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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37 matches:

  1.    wt: 6:   38 Lessons on Calculating Derivatives/
  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:   13 Lessons on Limits and Continuity/
  6.    wt: 4:   10 Examples of Algebraic Reasoning/
  7.    wt: 4:   4 Computation Rules and Function Notation/
  8.    wt: 4:   Step 2 Algebraic solutions for one unknown/
  9.    wt: 4:   2 Formula Forward Use Evaluation/
  10.    wt: 4:   70 Calculus Starter Lessons/
  11.    wt: 3:   B Real Numbers Extrinsic Development/
  12.    wt: 3:   A Origins of Counting and Figuring Methods/
  13.    wt: 3:   9 Proportionality Backwards and Forwards/
  14.    wt: 3:   8 Unifying Theme For Algebra/
  15.    wt: 3:   7 Axioms Logic and Equivalent Equations/
  16.    wt: 3:   6 More Less Greater Than Inequalities and Comparison/
  17.    wt: 3:   5 Real Numbers/
  18.    wt: 3:   Step 4 Gaussian Elimination/
  19.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  20.    wt: 3:   Step 1 Stick diagram and fractions/
  21.    wt: 3:   3 Solving Linear Equations/
  22.    wt: 3:   1 Working With Sets/
  23.    wt: 3:   Algebra Starter Lessons/
  24.    wt: 3:   B Decimal Comparing and Subtracting Methods/
  25.    wt: 2:   2 Euclidean Geometry Constructions Theory extras/
  26.    wt: 2:   D Decimal Long Division Methods/
  27.    wt: 2:   C Decimal Multiplication Methods/
  28.    wt: 2:   A Decimal Counting and Adding Methods/
  29.    wt: 2:   2 Arithmetic with Decimals/
  30.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  31.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  32.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  33.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  34.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  35.    wt: 1:   Volume 1A Pattern Based Reason/
  36.    wt: 1:   Volume 1 Elements of Reason/
  37.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

112 matches:

  1.    wt: 3:   A Chain Rule Real Player video examples
  2.    wt: 3:   33 Chain Rule Real Player video examples
  3.    wt: 3:   25 Chain Rule Animated Examples Continued
  4.    wt: 3:   24 Chain Rule Animated Examples
  5.    wt: 2:   3 Two Chain Rule Method Exercises
  6.    wt: 2:   1 Chain Rule in Reverse Integration Method
  7.    wt: 2:   30Chain Rule A Proof
  8.    wt: 2:   29 Chain Rule Optional Reading
  9.    wt: 2:   28 Chain Rule Preparation for a Proof
  10.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  11.    wt: 2:   26 Chain Rule Recognising outer inner functions
  12.    wt: 2:   23 Chain Rule in general
  13.    wt: 2:   22 Chain Rule for polynomials
  14.    wt: 2:   21 Chain Rule for powers
  15.    wt: 2:   20 Chain Rule for Pulley Systems
  16.    wt: 2:   19 Chain Rule for linear functions
  17.    wt: 2:   18 Chain Rule Introduction
  18.    wt: 2:   12 Quotient rule examples
  19.    wt: 2:   7 Animated Differentiation Examples
  20.    wt: 2:   6 Power rule from product rule
  21.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  22.    wt: 2:   Chapter 3 Algebra Starter Lessons
  23.    wt: 1:   Skills Chapter 5 Calculus
  24.    wt: 1:   02 21 words for teachers
  25.    wt: 1:   02 20 mathematics education references
  26.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  27.    wt: 1:   chapitre 06 00 Chaines de la raison
  28.    wt: 1:   chapitre 04 02 Deuxieme enigme
  29.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  30.    wt: 1:   chapitre 02 00 La Communication des idees
  31.    wt: 1:   B Energy Power02
  32.    wt: 1:   2 Conductance Resistance Duality02
  33.    wt: 1:   D Wire Resistance Calculation02
  34.    wt: 1:   B Wire Resistance Qualitative02
  35.    wt: 1:   H Series Circuit02
  36.    wt: 1:   C Electromotive force conventional current02
  37.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  38.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  39.    wt: 1:   19 Horizontal line rule and method
  40.    wt: 1:   18 Vertical Line Rule and Method
  41.    wt: 1:   1 Calculator Starter Exercises
  42.    wt: 1:   7 Links Lessons Elsewhere
  43.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  44.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  45.    wt: 1:   12 Links Lessons elsewhere
  46.    wt: 1:   6 Ruler and compass Angle Bisection
  47.    wt: 1:   A Measurement with Ruler Proper Use
  48.    wt: 1:   7 Decimals Multiplication Methods Examples
  49.    wt: 1:   3 Proportionality Examples
  50.    wt: 1:   1 Equivalent Computation Rules
  51.    wt: 1:   2 Computation Rules Evaluation
  52.    wt: 1:   4 GE III Animated Examples
  53.    wt: 1:   1 GE Substitution four examples
  54.    wt: 1:   4 Four Examples Fractional Coefficients
  55.    wt: 1:   3 Four Examples
  56.    wt: 1:   2 Three Examples
  57.    wt: 1:   9 Three Examples
  58.    wt: 1:   7 Two Examples
  59.    wt: 1:   6 Three Examples
  60.    wt: 1:   5 Three Examples
  61.    wt: 1:   4 Two Examples
  62.    wt: 1:   3 Two Examples
  63.    wt: 1:   2 Three Examples
  64.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  65.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  66.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  67.    wt: 1:   4 Counting with Trees Product Rule Take I
  68.    wt: 1:   D Remainders Modulo 11 Pair Rule
  69.    wt: 1:   12 Adding Integers More Examples
  70.    wt: 1:   11 Adding Integers Formulas and Examples
  71.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  72.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  73.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  74.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  75.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  76.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  77.    wt: 1:   11 Efficient Square Rule Use
  78.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  79.    wt: 1:   5 Prime Factorization and a Square Rule
  80.    wt: 1:   1 Divsion Physical Examples
  81.    wt: 1:   2 Subtraction Easy Case Examples
  82.    wt: 1:   5. How to add decimals C. Examples
  83.    wt: 1:   A Related lessons in Volume 3
  84.    wt: 1:   11 Quotient rule
  85.    wt: 1:   10 Power rule for negative integers
  86.    wt: 1:   9 Reciprocal rule
  87.    wt: 1:   8 Differentiation of polynomials
  88.    wt: 1:   5 Product Rule
  89.    wt: 1:   4 Sum Rule
  90.    wt: 1:   11 Limits at infinity Three Examples
  91.    wt: 1:   8 Four Animated Examples
  92.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  93.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  94.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  95.    wt: 1:   Chapter 9 About First Courses in Calculus
  96.    wt: 1:   Fall 1983 Calculus Appetizer
  97.    wt: 1:   Chapter 25. Mathematical Induction Examples
  98.    wt: 1:   Chapter 18. Rules for Algebra
  99.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  100.    wt: 1:   Chapter 4 Longer Chains of Reason
  101.    wt: 1:   Chapter 3 Chains of Reason
  102.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  103.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  104.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  105.    wt: 1:   Chapter 7 Longer Chains of Reason
  106.    wt: 1:   Chapter 6 Chains of Reason
  107.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  108.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  109.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  110.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  111.    wt: 1:   More Algebra and Slope based Calculus Preview
  112.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

575 matches:

  1.    wt: 9:   A Chain Rule Real Player video examples
  2.    wt: 9:   33 Chain Rule Real Player video examples
  3.    wt: 9:   29 Chain Rule Optional Reading
  4.    wt: 9:   28 Chain Rule Preparation for a Proof
  5.    wt: 9:   27 Chain Rule sinusoidal outer inner functions EGS
  6.    wt: 9:   26 Chain Rule Recognising outer inner functions
  7.    wt: 9:   25 Chain Rule Animated Examples Continued
  8.    wt: 9:   24 Chain Rule Animated Examples
  9.    wt: 9:   23 Chain Rule in general
  10.    wt: 9:   22 Chain Rule for polynomials
  11.    wt: 9:   21 Chain Rule for powers
  12.    wt: 9:   7 Animated Differentiation Examples
  13.    wt: 9:   6 Power rule from product rule
  14.    wt: 8:   1 Chain Rule in Reverse Integration Method
  15.    wt: 8:   30Chain Rule A Proof
  16.    wt: 8:   20 Chain Rule for Pulley Systems
  17.    wt: 8:   19 Chain Rule for linear functions
  18.    wt: 8:   18 Chain Rule Introduction
  19.    wt: 8:   12 Quotient rule examples
  20.    wt: 8:   11 Quotient rule
  21.    wt: 8:   10 Power rule for negative integers
  22.    wt: 8:   9 Reciprocal rule
  23.    wt: 8:   8 Differentiation of polynomials
  24.    wt: 8:   5 Product Rule
  25.    wt: 8:   4 Sum Rule
  26.    wt: 7:   2 Three Examples
  27.    wt: 7:   3 Two Chain Rule Method Exercises
  28.    wt: 7:   2 Motivation for Limit Definition Take 1
  29.    wt: 7:   2 Algebraic codification
  30.    wt: 6:   2 Computation Rules Evaluation
  31.    wt: 6:   2 Three Examples
  32.    wt: 6:   2 Subtraction Easy Case Examples
  33.    wt: 6:   2 Indefinite Integrals Exercises
  34.    wt: 6:   A Related lessons in Volume 3
  35.    wt: 6:   2 Second derivative test prequel
  36.    wt: 6:   1 Two cubic sketching exercises with 1st derivative
  37.    wt: 6:   38 Formulas and derivatives for powers and roots
  38.    wt: 6:   36 Cube root derivative animated
  39.    wt: 6:   34 Derivative of exponential function
  40.    wt: 6:   31 Derivatives of inverse functions
  41.    wt: 6:   17 Derivatives of quotients of sine and cosine
  42.    wt: 6:   16 Derivatives of reciprocals of sine and cosine
  43.    wt: 6:   15 sine and cosine derivatives 3rd step
  44.    wt: 6:   14 sine and cosine derivatives 2nd step
  45.    wt: 6:   13 sine and cosine derivatives 1st step
  46.    wt: 6:   3 Motivation for Limit Definition Take 2
  47.    wt: 6:   1 Fall 1983 Why Slopes Appetizer
  48.    wt: 6:   11 Limits at infinity Three Examples
  49.    wt: 6:   8 Four Animated Examples
  50.    wt: 6:   3 Decimal insights for limits continuity convergence
  51.    wt: 5:   21 Addition of Multiples of a Single Vector
  52.    wt: 5:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  53.    wt: 5:   2 Combing Counts Addition Skills and Principles
  54.    wt: 5:   2 Fraction Operations Physical Development
  55.    wt: 5:   2 Algebraic View
  56.    wt: 5:   2 GE II Comparison
  57.    wt: 5:   2 Essentially one exercises three with solution
  58.    wt: 5:   4 Four Examples Fractional Coefficients
  59.    wt: 5:   3 Four Examples
  60.    wt: 5:   2 Another Rectangle Area Formula Example
  61.    wt: 5:   Example 2 volume of a cone
  62.    wt: 5:   Example 1 volume of a pyramid
  63.    wt: 5:   Volume of Solid by Cross Sections Lesson
  64.    wt: 5:   Example 1. Area Between x and x squared
  65.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  66.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  67.    wt: 5:   Example 4 with x function of y
  68.    wt: 5:   Example 3
  69.    wt: 5:   Example 2
  70.    wt: 5:   Example 1
  71.    wt: 5:   Area Between Curves Lesson Take 2
  72.    wt: 5:   Area Between Curves Lesson Take 1
  73.    wt: 5:   Summary
  74.    wt: 5:   A Related Material in Volume 3
  75.    wt: 5:   5 Area Under Curve Exercise
  76.    wt: 5:   4 Definite Integrals Evaluation Exercises
  77.    wt: 5:   4 Second derivative test exercise example
  78.    wt: 5:   3 Second derivative test
  79.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  80.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  81.    wt: 5:   10 Three one sided limits with infinite values
  82.    wt: 5:   9 Limits Continuity and Composition
  83.    wt: 5:   7 Evaluation by immediate or delayed substitution
  84.    wt: 5:   6 Continuity at a point
  85.    wt: 5:   5 Jumps and absence of unlimited error control
  86.    wt: 5:   4 Numerical properties
  87.    wt: 5:   1 Numerical introduction
  88.    wt: 4:   2 Correspondence between Triangles
  89.    wt: 4:   26 More Less Greater Than Comparison
  90.    wt: 4:   25 Mid way Convergence to Axiomatic Approach
  91.    wt: 4:   24 Signed Numbers Arithmmetic Properties
  92.    wt: 4:   23 Distributive Law Two Derivations
  93.    wt: 4:   22 Multiplication of Signed Numbers
  94.    wt: 4:   19 Signed Multiples of Vectors
  95.    wt: 4:   18 Geometrically Why Vector Addition Commutes
  96.    wt: 4:   17 Arrows Rotate to Reverse with Length Unchanged
  97.    wt: 4:   16 Collinear Horizontal Arrows Vectors
  98.    wt: 4:   15 Head to Tails in place Addition Associative
  99.    wt: 4:   14 Vector Head to Tail Sums and Resultants
  100.    wt: 4:   13 Arrows and Vectors in a Plane
  101.    wt: 4:   12 Real Numbers Line Signed Coordinates
  102.    wt: 4:   11 Signed Number Addition and Addition Properties
  103.    wt: 4:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  104.    wt: 4:   2 Counting Digits in Decimal Multiplication
  105.    wt: 4:   7 Decimals Multiplication Methods Examples
  106.    wt: 4:   5 Areas of Rectangles Revisited
  107.    wt: 4:   4 Fraction Operations Axiomatic Development
  108.    wt: 4:   3 Inequalities Algebraically
  109.    wt: 4:   1 Decimals Modular and Remainder Arithmetic
  110.    wt: 4:   3 Proportionality Examples
  111.    wt: 4:   2 Linear Equation Literal Solution
  112.    wt: 4:   2 Addition and Multiplication Axioms
  113.    wt: 4:   1 Equivalent Computation Rules
  114.    wt: 4:   2 More and Less Than for Counts and Measures
  115.    wt: 4:   16 Real Numbers Comparison
  116.    wt: 4:   15 Real Number Division
  117.    wt: 4:   14 Real Number Multiplication
  118.    wt: 4:   13 Real Number Subtraction
  119.    wt: 4:   12 Real Number Additive Inverses or Negatives
  120.    wt: 4:   11 Real Number Addition
  121.    wt: 4:   10 Real Number Lengths and Signs
  122.    wt: 4:   2 Integers
  123.    wt: 4:   5 Independent versus Dependent Variables
  124.    wt: 4:   4 Changing Letters
  125.    wt: 4:   3 Geometric Formulas and Function Notation
  126.    wt: 4:   1 Formulas Dependence and Function Notation
  127.    wt: 4:   4 GE III Animated Examples
  128.    wt: 4:   1 GE Substitution four examples
  129.    wt: 4:   6 Algebraic Solution Example
  130.    wt: 4:   5 Algebraic Solutions Introduction
  131.    wt: 4:   1 Proper Equal Sign Usage
  132.    wt: 4:   9 Three Examples
  133.    wt: 4:   7 Two Examples
  134.    wt: 4:   6 Three Examples
  135.    wt: 4:   5 Three Examples
  136.    wt: 4:   4 Two Examples
  137.    wt: 4:   3 Two Examples
  138.    wt: 4:   13 Naming Identifying Formulas with Words
  139.    wt: 4:   12 Cone Cylinder Sphere Lesson Idea
  140.    wt: 4:   11 Volume of Sphere
  141.    wt: 4:   10 Volume of Pyramid
  142.    wt: 4:   9 Volume of Cone
  143.    wt: 4:   8 Compound Interest Formula Evaluation
  144.    wt: 4:   7 Compound Interest Formula Introduction
  145.    wt: 4:   6 Pythagorean Hypotenuse Calculation Example
  146.    wt: 4:   5 Box Volume Formula Example
  147.    wt: 4:   4 Circle Area Formula Example
  148.    wt: 4:   3 Triangle Area Formula Example
  149.    wt: 4:   1 Written work formats for developing and showing skill
  150.    wt: 4:   2 Venn Diagrams
  151.    wt: 4:   2 What is a Variable
  152.    wt: 4:   2 Division with Single Digit Divisors
  153.    wt: 4:   2 One Digit Multipliers
  154.    wt: 4:   Subtraction with J Conversions Example
  155.    wt: 3:   2 Conductance Resistance Duality02
  156.    wt: 3:   2 Square Root Simplification a prequel
  157.    wt: 3:   21 Parallelograms
  158.    wt: 3:   6 Ruler and compass Angle Bisection
  159.    wt: 3:   musings do not puiblish real numbers
  160.    wt: 3:   A Modular and Remainder Arithmetic
  161.    wt: 3:   A Signed Number Arithmetic Review
  162.    wt: 3:   9 Division with Digits after Decimal Point
  163.    wt: 3:   8 Division and Mulplication of Compound Fractions
  164.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  165.    wt: 3:   6 Infinite Decimals Ending in 9 repeating
  166.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  167.    wt: 3:   4 Location of Point in Decimal Addition
  168.    wt: 3:   3 Location of Point in Decimal Multiplication
  169.    wt: 3:   1 Fractions with Finite Decimal Expansions
  170.    wt: 3:   E Long Division Methods more
  171.    wt: 3:   D Long Division Methods
  172.    wt: 3:   C Three Decimal Subtraction Methods
  173.    wt: 3:   B Decimal Comparison and Subtraction
  174.    wt: 3:   A Decimal Addition Columm Methods
  175.    wt: 3:   8 Column Multiplication Methods in General
  176.    wt: 3:   6 Column Methods for Decimal Multiplication
  177.    wt: 3:   5 Distributive Law for Whole Numbers
  178.    wt: 3:   4 Commutative Law Groups Counting Form
  179.    wt: 3:   3 Multiplicative Counting Skills Principles
  180.    wt: 3:   1 The Counting Origins of Numbers
  181.    wt: 3:   5 Proportionality in Equivalent Fractions
  182.    wt: 3:   4 Rates Ratios and Proporitionality
  183.    wt: 3:   1 What is Proportionality
  184.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  185.    wt: 3:   8 Pythagorean Relation Forwards Backwards
  186.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  187.    wt: 3:   6 Compound Interest Forward and Backwards
  188.    wt: 3:   5 Triangle Area Formula Backwards
  189.    wt: 3:   4 Rectangle Area and Like Formulas Backwards
  190.    wt: 3:   3 Linear Equation Literal Solution More
  191.    wt: 3:   1 Changing Calculations
  192.    wt: 3:   6 Equations and Systems Equivalent or Implied
  193.    wt: 3:   5 Equality in Algebra
  194.    wt: 3:   4 Subtraction and Division Axioms
  195.    wt: 3:   3 Product Axioms Two Forms
  196.    wt: 3:   5 Greater More Less Than Signs in General
  197.    wt: 3:   4 Comparison of Negative Numbers
  198.    wt: 3:   3 More and Less Than with Unlike Signs
  199.    wt: 3:   1 Real Numbers Comparison
  200.    wt: 3:   9 Coordinates for Regions in Space
  201.    wt: 3:   8 Coordinates for Maps and Planes
  202.    wt: 3:   7 Real Numbers as Line Cordinates
  203.    wt: 3:   6 Unsigned Real Numbers
  204.    wt: 3:   5 Rational Numbers More
  205.    wt: 3:   4 Rational Numbers
  206.    wt: 3:   3 Fractions
  207.    wt: 3:   1 Whole and Natural Numbers
  208.    wt: 3:   More Exercises
  209.    wt: 3:   Simple Exercises
  210.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  211.    wt: 3:   3 Gaussian Elimination 3 unknowns first example
  212.    wt: 3:   3 GE III Equation Addition and Multiplication
  213.    wt: 3:   4 Solving a triangular system exercise
  214.    wt: 3:   3 Solving triangular system example
  215.    wt: 3:   1 Essentially One Unknown
  216.    wt: 3:   Skill Development Notes
  217.    wt: 3:   10 One Example
  218.    wt: 3:   8 One Example
  219.    wt: 3:   Using Letters for Physical Quantities
  220.    wt: 3:   Formula Usage Show Work Format
  221.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  222.    wt: 3:   9 Sets in Probability and Statistics
  223.    wt: 3:   8 Sets of Numbers
  224.    wt: 3:   7 Cautious or Safe Set Construction
  225.    wt: 3:   6 Power Set Notation
  226.    wt: 3:   5 Product Builder Notation
  227.    wt: 3:   4 Subset Builder Notation
  228.    wt: 3:   3 Counting with Sets etc
  229.    wt: 3:   1 Finite Sets
  230.    wt: 3:   6 Three Notions of What is a Variable
  231.    wt: 3:   5 Talking about Numbers and Quantities
  232.    wt: 3:   4 A Brief Story of numbers and algebra
  233.    wt: 3:   3 Adding Words To Arithmetic
  234.    wt: 3:   1 Three Skills For Algebra
  235.    wt: 3:   About Folder Contents
  236.    wt: 3:   Long Division Backwards more
  237.    wt: 3:   Long Division Backward
  238.    wt: 3:   1 Divsion Physical Examples
  239.    wt: 3:   Appendix 2 Three Decimal Subtraction Methods
  240.    wt: 3:   Appendix 1 Decimals Comparison Method Take II
  241.    wt: 3:   Subtraction Another Video Lesson
  242.    wt: 3:   9 22 Minute Subtraction Review Video
  243.    wt: 3:   8 Subtraction with Units of Measure
  244.    wt: 3:   7 Subtraction for Decimal Fractions with Exercises
  245.    wt: 3:   6 Subtraction with Conversion Example with Exercises
  246.    wt: 3:   5 A Tip for Efficent Subtraction
  247.    wt: 3:   4 Subtraction with Conversions Borrows and Letter J
  248.    wt: 3:   3 Harder Cases Convert to Compare and Subtract
  249.    wt: 3:   1 Comparison and Subtraction Easy Direct Cases
  250.    wt: 3:   5. How to add decimals C. Examples
  251.    wt: 3:   2 Decimal Counting Practices
  252.    wt: 3:   Fall 1983 Calculus Appetizer
  253.    wt: 2:   2 Energy Power Heat07
  254.    wt: 2:   B Energy Power02
  255.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  256.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  257.    wt: 2:   2 Reading and Writing Skills
  258.    wt: 2:   26 Function definitions done and coming
  259.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  260.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  261.    wt: 2:   23 Inverse Functions
  262.    wt: 2:   22 Square Root function graphically
  263.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  264.    wt: 2:   20 Interchanging coordinates a reflection
  265.    wt: 2:   2 Algebraic use of function notation
  266.    wt: 2:   1 Calculator Starter Exercises
  267.    wt: 2:   2 Signed Coordinates
  268.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  269.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  270.    wt: 2:   2 Complex Numbers made easier we hope
  271.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  272.    wt: 2:   2 Similarity By Design
  273.    wt: 2:   2 point slope equation for a line
  274.    wt: 2:   2 Cartesian Coordinates with signs
  275.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  276.    wt: 2:   PS H Distributive Law For Complex Numbers
  277.    wt: 2:   PS G Rotation Distributes over Addition
  278.    wt: 2:   PS F Scalar Multiplication Distributes over Addition
  279.    wt: 2:   PS E Multiplication with Polar Coordinates
  280.    wt: 2:   PS D Addition with Cartesian Coordinates
  281.    wt: 2:   PS C Similarity Use Recognize it in Trigonometry
  282.    wt: 2:   PS B Parallelogram Construction Methods
  283.    wt: 2:   PS A Kite Construction Methods
  284.    wt: 2:   19 Right Triangle Similarity
  285.    wt: 2:   18 Triangle Similarity Take 1
  286.    wt: 2:   17 Right Bisectors of Triangle Sides
  287.    wt: 2:   16 Angles Subtended By Chords and Diameters
  288.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  289.    wt: 2:   14 Parallel Lines Postulate
  290.    wt: 2:   13 Angle Side Angle Failure
  291.    wt: 2:   12 Side Angle Side Failure
  292.    wt: 2:   11 Triangle Construction Fails
  293.    wt: 2:   10 Dropping a perpendicular to line
  294.    wt: 2:   9 Construction of a right bisector
  295.    wt: 2:   8 Isoceles Triangles
  296.    wt: 2:   7 Angle Side Angle
  297.    wt: 2:   5 Side Angle Side
  298.    wt: 2:   4 Side Side Side
  299.    wt: 2:   3 Isometry of Triangles Congruence
  300.    wt: 2:   1 Initial Concepts and Terms
  301.    wt: 2:   Short Course on Euclidean Geometry
  302.    wt: 2:   2 More and Less Than with Unlike Signs
  303.    wt: 2:   2 signed and unsigned numbers as coordinates
  304.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  305.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  306.    wt: 2:   2 Prime and Composites less than 16
  307.    wt: 2:   Division with Counts and Length
  308.    wt: 2:   Long Division forwards and backwards Example 3
  309.    wt: 2:   Long Division forwards and backwards Example 2
  310.    wt: 2:   Long Division forwards and backwards Example 1
  311.    wt: 2:   12 Why Long Division Works Take III
  312.    wt: 2:   11 Another Single Digit Divisor Example
  313.    wt: 2:   10 Division by Five Long and Short Ways
  314.    wt: 2:   9 Why Long Division Works Take II
  315.    wt: 2:   8 Correcting the Mistake
  316.    wt: 2:   7 Long Divison Mistake Catching
  317.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  318.    wt: 2:   5 Long Division Include Zeroes or not
  319.    wt: 2:   4 Division with 2 Digit Divsors
  320.    wt: 2:   3 Division Single Digit Divisor Example
  321.    wt: 2:   D Decimal Multiplication Methods Derived
  322.    wt: 2:   C Counting Areas with Powers of Ten
  323.    wt: 2:   B Powers of Ten
  324.    wt: 2:   A Elementary Basis for Multiplication Methods
  325.    wt: 2:   6 Multiplication Commutes Order Not Important
  326.    wt: 2:   5 Decimal Fraction Multiplication
  327.    wt: 2:   4 Two and Three Digit Multipliers
  328.    wt: 2:   3 More One Digit Multipliers
  329.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  330.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  331.    wt: 2:   Video Power Notation in Decimal Expansion
  332.    wt: 2:   1 Why 3 times 5 gives 15
  333.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  334.    wt: 2:   8 What skills and work habits to require
  335.    wt: 2:   7 Adding decimal fractions using decimal point
  336.    wt: 2:   6. Counting and adding units and mixed units
  337.    wt: 2:   4. How to add with decimals B with conversions
  338.    wt: 2:   3. How to add with decimals A sans conversions
  339.    wt: 2:   1. Explaining Addition Table
  340.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  341.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  342.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  343.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  344.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  345.    wt: 2:   Chapter 9 About First Courses in Calculus
  346.    wt: 2:   Chapter 2. Slopes and Ski Trails
  347.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  348.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  349.    wt: 2:   Chapter 2 For and Against Mathematics
  350.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  351.    wt: 2:   Chapter 7 Longer Chains of Reason
  352.    wt: 2:   Chapter 6 Chains of Reason
  353.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  354.    wt: 2:   Chapter 2 Skill Development
  355.    wt: 2:   Three Remarks
  356.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  357.    wt: 2:   Chapter 3 Algebra Starter Lessons
  358.    wt: 1:   Skills Chapter 5 Calculus
  359.    wt: 1:   2 arithmetic with signed numbers
  360.    wt: 1:   why bother
  361.    wt: 1:   Applied Maths Program14092009 POMME variant
  362.    wt: 1:   About site lesson plans
  363.    wt: 1:   Lessening Algebra Difficulties
  364.    wt: 1:   the trouble with algebra
  365.    wt: 1:   three goals for Mathematics Education
  366.    wt: 1:   02 21 words for teachers
  367.    wt: 1:   02 20 mathematics education references
  368.    wt: 1:   three kinds of reason in mathematics
  369.    wt: 1:   Prequel In For A Penny In For A Pound
  370.    wt: 1:   education an empirical art
  371.    wt: 1:   fairness and inductive principles for instruction
  372.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  373.    wt: 1:   chapitre 06 00 Chaines de la raison
  374.    wt: 1:   chapitre 04 02 Deuxieme enigme
  375.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  376.    wt: 1:   chapitre 02 00 La Communication des idees
  377.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  378.    wt: 1:   4 Energy Power Heat09
  379.    wt: 1:   3 Energy Power Heat08
  380.    wt: 1:   1 Energy Power Heat06
  381.    wt: 1:   E Energy Power05
  382.    wt: 1:   D Energy Power04
  383.    wt: 1:   C Energy Power03
  384.    wt: 1:   A Energy Power01
  385.    wt: 1:   D Wire Resistance Calculation02
  386.    wt: 1:   B Wire Resistance Qualitative02
  387.    wt: 1:   H Series Circuit02
  388.    wt: 1:   C Electromotive force conventional current02
  389.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  390.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  391.    wt: 1:   24 Standards For Skill Develoment Take II
  392.    wt: 1:   24 Standards For Skill Develoment
  393.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  394.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  395.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  396.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  397.    wt: 1:   22 Student Centered Highschool Mathematics
  398.    wt: 1:   sign monoticity analysis example 4
  399.    wt: 1:   sign monoticity analysis example 3
  400.    wt: 1:   sign monoticity analysis example 2
  401.    wt: 1:   sign monoticity analysis example 1
  402.    wt: 1:   19 Horizontal line rule and method
  403.    wt: 1:   18 Vertical Line Rule and Method
  404.    wt: 1:   2 quadratics graphing in general
  405.    wt: 1:   11 Growth and Decay in Biology
  406.    wt: 1:   10 Exponential Growth and Decay Models
  407.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  408.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  409.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  410.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  411.    wt: 1:   5 Natural Logarithm Calculator Exercises
  412.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  413.    wt: 1:   7 Links Lessons Elsewhere
  414.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  415.    wt: 1:   2 Column Multiplication Method
  416.    wt: 1:   16 cotangent function Definition Graph and Inverse
  417.    wt: 1:   15 cosecant function Definition Graph and Inverse
  418.    wt: 1:   14 secant function Definition Graph and Inverse
  419.    wt: 1:   13 cosecant function Definition Graph and Inverse
  420.    wt: 1:   12 motivation for term arctan
  421.    wt: 1:   11 arctan left inverse of tangent Graph
  422.    wt: 1:   10 arctan left inverse of tangent Definition
  423.    wt: 1:   9 Summary Degrees to Radians and back
  424.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  425.    wt: 1:   C Straight Lines Slope from Coordinates
  426.    wt: 1:   B Straight Line Slope Scaling Properties More
  427.    wt: 1:   A Straight Line Slope Scaling Properties
  428.    wt: 1:   8 Straight Lines Equation for vertical
  429.    wt: 1:   7 Tangent Function is odd on this domain
  430.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  431.    wt: 1:   5 Tangent Function Graph
  432.    wt: 1:   4 Tangent Function Properties
  433.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  434.    wt: 1:   21 sine and cosine Half Angle Formulas
  435.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  436.    wt: 1:   21 Logarithms Powers and Exponentials
  437.    wt: 1:   20 N th Roots of Complex Numbers
  438.    wt: 1:   8 Triangles Cascade Problem Solving
  439.    wt: 1:   7 Trignometric Ratios Unit Circle
  440.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  441.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  442.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  443.    wt: 1:   3 Trigonometric Ratios sine and cosine
  444.    wt: 1:   12 Links Lessons elsewhere
  445.    wt: 1:   A Measurement with Ruler Proper Use
  446.    wt: 1:   2 Measuring Area Directly
  447.    wt: 1:   3 Properties of Square Roots with example
  448.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  449.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  450.    wt: 1:   8 GCD from Euclidean Algorithm
  451.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  452.    wt: 1:   4 Counting with Trees Product Rule Take I
  453.    wt: 1:   3 signed coordinates for maps and planes
  454.    wt: 1:   2 Unit Fraction Multiplication
  455.    wt: 1:   D Remainders Modulo 11 Pair Rule
  456.    wt: 1:   12 Adding Integers More Examples
  457.    wt: 1:   11 Adding Integers Formulas and Examples
  458.    wt: 1:   26 Divisibility by 2 3 5 Example
  459.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  460.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  461.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  462.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  463.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  464.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  465.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  466.    wt: 1:   5 Remainder Arithmetic Modulo 5
  467.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  468.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  469.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  470.    wt: 1:   1 Remainder Arithmetic Modulo 10
  471.    wt: 1:   20 Uniqueness of Prime Factorization
  472.    wt: 1:   11 Efficient Square Rule Use
  473.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  474.    wt: 1:   5 Prime Factorization and a Square Rule
  475.    wt: 1:   The 20 Times Table
  476.    wt: 1:   2 Time and Date Matters in School
  477.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  478.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  479.    wt: 1:   G.5 Motions With Bounded Velocities
  480.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  481.    wt: 1:   G.3 Constant Difference Theorem Proof
  482.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  483.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  484.    wt: 1:   F.5b Extreme Value Theorem
  485.    wt: 1:   F.5a Equicontinuity Theorems
  486.    wt: 1:   F.4 Finite Covering Theorem
  487.    wt: 1:   F.3 Intermediate Value Theorem
  488.    wt: 1:   F.2 Closed Range Theorem
  489.    wt: 1:   F.1 What Functions are Continuous
  490.    wt: 1:   E2 Algebraic Properties of Limits
  491.    wt: 1:   E1 Error Control Inequalities
  492.    wt: 1:   D2 Limits of Monotone Sequences
  493.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  494.    wt: 1:   C Triangle Inequalities
  495.    wt: 1:   B3 Bolzano Weierstrass Theorem
  496.    wt: 1:   PostScript For and Against Decimal Perspectives
  497.    wt: 1:   A1. Introduction
  498.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  499.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  500.    wt: 1:   Chapter 23 Links To Trigonometry
  501.    wt: 1:   Chapter 22 Complex Numbers
  502.    wt: 1:   Chapter 21 Arrow Addition
  503.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  504.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  505.    wt: 1:   Chapter 18. Slopes Areas Integration
  506.    wt: 1:   Chapter 17. Area Approximation
  507.    wt: 1:   Chapter 16. Velocity Approximation
  508.    wt: 1:   Chapter 15. Slope Approximation
  509.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  510.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  511.    wt: 1:   Chapter 13. Acceleration
  512.    wt: 1:   Chapter 12. Units and Slopes
  513.    wt: 1:   Chapter 11. Graphing Slope versus Position
  514.    wt: 1:   Chapter 10 Slopes and Units
  515.    wt: 1:   Chapter 8. Slope Interpretation
  516.    wt: 1:   Chapter 7 Slopes and Velocity
  517.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  518.    wt: 1:   Chapter 5. Slope Sign Tests
  519.    wt: 1:   Chapter 4. More Slope Sign Analysis
  520.    wt: 1:   Chapter 3. Slope Sign Analysis
  521.    wt: 1:   Chapter 1.Introduction
  522.    wt: 1:   Foreword
  523.    wt: 1:   Chapter 25. Mathematical Induction Examples
  524.    wt: 1:   Chapter 18. Rules for Algebra
  525.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  526.    wt: 1:   Chapter 4 Longer Chains of Reason
  527.    wt: 1:   Chapter 3 Chains of Reason
  528.    wt: 1:   Annotated Links to Material Elsehwere
  529.    wt: 1:   Postscript B Mathematics Education References
  530.    wt: 1:   Postscript A Three Remarks
  531.    wt: 1:   Chapter 12 Four Phases
  532.    wt: 1:   Chapter 11 Elementary Instruction
  533.    wt: 1:   Chapter 10 Transition
  534.    wt: 1:   Chapter 9 The Two Ends
  535.    wt: 1:   Chapter 8 Modern Instruction
  536.    wt: 1:   Chapter 7 Two Treatments of Geometry
  537.    wt: 1:   Chapter 5 Four References
  538.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  539.    wt: 1:   Chapter 3 Algebra Difficulties
  540.    wt: 1:   Chapter 1 Introduction
  541.    wt: 1:   Foreword
  542.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  543.    wt: 1:   Postscript C Consistency as a Tool for Reason
  544.    wt: 1:   Postscript B More on Story Telling and Reason
  545.    wt: 1:   Postscript A Story Telling
  546.    wt: 1:   Chapter 24 Direct and Indirect Reason
  547.    wt: 1:   Chapter 23 Truth Tables
  548.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  549.    wt: 1:   Chapter 21 Occurrence Tables
  550.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  551.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  552.    wt: 1:   Chapter 18 Sense and Knowledge
  553.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  554.    wt: 1:   Chapter 15 Objective Processes
  555.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  556.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  557.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  558.    wt: 1:   Chapter 11 Accidental Patterns
  559.    wt: 1:   Chapter 10 Responsibility
  560.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  561.    wt: 1:   Chapter 8 Change of Language
  562.    wt: 1:   Chapter 5 Deception
  563.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  564.    wt: 1:   Chapter 1 Introduction
  565.    wt: 1:   Foreword
  566.    wt: 1:   B. Domino effect of errors
  567.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  568.    wt: 1:   Chapter 2 Why Sets
  569.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  570.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  571.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  572.    wt: 1:   More Algebra and Slope based Calculus Preview
  573.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  574.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  575.    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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