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.

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29 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:   A Origins of Counting and Figuring Methods/
  8.    wt: 3:   10 Examples of Algebraic Reasoning/
  9.    wt: 2:   B Real Numbers Extrinsic Development/
  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:   4 Functions/
  25.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  26.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  27.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  28.    wt: 1:   Volume 1 Elements of Reason/
  29.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

202 matches:

  1.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  2.    wt: 2:   15 Sign analysis of functions
  3.    wt: 2:   8 Set view of relations and functions
  4.    wt: 2:   7 Functions with finite domains
  5.    wt: 2:   4 Resultant of a Sum of Movements
  6.    wt: 2:   30 unit circle calculation of six trigonometric functions
  7.    wt: 2:   27 Logarithmic use of products of sines and cosines
  8.    wt: 2:   5 An Easy Proof of the Distributive Law
  9.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  10.    wt: 2:   21 Addition of Multiples of a Single Vector
  11.    wt: 2:   31 Derivatives of inverse functions
  12.    wt: 2:   17 Derivatives of quotients of sine and cosine
  13.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  14.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  15.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  16.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  17.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  18.    wt: 2:   Chapter 3 Algebra Starter Lessons
  19.    wt: 1:   Skills Chapter 5 Calculus
  20.    wt: 1:   Mathematics Education Professors
  21.    wt: 1:   Theory of Knowledge
  22.    wt: 1:   Different Kinds of Reasoning in maths
  23.    wt: 1:   three kinds of reason in mathematics
  24.    wt: 1:   E Kirchoffs Second Law
  25.    wt: 1:   D Kirchoff First Law
  26.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  27.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  28.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  29.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  30.    wt: 1:   8 The Effect of Negative Remarks
  31.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  32.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  33.    wt: 1:   23 Inverse Functions
  34.    wt: 1:   2 Algebraic use of function notation
  35.    wt: 1:   1 Geometric Introduction of Function Notation
  36.    wt: 1:   8 quadratics backward use of various formulas
  37.    wt: 1:   4 quadratics difference of two squares
  38.    wt: 1:   1 Calculator Starter Exercises
  39.    wt: 1:   7 Links Lessons Elsewhere
  40.    wt: 1:   11 arctan left inverse of tangent Graph
  41.    wt: 1:   10 arctan left inverse of tangent Definition
  42.    wt: 1:   8 arcsin left inverse of sine Graph
  43.    wt: 1:   7 arcsin left inverse of sine Definition
  44.    wt: 1:   6 Graph of arccos function
  45.    wt: 1:   3 Left Inverse of cosine arccos definition
  46.    wt: 1:   8 Radian Measures of Common Angles
  47.    wt: 1:   2 Radian Measure Numerical Value of one degree
  48.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  49.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  50.    wt: 1:   Straight Lines Intersection of
  51.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  52.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  53.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  54.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  55.    wt: 1:   32 seven rows of pascals triangle
  56.    wt: 1:   28 Expressing products of sines cosines as sums
  57.    wt: 1:   26 Formulas for products of sines and cosines
  58.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  59.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  60.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  61.    wt: 1:   18 sum of sinusoidal waves as a single wave
  62.    wt: 1:   17F Law of cosines
  63.    wt: 1:   13 Graph of tangent function many periods
  64.    wt: 1:   12 Graph of tangent function for one period
  65.    wt: 1:   10 Graphs of sines and cosines many periods
  66.    wt: 1:   9 Graphs of sine and cosine over one period
  67.    wt: 1:   8 period of tangent function
  68.    wt: 1:   7 period of sine and cosine
  69.    wt: 1:   Unit Circle Development of Trigonometry
  70.    wt: 1:   20 N th Roots of Complex Numbers
  71.    wt: 1:   19 N th Roots of Unity
  72.    wt: 1:   18 Sixth Roots of Unity
  73.    wt: 1:   17 Cube Roots of unity
  74.    wt: 1:   14 Law of cosines
  75.    wt: 1:   8 Unit Circle Development of Trigonometry
  76.    wt: 1:   6 Field Properties of Complex Number
  77.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  78.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  79.    wt: 1:   9 Similarity of Triangles Usual Criteria
  80.    wt: 1:   8 Similarity of Triangles and Polygons
  81.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  82.    wt: 1:   1 Early Concept of Like or Similar Shapes
  83.    wt: 1:   12 Links Lessons elsewhere
  84.    wt: 1:   10 Midpoint of [a b] and [b a]
  85.    wt: 1:   6 Intersection of lines by solving linear systems
  86.    wt: 1:   5 Algebraic View of Slopes
  87.    wt: 1:   1 Numerical view of lines and their equations
  88.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  89.    wt: 1:   17 Right Bisectors of Triangle Sides
  90.    wt: 1:   9 Construction of a right bisector
  91.    wt: 1:   3 Isometry of Triangles Congruence
  92.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  93.    wt: 1:   22 Multiplication of Signed Numbers
  94.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  95.    wt: 1:   19 Signed Multiples of Vectors
  96.    wt: 1:   8 Division and Mulplication of Compound Fractions
  97.    wt: 1:   4 Location of Point in Decimal Addition
  98.    wt: 1:   3 Location of Point in Decimal Multiplication
  99.    wt: 1:   1 The Counting Origins of Numbers
  100.    wt: 1:   5 Areas of Rectangles Revisited
  101.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  102.    wt: 1:   4 Comparison of Negative Numbers
  103.    wt: 1:   11 Volume of Sphere
  104.    wt: 1:   10 Volume of Pyramid
  105.    wt: 1:   9 Volume of Cone
  106.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  107.    wt: 1:   8 Sets of Numbers
  108.    wt: 1:   6 Three Notions of What is a Variable
  109.    wt: 1:   4 A Brief Story of numbers and algebra
  110.    wt: 1:   3 Comparison of Negative Numbers
  111.    wt: 1:   3 Properties of Square Roots with example
  112.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  113.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  114.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  115.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  116.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  117.    wt: 1:   4 LCM of 8 and 10 via Prime
  118.    wt: 1:   5 lengths and signs of numbers
  119.    wt: 1:   6 Simplification of Fractions with Units
  120.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  121.    wt: 1:   6 Multiplication of Mixed Numbers
  122.    wt: 1:   3 Unit fraction of a fraction
  123.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  124.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  125.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  126.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  127.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  128.    wt: 1:   20 Uniqueness of Prime Factorization
  129.    wt: 1:   16 video Factors of 980 using prime
  130.    wt: 1:   15 video Factors of 20 using Prime Factorization
  131.    wt: 1:   14 video Factors of 24 Take II
  132.    wt: 1:   13 video Factors of 24 using prime
  133.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  134.    wt: 1:   C Counting Areas with Powers of Ten
  135.    wt: 1:   B Powers of Ten
  136.    wt: 1:   8 Subtraction with Units of Measure
  137.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  138.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  139.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  140.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  141.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  142.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  143.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  144.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  145.    wt: 1:   Quick history of numbers and algebra
  146.    wt: 1:   012 Division of Time Intervals by Time Intervals
  147.    wt: 1:   011 Division of Time Intervals By Numbers
  148.    wt: 1:   010 Repeated Addition of Time Intervals
  149.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  150.    wt: 1:   8 Addition of Time Intervals via subtotaling
  151.    wt: 1:   7 Addition of Time Intervals
  152.    wt: 1:   4 Mixing and Changing Units of Time
  153.    wt: 1:   3 Units and Lengths of Time
  154.    wt: 1:   1 Intro of Kids To Time Date Skills
  155.    wt: 1:   Example 2 volume of a cone
  156.    wt: 1:   Example 1 volume of a pyramid
  157.    wt: 1:   Volume of Solid by Cross Sections Lesson
  158.    wt: 1:   Example 4 with x function of y
  159.    wt: 1:   A Related lessons in Volume 3
  160.    wt: 1:   34 Derivative of exponential function
  161.    wt: 1:   30Chain Rule A Proof
  162.    wt: 1:   28 Chain Rule Preparation for a Proof
  163.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  164.    wt: 1:   26 Chain Rule Recognising outer inner functions
  165.    wt: 1:   19 Chain Rule for linear functions
  166.    wt: 1:   8 Differentiation of polynomials
  167.    wt: 1:   5 Jumps and absence of unlimited error control
  168.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  169.    wt: 1:   G.3 Constant Difference Theorem Proof
  170.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  171.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  172.    wt: 1:   F.1 What Functions are Continuous
  173.    wt: 1:   E2 Algebraic Properties of Limits
  174.    wt: 1:   D2 Limits of Monotone Sequences
  175.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  176.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  177.    wt: 1:   Chapter 9 About First Courses in Calculus
  178.    wt: 1:   Fall 1983 Calculus Appetizer
  179.    wt: 1:   Chapter 19. Functions and Sets
  180.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  181.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  182.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  183.    wt: 1:   Chapter 6 Change of Language
  184.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  185.    wt: 1:   Chapter 4 Longer Chains of Reason
  186.    wt: 1:   Chapter 3 Chains of Reason
  187.    wt: 1:   Chapter 7 Two Treatments of Geometry
  188.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  189.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  190.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  191.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  192.    wt: 1:   Chapter 8 Change of Language
  193.    wt: 1:   Chapter 7 Longer Chains of Reason
  194.    wt: 1:   Chapter 6 Chains of Reason
  195.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  196.    wt: 1:   C. Domino effect of being careful
  197.    wt: 1:   B. Domino effect of errors
  198.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  199.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  200.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  201.    wt: 1:   More Algebra and Slope based Calculus Preview
  202.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

455 matches:

  1.    wt: 7:   31 Derivatives of inverse functions
  2.    wt: 7:   17 Derivatives of quotients of sine and cosine
  3.    wt: 7:   16 Derivatives of reciprocals of sine and cosine
  4.    wt: 6:   Example 2 volume of a cone
  5.    wt: 6:   Example 1 volume of a pyramid
  6.    wt: 6:   Volume of Solid by Cross Sections Lesson
  7.    wt: 6:   Example 4 with x function of y
  8.    wt: 6:   A Related lessons in Volume 3
  9.    wt: 6:   34 Derivative of exponential function
  10.    wt: 6:   30Chain Rule A Proof
  11.    wt: 6:   28 Chain Rule Preparation for a Proof
  12.    wt: 6:   27 Chain Rule sinusoidal outer inner functions EGS
  13.    wt: 6:   26 Chain Rule Recognising outer inner functions
  14.    wt: 6:   19 Chain Rule for linear functions
  15.    wt: 6:   8 Differentiation of polynomials
  16.    wt: 6:   5 Jumps and absence of unlimited error control
  17.    wt: 5:   Example 1. Area Between x and x squared
  18.    wt: 5:   Area Between Crossing Curves Lesson Take 2
  19.    wt: 5:   Area Between Crossing Curves Lesson Take 1
  20.    wt: 5:   Example 3
  21.    wt: 5:   Example 2
  22.    wt: 5:   Example 1
  23.    wt: 5:   Area Between Curves Lesson Take 2
  24.    wt: 5:   Area Between Curves Lesson Take 1
  25.    wt: 5:   Summary
  26.    wt: 5:   A Related Material in Volume 3
  27.    wt: 5:   5 Area Under Curve Exercise
  28.    wt: 5:   4 Definite Integrals Evaluation Exercises
  29.    wt: 5:   3 Two Chain Rule Method Exercises
  30.    wt: 5:   2 Indefinite Integrals Exercises
  31.    wt: 5:   1 Chain Rule in Reverse Integration Method
  32.    wt: 5:   4 Second derivative test exercise example
  33.    wt: 5:   3 Second derivative test
  34.    wt: 5:   2 Second derivative test prequel
  35.    wt: 5:   1 Two cubic sketching exercises with 1st derivative
  36.    wt: 5:   A Chain Rule Real Player video examples
  37.    wt: 5:   38 Formulas and derivatives for powers and roots
  38.    wt: 5:   36 Cube root derivative animated
  39.    wt: 5:   33 Chain Rule Real Player video examples
  40.    wt: 5:   29 Chain Rule Optional Reading
  41.    wt: 5:   25 Chain Rule Animated Examples Continued
  42.    wt: 5:   24 Chain Rule Animated Examples
  43.    wt: 5:   23 Chain Rule in general
  44.    wt: 5:   22 Chain Rule for polynomials
  45.    wt: 5:   21 Chain Rule for powers
  46.    wt: 5:   20 Chain Rule for Pulley Systems
  47.    wt: 5:   18 Chain Rule Introduction
  48.    wt: 5:   15 sine and cosine derivatives 3rd step
  49.    wt: 5:   14 sine and cosine derivatives 2nd step
  50.    wt: 5:   13 sine and cosine derivatives 1st step
  51.    wt: 5:   12 Quotient rule examples
  52.    wt: 5:   11 Quotient rule
  53.    wt: 5:   10 Power rule for negative integers
  54.    wt: 5:   9 Reciprocal rule
  55.    wt: 5:   7 Animated Differentiation Examples
  56.    wt: 5:   6 Power rule from product rule
  57.    wt: 5:   5 Product Rule
  58.    wt: 5:   4 Sum Rule
  59.    wt: 5:   3 Motivation for Limit Definition Take 2
  60.    wt: 5:   2 Motivation for Limit Definition Take 1
  61.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  62.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  63.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  64.    wt: 5:   11 Limits at infinity Three Examples
  65.    wt: 5:   10 Three one sided limits with infinite values
  66.    wt: 5:   9 Limits Continuity and Composition
  67.    wt: 5:   8 Four Animated Examples
  68.    wt: 5:   7 Evaluation by immediate or delayed substitution
  69.    wt: 5:   6 Continuity at a point
  70.    wt: 5:   4 Numerical properties
  71.    wt: 5:   3 Decimal insights for limits continuity convergence
  72.    wt: 5:   2 Algebraic codification
  73.    wt: 5:   1 Numerical introduction
  74.    wt: 4:   21 Addition of Multiples of a Single Vector
  75.    wt: 4:   1 The Counting Origins of Numbers
  76.    wt: 4:   5 Areas of Rectangles Revisited
  77.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  78.    wt: 3:   15 Sign analysis of functions
  79.    wt: 3:   8 Set view of relations and functions
  80.    wt: 3:   7 Functions with finite domains
  81.    wt: 3:   22 Multiplication of Signed Numbers
  82.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  83.    wt: 3:   19 Signed Multiples of Vectors
  84.    wt: 3:   8 Division and Mulplication of Compound Fractions
  85.    wt: 3:   4 Location of Point in Decimal Addition
  86.    wt: 3:   3 Location of Point in Decimal Multiplication
  87.    wt: 3:   E Long Division Methods more
  88.    wt: 3:   D Long Division Methods
  89.    wt: 3:   C Three Decimal Subtraction Methods
  90.    wt: 3:   B Decimal Comparison and Subtraction
  91.    wt: 3:   A Decimal Addition Columm Methods
  92.    wt: 3:   8 Column Multiplication Methods in General
  93.    wt: 3:   7 Decimals Multiplication Methods Examples
  94.    wt: 3:   6 Column Methods for Decimal Multiplication
  95.    wt: 3:   5 Distributive Law for Whole Numbers
  96.    wt: 3:   4 Commutative Law Groups Counting Form
  97.    wt: 3:   3 Multiplicative Counting Skills Principles
  98.    wt: 3:   2 Combing Counts Addition Skills and Principles
  99.    wt: 3:   4 Fraction Operations Axiomatic Development
  100.    wt: 3:   3 Inequalities Algebraically
  101.    wt: 3:   2 Fraction Operations Physical Development
  102.    wt: 3:   1 Decimals Modular and Remainder Arithmetic
  103.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  104.    wt: 3:   4 Comparison of Negative Numbers
  105.    wt: 3:   11 Volume of Sphere
  106.    wt: 3:   10 Volume of Pyramid
  107.    wt: 3:   9 Volume of Cone
  108.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  109.    wt: 3:   8 Sets of Numbers
  110.    wt: 3:   6 Three Notions of What is a Variable
  111.    wt: 3:   4 A Brief Story of numbers and algebra
  112.    wt: 3:   G.1 First Fundamental Theorem of Calculus
  113.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  114.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  115.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  116.    wt: 2:   23 Inverse Functions
  117.    wt: 2:   2 Algebraic use of function notation
  118.    wt: 2:   1 Geometric Introduction of Function Notation
  119.    wt: 2:   4 Resultant of a Sum of Movements
  120.    wt: 2:   30 unit circle calculation of six trigonometric functions
  121.    wt: 2:   27 Logarithmic use of products of sines and cosines
  122.    wt: 2:   5 An Easy Proof of the Distributive Law
  123.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  124.    wt: 2:   musings do not puiblish real numbers
  125.    wt: 2:   A Modular and Remainder Arithmetic
  126.    wt: 2:   A Signed Number Arithmetic Review
  127.    wt: 2:   26 More Less Greater Than Comparison
  128.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  129.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  130.    wt: 2:   23 Distributive Law Two Derivations
  131.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  132.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  133.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  134.    wt: 2:   15 Head to Tails in place Addition Associative
  135.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  136.    wt: 2:   13 Arrows and Vectors in a Plane
  137.    wt: 2:   12 Real Numbers Line Signed Coordinates
  138.    wt: 2:   11 Signed Number Addition and Addition Properties
  139.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  140.    wt: 2:   9 Division with Digits after Decimal Point
  141.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  142.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  143.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  144.    wt: 2:   2 Counting Digits in Decimal Multiplication
  145.    wt: 2:   1 Fractions with Finite Decimal Expansions
  146.    wt: 2:   5 Proportionality in Equivalent Fractions
  147.    wt: 2:   4 Rates Ratios and Proporitionality
  148.    wt: 2:   3 Proportionality Examples
  149.    wt: 2:   2 Algebraic View
  150.    wt: 2:   1 What is Proportionality
  151.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  152.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  153.    wt: 2:   6 Compound Interest Forward and Backwards
  154.    wt: 2:   5 Triangle Area Formula Backwards
  155.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  156.    wt: 2:   3 Linear Equation Literal Solution More
  157.    wt: 2:   2 Linear Equation Literal Solution
  158.    wt: 2:   1 Changing Calculations
  159.    wt: 2:   6 Equations and Systems Equivalent or Implied
  160.    wt: 2:   5 Equality in Algebra
  161.    wt: 2:   4 Subtraction and Division Axioms
  162.    wt: 2:   3 Product Axioms Two Forms
  163.    wt: 2:   2 Addition and Multiplication Axioms
  164.    wt: 2:   1 Equivalent Computation Rules
  165.    wt: 2:   5 Greater More Less Than Signs in General
  166.    wt: 2:   3 More and Less Than with Unlike Signs
  167.    wt: 2:   2 More and Less Than for Counts and Measures
  168.    wt: 2:   1 Real Numbers Comparison
  169.    wt: 2:   16 Real Numbers Comparison
  170.    wt: 2:   15 Real Number Division
  171.    wt: 2:   14 Real Number Multiplication
  172.    wt: 2:   13 Real Number Subtraction
  173.    wt: 2:   12 Real Number Additive Inverses or Negatives
  174.    wt: 2:   11 Real Number Addition
  175.    wt: 2:   10 Real Number Lengths and Signs
  176.    wt: 2:   9 Coordinates for Regions in Space
  177.    wt: 2:   8 Coordinates for Maps and Planes
  178.    wt: 2:   7 Real Numbers as Line Cordinates
  179.    wt: 2:   6 Unsigned Real Numbers
  180.    wt: 2:   5 Rational Numbers More
  181.    wt: 2:   4 Rational Numbers
  182.    wt: 2:   3 Fractions
  183.    wt: 2:   2 Integers
  184.    wt: 2:   1 Whole and Natural Numbers
  185.    wt: 2:   5 Independent versus Dependent Variables
  186.    wt: 2:   4 Changing Letters
  187.    wt: 2:   3 Geometric Formulas and Function Notation
  188.    wt: 2:   2 Computation Rules Evaluation
  189.    wt: 2:   1 Formulas Dependence and Function Notation
  190.    wt: 2:   More Exercises
  191.    wt: 2:   Simple Exercises
  192.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  193.    wt: 2:   4 GE III Animated Examples
  194.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  195.    wt: 2:   3 GE III Equation Addition and Multiplication
  196.    wt: 2:   2 GE II Comparison
  197.    wt: 2:   1 GE Substitution four examples
  198.    wt: 2:   4 Solving a triangular system exercise
  199.    wt: 2:   3 Solving triangular system example
  200.    wt: 2:   2 Essentially one exercises three with solution
  201.    wt: 2:   1 Essentially One Unknown
  202.    wt: 2:   6 Algebraic Solution Example
  203.    wt: 2:   5 Algebraic Solutions Introduction
  204.    wt: 2:   4 Four Examples Fractional Coefficients
  205.    wt: 2:   3 Four Examples
  206.    wt: 2:   2 Three Examples
  207.    wt: 2:   1 Proper Equal Sign Usage
  208.    wt: 2:   Skill Development Notes
  209.    wt: 2:   10 One Example
  210.    wt: 2:   9 Three Examples
  211.    wt: 2:   8 One Example
  212.    wt: 2:   7 Two Examples
  213.    wt: 2:   6 Three Examples
  214.    wt: 2:   5 Three Examples
  215.    wt: 2:   4 Two Examples
  216.    wt: 2:   3 Two Examples
  217.    wt: 2:   2 Three Examples
  218.    wt: 2:   Using Letters for Physical Quantities
  219.    wt: 2:   Formula Usage Show Work Format
  220.    wt: 2:   13 Naming Identifying Formulas with Words
  221.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  222.    wt: 2:   8 Compound Interest Formula Evaluation
  223.    wt: 2:   7 Compound Interest Formula Introduction
  224.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  225.    wt: 2:   5 Box Volume Formula Example
  226.    wt: 2:   4 Circle Area Formula Example
  227.    wt: 2:   3 Triangle Area Formula Example
  228.    wt: 2:   2 Another Rectangle Area Formula Example
  229.    wt: 2:   1 Written work formats for developing and showing skill
  230.    wt: 2:   9 Sets in Probability and Statistics
  231.    wt: 2:   7 Cautious or Safe Set Construction
  232.    wt: 2:   6 Power Set Notation
  233.    wt: 2:   5 Product Builder Notation
  234.    wt: 2:   4 Subset Builder Notation
  235.    wt: 2:   3 Counting with Sets etc
  236.    wt: 2:   2 Venn Diagrams
  237.    wt: 2:   1 Finite Sets
  238.    wt: 2:   5 Talking about Numbers and Quantities
  239.    wt: 2:   3 Adding Words To Arithmetic
  240.    wt: 2:   2 What is a Variable
  241.    wt: 2:   1 Three Skills For Algebra
  242.    wt: 2:   About Folder Contents
  243.    wt: 2:   3 Comparison of Negative Numbers
  244.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  245.    wt: 2:   G.3 Constant Difference Theorem Proof
  246.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  247.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  248.    wt: 2:   F.1 What Functions are Continuous
  249.    wt: 2:   E2 Algebraic Properties of Limits
  250.    wt: 2:   D2 Limits of Monotone Sequences
  251.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  252.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  253.    wt: 2:   Chapter 9 About First Courses in Calculus
  254.    wt: 2:   Fall 1983 Calculus Appetizer
  255.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  256.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  257.    wt: 2:   Chapter 3 Algebra Starter Lessons
  258.    wt: 1:   Skills Chapter 5 Calculus
  259.    wt: 1:   Mathematics Education Professors
  260.    wt: 1:   Theory of Knowledge
  261.    wt: 1:   Different Kinds of Reasoning in maths
  262.    wt: 1:   three kinds of reason in mathematics
  263.    wt: 1:   E Kirchoffs Second Law
  264.    wt: 1:   D Kirchoff First Law
  265.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  266.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  267.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  268.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  269.    wt: 1:   8 The Effect of Negative Remarks
  270.    wt: 1:   26 Function definitions done and coming
  271.    wt: 1:   22 Square Root function graphically
  272.    wt: 1:   20 Interchanging coordinates a reflection
  273.    wt: 1:   19 Horizontal line rule and method
  274.    wt: 1:   18 Vertical Line Rule and Method
  275.    wt: 1:   17 Function maxima minima and their location
  276.    wt: 1:   16 Increasing or decreasing on intervals
  277.    wt: 1:   14 Surjections Injections Bijections
  278.    wt: 1:   13 From one to one to many to one
  279.    wt: 1:   12 Function Domain Recognition Exercises
  280.    wt: 1:   11 Function Domain Range Source and Targets
  281.    wt: 1:   10 Interval Notation
  282.    wt: 1:   9 Set theory term relation possible origins
  283.    wt: 1:   6 Set Existence Formation and Notation
  284.    wt: 1:   5 Function notation for geometric transformations
  285.    wt: 1:   4 Function notation in and beyond mathematics
  286.    wt: 1:   3 Formula or function graphing exercise
  287.    wt: 1:   Introduction Reading Guide
  288.    wt: 1:   8 quadratics backward use of various formulas
  289.    wt: 1:   4 quadratics difference of two squares
  290.    wt: 1:   1 Calculator Starter Exercises
  291.    wt: 1:   7 Links Lessons Elsewhere
  292.    wt: 1:   11 arctan left inverse of tangent Graph
  293.    wt: 1:   10 arctan left inverse of tangent Definition
  294.    wt: 1:   8 arcsin left inverse of sine Graph
  295.    wt: 1:   7 arcsin left inverse of sine Definition
  296.    wt: 1:   6 Graph of arccos function
  297.    wt: 1:   3 Left Inverse of cosine arccos definition
  298.    wt: 1:   8 Radian Measures of Common Angles
  299.    wt: 1:   2 Radian Measure Numerical Value of one degree
  300.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  301.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  302.    wt: 1:   Straight Lines Intersection of
  303.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  304.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  305.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  306.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  307.    wt: 1:   32 seven rows of pascals triangle
  308.    wt: 1:   28 Expressing products of sines cosines as sums
  309.    wt: 1:   26 Formulas for products of sines and cosines
  310.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  311.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  312.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  313.    wt: 1:   18 sum of sinusoidal waves as a single wave
  314.    wt: 1:   17F Law of cosines
  315.    wt: 1:   13 Graph of tangent function many periods
  316.    wt: 1:   12 Graph of tangent function for one period
  317.    wt: 1:   10 Graphs of sines and cosines many periods
  318.    wt: 1:   9 Graphs of sine and cosine over one period
  319.    wt: 1:   8 period of tangent function
  320.    wt: 1:   7 period of sine and cosine
  321.    wt: 1:   Unit Circle Development of Trigonometry
  322.    wt: 1:   20 N th Roots of Complex Numbers
  323.    wt: 1:   19 N th Roots of Unity
  324.    wt: 1:   18 Sixth Roots of Unity
  325.    wt: 1:   17 Cube Roots of unity
  326.    wt: 1:   14 Law of cosines
  327.    wt: 1:   8 Unit Circle Development of Trigonometry
  328.    wt: 1:   6 Field Properties of Complex Number
  329.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  330.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  331.    wt: 1:   9 Similarity of Triangles Usual Criteria
  332.    wt: 1:   8 Similarity of Triangles and Polygons
  333.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  334.    wt: 1:   1 Early Concept of Like or Similar Shapes
  335.    wt: 1:   12 Links Lessons elsewhere
  336.    wt: 1:   10 Midpoint of [a b] and [b a]
  337.    wt: 1:   6 Intersection of lines by solving linear systems
  338.    wt: 1:   5 Algebraic View of Slopes
  339.    wt: 1:   1 Numerical view of lines and their equations
  340.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  341.    wt: 1:   17 Right Bisectors of Triangle Sides
  342.    wt: 1:   9 Construction of a right bisector
  343.    wt: 1:   3 Isometry of Triangles Congruence
  344.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  345.    wt: 1:   4 Greater More Less Than Signs in General
  346.    wt: 1:   2 More and Less Than with Unlike Signs
  347.    wt: 1:   1 More and Less Than for Counts and Measures
  348.    wt: 1:   3 Properties of Square Roots with example
  349.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  350.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  351.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  352.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  353.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  354.    wt: 1:   4 LCM of 8 and 10 via Prime
  355.    wt: 1:   5 lengths and signs of numbers
  356.    wt: 1:   6 Simplification of Fractions with Units
  357.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  358.    wt: 1:   6 Multiplication of Mixed Numbers
  359.    wt: 1:   3 Unit fraction of a fraction
  360.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  361.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  362.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  363.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  364.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  365.    wt: 1:   20 Uniqueness of Prime Factorization
  366.    wt: 1:   16 video Factors of 980 using prime
  367.    wt: 1:   15 video Factors of 20 using Prime Factorization
  368.    wt: 1:   14 video Factors of 24 Take II
  369.    wt: 1:   13 video Factors of 24 using prime
  370.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  371.    wt: 1:   C Counting Areas with Powers of Ten
  372.    wt: 1:   B Powers of Ten
  373.    wt: 1:   8 Subtraction with Units of Measure
  374.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  375.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  376.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  377.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  378.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  379.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  380.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  381.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  382.    wt: 1:   Quick history of numbers and algebra
  383.    wt: 1:   012 Division of Time Intervals by Time Intervals
  384.    wt: 1:   011 Division of Time Intervals By Numbers
  385.    wt: 1:   010 Repeated Addition of Time Intervals
  386.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  387.    wt: 1:   8 Addition of Time Intervals via subtotaling
  388.    wt: 1:   7 Addition of Time Intervals
  389.    wt: 1:   4 Mixing and Changing Units of Time
  390.    wt: 1:   3 Units and Lengths of Time
  391.    wt: 1:   1 Intro of Kids To Time Date Skills
  392.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  393.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  394.    wt: 1:   G.5 Motions With Bounded Velocities
  395.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  396.    wt: 1:   F.5b Extreme Value Theorem
  397.    wt: 1:   F.5a Equicontinuity Theorems
  398.    wt: 1:   F.4 Finite Covering Theorem
  399.    wt: 1:   F.3 Intermediate Value Theorem
  400.    wt: 1:   F.2 Closed Range Theorem
  401.    wt: 1:   E1 Error Control Inequalities
  402.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  403.    wt: 1:   C Triangle Inequalities
  404.    wt: 1:   B3 Bolzano Weierstrass Theorem
  405.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  406.    wt: 1:   PostScript For and Against Decimal Perspectives
  407.    wt: 1:   A1. Introduction
  408.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  409.    wt: 1:   Chapter 23 Links To Trigonometry
  410.    wt: 1:   Chapter 22 Complex Numbers
  411.    wt: 1:   Chapter 21 Arrow Addition
  412.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  413.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  414.    wt: 1:   Chapter 18. Slopes Areas Integration
  415.    wt: 1:   Chapter 17. Area Approximation
  416.    wt: 1:   Chapter 16. Velocity Approximation
  417.    wt: 1:   Chapter 15. Slope Approximation
  418.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  419.    wt: 1:   Chapter 13. Acceleration
  420.    wt: 1:   Chapter 12. Units and Slopes
  421.    wt: 1:   Chapter 11. Graphing Slope versus Position
  422.    wt: 1:   Chapter 10 Slopes and Units
  423.    wt: 1:   Chapter 8. Slope Interpretation
  424.    wt: 1:   Chapter 7 Slopes and Velocity
  425.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  426.    wt: 1:   Chapter 5. Slope Sign Tests
  427.    wt: 1:   Chapter 4. More Slope Sign Analysis
  428.    wt: 1:   Chapter 3. Slope Sign Analysis
  429.    wt: 1:   Chapter 2. Slopes and Ski Trails
  430.    wt: 1:   Chapter 1.Introduction
  431.    wt: 1:   Foreword
  432.    wt: 1:   Chapter 19. Functions and Sets
  433.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  434.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  435.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  436.    wt: 1:   Chapter 6 Change of Language
  437.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  438.    wt: 1:   Chapter 4 Longer Chains of Reason
  439.    wt: 1:   Chapter 3 Chains of Reason
  440.    wt: 1:   Chapter 7 Two Treatments of Geometry
  441.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  442.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  443.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  444.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  445.    wt: 1:   Chapter 8 Change of Language
  446.    wt: 1:   Chapter 7 Longer Chains of Reason
  447.    wt: 1:   Chapter 6 Chains of Reason
  448.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  449.    wt: 1:   C. Domino effect of being careful
  450.    wt: 1:   B. Domino effect of errors
  451.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  452.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  453.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  454.    wt: 1:   More Algebra and Slope based Calculus Preview
  455.    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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