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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36 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:   1 Working With Sets/
  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:   2 Formula Forward Use Evaluation/
  23.    wt: 2:   Algebra Starter Lessons/
  24.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  25.    wt: 1:   8 Arithmetic with Signed Numbers/
  26.    wt: 1:   7 Arithmetic and Fractions with Units/
  27.    wt: 1:   D Decimal Long Division Methods/
  28.    wt: 1:   C Decimal Multiplication Methods/
  29.    wt: 1:   B Decimal Comparing and Subtracting Methods/
  30.    wt: 1:   A Decimal Counting and Adding Methods/
  31.    wt: 1:   2 Arithmetic with Decimals/
  32.    wt: 1:   Time Date Matters/
  33.    wt: 1:   Skills with take home value/
  34.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  35.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  36.    wt: 1:   Mathematics 506 Lessons/

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100 matches:

  1.    wt: 3:   13 Limits with Parameters and Derivatives Take II
  2.    wt: 3:   12 Limits with Parameters and Derivatives Take I
  3.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  4.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  5.    wt: 2:   4. How to add with decimals B with conversions
  6.    wt: 2:   10 Three one sided limits with infinite values
  7.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  8.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  9.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  10.    wt: 2:   Chapter 3 Algebra Starter Lessons
  11.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  12.    wt: 1:   Skills Chapter 5 Calculus
  13.    wt: 1:   2 arithmetic with signed numbers
  14.    wt: 1:   1 arithmetic with unsigned numbers
  15.    wt: 1:   the trouble with algebra
  16.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  17.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  18.    wt: 1:   Ages 12 to 14 Skills with take home value
  19.    wt: 1:   7 Functions with finite domains
  20.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  21.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  22.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  23.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  24.    wt: 1:   1 Calculator Starter Exercises
  25.    wt: 1:   7 Links Lessons Elsewhere
  26.    wt: 1:   6 Vectors with Coordinates
  27.    wt: 1:   3 Navigation with Arrows or Vectors
  28.    wt: 1:   1 Angle Measurement with Degrees
  29.    wt: 1:   4 Similarity Definition with Coordinate
  30.    wt: 1:   3 Similarity by Design with coordinates
  31.    wt: 1:   12 Links Lessons elsewhere
  32.    wt: 1:   2 Cartesian Coordinates with signs
  33.    wt: 1:   PS E Multiplication with Polar Coordinates
  34.    wt: 1:   PS D Addition with Cartesian Coordinates
  35.    wt: 1:   A Measurement with Ruler Proper Use
  36.    wt: 1:   6 Figuring with Maps Not to Scale
  37.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  38.    wt: 1:   9 Division with Digits after Decimal Point
  39.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  40.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  41.    wt: 1:   1 Fractions with Finite Decimal Expansions
  42.    wt: 1:   3 More and Less Than with Unlike Signs
  43.    wt: 1:   2 Essentially one exercises three with solution
  44.    wt: 1:   13 Naming Identifying Formulas with Words
  45.    wt: 1:   3 Counting with Sets etc
  46.    wt: 1:   2 More and Less Than with Unlike Signs
  47.    wt: 1:   5 Square Roots with primes more still
  48.    wt: 1:   4 Square Roots with primes more
  49.    wt: 1:   3 Properties of Square Roots with example
  50.    wt: 1:   2 Square Roots with Prime
  51.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  52.    wt: 1:   4 Counting with Trees Product Rule Take I
  53.    wt: 1:   3 Counting with Tables and Trees II
  54.    wt: 1:   2 Counting with Tables and Trees I
  55.    wt: 1:   6 Simplification of Fractions with Units
  56.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  57.    wt: 1:   4 Fractions with Units
  58.    wt: 1:   1 Addition and Subtraction with Units
  59.    wt: 1:   21 Working With Signs
  60.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  61.    wt: 1:   14 Adding and Subtracting with Like Denominators
  62.    wt: 1:   13 Subtraction with Additive Inverse
  63.    wt: 1:   3 Adding Movements with same direction
  64.    wt: 1:   Division with Counts and Length
  65.    wt: 1:   4 Division with 2 Digit Divsors
  66.    wt: 1:   2 Division with Single Digit Divisors
  67.    wt: 1:   C Counting Areas with Powers of Ten
  68.    wt: 1:   Subtraction with J Conversions Example
  69.    wt: 1:   8 Subtraction with Units of Measure
  70.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  71.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  72.    wt: 1:   3. How to add with decimals A sans conversions
  73.    wt: 1:   014 Counting Days with Calendars
  74.    wt: 1:   Example 4 with x function of y
  75.    wt: 1:   A Related lessons in Volume 3
  76.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  77.    wt: 1:   11 Limits at infinity Three Examples
  78.    wt: 1:   9 Limits Continuity and Composition
  79.    wt: 1:   3 Decimal insights for limits continuity convergence
  80.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  81.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  82.    wt: 1:   G.5 Motions With Bounded Velocities
  83.    wt: 1:   E2 Algebraic Properties of Limits
  84.    wt: 1:   D2 Limits of Monotone Sequences
  85.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  86.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  87.    wt: 1:   Chapter 9 About First Courses in Calculus
  88.    wt: 1:   Fall 1983 Calculus Appetizer
  89.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  90.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  91.    wt: 1:   L Skills with take home value
  92.    wt: 1:   D. Check work a must with a caution
  93.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  94.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  95.    wt: 1:   More Algebra and Slope based Calculus Preview
  96.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  97.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  98.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  99.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  100.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

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439 matches:

  1.    wt: 9:   13 Limits with Parameters and Derivatives Take II
  2.    wt: 9:   12 Limits with Parameters and Derivatives Take I
  3.    wt: 8:   10 Three one sided limits with infinite values
  4.    wt: 7:   11 Limits at infinity Three Examples
  5.    wt: 7:   9 Limits Continuity and Composition
  6.    wt: 7:   3 Decimal insights for limits continuity convergence
  7.    wt: 6:   Example 4 with x function of y
  8.    wt: 6:   A Related lessons in Volume 3
  9.    wt: 6:   1 Two cubic sketching exercises with 1st derivative
  10.    wt: 6:   8 Four Animated Examples
  11.    wt: 6:   7 Evaluation by immediate or delayed substitution
  12.    wt: 6:   6 Continuity at a point
  13.    wt: 6:   5 Jumps and absence of unlimited error control
  14.    wt: 6:   4 Numerical properties
  15.    wt: 6:   2 Algebraic codification
  16.    wt: 6:   1 Numerical introduction
  17.    wt: 5:   Example 2 volume of a cone
  18.    wt: 5:   Example 1 volume of a pyramid
  19.    wt: 5:   Volume of Solid by Cross Sections Lesson
  20.    wt: 5:   Example 1. Area Between x and x squared
  21.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  22.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  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:   4 Definite Integrals Evaluation Exercises
  32.    wt: 5:   3 Two Chain Rule Method Exercises
  33.    wt: 5:   2 Indefinite Integrals Exercises
  34.    wt: 5:   1 Chain Rule in Reverse Integration Method
  35.    wt: 5:   4 Second derivative test exercise example
  36.    wt: 5:   3 Second derivative test
  37.    wt: 5:   2 Second derivative test prequel
  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:   3 Counting with Sets etc
  75.    wt: 3:   17 Arrows Rotate to Reverse with Length Unchanged
  76.    wt: 3:   9 Division with Digits after Decimal Point
  77.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  78.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  79.    wt: 3:   1 Fractions with Finite Decimal Expansions
  80.    wt: 3:   3 More and Less Than with Unlike Signs
  81.    wt: 3:   2 Essentially one exercises three with solution
  82.    wt: 3:   13 Naming Identifying Formulas with Words
  83.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  84.    wt: 3:   9 Sets in Probability and Statistics
  85.    wt: 3:   8 Sets of Numbers
  86.    wt: 3:   7 Cautious or Safe Set Construction
  87.    wt: 3:   6 Power Set Notation
  88.    wt: 3:   5 Product Builder Notation
  89.    wt: 3:   4 Subset Builder Notation
  90.    wt: 3:   2 Venn Diagrams
  91.    wt: 3:   1 Finite Sets
  92.    wt: 3:   6 Subtraction with Conversion Example with Exercises
  93.    wt: 3:   4. How to add with decimals B with conversions
  94.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  95.    wt: 2:   musings do not puiblish real numbers
  96.    wt: 2:   A Modular and Remainder Arithmetic
  97.    wt: 2:   A Signed Number Arithmetic Review
  98.    wt: 2:   26 More Less Greater Than Comparison
  99.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  100.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  101.    wt: 2:   23 Distributive Law Two Derivations
  102.    wt: 2:   22 Multiplication of Signed Numbers
  103.    wt: 2:   21 Addition of Multiples of a Single Vector
  104.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  105.    wt: 2:   19 Signed Multiples of Vectors
  106.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  107.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  108.    wt: 2:   15 Head to Tails in place Addition Associative
  109.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  110.    wt: 2:   13 Arrows and Vectors in a Plane
  111.    wt: 2:   12 Real Numbers Line Signed Coordinates
  112.    wt: 2:   11 Signed Number Addition and Addition Properties
  113.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  114.    wt: 2:   8 Division and Mulplication of Compound Fractions
  115.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  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:   E Long Division Methods more
  120.    wt: 2:   D Long Division Methods
  121.    wt: 2:   C Three Decimal Subtraction Methods
  122.    wt: 2:   B Decimal Comparison and Subtraction
  123.    wt: 2:   A Decimal Addition Columm Methods
  124.    wt: 2:   8 Column Multiplication Methods in General
  125.    wt: 2:   7 Decimals Multiplication Methods Examples
  126.    wt: 2:   6 Column Methods for Decimal Multiplication
  127.    wt: 2:   5 Distributive Law for Whole Numbers
  128.    wt: 2:   4 Commutative Law Groups Counting Form
  129.    wt: 2:   3 Multiplicative Counting Skills Principles
  130.    wt: 2:   2 Combing Counts Addition Skills and Principles
  131.    wt: 2:   1 The Counting Origins of Numbers
  132.    wt: 2:   5 Areas of Rectangles Revisited
  133.    wt: 2:   4 Fraction Operations Axiomatic Development
  134.    wt: 2:   3 Inequalities Algebraically
  135.    wt: 2:   2 Fraction Operations Physical Development
  136.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  137.    wt: 2:   5 Proportionality in Equivalent Fractions
  138.    wt: 2:   4 Rates Ratios and Proporitionality
  139.    wt: 2:   3 Proportionality Examples
  140.    wt: 2:   2 Algebraic View
  141.    wt: 2:   1 What is Proportionality
  142.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  143.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  144.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  145.    wt: 2:   6 Compound Interest Forward and Backwards
  146.    wt: 2:   5 Triangle Area Formula Backwards
  147.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  148.    wt: 2:   3 Linear Equation Literal Solution More
  149.    wt: 2:   2 Linear Equation Literal Solution
  150.    wt: 2:   1 Changing Calculations
  151.    wt: 2:   6 Equations and Systems Equivalent or Implied
  152.    wt: 2:   5 Equality in Algebra
  153.    wt: 2:   4 Subtraction and Division Axioms
  154.    wt: 2:   3 Product Axioms Two Forms
  155.    wt: 2:   2 Addition and Multiplication Axioms
  156.    wt: 2:   1 Equivalent Computation Rules
  157.    wt: 2:   5 Greater More Less Than Signs in General
  158.    wt: 2:   4 Comparison of Negative Numbers
  159.    wt: 2:   2 More and Less Than for Counts and Measures
  160.    wt: 2:   1 Real Numbers Comparison
  161.    wt: 2:   16 Real Numbers Comparison
  162.    wt: 2:   15 Real Number Division
  163.    wt: 2:   14 Real Number Multiplication
  164.    wt: 2:   13 Real Number Subtraction
  165.    wt: 2:   12 Real Number Additive Inverses or Negatives
  166.    wt: 2:   11 Real Number Addition
  167.    wt: 2:   10 Real Number Lengths and Signs
  168.    wt: 2:   9 Coordinates for Regions in Space
  169.    wt: 2:   8 Coordinates for Maps and Planes
  170.    wt: 2:   7 Real Numbers as Line Cordinates
  171.    wt: 2:   6 Unsigned Real Numbers
  172.    wt: 2:   5 Rational Numbers More
  173.    wt: 2:   4 Rational Numbers
  174.    wt: 2:   3 Fractions
  175.    wt: 2:   2 Integers
  176.    wt: 2:   1 Whole and Natural Numbers
  177.    wt: 2:   5 Independent versus Dependent Variables
  178.    wt: 2:   4 Changing Letters
  179.    wt: 2:   3 Geometric Formulas and Function Notation
  180.    wt: 2:   2 Computation Rules Evaluation
  181.    wt: 2:   1 Formulas Dependence and Function Notation
  182.    wt: 2:   More Exercises
  183.    wt: 2:   Simple Exercises
  184.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  185.    wt: 2:   4 GE III Animated Examples
  186.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  187.    wt: 2:   3 GE III Equation Addition and Multiplication
  188.    wt: 2:   2 GE II Comparison
  189.    wt: 2:   1 GE Substitution four examples
  190.    wt: 2:   4 Solving a triangular system exercise
  191.    wt: 2:   3 Solving triangular system example
  192.    wt: 2:   1 Essentially One Unknown
  193.    wt: 2:   6 Algebraic Solution Example
  194.    wt: 2:   5 Algebraic Solutions Introduction
  195.    wt: 2:   4 Four Examples Fractional Coefficients
  196.    wt: 2:   3 Four Examples
  197.    wt: 2:   2 Three Examples
  198.    wt: 2:   1 Proper Equal Sign Usage
  199.    wt: 2:   Skill Development Notes
  200.    wt: 2:   10 One Example
  201.    wt: 2:   9 Three Examples
  202.    wt: 2:   8 One Example
  203.    wt: 2:   7 Two Examples
  204.    wt: 2:   6 Three Examples
  205.    wt: 2:   5 Three Examples
  206.    wt: 2:   4 Two Examples
  207.    wt: 2:   3 Two Examples
  208.    wt: 2:   2 Three Examples
  209.    wt: 2:   Using Letters for Physical Quantities
  210.    wt: 2:   Formula Usage Show Work Format
  211.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  212.    wt: 2:   11 Volume of Sphere
  213.    wt: 2:   10 Volume of Pyramid
  214.    wt: 2:   9 Volume of Cone
  215.    wt: 2:   8 Compound Interest Formula Evaluation
  216.    wt: 2:   7 Compound Interest Formula Introduction
  217.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  218.    wt: 2:   5 Box Volume Formula Example
  219.    wt: 2:   4 Circle Area Formula Example
  220.    wt: 2:   3 Triangle Area Formula Example
  221.    wt: 2:   2 Another Rectangle Area Formula Example
  222.    wt: 2:   1 Written work formats for developing and showing skill
  223.    wt: 2:   6 Three Notions of What is a Variable
  224.    wt: 2:   5 Talking about Numbers and Quantities
  225.    wt: 2:   4 A Brief Story of numbers and algebra
  226.    wt: 2:   3 Adding Words To Arithmetic
  227.    wt: 2:   2 What is a Variable
  228.    wt: 2:   1 Three Skills For Algebra
  229.    wt: 2:   About Folder Contents
  230.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  231.    wt: 2:   6 Simplification of Fractions with Units
  232.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  233.    wt: 2:   4 Fractions with Units
  234.    wt: 2:   1 Addition and Subtraction with Units
  235.    wt: 2:   Division with Counts and Length
  236.    wt: 2:   4 Division with 2 Digit Divsors
  237.    wt: 2:   2 Division with Single Digit Divisors
  238.    wt: 2:   C Counting Areas with Powers of Ten
  239.    wt: 2:   Subtraction with J Conversions Example
  240.    wt: 2:   8 Subtraction with Units of Measure
  241.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  242.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  243.    wt: 2:   3. How to add with decimals A sans conversions
  244.    wt: 2:   014 Counting Days with Calendars
  245.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  246.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  247.    wt: 2:   G.5 Motions With Bounded Velocities
  248.    wt: 2:   E2 Algebraic Properties of Limits
  249.    wt: 2:   D2 Limits of Monotone Sequences
  250.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  251.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  252.    wt: 2:   Chapter 9 About First Courses in Calculus
  253.    wt: 2:   Fall 1983 Calculus Appetizer
  254.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  255.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  256.    wt: 2:   Chapter 3 Algebra Starter Lessons
  257.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  258.    wt: 1:   Skills Chapter 5 Calculus
  259.    wt: 1:   2 arithmetic with signed numbers
  260.    wt: 1:   1 arithmetic with unsigned numbers
  261.    wt: 1:   the trouble with algebra
  262.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  263.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  264.    wt: 1:   Ages 12 to 14 Skills with take home value
  265.    wt: 1:   7 Functions with finite domains
  266.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  267.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  268.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  269.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  270.    wt: 1:   1 Calculator Starter Exercises
  271.    wt: 1:   7 Links Lessons Elsewhere
  272.    wt: 1:   6 Vectors with Coordinates
  273.    wt: 1:   3 Navigation with Arrows or Vectors
  274.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  275.    wt: 1:   C Straight Lines Slope from Coordinates
  276.    wt: 1:   B Straight Line Slope Scaling Properties More
  277.    wt: 1:   A Straight Line Slope Scaling Properties
  278.    wt: 1:   14 Straight Lines Equations General Case
  279.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  280.    wt: 1:   12 Straight Lines Graphing mx plus b
  281.    wt: 1:   11 Straight Lines Graphing y=mx
  282.    wt: 1:   10 Straight Lines through Origin Equations More
  283.    wt: 1:   9 Straight Lines through Origin Equations
  284.    wt: 1:   8 Straight Lines Equation for vertical
  285.    wt: 1:   7 Tangent Function is odd on this domain
  286.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  287.    wt: 1:   5 Tangent Function Graph
  288.    wt: 1:   4 Tangent Function Properties
  289.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  290.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  291.    wt: 1:   1 Straight Lines Slope Concept
  292.    wt: 1:   1 Angle Measurement with Degrees
  293.    wt: 1:   4 Similarity Definition with Coordinate
  294.    wt: 1:   3 Similarity by Design with coordinates
  295.    wt: 1:   12 Links Lessons elsewhere
  296.    wt: 1:   2 Cartesian Coordinates with signs
  297.    wt: 1:   PS E Multiplication with Polar Coordinates
  298.    wt: 1:   PS D Addition with Cartesian Coordinates
  299.    wt: 1:   A Measurement with Ruler Proper Use
  300.    wt: 1:   6 Figuring with Maps Not to Scale
  301.    wt: 1:   2 More and Less Than with Unlike Signs
  302.    wt: 1:   5 Square Roots with primes more still
  303.    wt: 1:   4 Square Roots with primes more
  304.    wt: 1:   3 Properties of Square Roots with example
  305.    wt: 1:   2 Square Roots with Prime
  306.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  307.    wt: 1:   4 Counting with Trees Product Rule Take I
  308.    wt: 1:   3 Counting with Tables and Trees II
  309.    wt: 1:   2 Counting with Tables and Trees I
  310.    wt: 1:   11 What are real lengths and numbers
  311.    wt: 1:   10 dividing signed numbers
  312.    wt: 1:   9 subtracting signed numbers
  313.    wt: 1:   8 multiplying signed numbers
  314.    wt: 1:   7 negative and additive inverse
  315.    wt: 1:   6 adding signed numbers
  316.    wt: 1:   5 lengths and signs of numbers
  317.    wt: 1:   4 signed coordinates for regions in space
  318.    wt: 1:   3 signed coordinates for maps and planes
  319.    wt: 1:   2 signed and unsigned numbers as coordinates
  320.    wt: 1:   7 Converting or Changing Units
  321.    wt: 1:   3 Multiplying Units and Numbers
  322.    wt: 1:   2 Equality and Units
  323.    wt: 1:   21 Working With Signs
  324.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  325.    wt: 1:   14 Adding and Subtracting with Like Denominators
  326.    wt: 1:   13 Subtraction with Additive Inverse
  327.    wt: 1:   3 Adding Movements with same direction
  328.    wt: 1:   Long Division Backwards more
  329.    wt: 1:   Long Division Backward
  330.    wt: 1:   Long Division forwards and backwards Example 3
  331.    wt: 1:   Long Division forwards and backwards Example 2
  332.    wt: 1:   Long Division forwards and backwards Example 1
  333.    wt: 1:   12 Why Long Division Works Take III
  334.    wt: 1:   11 Another Single Digit Divisor Example
  335.    wt: 1:   10 Division by Five Long and Short Ways
  336.    wt: 1:   9 Why Long Division Works Take II
  337.    wt: 1:   8 Correcting the Mistake
  338.    wt: 1:   7 Long Divison Mistake Catching
  339.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  340.    wt: 1:   5 Long Division Include Zeroes or not
  341.    wt: 1:   3 Division Single Digit Divisor Example
  342.    wt: 1:   1 Divsion Physical Examples
  343.    wt: 1:   D Decimal Multiplication Methods Derived
  344.    wt: 1:   B Powers of Ten
  345.    wt: 1:   A Elementary Basis for Multiplication Methods
  346.    wt: 1:   6 Multiplication Commutes Order Not Important
  347.    wt: 1:   5 Decimal Fraction Multiplication
  348.    wt: 1:   4 Two and Three Digit Multipliers
  349.    wt: 1:   3 More One Digit Multipliers
  350.    wt: 1:   2 One Digit Multipliers
  351.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  352.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  353.    wt: 1:   Video Power Notation in Decimal Expansion
  354.    wt: 1:   1 Why 3 times 5 gives 15
  355.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  356.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  357.    wt: 1:   Subtraction Another Video Lesson
  358.    wt: 1:   9 22 Minute Subtraction Review Video
  359.    wt: 1:   5 A Tip for Efficent Subtraction
  360.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  361.    wt: 1:   2 Subtraction Easy Case Examples
  362.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  363.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  364.    wt: 1:   8 What skills and work habits to require
  365.    wt: 1:   7 Adding decimal fractions using decimal point
  366.    wt: 1:   6. Counting and adding units and mixed units
  367.    wt: 1:   5. How to add decimals C. Examples
  368.    wt: 1:   2 Decimal Counting Practices
  369.    wt: 1:   1. Explaining Addition Table
  370.    wt: 1:   016 Numbering Occidental Calendar Days
  371.    wt: 1:   015 School and work day counting tables
  372.    wt: 1:   013 Travel Time Tables
  373.    wt: 1:   012 Division of Time Intervals by Time Intervals
  374.    wt: 1:   011 Division of Time Intervals By Numbers
  375.    wt: 1:   010 Repeated Addition of Time Intervals
  376.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  377.    wt: 1:   8 Addition of Time Intervals via subtotaling
  378.    wt: 1:   7 Addition of Time Intervals
  379.    wt: 1:   6 How long is a million seconds
  380.    wt: 1:   5 Conversion Arithmetic
  381.    wt: 1:   4 Mixing and Changing Units of Time
  382.    wt: 1:   3 Units and Lengths of Time
  383.    wt: 1:   2 Time and Date Matters in School
  384.    wt: 1:   1 Intro of Kids To Time Date Skills
  385.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  386.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  387.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  388.    wt: 1:   G.3 Constant Difference Theorem Proof
  389.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  390.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  391.    wt: 1:   F.5b Extreme Value Theorem
  392.    wt: 1:   F.5a Equicontinuity Theorems
  393.    wt: 1:   F.4 Finite Covering Theorem
  394.    wt: 1:   F.3 Intermediate Value Theorem
  395.    wt: 1:   F.2 Closed Range Theorem
  396.    wt: 1:   F.1 What Functions are Continuous
  397.    wt: 1:   E1 Error Control Inequalities
  398.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  399.    wt: 1:   C Triangle Inequalities
  400.    wt: 1:   B3 Bolzano Weierstrass Theorem
  401.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  402.    wt: 1:   PostScript For and Against Decimal Perspectives
  403.    wt: 1:   A1. Introduction
  404.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  405.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  406.    wt: 1:   Chapter 23 Links To Trigonometry
  407.    wt: 1:   Chapter 22 Complex Numbers
  408.    wt: 1:   Chapter 21 Arrow Addition
  409.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  410.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  411.    wt: 1:   Chapter 18. Slopes Areas Integration
  412.    wt: 1:   Chapter 17. Area Approximation
  413.    wt: 1:   Chapter 16. Velocity Approximation
  414.    wt: 1:   Chapter 15. Slope Approximation
  415.    wt: 1:   Chapter 13. Acceleration
  416.    wt: 1:   Chapter 12. Units and Slopes
  417.    wt: 1:   Chapter 11. Graphing Slope versus Position
  418.    wt: 1:   Chapter 10 Slopes and Units
  419.    wt: 1:   Chapter 8. Slope Interpretation
  420.    wt: 1:   Chapter 7 Slopes and Velocity
  421.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  422.    wt: 1:   Chapter 5. Slope Sign Tests
  423.    wt: 1:   Chapter 4. More Slope Sign Analysis
  424.    wt: 1:   Chapter 3. Slope Sign Analysis
  425.    wt: 1:   Chapter 2. Slopes and Ski Trails
  426.    wt: 1:   Chapter 1.Introduction
  427.    wt: 1:   Foreword
  428.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  429.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  430.    wt: 1:   L Skills with take home value
  431.    wt: 1:   D. Check work a must with a caution
  432.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  433.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  434.    wt: 1:   More Algebra and Slope based Calculus Preview
  435.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  436.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  437.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  438.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  439.    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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