Skills and Principles
  152.    wt: 2:   1 The Counting Origins of Numbers
  153.    wt: 2:   5 Areas of Rectangles Revisited
  154.    wt: 2:   4 Fraction Operations Axiomatic Development
  155.    wt: 2:   3 Inequalities Algebraically
  156.    wt: 2:   2 Fraction Operations Physical Development
  157.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  158.    wt: 2:   5 Proportionality in Equivalent Fractions
  159.    wt: 2:   4 Rates Ratios and Proporitionality
  160.    wt: 2:   3 Proportionality Examples
  161.    wt: 2:   2 Algebraic View
  162.    wt: 2:   1 What is Proportionality
  163.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  164.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  165.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  166.    wt: 2:   6 Compound Interest Forward and Backwards
  167.    wt: 2:   5 Triangle Area Formula Backwards
  168.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  169.    wt: 2:   3 Linear Equation Literal Solution More
  170.    wt: 2:   2 Linear Equation Literal Solution
  171.    wt: 2:   1 Changing Calculations
  172.    wt: 2:   6 Equations and Systems Equivalent or Implied
  173.    wt: 2:   5 Equality in Algebra
  174.    wt: 2:   4 Subtraction and Division Axioms
  175.    wt: 2:   3 Product Axioms Two Forms
  176.    wt: 2:   2 Addition and Multiplication Axioms
  177.    wt: 2:   1 Equivalent Computation Rules
  178.    wt: 2:   5 Greater More Less Than Signs in General
  179.    wt: 2:   4 Comparison of Negative Numbers
  180.    wt: 2:   3 More and Less Than with Unlike Signs
  181.    wt: 2:   2 More and Less Than for Counts and Measures
  182.    wt: 2:   1 Real Numbers Comparison
  183.    wt: 2:   16 Real Numbers Comparison
  184.    wt: 2:   15 Real Number Division
  185.    wt: 2:   14 Real Number Multiplication
  186.    wt: 2:   13 Real Number Subtraction
  187.    wt: 2:   12 Real Number Additive Inverses or Negatives
  188.    wt: 2:   11 Real Number Addition
  189.    wt: 2:   10 Real Number Lengths and Signs
  190.    wt: 2:   9 Coordinates for Regions in Space
  191.    wt: 2:   8 Coordinates for Maps and Planes
  192.    wt: 2:   7 Real Numbers as Line Cordinates
  193.    wt: 2:   6 Unsigned Real Numbers
  194.    wt: 2:   5 Rational Numbers More
  195.    wt: 2:   4 Rational Numbers
  196.    wt: 2:   3 Fractions
  197.    wt: 2:   2 Integers
  198.    wt: 2:   1 Whole and Natural Numbers
  199.    wt: 2:   More Exercises
  200.    wt: 2:   Simple Exercises
  201.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  202.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  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:   G.2 Differentiable Functions Mean Value Theorem
  259.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  260.    wt: 2:   F.1 What Functions are Continuous
  261.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  262.    wt: 2:   Chapter 9 About First Courses in Calculus
  263.    wt: 2:   Fall 1983 Calculus Appetizer
  264.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  265.    wt: 2:   Chapter 3 Algebra Starter Lessons
  266.    wt: 1:   Skills Chapter 5 Calculus
  267.    wt: 1:   24 Standards For Skill Develoment Take II
  268.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  269.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  270.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  271.    wt: 1:   20 Interchanging coordinates a reflection
  272.    wt: 1:   19 Horizontal line rule and method
  273.    wt: 1:   18 Vertical Line Rule and Method
  274.    wt: 1:   16 Increasing or decreasing on intervals
  275.    wt: 1:   14 Surjections Injections Bijections
  276.    wt: 1:   13 From one to one to many to one
  277.    wt: 1:   10 Interval Notation
  278.    wt: 1:   9 Set theory term relation possible origins
  279.    wt: 1:   6 Set Existence Formation and Notation
  280.    wt: 1:   Introduction Reading Guide
  281.    wt: 1:   1 Calculator Starter Exercises
  282.    wt: 1:   7 Links Lessons Elsewhere
  283.    wt: 1:   Rewriting algebraic substitution as function substitutions
  284.    wt: 1:   12 motivation for term arctan
  285.    wt: 1:   11 arctan left inverse of tangent Graph
  286.    wt: 1:   10 arctan left inverse of tangent Definition
  287.    wt: 1:   9 motivation for name arcsin
  288.    wt: 1:   8 arcsin left inverse of sine Graph
  289.    wt: 1:   7 arcsin left inverse of sine Definition
  290.    wt: 1:   5 Swapping Coordinates is a reflection
  291.    wt: 1:   4 possible motivation for term arccos
  292.    wt: 1:   3 Left Inverse of cosine arccos definition
  293.    wt: 1:   4 graphing y=Asin(x c)
  294.    wt: 1:   3 graphing y=f(x c) plus K
  295.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  296.    wt: 1:   1 graphing y=f(x a)
  297.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  298.    wt: 1:   C Straight Lines Slope from Coordinates
  299.    wt: 1:   B Straight Line Slope Scaling Properties More
  300.    wt: 1:   A Straight Line Slope Scaling Properties
  301.    wt: 1:   14 Straight Lines Equations General Case
  302.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  303.    wt: 1:   12 Straight Lines Graphing mx plus b
  304.    wt: 1:   11 Straight Lines Graphing y=mx
  305.    wt: 1:   10 Straight Lines through Origin Equations More
  306.    wt: 1:   9 Straight Lines through Origin Equations
  307.    wt: 1:   8 Straight Lines Equation for vertical
  308.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  309.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  310.    wt: 1:   1 Straight Lines Slope Concept
  311.    wt: 1:   17 tangent function angle sum formulas
  312.    wt: 1:   30 unit circle calculation of six trigonometric functions
  313.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  314.    wt: 1:   17A The complex number valued trig function cis
  315.    wt: 1:   13 Graph of tangent function many periods
  316.    wt: 1:   12 Graph of tangent function for one period
  317.    wt: 1:   11 tangent function undefined when terminal side vertical
  318.    wt: 1:   8 period of tangent function
  319.    wt: 1:   9 The complex number valued trig function cis
  320.    wt: 1:   12 Links Lessons elsewhere
  321.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  322.    wt: 1:   3 Counting with Tables and Trees II
  323.    wt: 1:   8 Numerals Fractionals Quantals Take II
  324.    wt: 1:   6 Multiplication Algebraically Take II
  325.    wt: 1:   1 What is a fraction Take II
  326.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  327.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  328.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  329.    wt: 1:   14 video Factors of 24 Take II
  330.    wt: 1:   12 Why Long Division Works Take III
  331.    wt: 1:   9 Why Long Division Works Take II
  332.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  333.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  334.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  335.    wt: 1:   G.5 Motions With Bounded Velocities
  336.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  337.    wt: 1:   G.3 Constant Difference Theorem Proof
  338.    wt: 1:   F.5b Extreme Value Theorem
  339.    wt: 1:   F.5a Equicontinuity Theorems
  340.    wt: 1:   F.4 Finite Covering Theorem
  341.    wt: 1:   F.3 Intermediate Value Theorem
  342.    wt: 1:   F.2 Closed Range Theorem
  343.    wt: 1:   E2 Algebraic Properties of Limits
  344.    wt: 1:   E1 Error Control Inequalities
  345.    wt: 1:   D2 Limits of Monotone Sequences
  346.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  347.    wt: 1:   C Triangle Inequalities
  348.    wt: 1:   B3 Bolzano Weierstrass Theorem
  349.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  350.    wt: 1:   PostScript For and Against Decimal Perspectives
  351.    wt: 1:   A1. Introduction
  352.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  353.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  354.    wt: 1:   Chapter 23 Links To Trigonometry
  355.    wt: 1:   Chapter 22 Complex Numbers
  356.    wt: 1:   Chapter 21 Arrow Addition
  357.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  358.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  359.    wt: 1:   Chapter 18. Slopes Areas Integration
  360.    wt: 1:   Chapter 17. Area Approximation
  361.    wt: 1:   Chapter 16. Velocity Approximation
  362.    wt: 1:   Chapter 15. Slope Approximation
  363.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  364.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  365.    wt: 1:   Chapter 13. Acceleration
  366.    wt: 1:   Chapter 12. Units and Slopes
  367.    wt: 1:   Chapter 11. Graphing Slope versus Position
  368.    wt: 1:   Chapter 10 Slopes and Units
  369.    wt: 1:   Chapter 8. Slope Interpretation
  370.    wt: 1:   Chapter 7 Slopes and Velocity
  371.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  372.    wt: 1:   Chapter 5. Slope Sign Tests
  373.    wt: 1:   Chapter 4. More Slope Sign Analysis
  374.    wt: 1:   Chapter 3. Slope Sign Analysis
  375.    wt: 1:   Chapter 2. Slopes and Ski Trails
  376.    wt: 1:   Chapter 1.Introduction
  377.    wt: 1:   Foreword
  378.    wt: 1:   Chapter 19. Functions and Sets
  379.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  380.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  381.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  382.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  383.    wt: 1:   More Algebra and Slope based Calculus Preview
  384.    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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