Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic
and Pattern Based Reason to inform and amuse thinkers and avid readers, studying or not. Enjoy.

Logic mastery strengthens comprehension and improve home, work & study habits.
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
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About: Site material shows how common troubles stem from steps too large or missing. Site material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin. If one site element is not to your liking, try another. Each is different. Many are unique

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local 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. Reform: look before you leap - plan all in detail first.

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  1.    wt: 6:   Advanced Calculus Volume 3 Appendices/
  2.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  3.    wt: 3:   Volume 3 Why Slopes A Calculus Intro Etc/
  4.    wt: 2:   3 Quadratics Geometrically/
  5.    wt: 2:   13 Vectors/
  6.    wt: 2:   3 Cartesian and Polar Coordinates/
  7.    wt: 2:   3 Prime Factorization Skills/
  8.    wt: 2:   12 Webvideo Lessons on Area and Volume Calculation/
  9.    wt: 2:   4 Lessons on Using Derivatives/
  10.    wt: 2:   38 Lessons on Calculating Derivatives/
  11.    wt: 2:   13 Lessons on Limits and Continuity/
  12.    wt: 2:   Volume 1 Elements of Reason/
  13.    wt: 1:   LAMP Lean Applied Mathematics Program/
  14.    wt: 1:   Volume 1A Regles et modeles/
  15.    wt: 1:   6 Trigonometry first steps/
  16.    wt: 1:   A Origins of Counting and Figuring Methods/
  17.    wt: 1:   10 Examples of Algebraic Reasoning/
  18.    wt: 1:   Step 4 Gaussian Elimination/
  19.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  20.    wt: 1:   Step 1 Stick diagram and fractions/
  21.    wt: 1:   3 Solving Linear Equations/
  22.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  23.    wt: 1:   C Decimal Multiplication Methods/
  24.    wt: 1:   5 Lessons on Integration/
  25.    wt: 1:   70 Calculus Starter Lessons/
  26.    wt: 1:   Volume 2 Three Skills For Algebra/
  27.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  28.    wt: 1:   Volume 1A Pattern Based Reason/
  29.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

321 matches:

  1.    wt: 5:   G.1 First Fundamental Theorem of Calculus
  2.    wt: 4:   33 sines and cosines of 2A 3A 4A 5A
  3.    wt: 3:   35 sines and cosines of 2A 3A 4A 5A
  4.    wt: 3:   34 sines and cosines of 2A 3A 4A 5A
  5.    wt: 3:   3 Gaussian Elimination 3 unknowns first example
  6.    wt: 3:   3 More on Groups of 3 Multi Digit Place Value
  7.    wt: 3:   G.3 Constant Difference Theorem Proof
  8.    wt: 2:   D Kirchoff First Law
  9.    wt: 2:   3 Left Inverse of cosine arccos definition
  10.    wt: 2:   4 Resultant of a Sum of Movements
  11.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  12.    wt: 2:   32 seven rows of pascals triangle
  13.    wt: 2:   30 unit circle calculation of six trigonometric functions
  14.    wt: 2:   27 Logarithmic use of products of sines and cosines
  15.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  16.    wt: 2:   13 Graph of tangent function many periods
  17.    wt: 2:   5 An Easy Proof of the Distributive Law
  18.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  19.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  20.    wt: 2:   3 Isometry of Triangles Congruence
  21.    wt: 2:   21 Addition of Multiples of a Single Vector
  22.    wt: 2:   3 Location of Point in Decimal Multiplication
  23.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  24.    wt: 2:   11 Volume of Sphere
  25.    wt: 2:   10 Volume of Pyramid
  26.    wt: 2:   9 Volume of Cone
  27.    wt: 2:   3 Comparison of Negative Numbers
  28.    wt: 2:   3 Properties of Square Roots with example
  29.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  30.    wt: 2:   3 Unit fraction of a fraction
  31.    wt: 2:   13 video Factors of 24 using prime
  32.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  33.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  34.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  35.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  36.    wt: 2:   3 Units and Lengths of Time
  37.    wt: 2:   Example 2 volume of a cone
  38.    wt: 2:   Example 1 volume of a pyramid
  39.    wt: 2:   Volume of Solid by Cross Sections Lesson
  40.    wt: 2:   A Related Material in Volume 3
  41.    wt: 2:   A Related lessons in Volume 3
  42.    wt: 2:   34 Derivative of exponential function
  43.    wt: 2:   33 Chain Rule Real Player video examples
  44.    wt: 2:   31 Derivatives of inverse functions
  45.    wt: 2:   30Chain Rule A Proof
  46.    wt: 2:   17 Derivatives of quotients of sine and cosine
  47.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  48.    wt: 2:   F.3 Intermediate Value Theorem
  49.    wt: 2:   B3 Bolzano Weierstrass Theorem
  50.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  51.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  52.    wt: 2:   Chapter 9 About First Courses in Calculus
  53.    wt: 2:   Fall 1983 Calculus Appetizer
  54.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  55.    wt: 2:   Chapter 3 Chains of Reason
  56.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  57.    wt: 2:   Chapter 7 Calculus Previews and Calculus Lightly
  58.    wt: 1:   Skills Chapter 5 Calculus
  59.    wt: 1:   Skills Chapter 3 Algebra
  60.    wt: 1:   3 Euclidean Geometry Leanly
  61.    wt: 1:   Mathematics Education Professors
  62.    wt: 1:   mathematics in context
  63.    wt: 1:   05 13 OldSiteEntrancePage
  64.    wt: 1:   Theory of Knowledge
  65.    wt: 1:   Different Kinds of Reasoning in maths
  66.    wt: 1:   three kinds of reason in mathematics
  67.    wt: 1:   Motivation and Context Problem
  68.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  69.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  70.    wt: 1:   3 Energy Power Heat08
  71.    wt: 1:   C Energy Power03
  72.    wt: 1:   E Wire Resistance Calculation03
  73.    wt: 1:   3 Like resistors in parallel
  74.    wt: 1:   E Kirchoffs Second Law
  75.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  76.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  77.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  78.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  79.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  80.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  81.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  82.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  83.    wt: 1:   13 Addition and Addition Tables
  84.    wt: 1:   8 The Effect of Negative Remarks
  85.    wt: 1:   3 Preparing for Science Studies
  86.    wt: 1:   Ages 3 plus to 4 plus
  87.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  88.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  89.    wt: 1:   sign monoticity analysis example 3
  90.    wt: 1:   23 Inverse Functions
  91.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  92.    wt: 1:   15 Sign analysis of functions
  93.    wt: 1:   13 From one to one to many to one
  94.    wt: 1:   8 Set view of relations and functions
  95.    wt: 1:   3 Formula or function graphing exercise
  96.    wt: 1:   2 Algebraic use of function notation
  97.    wt: 1:   1 Geometric Introduction of Function Notation
  98.    wt: 1:   9 quadratics physical and further context
  99.    wt: 1:   8 quadratics backward use of various formulas
  100.    wt: 1:   4 quadratics difference of two squares
  101.    wt: 1:   3 quadratics factoring by inspection
  102.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  103.    wt: 1:   3 Polynomials Multiplication Addition
  104.    wt: 1:   13 cosecant function Definition Graph and Inverse
  105.    wt: 1:   11 arctan left inverse of tangent Graph
  106.    wt: 1:   10 arctan left inverse of tangent Definition
  107.    wt: 1:   8 arcsin left inverse of sine Graph
  108.    wt: 1:   7 arcsin left inverse of sine Definition
  109.    wt: 1:   6 Graph of arccos function
  110.    wt: 1:   8 Radian Measures of Common Angles
  111.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  112.    wt: 1:   2 Radian Measure Numerical Value of one degree
  113.    wt: 1:   13 Velocity Vectors in Physics
  114.    wt: 1:   3 Navigation with Arrows or Vectors
  115.    wt: 1:   3 graphing y=f(x c) plus K
  116.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  117.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  118.    wt: 1:   Straight Lines Intersection of
  119.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  120.    wt: 1:   31 basic secant cosecant cotangent trig identities
  121.    wt: 1:   28 Expressing products of sines cosines as sums
  122.    wt: 1:   26 Formulas for products of sines and cosines
  123.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  124.    wt: 1:   18 sum of sinusoidal waves as a single wave
  125.    wt: 1:   17G Pythagorean Theorem Converse
  126.    wt: 1:   17F Law of cosines
  127.    wt: 1:   12 Graph of tangent function for one period
  128.    wt: 1:   10 Graphs of sines and cosines many periods
  129.    wt: 1:   9 Graphs of sine and cosine over one period
  130.    wt: 1:   8 period of tangent function
  131.    wt: 1:   7 period of sine and cosine
  132.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  133.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  134.    wt: 1:   Unit Circle Development of Trigonometry
  135.    wt: 1:   20 N th Roots of Complex Numbers
  136.    wt: 1:   19 N th Roots of Unity
  137.    wt: 1:   18 Sixth Roots of Unity
  138.    wt: 1:   17 Cube Roots of unity
  139.    wt: 1:   15 Pythagorean Theorem Converse
  140.    wt: 1:   14 Law of cosines
  141.    wt: 1:   13 Trig Formulas for dot and cross Products
  142.    wt: 1:   8 Unit Circle Development of Trigonometry
  143.    wt: 1:   6 Field Properties of Complex Number
  144.    wt: 1:   3 Addition Properties
  145.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  146.    wt: 1:   3 Trigonometric Ratios sine and cosine
  147.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  148.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  149.    wt: 1:   9 Similarity of Triangles Usual Criteria
  150.    wt: 1:   8 Similarity of Triangles and Polygons
  151.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  152.    wt: 1:   3 Similarity by Design with coordinates
  153.    wt: 1:   1 Early Concept of Like or Similar Shapes
  154.    wt: 1:   10 Midpoint of [a b] and [b a]
  155.    wt: 1:   6 Intersection of lines by solving linear systems
  156.    wt: 1:   5 Algebraic View of Slopes
  157.    wt: 1:   3 Slope product for perpendicular lines
  158.    wt: 1:   1 Numerical view of lines and their equations
  159.    wt: 1:   13 Pythagorean spatial distance formulas
  160.    wt: 1:   3 Rectangular Coordinates Review
  161.    wt: 1:   17 Right Bisectors of Triangle Sides
  162.    wt: 1:   13 Angle Side Angle Failure
  163.    wt: 1:   9 Construction of a right bisector
  164.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  165.    wt: 1:   3 Lengths and Areas on Maps and Plans
  166.    wt: 1:   23 Distributive Law Two Derivations
  167.    wt: 1:   22 Multiplication of Signed Numbers
  168.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  169.    wt: 1:   19 Signed Multiples of Vectors
  170.    wt: 1:   13 Arrows and Vectors in a Plane
  171.    wt: 1:   8 Division and Mulplication of Compound Fractions
  172.    wt: 1:   4 Location of Point in Decimal Addition
  173.    wt: 1:   3 Multiplicative Counting Skills Principles
  174.    wt: 1:   1 The Counting Origins of Numbers
  175.    wt: 1:   5 Areas of Rectangles Revisited
  176.    wt: 1:   3 Inequalities Algebraically
  177.    wt: 1:   3 Proportionality Examples
  178.    wt: 1:   3 Linear Equation Literal Solution More
  179.    wt: 1:   3 Product Axioms Two Forms
  180.    wt: 1:   4 Comparison of Negative Numbers
  181.    wt: 1:   3 More and Less Than with Unlike Signs
  182.    wt: 1:   13 Real Number Subtraction
  183.    wt: 1:   3 Fractions
  184.    wt: 1:   3 Geometric Formulas and Function Notation
  185.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  186.    wt: 1:   3 GE III Equation Addition and Multiplication
  187.    wt: 1:   3 Solving triangular system example
  188.    wt: 1:   3 Four Examples
  189.    wt: 1:   3 Two Examples
  190.    wt: 1:   13 Naming Identifying Formulas with Words
  191.    wt: 1:   5 Box Volume Formula Example
  192.    wt: 1:   3 Triangle Area Formula Example
  193.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  194.    wt: 1:   8 Sets of Numbers
  195.    wt: 1:   3 Counting with Sets etc
  196.    wt: 1:   6 Three Notions of What is a Variable
  197.    wt: 1:   4 A Brief Story of numbers and algebra
  198.    wt: 1:   3 Adding Words To Arithmetic
  199.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  200.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  201.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  202.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  203.    wt: 1:   13 GCD from given Prime Factorization
  204.    wt: 1:   4 LCM of 8 and 10 via Prime
  205.    wt: 1:   3 Counting with Tables and Trees II
  206.    wt: 1:   5 lengths and signs of numbers
  207.    wt: 1:   3 signed coordinates for maps and planes
  208.    wt: 1:   6 Simplification of Fractions with Units
  209.    wt: 1:   3 Multiplying Units and Numbers
  210.    wt: 1:   13 Fraction Comparison Algebraic View
  211.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  212.    wt: 1:   6 Multiplication of Mixed Numbers
  213.    wt: 1:   13 Subtraction with Additive Inverse
  214.    wt: 1:   3 Adding Movements with same direction
  215.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  216.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  217.    wt: 1:   26 Divisibility by 2 3 5 Example
  218.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  219.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  220.    wt: 1:   23 Remainder Arithmetic Modulo 2
  221.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  222.    wt: 1:   21 Remainder Arithmetic Modulo 3
  223.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  224.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  225.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  226.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  227.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  228.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  229.    wt: 1:   20 Uniqueness of Prime Factorization
  230.    wt: 1:   16 video Factors of 980 using prime
  231.    wt: 1:   15 video Factors of 20 using Prime Factorization
  232.    wt: 1:   14 video Factors of 24 Take II
  233.    wt: 1:   10 video Prime Factorization upto 23 squared
  234.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  235.    wt: 1:   3 video Primes and Composites from 9 times table
  236.    wt: 1:   Long Division forwards and backwards Example 3
  237.    wt: 1:   3 Division Single Digit Divisor Example
  238.    wt: 1:   C Counting Areas with Powers of Ten
  239.    wt: 1:   B Powers of Ten
  240.    wt: 1:   3 More One Digit Multipliers
  241.    wt: 1:   1 Why 3 times 5 gives 15
  242.    wt: 1:   8 Subtraction with Units of Measure
  243.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  244.    wt: 1:   3. How to add with decimals A sans conversions
  245.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  246.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  247.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  248.    wt: 1:   Quick history of numbers and algebra
  249.    wt: 1:   013 Travel Time Tables
  250.    wt: 1:   012 Division of Time Intervals by Time Intervals
  251.    wt: 1:   011 Division of Time Intervals By Numbers
  252.    wt: 1:   010 Repeated Addition of Time Intervals
  253.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  254.    wt: 1:   8 Addition of Time Intervals via subtotaling
  255.    wt: 1:   7 Addition of Time Intervals
  256.    wt: 1:   4 Mixing and Changing Units of Time
  257.    wt: 1:   1 Intro of Kids To Time Date Skills
  258.    wt: 1:   Example 4 with x function of y
  259.    wt: 1:   Example 3
  260.    wt: 1:   3 Two Chain Rule Method Exercises
  261.    wt: 1:   3 Second derivative test
  262.    wt: 1:   38 Formulas and derivatives for powers and roots
  263.    wt: 1:   36 Cube root derivative animated
  264.    wt: 1:   28 Chain Rule Preparation for a Proof
  265.    wt: 1:   23 Chain Rule in general
  266.    wt: 1:   15 sine and cosine derivatives 3rd step
  267.    wt: 1:   13 sine and cosine derivatives 1st step
  268.    wt: 1:   8 Differentiation of polynomials
  269.    wt: 1:   3 Motivation for Limit Definition Take 2
  270.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  271.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  272.    wt: 1:   5 Jumps and absence of unlimited error control
  273.    wt: 1:   3 Decimal insights for limits continuity convergence
  274.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  275.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  276.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  277.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  278.    wt: 1:   F.5b Extreme Value Theorem
  279.    wt: 1:   F.5a Equicontinuity Theorems
  280.    wt: 1:   F.4 Finite Covering Theorem
  281.    wt: 1:   F.2 Closed Range Theorem
  282.    wt: 1:   E2 Algebraic Properties of Limits
  283.    wt: 1:   D2 Limits of Monotone Sequences
  284.    wt: 1:   Chapter 23 Links To Trigonometry
  285.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  286.    wt: 1:   Chapter 13. Acceleration
  287.    wt: 1:   Chapter 3. Slope Sign Analysis
  288.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  289.    wt: 1:   Chapter 31 Direct and Indirect Reason
  290.    wt: 1:   Chapter 30 Truth Tables
  291.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  292.    wt: 1:   Chapter 23. Notation For Sums
  293.    wt: 1:   Chapter 16. Painless Theorem Proving
  294.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  295.    wt: 1:   Chapter 13. Second Reading Guide
  296.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  297.    wt: 1:   Chapter 6 Change of Language
  298.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  299.    wt: 1:   Chapter 4 Longer Chains of Reason
  300.    wt: 1:   Chapter 7 Two Treatments of Geometry
  301.    wt: 1:   Chapter 3 Algebra Difficulties
  302.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  303.    wt: 1:   Chapter 23 Truth Tables
  304.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  305.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  306.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  307.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  308.    wt: 1:   Chapter 8 Change of Language
  309.    wt: 1:   Chapter 7 Longer Chains of Reason
  310.    wt: 1:   Chapter 6 Chains of Reason
  311.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  312.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  313.    wt: 1:   C. Domino effect of being careful
  314.    wt: 1:   B. Domino effect of errors
  315.    wt: 1:   Chapter 3 Algebra Starter Lessons
  316.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  317.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  318.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  319.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  320.    wt: 1:   More Algebra and Slope based Calculus Preview
  321.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

738 matches:

  1.    wt: 9:   F.5a Equicontinuity Theorems
  2.    wt: 9:   F.3 Intermediate Value Theorem
  3.    wt: 8:   Postscript One Sided and Intermediate Value Theorems
  4.    wt: 8:   G.2 Lipshitz Conditions Integration Calculus Reform
  5.    wt: 8:   G.2 Differentiable Functions Mean Value Theorem
  6.    wt: 8:   G.1 Differentiable Functions Rolles Theorem
  7.    wt: 8:   F.5b Extreme Value Theorem
  8.    wt: 8:   F.4 Finite Covering Theorem
  9.    wt: 8:   F.2 Closed Range Theorem
  10.    wt: 8:   E2 Algebraic Properties of Limits
  11.    wt: 8:   D2 Limits of Monotone Sequences
  12.    wt: 8:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  13.    wt: 7:   G.6 Bounded Derivatives implies Lipshitz Continuity
  14.    wt: 7:   G.5 Motions With Bounded Velocities
  15.    wt: 7:   G.4 Lipschitz Continuity implies EquiContinuity
  16.    wt: 7:   F.1 What Functions are Continuous
  17.    wt: 7:   E1 Error Control Inequalities
  18.    wt: 7:   D1 Sets and Sequences GLBs and LGBs
  19.    wt: 7:   C Triangle Inequalities
  20.    wt: 6:   31 Derivatives of inverse functions
  21.    wt: 6:   B1 Pigeon Hole Principles from combinatorics
  22.    wt: 6:   PostScript For and Against Decimal Perspectives
  23.    wt: 6:   A1. Introduction
  24.    wt: 5:   34 sines and cosines of 2A 3A 4A 5A
  25.    wt: 5:   33 sines and cosines of 2A 3A 4A 5A
  26.    wt: 5:   3 Gaussian Elimination 3 unknowns first example
  27.    wt: 5:   3 Solving triangular system example
  28.    wt: 5:   13 video Factors of 24 using prime
  29.    wt: 5:   34 Derivative of exponential function
  30.    wt: 5:   Postscript Pythagorean Theorem yet another proof
  31.    wt: 5:   Chapter 23 Links To Trigonometry
  32.    wt: 5:   Chapter 15. Algebraic Evaluation of Limits
  33.    wt: 5:   Chapter 13. Acceleration
  34.    wt: 5:   Chapter 9 About First Courses in Calculus
  35.    wt: 5:   Chapter 3. Slope Sign Analysis
  36.    wt: 5:   Fall 1983 Calculus Appetizer
  37.    wt: 4:   3 quadratics factoring by inspection
  38.    wt: 4:   13 Velocity Vectors in Physics
  39.    wt: 4:   4 Resultant of a Sum of Movements
  40.    wt: 4:   3 Navigation with Arrows or Vectors
  41.    wt: 4:   35 sines and cosines of 2A 3A 4A 5A
  42.    wt: 4:   13 Pythagorean spatial distance formulas
  43.    wt: 4:   9 Pythagorean Theorem Chinese Square Proof
  44.    wt: 4:   3 Rectangular Coordinates Review
  45.    wt: 4:   3 Comparison of Negative Numbers
  46.    wt: 4:   3 video Primes and Composites from 9 times table
  47.    wt: 4:   3 More on Groups of 3 Multi Digit Place Value
  48.    wt: 4:   Example 2 volume of a cone
  49.    wt: 4:   Example 1 volume of a pyramid
  50.    wt: 4:   Volume of Solid by Cross Sections Lesson
  51.    wt: 4:   Example 4 with x function of y
  52.    wt: 4:   Example 3
  53.    wt: 4:   A Related lessons in Volume 3
  54.    wt: 4:   38 Formulas and derivatives for powers and roots
  55.    wt: 4:   33 Chain Rule Real Player video examples
  56.    wt: 4:   30Chain Rule A Proof
  57.    wt: 4:   28 Chain Rule Preparation for a Proof
  58.    wt: 4:   23 Chain Rule in general
  59.    wt: 4:   22 Chain Rule for polynomials
  60.    wt: 4:   17 Derivatives of quotients of sine and cosine
  61.    wt: 4:   16 Derivatives of reciprocals of sine and cosine
  62.    wt: 4:   15 sine and cosine derivatives 3rd step
  63.    wt: 4:   13 sine and cosine derivatives 1st step
  64.    wt: 4:   8 Differentiation of polynomials
  65.    wt: 4:   3 Motivation for Limit Definition Take 2
  66.    wt: 4:   13 Limits with Parameters and Derivatives Take II
  67.    wt: 4:   5 Jumps and absence of unlimited error control
  68.    wt: 4:   4 Numerical properties
  69.    wt: 4:   Chapter 24 Logarithms Powers and Exponentials
  70.    wt: 4:   Chapter 22 Complex Numbers
  71.    wt: 4:   Chapter 21 Arrow Addition
  72.    wt: 4:   Chapter 19. Exponentials and Natural Logarithms
  73.    wt: 4:   Chapter 18. Slopes Areas Integration
  74.    wt: 4:   Chapter 17. Area Approximation
  75.    wt: 4:   Chapter 16. Velocity Approximation
  76.    wt: 4:   Chapter 15. Slope Approximation
  77.    wt: 4:   Chapter 14 Limits and Continuity with and sans Decimals
  78.    wt: 4:   Chapter 6. Slopes and Vertical Shifts
  79.    wt: 4:   Chapter 4. More Slope Sign Analysis
  80.    wt: 4:   Chapter 2. Slopes and Ski Trails
  81.    wt: 4:   Chapter 23. Notation For Sums
  82.    wt: 4:   Chapter 3 Chains of Reason
  83.    wt: 4:   More Algebra and Slope based Calculus Preview
  84.    wt: 4:   Systematic Algebra Skill Development Missing Links
  85.    wt: 4:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  86.    wt: 3:   Skills Chapter 3 Algebra
  87.    wt: 3:   A Quadratics Summary
  88.    wt: 3:   9 quadratics physical and further context
  89.    wt: 3:   8 quadratics backward use of various formulas
  90.    wt: 3:   7 quadratic formulla derivation
  91.    wt: 3:   5 quadratics completing the square
  92.    wt: 3:   4 quadratics difference of two squares
  93.    wt: 3:   2 quadratics graphing in general
  94.    wt: 3:   3 Natural Logarithms and Exponentials Basic Properties
  95.    wt: 3:   14 Why Scalar Multiplication Distributes Physical Argument
  96.    wt: 3:   8 Parallel Vectors
  97.    wt: 3:   32 seven rows of pascals triangle
  98.    wt: 3:   13 Trig Formulas for dot and cross Products
  99.    wt: 3:   5 An Easy Proof of the Distributive Law
  100.    wt: 3:   3 Slope product for perpendicular lines
  101.    wt: 3:   8 Distance Between Points on a Line
  102.    wt: 3:   3 Isometry of Triangles Congruence
  103.    wt: 3:   3 Multiplicative Counting Skills Principles
  104.    wt: 3:   5 Areas of Rectangles Revisited
  105.    wt: 3:   3 Inequalities Algebraically
  106.    wt: 3:   3 GE III Equation Addition and Multiplication
  107.    wt: 3:   4 Solving a triangular system exercise
  108.    wt: 3:   2 Essentially one exercises three with solution
  109.    wt: 3:   1 Essentially One Unknown
  110.    wt: 3:   3 Four Examples
  111.    wt: 3:   3 Two Examples
  112.    wt: 3:   9 GCD of 360 110 via Primes and Euclid Algorithm
  113.    wt: 3:   3 Unit fraction of a fraction
  114.    wt: 3:   20 Uniqueness of Prime Factorization
  115.    wt: 3:   16 video Factors of 980 using prime
  116.    wt: 3:   15 video Factors of 20 using Prime Factorization
  117.    wt: 3:   14 video Factors of 24 Take II
  118.    wt: 3:   10 video Prime Factorization upto 23 squared
  119.    wt: 3:   7 Calculator Usage Notes and Cautions
  120.    wt: 3:   6 Sieve of Eratosthenes and Square Rule
  121.    wt: 3:   5 Prime Factorization and a Square Rule
  122.    wt: 3:   3 More One Digit Multipliers
  123.    wt: 3:   Example 2
  124.    wt: 3:   Example 1
  125.    wt: 3:   Summary
  126.    wt: 3:   A Related Material in Volume 3
  127.    wt: 3:   3 Two Chain Rule Method Exercises
  128.    wt: 3:   4 Second derivative test exercise example
  129.    wt: 3:   3 Second derivative test
  130.    wt: 3:   2 Second derivative test prequel
  131.    wt: 3:   36 Cube root derivative animated
  132.    wt: 3:   26 Chain Rule Recognising outer inner functions
  133.    wt: 3:   21 Chain Rule for powers
  134.    wt: 3:   19 Chain Rule for linear functions
  135.    wt: 3:   14 sine and cosine derivatives 2nd step
  136.    wt: 3:   12 Quotient rule examples
  137.    wt: 3:   5 Product Rule
  138.    wt: 3:   4 Sum Rule
  139.    wt: 3:   2 Motivation for Limit Definition Take 1
  140.    wt: 3:   1 Fall 1983 Why Slopes Appetizer
  141.    wt: 3:   6 Continuity at a point
  142.    wt: 3:   3 Decimal insights for limits continuity convergence
  143.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  144.    wt: 3:   Chapter 12. Units and Slopes
  145.    wt: 3:   Chapter 11. Graphing Slope versus Position
  146.    wt: 3:   Chapter 10 Slopes and Units
  147.    wt: 3:   Chapter 8. Slope Interpretation
  148.    wt: 3:   Chapter 7 Slopes and Velocity
  149.    wt: 3:   Chapter 5. Slope Sign Tests
  150.    wt: 3:   Chapter 1.Introduction
  151.    wt: 3:   Foreword
  152.    wt: 3:   Chapter 31 Direct and Indirect Reason
  153.    wt: 3:   Chapter 30 Truth Tables
  154.    wt: 3:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  155.    wt: 3:   Chapter 13. Second Reading Guide
  156.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  157.    wt: 3:   Chapter 3 Algebra Difficulties
  158.    wt: 3:   Chapter 23 Truth Tables
  159.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  160.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  161.    wt: 3:   Appendix A Calculus with Proofs for Keen or Gifted
  162.    wt: 3:   Chapter 7 Calculus Previews and Calculus Lightly
  163.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  164.    wt: 2:   Skills Chapter 5 Calculus
  165.    wt: 2:   Ramblings Extrinsic numbers theory
  166.    wt: 2:   Ramblings Introduction Algebra Essay
  167.    wt: 2:   3 Euclidean Geometry Leanly
  168.    wt: 2:   mathematics in context
  169.    wt: 2:   Education Reform Inconsistencies
  170.    wt: 2:   Theory of Knowledge
  171.    wt: 2:   Different Kinds of Reasoning in maths
  172.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  173.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  174.    wt: 2:   C Energy Power03
  175.    wt: 2:   D Kirchoff First Law
  176.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  177.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  178.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  179.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  180.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  181.    wt: 2:   13 Addition and Addition Tables
  182.    wt: 2:   3 Preparing for Science Studies
  183.    wt: 2:   Ages 3 plus to 4 plus
  184.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  185.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  186.    wt: 2:   sign monoticity analysis example 3
  187.    wt: 2:   23 Inverse Functions
  188.    wt: 2:   13 From one to one to many to one
  189.    wt: 2:   3 Formula or function graphing exercise
  190.    wt: 2:   10 quadratic exercises
  191.    wt: 2:   6 quadratics numerical approach
  192.    wt: 2:   1 quadratics graphing exercises
  193.    wt: 2:   Quadratics in 10 steps
  194.    wt: 2:   3 Left Inverse of cosine arccos definition
  195.    wt: 2:   3 Circle Arclengh Proportional to Central Angle
  196.    wt: 2:   2 Radian Measure Numerical Value of one degree
  197.    wt: 2:   A Global Time and Navigation
  198.    wt: 2:   15 Dot and Cross Product
  199.    wt: 2:   12 From Applied To Pure Mathematics
  200.    wt: 2:   11 Component Method
  201.    wt: 2:   10 Parallelogram Addition Method
  202.    wt: 2:   9 Head to Tail Coordinate View
  203.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  204.    wt: 2:   6 Vectors with Coordinates
  205.    wt: 2:   5 Head To Tail Arrow Addition
  206.    wt: 2:   2 Signed Coordinates
  207.    wt: 2:   1 Unsigned Coordinates
  208.    wt: 2:   Vector and Complex Number Applet
  209.    wt: 2:   Straight Lines Intersection of
  210.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  211.    wt: 2:   12 Straight Lines Graphing mx plus b
  212.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  213.    wt: 2:   31 basic secant cosecant cotangent trig identities
  214.    wt: 2:   30 unit circle calculation of six trigonometric functions
  215.    wt: 2:   27 Logarithmic use of products of sines and cosines
  216.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  217.    wt: 2:   17G Pythagorean Theorem Converse
  218.    wt: 2:   17F Law of cosines
  219.    wt: 2:   13 Graph of tangent function many periods
  220.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  221.    wt: 2:   21 Logarithms Powers and Exponentials
  222.    wt: 2:   20 N th Roots of Complex Numbers
  223.    wt: 2:   15 Pythagorean Theorem Converse
  224.    wt: 2:   14 Law of cosines
  225.    wt: 2:   3 Addition Properties
  226.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  227.    wt: 2:   3 Trigonometric Ratios sine and cosine
  228.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  229.    wt: 2:   Why Trigonometry the whyslopes view
  230.    wt: 2:   13 Navigation Location from Angles to 2 Landmarks
  231.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  232.    wt: 2:   3 Similarity by Design with coordinates
  233.    wt: 2:   10 Midpoint of [a b] and [b a]
  234.    wt: 2:   12 Spatial Coordinates
  235.    wt: 2:   11 Triangle Inequality
  236.    wt: 2:   10 Pythagorean plane distance formula
  237.    wt: 2:   7 Complex Numbers Appetizer
  238.    wt: 2:   6 Polar Multiplication and Rotation
  239.    wt: 2:   5 Cartesian Addition and Translation
  240.    wt: 2:   4 Polar Coordinates to and from
  241.    wt: 2:   2 Cartesian Coordinates with signs
  242.    wt: 2:   1 Cartesian Coordinates sans signs
  243.    wt: 2:   13 Angle Side Angle Failure
  244.    wt: 2:   23 Distributive Law Two Derivations
  245.    wt: 2:   22 Multiplication of Signed Numbers
  246.    wt: 2:   21 Addition of Multiples of a Single Vector
  247.    wt: 2:   3 Location of Point in Decimal Multiplication
  248.    wt: 2:   1 The Counting Origins of Numbers
  249.    wt: 2:   4 Fraction Operations Axiomatic Development
  250.    wt: 2:   2 Fraction Operations Physical Development
  251.    wt: 2:   3 Proportionality Examples
  252.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  253.    wt: 2:   3 Product Axioms Two Forms
  254.    wt: 2:   13 Real Number Subtraction
  255.    wt: 2:   3 Fractions
  256.    wt: 2:   3 Geometric Formulas and Function Notation
  257.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  258.    wt: 2:   1 Proper Equal Sign Usage
  259.    wt: 2:   Formula Usage Show Work Format
  260.    wt: 2:   11 Volume of Sphere
  261.    wt: 2:   10 Volume of Pyramid
  262.    wt: 2:   9 Volume of Cone
  263.    wt: 2:   5 Box Volume Formula Example
  264.    wt: 2:   3 Triangle Area Formula Example
  265.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  266.    wt: 2:   8 Sets of Numbers
  267.    wt: 2:   3 Counting with Sets etc
  268.    wt: 2:   3 Properties of Square Roots with example
  269.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  270.    wt: 2:   3 signed coordinates for maps and planes
  271.    wt: 2:   6 Multiplication of Mixed Numbers
  272.    wt: 2:   3 Adding Movements with same direction
  273.    wt: 2:   A Decimals Modular and Remainder Arithmetic
  274.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  275.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  276.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  277.    wt: 2:   19 video Prime Factorization Unique
  278.    wt: 2:   18 video Count Factors given Prime Factorization
  279.    wt: 2:   17 Identify and Count Factors using Primes
  280.    wt: 2:   12 LCD GCD and LCM using Primes
  281.    wt: 2:   11 Efficient Square Rule Use
  282.    wt: 2:   9 video Prime Factorization upto 19 squared
  283.    wt: 2:   8 video Prime Factorization upto 19
  284.    wt: 2:   4 video Prime Factorization Introduction
  285.    wt: 2:   2 Prime and Composites less than 16
  286.    wt: 2:   1 video how Products are bigger than factor
  287.    wt: 2:   3 Division Single Digit Divisor Example
  288.    wt: 2:   C Counting Areas with Powers of Ten
  289.    wt: 2:   B Powers of Ten
  290.    wt: 2:   5 Decimal Fraction Multiplication
  291.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  292.    wt: 2:   1 Why 3 times 5 gives 15
  293.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  294.    wt: 2:   3. How to add with decimals A sans conversions
  295.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  296.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  297.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  298.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  299.    wt: 2:   3 Units and Lengths of Time
  300.    wt: 2:   Example 1. Area Between x and x squared
  301.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  302.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  303.    wt: 2:   Area Between Curves Lesson Take 2
  304.    wt: 2:   Area Between Curves Lesson Take 1
  305.    wt: 2:   4 Definite Integrals Evaluation Exercises
  306.    wt: 2:   2 Indefinite Integrals Exercises
  307.    wt: 2:   1 Chain Rule in Reverse Integration Method
  308.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  309.    wt: 2:   A Chain Rule Real Player video examples
  310.    wt: 2:   29 Chain Rule Optional Reading
  311.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  312.    wt: 2:   25 Chain Rule Animated Examples Continued
  313.    wt: 2:   24 Chain Rule Animated Examples
  314.    wt: 2:   20 Chain Rule for Pulley Systems
  315.    wt: 2:   18 Chain Rule Introduction
  316.    wt: 2:   11 Quotient rule
  317.    wt: 2:   10 Power rule for negative integers
  318.    wt: 2:   9 Reciprocal rule
  319.    wt: 2:   7 Animated Differentiation Examples
  320.    wt: 2:   6 Power rule from product rule
  321.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  322.    wt: 2:   11 Limits at infinity Three Examples
  323.    wt: 2:   10 Three one sided limits with infinite values
  324.    wt: 2:   9 Limits Continuity and Composition
  325.    wt: 2:   8 Four Animated Examples
  326.    wt: 2:   7 Evaluation by immediate or delayed substitution
  327.    wt: 2:   2 Algebraic codification
  328.    wt: 2:   1 Numerical introduction
  329.    wt: 2:   Appendix C. How to Read
  330.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  331.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  332.    wt: 2:   Chapter 25. Mathematical Induction Examples
  333.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  334.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  335.    wt: 2:   Chapter 21. Third Reading Guide
  336.    wt: 2:   Chapter 20. Degrees and Radians
  337.    wt: 2:   Chapter 16. Painless Theorem Proving
  338.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  339.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  340.    wt: 2:   Chapter 8 Three Skills For Algebra
  341.    wt: 2:   Chapter 6 Change of Language
  342.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  343.    wt: 2:   Chapter 4 Longer Chains of Reason
  344.    wt: 2:   Postscript A Three Remarks
  345.    wt: 2:   Chapter 7 Two Treatments of Geometry
  346.    wt: 2:   Postscript D Reflections on Law of the Excluded Middle
  347.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  348.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  349.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  350.    wt: 2:   Chapter 8 Change of Language
  351.    wt: 2:   Chapter 7 Longer Chains of Reason
  352.    wt: 2:   Chapter 6 Chains of Reason
  353.    wt: 2:   C. Domino effect of being careful
  354.    wt: 2:   Chapter 3 Algebra Starter Lessons
  355.    wt: 2:   3 Telling Tracking Time Temporal and More Place Sense
  356.    wt: 2:   Ends Values Methods For Skill Development Framework Prequel
  357.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  358.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  359.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  360.    wt: 2:   Implementation Notes
  361.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  362.    wt: 1:   Appendix 2 primary school Arithmetic 01
  363.    wt: 1:   Appendix 1 primary and preschool mathematic
  364.    wt: 1:   K LAMP Musings Science Education
  365.    wt: 1:   J LAMP Introduction Extrinsic Origins
  366.    wt: 1:   I LAMP Introduction Study Habits
  367.    wt: 1:   H LAMP Introduction Instructional Concepts
  368.    wt: 1:   G LAMP Introduction Problem Solving Skills
  369.    wt: 1:   F LAMP Introduction Prerequisites
  370.    wt: 1:   E LAMP Introduction Modern Mathematics
  371.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  372.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  373.    wt: 1:   A Introduction Objectives
  374.    wt: 1:   Skills Chapter 4 Logic
  375.    wt: 1:   Skills Chapter 2 Geometry
  376.    wt: 1:   Skills Chapter 1 Arithmetic
  377.    wt: 1:   Skills Chapter 0 Introduction
  378.    wt: 1:   permissions for teachers
  379.    wt: 1:   Math Ed if it must be short make it lean effective
  380.    wt: 1:   Mathematics Education Professors
  381.    wt: 1:   modern education
  382.    wt: 1:   learning takes time
  383.    wt: 1:   grouping students according to ability
  384.    wt: 1:   what should be learnt and When
  385.    wt: 1:   Postscript 2007 01 10
  386.    wt: 1:   five decades make a difference
  387.    wt: 1:   Secondary Two Mathematics
  388.    wt: 1:   teaching tutoring algebraic reason
  389.    wt: 1:   the trouble with algebra
  390.    wt: 1:   05 13 OldSiteEntrancePage
  391.    wt: 1:   three kinds of reason in mathematics
  392.    wt: 1:   Motivation and Context Problem
  393.    wt: 1:   chapitre 12 00 les iles et division
  394.    wt: 1:   chapitre 07 01 principle D induction mathematique
  395.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  396.    wt: 1:   chapitre 06 00 Chaines de la raison
  397.    wt: 1:   chapitre 05 00 Deception
  398.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  399.    wt: 1:   chapitre 04 09 Regles accidentelles
  400.    wt: 1:   chapitre 04 08 Limitations et benefices
  401.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  402.    wt: 1:   chapitre 04 06 engagements
  403.    wt: 1:   chapitre 04 05 Implication versus suggestion
  404.    wt: 1:   chapitre 04 04 Parlons de la logique
  405.    wt: 1:   chapitre 04 02 Deuxieme enigme
  406.    wt: 1:   chapitre 04 01 Premiere enigme
  407.    wt: 1:   chapitre 04 00 Les regles d implication
  408.    wt: 1:   chapitre 02 00 La Communication des idees
  409.    wt: 1:   chapitre 01 00 Introduction
  410.    wt: 1:   liens
  411.    wt: 1:   3 Energy Power Heat08
  412.    wt: 1:   E Wire Resistance Calculation03
  413.    wt: 1:   A Wire Resistance Qualitative01
  414.    wt: 1:   3 Like resistors in parallel
  415.    wt: 1:   E Kirchoffs Second Law
  416.    wt: 1:   B Electromotive force conventional current01
  417.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  418.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  419.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  420.    wt: 1:   8 The Effect of Negative Remarks
  421.    wt: 1:   Ages 12 to 14 Skills with take home value
  422.    wt: 1:   Ages 12 to 14 Geometry
  423.    wt: 1:   Ages 12 to 14 Arithmetic
  424.    wt: 1:   Ages 10 to 12 Geometry
  425.    wt: 1:   Ages 10 to 12 Arithmetic
  426.    wt: 1:   Ages 9 to 10
  427.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  428.    wt: 1:   15 Sign analysis of functions
  429.    wt: 1:   8 Set view of relations and functions
  430.    wt: 1:   2 Algebraic use of function notation
  431.    wt: 1:   1 Geometric Introduction of Function Notation
  432.    wt: 1:   10 Exponential Growth and Decay Models
  433.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  434.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  435.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  436.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  437.    wt: 1:   2 Square Root Simplification a prequel
  438.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  439.    wt: 1:   3 Polynomials Multiplication Addition
  440.    wt: 1:   13 cosecant function Definition Graph and Inverse
  441.    wt: 1:   11 arctan left inverse of tangent Graph
  442.    wt: 1:   10 arctan left inverse of tangent Definition
  443.    wt: 1:   8 arcsin left inverse of sine Graph
  444.    wt: 1:   7 arcsin left inverse of sine Definition
  445.    wt: 1:   6 Graph of arccos function
  446.    wt: 1:   8 Radian Measures of Common Angles
  447.    wt: 1:   1 Degrees and Radians Introduction
  448.    wt: 1:   3 graphing y=f(x c) plus K
  449.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  450.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  451.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  452.    wt: 1:   14 Straight Lines Equations General Case
  453.    wt: 1:   11 Straight Lines Graphing y=mx
  454.    wt: 1:   10 Straight Lines through Origin Equations More
  455.    wt: 1:   9 Straight Lines through Origin Equations
  456.    wt: 1:   28 Expressing products of sines cosines as sums
  457.    wt: 1:   26 Formulas for products of sines and cosines
  458.    wt: 1:   24 tangent Angle Difference Formula
  459.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  460.    wt: 1:   18 sum of sinusoidal waves as a single wave
  461.    wt: 1:   17E Trig Formulas for dot and cross Products
  462.    wt: 1:   17D cis formulas for sine cosines and tangent
  463.    wt: 1:   17C sine and cosine double triple angle formulas
  464.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  465.    wt: 1:   17A The complex number valued trig function cis
  466.    wt: 1:   15 sine cosine Complementary Angle Relations
  467.    wt: 1:   12 Graph of tangent function for one period
  468.    wt: 1:   10 Graphs of sines and cosines many periods
  469.    wt: 1:   9 Graphs of sine and cosine over one period
  470.    wt: 1:   8 period of tangent function
  471.    wt: 1:   7 period of sine and cosine
  472.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  473.    wt: 1:   Unit Circle Development of Trigonometry
  474.    wt: 1:   19 N th Roots of Unity
  475.    wt: 1:   18 Sixth Roots of Unity
  476.    wt: 1:   17 Cube Roots of unity
  477.    wt: 1:   12 cis formulas for sine cosines and tangent
  478.    wt: 1:   11 sine and cosine double triple angle formulas
  479.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  480.    wt: 1:   9 The complex number valued trig function cis
  481.    wt: 1:   8 Unit Circle Development of Trigonometry
  482.    wt: 1:   7 Second Way to Calculate Products
  483.    wt: 1:   6 Field Properties of Complex Number
  484.    wt: 1:   2 Complex Numbers made easier we hope
  485.    wt: 1:   8 Triangles Cascade Problem Solving
  486.    wt: 1:   7 Trignometric Ratios Unit Circle
  487.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  488.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  489.    wt: 1:   1 Angle Measurement with Degrees
  490.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  491.    wt: 1:   9 Similarity of Triangles Usual Criteria
  492.    wt: 1:   8 Similarity of Triangles and Polygons
  493.    wt: 1:   6 Geometric Diagrams in Class
  494.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  495.    wt: 1:   1 Early Concept of Like or Similar Shapes
  496.    wt: 1:   11 A Partial Summary
  497.    wt: 1:   6 Intersection of lines by solving linear systems
  498.    wt: 1:   5 Algebraic View of Slopes
  499.    wt: 1:   4 Equations for lines three forms
  500.    wt: 1:   1 Numerical view of lines and their equations
  501.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  502.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  503.    wt: 1:   PS A Kite Construction Methods
  504.    wt: 1:   21 Parallelograms
  505.    wt: 1:   17 Right Bisectors of Triangle Sides
  506.    wt: 1:   9 Construction of a right bisector
  507.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  508.    wt: 1:   3 Lengths and Areas on Maps and Plans
  509.    wt: 1:   26 More Less Greater Than Comparison
  510.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  511.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  512.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  513.    wt: 1:   19 Signed Multiples of Vectors
  514.    wt: 1:   13 Arrows and Vectors in a Plane
  515.    wt: 1:   8 Division and Mulplication of Compound Fractions
  516.    wt: 1:   4 Location of Point in Decimal Addition
  517.    wt: 1:   E Long Division Methods more
  518.    wt: 1:   D Long Division Methods
  519.    wt: 1:   C Three Decimal Subtraction Methods
  520.    wt: 1:   B Decimal Comparison and Subtraction
  521.    wt: 1:   A Decimal Addition Columm Methods
  522.    wt: 1:   8 Column Multiplication Methods in General
  523.    wt: 1:   7 Decimals Multiplication Methods Examples
  524.    wt: 1:   6 Column Methods for Decimal Multiplication
  525.    wt: 1:   5 Distributive Law for Whole Numbers
  526.    wt: 1:   4 Commutative Law Groups Counting Form
  527.    wt: 1:   2 Combing Counts Addition Skills and Principles
  528.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  529.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  530.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  531.    wt: 1:   5 Triangle Area Formula Backwards
  532.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  533.    wt: 1:   3 Linear Equation Literal Solution More
  534.    wt: 1:   1 Changing Calculations
  535.    wt: 1:   6 Equations and Systems Equivalent or Implied
  536.    wt: 1:   5 Equality in Algebra
  537.    wt: 1:   4 Subtraction and Division Axioms
  538.    wt: 1:   2 Addition and Multiplication Axioms
  539.    wt: 1:   1 Equivalent Computation Rules
  540.    wt: 1:   4 Comparison of Negative Numbers
  541.    wt: 1:   3 More and Less Than with Unlike Signs
  542.    wt: 1:   1 Real Numbers Comparison
  543.    wt: 1:   16 Real Numbers Comparison
  544.    wt: 1:   15 Real Number Division
  545.    wt: 1:   14 Real Number Multiplication
  546.    wt: 1:   11 Real Number Addition
  547.    wt: 1:   8 Coordinates for Maps and Planes
  548.    wt: 1:   7 Real Numbers as Line Cordinates
  549.    wt: 1:   6 Unsigned Real Numbers
  550.    wt: 1:   5 Rational Numbers More
  551.    wt: 1:   4 Rational Numbers
  552.    wt: 1:   2 Integers
  553.    wt: 1:   1 Whole and Natural Numbers
  554.    wt: 1:   4 Changing Letters
  555.    wt: 1:   2 Computation Rules Evaluation
  556.    wt: 1:   1 Formulas Dependence and Function Notation
  557.    wt: 1:   More Exercises
  558.    wt: 1:   Simple Exercises
  559.    wt: 1:   4 GE III Animated Examples
  560.    wt: 1:   2 GE II Comparison
  561.    wt: 1:   1 GE Substitution four examples
  562.    wt: 1:   6 Algebraic Solution Example
  563.    wt: 1:   5 Algebraic Solutions Introduction
  564.    wt: 1:   4 Four Examples Fractional Coefficients
  565.    wt: 1:   2 Three Examples
  566.    wt: 1:   Skill Development Notes
  567.    wt: 1:   10 One Example
  568.    wt: 1:   9 Three Examples
  569.    wt: 1:   8 One Example
  570.    wt: 1:   7 Two Examples
  571.    wt: 1:   6 Three Examples
  572.    wt: 1:   5 Three Examples
  573.    wt: 1:   4 Two Examples
  574.    wt: 1:   2 Three Examples
  575.    wt: 1:   Using Letters for Physical Quantities
  576.    wt: 1:   13 Naming Identifying Formulas with Words
  577.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  578.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  579.    wt: 1:   4 Circle Area Formula Example
  580.    wt: 1:   2 Another Rectangle Area Formula Example
  581.    wt: 1:   1 Written work formats for developing and showing skill
  582.    wt: 1:   6 Power Set Notation
  583.    wt: 1:   5 Product Builder Notation
  584.    wt: 1:   4 Subset Builder Notation
  585.    wt: 1:   1 Finite Sets
  586.    wt: 1:   6 Three Notions of What is a Variable
  587.    wt: 1:   5 Talking about Numbers and Quantities
  588.    wt: 1:   4 A Brief Story of numbers and algebra
  589.    wt: 1:   3 Adding Words To Arithmetic
  590.    wt: 1:   1 Three Skills For Algebra
  591.    wt: 1:   4 Greater More Less Than Signs in General
  592.    wt: 1:   2 More and Less Than with Unlike Signs
  593.    wt: 1:   1 More and Less Than for Counts and Measures
  594.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  595.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  596.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  597.    wt: 1:   13 GCD from given Prime Factorization
  598.    wt: 1:   8 GCD from Euclidean Algorithm
  599.    wt: 1:   4 LCM of 8 and 10 via Prime
  600.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  601.    wt: 1:   2 Least Common Multiple LCM intro via list method
  602.    wt: 1:   3 Counting with Tables and Trees II
  603.    wt: 1:   11 What are real lengths and numbers
  604.    wt: 1:   10 dividing signed numbers
  605.    wt: 1:   9 subtracting signed numbers
  606.    wt: 1:   8 multiplying signed numbers
  607.    wt: 1:   5 lengths and signs of numbers
  608.    wt: 1:   2 signed and unsigned numbers as coordinates
  609.    wt: 1:   6 Simplification of Fractions with Units
  610.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  611.    wt: 1:   3 Multiplying Units and Numbers
  612.    wt: 1:   22 Complex Compound Fractions
  613.    wt: 1:   13 Fraction Comparison Algebraic View
  614.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  615.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  616.    wt: 1:   A Associative Law Theorectical Note
  617.    wt: 1:   13 Subtraction with Additive Inverse
  618.    wt: 1:   10 Integer Multiplication Formulas
  619.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  620.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  621.    wt: 1:   26 Divisibility by 2 3 5 Example
  622.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  623.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  624.    wt: 1:   23 Remainder Arithmetic Modulo 2
  625.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  626.    wt: 1:   21 Remainder Arithmetic Modulo 3
  627.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  628.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  629.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  630.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  631.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  632.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  633.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  634.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  635.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  636.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  637.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  638.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  639.    wt: 1:   Long Division Backward
  640.    wt: 1:   Long Division forwards and backwards Example 3
  641.    wt: 1:   D Decimal Multiplication Methods Derived
  642.    wt: 1:   A Elementary Basis for Multiplication Methods
  643.    wt: 1:   6 Multiplication Commutes Order Not Important
  644.    wt: 1:   4 Two and Three Digit Multipliers
  645.    wt: 1:   2 One Digit Multipliers
  646.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  647.    wt: 1:   Video Power Notation in Decimal Expansion
  648.    wt: 1:   Subtraction Another Video Lesson
  649.    wt: 1:   8 Subtraction with Units of Measure
  650.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  651.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  652.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  653.    wt: 1:   Quick history of numbers and algebra
  654.    wt: 1:   Expression Evaluation how to show work
  655.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  656.    wt: 1:   013 Travel Time Tables
  657.    wt: 1:   012 Division of Time Intervals by Time Intervals
  658.    wt: 1:   011 Division of Time Intervals By Numbers
  659.    wt: 1:   010 Repeated Addition of Time Intervals
  660.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  661.    wt: 1:   8 Addition of Time Intervals via subtotaling
  662.    wt: 1:   7 Addition of Time Intervals
  663.    wt: 1:   6 How long is a million seconds
  664.    wt: 1:   4 Mixing and Changing Units of Time
  665.    wt: 1:   1 Intro of Kids To Time Date Skills
  666.    wt: 1:   5 Area Under Curve Exercise
  667.    wt: 1:   Postscript More on Better Performance
  668.    wt: 1:   Postscript For Better Performance
  669.    wt: 1:   Appendix E. How To Study Mathematics and Why
  670.    wt: 1:   Appendix D. What to do in School and Why
  671.    wt: 1:   Appendix B. How To Learn
  672.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  673.    wt: 1:   Chapter 28 Occurrence Tables
  674.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  675.    wt: 1:   Chapter 19. Functions and Sets
  676.    wt: 1:   Chapter 18. Rules for Algebra
  677.    wt: 1:   Chapter 15. Solving Linear Equations
  678.    wt: 1:   Chapter 12. Shorthand Usage Guide
  679.    wt: 1:   Chapter 11. Why Shorthand
  680.    wt: 1:   Chapter 10 Describing and Changing Calculations
  681.    wt: 1:   Postscript What is a Variable
  682.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  683.    wt: 1:   Solutions For Arithmetic Exercises
  684.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  685.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  686.    wt: 1:   Foreword
  687.    wt: 1:   Annotated Links to Material Elsehwere
  688.    wt: 1:   Postscript B Mathematics Education References
  689.    wt: 1:   Chapter 12 Four Phases
  690.    wt: 1:   Chapter 11 Elementary Instruction
  691.    wt: 1:   Chapter 10 Transition
  692.    wt: 1:   Chapter 9 The Two Ends
  693.    wt: 1:   Chapter 8 Modern Instruction
  694.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  695.    wt: 1:   Chapter 5 Four References
  696.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  697.    wt: 1:   Chapter 2 For and Against Mathematics
  698.    wt: 1:   Chapter 1 Introduction
  699.    wt: 1:   Foreword
  700.    wt: 1:   Postscript C Consistency as a Tool for Reason
  701.    wt: 1:   Postscript B More on Story Telling and Reason
  702.    wt: 1:   Postscript A Story Telling
  703.    wt: 1:   Chapter 24 Direct and Indirect Reason
  704.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  705.    wt: 1:   Chapter 21 Occurrence Tables
  706.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  707.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  708.    wt: 1:   Chapter 18 Sense and Knowledge
  709.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  710.    wt: 1:   Chapter 15 Objective Processes
  711.    wt: 1:   Chapter 11 Accidental Patterns
  712.    wt: 1:   Chapter 10 Responsibility
  713.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  714.    wt: 1:   Chapter 5 Deception
  715.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  716.    wt: 1:   Chapter 2 Skill Development
  717.    wt: 1:   Chapter 1 Introduction
  718.    wt: 1:   Three Remarks
  719.    wt: 1:   Foreword
  720.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  721.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  722.    wt: 1:   M Words to extend arithmetic
  723.    wt: 1:   N Improving Marks on Tests and Finals
  724.    wt: 1:   G. Written work formats for developing and showing skill
  725.    wt: 1:   B. Domino effect of errors
  726.    wt: 1:   Chapter 1 Arithmetic
  727.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  728.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  729.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  730.    wt: 1:   Helping the Blind in Logic and Mathematics
  731.    wt: 1:   Mathematics Education References
  732.    wt: 1:   Mathematics Education References
  733.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  734.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  735.    wt: 1:   Which Way To Go
  736.    wt: 13:   G.1 First Fundamental Theorem of Calculus
  737.    wt: 10:   G.3 Constant Difference Theorem Proof
  738.    wt: 10:   B3 Bolzano Weierstrass Theorem
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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