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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30 matches:

  1.    wt: 8:   13 Vectors/
  2.    wt: 7:   1 Maps Plans Measurement/
  3.    wt: 6:   15 Arc or Inverse Trigonometric Function/
  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: 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:   4 Remainder Arithmetic and Divisibility/
  28.    wt: 1:   D Decimal Long Division Methods/
  29.    wt: 1:   13 Lessons on Limits and Continuity/
  30.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/

Web Page Search

218 matches:

  1.    wt: 3:   13 cosecant function Definition Graph and Inverse
  2.    wt: 3:   34 Derivative of exponential function
  3.    wt: 3:   31 Derivatives of inverse functions
  4.    wt: 3:   13 sine and cosine derivatives 1st step
  5.    wt: 3:   13 Limits with Parameters and Derivatives Take II
  6.    wt: 2:   Maps Plans Drawings
  7.    wt: 2:   26 Function definitions done and coming
  8.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  9.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  10.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  11.    wt: 2:   4 Polynomials Long division linear divisor
  12.    wt: 2:   16 cotangent function Definition Graph and Inverse
  13.    wt: 2:   15 cosecant function Definition Graph and Inverse
  14.    wt: 2:   14 secant function Definition Graph and Inverse
  15.    wt: 2:   13 Velocity Vectors in Physics
  16.    wt: 2:   13 Graph of tangent function many periods
  17.    wt: 2:   4 Angles on Maps Plans drawn to scale
  18.    wt: 2:   3 Lengths and Areas on Maps and Plans
  19.    wt: 2:   23 Distributive Law Two Derivations
  20.    wt: 2:   13 Arrows and Vectors in a Plane
  21.    wt: 2:   12 Real Number Additive Inverses or Negatives
  22.    wt: 2:   13 GCD from given Prime Factorization
  23.    wt: 2:   7 negative and additive inverse
  24.    wt: 2:   13 Subtraction with Additive Inverse
  25.    wt: 2:   10 Division by Five Long and Short Ways
  26.    wt: 2:   4 Division with 2 Digit Divsors
  27.    wt: 2:   3 Division Single Digit Divisor Example
  28.    wt: 2:   2 Division with Single Digit Divisors
  29.    wt: 2:   4 Second derivative test exercise example
  30.    wt: 2:   3 Second derivative test
  31.    wt: 2:   2 Second derivative test prequel
  32.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  33.    wt: 2:   38 Formulas and derivatives for powers and roots
  34.    wt: 2:   36 Cube root derivative animated
  35.    wt: 2:   17 Derivatives of quotients of sine and cosine
  36.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  37.    wt: 2:   15 sine and cosine derivatives 3rd step
  38.    wt: 2:   14 sine and cosine derivatives 2nd step
  39.    wt: 2:   3 Motivation for Limit Definition Take 2
  40.    wt: 2:   2 Motivation for Limit Definition Take 1
  41.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  42.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  43.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  44.    wt: 1:   A Introduction Objectives
  45.    wt: 1:   Math Ed if it must be short make it lean effective
  46.    wt: 1:   activities for students
  47.    wt: 1:   About site lesson plans
  48.    wt: 1:   five decades make a difference
  49.    wt: 1:   05 13 OldSiteEntrancePage
  50.    wt: 1:   cultivating intelligence
  51.    wt: 1:   Motivation and Context Problem
  52.    wt: 1:   fairness and inductive principles for instruction
  53.    wt: 1:   chapitre 12 00 les iles et division
  54.    wt: 1:   deux definitions pour variable
  55.    wt: 1:   B Wire Resistance Qualitative02
  56.    wt: 1:   A Wire Resistance Qualitative01
  57.    wt: 1:   C Electromotive force conventional current02
  58.    wt: 1:   B Electromotive force conventional current01
  59.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  60.    wt: 1:   13 Addition and Addition Tables
  61.    wt: 1:   12 Goals and Objectives For Mathematics
  62.    wt: 1:   8 The Effect of Negative Remarks
  63.    wt: 1:   7 Student Motivation
  64.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  65.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  66.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  67.    wt: 1:   23 Inverse Functions
  68.    wt: 1:   22 Square Root function graphically
  69.    wt: 1:   17 Function maxima minima and their location
  70.    wt: 1:   15 Sign analysis of functions
  71.    wt: 1:   13 From one to one to many to one
  72.    wt: 1:   12 Function Domain Recognition Exercises
  73.    wt: 1:   11 Function Domain Range Source and Targets
  74.    wt: 1:   8 Set view of relations and functions
  75.    wt: 1:   7 Functions with finite domains
  76.    wt: 1:   5 Function notation for geometric transformations
  77.    wt: 1:   4 Function notation in and beyond mathematics
  78.    wt: 1:   3 Formula or function graphing exercise
  79.    wt: 1:   2 Algebraic use of function notation
  80.    wt: 1:   1 Geometric Introduction of Function Notation
  81.    wt: 1:   7 quadratic formulla derivation
  82.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  83.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  84.    wt: 1:   1 Polynomials Distributive Law
  85.    wt: 1:   Rewriting algebraic substitution as function substitutions
  86.    wt: 1:   12 motivation for term arctan
  87.    wt: 1:   10 arctan left inverse of tangent Definition
  88.    wt: 1:   9 motivation for name arcsin
  89.    wt: 1:   7 arcsin left inverse of sine Definition
  90.    wt: 1:   6 Graph of arccos function
  91.    wt: 1:   4 possible motivation for term arccos
  92.    wt: 1:   3 Left Inverse of cosine arccos definition
  93.    wt: 1:   2 cosine function more properties
  94.    wt: 1:   1 cosine function properties
  95.    wt: 1:   8 Parallel Vectors
  96.    wt: 1:   6 Vectors with Coordinates
  97.    wt: 1:   3 Navigation with Arrows or Vectors
  98.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  99.    wt: 1:   7 Tangent Function is odd on this domain
  100.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  101.    wt: 1:   5 Tangent Function Graph
  102.    wt: 1:   4 Tangent Function Properties
  103.    wt: 1:   17 tangent function angle sum formulas
  104.    wt: 1:   30 unit circle calculation of six trigonometric functions
  105.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  106.    wt: 1:   17A The complex number valued trig function cis
  107.    wt: 1:   12 Graph of tangent function for one period
  108.    wt: 1:   11 tangent function undefined when terminal side vertical
  109.    wt: 1:   8 period of tangent function
  110.    wt: 1:   Unit Circle Development of Trigonometry
  111.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  112.    wt: 1:   13 Trig Formulas for dot and cross Products
  113.    wt: 1:   9 The complex number valued trig function cis
  114.    wt: 1:   8 Unit Circle Development of Trigonometry
  115.    wt: 1:   5 An Easy Proof of the Distributive Law
  116.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  117.    wt: 1:   Why Trigonometry the whyslopes view
  118.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  119.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  120.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  121.    wt: 1:   4 Similarity Definition with Coordinate
  122.    wt: 1:   13 Pythagorean spatial distance formulas
  123.    wt: 1:   PS H Distributive Law For Complex Numbers
  124.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  125.    wt: 1:   13 Angle Side Angle Failure
  126.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  127.    wt: 1:   6 Figuring with Maps Not to Scale
  128.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  129.    wt: 1:   19 Signed Multiples of Vectors
  130.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  131.    wt: 1:   15 Head to Tails in place Addition Associative
  132.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  133.    wt: 1:   9 Division with Digits after Decimal Point
  134.    wt: 1:   8 Division and Mulplication of Compound Fractions
  135.    wt: 1:   E Long Division Methods more
  136.    wt: 1:   D Long Division Methods
  137.    wt: 1:   5 Distributive Law for Whole Numbers
  138.    wt: 1:   4 Commutative Law Groups Counting Form
  139.    wt: 1:   3 Multiplicative Counting Skills Principles
  140.    wt: 1:   5 Proportionality in Equivalent Fractions
  141.    wt: 1:   6 Equations and Systems Equivalent or Implied
  142.    wt: 1:   4 Subtraction and Division Axioms
  143.    wt: 1:   1 Equivalent Computation Rules
  144.    wt: 1:   4 Comparison of Negative Numbers
  145.    wt: 1:   15 Real Number Division
  146.    wt: 1:   13 Real Number Subtraction
  147.    wt: 1:   8 Coordinates for Maps and Planes
  148.    wt: 1:   3 Geometric Formulas and Function Notation
  149.    wt: 1:   1 Formulas Dependence and Function Notation
  150.    wt: 1:   13 Naming Identifying Formulas with Words
  151.    wt: 1:   3 Comparison of Negative Numbers
  152.    wt: 1:   5 Common Divisors 60 45 via Prime
  153.    wt: 1:   10 dividing signed numbers
  154.    wt: 1:   3 signed coordinates for maps and planes
  155.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  156.    wt: 1:   20 Dividing Fractions the Why
  157.    wt: 1:   19 Dividing Fractions How TO
  158.    wt: 1:   13 Fraction Comparison Algebraic View
  159.    wt: 1:   5 Equivalent Fractions
  160.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  161.    wt: 1:   B Integer Long Division Multiple Choices
  162.    wt: 1:   A Associative Law Theorectical Note
  163.    wt: 1:   5 Zero Movement and Additive Inverses
  164.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  165.    wt: 1:   26 Divisibility by 2 3 5 Example
  166.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  167.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  168.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  169.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  170.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  171.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  172.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  173.    wt: 1:   18 video Count Factors given Prime Factorization
  174.    wt: 1:   13 video Factors of 24 using prime
  175.    wt: 1:   Long Division Backwards more
  176.    wt: 1:   Long Division Backward
  177.    wt: 1:   Division with Counts and Length
  178.    wt: 1:   Long Division forwards and backwards Example 3
  179.    wt: 1:   Long Division forwards and backwards Example 2
  180.    wt: 1:   Long Division forwards and backwards Example 1
  181.    wt: 1:   12 Why Long Division Works Take III
  182.    wt: 1:   11 Another Single Digit Divisor Example
  183.    wt: 1:   9 Why Long Division Works Take II
  184.    wt: 1:   7 Long Divison Mistake Catching
  185.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  186.    wt: 1:   5 Long Division Include Zeroes or not
  187.    wt: 1:   1 Divsion Physical Examples
  188.    wt: 1:   D Decimal Multiplication Methods Derived
  189.    wt: 1:   1 Why 3 times 5 gives 15
  190.    wt: 1:   013 Travel Time Tables
  191.    wt: 1:   012 Division of Time Intervals by Time Intervals
  192.    wt: 1:   011 Division of Time Intervals By Numbers
  193.    wt: 1:   Example 4 with x function of y
  194.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  195.    wt: 1:   26 Chain Rule Recognising outer inner functions
  196.    wt: 1:   19 Chain Rule for linear functions
  197.    wt: 1:   10 Power rule for negative integers
  198.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  199.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  200.    wt: 1:   F.1 What Functions are Continuous
  201.    wt: 1:   PostScript For and Against Decimal Perspectives
  202.    wt: 1:   Chapter 23 Links To Trigonometry
  203.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  204.    wt: 1:   Chapter 13. Acceleration
  205.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  206.    wt: 1:   Chapter 19. Functions and Sets
  207.    wt: 1:   Chapter 13. Second Reading Guide
  208.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  209.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  210.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  211.    wt: 1:   Chapter 15 Objective Processes
  212.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  213.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  214.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  215.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  216.    wt: 1:   7 Games and Activities for Instruction
  217.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  218.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

568 matches:

  1.    wt: 9:   13 cosecant function Definition Graph and Inverse
  2.    wt: 9:   8 Parallel Vectors
  3.    wt: 9:   6 Vectors with Coordinates
  4.    wt: 9:   3 Navigation with Arrows or Vectors
  5.    wt: 9:   4 Angles on Maps Plans drawn to scale
  6.    wt: 9:   3 Lengths and Areas on Maps and Plans
  7.    wt: 8:   16 cotangent function Definition Graph and Inverse
  8.    wt: 8:   15 cosecant function Definition Graph and Inverse
  9.    wt: 8:   14 secant function Definition Graph and Inverse
  10.    wt: 8:   3 Left Inverse of cosine arccos definition
  11.    wt: 8:   A Global Time and Navigation
  12.    wt: 8:   15 Dot and Cross Product
  13.    wt: 8:   14 Why Scalar Multiplication Distributes Physical Argument
  14.    wt: 8:   12 From Applied To Pure Mathematics
  15.    wt: 8:   11 Component Method
  16.    wt: 8:   10 Parallelogram Addition Method
  17.    wt: 8:   9 Head to Tail Coordinate View
  18.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  19.    wt: 8:   5 Head To Tail Arrow Addition
  20.    wt: 8:   4 Resultant of a Sum of Movements
  21.    wt: 8:   2 Signed Coordinates
  22.    wt: 8:   1 Unsigned Coordinates
  23.    wt: 8:   Vector and Complex Number Applet
  24.    wt: 8:   32 seven rows of pascals triangle
  25.    wt: 8:   13 Graph of tangent function many periods
  26.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  27.    wt: 8:   6 Figuring with Maps Not to Scale
  28.    wt: 7:   12 motivation for term arctan
  29.    wt: 7:   10 arctan left inverse of tangent Definition
  30.    wt: 7:   9 motivation for name arcsin
  31.    wt: 7:   7 arcsin left inverse of sine Definition
  32.    wt: 7:   6 Graph of arccos function
  33.    wt: 7:   4 possible motivation for term arccos
  34.    wt: 7:   2 cosine function more properties
  35.    wt: 7:   1 cosine function properties
  36.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  37.    wt: 7:   7 Tangent Function is odd on this domain
  38.    wt: 7:   6 Tangent Function Inclination Angle Take 2
  39.    wt: 7:   5 Tangent Function Graph
  40.    wt: 7:   4 Tangent Function Properties
  41.    wt: 7:   17 tangent function angle sum formulas
  42.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  43.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  44.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  45.    wt: 7:   31 basic secant cosecant cotangent trig identities
  46.    wt: 7:   30 unit circle calculation of six trigonometric functions
  47.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  48.    wt: 7:   17A The complex number valued trig function cis
  49.    wt: 7:   15 sine cosine Complementary Angle Relations
  50.    wt: 7:   12 Graph of tangent function for one period
  51.    wt: 7:   11 tangent function undefined when terminal side vertical
  52.    wt: 7:   8 period of tangent function
  53.    wt: 7:   Unit Circle Development of Trigonometry
  54.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  55.    wt: 7:   13 Trig Formulas for dot and cross Products
  56.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  57.    wt: 7:   Why Trigonometry the whyslopes view
  58.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  59.    wt: 7:   13 Navigation Location from Angles to 2 Landmarks
  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:   11 arctan left inverse of tangent Graph
  67.    wt: 6:   8 arcsin left inverse of sine Graph
  68.    wt: 6:   5 Swapping Coordinates is a reflection
  69.    wt: 6:   4 graphing y=Asin(x c)
  70.    wt: 6:   3 graphing y=f(x c) plus K
  71.    wt: 6:   2 Graphing y=Af(x) Vertical Scaling
  72.    wt: 6:   1 graphing y=f(x a)
  73.    wt: 6:   D Straight Lines Slope from Coordinates Examples
  74.    wt: 6:   C Straight Lines Slope from Coordinates
  75.    wt: 6:   B Straight Line Slope Scaling Properties More
  76.    wt: 6:   A Straight Line Slope Scaling Properties
  77.    wt: 6:   14 Straight Lines Equations General Case
  78.    wt: 6:   12 Straight Lines Graphing mx plus b
  79.    wt: 6:   11 Straight Lines Graphing y=mx
  80.    wt: 6:   10 Straight Lines through Origin Equations More
  81.    wt: 6:   9 Straight Lines through Origin Equations
  82.    wt: 6:   8 Straight Lines Equation for vertical
  83.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  84.    wt: 6:   2 Straight Lines Slopes As Rise Over Run
  85.    wt: 6:   1 Straight Lines Slope Concept
  86.    wt: 6:   29 secant cosecant and cotangent for acute angles
  87.    wt: 6:   28 Expressing products of sines cosines as sums
  88.    wt: 6:   27 Logarithmic use of products of sines and cosines
  89.    wt: 6:   26 Formulas for products of sines and cosines
  90.    wt: 6:   25 tangent double angle formula Slope connection
  91.    wt: 6:   24 tangent Angle Difference Formula
  92.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  93.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  94.    wt: 6:   21 sine and cosine Half Angle Formulas
  95.    wt: 6:   20 sine and cosine Double Angle Formulas
  96.    wt: 6:   18 sum of sinusoidal waves as a single wave
  97.    wt: 6:   17G Pythagorean Theorem Converse
  98.    wt: 6:   17F Law of cosines
  99.    wt: 6:   17E Trig Formulas for dot and cross Products
  100.    wt: 6:   17D cis formulas for sine cosines and tangent
  101.    wt: 6:   17C sine and cosine double triple angle formulas
  102.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  103.    wt: 6:   16 Right Triangle Complementary Angle Relations
  104.    wt: 6:   14 cosine even and sine and tangent are odd
  105.    wt: 6:   10 Graphs of sines and cosines many periods
  106.    wt: 6:   9 Graphs of sine and cosine over one period
  107.    wt: 6:   7 period of sine and cosine
  108.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  109.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  110.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  111.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  112.    wt: 6:   2 Quadrant I reference Angles
  113.    wt: 6:   1 Unit Points Reflections Rotations
  114.    wt: 6:   9 The complex number valued trig function cis
  115.    wt: 6:   8 Unit Circle Development of Trigonometry
  116.    wt: 6:   5 An Easy Proof of the Distributive Law
  117.    wt: 6:   8 Triangles Cascade Problem Solving
  118.    wt: 6:   7 Trignometric Ratios Unit Circle
  119.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  120.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  121.    wt: 6:   3 Trigonometric Ratios sine and cosine
  122.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  123.    wt: 6:   1 Angle Measurement with Degrees
  124.    wt: 6:   10 Similarity of Triangles Equivalent of Two Criteria
  125.    wt: 6:   6 Geometric Diagrams in Class
  126.    wt: 6:   4 Similarity Definition with Coordinate
  127.    wt: 6:   3 Similarity by Design with coordinates
  128.    wt: 6:   PS H Distributive Law For Complex Numbers
  129.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  130.    wt: 5:   9 Summary Degrees to Radians and back
  131.    wt: 5:   8 Radian Measures of Common Angles
  132.    wt: 5:   7 Radian Measures in special Triangles
  133.    wt: 5:   6 Radian Measure to Degrees
  134.    wt: 5:   5 Degrees to Radian Measure
  135.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  136.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  137.    wt: 5:   2 Radian Measure Numerical Value of one degree
  138.    wt: 5:   1 Degrees and Radians Introduction
  139.    wt: 5:   Parallel Lines and Parallel Transversals
  140.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  141.    wt: 5:   Triangle Angles Sum To 180 Degrees
  142.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  143.    wt: 5:   Parallel Lines and Interior Angles
  144.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  145.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  146.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  147.    wt: 5:   Straight Lines ASA Intersection Study More
  148.    wt: 5:   Straight Lines ASA Intersection Study
  149.    wt: 5:   Straight Lines Instersection Solving Equations
  150.    wt: 5:   Straight Lines Intersection of
  151.    wt: 5:   21 Logarithms Powers and Exponentials
  152.    wt: 5:   20 N th Roots of Complex Numbers
  153.    wt: 5:   19 N th Roots of Unity
  154.    wt: 5:   18 Sixth Roots of Unity
  155.    wt: 5:   17 Cube Roots of unity
  156.    wt: 5:   16 References and Originality Question
  157.    wt: 5:   15 Pythagorean Theorem Converse
  158.    wt: 5:   14 Law of cosines
  159.    wt: 5:   12 cis formulas for sine cosines and tangent
  160.    wt: 5:   11 sine and cosine double triple angle formulas
  161.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  162.    wt: 5:   7 Second Way to Calculate Products
  163.    wt: 5:   6 Field Properties of Complex Number
  164.    wt: 5:   4 Multiplication Properties
  165.    wt: 5:   3 Addition Properties
  166.    wt: 5:   2 Complex Numbers made easier we hope
  167.    wt: 5:   1 Rectangular Polar Coordinates Review
  168.    wt: 5:   Appetizer A Complex Number Applet
  169.    wt: 5:   12 Triangles Similarity More Problems
  170.    wt: 5:   11 Triangle Similarity Missing Side Problem
  171.    wt: 5:   9 Similarity of Triangles Usual Criteria
  172.    wt: 5:   8 Similarity of Triangles and Polygons
  173.    wt: 5:   7 Translations Rotations Reflections Dilatations
  174.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  175.    wt: 5:   2 Similarity By Design
  176.    wt: 5:   1 Early Concept of Like or Similar Shapes
  177.    wt: 5:   Four Simple Exercises
  178.    wt: 5:   12 Links Lessons elsewhere
  179.    wt: 5:   11 A Partial Summary
  180.    wt: 5:   10 Midpoint of [a b] and [b a]
  181.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  182.    wt: 5:   8 Mid Point Formula
  183.    wt: 5:   7 Exercises to test skill and concept mastery
  184.    wt: 5:   6 Intersection of lines by solving linear systems
  185.    wt: 5:   5 Algebraic View of Slopes
  186.    wt: 5:   4 Equations for lines three forms
  187.    wt: 5:   3 Slope product for perpendicular lines
  188.    wt: 5:   2 point slope equation for a line
  189.    wt: 5:   1 Numerical view of lines and their equations
  190.    wt: 5:   What is and is not here
  191.    wt: 5:   12 Spatial Coordinates
  192.    wt: 5:   11 Triangle Inequality
  193.    wt: 5:   10 Pythagorean plane distance formula
  194.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  195.    wt: 5:   8 Distance Between Points on a Line
  196.    wt: 5:   7 Complex Numbers Appetizer
  197.    wt: 5:   6 Polar Multiplication and Rotation
  198.    wt: 5:   5 Cartesian Addition and Translation
  199.    wt: 5:   4 Polar Coordinates to and from
  200.    wt: 5:   3 Rectangular Coordinates Review
  201.    wt: 5:   2 Cartesian Coordinates with signs
  202.    wt: 5:   1 Cartesian Coordinates sans signs
  203.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  204.    wt: 5:   PS G Rotation Distributes over Addition
  205.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  206.    wt: 5:   PS E Multiplication with Polar Coordinates
  207.    wt: 5:   PS D Addition with Cartesian Coordinates
  208.    wt: 5:   PS B Parallelogram Construction Methods
  209.    wt: 5:   PS A Kite Construction Methods
  210.    wt: 5:   21 Parallelograms
  211.    wt: 5:   19 Right Triangle Similarity
  212.    wt: 5:   18 Triangle Similarity Take 1
  213.    wt: 5:   17 Right Bisectors of Triangle Sides
  214.    wt: 5:   16 Angles Subtended By Chords and Diameters
  215.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  216.    wt: 5:   14 Parallel Lines Postulate
  217.    wt: 5:   12 Side Angle Side Failure
  218.    wt: 5:   11 Triangle Construction Fails
  219.    wt: 5:   10 Dropping a perpendicular to line
  220.    wt: 5:   9 Construction of a right bisector
  221.    wt: 5:   8 Isoceles Triangles
  222.    wt: 5:   7 Angle Side Angle
  223.    wt: 5:   6 Ruler and compass Angle Bisection
  224.    wt: 5:   5 Side Angle Side
  225.    wt: 5:   4 Side Side Side
  226.    wt: 5:   3 Isometry of Triangles Congruence
  227.    wt: 5:   2 Correspondence between Triangles
  228.    wt: 5:   1 Initial Concepts and Terms
  229.    wt: 5:   Short Course on Euclidean Geometry
  230.    wt: 5:   About Folder Contents
  231.    wt: 5:   34 Derivative of exponential function
  232.    wt: 5:   31 Derivatives of inverse functions
  233.    wt: 5:   13 sine and cosine derivatives 1st step
  234.    wt: 4:   4 Second derivative test exercise example
  235.    wt: 4:   3 Second derivative test
  236.    wt: 4:   2 Second derivative test prequel
  237.    wt: 4:   1 Two cubic sketching exercises with 1st derivative
  238.    wt: 4:   38 Formulas and derivatives for powers and roots
  239.    wt: 4:   36 Cube root derivative animated
  240.    wt: 4:   17 Derivatives of quotients of sine and cosine
  241.    wt: 4:   16 Derivatives of reciprocals of sine and cosine
  242.    wt: 4:   15 sine and cosine derivatives 3rd step
  243.    wt: 4:   14 sine and cosine derivatives 2nd step
  244.    wt: 4:   3 Motivation for Limit Definition Take 2
  245.    wt: 4:   2 Motivation for Limit Definition Take 1
  246.    wt: 4:   13 Limits with Parameters and Derivatives Take II
  247.    wt: 3:   11 pure mathematics
  248.    wt: 3:   10 statistics
  249.    wt: 3:   9 combinatorics probability sets
  250.    wt: 3:   8 analytic geometry etc
  251.    wt: 3:   7 logic review and decimals an odd combination
  252.    wt: 3:   6 polynomials etc
  253.    wt: 3:   5 logarithms and exponentials etc
  254.    wt: 3:   4 algebra
  255.    wt: 3:   3 Euclidean Geometry Leanly
  256.    wt: 3:   2 arithmetic with signed numbers
  257.    wt: 3:   1 arithmetic with unsigned numbers
  258.    wt: 3:   What is POMME
  259.    wt: 3:   Maps Plans Drawings
  260.    wt: 3:   26 Function definitions done and coming
  261.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  262.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  263.    wt: 3:   13 From one to one to many to one
  264.    wt: 3:   5 Polynomials Long division Nonlinear divisor
  265.    wt: 3:   4 Polynomials Long division linear divisor
  266.    wt: 3:   10 Division by Five Long and Short Ways
  267.    wt: 3:   4 Division with 2 Digit Divsors
  268.    wt: 3:   3 Division Single Digit Divisor Example
  269.    wt: 3:   2 Division with Single Digit Divisors
  270.    wt: 3:   27 Chain Rule sinusoidal outer inner functions EGS
  271.    wt: 3:   26 Chain Rule Recognising outer inner functions
  272.    wt: 3:   19 Chain Rule for linear functions
  273.    wt: 3:   10 Power rule for negative integers
  274.    wt: 3:   12 Limits with Parameters and Derivatives Take I
  275.    wt: 3:   5 Interpreting and Drawing Maps and Plans.
  276.    wt: 2:   A Introduction Objectives
  277.    wt: 2:   Ramblings Extrinsic numbers theory
  278.    wt: 2:   Ramblings Introduction Algebra Essay
  279.    wt: 2:   Skills Chapter 3 Algebra
  280.    wt: 2:   Math Ed if it must be short make it lean effective
  281.    wt: 2:   activities for students
  282.    wt: 2:   About site lesson plans
  283.    wt: 2:   five decades make a difference
  284.    wt: 2:   05 13 OldSiteEntrancePage
  285.    wt: 2:   cultivating intelligence
  286.    wt: 2:   Motivation and Context Problem
  287.    wt: 2:   fairness and inductive principles for instruction
  288.    wt: 2:   A Wire Resistance Qualitative01
  289.    wt: 2:   13 Addition and Addition Tables
  290.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  291.    wt: 2:   23 Inverse Functions
  292.    wt: 2:   22 Square Root function graphically
  293.    wt: 2:   17 Function maxima minima and their location
  294.    wt: 2:   15 Sign analysis of functions
  295.    wt: 2:   12 Function Domain Recognition Exercises
  296.    wt: 2:   11 Function Domain Range Source and Targets
  297.    wt: 2:   8 Set view of relations and functions
  298.    wt: 2:   7 Functions with finite domains
  299.    wt: 2:   5 Function notation for geometric transformations
  300.    wt: 2:   4 Function notation in and beyond mathematics
  301.    wt: 2:   3 Formula or function graphing exercise
  302.    wt: 2:   2 Algebraic use of function notation
  303.    wt: 2:   1 Geometric Introduction of Function Notation
  304.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  305.    wt: 2:   1 Polynomials Distributive Law
  306.    wt: 2:   23 Distributive Law Two Derivations
  307.    wt: 2:   13 Arrows and Vectors in a Plane
  308.    wt: 2:   6 Equations and Systems Equivalent or Implied
  309.    wt: 2:   4 Subtraction and Division Axioms
  310.    wt: 2:   1 Equivalent Computation Rules
  311.    wt: 2:   12 Real Number Additive Inverses or Negatives
  312.    wt: 2:   3 Geometric Formulas and Function Notation
  313.    wt: 2:   1 Formulas Dependence and Function Notation
  314.    wt: 2:   13 GCD from given Prime Factorization
  315.    wt: 2:   7 negative and additive inverse
  316.    wt: 2:   A Associative Law Theorectical Note
  317.    wt: 2:   13 Subtraction with Additive Inverse
  318.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  319.    wt: 2:   26 Divisibility by 2 3 5 Example
  320.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  321.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  322.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  323.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  324.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  325.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  326.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  327.    wt: 2:   13 video Factors of 24 using prime
  328.    wt: 2:   Long Division Backwards more
  329.    wt: 2:   Long Division Backward
  330.    wt: 2:   Division with Counts and Length
  331.    wt: 2:   Long Division forwards and backwards Example 3
  332.    wt: 2:   Long Division forwards and backwards Example 2
  333.    wt: 2:   Long Division forwards and backwards Example 1
  334.    wt: 2:   12 Why Long Division Works Take III
  335.    wt: 2:   11 Another Single Digit Divisor Example
  336.    wt: 2:   9 Why Long Division Works Take II
  337.    wt: 2:   7 Long Divison Mistake Catching
  338.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  339.    wt: 2:   5 Long Division Include Zeroes or not
  340.    wt: 2:   1 Divsion Physical Examples
  341.    wt: 2:   A Related lessons in Volume 3
  342.    wt: 2:   A Chain Rule Real Player video examples
  343.    wt: 2:   33 Chain Rule Real Player video examples
  344.    wt: 2:   30Chain Rule A Proof
  345.    wt: 2:   29 Chain Rule Optional Reading
  346.    wt: 2:   28 Chain Rule Preparation for a Proof
  347.    wt: 2:   25 Chain Rule Animated Examples Continued
  348.    wt: 2:   24 Chain Rule Animated Examples
  349.    wt: 2:   23 Chain Rule in general
  350.    wt: 2:   22 Chain Rule for polynomials
  351.    wt: 2:   21 Chain Rule for powers
  352.    wt: 2:   20 Chain Rule for Pulley Systems
  353.    wt: 2:   18 Chain Rule Introduction
  354.    wt: 2:   12 Quotient rule examples
  355.    wt: 2:   11 Quotient rule
  356.    wt: 2:   9 Reciprocal rule
  357.    wt: 2:   8 Differentiation of polynomials
  358.    wt: 2:   7 Animated Differentiation Examples
  359.    wt: 2:   6 Power rule from product rule
  360.    wt: 2:   5 Product Rule
  361.    wt: 2:   4 Sum Rule
  362.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  363.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  364.    wt: 2:   Chapter 13. Acceleration
  365.    wt: 2:   Chapter 13. Second Reading Guide
  366.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  367.    wt: 2:   7 Games and Activities for Instruction
  368.    wt: 1:   Appendix 2 primary school Arithmetic 01
  369.    wt: 1:   Appendix 1 primary and preschool mathematic
  370.    wt: 1:   K LAMP Musings Science Education
  371.    wt: 1:   J LAMP Introduction Extrinsic Origins
  372.    wt: 1:   I LAMP Introduction Study Habits
  373.    wt: 1:   H LAMP Introduction Instructional Concepts
  374.    wt: 1:   G LAMP Introduction Problem Solving Skills
  375.    wt: 1:   F LAMP Introduction Prerequisites
  376.    wt: 1:   E LAMP Introduction Modern Mathematics
  377.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  378.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  379.    wt: 1:   Skills Chapter 5 Calculus
  380.    wt: 1:   Skills Chapter 4 Logic
  381.    wt: 1:   Skills Chapter 2 Geometry
  382.    wt: 1:   Skills Chapter 1 Arithmetic
  383.    wt: 1:   Skills Chapter 0 Introduction
  384.    wt: 1:   why bother
  385.    wt: 1:   which way to go
  386.    wt: 1:   website reviews
  387.    wt: 1:   three goals to set for students
  388.    wt: 1:   Teach the teachers plus goals
  389.    wt: 1:   permissions for teachers
  390.    wt: 1:   Applied Maths Program14092009 POMME variant
  391.    wt: 1:   links Education Resources online
  392.    wt: 1:   site origins
  393.    wt: 1:   site eurekas
  394.    wt: 1:   key notes and themes
  395.    wt: 1:   Mathematics Education Professors
  396.    wt: 1:   teacher certification
  397.    wt: 1:   modern education
  398.    wt: 1:   learning takes time
  399.    wt: 1:   grouping students according to ability
  400.    wt: 1:   what should be learnt and When
  401.    wt: 1:   mathematics in context
  402.    wt: 1:   Postscript 2007 01 10
  403.    wt: 1:   Education Reform Inconsistencies
  404.    wt: 1:   how letters appear
  405.    wt: 1:   Secondary Three Mathematics
  406.    wt: 1:   Secondary Two Mathematics
  407.    wt: 1:   Secondary One Mathematics
  408.    wt: 1:   talk the algebra talk
  409.    wt: 1:   three difficulties
  410.    wt: 1:   teaching tips
  411.    wt: 1:   What to Tell Students
  412.    wt: 1:   mathematics curriculum shifts
  413.    wt: 1:   geometric implications for algebra
  414.    wt: 1:   teaching tutoring algebraic reason
  415.    wt: 1:   Lessening Algebra Difficulties
  416.    wt: 1:   the trouble with algebra
  417.    wt: 1:   three goals for Mathematics Education
  418.    wt: 1:   04 29 New Mathematics Curriculum
  419.    wt: 1:   04 25 when to stop or suspend mathemat
  420.    wt: 1:   02 21 words for teachers
  421.    wt: 1:   02 20 mathematics education references
  422.    wt: 1:   three aims for mathematics students
  423.    wt: 1:   standards for course material
  424.    wt: 1:   Operational Viewpoint to Value
  425.    wt: 1:   formal or informal peer review
  426.    wt: 1:   Theory of Knowledge
  427.    wt: 1:   mathematics instruction in general
  428.    wt: 1:   Education in mathematics science and technology
  429.    wt: 1:   Different Kinds of Reasoning in maths
  430.    wt: 1:   three kinds of reason in mathematics
  431.    wt: 1:   Four ways to improve education reform
  432.    wt: 1:   How to be a better instructor
  433.    wt: 1:   need for a mixed mathematics curriculum
  434.    wt: 1:   Leaner mathematics curriculum
  435.    wt: 1:   Prequel In For A Penny In For A Pound
  436.    wt: 1:   education an empirical art
  437.    wt: 1:   words for mathematics instructor
  438.    wt: 1:   chapitre 12 00 les iles et division
  439.    wt: 1:   deux definitions pour variable
  440.    wt: 1:   B Wire Resistance Qualitative02
  441.    wt: 1:   C Electromotive force conventional current02
  442.    wt: 1:   B Electromotive force conventional current01
  443.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  444.    wt: 1:   12 Goals and Objectives For Mathematics
  445.    wt: 1:   8 The Effect of Negative Remarks
  446.    wt: 1:   7 Student Motivation
  447.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  448.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  449.    wt: 1:   20 Interchanging coordinates a reflection
  450.    wt: 1:   19 Horizontal line rule and method
  451.    wt: 1:   18 Vertical Line Rule and Method
  452.    wt: 1:   16 Increasing or decreasing on intervals
  453.    wt: 1:   14 Surjections Injections Bijections
  454.    wt: 1:   10 Interval Notation
  455.    wt: 1:   9 Set theory term relation possible origins
  456.    wt: 1:   6 Set Existence Formation and Notation
  457.    wt: 1:   Introduction Reading Guide
  458.    wt: 1:   7 quadratic formulla derivation
  459.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  460.    wt: 1:   8 Notes for instructors or tutors
  461.    wt: 1:   7 Links Lessons Elsewhere
  462.    wt: 1:   3 Polynomials Multiplication Addition
  463.    wt: 1:   2 Column Multiplication Method
  464.    wt: 1:   Rewriting algebraic substitution as function substitutions
  465.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  466.    wt: 1:   19 Signed Multiples of Vectors
  467.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  468.    wt: 1:   15 Head to Tails in place Addition Associative
  469.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  470.    wt: 1:   9 Division with Digits after Decimal Point
  471.    wt: 1:   8 Division and Mulplication of Compound Fractions
  472.    wt: 1:   E Long Division Methods more
  473.    wt: 1:   D Long Division Methods
  474.    wt: 1:   5 Distributive Law for Whole Numbers
  475.    wt: 1:   4 Commutative Law Groups Counting Form
  476.    wt: 1:   3 Multiplicative Counting Skills Principles
  477.    wt: 1:   5 Proportionality in Equivalent Fractions
  478.    wt: 1:   5 Equality in Algebra
  479.    wt: 1:   3 Product Axioms Two Forms
  480.    wt: 1:   2 Addition and Multiplication Axioms
  481.    wt: 1:   4 Comparison of Negative Numbers
  482.    wt: 1:   15 Real Number Division
  483.    wt: 1:   13 Real Number Subtraction
  484.    wt: 1:   8 Coordinates for Maps and Planes
  485.    wt: 1:   5 Independent versus Dependent Variables
  486.    wt: 1:   4 Changing Letters
  487.    wt: 1:   2 Computation Rules Evaluation
  488.    wt: 1:   13 Naming Identifying Formulas with Words
  489.    wt: 1:   3 Comparison of Negative Numbers
  490.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  491.    wt: 1:   5 Common Divisors 60 45 via Prime
  492.    wt: 1:   10 dividing signed numbers
  493.    wt: 1:   3 signed coordinates for maps and planes
  494.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  495.    wt: 1:   20 Dividing Fractions the Why
  496.    wt: 1:   19 Dividing Fractions How TO
  497.    wt: 1:   13 Fraction Comparison Algebraic View
  498.    wt: 1:   5 Equivalent Fractions
  499.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  500.    wt: 1:   B Integer Long Division Multiple Choices
  501.    wt: 1:   5 Zero Movement and Additive Inverses
  502.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  503.    wt: 1:   23 Remainder Arithmetic Modulo 2
  504.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  505.    wt: 1:   21 Remainder Arithmetic Modulo 3
  506.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  507.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  508.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  509.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  510.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  511.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  512.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  513.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  514.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  515.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  516.    wt: 1:   5 Remainder Arithmetic Modulo 5
  517.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  518.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  519.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  520.    wt: 1:   1 Remainder Arithmetic Modulo 10
  521.    wt: 1:   18 video Count Factors given Prime Factorization
  522.    wt: 1:   8 Correcting the Mistake
  523.    wt: 1:   D Decimal Multiplication Methods Derived
  524.    wt: 1:   1 Why 3 times 5 gives 15
  525.    wt: 1:   013 Travel Time Tables
  526.    wt: 1:   012 Division of Time Intervals by Time Intervals
  527.    wt: 1:   011 Division of Time Intervals By Numbers
  528.    wt: 1:   Example 4 with x function of y
  529.    wt: 1:   11 Limits at infinity Three Examples
  530.    wt: 1:   10 Three one sided limits with infinite values
  531.    wt: 1:   9 Limits Continuity and Composition
  532.    wt: 1:   8 Four Animated Examples
  533.    wt: 1:   7 Evaluation by immediate or delayed substitution
  534.    wt: 1:   6 Continuity at a point
  535.    wt: 1:   5 Jumps and absence of unlimited error control
  536.    wt: 1:   4 Numerical properties
  537.    wt: 1:   3 Decimal insights for limits continuity convergence
  538.    wt: 1:   2 Algebraic codification
  539.    wt: 1:   1 Numerical introduction
  540.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  541.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  542.    wt: 1:   F.5a Equicontinuity Theorems
  543.    wt: 1:   F.1 What Functions are Continuous
  544.    wt: 1:   PostScript For and Against Decimal Perspectives
  545.    wt: 1:   Chapter 23 Links To Trigonometry
  546.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  547.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  548.    wt: 1:   Chapter 19. Functions and Sets
  549.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  550.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  551.    wt: 1:   Postscript A Three Remarks
  552.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  553.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  554.    wt: 1:   Chapter 15 Objective Processes
  555.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  556.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  557.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  558.    wt: 1:   M Words to extend arithmetic
  559.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  560.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  561.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  562.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  563.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  564.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  565.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  566.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  567.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  568.    wt: 11:   13 Velocity Vectors in Physics
Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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