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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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: 3:   6 More Less Greater Than Inequalities and Comparison/
  8.    wt: 3:   Step 4 Gaussian Elimination/
  9.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  10.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  11.    wt: 3:   Step 1 Stick diagram and fractions/
  12.    wt: 3:   3 Solving Linear Equations/
  13.    wt: 2:   B Real Numbers Extrinsic Development/
  14.    wt: 2:   A Origins of Counting and Figuring Methods/
  15.    wt: 2:   10 Examples of Algebraic Reasoning/
  16.    wt: 2:   9 Proportionality Backwards and Forwards/
  17.    wt: 2:   8 Unifying Theme For Algebra/
  18.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  19.    wt: 2:   5 Real Numbers/
  20.    wt: 2:   4 Computation Rules and Function Notation/
  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

32 matches:

  1.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  2.    wt: 2:   Chapter 3 Algebra Starter Lessons
  3.    wt: 1:   G LAMP Introduction Problem Solving Skills
  4.    wt: 1:   Skills Chapter 5 Calculus
  5.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  6.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  7.    wt: 1:   1 Calculator Starter Exercises
  8.    wt: 1:   7 Links Lessons Elsewhere
  9.    wt: 1:   Straight Lines Instersection Solving Equations
  10.    wt: 1:   8 Triangles Cascade Problem Solving
  11.    wt: 1:   12 Links Lessons elsewhere
  12.    wt: 1:   6 Intersection of lines by solving linear systems
  13.    wt: 1:   3 Inequalities Algebraically
  14.    wt: 1:   4 Solving a triangular system exercise
  15.    wt: 1:   3 Solving triangular system example
  16.    wt: 1:   A Related lessons in Volume 3
  17.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  18.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  19.    wt: 1:   E1 Error Control Inequalities
  20.    wt: 1:   C Triangle Inequalities
  21.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  22.    wt: 1:   Chapter 9 About First Courses in Calculus
  23.    wt: 1:   Fall 1983 Calculus Appetizer
  24.    wt: 1:   Chapter 15. Solving Linear Equations
  25.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  26.    wt: 1:   H more Routine to non routine problem solving
  27.    wt: 1:   H Jigsaw puzzles and problem solving
  28.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  29.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  30.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  31.    wt: 1:   More Algebra and Slope based Calculus Preview
  32.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

300 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: 4:   4 Solving a triangular system exercise
  75.    wt: 4:   3 Solving triangular system example
  76.    wt: 3:   3 Inequalities Algebraically
  77.    wt: 3:   5 Greater More Less Than Signs in General
  78.    wt: 3:   4 Comparison of Negative Numbers
  79.    wt: 3:   3 More and Less Than with Unlike Signs
  80.    wt: 3:   2 More and Less Than for Counts and Measures
  81.    wt: 3:   1 Real Numbers Comparison
  82.    wt: 3:   More Exercises
  83.    wt: 3:   Simple Exercises
  84.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  85.    wt: 3:   4 GE III Animated Examples
  86.    wt: 3:   3 Gaussian Elimination 3 unknowns first example
  87.    wt: 3:   3 GE III Equation Addition and Multiplication
  88.    wt: 3:   2 GE II Comparison
  89.    wt: 3:   1 GE Substitution four examples
  90.    wt: 3:   2 Essentially one exercises three with solution
  91.    wt: 3:   1 Essentially One Unknown
  92.    wt: 3:   6 Algebraic Solution Example
  93.    wt: 3:   5 Algebraic Solutions Introduction
  94.    wt: 3:   4 Four Examples Fractional Coefficients
  95.    wt: 3:   3 Four Examples
  96.    wt: 3:   2 Three Examples
  97.    wt: 3:   1 Proper Equal Sign Usage
  98.    wt: 3:   Skill Development Notes
  99.    wt: 3:   10 One Example
  100.    wt: 3:   9 Three Examples
  101.    wt: 3:   8 One Example
  102.    wt: 3:   7 Two Examples
  103.    wt: 3:   6 Three Examples
  104.    wt: 3:   5 Three Examples
  105.    wt: 3:   4 Two Examples
  106.    wt: 3:   3 Two Examples
  107.    wt: 3:   2 Three Examples
  108.    wt: 3:   Using Letters for Physical Quantities
  109.    wt: 3:   Formula Usage Show Work Format
  110.    wt: 2:   musings do not puiblish real numbers
  111.    wt: 2:   A Modular and Remainder Arithmetic
  112.    wt: 2:   A Signed Number Arithmetic Review
  113.    wt: 2:   26 More Less Greater Than Comparison
  114.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  115.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  116.    wt: 2:   23 Distributive Law Two Derivations
  117.    wt: 2:   22 Multiplication of Signed Numbers
  118.    wt: 2:   21 Addition of Multiples of a Single Vector
  119.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  120.    wt: 2:   19 Signed Multiples of Vectors
  121.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  122.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  123.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  124.    wt: 2:   15 Head to Tails in place Addition Associative
  125.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  126.    wt: 2:   13 Arrows and Vectors in a Plane
  127.    wt: 2:   12 Real Numbers Line Signed Coordinates
  128.    wt: 2:   11 Signed Number Addition and Addition Properties
  129.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  130.    wt: 2:   9 Division with Digits after Decimal Point
  131.    wt: 2:   8 Division and Mulplication of Compound Fractions
  132.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  133.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  134.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  135.    wt: 2:   4 Location of Point in Decimal Addition
  136.    wt: 2:   3 Location of Point in Decimal Multiplication
  137.    wt: 2:   2 Counting Digits in Decimal Multiplication
  138.    wt: 2:   1 Fractions with Finite Decimal Expansions
  139.    wt: 2:   E Long Division Methods more
  140.    wt: 2:   D Long Division Methods
  141.    wt: 2:   C Three Decimal Subtraction Methods
  142.    wt: 2:   B Decimal Comparison and Subtraction
  143.    wt: 2:   A Decimal Addition Columm Methods
  144.    wt: 2:   8 Column Multiplication Methods in General
  145.    wt: 2:   7 Decimals Multiplication Methods Examples
  146.    wt: 2:   6 Column Methods for Decimal Multiplication
  147.    wt: 2:   5 Distributive Law for Whole Numbers
  148.    wt: 2:   4 Commutative Law Groups Counting Form
  149.    wt: 2:   3 Multiplicative Counting Skills Principles
  150.    wt: 2:   2 Combing Counts Addition Skills and Principles
  151.    wt: 2:   1 The Counting Origins of Numbers
  152.    wt: 2:   5 Areas of Rectangles Revisited
  153.    wt: 2:   4 Fraction Operations Axiomatic Development
  154.    wt: 2:   2 Fraction Operations Physical Development
  155.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  156.    wt: 2:   5 Proportionality in Equivalent Fractions
  157.    wt: 2:   4 Rates Ratios and Proporitionality
  158.    wt: 2:   3 Proportionality Examples
  159.    wt: 2:   2 Algebraic View
  160.    wt: 2:   1 What is Proportionality
  161.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  162.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  163.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  164.    wt: 2:   6 Compound Interest Forward and Backwards
  165.    wt: 2:   5 Triangle Area Formula Backwards
  166.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  167.    wt: 2:   3 Linear Equation Literal Solution More
  168.    wt: 2:   2 Linear Equation Literal Solution
  169.    wt: 2:   1 Changing Calculations
  170.    wt: 2:   6 Equations and Systems Equivalent or Implied
  171.    wt: 2:   5 Equality in Algebra
  172.    wt: 2:   4 Subtraction and Division Axioms
  173.    wt: 2:   3 Product Axioms Two Forms
  174.    wt: 2:   2 Addition and Multiplication Axioms
  175.    wt: 2:   1 Equivalent Computation Rules
  176.    wt: 2:   16 Real Numbers Comparison
  177.    wt: 2:   15 Real Number Division
  178.    wt: 2:   14 Real Number Multiplication
  179.    wt: 2:   13 Real Number Subtraction
  180.    wt: 2:   12 Real Number Additive Inverses or Negatives
  181.    wt: 2:   11 Real Number Addition
  182.    wt: 2:   10 Real Number Lengths and Signs
  183.    wt: 2:   9 Coordinates for Regions in Space
  184.    wt: 2:   8 Coordinates for Maps and Planes
  185.    wt: 2:   7 Real Numbers as Line Cordinates
  186.    wt: 2:   6 Unsigned Real Numbers
  187.    wt: 2:   5 Rational Numbers More
  188.    wt: 2:   4 Rational Numbers
  189.    wt: 2:   3 Fractions
  190.    wt: 2:   2 Integers
  191.    wt: 2:   1 Whole and Natural Numbers
  192.    wt: 2:   5 Independent versus Dependent Variables
  193.    wt: 2:   4 Changing Letters
  194.    wt: 2:   3 Geometric Formulas and Function Notation
  195.    wt: 2:   2 Computation Rules Evaluation
  196.    wt: 2:   1 Formulas Dependence and Function Notation
  197.    wt: 2:   13 Naming Identifying Formulas with Words
  198.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  199.    wt: 2:   11 Volume of Sphere
  200.    wt: 2:   10 Volume of Pyramid
  201.    wt: 2:   9 Volume of Cone
  202.    wt: 2:   8 Compound Interest Formula Evaluation
  203.    wt: 2:   7 Compound Interest Formula Introduction
  204.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  205.    wt: 2:   5 Box Volume Formula Example
  206.    wt: 2:   4 Circle Area Formula Example
  207.    wt: 2:   3 Triangle Area Formula Example
  208.    wt: 2:   2 Another Rectangle Area Formula Example
  209.    wt: 2:   1 Written work formats for developing and showing skill
  210.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  211.    wt: 2:   9 Sets in Probability and Statistics
  212.    wt: 2:   8 Sets of Numbers
  213.    wt: 2:   7 Cautious or Safe Set Construction
  214.    wt: 2:   6 Power Set Notation
  215.    wt: 2:   5 Product Builder Notation
  216.    wt: 2:   4 Subset Builder Notation
  217.    wt: 2:   3 Counting with Sets etc
  218.    wt: 2:   2 Venn Diagrams
  219.    wt: 2:   1 Finite Sets
  220.    wt: 2:   6 Three Notions of What is a Variable
  221.    wt: 2:   5 Talking about Numbers and Quantities
  222.    wt: 2:   4 A Brief Story of numbers and algebra
  223.    wt: 2:   3 Adding Words To Arithmetic
  224.    wt: 2:   2 What is a Variable
  225.    wt: 2:   1 Three Skills For Algebra
  226.    wt: 2:   About Folder Contents
  227.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  228.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  229.    wt: 2:   E1 Error Control Inequalities
  230.    wt: 2:   C Triangle Inequalities
  231.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  232.    wt: 2:   Chapter 9 About First Courses in Calculus
  233.    wt: 2:   Fall 1983 Calculus Appetizer
  234.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  235.    wt: 2:   Chapter 3 Algebra Starter Lessons
  236.    wt: 1:   G LAMP Introduction Problem Solving Skills
  237.    wt: 1:   Skills Chapter 5 Calculus
  238.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  239.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  240.    wt: 1:   1 Calculator Starter Exercises
  241.    wt: 1:   7 Links Lessons Elsewhere
  242.    wt: 1:   Straight Lines Instersection Solving Equations
  243.    wt: 1:   8 Triangles Cascade Problem Solving
  244.    wt: 1:   12 Links Lessons elsewhere
  245.    wt: 1:   6 Intersection of lines by solving linear systems
  246.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  247.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  248.    wt: 1:   G.5 Motions With Bounded Velocities
  249.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  250.    wt: 1:   G.3 Constant Difference Theorem Proof
  251.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  252.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  253.    wt: 1:   F.5b Extreme Value Theorem
  254.    wt: 1:   F.5a Equicontinuity Theorems
  255.    wt: 1:   F.4 Finite Covering Theorem
  256.    wt: 1:   F.3 Intermediate Value Theorem
  257.    wt: 1:   F.2 Closed Range Theorem
  258.    wt: 1:   F.1 What Functions are Continuous
  259.    wt: 1:   E2 Algebraic Properties of Limits
  260.    wt: 1:   D2 Limits of Monotone Sequences
  261.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  262.    wt: 1:   B3 Bolzano Weierstrass Theorem
  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:   Postscript Pythagorean Theorem yet another proof
  267.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  268.    wt: 1:   Chapter 23 Links To Trigonometry
  269.    wt: 1:   Chapter 22 Complex Numbers
  270.    wt: 1:   Chapter 21 Arrow Addition
  271.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  272.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  273.    wt: 1:   Chapter 18. Slopes Areas Integration
  274.    wt: 1:   Chapter 17. Area Approximation
  275.    wt: 1:   Chapter 16. Velocity Approximation
  276.    wt: 1:   Chapter 15. Slope Approximation
  277.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  278.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  279.    wt: 1:   Chapter 13. Acceleration
  280.    wt: 1:   Chapter 12. Units and Slopes
  281.    wt: 1:   Chapter 11. Graphing Slope versus Position
  282.    wt: 1:   Chapter 10 Slopes and Units
  283.    wt: 1:   Chapter 8. Slope Interpretation
  284.    wt: 1:   Chapter 7 Slopes and Velocity
  285.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  286.    wt: 1:   Chapter 5. Slope Sign Tests
  287.    wt: 1:   Chapter 4. More Slope Sign Analysis
  288.    wt: 1:   Chapter 3. Slope Sign Analysis
  289.    wt: 1:   Chapter 2. Slopes and Ski Trails
  290.    wt: 1:   Chapter 1.Introduction
  291.    wt: 1:   Foreword
  292.    wt: 1:   Chapter 15. Solving Linear Equations
  293.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  294.    wt: 1:   H more Routine to non routine problem solving
  295.    wt: 1:   H Jigsaw puzzles and problem solving
  296.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  297.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  298.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  299.    wt: 1:   More Algebra and Slope based Calculus Preview
  300.    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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