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.

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27 matches:

  1.    wt: 8:   13 Vectors/
  2.    wt: 7:   15 Arc or Inverse Trigonometric Function/
  3.    wt: 7:   1 Maps Plans Measurement/
  4.    wt: 6:   12 Function Translating and Rescaling/
  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: 5:   14 Degrees to Radians and Radians to Degrees/
  9.    wt: 5:   11 Parallel Straight Lines and Transversals/
  10.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  11.    wt: 5:   7 Complex Numbers/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  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: 1:   4 Functions/
  18.    wt: 1:   4 Computation Rules and Function Notation/
  19.    wt: 1:   Step 4 Gaussian Elimination/
  20.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  21.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  22.    wt: 1:   Step 1 Stick diagram and fractions/
  23.    wt: 1:   3 Solving Linear Equations/
  24.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  25.    wt: 1:   D Decimal Long Division Methods/
  26.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  27.    wt: 1:   13 Lessons on Limits and Continuity/

Web Page Search

227 matches:

  1.    wt: 4:   13 cosecant function Definition Graph and Inverse
  2.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  3.    wt: 3:   16 cotangent function Definition Graph and Inverse
  4.    wt: 3:   15 cosecant function Definition Graph and Inverse
  5.    wt: 3:   14 secant function Definition Graph and Inverse
  6.    wt: 2:   Maps Plans Drawings
  7.    wt: 2:   26 Function definitions done and coming
  8.    wt: 2:   23 Inverse Functions
  9.    wt: 2:   8 Set view of relations and functions
  10.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  11.    wt: 2:   4 Polynomials Long division linear divisor
  12.    wt: 2:   10 arctan left inverse of tangent Definition
  13.    wt: 2:   7 arcsin left inverse of sine Definition
  14.    wt: 2:   3 Left Inverse of cosine arccos definition
  15.    wt: 2:   13 Velocity Vectors in Physics
  16.    wt: 2:   3 Navigation with Arrows or Vectors
  17.    wt: 2:   13 Graph of tangent function many periods
  18.    wt: 2:   Why Trigonometry the whyslopes view
  19.    wt: 2:   13 Navigation Location from Angles to 2 Landmarks
  20.    wt: 2:   4 Angles on Maps Plans drawn to scale
  21.    wt: 2:   3 Lengths and Areas on Maps and Plans
  22.    wt: 2:   13 Arrows and Vectors in a Plane
  23.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  24.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  25.    wt: 2:   5 Common Divisors 60 45 via Prime
  26.    wt: 2:   13 Fraction Comparison Algebraic View
  27.    wt: 2:   13 Subtraction with Additive Inverse
  28.    wt: 2:   13 video Factors of 24 using prime
  29.    wt: 2:   3 Division Single Digit Divisor Example
  30.    wt: 2:   2 Division with Single Digit Divisors
  31.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  32.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  33.    wt: 2:   9 22 Minute Subtraction Review Video
  34.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  35.    wt: 2:   31 Derivatives of inverse functions
  36.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  37.    wt: 1:   G LAMP Introduction Problem Solving Skills
  38.    wt: 1:   7 logic review and decimals an odd combination
  39.    wt: 1:   website reviews
  40.    wt: 1:   activities for students
  41.    wt: 1:   About site lesson plans
  42.    wt: 1:   05 13 OldSiteEntrancePage
  43.    wt: 1:   Operational Viewpoint to Value
  44.    wt: 1:   formal or informal peer review
  45.    wt: 1:   chapitre 12 00 les iles et division
  46.    wt: 1:   deux definitions pour variable
  47.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  48.    wt: 1:   13 Addition and Addition Tables
  49.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  50.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  51.    wt: 1:   22 Square Root function graphically
  52.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  53.    wt: 1:   17 Function maxima minima and their location
  54.    wt: 1:   15 Sign analysis of functions
  55.    wt: 1:   13 From one to one to many to one
  56.    wt: 1:   12 Function Domain Recognition Exercises
  57.    wt: 1:   11 Function Domain Range Source and Targets
  58.    wt: 1:   7 Functions with finite domains
  59.    wt: 1:   5 Function notation for geometric transformations
  60.    wt: 1:   4 Function notation in and beyond mathematics
  61.    wt: 1:   3 Formula or function graphing exercise
  62.    wt: 1:   2 Algebraic use of function notation
  63.    wt: 1:   1 Geometric Introduction of Function Notation
  64.    wt: 1:   Rewriting algebraic substitution as function substitutions
  65.    wt: 1:   11 arctan left inverse of tangent Graph
  66.    wt: 1:   8 arcsin left inverse of sine Graph
  67.    wt: 1:   6 Graph of arccos function
  68.    wt: 1:   2 cosine function more properties
  69.    wt: 1:   1 cosine function properties
  70.    wt: 1:   A Global Time and Navigation
  71.    wt: 1:   9 Head to Tail Coordinate View
  72.    wt: 1:   8 Parallel Vectors
  73.    wt: 1:   6 Vectors with Coordinates
  74.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  75.    wt: 1:   Straight Lines Instersection Solving Equations
  76.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  77.    wt: 1:   7 Tangent Function is odd on this domain
  78.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  79.    wt: 1:   5 Tangent Function Graph
  80.    wt: 1:   4 Tangent Function Properties
  81.    wt: 1:   17 tangent function angle sum formulas
  82.    wt: 1:   30 unit circle calculation of six trigonometric functions
  83.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  84.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  85.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  86.    wt: 1:   17A The complex number valued trig function cis
  87.    wt: 1:   12 Graph of tangent function for one period
  88.    wt: 1:   11 tangent function undefined when terminal side vertical
  89.    wt: 1:   8 period of tangent function
  90.    wt: 1:   Unit Circle Development of Trigonometry
  91.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  92.    wt: 1:   13 Trig Formulas for dot and cross Products
  93.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  94.    wt: 1:   9 The complex number valued trig function cis
  95.    wt: 1:   8 Unit Circle Development of Trigonometry
  96.    wt: 1:   1 Rectangular Polar Coordinates Review
  97.    wt: 1:   8 Triangles Cascade Problem Solving
  98.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  99.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  100.    wt: 1:   4 Similarity Definition with Coordinate
  101.    wt: 1:   6 Intersection of lines by solving linear systems
  102.    wt: 1:   5 Algebraic View of Slopes
  103.    wt: 1:   1 Numerical view of lines and their equations
  104.    wt: 1:   13 Pythagorean spatial distance formulas
  105.    wt: 1:   3 Rectangular Coordinates Review
  106.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  107.    wt: 1:   13 Angle Side Angle Failure
  108.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  109.    wt: 1:   6 Figuring with Maps Not to Scale
  110.    wt: 1:   A Signed Number Arithmetic Review
  111.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  112.    wt: 1:   19 Signed Multiples of Vectors
  113.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  114.    wt: 1:   9 Division with Digits after Decimal Point
  115.    wt: 1:   8 Division and Mulplication of Compound Fractions
  116.    wt: 1:   E Long Division Methods more
  117.    wt: 1:   D Long Division Methods
  118.    wt: 1:   5 Areas of Rectangles Revisited
  119.    wt: 1:   2 Algebraic View
  120.    wt: 1:   4 Subtraction and Division Axioms
  121.    wt: 1:   15 Real Number Division
  122.    wt: 1:   13 Real Number Subtraction
  123.    wt: 1:   12 Real Number Additive Inverses or Negatives
  124.    wt: 1:   8 Coordinates for Maps and Planes
  125.    wt: 1:   3 Geometric Formulas and Function Notation
  126.    wt: 1:   1 Formulas Dependence and Function Notation
  127.    wt: 1:   4 Solving a triangular system exercise
  128.    wt: 1:   3 Solving triangular system example
  129.    wt: 1:   13 Naming Identifying Formulas with Words
  130.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  131.    wt: 1:   arithmetic videos Real Player Format
  132.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  133.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  134.    wt: 1:   13 GCD from given Prime Factorization
  135.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  136.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  137.    wt: 1:   4 LCM of 8 and 10 via Prime
  138.    wt: 1:   2 Least Common Multiple LCM intro via list method
  139.    wt: 1:   12 GCD 2700 288 via Prime
  140.    wt: 1:   10 dividing signed numbers
  141.    wt: 1:   7 negative and additive inverse
  142.    wt: 1:   3 signed coordinates for maps and planes
  143.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  144.    wt: 1:   20 Dividing Fractions the Why
  145.    wt: 1:   19 Dividing Fractions How TO
  146.    wt: 1:   11 Simplification an Algebraic View
  147.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  148.    wt: 1:   B Integer Long Division Multiple Choices
  149.    wt: 1:   5 Zero Movement and Additive Inverses
  150.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  151.    wt: 1:   26 Divisibility by 2 3 5 Example
  152.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  153.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  154.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  155.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  156.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  157.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  158.    wt: 1:   19 video Prime Factorization Unique
  159.    wt: 1:   18 video Count Factors given Prime Factorization
  160.    wt: 1:   16 video Factors of 980 using prime
  161.    wt: 1:   15 video Factors of 20 using Prime Factorization
  162.    wt: 1:   14 video Factors of 24 Take II
  163.    wt: 1:   10 video Prime Factorization upto 23 squared
  164.    wt: 1:   9 video Prime Factorization upto 19 squared
  165.    wt: 1:   8 video Prime Factorization upto 19
  166.    wt: 1:   4 video Prime Factorization Introduction
  167.    wt: 1:   3 video Primes and Composites from 9 times table
  168.    wt: 1:   1 video how Products are bigger than factor
  169.    wt: 1:   Long Division Backwards more
  170.    wt: 1:   Long Division Backward
  171.    wt: 1:   Division with Counts and Length
  172.    wt: 1:   Long Division forwards and backwards Example 3
  173.    wt: 1:   Long Division forwards and backwards Example 2
  174.    wt: 1:   Long Division forwards and backwards Example 1
  175.    wt: 1:   12 Why Long Division Works Take III
  176.    wt: 1:   11 Another Single Digit Divisor Example
  177.    wt: 1:   10 Division by Five Long and Short Ways
  178.    wt: 1:   9 Why Long Division Works Take II
  179.    wt: 1:   7 Long Divison Mistake Catching
  180.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  181.    wt: 1:   5 Long Division Include Zeroes or not
  182.    wt: 1:   4 Division with 2 Digit Divsors
  183.    wt: 1:   Video Power Notation in Decimal Expansion
  184.    wt: 1:   Subtraction Another Video Lesson
  185.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  186.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  187.    wt: 1:   The 12 Times Table Visually
  188.    wt: 1:   013 Travel Time Tables
  189.    wt: 1:   012 Division of Time Intervals by Time Intervals
  190.    wt: 1:   011 Division of Time Intervals By Numbers
  191.    wt: 1:   8 Addition of Time Intervals via subtotaling
  192.    wt: 1:   Example 4 with x function of y
  193.    wt: 1:   A Chain Rule Real Player video examples
  194.    wt: 1:   34 Derivative of exponential function
  195.    wt: 1:   33 Chain Rule Real Player video examples
  196.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  197.    wt: 1:   26 Chain Rule Recognising outer inner functions
  198.    wt: 1:   19 Chain Rule for linear functions
  199.    wt: 1:   13 sine and cosine derivatives 1st step
  200.    wt: 1:   3 Motivation for Limit Definition Take 2
  201.    wt: 1:   2 Motivation for Limit Definition Take 1
  202.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  203.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  204.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  205.    wt: 1:   F.1 What Functions are Continuous
  206.    wt: 1:   Chapter 23 Links To Trigonometry
  207.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  208.    wt: 1:   Chapter 13. Acceleration
  209.    wt: 1:   Chapter 19. Functions and Sets
  210.    wt: 1:   Chapter 16. Painless Theorem Proving
  211.    wt: 1:   Chapter 15. Solving Linear Equations
  212.    wt: 1:   Chapter 13. Second Reading Guide
  213.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  214.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  215.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  216.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  217.    wt: 1:   N Improving Marks on Tests and Finals
  218.    wt: 1:   H more Routine to non routine problem solving
  219.    wt: 1:   H Jigsaw puzzles and problem solving
  220.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  221.    wt: 1:   7 Games and Activities for Instruction
  222.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  223.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  224.    wt: 1:   More Algebra and Slope based Calculus Preview
  225.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  226.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  227.    wt: 1:   Site Reviews

Extended Search

494 matches:

  1.    wt: 9:   10 arctan left inverse of tangent Definition
  2.    wt: 9:   7 arcsin left inverse of sine Definition
  3.    wt: 9:   A Global Time and Navigation
  4.    wt: 9:   9 Head to Tail Coordinate View
  5.    wt: 9:   8 Parallel Vectors
  6.    wt: 9:   6 Vectors with Coordinates
  7.    wt: 9:   4 Angles on Maps Plans drawn to scale
  8.    wt: 9:   3 Lengths and Areas on Maps and Plans
  9.    wt: 8:   11 arctan left inverse of tangent Graph
  10.    wt: 8:   8 arcsin left inverse of sine Graph
  11.    wt: 8:   6 Graph of arccos function
  12.    wt: 8:   2 cosine function more properties
  13.    wt: 8:   1 cosine function properties
  14.    wt: 8:   15 Dot and Cross Product
  15.    wt: 8:   14 Why Scalar Multiplication Distributes Physical Argument
  16.    wt: 8:   12 From Applied To Pure Mathematics
  17.    wt: 8:   11 Component Method
  18.    wt: 8:   10 Parallelogram Addition Method
  19.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  20.    wt: 8:   5 Head To Tail Arrow Addition
  21.    wt: 8:   4 Resultant of a Sum of Movements
  22.    wt: 8:   2 Signed Coordinates
  23.    wt: 8:   1 Unsigned Coordinates
  24.    wt: 8:   Vector and Complex Number Applet
  25.    wt: 8:   32 seven rows of pascals triangle
  26.    wt: 8:   13 Graph of tangent function many periods
  27.    wt: 8:   Why Trigonometry the whyslopes view
  28.    wt: 8:   13 Navigation Location from Angles to 2 Landmarks
  29.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  30.    wt: 8:   6 Figuring with Maps Not to Scale
  31.    wt: 7:   12 motivation for term arctan
  32.    wt: 7:   9 motivation for name arcsin
  33.    wt: 7:   5 Swapping Coordinates is a reflection
  34.    wt: 7:   4 possible motivation for term arccos
  35.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  36.    wt: 7:   7 Tangent Function is odd on this domain
  37.    wt: 7:   6 Tangent Function Inclination Angle Take 2
  38.    wt: 7:   5 Tangent Function Graph
  39.    wt: 7:   4 Tangent Function Properties
  40.    wt: 7:   17 tangent function angle sum formulas
  41.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  42.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  43.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  44.    wt: 7:   31 basic secant cosecant cotangent trig identities
  45.    wt: 7:   30 unit circle calculation of six trigonometric functions
  46.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  47.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  48.    wt: 7:   17B sine cosine Angle Sum Formulas via cis
  49.    wt: 7:   17A The complex number valued trig function cis
  50.    wt: 7:   15 sine cosine Complementary Angle Relations
  51.    wt: 7:   12 Graph of tangent function for one period
  52.    wt: 7:   11 tangent function undefined when terminal side vertical
  53.    wt: 7:   8 period of tangent function
  54.    wt: 7:   Unit Circle Development of Trigonometry
  55.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  56.    wt: 7:   13 Trig Formulas for dot and cross Products
  57.    wt: 7:   8 Triangles Cascade Problem Solving
  58.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  59.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  60.    wt: 7:   13 Pythagorean spatial distance formulas
  61.    wt: 7:   13 Angle Side Angle Failure
  62.    wt: 7:   A Measurement with Ruler Proper Use
  63.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  64.    wt: 7:   2 Measuring Area Directly
  65.    wt: 7:   1 Length Measurement
  66.    wt: 6:   4 graphing y=Asin(x c)
  67.    wt: 6:   3 graphing y=f(x c) plus K
  68.    wt: 6:   2 Graphing y=Af(x) Vertical Scaling
  69.    wt: 6:   1 graphing y=f(x a)
  70.    wt: 6:   Analytic View of Triangle Construction or Line Instersection More
  71.    wt: 6:   Straight Lines Instersection Solving Equations
  72.    wt: 6:   D Straight Lines Slope from Coordinates Examples
  73.    wt: 6:   C Straight Lines Slope from Coordinates
  74.    wt: 6:   B Straight Line Slope Scaling Properties More
  75.    wt: 6:   A Straight Line Slope Scaling Properties
  76.    wt: 6:   14 Straight Lines Equations General Case
  77.    wt: 6:   12 Straight Lines Graphing mx plus b
  78.    wt: 6:   11 Straight Lines Graphing y=mx
  79.    wt: 6:   10 Straight Lines through Origin Equations More
  80.    wt: 6:   9 Straight Lines through Origin Equations
  81.    wt: 6:   8 Straight Lines Equation for vertical
  82.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  83.    wt: 6:   2 Straight Lines Slopes As Rise Over Run
  84.    wt: 6:   1 Straight Lines Slope Concept
  85.    wt: 6:   29 secant cosecant and cotangent for acute angles
  86.    wt: 6:   28 Expressing products of sines cosines as sums
  87.    wt: 6:   27 Logarithmic use of products of sines and cosines
  88.    wt: 6:   26 Formulas for products of sines and cosines
  89.    wt: 6:   25 tangent double angle formula Slope connection
  90.    wt: 6:   24 tangent Angle Difference Formula
  91.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  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:   16 Right Triangle Complementary Angle Relations
  101.    wt: 6:   14 cosine even and sine and tangent are odd
  102.    wt: 6:   10 Graphs of sines and cosines many periods
  103.    wt: 6:   9 Graphs of sine and cosine over one period
  104.    wt: 6:   7 period of sine and cosine
  105.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  106.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  107.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  108.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  109.    wt: 6:   2 Quadrant I reference Angles
  110.    wt: 6:   1 Unit Points Reflections Rotations
  111.    wt: 6:   10 sine cosine Angle Sum Formulas via cis
  112.    wt: 6:   9 The complex number valued trig function cis
  113.    wt: 6:   8 Unit Circle Development of Trigonometry
  114.    wt: 6:   1 Rectangular Polar Coordinates Review
  115.    wt: 6:   7 Trignometric Ratios Unit Circle
  116.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  117.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  118.    wt: 6:   3 Trigonometric Ratios sine and cosine
  119.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  120.    wt: 6:   1 Angle Measurement with Degrees
  121.    wt: 6:   6 Geometric Diagrams in Class
  122.    wt: 6:   4 Similarity Definition with Coordinate
  123.    wt: 6:   3 Similarity by Design with coordinates
  124.    wt: 6:   6 Intersection of lines by solving linear systems
  125.    wt: 6:   5 Algebraic View of Slopes
  126.    wt: 6:   1 Numerical view of lines and their equations
  127.    wt: 6:   3 Rectangular Coordinates Review
  128.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  129.    wt: 5:   9 Summary Degrees to Radians and back
  130.    wt: 5:   8 Radian Measures of Common Angles
  131.    wt: 5:   7 Radian Measures in special Triangles
  132.    wt: 5:   6 Radian Measure to Degrees
  133.    wt: 5:   5 Degrees to Radian Measure
  134.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  135.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  136.    wt: 5:   2 Radian Measure Numerical Value of one degree
  137.    wt: 5:   1 Degrees and Radians Introduction
  138.    wt: 5:   Parallel Lines and Parallel Transversals
  139.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  140.    wt: 5:   Triangle Angles Sum To 180 Degrees
  141.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  142.    wt: 5:   Parallel Lines and Interior Angles
  143.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  144.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  145.    wt: 5:   Straight Lines ASA Intersection Study More
  146.    wt: 5:   Straight Lines ASA Intersection Study
  147.    wt: 5:   Straight Lines Intersection of
  148.    wt: 5:   21 Logarithms Powers and Exponentials
  149.    wt: 5:   20 N th Roots of Complex Numbers
  150.    wt: 5:   19 N th Roots of Unity
  151.    wt: 5:   18 Sixth Roots of Unity
  152.    wt: 5:   17 Cube Roots of unity
  153.    wt: 5:   16 References and Originality Question
  154.    wt: 5:   15 Pythagorean Theorem Converse
  155.    wt: 5:   14 Law of cosines
  156.    wt: 5:   12 cis formulas for sine cosines and tangent
  157.    wt: 5:   11 sine and cosine double triple angle formulas
  158.    wt: 5:   7 Second Way to Calculate Products
  159.    wt: 5:   6 Field Properties of Complex Number
  160.    wt: 5:   5 An Easy Proof of the Distributive Law
  161.    wt: 5:   4 Multiplication Properties
  162.    wt: 5:   3 Addition Properties
  163.    wt: 5:   2 Complex Numbers made easier we hope
  164.    wt: 5:   Appetizer A Complex Number Applet
  165.    wt: 5:   12 Triangles Similarity More Problems
  166.    wt: 5:   11 Triangle Similarity Missing Side Problem
  167.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  168.    wt: 5:   9 Similarity of Triangles Usual Criteria
  169.    wt: 5:   8 Similarity of Triangles and Polygons
  170.    wt: 5:   7 Translations Rotations Reflections Dilatations
  171.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  172.    wt: 5:   2 Similarity By Design
  173.    wt: 5:   1 Early Concept of Like or Similar Shapes
  174.    wt: 5:   Four Simple Exercises
  175.    wt: 5:   12 Links Lessons elsewhere
  176.    wt: 5:   11 A Partial Summary
  177.    wt: 5:   10 Midpoint of [a b] and [b a]
  178.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  179.    wt: 5:   8 Mid Point Formula
  180.    wt: 5:   7 Exercises to test skill and concept mastery
  181.    wt: 5:   4 Equations for lines three forms
  182.    wt: 5:   3 Slope product for perpendicular lines
  183.    wt: 5:   2 point slope equation for a line
  184.    wt: 5:   What is and is not here
  185.    wt: 5:   12 Spatial Coordinates
  186.    wt: 5:   11 Triangle Inequality
  187.    wt: 5:   10 Pythagorean plane distance formula
  188.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  189.    wt: 5:   8 Distance Between Points on a Line
  190.    wt: 5:   7 Complex Numbers Appetizer
  191.    wt: 5:   6 Polar Multiplication and Rotation
  192.    wt: 5:   5 Cartesian Addition and Translation
  193.    wt: 5:   4 Polar Coordinates to and from
  194.    wt: 5:   2 Cartesian Coordinates with signs
  195.    wt: 5:   1 Cartesian Coordinates sans signs
  196.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  197.    wt: 5:   PS H Distributive Law For Complex Numbers
  198.    wt: 5:   PS G Rotation Distributes over Addition
  199.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  200.    wt: 5:   PS E Multiplication with Polar Coordinates
  201.    wt: 5:   PS D Addition with Cartesian Coordinates
  202.    wt: 5:   PS B Parallelogram Construction Methods
  203.    wt: 5:   PS A Kite Construction Methods
  204.    wt: 5:   21 Parallelograms
  205.    wt: 5:   19 Right Triangle Similarity
  206.    wt: 5:   18 Triangle Similarity Take 1
  207.    wt: 5:   17 Right Bisectors of Triangle Sides
  208.    wt: 5:   16 Angles Subtended By Chords and Diameters
  209.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  210.    wt: 5:   14 Parallel Lines Postulate
  211.    wt: 5:   12 Side Angle Side Failure
  212.    wt: 5:   11 Triangle Construction Fails
  213.    wt: 5:   10 Dropping a perpendicular to line
  214.    wt: 5:   9 Construction of a right bisector
  215.    wt: 5:   8 Isoceles Triangles
  216.    wt: 5:   7 Angle Side Angle
  217.    wt: 5:   6 Ruler and compass Angle Bisection
  218.    wt: 5:   5 Side Angle Side
  219.    wt: 5:   4 Side Side Side
  220.    wt: 5:   3 Isometry of Triangles Congruence
  221.    wt: 5:   2 Correspondence between Triangles
  222.    wt: 5:   1 Initial Concepts and Terms
  223.    wt: 5:   Short Course on Euclidean Geometry
  224.    wt: 5:   About Folder Contents
  225.    wt: 4:   24 Monotoncity Injectivity and Inverse Functions
  226.    wt: 3:   26 Function definitions done and coming
  227.    wt: 3:   23 Inverse Functions
  228.    wt: 3:   13 From one to one to many to one
  229.    wt: 3:   8 Set view of relations and functions
  230.    wt: 3:   13 video Factors of 24 using prime
  231.    wt: 3:   3 Division Single Digit Divisor Example
  232.    wt: 3:   2 Division with Single Digit Divisors
  233.    wt: 2:   Maps Plans Drawings
  234.    wt: 2:   13 Addition and Addition Tables
  235.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  236.    wt: 2:   22 Square Root function graphically
  237.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  238.    wt: 2:   17 Function maxima minima and their location
  239.    wt: 2:   15 Sign analysis of functions
  240.    wt: 2:   12 Function Domain Recognition Exercises
  241.    wt: 2:   11 Function Domain Range Source and Targets
  242.    wt: 2:   7 Functions with finite domains
  243.    wt: 2:   5 Function notation for geometric transformations
  244.    wt: 2:   4 Function notation in and beyond mathematics
  245.    wt: 2:   3 Formula or function graphing exercise
  246.    wt: 2:   2 Algebraic use of function notation
  247.    wt: 2:   1 Geometric Introduction of Function Notation
  248.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  249.    wt: 2:   4 Polynomials Long division linear divisor
  250.    wt: 2:   13 Arrows and Vectors in a Plane
  251.    wt: 2:   3 Geometric Formulas and Function Notation
  252.    wt: 2:   1 Formulas Dependence and Function Notation
  253.    wt: 2:   4 Solving a triangular system exercise
  254.    wt: 2:   3 Solving triangular system example
  255.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  256.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  257.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  258.    wt: 2:   5 Common Divisors 60 45 via Prime
  259.    wt: 2:   13 Fraction Comparison Algebraic View
  260.    wt: 2:   13 Subtraction with Additive Inverse
  261.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  262.    wt: 2:   26 Divisibility by 2 3 5 Example
  263.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  264.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  265.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  266.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  267.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  268.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  269.    wt: 2:   Long Division Backwards more
  270.    wt: 2:   Long Division Backward
  271.    wt: 2:   Division with Counts and Length
  272.    wt: 2:   Long Division forwards and backwards Example 3
  273.    wt: 2:   Long Division forwards and backwards Example 2
  274.    wt: 2:   Long Division forwards and backwards Example 1
  275.    wt: 2:   12 Why Long Division Works Take III
  276.    wt: 2:   11 Another Single Digit Divisor Example
  277.    wt: 2:   10 Division by Five Long and Short Ways
  278.    wt: 2:   9 Why Long Division Works Take II
  279.    wt: 2:   7 Long Divison Mistake Catching
  280.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  281.    wt: 2:   5 Long Division Include Zeroes or not
  282.    wt: 2:   4 Division with 2 Digit Divsors
  283.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  284.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  285.    wt: 2:   9 22 Minute Subtraction Review Video
  286.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  287.    wt: 2:   Example 4 with x function of y
  288.    wt: 2:   31 Derivatives of inverse functions
  289.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  290.    wt: 2:   Chapter 13. Acceleration
  291.    wt: 2:   Chapter 13. Second Reading Guide
  292.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  293.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  294.    wt: 1:   G LAMP Introduction Problem Solving Skills
  295.    wt: 1:   Ramblings Extrinsic numbers theory
  296.    wt: 1:   Ramblings Introduction Algebra Essay
  297.    wt: 1:   Skills Chapter 3 Algebra
  298.    wt: 1:   7 logic review and decimals an odd combination
  299.    wt: 1:   website reviews
  300.    wt: 1:   activities for students
  301.    wt: 1:   About site lesson plans
  302.    wt: 1:   05 13 OldSiteEntrancePage
  303.    wt: 1:   Operational Viewpoint to Value
  304.    wt: 1:   formal or informal peer review
  305.    wt: 1:   chapitre 12 00 les iles et division
  306.    wt: 1:   deux definitions pour variable
  307.    wt: 1:   A Wire Resistance Qualitative01
  308.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  309.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  310.    wt: 1:   20 Interchanging coordinates a reflection
  311.    wt: 1:   19 Horizontal line rule and method
  312.    wt: 1:   18 Vertical Line Rule and Method
  313.    wt: 1:   16 Increasing or decreasing on intervals
  314.    wt: 1:   14 Surjections Injections Bijections
  315.    wt: 1:   10 Interval Notation
  316.    wt: 1:   9 Set theory term relation possible origins
  317.    wt: 1:   6 Set Existence Formation and Notation
  318.    wt: 1:   Introduction Reading Guide
  319.    wt: 1:   Rewriting algebraic substitution as function substitutions
  320.    wt: 1:   A Signed Number Arithmetic Review
  321.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  322.    wt: 1:   19 Signed Multiples of Vectors
  323.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  324.    wt: 1:   9 Division with Digits after Decimal Point
  325.    wt: 1:   8 Division and Mulplication of Compound Fractions
  326.    wt: 1:   E Long Division Methods more
  327.    wt: 1:   D Long Division Methods
  328.    wt: 1:   5 Areas of Rectangles Revisited
  329.    wt: 1:   2 Algebraic View
  330.    wt: 1:   4 Subtraction and Division Axioms
  331.    wt: 1:   15 Real Number Division
  332.    wt: 1:   13 Real Number Subtraction
  333.    wt: 1:   12 Real Number Additive Inverses or Negatives
  334.    wt: 1:   8 Coordinates for Maps and Planes
  335.    wt: 1:   5 Independent versus Dependent Variables
  336.    wt: 1:   4 Changing Letters
  337.    wt: 1:   2 Computation Rules Evaluation
  338.    wt: 1:   More Exercises
  339.    wt: 1:   Simple Exercises
  340.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  341.    wt: 1:   4 GE III Animated Examples
  342.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  343.    wt: 1:   3 GE III Equation Addition and Multiplication
  344.    wt: 1:   2 GE II Comparison
  345.    wt: 1:   1 GE Substitution four examples
  346.    wt: 1:   2 Essentially one exercises three with solution
  347.    wt: 1:   1 Essentially One Unknown
  348.    wt: 1:   6 Algebraic Solution Example
  349.    wt: 1:   5 Algebraic Solutions Introduction
  350.    wt: 1:   4 Four Examples Fractional Coefficients
  351.    wt: 1:   3 Four Examples
  352.    wt: 1:   2 Three Examples
  353.    wt: 1:   1 Proper Equal Sign Usage
  354.    wt: 1:   Skill Development Notes
  355.    wt: 1:   10 One Example
  356.    wt: 1:   9 Three Examples
  357.    wt: 1:   8 One Example
  358.    wt: 1:   7 Two Examples
  359.    wt: 1:   6 Three Examples
  360.    wt: 1:   5 Three Examples
  361.    wt: 1:   4 Two Examples
  362.    wt: 1:   3 Two Examples
  363.    wt: 1:   2 Three Examples
  364.    wt: 1:   Using Letters for Physical Quantities
  365.    wt: 1:   Formula Usage Show Work Format
  366.    wt: 1:   13 Naming Identifying Formulas with Words
  367.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  368.    wt: 1:   arithmetic videos Real Player Format
  369.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  370.    wt: 1:   13 GCD from given Prime Factorization
  371.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  372.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  373.    wt: 1:   4 LCM of 8 and 10 via Prime
  374.    wt: 1:   2 Least Common Multiple LCM intro via list method
  375.    wt: 1:   12 GCD 2700 288 via Prime
  376.    wt: 1:   10 dividing signed numbers
  377.    wt: 1:   7 negative and additive inverse
  378.    wt: 1:   3 signed coordinates for maps and planes
  379.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  380.    wt: 1:   20 Dividing Fractions the Why
  381.    wt: 1:   19 Dividing Fractions How TO
  382.    wt: 1:   11 Simplification an Algebraic View
  383.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  384.    wt: 1:   B Integer Long Division Multiple Choices
  385.    wt: 1:   A Associative Law Theorectical Note
  386.    wt: 1:   5 Zero Movement and Additive Inverses
  387.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  388.    wt: 1:   23 Remainder Arithmetic Modulo 2
  389.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  390.    wt: 1:   21 Remainder Arithmetic Modulo 3
  391.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  392.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  393.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  394.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  395.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  396.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  397.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  398.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  399.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  400.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  401.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  402.    wt: 1:   5 Remainder Arithmetic Modulo 5
  403.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  404.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  405.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  406.    wt: 1:   1 Remainder Arithmetic Modulo 10
  407.    wt: 1:   19 video Prime Factorization Unique
  408.    wt: 1:   18 video Count Factors given Prime Factorization
  409.    wt: 1:   16 video Factors of 980 using prime
  410.    wt: 1:   15 video Factors of 20 using Prime Factorization
  411.    wt: 1:   14 video Factors of 24 Take II
  412.    wt: 1:   10 video Prime Factorization upto 23 squared
  413.    wt: 1:   9 video Prime Factorization upto 19 squared
  414.    wt: 1:   8 video Prime Factorization upto 19
  415.    wt: 1:   4 video Prime Factorization Introduction
  416.    wt: 1:   3 video Primes and Composites from 9 times table
  417.    wt: 1:   1 video how Products are bigger than factor
  418.    wt: 1:   8 Correcting the Mistake
  419.    wt: 1:   1 Divsion Physical Examples
  420.    wt: 1:   Video Power Notation in Decimal Expansion
  421.    wt: 1:   Subtraction Another Video Lesson
  422.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  423.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  424.    wt: 1:   The 12 Times Table Visually
  425.    wt: 1:   013 Travel Time Tables
  426.    wt: 1:   012 Division of Time Intervals by Time Intervals
  427.    wt: 1:   011 Division of Time Intervals By Numbers
  428.    wt: 1:   8 Addition of Time Intervals via subtotaling
  429.    wt: 1:   Example 2 volume of a cone
  430.    wt: 1:   Example 1 volume of a pyramid
  431.    wt: 1:   Volume of Solid by Cross Sections Lesson
  432.    wt: 1:   Example 1. Area Between x and x squared
  433.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  434.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  435.    wt: 1:   Example 3
  436.    wt: 1:   Example 2
  437.    wt: 1:   Example 1
  438.    wt: 1:   Area Between Curves Lesson Take 2
  439.    wt: 1:   Area Between Curves Lesson Take 1
  440.    wt: 1:   Summary
  441.    wt: 1:   A Chain Rule Real Player video examples
  442.    wt: 1:   34 Derivative of exponential function
  443.    wt: 1:   33 Chain Rule Real Player video examples
  444.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  445.    wt: 1:   26 Chain Rule Recognising outer inner functions
  446.    wt: 1:   19 Chain Rule for linear functions
  447.    wt: 1:   13 sine and cosine derivatives 1st step
  448.    wt: 1:   3 Motivation for Limit Definition Take 2
  449.    wt: 1:   2 Motivation for Limit Definition Take 1
  450.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  451.    wt: 1:   11 Limits at infinity Three Examples
  452.    wt: 1:   10 Three one sided limits with infinite values
  453.    wt: 1:   9 Limits Continuity and Composition
  454.    wt: 1:   8 Four Animated Examples
  455.    wt: 1:   7 Evaluation by immediate or delayed substitution
  456.    wt: 1:   6 Continuity at a point
  457.    wt: 1:   5 Jumps and absence of unlimited error control
  458.    wt: 1:   4 Numerical properties
  459.    wt: 1:   3 Decimal insights for limits continuity convergence
  460.    wt: 1:   2 Algebraic codification
  461.    wt: 1:   1 Numerical introduction
  462.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  463.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  464.    wt: 1:   F.5a Equicontinuity Theorems
  465.    wt: 1:   F.1 What Functions are Continuous
  466.    wt: 1:   Chapter 23 Links To Trigonometry
  467.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  468.    wt: 1:   Chapter 19. Functions and Sets
  469.    wt: 1:   Chapter 16. Painless Theorem Proving
  470.    wt: 1:   Chapter 15. Solving Linear Equations
  471.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  472.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  473.    wt: 1:   Postscript A Three Remarks
  474.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  475.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  476.    wt: 1:   M Words to extend arithmetic
  477.    wt: 1:   N Improving Marks on Tests and Finals
  478.    wt: 1:   H more Routine to non routine problem solving
  479.    wt: 1:   H Jigsaw puzzles and problem solving
  480.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  481.    wt: 1:   7 Games and Activities for Instruction
  482.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  483.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  484.    wt: 1:   More Algebra and Slope based Calculus Preview
  485.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  486.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  487.    wt: 1:   Site Reviews
  488.    wt: 11:   13 cosecant function Definition Graph and Inverse
  489.    wt: 11:   13 Velocity Vectors in Physics
  490.    wt: 10:   16 cotangent function Definition Graph and Inverse
  491.    wt: 10:   15 cosecant function Definition Graph and Inverse
  492.    wt: 10:   14 secant function Definition Graph and Inverse
  493.    wt: 10:   3 Left Inverse of cosine arccos definition
  494.    wt: 10:   3 Navigation with Arrows or Vectors
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
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Responsibility
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Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
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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
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More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
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Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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