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:   Step 4 Gaussian Elimination/
  8.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  9.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  10.    wt: 3:   Step 1 Stick diagram and fractions/
  11.    wt: 3:   3 Solving Linear Equations/
  12.    wt: 2:   B Real Numbers Extrinsic Development/
  13.    wt: 2:   A Origins of Counting and Figuring Methods/
  14.    wt: 2:   10 Examples of Algebraic Reasoning/
  15.    wt: 2:   9 Proportionality Backwards and Forwards/
  16.    wt: 2:   8 Unifying Theme For Algebra/
  17.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  18.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  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:   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:   5 Polynomials Long division Nonlinear divisor
  9.    wt: 1:   4 Polynomials Long division linear divisor
  10.    wt: 1:   12 Links Lessons elsewhere
  11.    wt: 1:   6 Intersection of lines by solving linear systems
  12.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  13.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  14.    wt: 1:   3 Linear Equation Literal Solution More
  15.    wt: 1:   2 Linear Equation Literal Solution
  16.    wt: 1:   A Related lessons in Volume 3
  17.    wt: 1:   19 Chain Rule for linear functions
  18.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  19.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  20.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  21.    wt: 1:   Chapter 17. Area Approximation
  22.    wt: 1:   Chapter 16. Velocity Approximation
  23.    wt: 1:   Chapter 15. Slope Approximation
  24.    wt: 1:   Chapter 9 About First Courses in Calculus
  25.    wt: 1:   Fall 1983 Calculus Appetizer
  26.    wt: 1:   Chapter 15. Solving Linear Equations
  27.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  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

297 matches:

  1.    wt: 6:   A Related lessons in Volume 3
  2.    wt: 6:   19 Chain Rule for linear functions
  3.    wt: 5:   Example 2 volume of a cone
  4.    wt: 5:   Example 1 volume of a pyramid
  5.    wt: 5:   Volume of Solid by Cross Sections Lesson
  6.    wt: 5:   Example 1. Area Between x and x squared
  7.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  8.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  9.    wt: 5:   Example 4 with x function of y
  10.    wt: 5:   Example 3
  11.    wt: 5:   Example 2
  12.    wt: 5:   Example 1
  13.    wt: 5:   Area Between Curves Lesson Take 2
  14.    wt: 5:   Area Between Curves Lesson Take 1
  15.    wt: 5:   Summary
  16.    wt: 5:   A Related Material in Volume 3
  17.    wt: 5:   5 Area Under Curve Exercise
  18.    wt: 5:   4 Definite Integrals Evaluation Exercises
  19.    wt: 5:   3 Two Chain Rule Method Exercises
  20.    wt: 5:   2 Indefinite Integrals Exercises
  21.    wt: 5:   1 Chain Rule in Reverse Integration Method
  22.    wt: 5:   4 Second derivative test exercise example
  23.    wt: 5:   3 Second derivative test
  24.    wt: 5:   2 Second derivative test prequel
  25.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  26.    wt: 5:   A Chain Rule Real Player video examples
  27.    wt: 5:   38 Formulas and derivatives for powers and roots
  28.    wt: 5:   36 Cube root derivative animated
  29.    wt: 5:   34 Derivative of exponential function
  30.    wt: 5:   33 Chain Rule Real Player video examples
  31.    wt: 5:   31 Derivatives of inverse functions
  32.    wt: 5:   30Chain Rule A Proof
  33.    wt: 5:   29 Chain Rule Optional Reading
  34.    wt: 5:   28 Chain Rule Preparation for a Proof
  35.    wt: 5:   27 Chain Rule sinusoidal outer inner functions EGS
  36.    wt: 5:   26 Chain Rule Recognising outer inner functions
  37.    wt: 5:   25 Chain Rule Animated Examples Continued
  38.    wt: 5:   24 Chain Rule Animated Examples
  39.    wt: 5:   23 Chain Rule in general
  40.    wt: 5:   22 Chain Rule for polynomials
  41.    wt: 5:   21 Chain Rule for powers
  42.    wt: 5:   20 Chain Rule for Pulley Systems
  43.    wt: 5:   18 Chain Rule Introduction
  44.    wt: 5:   17 Derivatives of quotients of sine and cosine
  45.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  46.    wt: 5:   15 sine and cosine derivatives 3rd step
  47.    wt: 5:   14 sine and cosine derivatives 2nd step
  48.    wt: 5:   13 sine and cosine derivatives 1st step
  49.    wt: 5:   12 Quotient rule examples
  50.    wt: 5:   11 Quotient rule
  51.    wt: 5:   10 Power rule for negative integers
  52.    wt: 5:   9 Reciprocal rule
  53.    wt: 5:   8 Differentiation of polynomials
  54.    wt: 5:   7 Animated Differentiation Examples
  55.    wt: 5:   6 Power rule from product rule
  56.    wt: 5:   5 Product Rule
  57.    wt: 5:   4 Sum Rule
  58.    wt: 5:   3 Motivation for Limit Definition Take 2
  59.    wt: 5:   2 Motivation for Limit Definition Take 1
  60.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  61.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  62.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  63.    wt: 5:   11 Limits at infinity Three Examples
  64.    wt: 5:   10 Three one sided limits with infinite values
  65.    wt: 5:   9 Limits Continuity and Composition
  66.    wt: 5:   8 Four Animated Examples
  67.    wt: 5:   7 Evaluation by immediate or delayed substitution
  68.    wt: 5:   6 Continuity at a point
  69.    wt: 5:   5 Jumps and absence of unlimited error control
  70.    wt: 5:   4 Numerical properties
  71.    wt: 5:   3 Decimal insights for limits continuity convergence
  72.    wt: 5:   2 Algebraic codification
  73.    wt: 5:   1 Numerical introduction
  74.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  75.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  76.    wt: 3:   3 Linear Equation Literal Solution More
  77.    wt: 3:   2 Linear Equation Literal Solution
  78.    wt: 3:   More Exercises
  79.    wt: 3:   Simple Exercises
  80.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  81.    wt: 3:   4 GE III Animated Examples
  82.    wt: 3:   3 Gaussian Elimination 3 unknowns first example
  83.    wt: 3:   3 GE III Equation Addition and Multiplication
  84.    wt: 3:   2 GE II Comparison
  85.    wt: 3:   1 GE Substitution four examples
  86.    wt: 3:   4 Solving a triangular system exercise
  87.    wt: 3:   3 Solving triangular system example
  88.    wt: 3:   2 Essentially one exercises three with solution
  89.    wt: 3:   1 Essentially One Unknown
  90.    wt: 3:   6 Algebraic Solution Example
  91.    wt: 3:   5 Algebraic Solutions Introduction
  92.    wt: 3:   4 Four Examples Fractional Coefficients
  93.    wt: 3:   3 Four Examples
  94.    wt: 3:   2 Three Examples
  95.    wt: 3:   1 Proper Equal Sign Usage
  96.    wt: 3:   Skill Development Notes
  97.    wt: 3:   10 One Example
  98.    wt: 3:   9 Three Examples
  99.    wt: 3:   8 One Example
  100.    wt: 3:   7 Two Examples
  101.    wt: 3:   6 Three Examples
  102.    wt: 3:   5 Three Examples
  103.    wt: 3:   4 Two Examples
  104.    wt: 3:   3 Two Examples
  105.    wt: 3:   2 Three Examples
  106.    wt: 3:   Using Letters for Physical Quantities
  107.    wt: 3:   Formula Usage Show Work Format
  108.    wt: 2:   musings do not puiblish real numbers
  109.    wt: 2:   A Modular and Remainder Arithmetic
  110.    wt: 2:   A Signed Number Arithmetic Review
  111.    wt: 2:   26 More Less Greater Than Comparison
  112.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  113.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  114.    wt: 2:   23 Distributive Law Two Derivations
  115.    wt: 2:   22 Multiplication of Signed Numbers
  116.    wt: 2:   21 Addition of Multiples of a Single Vector
  117.    wt: 2:   19 Signed Multiples of Vectors
  118.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  119.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  120.    wt: 2:   15 Head to Tails in place Addition Associative
  121.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  122.    wt: 2:   13 Arrows and Vectors in a Plane
  123.    wt: 2:   12 Real Numbers Line Signed Coordinates
  124.    wt: 2:   11 Signed Number Addition and Addition Properties
  125.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  126.    wt: 2:   9 Division with Digits after Decimal Point
  127.    wt: 2:   8 Division and Mulplication of Compound Fractions
  128.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  129.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  130.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  131.    wt: 2:   4 Location of Point in Decimal Addition
  132.    wt: 2:   3 Location of Point in Decimal Multiplication
  133.    wt: 2:   2 Counting Digits in Decimal Multiplication
  134.    wt: 2:   1 Fractions with Finite Decimal Expansions
  135.    wt: 2:   E Long Division Methods more
  136.    wt: 2:   D Long Division Methods
  137.    wt: 2:   C Three Decimal Subtraction Methods
  138.    wt: 2:   B Decimal Comparison and Subtraction
  139.    wt: 2:   A Decimal Addition Columm Methods
  140.    wt: 2:   8 Column Multiplication Methods in General
  141.    wt: 2:   7 Decimals Multiplication Methods Examples
  142.    wt: 2:   6 Column Methods for Decimal Multiplication
  143.    wt: 2:   5 Distributive Law for Whole Numbers
  144.    wt: 2:   4 Commutative Law Groups Counting Form
  145.    wt: 2:   3 Multiplicative Counting Skills Principles
  146.    wt: 2:   2 Combing Counts Addition Skills and Principles
  147.    wt: 2:   1 The Counting Origins of Numbers
  148.    wt: 2:   5 Areas of Rectangles Revisited
  149.    wt: 2:   4 Fraction Operations Axiomatic Development
  150.    wt: 2:   3 Inequalities Algebraically
  151.    wt: 2:   2 Fraction Operations Physical Development
  152.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  153.    wt: 2:   5 Proportionality in Equivalent Fractions
  154.    wt: 2:   4 Rates Ratios and Proporitionality
  155.    wt: 2:   3 Proportionality Examples
  156.    wt: 2:   2 Algebraic View
  157.    wt: 2:   1 What is Proportionality
  158.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  159.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  160.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  161.    wt: 2:   6 Compound Interest Forward and Backwards
  162.    wt: 2:   5 Triangle Area Formula Backwards
  163.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  164.    wt: 2:   1 Changing Calculations
  165.    wt: 2:   6 Equations and Systems Equivalent or Implied
  166.    wt: 2:   5 Equality in Algebra
  167.    wt: 2:   4 Subtraction and Division Axioms
  168.    wt: 2:   3 Product Axioms Two Forms
  169.    wt: 2:   2 Addition and Multiplication Axioms
  170.    wt: 2:   1 Equivalent Computation Rules
  171.    wt: 2:   5 Greater More Less Than Signs in General
  172.    wt: 2:   4 Comparison of Negative Numbers
  173.    wt: 2:   3 More and Less Than with Unlike Signs
  174.    wt: 2:   2 More and Less Than for Counts and Measures
  175.    wt: 2:   1 Real Numbers Comparison
  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:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  230.    wt: 2:   Chapter 17. Area Approximation
  231.    wt: 2:   Chapter 16. Velocity Approximation
  232.    wt: 2:   Chapter 15. Slope Approximation
  233.    wt: 2:   Chapter 9 About First Courses in Calculus
  234.    wt: 2:   Fall 1983 Calculus Appetizer
  235.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  236.    wt: 2:   Chapter 3 Algebra Starter Lessons
  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:   5 Polynomials Long division Nonlinear divisor
  243.    wt: 1:   4 Polynomials Long division linear divisor
  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:   E1 Error Control Inequalities
  261.    wt: 1:   D2 Limits of Monotone Sequences
  262.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  263.    wt: 1:   C Triangle Inequalities
  264.    wt: 1:   B3 Bolzano Weierstrass Theorem
  265.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  266.    wt: 1:   PostScript For and Against Decimal Perspectives
  267.    wt: 1:   A1. Introduction
  268.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  269.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  270.    wt: 1:   Chapter 23 Links To Trigonometry
  271.    wt: 1:   Chapter 22 Complex Numbers
  272.    wt: 1:   Chapter 21 Arrow Addition
  273.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  274.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  275.    wt: 1:   Chapter 18. Slopes Areas Integration
  276.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  277.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  278.    wt: 1:   Chapter 13. Acceleration
  279.    wt: 1:   Chapter 12. Units and Slopes
  280.    wt: 1:   Chapter 11. Graphing Slope versus Position
  281.    wt: 1:   Chapter 10 Slopes and Units
  282.    wt: 1:   Chapter 8. Slope Interpretation
  283.    wt: 1:   Chapter 7 Slopes and Velocity
  284.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  285.    wt: 1:   Chapter 5. Slope Sign Tests
  286.    wt: 1:   Chapter 4. More Slope Sign Analysis
  287.    wt: 1:   Chapter 3. Slope Sign Analysis
  288.    wt: 1:   Chapter 2. Slopes and Ski Trails
  289.    wt: 1:   Chapter 1.Introduction
  290.    wt: 1:   Foreword
  291.    wt: 1:   Chapter 15. Solving Linear Equations
  292.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  293.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  294.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  295.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  296.    wt: 1:   More Algebra and Slope based Calculus Preview
  297.    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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