Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers in school and out. See site volumes.

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons. See Site Map

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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22 matches:

  1.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  2.    wt: 2:   3 Quadratics Geometrically/
  3.    wt: 2:   13 Vectors/
  4.    wt: 2:   3 Cartesian and Polar Coordinates/
  5.    wt: 2:   10 Examples of Algebraic Reasoning/
  6.    wt: 2:   3 Prime Factorization Skills/
  7.    wt: 2:   Volume 1 Elements of Reason/
  8.    wt: 1:   LAMP Lean Applied Mathematics Program/
  9.    wt: 1:   A Origins of Counting and Figuring Methods/
  10.    wt: 1:   Step 4 Gaussian Elimination/
  11.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  12.    wt: 1:   Step 1 Stick diagram and fractions/
  13.    wt: 1:   3 Solving Linear Equations/
  14.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  15.    wt: 1:   C Decimal Multiplication Methods/
  16.    wt: 1:   4 Lessons on Using Derivatives/
  17.    wt: 1:   38 Lessons on Calculating Derivatives/
  18.    wt: 1:   13 Lessons on Limits and Continuity/
  19.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  20.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  21.    wt: 1:   Volume 1A Pattern Based Reason/
  22.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

302 matches:

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

Extended Search

572 matches:

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

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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