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
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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.

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: 6:   13 Lessons on Limits and Continuity/
  2.    wt: 5:   12 Webvideo Lessons on Area and Volume Calculation/
  3.    wt: 5:   5 Lessons on Integration/
  4.    wt: 5:   4 Lessons on Using Derivatives/
  5.    wt: 5:   38 Lessons on Calculating Derivatives/
  6.    wt: 4:   70 Calculus Starter Lessons/
  7.    wt: 3:   2 Formula Forward Use Evaluation/
  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:   4 Computation Rules and Function Notation/
  17.    wt: 2:   Step 4 Gaussian Elimination/
  18.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  19.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  20.    wt: 2:   Step 1 Stick diagram and fractions/
  21.    wt: 2:   3 Solving Linear Equations/
  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

53 matches:

  1.    wt: 2:   Rewriting algebraic substitution as function substitutions
  2.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  3.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  4.    wt: 2:   7 Evaluation by immediate or delayed substitution
  5.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  6.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  7.    wt: 2:   Chapter 3 Algebra Starter Lessons
  8.    wt: 1:   Skills Chapter 5 Calculus
  9.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  10.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  11.    wt: 1:   1 Calculator Starter Exercises
  12.    wt: 1:   7 Links Lessons Elsewhere
  13.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  14.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  15.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  16.    wt: 1:   12 Links Lessons elsewhere
  17.    wt: 1:   2 Computation Rules Evaluation
  18.    wt: 1:   1 GE Substitution four examples
  19.    wt: 1:   8 Compound Interest Formula Evaluation
  20.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  21.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  22.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  23.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  24.    wt: 1:   5 Common Divisors 60 45 via Prime
  25.    wt: 1:   4 LCM of 8 and 10 via Prime
  26.    wt: 1:   2 Least Common Multiple LCM intro via list method
  27.    wt: 1:   12 GCD 2700 288 via Prime
  28.    wt: 1:   Formula Evaluation how to show work
  29.    wt: 1:   Expression Evaluation how to show work
  30.    wt: 1:   8 Addition of Time Intervals via subtotaling
  31.    wt: 1:   4 Definite Integrals Evaluation Exercises
  32.    wt: 1:   A Related lessons in Volume 3
  33.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  34.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  35.    wt: 1:   11 Limits at infinity Three Examples
  36.    wt: 1:   10 Three one sided limits with infinite values
  37.    wt: 1:   9 Limits Continuity and Composition
  38.    wt: 1:   3 Decimal insights for limits continuity convergence
  39.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  40.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  41.    wt: 1:   E2 Algebraic Properties of Limits
  42.    wt: 1:   D2 Limits of Monotone Sequences
  43.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  44.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  45.    wt: 1:   Chapter 9 About First Courses in Calculus
  46.    wt: 1:   Fall 1983 Calculus Appetizer
  47.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  48.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  49.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  50.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  51.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  52.    wt: 1:   More Algebra and Slope based Calculus Preview
  53.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

311 matches:

  1.    wt: 8:   7 Evaluation by immediate or delayed substitution
  2.    wt: 7:   13 Limits with Parameters and Derivatives Take II
  3.    wt: 7:   12 Limits with Parameters and Derivatives Take I
  4.    wt: 7:   11 Limits at infinity Three Examples
  5.    wt: 7:   10 Three one sided limits with infinite values
  6.    wt: 7:   9 Limits Continuity and Composition
  7.    wt: 7:   3 Decimal insights for limits continuity convergence
  8.    wt: 6:   4 Definite Integrals Evaluation Exercises
  9.    wt: 6:   A Related lessons in Volume 3
  10.    wt: 6:   8 Four Animated Examples
  11.    wt: 6:   6 Continuity at a point
  12.    wt: 6:   5 Jumps and absence of unlimited error control
  13.    wt: 6:   4 Numerical properties
  14.    wt: 6:   2 Algebraic codification
  15.    wt: 6:   1 Numerical introduction
  16.    wt: 5:   Example 2 volume of a cone
  17.    wt: 5:   Example 1 volume of a pyramid
  18.    wt: 5:   Volume of Solid by Cross Sections Lesson
  19.    wt: 5:   Example 1. Area Between x and x squared
  20.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  21.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  22.    wt: 5:   Example 4 with x function of y
  23.    wt: 5:   Example 3
  24.    wt: 5:   Example 2
  25.    wt: 5:   Example 1
  26.    wt: 5:   Area Between Curves Lesson Take 2
  27.    wt: 5:   Area Between Curves Lesson Take 1
  28.    wt: 5:   Summary
  29.    wt: 5:   A Related Material in Volume 3
  30.    wt: 5:   5 Area Under Curve Exercise
  31.    wt: 5:   3 Two Chain Rule Method Exercises
  32.    wt: 5:   2 Indefinite Integrals Exercises
  33.    wt: 5:   1 Chain Rule in Reverse Integration Method
  34.    wt: 5:   4 Second derivative test exercise example
  35.    wt: 5:   3 Second derivative test
  36.    wt: 5:   2 Second derivative test prequel
  37.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  38.    wt: 5:   A Chain Rule Real Player video examples
  39.    wt: 5:   38 Formulas and derivatives for powers and roots
  40.    wt: 5:   36 Cube root derivative animated
  41.    wt: 5:   34 Derivative of exponential function
  42.    wt: 5:   33 Chain Rule Real Player video examples
  43.    wt: 5:   31 Derivatives of inverse functions
  44.    wt: 5:   30Chain Rule A Proof
  45.    wt: 5:   29 Chain Rule Optional Reading
  46.    wt: 5:   28 Chain Rule Preparation for a Proof
  47.    wt: 5:   27 Chain Rule sinusoidal outer inner functions EGS
  48.    wt: 5:   26 Chain Rule Recognising outer inner functions
  49.    wt: 5:   25 Chain Rule Animated Examples Continued
  50.    wt: 5:   24 Chain Rule Animated Examples
  51.    wt: 5:   23 Chain Rule in general
  52.    wt: 5:   22 Chain Rule for polynomials
  53.    wt: 5:   21 Chain Rule for powers
  54.    wt: 5:   20 Chain Rule for Pulley Systems
  55.    wt: 5:   19 Chain Rule for linear functions
  56.    wt: 5:   18 Chain Rule Introduction
  57.    wt: 5:   17 Derivatives of quotients of sine and cosine
  58.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  59.    wt: 5:   15 sine and cosine derivatives 3rd step
  60.    wt: 5:   14 sine and cosine derivatives 2nd step
  61.    wt: 5:   13 sine and cosine derivatives 1st step
  62.    wt: 5:   12 Quotient rule examples
  63.    wt: 5:   11 Quotient rule
  64.    wt: 5:   10 Power rule for negative integers
  65.    wt: 5:   9 Reciprocal rule
  66.    wt: 5:   8 Differentiation of polynomials
  67.    wt: 5:   7 Animated Differentiation Examples
  68.    wt: 5:   6 Power rule from product rule
  69.    wt: 5:   5 Product Rule
  70.    wt: 5:   4 Sum Rule
  71.    wt: 5:   3 Motivation for Limit Definition Take 2
  72.    wt: 5:   2 Motivation for Limit Definition Take 1
  73.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  74.    wt: 4:   8 Compound Interest Formula Evaluation
  75.    wt: 3:   2 Computation Rules Evaluation
  76.    wt: 3:   1 GE Substitution four examples
  77.    wt: 3:   13 Naming Identifying Formulas with Words
  78.    wt: 3:   12 Cone Cylinder Sphere Lesson Idea
  79.    wt: 3:   11 Volume of Sphere
  80.    wt: 3:   10 Volume of Pyramid
  81.    wt: 3:   9 Volume of Cone
  82.    wt: 3:   7 Compound Interest Formula Introduction
  83.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  84.    wt: 3:   5 Box Volume Formula Example
  85.    wt: 3:   4 Circle Area Formula Example
  86.    wt: 3:   3 Triangle Area Formula Example
  87.    wt: 3:   2 Another Rectangle Area Formula Example
  88.    wt: 3:   1 Written work formats for developing and showing skill
  89.    wt: 3:   Chapter 15. Algebraic Evaluation of Limits
  90.    wt: 2:   Rewriting algebraic substitution as function substitutions
  91.    wt: 2:   musings do not puiblish real numbers
  92.    wt: 2:   A Modular and Remainder Arithmetic
  93.    wt: 2:   A Signed Number Arithmetic Review
  94.    wt: 2:   26 More Less Greater Than Comparison
  95.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  96.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  97.    wt: 2:   23 Distributive Law Two Derivations
  98.    wt: 2:   22 Multiplication of Signed Numbers
  99.    wt: 2:   21 Addition of Multiples of a Single Vector
  100.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  101.    wt: 2:   19 Signed Multiples of Vectors
  102.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  103.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  104.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  105.    wt: 2:   15 Head to Tails in place Addition Associative
  106.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  107.    wt: 2:   13 Arrows and Vectors in a Plane
  108.    wt: 2:   12 Real Numbers Line Signed Coordinates
  109.    wt: 2:   11 Signed Number Addition and Addition Properties
  110.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  111.    wt: 2:   9 Division with Digits after Decimal Point
  112.    wt: 2:   8 Division and Mulplication of Compound Fractions
  113.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  114.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  115.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  116.    wt: 2:   4 Location of Point in Decimal Addition
  117.    wt: 2:   3 Location of Point in Decimal Multiplication
  118.    wt: 2:   2 Counting Digits in Decimal Multiplication
  119.    wt: 2:   1 Fractions with Finite Decimal Expansions
  120.    wt: 2:   E Long Division Methods more
  121.    wt: 2:   D Long Division Methods
  122.    wt: 2:   C Three Decimal Subtraction Methods
  123.    wt: 2:   B Decimal Comparison and Subtraction
  124.    wt: 2:   A Decimal Addition Columm Methods
  125.    wt: 2:   8 Column Multiplication Methods in General
  126.    wt: 2:   7 Decimals Multiplication Methods Examples
  127.    wt: 2:   6 Column Methods for Decimal Multiplication
  128.    wt: 2:   5 Distributive Law for Whole Numbers
  129.    wt: 2:   4 Commutative Law Groups Counting Form
  130.    wt: 2:   3 Multiplicative Counting Skills Principles
  131.    wt: 2:   2 Combing Counts Addition Skills and Principles
  132.    wt: 2:   1 The Counting Origins of Numbers
  133.    wt: 2:   5 Areas of Rectangles Revisited
  134.    wt: 2:   4 Fraction Operations Axiomatic Development
  135.    wt: 2:   3 Inequalities Algebraically
  136.    wt: 2:   2 Fraction Operations Physical Development
  137.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  138.    wt: 2:   5 Proportionality in Equivalent Fractions
  139.    wt: 2:   4 Rates Ratios and Proporitionality
  140.    wt: 2:   3 Proportionality Examples
  141.    wt: 2:   2 Algebraic View
  142.    wt: 2:   1 What is Proportionality
  143.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  144.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  145.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  146.    wt: 2:   6 Compound Interest Forward and Backwards
  147.    wt: 2:   5 Triangle Area Formula Backwards
  148.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  149.    wt: 2:   3 Linear Equation Literal Solution More
  150.    wt: 2:   2 Linear Equation Literal Solution
  151.    wt: 2:   1 Changing Calculations
  152.    wt: 2:   6 Equations and Systems Equivalent or Implied
  153.    wt: 2:   5 Equality in Algebra
  154.    wt: 2:   4 Subtraction and Division Axioms
  155.    wt: 2:   3 Product Axioms Two Forms
  156.    wt: 2:   2 Addition and Multiplication Axioms
  157.    wt: 2:   1 Equivalent Computation Rules
  158.    wt: 2:   5 Greater More Less Than Signs in General
  159.    wt: 2:   4 Comparison of Negative Numbers
  160.    wt: 2:   3 More and Less Than with Unlike Signs
  161.    wt: 2:   2 More and Less Than for Counts and Measures
  162.    wt: 2:   1 Real Numbers Comparison
  163.    wt: 2:   16 Real Numbers Comparison
  164.    wt: 2:   15 Real Number Division
  165.    wt: 2:   14 Real Number Multiplication
  166.    wt: 2:   13 Real Number Subtraction
  167.    wt: 2:   12 Real Number Additive Inverses or Negatives
  168.    wt: 2:   11 Real Number Addition
  169.    wt: 2:   10 Real Number Lengths and Signs
  170.    wt: 2:   9 Coordinates for Regions in Space
  171.    wt: 2:   8 Coordinates for Maps and Planes
  172.    wt: 2:   7 Real Numbers as Line Cordinates
  173.    wt: 2:   6 Unsigned Real Numbers
  174.    wt: 2:   5 Rational Numbers More
  175.    wt: 2:   4 Rational Numbers
  176.    wt: 2:   3 Fractions
  177.    wt: 2:   2 Integers
  178.    wt: 2:   1 Whole and Natural Numbers
  179.    wt: 2:   5 Independent versus Dependent Variables
  180.    wt: 2:   4 Changing Letters
  181.    wt: 2:   3 Geometric Formulas and Function Notation
  182.    wt: 2:   1 Formulas Dependence and Function Notation
  183.    wt: 2:   More Exercises
  184.    wt: 2:   Simple Exercises
  185.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  186.    wt: 2:   4 GE III Animated Examples
  187.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  188.    wt: 2:   3 GE III Equation Addition and Multiplication
  189.    wt: 2:   2 GE II Comparison
  190.    wt: 2:   4 Solving a triangular system exercise
  191.    wt: 2:   3 Solving triangular system example
  192.    wt: 2:   2 Essentially one exercises three with solution
  193.    wt: 2:   1 Essentially One Unknown
  194.    wt: 2:   6 Algebraic Solution Example
  195.    wt: 2:   5 Algebraic Solutions Introduction
  196.    wt: 2:   4 Four Examples Fractional Coefficients
  197.    wt: 2:   3 Four Examples
  198.    wt: 2:   2 Three Examples
  199.    wt: 2:   1 Proper Equal Sign Usage
  200.    wt: 2:   Skill Development Notes
  201.    wt: 2:   10 One Example
  202.    wt: 2:   9 Three Examples
  203.    wt: 2:   8 One Example
  204.    wt: 2:   7 Two Examples
  205.    wt: 2:   6 Three Examples
  206.    wt: 2:   5 Three Examples
  207.    wt: 2:   4 Two Examples
  208.    wt: 2:   3 Two Examples
  209.    wt: 2:   2 Three Examples
  210.    wt: 2:   Using Letters for Physical Quantities
  211.    wt: 2:   Formula Usage Show Work Format
  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:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  230.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  231.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  232.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  233.    wt: 2:   E2 Algebraic Properties of Limits
  234.    wt: 2:   D2 Limits of Monotone Sequences
  235.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  236.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  237.    wt: 2:   Chapter 9 About First Courses in Calculus
  238.    wt: 2:   Fall 1983 Calculus Appetizer
  239.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  240.    wt: 2:   Chapter 3 Algebra Starter Lessons
  241.    wt: 1:   Skills Chapter 5 Calculus
  242.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  243.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  244.    wt: 1:   1 Calculator Starter Exercises
  245.    wt: 1:   7 Links Lessons Elsewhere
  246.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  247.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  248.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  249.    wt: 1:   12 Links Lessons elsewhere
  250.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  251.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  252.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  253.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  254.    wt: 1:   5 Common Divisors 60 45 via Prime
  255.    wt: 1:   4 LCM of 8 and 10 via Prime
  256.    wt: 1:   2 Least Common Multiple LCM intro via list method
  257.    wt: 1:   12 GCD 2700 288 via Prime
  258.    wt: 1:   Formula Evaluation how to show work
  259.    wt: 1:   Expression Evaluation how to show work
  260.    wt: 1:   8 Addition of Time Intervals via subtotaling
  261.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  262.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  263.    wt: 1:   G.5 Motions With Bounded Velocities
  264.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  265.    wt: 1:   G.3 Constant Difference Theorem Proof
  266.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  267.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  268.    wt: 1:   F.5b Extreme Value Theorem
  269.    wt: 1:   F.5a Equicontinuity Theorems
  270.    wt: 1:   F.4 Finite Covering Theorem
  271.    wt: 1:   F.3 Intermediate Value Theorem
  272.    wt: 1:   F.2 Closed Range Theorem
  273.    wt: 1:   F.1 What Functions are Continuous
  274.    wt: 1:   E1 Error Control Inequalities
  275.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  276.    wt: 1:   C Triangle Inequalities
  277.    wt: 1:   B3 Bolzano Weierstrass Theorem
  278.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  279.    wt: 1:   PostScript For and Against Decimal Perspectives
  280.    wt: 1:   A1. Introduction
  281.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  282.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  283.    wt: 1:   Chapter 23 Links To Trigonometry
  284.    wt: 1:   Chapter 22 Complex Numbers
  285.    wt: 1:   Chapter 21 Arrow Addition
  286.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  287.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  288.    wt: 1:   Chapter 18. Slopes Areas Integration
  289.    wt: 1:   Chapter 17. Area Approximation
  290.    wt: 1:   Chapter 16. Velocity Approximation
  291.    wt: 1:   Chapter 15. Slope Approximation
  292.    wt: 1:   Chapter 13. Acceleration
  293.    wt: 1:   Chapter 12. Units and Slopes
  294.    wt: 1:   Chapter 11. Graphing Slope versus Position
  295.    wt: 1:   Chapter 10 Slopes and Units
  296.    wt: 1:   Chapter 8. Slope Interpretation
  297.    wt: 1:   Chapter 7 Slopes and Velocity
  298.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  299.    wt: 1:   Chapter 5. Slope Sign Tests
  300.    wt: 1:   Chapter 4. More Slope Sign Analysis
  301.    wt: 1:   Chapter 3. Slope Sign Analysis
  302.    wt: 1:   Chapter 2. Slopes and Ski Trails
  303.    wt: 1:   Chapter 1.Introduction
  304.    wt: 1:   Foreword
  305.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  306.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  307.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  308.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  309.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  310.    wt: 1:   More Algebra and Slope based Calculus Preview
  311.    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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