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Logic and Mathematics Skill & Concept Development How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

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

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

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

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

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

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26 matches:

  1.    wt: 5:   12 Webvideo Lessons on Area and Volume Calculation/
  2.    wt: 5:   5 Lessons on Integration/
  3.    wt: 5:   4 Lessons on Using Derivatives/
  4.    wt: 5:   38 Lessons on Calculating Derivatives/
  5.    wt: 5:   13 Lessons on Limits and Continuity/
  6.    wt: 4:   70 Calculus Starter Lessons/
  7.    wt: 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: 1:   Advanced Calculus Volume 3 Appendices/
  25.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  26.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

38 matches:

  1.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  2.    wt: 2:   F.5a Equicontinuity Theorems
  3.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  4.    wt: 2:   Chapter 3 Algebra Starter Lessons
  5.    wt: 1:   Skills Chapter 5 Calculus
  6.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  7.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  8.    wt: 1:   1 Calculator Starter Exercises
  9.    wt: 1:   7 Links Lessons Elsewhere
  10.    wt: 1:   17G Pythagorean Theorem Converse
  11.    wt: 1:   15 Pythagorean Theorem Converse
  12.    wt: 1:   12 Links Lessons elsewhere
  13.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  14.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  15.    wt: 1:   A Related lessons in Volume 3
  16.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  17.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  18.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  19.    wt: 1:   G.3 Constant Difference Theorem Proof
  20.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  21.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  22.    wt: 1:   F.5b Extreme Value Theorem
  23.    wt: 1:   F.4 Finite Covering Theorem
  24.    wt: 1:   F.3 Intermediate Value Theorem
  25.    wt: 1:   F.2 Closed Range Theorem
  26.    wt: 1:   B3 Bolzano Weierstrass Theorem
  27.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  28.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  29.    wt: 1:   Chapter 9 About First Courses in Calculus
  30.    wt: 1:   Fall 1983 Calculus Appetizer
  31.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  32.    wt: 1:   Chapter 16. Painless Theorem Proving
  33.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  34.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  35.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  36.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  37.    wt: 1:   More Algebra and Slope based Calculus Preview
  38.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

298 matches:

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