Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

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

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

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

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

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

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

Home << Search

[1] [2] [3] [4]

Key Word Search

Folder Search

34 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   11 Parallel Straight Lines and Transversals/
  4.    wt: 6:   10 Intersecting Straight Lines and Transversals/
  5.    wt: 6:   9 Lines and Slopes Take 2 with tangent function/
  6.    wt: 6:   8 Unit Circle Trigonometry/
  7.    wt: 6:   6 Trigonometry first steps/
  8.    wt: 6:   4 Lines and Slopes Take 1/
  9.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  10.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  11.    wt: 5:   12 Function Translating and Rescaling/
  12.    wt: 5:   7 Complex Numbers/
  13.    wt: 5:   5 What is Similarity/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 3:   Progressive Observable Motivated Mathematics Education/
  18.    wt: 2:   4 Lessons on Using Derivatives/
  19.    wt: 2:   38 Lessons on Calculating Derivatives/
  20.    wt: 1:   LAMP Lean Applied Mathematics Program/
  21.    wt: 1:   Mathematics Education Essays/
  22.    wt: 1:   Archives/
  23.    wt: 1:   4 Functions/
  24.    wt: 1:   1 Five Polynomial Operations/
  25.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  26.    wt: 1:   4 Computation Rules and Function Notation/
  27.    wt: 1:   Step 4 Gaussian Elimination/
  28.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  29.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  30.    wt: 1:   Step 1 Stick diagram and fractions/
  31.    wt: 1:   3 Solving Linear Equations/
  32.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  33.    wt: 1:   D Decimal Long Division Methods/
  34.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/

Web Page Search

254 matches:

  1.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  2.    wt: 3:   19 Horizontal line rule and method
  3.    wt: 3:   5 Polynomials Long division Nonlinear divisor
  4.    wt: 3:   4 Polynomials Long division linear divisor
  5.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  6.    wt: 3:   31 Derivatives of inverse functions
  7.    wt: 3:   19 Chain Rule for linear functions
  8.    wt: 2:   Maps Plans Drawings
  9.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  10.    wt: 2:   18 Vertical Line Rule and Method
  11.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  12.    wt: 2:   6 Intersection of lines by solving linear systems
  13.    wt: 2:   4 Angles on Maps Plans drawn to scale
  14.    wt: 2:   3 Lengths and Areas on Maps and Plans
  15.    wt: 2:   23 Distributive Law Two Derivations
  16.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  17.    wt: 2:   1 Equivalent Computation Rules
  18.    wt: 2:   12 Real Number Additive Inverses or Negatives
  19.    wt: 2:   7 negative and additive inverse
  20.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  21.    wt: 2:   10 Division by Five Long and Short Ways
  22.    wt: 2:   4 Division with 2 Digit Divsors
  23.    wt: 2:   3 Division Single Digit Divisor Example
  24.    wt: 2:   2 Division with Single Digit Divisors
  25.    wt: 2:   4 Second derivative test exercise example
  26.    wt: 2:   3 Second derivative test
  27.    wt: 2:   2 Second derivative test prequel
  28.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  29.    wt: 2:   38 Formulas and derivatives for powers and roots
  30.    wt: 2:   36 Cube root derivative animated
  31.    wt: 2:   34 Derivative of exponential function
  32.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  33.    wt: 2:   26 Chain Rule Recognising outer inner functions
  34.    wt: 2:   17 Derivatives of quotients of sine and cosine
  35.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  36.    wt: 2:   15 sine and cosine derivatives 3rd step
  37.    wt: 2:   14 sine and cosine derivatives 2nd step
  38.    wt: 2:   13 sine and cosine derivatives 1st step
  39.    wt: 2:   10 Power rule for negative integers
  40.    wt: 2:   6 Power rule from product rule
  41.    wt: 2:   3 Motivation for Limit Definition Take 2
  42.    wt: 2:   2 Motivation for Limit Definition Take 1
  43.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  44.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  45.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  46.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  47.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  48.    wt: 1:   A Introduction Objectives
  49.    wt: 1:   Math Ed if it must be short make it lean effective
  50.    wt: 1:   activities for students
  51.    wt: 1:   links Education Resources online
  52.    wt: 1:   About site lesson plans
  53.    wt: 1:   five decades make a difference
  54.    wt: 1:   cultivating intelligence
  55.    wt: 1:   Motivation and Context Problem
  56.    wt: 1:   fairness and inductive principles for instruction
  57.    wt: 1:   chapitre 12 00 les iles et division
  58.    wt: 1:   deux definitions pour variable
  59.    wt: 1:   B Wire Resistance Qualitative02
  60.    wt: 1:   A Wire Resistance Qualitative01
  61.    wt: 1:   C Electromotive force conventional current02
  62.    wt: 1:   B Electromotive force conventional current01
  63.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  64.    wt: 1:   12 Goals and Objectives For Mathematics
  65.    wt: 1:   8 The Effect of Negative Remarks
  66.    wt: 1:   7 Student Motivation
  67.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  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:   26 Function definitions done and coming
  71.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  72.    wt: 1:   23 Inverse Functions
  73.    wt: 1:   15 Sign analysis of functions
  74.    wt: 1:   8 Set view of relations and functions
  75.    wt: 1:   7 Functions with finite domains
  76.    wt: 1:   7 quadratic formulla derivation
  77.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  78.    wt: 1:   1 Polynomials Distributive Law
  79.    wt: 1:   16 cotangent function Definition Graph and Inverse
  80.    wt: 1:   15 cosecant function Definition Graph and Inverse
  81.    wt: 1:   14 secant function Definition Graph and Inverse
  82.    wt: 1:   13 cosecant function Definition Graph and Inverse
  83.    wt: 1:   12 motivation for term arctan
  84.    wt: 1:   10 arctan left inverse of tangent Definition
  85.    wt: 1:   9 motivation for name arcsin
  86.    wt: 1:   7 arcsin left inverse of sine Definition
  87.    wt: 1:   4 possible motivation for term arccos
  88.    wt: 1:   3 Left Inverse of cosine arccos definition
  89.    wt: 1:   13 Velocity Vectors in Physics
  90.    wt: 1:   8 Parallel Vectors
  91.    wt: 1:   6 Vectors with Coordinates
  92.    wt: 1:   3 Navigation with Arrows or Vectors
  93.    wt: 1:   Parallel Lines and Parallel Transversals
  94.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  95.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  96.    wt: 1:   Parallel Lines and Interior Angles
  97.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  98.    wt: 1:   Straight Lines ASA Intersection Study More
  99.    wt: 1:   Straight Lines ASA Intersection Study
  100.    wt: 1:   Straight Lines Instersection Solving Equations
  101.    wt: 1:   Straight Lines Intersection of
  102.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  103.    wt: 1:   C Straight Lines Slope from Coordinates
  104.    wt: 1:   B Straight Line Slope Scaling Properties More
  105.    wt: 1:   A Straight Line Slope Scaling Properties
  106.    wt: 1:   14 Straight Lines Equations General Case
  107.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  108.    wt: 1:   12 Straight Lines Graphing mx plus b
  109.    wt: 1:   11 Straight Lines Graphing y=mx
  110.    wt: 1:   10 Straight Lines through Origin Equations More
  111.    wt: 1:   9 Straight Lines through Origin Equations
  112.    wt: 1:   8 Straight Lines Equation for vertical
  113.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  114.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  115.    wt: 1:   1 Straight Lines Slope Concept
  116.    wt: 1:   30 unit circle calculation of six trigonometric functions
  117.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  118.    wt: 1:   Unit Circle Development of Trigonometry
  119.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  120.    wt: 1:   8 Unit Circle Development of Trigonometry
  121.    wt: 1:   5 An Easy Proof of the Distributive Law
  122.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  123.    wt: 1:   Why Trigonometry the whyslopes view
  124.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  125.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  126.    wt: 1:   4 Similarity Definition with Coordinate
  127.    wt: 1:   4 Equations for lines three forms
  128.    wt: 1:   3 Slope product for perpendicular lines
  129.    wt: 1:   2 point slope equation for a line
  130.    wt: 1:   1 Numerical view of lines and their equations
  131.    wt: 1:   8 Distance Between Points on a Line
  132.    wt: 1:   PS H Distributive Law For Complex Numbers
  133.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  134.    wt: 1:   14 Parallel Lines Postulate
  135.    wt: 1:   10 Dropping a perpendicular to line
  136.    wt: 1:   6 Ruler and compass Angle Bisection
  137.    wt: 1:   A Measurement with Ruler Proper Use
  138.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  139.    wt: 1:   6 Figuring with Maps Not to Scale
  140.    wt: 1:   19 Signed Multiples of Vectors
  141.    wt: 1:   15 Head to Tails in place Addition Associative
  142.    wt: 1:   13 Arrows and Vectors in a Plane
  143.    wt: 1:   12 Real Numbers Line Signed Coordinates
  144.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  145.    wt: 1:   9 Division with Digits after Decimal Point
  146.    wt: 1:   8 Division and Mulplication of Compound Fractions
  147.    wt: 1:   E Long Division Methods more
  148.    wt: 1:   D Long Division Methods
  149.    wt: 1:   5 Distributive Law for Whole Numbers
  150.    wt: 1:   4 Commutative Law Groups Counting Form
  151.    wt: 1:   3 Multiplicative Counting Skills Principles
  152.    wt: 1:   5 Proportionality in Equivalent Fractions
  153.    wt: 1:   3 Linear Equation Literal Solution More
  154.    wt: 1:   2 Linear Equation Literal Solution
  155.    wt: 1:   6 Equations and Systems Equivalent or Implied
  156.    wt: 1:   4 Subtraction and Division Axioms
  157.    wt: 1:   4 Comparison of Negative Numbers
  158.    wt: 1:   15 Real Number Division
  159.    wt: 1:   8 Coordinates for Maps and Planes
  160.    wt: 1:   7 Real Numbers as Line Cordinates
  161.    wt: 1:   2 Computation Rules Evaluation
  162.    wt: 1:   3 Comparison of Negative Numbers
  163.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  164.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  165.    wt: 1:   13 GCD from given Prime Factorization
  166.    wt: 1:   5 Common Divisors 60 45 via Prime
  167.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  168.    wt: 1:   4 Counting with Trees Product Rule Take I
  169.    wt: 1:   10 dividing signed numbers
  170.    wt: 1:   3 signed coordinates for maps and planes
  171.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  172.    wt: 1:   20 Dividing Fractions the Why
  173.    wt: 1:   19 Dividing Fractions How TO
  174.    wt: 1:   5 Equivalent Fractions
  175.    wt: 1:   D Remainders Modulo 11 Pair Rule
  176.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  177.    wt: 1:   B Integer Long Division Multiple Choices
  178.    wt: 1:   A Associative Law Theorectical Note
  179.    wt: 1:   13 Subtraction with Additive Inverse
  180.    wt: 1:   5 Zero Movement and Additive Inverses
  181.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  182.    wt: 1:   26 Divisibility by 2 3 5 Example
  183.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  184.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  185.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  186.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  187.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  188.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  189.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  190.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  191.    wt: 1:   18 video Count Factors given Prime Factorization
  192.    wt: 1:   11 Efficient Square Rule Use
  193.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  194.    wt: 1:   5 Prime Factorization and a Square Rule
  195.    wt: 1:   Long Division Backwards more
  196.    wt: 1:   Long Division Backward
  197.    wt: 1:   Division with Counts and Length
  198.    wt: 1:   Long Division forwards and backwards Example 3
  199.    wt: 1:   Long Division forwards and backwards Example 2
  200.    wt: 1:   Long Division forwards and backwards Example 1
  201.    wt: 1:   12 Why Long Division Works Take III
  202.    wt: 1:   11 Another Single Digit Divisor Example
  203.    wt: 1:   9 Why Long Division Works Take II
  204.    wt: 1:   7 Long Divison Mistake Catching
  205.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  206.    wt: 1:   5 Long Division Include Zeroes or not
  207.    wt: 1:   1 Divsion Physical Examples
  208.    wt: 1:   D Decimal Multiplication Methods Derived
  209.    wt: 1:   1 Why 3 times 5 gives 15
  210.    wt: 1:   012 Division of Time Intervals by Time Intervals
  211.    wt: 1:   011 Division of Time Intervals By Numbers
  212.    wt: 1:   3 Two Chain Rule Method Exercises
  213.    wt: 1:   1 Chain Rule in Reverse Integration Method
  214.    wt: 1:   A Chain Rule Real Player video examples
  215.    wt: 1:   33 Chain Rule Real Player video examples
  216.    wt: 1:   30Chain Rule A Proof
  217.    wt: 1:   29 Chain Rule Optional Reading
  218.    wt: 1:   28 Chain Rule Preparation for a Proof
  219.    wt: 1:   25 Chain Rule Animated Examples Continued
  220.    wt: 1:   24 Chain Rule Animated Examples
  221.    wt: 1:   23 Chain Rule in general
  222.    wt: 1:   22 Chain Rule for polynomials
  223.    wt: 1:   21 Chain Rule for powers
  224.    wt: 1:   20 Chain Rule for Pulley Systems
  225.    wt: 1:   18 Chain Rule Introduction
  226.    wt: 1:   12 Quotient rule examples
  227.    wt: 1:   11 Quotient rule
  228.    wt: 1:   9 Reciprocal rule
  229.    wt: 1:   5 Product Rule
  230.    wt: 1:   4 Sum Rule
  231.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  232.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  233.    wt: 1:   F.1 What Functions are Continuous
  234.    wt: 1:   PostScript For and Against Decimal Perspectives
  235.    wt: 1:   Chapter 23 Links To Trigonometry
  236.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  237.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  238.    wt: 1:   Chapter 19. Functions and Sets
  239.    wt: 1:   Chapter 18. Rules for Algebra
  240.    wt: 1:   Chapter 15. Solving Linear Equations
  241.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  242.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  243.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  244.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  245.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  246.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  247.    wt: 1:   Chapter 15 Objective Processes
  248.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  249.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  250.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  251.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  252.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  253.    wt: 1:   7 Games and Activities for Instruction
  254.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

593 matches:

  1.    wt: 9:   4 Angles on Maps Plans drawn to scale
  2.    wt: 9:   3 Lengths and Areas on Maps and Plans
  3.    wt: 8:   6 Intersection of lines by solving linear systems
  4.    wt: 8:   A Measurement with Ruler Proper Use
  5.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  6.    wt: 8:   6 Figuring with Maps Not to Scale
  7.    wt: 7:   13 Velocity Vectors in Physics
  8.    wt: 7:   8 Parallel Vectors
  9.    wt: 7:   6 Vectors with Coordinates
  10.    wt: 7:   3 Navigation with Arrows or Vectors
  11.    wt: 7:   Parallel Lines and Parallel Transversals
  12.    wt: 7:   Proportionality of Line Segments From Parallel Transversals
  13.    wt: 7:   Parallel Lines and Alternating Corresponding Angles
  14.    wt: 7:   Parallel Lines and Interior Angles
  15.    wt: 7:   Analytic View of Triangle Construction or Line Instersection More
  16.    wt: 7:   Straight Lines ASA Intersection Study More
  17.    wt: 7:   Straight Lines ASA Intersection Study
  18.    wt: 7:   Straight Lines Instersection Solving Equations
  19.    wt: 7:   Straight Lines Intersection of
  20.    wt: 7:   D Straight Lines Slope from Coordinates Examples
  21.    wt: 7:   C Straight Lines Slope from Coordinates
  22.    wt: 7:   B Straight Line Slope Scaling Properties More
  23.    wt: 7:   A Straight Line Slope Scaling Properties
  24.    wt: 7:   14 Straight Lines Equations General Case
  25.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  26.    wt: 7:   12 Straight Lines Graphing mx plus b
  27.    wt: 7:   11 Straight Lines Graphing y=mx
  28.    wt: 7:   10 Straight Lines through Origin Equations More
  29.    wt: 7:   9 Straight Lines through Origin Equations
  30.    wt: 7:   8 Straight Lines Equation for vertical
  31.    wt: 7:   3 Straight Lines Slope as Tangent of Inclination Angle
  32.    wt: 7:   2 Straight Lines Slopes As Rise Over Run
  33.    wt: 7:   1 Straight Lines Slope Concept
  34.    wt: 7:   30 unit circle calculation of six trigonometric functions
  35.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  36.    wt: 7:   Unit Circle Development of Trigonometry
  37.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  38.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  39.    wt: 7:   Why Trigonometry the whyslopes view
  40.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  41.    wt: 7:   4 Equations for lines three forms
  42.    wt: 7:   3 Slope product for perpendicular lines
  43.    wt: 7:   2 point slope equation for a line
  44.    wt: 7:   1 Numerical view of lines and their equations
  45.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  46.    wt: 7:   2 Measuring Area Directly
  47.    wt: 7:   1 Length Measurement
  48.    wt: 6:   16 cotangent function Definition Graph and Inverse
  49.    wt: 6:   15 cosecant function Definition Graph and Inverse
  50.    wt: 6:   14 secant function Definition Graph and Inverse
  51.    wt: 6:   13 cosecant function Definition Graph and Inverse
  52.    wt: 6:   12 motivation for term arctan
  53.    wt: 6:   10 arctan left inverse of tangent Definition
  54.    wt: 6:   9 motivation for name arcsin
  55.    wt: 6:   7 arcsin left inverse of sine Definition
  56.    wt: 6:   4 possible motivation for term arccos
  57.    wt: 6:   3 Left Inverse of cosine arccos definition
  58.    wt: 6:   A Global Time and Navigation
  59.    wt: 6:   15 Dot and Cross Product
  60.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  61.    wt: 6:   12 From Applied To Pure Mathematics
  62.    wt: 6:   11 Component Method
  63.    wt: 6:   10 Parallelogram Addition Method
  64.    wt: 6:   9 Head to Tail Coordinate View
  65.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  66.    wt: 6:   5 Head To Tail Arrow Addition
  67.    wt: 6:   4 Resultant of a Sum of Movements
  68.    wt: 6:   2 Signed Coordinates
  69.    wt: 6:   1 Unsigned Coordinates
  70.    wt: 6:   Vector and Complex Number Applet
  71.    wt: 6:   Triangle Angles Sum To 180 Degrees
  72.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  73.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  74.    wt: 6:   7 Tangent Function is odd on this domain
  75.    wt: 6:   6 Tangent Function Inclination Angle Take 2
  76.    wt: 6:   5 Tangent Function Graph
  77.    wt: 6:   4 Tangent Function Properties
  78.    wt: 6:   17 tangent function angle sum formulas
  79.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  80.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  81.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  82.    wt: 6:   32 seven rows of pascals triangle
  83.    wt: 6:   31 basic secant cosecant cotangent trig identities
  84.    wt: 6:   29 secant cosecant and cotangent for acute angles
  85.    wt: 6:   28 Expressing products of sines cosines as sums
  86.    wt: 6:   27 Logarithmic use of products of sines and cosines
  87.    wt: 6:   26 Formulas for products of sines and cosines
  88.    wt: 6:   25 tangent double angle formula Slope connection
  89.    wt: 6:   24 tangent Angle Difference Formula
  90.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  91.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  92.    wt: 6:   21 sine and cosine Half Angle Formulas
  93.    wt: 6:   20 sine and cosine Double Angle Formulas
  94.    wt: 6:   18 sum of sinusoidal waves as a single wave
  95.    wt: 6:   17G Pythagorean Theorem Converse
  96.    wt: 6:   17F Law of cosines
  97.    wt: 6:   17E Trig Formulas for dot and cross Products
  98.    wt: 6:   17D cis formulas for sine cosines and tangent
  99.    wt: 6:   17C sine and cosine double triple angle formulas
  100.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  101.    wt: 6:   17A The complex number valued trig function cis
  102.    wt: 6:   16 Right Triangle Complementary Angle Relations
  103.    wt: 6:   15 sine cosine Complementary Angle Relations
  104.    wt: 6:   14 cosine even and sine and tangent are odd
  105.    wt: 6:   13 Graph of tangent function many periods
  106.    wt: 6:   12 Graph of tangent function for one period
  107.    wt: 6:   11 tangent function undefined when terminal side vertical
  108.    wt: 6:   10 Graphs of sines and cosines many periods
  109.    wt: 6:   9 Graphs of sine and cosine over one period
  110.    wt: 6:   8 period of tangent function
  111.    wt: 6:   7 period of sine and cosine
  112.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  113.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  114.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  115.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  116.    wt: 6:   2 Quadrant I reference Angles
  117.    wt: 6:   1 Unit Points Reflections Rotations
  118.    wt: 6:   8 Unit Circle Development of Trigonometry
  119.    wt: 6:   5 An Easy Proof of the Distributive Law
  120.    wt: 6:   8 Triangles Cascade Problem Solving
  121.    wt: 6:   7 Trignometric Ratios Unit Circle
  122.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  123.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  124.    wt: 6:   3 Trigonometric Ratios sine and cosine
  125.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  126.    wt: 6:   1 Angle Measurement with Degrees
  127.    wt: 6:   10 Similarity of Triangles Equivalent of Two Criteria
  128.    wt: 6:   4 Similarity Definition with Coordinate
  129.    wt: 6:   Four Simple Exercises
  130.    wt: 6:   12 Links Lessons elsewhere
  131.    wt: 6:   11 A Partial Summary
  132.    wt: 6:   10 Midpoint of [a b] and [b a]
  133.    wt: 6:   9 Midpoint Coordinates Half Endpoint Sum
  134.    wt: 6:   8 Mid Point Formula
  135.    wt: 6:   7 Exercises to test skill and concept mastery
  136.    wt: 6:   5 Algebraic View of Slopes
  137.    wt: 6:   What is and is not here
  138.    wt: 6:   8 Distance Between Points on a Line
  139.    wt: 6:   PS H Distributive Law For Complex Numbers
  140.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  141.    wt: 6:   14 Parallel Lines Postulate
  142.    wt: 6:   10 Dropping a perpendicular to line
  143.    wt: 6:   6 Ruler and compass Angle Bisection
  144.    wt: 5:   21 Graphs of functions given by Horizontal Line Method
  145.    wt: 5:   11 arctan left inverse of tangent Graph
  146.    wt: 5:   8 arcsin left inverse of sine Graph
  147.    wt: 5:   6 Graph of arccos function
  148.    wt: 5:   5 Swapping Coordinates is a reflection
  149.    wt: 5:   2 cosine function more properties
  150.    wt: 5:   1 cosine function properties
  151.    wt: 5:   9 Summary Degrees to Radians and back
  152.    wt: 5:   8 Radian Measures of Common Angles
  153.    wt: 5:   7 Radian Measures in special Triangles
  154.    wt: 5:   6 Radian Measure to Degrees
  155.    wt: 5:   5 Degrees to Radian Measure
  156.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  157.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  158.    wt: 5:   2 Radian Measure Numerical Value of one degree
  159.    wt: 5:   1 Degrees and Radians Introduction
  160.    wt: 5:   4 graphing y=Asin(x c)
  161.    wt: 5:   3 graphing y=f(x c) plus K
  162.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  163.    wt: 5:   1 graphing y=f(x a)
  164.    wt: 5:   21 Logarithms Powers and Exponentials
  165.    wt: 5:   20 N th Roots of Complex Numbers
  166.    wt: 5:   19 N th Roots of Unity
  167.    wt: 5:   18 Sixth Roots of Unity
  168.    wt: 5:   17 Cube Roots of unity
  169.    wt: 5:   16 References and Originality Question
  170.    wt: 5:   15 Pythagorean Theorem Converse
  171.    wt: 5:   14 Law of cosines
  172.    wt: 5:   13 Trig Formulas for dot and cross Products
  173.    wt: 5:   12 cis formulas for sine cosines and tangent
  174.    wt: 5:   11 sine and cosine double triple angle formulas
  175.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  176.    wt: 5:   9 The complex number valued trig function cis
  177.    wt: 5:   7 Second Way to Calculate Products
  178.    wt: 5:   6 Field Properties of Complex Number
  179.    wt: 5:   4 Multiplication Properties
  180.    wt: 5:   3 Addition Properties
  181.    wt: 5:   2 Complex Numbers made easier we hope
  182.    wt: 5:   1 Rectangular Polar Coordinates Review
  183.    wt: 5:   Appetizer A Complex Number Applet
  184.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  185.    wt: 5:   12 Triangles Similarity More Problems
  186.    wt: 5:   11 Triangle Similarity Missing Side Problem
  187.    wt: 5:   9 Similarity of Triangles Usual Criteria
  188.    wt: 5:   8 Similarity of Triangles and Polygons
  189.    wt: 5:   7 Translations Rotations Reflections Dilatations
  190.    wt: 5:   6 Geometric Diagrams in Class
  191.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  192.    wt: 5:   3 Similarity by Design with coordinates
  193.    wt: 5:   2 Similarity By Design
  194.    wt: 5:   1 Early Concept of Like or Similar Shapes
  195.    wt: 5:   13 Pythagorean spatial distance formulas
  196.    wt: 5:   12 Spatial Coordinates
  197.    wt: 5:   11 Triangle Inequality
  198.    wt: 5:   10 Pythagorean plane distance formula
  199.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  200.    wt: 5:   7 Complex Numbers Appetizer
  201.    wt: 5:   6 Polar Multiplication and Rotation
  202.    wt: 5:   5 Cartesian Addition and Translation
  203.    wt: 5:   4 Polar Coordinates to and from
  204.    wt: 5:   3 Rectangular Coordinates Review
  205.    wt: 5:   2 Cartesian Coordinates with signs
  206.    wt: 5:   1 Cartesian Coordinates sans signs
  207.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  208.    wt: 5:   PS G Rotation Distributes over Addition
  209.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  210.    wt: 5:   PS E Multiplication with Polar Coordinates
  211.    wt: 5:   PS D Addition with Cartesian Coordinates
  212.    wt: 5:   PS B Parallelogram Construction Methods
  213.    wt: 5:   PS A Kite Construction Methods
  214.    wt: 5:   21 Parallelograms
  215.    wt: 5:   19 Right Triangle Similarity
  216.    wt: 5:   18 Triangle Similarity Take 1
  217.    wt: 5:   17 Right Bisectors of Triangle Sides
  218.    wt: 5:   16 Angles Subtended By Chords and Diameters
  219.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  220.    wt: 5:   13 Angle Side Angle Failure
  221.    wt: 5:   12 Side Angle Side Failure
  222.    wt: 5:   11 Triangle Construction Fails
  223.    wt: 5:   9 Construction of a right bisector
  224.    wt: 5:   8 Isoceles Triangles
  225.    wt: 5:   7 Angle Side Angle
  226.    wt: 5:   5 Side Angle Side
  227.    wt: 5:   4 Side Side Side
  228.    wt: 5:   3 Isometry of Triangles Congruence
  229.    wt: 5:   2 Correspondence between Triangles
  230.    wt: 5:   1 Initial Concepts and Terms
  231.    wt: 5:   Short Course on Euclidean Geometry
  232.    wt: 5:   About Folder Contents
  233.    wt: 5:   31 Derivatives of inverse functions
  234.    wt: 5:   19 Chain Rule for linear functions
  235.    wt: 4:   19 Horizontal line rule and method
  236.    wt: 4:   5 Polynomials Long division Nonlinear divisor
  237.    wt: 4:   4 Polynomials Long division linear divisor
  238.    wt: 4:   4 Second derivative test exercise example
  239.    wt: 4:   3 Second derivative test
  240.    wt: 4:   2 Second derivative test prequel
  241.    wt: 4:   1 Two cubic sketching exercises with 1st derivative
  242.    wt: 4:   38 Formulas and derivatives for powers and roots
  243.    wt: 4:   36 Cube root derivative animated
  244.    wt: 4:   34 Derivative of exponential function
  245.    wt: 4:   27 Chain Rule sinusoidal outer inner functions EGS
  246.    wt: 4:   26 Chain Rule Recognising outer inner functions
  247.    wt: 4:   17 Derivatives of quotients of sine and cosine
  248.    wt: 4:   16 Derivatives of reciprocals of sine and cosine
  249.    wt: 4:   15 sine and cosine derivatives 3rd step
  250.    wt: 4:   14 sine and cosine derivatives 2nd step
  251.    wt: 4:   13 sine and cosine derivatives 1st step
  252.    wt: 4:   10 Power rule for negative integers
  253.    wt: 4:   6 Power rule from product rule
  254.    wt: 4:   3 Motivation for Limit Definition Take 2
  255.    wt: 4:   2 Motivation for Limit Definition Take 1
  256.    wt: 3:   11 pure mathematics
  257.    wt: 3:   10 statistics
  258.    wt: 3:   9 combinatorics probability sets
  259.    wt: 3:   8 analytic geometry etc
  260.    wt: 3:   7 logic review and decimals an odd combination
  261.    wt: 3:   6 polynomials etc
  262.    wt: 3:   5 logarithms and exponentials etc
  263.    wt: 3:   4 algebra
  264.    wt: 3:   3 Euclidean Geometry Leanly
  265.    wt: 3:   2 arithmetic with signed numbers
  266.    wt: 3:   1 arithmetic with unsigned numbers
  267.    wt: 3:   What is POMME
  268.    wt: 3:   Maps Plans Drawings
  269.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  270.    wt: 3:   18 Vertical Line Rule and Method
  271.    wt: 3:   6 Polynomial Operations and Equivalent Computation Rules
  272.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  273.    wt: 3:   1 Equivalent Computation Rules
  274.    wt: 3:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  275.    wt: 3:   10 Division by Five Long and Short Ways
  276.    wt: 3:   4 Division with 2 Digit Divsors
  277.    wt: 3:   3 Division Single Digit Divisor Example
  278.    wt: 3:   2 Division with Single Digit Divisors
  279.    wt: 3:   A Chain Rule Real Player video examples
  280.    wt: 3:   33 Chain Rule Real Player video examples
  281.    wt: 3:   30Chain Rule A Proof
  282.    wt: 3:   29 Chain Rule Optional Reading
  283.    wt: 3:   28 Chain Rule Preparation for a Proof
  284.    wt: 3:   25 Chain Rule Animated Examples Continued
  285.    wt: 3:   24 Chain Rule Animated Examples
  286.    wt: 3:   23 Chain Rule in general
  287.    wt: 3:   22 Chain Rule for polynomials
  288.    wt: 3:   21 Chain Rule for powers
  289.    wt: 3:   20 Chain Rule for Pulley Systems
  290.    wt: 3:   18 Chain Rule Introduction
  291.    wt: 3:   12 Quotient rule examples
  292.    wt: 3:   11 Quotient rule
  293.    wt: 3:   9 Reciprocal rule
  294.    wt: 3:   5 Product Rule
  295.    wt: 3:   4 Sum Rule
  296.    wt: 3:   5 Interpreting and Drawing Maps and Plans.
  297.    wt: 2:   A Introduction Objectives
  298.    wt: 2:   Math Ed if it must be short make it lean effective
  299.    wt: 2:   activities for students
  300.    wt: 2:   links Education Resources online
  301.    wt: 2:   About site lesson plans
  302.    wt: 2:   five decades make a difference
  303.    wt: 2:   cultivating intelligence
  304.    wt: 2:   Motivation and Context Problem
  305.    wt: 2:   fairness and inductive principles for instruction
  306.    wt: 2:   26 Function definitions done and coming
  307.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  308.    wt: 2:   23 Inverse Functions
  309.    wt: 2:   15 Sign analysis of functions
  310.    wt: 2:   8 Set view of relations and functions
  311.    wt: 2:   7 Functions with finite domains
  312.    wt: 2:   1 Polynomials Distributive Law
  313.    wt: 2:   23 Distributive Law Two Derivations
  314.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  315.    wt: 2:   6 Equations and Systems Equivalent or Implied
  316.    wt: 2:   4 Subtraction and Division Axioms
  317.    wt: 2:   12 Real Number Additive Inverses or Negatives
  318.    wt: 2:   2 Computation Rules Evaluation
  319.    wt: 2:   7 negative and additive inverse
  320.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  321.    wt: 2:   26 Divisibility by 2 3 5 Example
  322.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  323.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  324.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  325.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  326.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  327.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  328.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  329.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  330.    wt: 2:   Long Division Backwards more
  331.    wt: 2:   Long Division Backward
  332.    wt: 2:   Division with Counts and Length
  333.    wt: 2:   Long Division forwards and backwards Example 3
  334.    wt: 2:   Long Division forwards and backwards Example 2
  335.    wt: 2:   Long Division forwards and backwards Example 1
  336.    wt: 2:   12 Why Long Division Works Take III
  337.    wt: 2:   11 Another Single Digit Divisor Example
  338.    wt: 2:   9 Why Long Division Works Take II
  339.    wt: 2:   7 Long Divison Mistake Catching
  340.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  341.    wt: 2:   5 Long Division Include Zeroes or not
  342.    wt: 2:   1 Divsion Physical Examples
  343.    wt: 2:   A Related lessons in Volume 3
  344.    wt: 2:   8 Differentiation of polynomials
  345.    wt: 2:   7 Animated Differentiation Examples
  346.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  347.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  348.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  349.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  350.    wt: 2:   7 Games and Activities for Instruction
  351.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  352.    wt: 1:   Appendix 2 primary school Arithmetic 01
  353.    wt: 1:   Appendix 1 primary and preschool mathematic
  354.    wt: 1:   K LAMP Musings Science Education
  355.    wt: 1:   J LAMP Introduction Extrinsic Origins
  356.    wt: 1:   I LAMP Introduction Study Habits
  357.    wt: 1:   H LAMP Introduction Instructional Concepts
  358.    wt: 1:   G LAMP Introduction Problem Solving Skills
  359.    wt: 1:   F LAMP Introduction Prerequisites
  360.    wt: 1:   E LAMP Introduction Modern Mathematics
  361.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  362.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  363.    wt: 1:   Skills Chapter 5 Calculus
  364.    wt: 1:   Skills Chapter 4 Logic
  365.    wt: 1:   Ramblings Extrinsic numbers theory
  366.    wt: 1:   Ramblings Introduction Algebra Essay
  367.    wt: 1:   Skills Chapter 3 Algebra
  368.    wt: 1:   Skills Chapter 2 Geometry
  369.    wt: 1:   Skills Chapter 1 Arithmetic
  370.    wt: 1:   Skills Chapter 0 Introduction
  371.    wt: 1:   why bother
  372.    wt: 1:   which way to go
  373.    wt: 1:   website reviews
  374.    wt: 1:   three goals to set for students
  375.    wt: 1:   Teach the teachers plus goals
  376.    wt: 1:   permissions for teachers
  377.    wt: 1:   Applied Maths Program14092009 POMME variant
  378.    wt: 1:   site origins
  379.    wt: 1:   site eurekas
  380.    wt: 1:   key notes and themes
  381.    wt: 1:   Mathematics Education Professors
  382.    wt: 1:   teacher certification
  383.    wt: 1:   modern education
  384.    wt: 1:   learning takes time
  385.    wt: 1:   grouping students according to ability
  386.    wt: 1:   what should be learnt and When
  387.    wt: 1:   mathematics in context
  388.    wt: 1:   Postscript 2007 01 10
  389.    wt: 1:   Education Reform Inconsistencies
  390.    wt: 1:   how letters appear
  391.    wt: 1:   Secondary Three Mathematics
  392.    wt: 1:   Secondary Two Mathematics
  393.    wt: 1:   Secondary One Mathematics
  394.    wt: 1:   talk the algebra talk
  395.    wt: 1:   three difficulties
  396.    wt: 1:   teaching tips
  397.    wt: 1:   What to Tell Students
  398.    wt: 1:   mathematics curriculum shifts
  399.    wt: 1:   geometric implications for algebra
  400.    wt: 1:   teaching tutoring algebraic reason
  401.    wt: 1:   Lessening Algebra Difficulties
  402.    wt: 1:   the trouble with algebra
  403.    wt: 1:   three goals for Mathematics Education
  404.    wt: 1:   05 13 OldSiteEntrancePage
  405.    wt: 1:   04 29 New Mathematics Curriculum
  406.    wt: 1:   04 25 when to stop or suspend mathemat
  407.    wt: 1:   02 21 words for teachers
  408.    wt: 1:   02 20 mathematics education references
  409.    wt: 1:   three aims for mathematics students
  410.    wt: 1:   standards for course material
  411.    wt: 1:   Operational Viewpoint to Value
  412.    wt: 1:   formal or informal peer review
  413.    wt: 1:   Theory of Knowledge
  414.    wt: 1:   mathematics instruction in general
  415.    wt: 1:   Education in mathematics science and technology
  416.    wt: 1:   Different Kinds of Reasoning in maths
  417.    wt: 1:   three kinds of reason in mathematics
  418.    wt: 1:   Four ways to improve education reform
  419.    wt: 1:   How to be a better instructor
  420.    wt: 1:   need for a mixed mathematics curriculum
  421.    wt: 1:   Leaner mathematics curriculum
  422.    wt: 1:   Prequel In For A Penny In For A Pound
  423.    wt: 1:   education an empirical art
  424.    wt: 1:   words for mathematics instructor
  425.    wt: 1:   chapitre 12 00 les iles et division
  426.    wt: 1:   deux definitions pour variable
  427.    wt: 1:   B Wire Resistance Qualitative02
  428.    wt: 1:   A Wire Resistance Qualitative01
  429.    wt: 1:   C Electromotive force conventional current02
  430.    wt: 1:   B Electromotive force conventional current01
  431.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  432.    wt: 1:   12 Goals and Objectives For Mathematics
  433.    wt: 1:   8 The Effect of Negative Remarks
  434.    wt: 1:   7 Student Motivation
  435.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  436.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  437.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  438.    wt: 1:   22 Square Root function graphically
  439.    wt: 1:   20 Interchanging coordinates a reflection
  440.    wt: 1:   17 Function maxima minima and their location
  441.    wt: 1:   16 Increasing or decreasing on intervals
  442.    wt: 1:   14 Surjections Injections Bijections
  443.    wt: 1:   13 From one to one to many to one
  444.    wt: 1:   12 Function Domain Recognition Exercises
  445.    wt: 1:   11 Function Domain Range Source and Targets
  446.    wt: 1:   10 Interval Notation
  447.    wt: 1:   9 Set theory term relation possible origins
  448.    wt: 1:   6 Set Existence Formation and Notation
  449.    wt: 1:   5 Function notation for geometric transformations
  450.    wt: 1:   4 Function notation in and beyond mathematics
  451.    wt: 1:   3 Formula or function graphing exercise
  452.    wt: 1:   2 Algebraic use of function notation
  453.    wt: 1:   1 Geometric Introduction of Function Notation
  454.    wt: 1:   Introduction Reading Guide
  455.    wt: 1:   7 quadratic formulla derivation
  456.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  457.    wt: 1:   8 Notes for instructors or tutors
  458.    wt: 1:   7 Links Lessons Elsewhere
  459.    wt: 1:   3 Polynomials Multiplication Addition
  460.    wt: 1:   2 Column Multiplication Method
  461.    wt: 1:   19 Signed Multiples of Vectors
  462.    wt: 1:   15 Head to Tails in place Addition Associative
  463.    wt: 1:   13 Arrows and Vectors in a Plane
  464.    wt: 1:   12 Real Numbers Line Signed Coordinates
  465.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  466.    wt: 1:   9 Division with Digits after Decimal Point
  467.    wt: 1:   8 Division and Mulplication of Compound Fractions
  468.    wt: 1:   E Long Division Methods more
  469.    wt: 1:   D Long Division Methods
  470.    wt: 1:   5 Distributive Law for Whole Numbers
  471.    wt: 1:   4 Commutative Law Groups Counting Form
  472.    wt: 1:   3 Multiplicative Counting Skills Principles
  473.    wt: 1:   5 Proportionality in Equivalent Fractions
  474.    wt: 1:   3 Linear Equation Literal Solution More
  475.    wt: 1:   2 Linear Equation Literal Solution
  476.    wt: 1:   5 Equality in Algebra
  477.    wt: 1:   3 Product Axioms Two Forms
  478.    wt: 1:   2 Addition and Multiplication Axioms
  479.    wt: 1:   4 Comparison of Negative Numbers
  480.    wt: 1:   15 Real Number Division
  481.    wt: 1:   8 Coordinates for Maps and Planes
  482.    wt: 1:   7 Real Numbers as Line Cordinates
  483.    wt: 1:   5 Independent versus Dependent Variables
  484.    wt: 1:   4 Changing Letters
  485.    wt: 1:   3 Geometric Formulas and Function Notation
  486.    wt: 1:   1 Formulas Dependence and Function Notation
  487.    wt: 1:   More Exercises
  488.    wt: 1:   Simple Exercises
  489.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  490.    wt: 1:   4 GE III Animated Examples
  491.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  492.    wt: 1:   3 GE III Equation Addition and Multiplication
  493.    wt: 1:   2 GE II Comparison
  494.    wt: 1:   1 GE Substitution four examples
  495.    wt: 1:   4 Solving a triangular system exercise
  496.    wt: 1:   3 Solving triangular system example
  497.    wt: 1:   2 Essentially one exercises three with solution
  498.    wt: 1:   1 Essentially One Unknown
  499.    wt: 1:   6 Algebraic Solution Example
  500.    wt: 1:   5 Algebraic Solutions Introduction
  501.    wt: 1:   4 Four Examples Fractional Coefficients
  502.    wt: 1:   3 Four Examples
  503.    wt: 1:   2 Three Examples
  504.    wt: 1:   1 Proper Equal Sign Usage
  505.    wt: 1:   Skill Development Notes
  506.    wt: 1:   10 One Example
  507.    wt: 1:   9 Three Examples
  508.    wt: 1:   8 One Example
  509.    wt: 1:   7 Two Examples
  510.    wt: 1:   6 Three Examples
  511.    wt: 1:   5 Three Examples
  512.    wt: 1:   4 Two Examples
  513.    wt: 1:   3 Two Examples
  514.    wt: 1:   2 Three Examples
  515.    wt: 1:   Using Letters for Physical Quantities
  516.    wt: 1:   Formula Usage Show Work Format
  517.    wt: 1:   3 Comparison of Negative Numbers
  518.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  519.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  520.    wt: 1:   13 GCD from given Prime Factorization
  521.    wt: 1:   5 Common Divisors 60 45 via Prime
  522.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  523.    wt: 1:   4 Counting with Trees Product Rule Take I
  524.    wt: 1:   10 dividing signed numbers
  525.    wt: 1:   3 signed coordinates for maps and planes
  526.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  527.    wt: 1:   20 Dividing Fractions the Why
  528.    wt: 1:   19 Dividing Fractions How TO
  529.    wt: 1:   5 Equivalent Fractions
  530.    wt: 1:   D Remainders Modulo 11 Pair Rule
  531.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  532.    wt: 1:   B Integer Long Division Multiple Choices
  533.    wt: 1:   A Associative Law Theorectical Note
  534.    wt: 1:   13 Subtraction with Additive Inverse
  535.    wt: 1:   5 Zero Movement and Additive Inverses
  536.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  537.    wt: 1:   23 Remainder Arithmetic Modulo 2
  538.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  539.    wt: 1:   21 Remainder Arithmetic Modulo 3
  540.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  541.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  542.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  543.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  544.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  545.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  546.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  547.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  548.    wt: 1:   5 Remainder Arithmetic Modulo 5
  549.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  550.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  551.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  552.    wt: 1:   1 Remainder Arithmetic Modulo 10
  553.    wt: 1:   18 video Count Factors given Prime Factorization
  554.    wt: 1:   11 Efficient Square Rule Use
  555.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  556.    wt: 1:   5 Prime Factorization and a Square Rule
  557.    wt: 1:   8 Correcting the Mistake
  558.    wt: 1:   D Decimal Multiplication Methods Derived
  559.    wt: 1:   1 Why 3 times 5 gives 15
  560.    wt: 1:   012 Division of Time Intervals by Time Intervals
  561.    wt: 1:   011 Division of Time Intervals By Numbers
  562.    wt: 1:   3 Two Chain Rule Method Exercises
  563.    wt: 1:   1 Chain Rule in Reverse Integration Method
  564.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  565.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  566.    wt: 1:   F.1 What Functions are Continuous
  567.    wt: 1:   PostScript For and Against Decimal Perspectives
  568.    wt: 1:   Chapter 23 Links To Trigonometry
  569.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  570.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  571.    wt: 1:   Chapter 19. Functions and Sets
  572.    wt: 1:   Chapter 18. Rules for Algebra
  573.    wt: 1:   Chapter 15. Solving Linear Equations
  574.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  575.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  576.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  577.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  578.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  579.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  580.    wt: 1:   Chapter 15 Objective Processes
  581.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  582.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  583.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  584.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  585.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  586.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  587.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  588.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  589.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  590.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  591.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  592.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  593.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
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.

Return to Page Top

Home << Search

[1] [2] [3] [4]

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

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.