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: 2:   B Real Numbers Extrinsic Development/
  8.    wt: 2:   A Origins of Counting and Figuring Methods/
  9.    wt: 2:   10 Examples of Algebraic Reasoning/
  10.    wt: 2:   9 Proportionality Backwards and Forwards/
  11.    wt: 2:   8 Unifying Theme For Algebra/
  12.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  13.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  14.    wt: 2:   5 Real Numbers/
  15.    wt: 2:   4 Computation Rules and Function Notation/
  16.    wt: 2:   Step 4 Gaussian Elimination/
  17.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  18.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  19.    wt: 2:   Step 1 Stick diagram and fractions/
  20.    wt: 2:   3 Solving Linear Equations/
  21.    wt: 2:   2 Formula Forward Use Evaluation/
  22.    wt: 2:   1 Working With Sets/
  23.    wt: 2:   Algebra Starter Lessons/
  24.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  25.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  26.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

20 matches:

  1.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  2.    wt: 2:   Chapter 3 Algebra Starter Lessons
  3.    wt: 1:   Skills Chapter 5 Calculus
  4.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  5.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  6.    wt: 1:   1 Calculator Starter Exercises
  7.    wt: 1:   7 Links Lessons Elsewhere
  8.    wt: 1:   12 Links Lessons elsewhere
  9.    wt: 1:   A Related lessons in Volume 3
  10.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  11.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  12.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  13.    wt: 1:   Chapter 9 About First Courses in Calculus
  14.    wt: 1:   Fall 1983 Calculus Appetizer
  15.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  16.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  17.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  18.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  19.    wt: 1:   More Algebra and Slope based Calculus Preview
  20.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

293 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: 2:   musings do not puiblish real numbers
  75.    wt: 2:   A Modular and Remainder Arithmetic
  76.    wt: 2:   A Signed Number Arithmetic Review
  77.    wt: 2:   26 More Less Greater Than Comparison
  78.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  79.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  80.    wt: 2:   23 Distributive Law Two Derivations
  81.    wt: 2:   22 Multiplication of Signed Numbers
  82.    wt: 2:   21 Addition of Multiples of a Single Vector
  83.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  84.    wt: 2:   19 Signed Multiples of Vectors
  85.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  86.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  87.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  88.    wt: 2:   15 Head to Tails in place Addition Associative
  89.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  90.    wt: 2:   13 Arrows and Vectors in a Plane
  91.    wt: 2:   12 Real Numbers Line Signed Coordinates
  92.    wt: 2:   11 Signed Number Addition and Addition Properties
  93.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  94.    wt: 2:   9 Division with Digits after Decimal Point
  95.    wt: 2:   8 Division and Mulplication of Compound Fractions
  96.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  97.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  98.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  99.    wt: 2:   4 Location of Point in Decimal Addition
  100.    wt: 2:   3 Location of Point in Decimal Multiplication
  101.    wt: 2:   2 Counting Digits in Decimal Multiplication
  102.    wt: 2:   1 Fractions with Finite Decimal Expansions
  103.    wt: 2:   E Long Division Methods more
  104.    wt: 2:   D Long Division Methods
  105.    wt: 2:   C Three Decimal Subtraction Methods
  106.    wt: 2:   B Decimal Comparison and Subtraction
  107.    wt: 2:   A Decimal Addition Columm Methods
  108.    wt: 2:   8 Column Multiplication Methods in General
  109.    wt: 2:   7 Decimals Multiplication Methods Examples
  110.    wt: 2:   6 Column Methods for Decimal Multiplication
  111.    wt: 2:   5 Distributive Law for Whole Numbers
  112.    wt: 2:   4 Commutative Law Groups Counting Form
  113.    wt: 2:   3 Multiplicative Counting Skills Principles
  114.    wt: 2:   2 Combing Counts Addition Skills and Principles
  115.    wt: 2:   1 The Counting Origins of Numbers
  116.    wt: 2:   5 Areas of Rectangles Revisited
  117.    wt: 2:   4 Fraction Operations Axiomatic Development
  118.    wt: 2:   3 Inequalities Algebraically
  119.    wt: 2:   2 Fraction Operations Physical Development
  120.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  121.    wt: 2:   5 Proportionality in Equivalent Fractions
  122.    wt: 2:   4 Rates Ratios and Proporitionality
  123.    wt: 2:   3 Proportionality Examples
  124.    wt: 2:   2 Algebraic View
  125.    wt: 2:   1 What is Proportionality
  126.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  127.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  128.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  129.    wt: 2:   6 Compound Interest Forward and Backwards
  130.    wt: 2:   5 Triangle Area Formula Backwards
  131.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  132.    wt: 2:   3 Linear Equation Literal Solution More
  133.    wt: 2:   2 Linear Equation Literal Solution
  134.    wt: 2:   1 Changing Calculations
  135.    wt: 2:   6 Equations and Systems Equivalent or Implied
  136.    wt: 2:   5 Equality in Algebra
  137.    wt: 2:   4 Subtraction and Division Axioms
  138.    wt: 2:   3 Product Axioms Two Forms
  139.    wt: 2:   2 Addition and Multiplication Axioms
  140.    wt: 2:   1 Equivalent Computation Rules
  141.    wt: 2:   5 Greater More Less Than Signs in General
  142.    wt: 2:   4 Comparison of Negative Numbers
  143.    wt: 2:   3 More and Less Than with Unlike Signs
  144.    wt: 2:   2 More and Less Than for Counts and Measures
  145.    wt: 2:   1 Real Numbers Comparison
  146.    wt: 2:   16 Real Numbers Comparison
  147.    wt: 2:   15 Real Number Division
  148.    wt: 2:   14 Real Number Multiplication
  149.    wt: 2:   13 Real Number Subtraction
  150.    wt: 2:   12 Real Number Additive Inverses or Negatives
  151.    wt: 2:   11 Real Number Addition
  152.    wt: 2:   10 Real Number Lengths and Signs
  153.    wt: 2:   9 Coordinates for Regions in Space
  154.    wt: 2:   8 Coordinates for Maps and Planes
  155.    wt: 2:   7 Real Numbers as Line Cordinates
  156.    wt: 2:   6 Unsigned Real Numbers
  157.    wt: 2:   5 Rational Numbers More
  158.    wt: 2:   4 Rational Numbers
  159.    wt: 2:   3 Fractions
  160.    wt: 2:   2 Integers
  161.    wt: 2:   1 Whole and Natural Numbers
  162.    wt: 2:   5 Independent versus Dependent Variables
  163.    wt: 2:   4 Changing Letters
  164.    wt: 2:   3 Geometric Formulas and Function Notation
  165.    wt: 2:   2 Computation Rules Evaluation
  166.    wt: 2:   1 Formulas Dependence and Function Notation
  167.    wt: 2:   More Exercises
  168.    wt: 2:   Simple Exercises
  169.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  170.    wt: 2:   4 GE III Animated Examples
  171.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  172.    wt: 2:   3 GE III Equation Addition and Multiplication
  173.    wt: 2:   2 GE II Comparison
  174.    wt: 2:   1 GE Substitution four examples
  175.    wt: 2:   4 Solving a triangular system exercise
  176.    wt: 2:   3 Solving triangular system example
  177.    wt: 2:   2 Essentially one exercises three with solution
  178.    wt: 2:   1 Essentially One Unknown
  179.    wt: 2:   6 Algebraic Solution Example
  180.    wt: 2:   5 Algebraic Solutions Introduction
  181.    wt: 2:   4 Four Examples Fractional Coefficients
  182.    wt: 2:   3 Four Examples
  183.    wt: 2:   2 Three Examples
  184.    wt: 2:   1 Proper Equal Sign Usage
  185.    wt: 2:   Skill Development Notes
  186.    wt: 2:   10 One Example
  187.    wt: 2:   9 Three Examples
  188.    wt: 2:   8 One Example
  189.    wt: 2:   7 Two Examples
  190.    wt: 2:   6 Three Examples
  191.    wt: 2:   5 Three Examples
  192.    wt: 2:   4 Two Examples
  193.    wt: 2:   3 Two Examples
  194.    wt: 2:   2 Three Examples
  195.    wt: 2:   Using Letters for Physical Quantities
  196.    wt: 2:   Formula Usage Show Work Format
  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:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  230.    wt: 2:   Chapter 9 About First Courses in Calculus
  231.    wt: 2:   Fall 1983 Calculus Appetizer
  232.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  233.    wt: 2:   Chapter 3 Algebra Starter Lessons
  234.    wt: 1:   Skills Chapter 5 Calculus
  235.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  236.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  237.    wt: 1:   1 Calculator Starter Exercises
  238.    wt: 1:   7 Links Lessons Elsewhere
  239.    wt: 1:   12 Links Lessons elsewhere
  240.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  241.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  242.    wt: 1:   G.5 Motions With Bounded Velocities
  243.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  244.    wt: 1:   G.3 Constant Difference Theorem Proof
  245.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  246.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  247.    wt: 1:   F.5b Extreme Value Theorem
  248.    wt: 1:   F.5a Equicontinuity Theorems
  249.    wt: 1:   F.4 Finite Covering Theorem
  250.    wt: 1:   F.3 Intermediate Value Theorem
  251.    wt: 1:   F.2 Closed Range Theorem
  252.    wt: 1:   F.1 What Functions are Continuous
  253.    wt: 1:   E2 Algebraic Properties of Limits
  254.    wt: 1:   E1 Error Control Inequalities
  255.    wt: 1:   D2 Limits of Monotone Sequences
  256.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  257.    wt: 1:   C Triangle Inequalities
  258.    wt: 1:   B3 Bolzano Weierstrass Theorem
  259.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  260.    wt: 1:   PostScript For and Against Decimal Perspectives
  261.    wt: 1:   A1. Introduction
  262.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  263.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  264.    wt: 1:   Chapter 23 Links To Trigonometry
  265.    wt: 1:   Chapter 22 Complex Numbers
  266.    wt: 1:   Chapter 21 Arrow Addition
  267.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  268.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  269.    wt: 1:   Chapter 18. Slopes Areas Integration
  270.    wt: 1:   Chapter 17. Area Approximation
  271.    wt: 1:   Chapter 16. Velocity Approximation
  272.    wt: 1:   Chapter 15. Slope Approximation
  273.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  274.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  275.    wt: 1:   Chapter 13. Acceleration
  276.    wt: 1:   Chapter 12. Units and Slopes
  277.    wt: 1:   Chapter 11. Graphing Slope versus Position
  278.    wt: 1:   Chapter 10 Slopes and Units
  279.    wt: 1:   Chapter 8. Slope Interpretation
  280.    wt: 1:   Chapter 7 Slopes and Velocity
  281.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  282.    wt: 1:   Chapter 5. Slope Sign Tests
  283.    wt: 1:   Chapter 4. More Slope Sign Analysis
  284.    wt: 1:   Chapter 3. Slope Sign Analysis
  285.    wt: 1:   Chapter 2. Slopes and Ski Trails
  286.    wt: 1:   Chapter 1.Introduction
  287.    wt: 1:   Foreword
  288.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  289.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  290.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  291.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  292.    wt: 1:   More Algebra and Slope based Calculus Preview
  293.    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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