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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35 matches:

  1.    wt: 8:   8 Unit Circle Trigonometry/
  2.    wt: 7:   3 Cartesian and Polar Coordinates/
  3.    wt: 7:   1 Maps Plans Measurement/
  4.    wt: 6:   13 Vectors/
  5.    wt: 6:   6 Trigonometry first steps/
  6.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  7.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  8.    wt: 5:   12 Function Translating and Rescaling/
  9.    wt: 5:   11 Parallel Straight Lines and Transversals/
  10.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  11.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  12.    wt: 5:   7 Complex Numbers/
  13.    wt: 5:   5 What is Similarity/
  14.    wt: 5:   4 Lines and Slopes Take 1/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 2:   3 Quadratics Geometrically/
  18.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  19.    wt: 2:   8 Arithmetic with Signed Numbers/
  20.    wt: 2:   3 Prime Factorization Skills/
  21.    wt: 2:   C Decimal Multiplication Methods/
  22.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  23.    wt: 1:   4 Functions/
  24.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  25.    wt: 1:   1 Five Polynomial Operations/
  26.    wt: 1:   More Algebra/
  27.    wt: 1:   8 Unifying Theme For Algebra/
  28.    wt: 1:   Step 4 Gaussian Elimination/
  29.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  30.    wt: 1:   Step 1 Stick diagram and fractions/
  31.    wt: 1:   3 Solving Linear Equations/
  32.    wt: 1:   4 Lessons on Using Derivatives/
  33.    wt: 1:   38 Lessons on Calculating Derivatives/
  34.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  35.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

92 matches:

  1.    wt: 3:   3 Polynomials Multiplication Addition
  2.    wt: 2:   Maps Plans Drawings
  3.    wt: 2:   13 Addition and Addition Tables
  4.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  5.    wt: 2:   PS F Scalar Multiplication Distributes over Addition
  6.    wt: 2:   4 Angles on Maps Plans drawn to scale
  7.    wt: 2:   3 Lengths and Areas on Maps and Plans
  8.    wt: 2:   11 Signed Number Addition and Addition Properties
  9.    wt: 2:   2 Addition and Multiplication Axioms
  10.    wt: 2:   3 GE III Equation Addition and Multiplication
  11.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  12.    wt: 1:   6 polynomials etc
  13.    wt: 1:   About site lesson plans
  14.    wt: 1:   chapitre 04 08 Limitations et benefices
  15.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  16.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  17.    wt: 1:   3 Energy Power Heat08
  18.    wt: 1:   C Energy Power03
  19.    wt: 1:   E Wire Resistance Calculation03
  20.    wt: 1:   14 Multiplication and Times Tables
  21.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  22.    wt: 1:   4 Polynomials Long division linear divisor
  23.    wt: 1:   2 Column Multiplication Method
  24.    wt: 1:   1 Polynomials Distributive Law
  25.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  26.    wt: 1:   13 Velocity Vectors in Physics
  27.    wt: 1:   10 Parallelogram Addition Method
  28.    wt: 1:   8 Parallel Vectors
  29.    wt: 1:   6 Vectors with Coordinates
  30.    wt: 1:   5 Head To Tail Arrow Addition
  31.    wt: 1:   3 Navigation with Arrows or Vectors
  32.    wt: 1:   Unit Circle Development of Trigonometry
  33.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  34.    wt: 1:   8 Unit Circle Development of Trigonometry
  35.    wt: 1:   4 Multiplication Properties
  36.    wt: 1:   3 Addition Properties
  37.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  38.    wt: 1:   Why Trigonometry the whyslopes view
  39.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  40.    wt: 1:   6 Polar Multiplication and Rotation
  41.    wt: 1:   5 Cartesian Addition and Translation
  42.    wt: 1:   PS G Rotation Distributes over Addition
  43.    wt: 1:   PS E Multiplication with Polar Coordinates
  44.    wt: 1:   PS D Addition with Cartesian Coordinates
  45.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  46.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  47.    wt: 1:   6 Figuring with Maps Not to Scale
  48.    wt: 1:   22 Multiplication of Signed Numbers
  49.    wt: 1:   21 Addition of Multiples of a Single Vector
  50.    wt: 1:   19 Signed Multiples of Vectors
  51.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  52.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  53.    wt: 1:   15 Head to Tails in place Addition Associative
  54.    wt: 1:   13 Arrows and Vectors in a Plane
  55.    wt: 1:   4 Location of Point in Decimal Addition
  56.    wt: 1:   3 Location of Point in Decimal Multiplication
  57.    wt: 1:   2 Counting Digits in Decimal Multiplication
  58.    wt: 1:   A Decimal Addition Columm Methods
  59.    wt: 1:   8 Column Multiplication Methods in General
  60.    wt: 1:   7 Decimals Multiplication Methods Examples
  61.    wt: 1:   6 Column Methods for Decimal Multiplication
  62.    wt: 1:   2 Combing Counts Addition Skills and Principles
  63.    wt: 1:   14 Real Number Multiplication
  64.    wt: 1:   11 Real Number Addition
  65.    wt: 1:   8 Coordinates for Maps and Planes
  66.    wt: 1:   3 signed coordinates for maps and planes
  67.    wt: 1:   1 Addition and Subtraction with Units
  68.    wt: 1:   16 Addition Subtraction Comparision Compared
  69.    wt: 1:   6 Multiplication of Mixed Numbers
  70.    wt: 1:   6 Multiplication Algebraically Take II
  71.    wt: 1:   4 Fraction Multiplication
  72.    wt: 1:   2 Unit Fraction Multiplication
  73.    wt: 1:   10 Integer Multiplication Formulas
  74.    wt: 1:   8 Multiplication by Signed Numbers Integers
  75.    wt: 1:   7 Multiplication by Signs
  76.    wt: 1:   6 Multiplication by Natural Numbers
  77.    wt: 1:   D Decimal Multiplication Methods Derived
  78.    wt: 1:   A Elementary Basis for Multiplication Methods
  79.    wt: 1:   6 Multiplication Commutes Order Not Important
  80.    wt: 1:   5 Decimal Fraction Multiplication
  81.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  82.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  83.    wt: 1:   1. Explaining Addition Table
  84.    wt: 1:   010 Repeated Addition of Time Intervals
  85.    wt: 1:   8 Addition of Time Intervals via subtotaling
  86.    wt: 1:   7 Addition of Time Intervals
  87.    wt: 1:   22 Chain Rule for polynomials
  88.    wt: 1:   8 Differentiation of polynomials
  89.    wt: 1:   Chapter 23 Links To Trigonometry
  90.    wt: 1:   Chapter 21 Arrow Addition
  91.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  92.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

593 matches:

  1.    wt: 9:   8 Parallel Vectors
  2.    wt: 9:   3 Navigation with Arrows or Vectors
  3.    wt: 9:   31 basic secant cosecant cotangent trig identities
  4.    wt: 9:   11 tangent function undefined when terminal side vertical
  5.    wt: 9:   6 sines and cosines for reference angle 30 degrees
  6.    wt: 9:   3 sines and cosines for reference angle 90 degrees
  7.    wt: 9:   Unit Circle Development of Trigonometry
  8.    wt: 9:   Right Triangle and Unit Circle Trigonometry
  9.    wt: 9:   8 Distance Between Points on a Line
  10.    wt: 9:   3 Rectangular Coordinates Review
  11.    wt: 9:   8 More Use of Maps Not Drawn to Scale
  12.    wt: 9:   4 Angles on Maps Plans drawn to scale
  13.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  14.    wt: 8:   17 tangent function angle sum formulas
  15.    wt: 8:   35 sines and cosines of 2A 3A 4A 5A
  16.    wt: 8:   34 sines and cosines of 2A 3A 4A 5A
  17.    wt: 8:   33 sines and cosines of 2A 3A 4A 5A
  18.    wt: 8:   32 seven rows of pascals triangle
  19.    wt: 8:   30 unit circle calculation of six trigonometric functions
  20.    wt: 8:   29 secant cosecant and cotangent for acute angles
  21.    wt: 8:   28 Expressing products of sines cosines as sums
  22.    wt: 8:   27 Logarithmic use of products of sines and cosines
  23.    wt: 8:   26 Formulas for products of sines and cosines
  24.    wt: 8:   25 tangent double angle formula Slope connection
  25.    wt: 8:   24 tangent Angle Difference Formula
  26.    wt: 8:   23 sine and cosine of 180 plus 22.5 degrees
  27.    wt: 8:   22 sine of 22.5 degrees via half angle formulas
  28.    wt: 8:   21 sine and cosine Half Angle Formulas
  29.    wt: 8:   20 sine and cosine Double Angle Formulas
  30.    wt: 8:   19 Pythagorean Identity For sine and cosine functions
  31.    wt: 8:   18 sum of sinusoidal waves as a single wave
  32.    wt: 8:   17G Pythagorean Theorem Converse
  33.    wt: 8:   17F Law of cosines
  34.    wt: 8:   17E Trig Formulas for dot and cross Products
  35.    wt: 8:   17D cis formulas for sine cosines and tangent
  36.    wt: 8:   17C sine and cosine double triple angle formulas
  37.    wt: 8:   17B sine cosine Angle Sum Formulas via cis
  38.    wt: 8:   17A The complex number valued trig function cis
  39.    wt: 8:   16 Right Triangle Complementary Angle Relations
  40.    wt: 8:   15 sine cosine Complementary Angle Relations
  41.    wt: 8:   14 cosine even and sine and tangent are odd
  42.    wt: 8:   13 Graph of tangent function many periods
  43.    wt: 8:   12 Graph of tangent function for one period
  44.    wt: 8:   10 Graphs of sines and cosines many periods
  45.    wt: 8:   9 Graphs of sine and cosine over one period
  46.    wt: 8:   8 period of tangent function
  47.    wt: 8:   7 period of sine and cosine
  48.    wt: 8:   5 sines and cosines for reference angle 60 degrees
  49.    wt: 8:   4 sines and cosines for reference angle 45 degrees
  50.    wt: 8:   2 Quadrant I reference Angles
  51.    wt: 8:   1 Unit Points Reflections Rotations
  52.    wt: 8:   8 Unit Circle Development of Trigonometry
  53.    wt: 8:   3 Addition Properties
  54.    wt: 8:   6 Polar Multiplication and Rotation
  55.    wt: 8:   5 Cartesian Addition and Translation
  56.    wt: 8:   6 Figuring with Maps Not to Scale
  57.    wt: 7:   14 Why Scalar Multiplication Distributes Physical Argument
  58.    wt: 7:   13 Velocity Vectors in Physics
  59.    wt: 7:   10 Parallelogram Addition Method
  60.    wt: 7:   6 Vectors with Coordinates
  61.    wt: 7:   5 Head To Tail Arrow Addition
  62.    wt: 7:   8 Triangles Cascade Problem Solving
  63.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  64.    wt: 7:   3 Trigonometric Ratios sine and cosine
  65.    wt: 7:   Why Trigonometry the whyslopes view
  66.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  67.    wt: 7:   8 Mid Point Formula
  68.    wt: 7:   3 Slope product for perpendicular lines
  69.    wt: 7:   13 Pythagorean spatial distance formulas
  70.    wt: 7:   12 Spatial Coordinates
  71.    wt: 7:   11 Triangle Inequality
  72.    wt: 7:   10 Pythagorean plane distance formula
  73.    wt: 7:   9 Pythagorean Theorem Chinese Square Proof
  74.    wt: 7:   7 Complex Numbers Appetizer
  75.    wt: 7:   4 Polar Coordinates to and from
  76.    wt: 7:   2 Cartesian Coordinates with signs
  77.    wt: 7:   1 Cartesian Coordinates sans signs
  78.    wt: 7:   PS F Scalar Multiplication Distributes over Addition
  79.    wt: 7:   8 Isoceles Triangles
  80.    wt: 7:   3 Isometry of Triangles Congruence
  81.    wt: 7:   A Measurement with Ruler Proper Use
  82.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  83.    wt: 7:   2 Measuring Area Directly
  84.    wt: 7:   1 Length Measurement
  85.    wt: 6:   3 Polynomials Multiplication Addition
  86.    wt: 6:   A Global Time and Navigation
  87.    wt: 6:   15 Dot and Cross Product
  88.    wt: 6:   12 From Applied To Pure Mathematics
  89.    wt: 6:   11 Component Method
  90.    wt: 6:   9 Head to Tail Coordinate View
  91.    wt: 6:   4 Resultant of a Sum of Movements
  92.    wt: 6:   2 Signed Coordinates
  93.    wt: 6:   1 Unsigned Coordinates
  94.    wt: 6:   Vector and Complex Number Applet
  95.    wt: 6:   3 graphing y=f(x c) plus K
  96.    wt: 6:   Straight Lines Intersection of
  97.    wt: 6:   14 Straight Lines Equations General Case
  98.    wt: 6:   13 Straight Lines Finding Equations from 2 points
  99.    wt: 6:   12 Straight Lines Graphing mx plus b
  100.    wt: 6:   11 Straight Lines Graphing y=mx
  101.    wt: 6:   10 Straight Lines through Origin Equations More
  102.    wt: 6:   9 Straight Lines through Origin Equations
  103.    wt: 6:   4 Multiplication Properties
  104.    wt: 6:   7 Trignometric Ratios Unit Circle
  105.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  106.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  107.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  108.    wt: 6:   1 Angle Measurement with Degrees
  109.    wt: 6:   8 Similarity of Triangles and Polygons
  110.    wt: 6:   3 Similarity by Design with coordinates
  111.    wt: 6:   PS G Rotation Distributes over Addition
  112.    wt: 6:   PS E Multiplication with Polar Coordinates
  113.    wt: 6:   PS D Addition with Cartesian Coordinates
  114.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  115.    wt: 5:   16 cotangent function Definition Graph and Inverse
  116.    wt: 5:   15 cosecant function Definition Graph and Inverse
  117.    wt: 5:   14 secant function Definition Graph and Inverse
  118.    wt: 5:   13 cosecant function Definition Graph and Inverse
  119.    wt: 5:   12 motivation for term arctan
  120.    wt: 5:   11 arctan left inverse of tangent Graph
  121.    wt: 5:   10 arctan left inverse of tangent Definition
  122.    wt: 5:   9 motivation for name arcsin
  123.    wt: 5:   8 arcsin left inverse of sine Graph
  124.    wt: 5:   7 arcsin left inverse of sine Definition
  125.    wt: 5:   6 Graph of arccos function
  126.    wt: 5:   5 Swapping Coordinates is a reflection
  127.    wt: 5:   4 possible motivation for term arccos
  128.    wt: 5:   3 Left Inverse of cosine arccos definition
  129.    wt: 5:   2 cosine function more properties
  130.    wt: 5:   1 cosine function properties
  131.    wt: 5:   9 Summary Degrees to Radians and back
  132.    wt: 5:   8 Radian Measures of Common Angles
  133.    wt: 5:   7 Radian Measures in special Triangles
  134.    wt: 5:   6 Radian Measure to Degrees
  135.    wt: 5:   5 Degrees to Radian Measure
  136.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  137.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  138.    wt: 5:   2 Radian Measure Numerical Value of one degree
  139.    wt: 5:   1 Degrees and Radians Introduction
  140.    wt: 5:   4 graphing y=Asin(x c)
  141.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  142.    wt: 5:   1 graphing y=f(x a)
  143.    wt: 5:   Parallel Lines and Parallel Transversals
  144.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  145.    wt: 5:   Triangle Angles Sum To 180 Degrees
  146.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  147.    wt: 5:   Parallel Lines and Interior Angles
  148.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  149.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  150.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  151.    wt: 5:   Straight Lines ASA Intersection Study More
  152.    wt: 5:   Straight Lines ASA Intersection Study
  153.    wt: 5:   Straight Lines Instersection Solving Equations
  154.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  155.    wt: 5:   C Straight Lines Slope from Coordinates
  156.    wt: 5:   B Straight Line Slope Scaling Properties More
  157.    wt: 5:   A Straight Line Slope Scaling Properties
  158.    wt: 5:   8 Straight Lines Equation for vertical
  159.    wt: 5:   7 Tangent Function is odd on this domain
  160.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  161.    wt: 5:   5 Tangent Function Graph
  162.    wt: 5:   4 Tangent Function Properties
  163.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  164.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  165.    wt: 5:   1 Straight Lines Slope Concept
  166.    wt: 5:   21 Logarithms Powers and Exponentials
  167.    wt: 5:   20 N th Roots of Complex Numbers
  168.    wt: 5:   19 N th Roots of Unity
  169.    wt: 5:   18 Sixth Roots of Unity
  170.    wt: 5:   17 Cube Roots of unity
  171.    wt: 5:   16 References and Originality Question
  172.    wt: 5:   15 Pythagorean Theorem Converse
  173.    wt: 5:   14 Law of cosines
  174.    wt: 5:   13 Trig Formulas for dot and cross Products
  175.    wt: 5:   12 cis formulas for sine cosines and tangent
  176.    wt: 5:   11 sine and cosine double triple angle formulas
  177.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  178.    wt: 5:   9 The complex number valued trig function cis
  179.    wt: 5:   7 Second Way to Calculate Products
  180.    wt: 5:   6 Field Properties of Complex Number
  181.    wt: 5:   5 An Easy Proof of the Distributive Law
  182.    wt: 5:   2 Complex Numbers made easier we hope
  183.    wt: 5:   1 Rectangular Polar Coordinates Review
  184.    wt: 5:   Appetizer A Complex Number Applet
  185.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  186.    wt: 5:   12 Triangles Similarity More Problems
  187.    wt: 5:   11 Triangle Similarity Missing Side Problem
  188.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  189.    wt: 5:   9 Similarity of Triangles Usual Criteria
  190.    wt: 5:   7 Translations Rotations Reflections Dilatations
  191.    wt: 5:   6 Geometric Diagrams in Class
  192.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  193.    wt: 5:   4 Similarity Definition with Coordinate
  194.    wt: 5:   2 Similarity By Design
  195.    wt: 5:   1 Early Concept of Like or Similar Shapes
  196.    wt: 5:   Four Simple Exercises
  197.    wt: 5:   12 Links Lessons elsewhere
  198.    wt: 5:   11 A Partial Summary
  199.    wt: 5:   10 Midpoint of [a b] and [b a]
  200.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  201.    wt: 5:   7 Exercises to test skill and concept mastery
  202.    wt: 5:   6 Intersection of lines by solving linear systems
  203.    wt: 5:   5 Algebraic View of Slopes
  204.    wt: 5:   4 Equations for lines three forms
  205.    wt: 5:   2 point slope equation for a line
  206.    wt: 5:   1 Numerical view of lines and their equations
  207.    wt: 5:   What is and is not here
  208.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  209.    wt: 5:   PS H Distributive Law For Complex Numbers
  210.    wt: 5:   PS B Parallelogram Construction Methods
  211.    wt: 5:   PS A Kite Construction Methods
  212.    wt: 5:   21 Parallelograms
  213.    wt: 5:   19 Right Triangle Similarity
  214.    wt: 5:   18 Triangle Similarity Take 1
  215.    wt: 5:   17 Right Bisectors of Triangle Sides
  216.    wt: 5:   16 Angles Subtended By Chords and Diameters
  217.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  218.    wt: 5:   14 Parallel Lines Postulate
  219.    wt: 5:   13 Angle Side Angle Failure
  220.    wt: 5:   12 Side Angle Side Failure
  221.    wt: 5:   11 Triangle Construction Fails
  222.    wt: 5:   10 Dropping a perpendicular to line
  223.    wt: 5:   9 Construction of a right bisector
  224.    wt: 5:   7 Angle Side Angle
  225.    wt: 5:   6 Ruler and compass Angle Bisection
  226.    wt: 5:   5 Side Angle Side
  227.    wt: 5:   4 Side Side Side
  228.    wt: 5:   2 Correspondence between Triangles
  229.    wt: 5:   1 Initial Concepts and Terms
  230.    wt: 5:   Short Course on Euclidean Geometry
  231.    wt: 5:   About Folder Contents
  232.    wt: 5:   3 GE III Equation Addition and Multiplication
  233.    wt: 4:   3 Solving triangular system example
  234.    wt: 4:   8 multiplying signed numbers
  235.    wt: 4:   3 signed coordinates for maps and planes
  236.    wt: 4:   8 video Prime Factorization upto 19
  237.    wt: 4:   3 video Primes and Composites from 9 times table
  238.    wt: 4:   3 More One Digit Multipliers
  239.    wt: 3:   8 Set view of relations and functions
  240.    wt: 3:   3 Formula or function graphing exercise
  241.    wt: 3:   8 quadratics backward use of various formulas
  242.    wt: 3:   3 quadratics factoring by inspection
  243.    wt: 3:   8 Formulas for Fractional Exponents with Logarithms
  244.    wt: 3:   3 Natural Logarithms and Exponentials Basic Properties
  245.    wt: 3:   8 Notes for instructors or tutors
  246.    wt: 3:   5 Polynomials Long division Nonlinear divisor
  247.    wt: 3:   4 Polynomials Long division linear divisor
  248.    wt: 3:   2 Column Multiplication Method
  249.    wt: 3:   1 Polynomials Distributive Law
  250.    wt: 3:   3 Gaussian Elimination 3 unknowns first example
  251.    wt: 3:   3 Four Examples
  252.    wt: 3:   8 One Example
  253.    wt: 3:   3 Two Examples
  254.    wt: 3:   8 Multiplication by Signed Numbers Integers
  255.    wt: 3:   D Decimal Multiplication Methods Derived
  256.    wt: 3:   B Powers of Ten
  257.    wt: 3:   A Elementary Basis for Multiplication Methods
  258.    wt: 3:   6 Multiplication Commutes Order Not Important
  259.    wt: 3:   5 Decimal Fraction Multiplication
  260.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  261.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  262.    wt: 3:   34 Derivative of exponential function
  263.    wt: 3:   33 Chain Rule Real Player video examples
  264.    wt: 3:   31 Derivatives of inverse functions
  265.    wt: 3:   30Chain Rule A Proof
  266.    wt: 3:   8 Differentiation of polynomials
  267.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  268.    wt: 3:   Systematic Algebra Skill Development Missing Links
  269.    wt: 2:   Maps Plans Drawings
  270.    wt: 2:   3 Energy Power Heat08
  271.    wt: 2:   13 Addition and Addition Tables
  272.    wt: 2:   8 The Effect of Negative Remarks
  273.    wt: 2:   3 Preparing for Science Studies
  274.    wt: 2:   A Quadratics Summary
  275.    wt: 2:   10 quadratic exercises
  276.    wt: 2:   9 quadratics physical and further context
  277.    wt: 2:   7 quadratic formulla derivation
  278.    wt: 2:   6 quadratics numerical approach
  279.    wt: 2:   5 quadratics completing the square
  280.    wt: 2:   4 quadratics difference of two squares
  281.    wt: 2:   2 quadratics graphing in general
  282.    wt: 2:   1 quadratics graphing exercises
  283.    wt: 2:   Quadratics in 10 steps
  284.    wt: 2:   7 Links Lessons Elsewhere
  285.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  286.    wt: 2:   22 Multiplication of Signed Numbers
  287.    wt: 2:   11 Signed Number Addition and Addition Properties
  288.    wt: 2:   3 Location of Point in Decimal Multiplication
  289.    wt: 2:   8 Column Multiplication Methods in General
  290.    wt: 2:   3 Multiplicative Counting Skills Principles
  291.    wt: 2:   3 Proportionality Examples
  292.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  293.    wt: 2:   3 Linear Equation Literal Solution More
  294.    wt: 2:   2 Addition and Multiplication Axioms
  295.    wt: 2:   8 Coordinates for Maps and Planes
  296.    wt: 2:   4 Solving a triangular system exercise
  297.    wt: 2:   2 Essentially one exercises three with solution
  298.    wt: 2:   1 Essentially One Unknown
  299.    wt: 2:   3 Comparison of Negative Numbers
  300.    wt: 2:   11 What are real lengths and numbers
  301.    wt: 2:   10 dividing signed numbers
  302.    wt: 2:   9 subtracting signed numbers
  303.    wt: 2:   7 negative and additive inverse
  304.    wt: 2:   6 adding signed numbers
  305.    wt: 2:   5 lengths and signs of numbers
  306.    wt: 2:   4 signed coordinates for regions in space
  307.    wt: 2:   2 signed and unsigned numbers as coordinates
  308.    wt: 2:   3 Adding Movements with same direction
  309.    wt: 2:   20 Uniqueness of Prime Factorization
  310.    wt: 2:   19 video Prime Factorization Unique
  311.    wt: 2:   18 video Count Factors given Prime Factorization
  312.    wt: 2:   17 Identify and Count Factors using Primes
  313.    wt: 2:   16 video Factors of 980 using prime
  314.    wt: 2:   15 video Factors of 20 using Prime Factorization
  315.    wt: 2:   14 video Factors of 24 Take II
  316.    wt: 2:   13 video Factors of 24 using prime
  317.    wt: 2:   12 LCD GCD and LCM using Primes
  318.    wt: 2:   11 Efficient Square Rule Use
  319.    wt: 2:   10 video Prime Factorization upto 23 squared
  320.    wt: 2:   9 video Prime Factorization upto 19 squared
  321.    wt: 2:   7 Calculator Usage Notes and Cautions
  322.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  323.    wt: 2:   5 Prime Factorization and a Square Rule
  324.    wt: 2:   4 video Prime Factorization Introduction
  325.    wt: 2:   2 Prime and Composites less than 16
  326.    wt: 2:   1 video how Products are bigger than factor
  327.    wt: 2:   8 Correcting the Mistake
  328.    wt: 2:   3 Division Single Digit Divisor Example
  329.    wt: 2:   C Counting Areas with Powers of Ten
  330.    wt: 2:   4 Two and Three Digit Multipliers
  331.    wt: 2:   2 One Digit Multipliers
  332.    wt: 2:   Video Power Notation in Decimal Expansion
  333.    wt: 2:   1 Why 3 times 5 gives 15
  334.    wt: 2:   8 Subtraction with Units of Measure
  335.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  336.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  337.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  338.    wt: 2:   8 Addition of Time Intervals via subtotaling
  339.    wt: 2:   3 Second derivative test
  340.    wt: 2:   2 Second derivative test prequel
  341.    wt: 2:   38 Formulas and derivatives for powers and roots
  342.    wt: 2:   36 Cube root derivative animated
  343.    wt: 2:   29 Chain Rule Optional Reading
  344.    wt: 2:   28 Chain Rule Preparation for a Proof
  345.    wt: 2:   22 Chain Rule for polynomials
  346.    wt: 2:   12 Quotient rule examples
  347.    wt: 2:   3 Motivation for Limit Definition Take 2
  348.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  349.    wt: 2:   8 Four Animated Examples
  350.    wt: 2:   E2 Algebraic Properties of Limits
  351.    wt: 2:   B3 Bolzano Weierstrass Theorem
  352.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  353.    wt: 2:   Implementation Notes
  354.    wt: 2:   More Algebra and Slope based Calculus Preview
  355.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  356.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  357.    wt: 1:   8 analytic geometry etc
  358.    wt: 1:   6 polynomials etc
  359.    wt: 1:   3 Euclidean Geometry Leanly
  360.    wt: 1:   permissions for teachers
  361.    wt: 1:   Math Ed if it must be short make it lean effective
  362.    wt: 1:   About site lesson plans
  363.    wt: 1:   Education Reform Inconsistencies
  364.    wt: 1:   talk the algebra talk
  365.    wt: 1:   teaching tutoring algebraic reason
  366.    wt: 1:   Different Kinds of Reasoning in maths
  367.    wt: 1:   chapitre 04 08 Limitations et benefices
  368.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  369.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  370.    wt: 1:   liens
  371.    wt: 1:   Trois Notions qui menent a algebre
  372.    wt: 1:   C Energy Power03
  373.    wt: 1:   E Wire Resistance Calculation03
  374.    wt: 1:   3 Like resistors in parallel
  375.    wt: 1:   G Series Circuit01
  376.    wt: 1:   B Electromotive force conventional current01
  377.    wt: 1:   14 Multiplication and Times Tables
  378.    wt: 1:   Ages 8 to 9
  379.    wt: 1:   Ages 3 plus to 4 plus
  380.    wt: 1:   sign monoticity analysis example 4
  381.    wt: 1:   sign monoticity analysis example 3
  382.    wt: 1:   sign monoticity analysis example 2
  383.    wt: 1:   sign monoticity analysis example 1
  384.    wt: 1:   26 Function definitions done and coming
  385.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  386.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  387.    wt: 1:   23 Inverse Functions
  388.    wt: 1:   22 Square Root function graphically
  389.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  390.    wt: 1:   20 Interchanging coordinates a reflection
  391.    wt: 1:   19 Horizontal line rule and method
  392.    wt: 1:   18 Vertical Line Rule and Method
  393.    wt: 1:   17 Function maxima minima and their location
  394.    wt: 1:   16 Increasing or decreasing on intervals
  395.    wt: 1:   15 Sign analysis of functions
  396.    wt: 1:   14 Surjections Injections Bijections
  397.    wt: 1:   13 From one to one to many to one
  398.    wt: 1:   12 Function Domain Recognition Exercises
  399.    wt: 1:   11 Function Domain Range Source and Targets
  400.    wt: 1:   10 Interval Notation
  401.    wt: 1:   9 Set theory term relation possible origins
  402.    wt: 1:   7 Functions with finite domains
  403.    wt: 1:   6 Set Existence Formation and Notation
  404.    wt: 1:   5 Function notation for geometric transformations
  405.    wt: 1:   4 Function notation in and beyond mathematics
  406.    wt: 1:   2 Algebraic use of function notation
  407.    wt: 1:   1 Geometric Introduction of Function Notation
  408.    wt: 1:   Introduction Reading Guide
  409.    wt: 1:   11 Growth and Decay in Biology
  410.    wt: 1:   10 Exponential Growth and Decay Models
  411.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  412.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  413.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  414.    wt: 1:   5 Natural Logarithm Calculator Exercises
  415.    wt: 1:   2 Square Root Simplification a prequel
  416.    wt: 1:   1 Calculator Starter Exercises
  417.    wt: 1:   Rewriting algebraic substitution as function substitutions
  418.    wt: 1:   26 More Less Greater Than Comparison
  419.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  420.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  421.    wt: 1:   23 Distributive Law Two Derivations
  422.    wt: 1:   21 Addition of Multiples of a Single Vector
  423.    wt: 1:   19 Signed Multiples of Vectors
  424.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  425.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  426.    wt: 1:   15 Head to Tails in place Addition Associative
  427.    wt: 1:   13 Arrows and Vectors in a Plane
  428.    wt: 1:   8 Division and Mulplication of Compound Fractions
  429.    wt: 1:   4 Location of Point in Decimal Addition
  430.    wt: 1:   2 Counting Digits in Decimal Multiplication
  431.    wt: 1:   A Decimal Addition Columm Methods
  432.    wt: 1:   7 Decimals Multiplication Methods Examples
  433.    wt: 1:   6 Column Methods for Decimal Multiplication
  434.    wt: 1:   2 Combing Counts Addition Skills and Principles
  435.    wt: 1:   3 Inequalities Algebraically
  436.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  437.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  438.    wt: 1:   6 Compound Interest Forward and Backwards
  439.    wt: 1:   5 Triangle Area Formula Backwards
  440.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  441.    wt: 1:   2 Linear Equation Literal Solution
  442.    wt: 1:   1 Changing Calculations
  443.    wt: 1:   3 Product Axioms Two Forms
  444.    wt: 1:   3 More and Less Than with Unlike Signs
  445.    wt: 1:   14 Real Number Multiplication
  446.    wt: 1:   11 Real Number Addition
  447.    wt: 1:   3 Fractions
  448.    wt: 1:   3 Geometric Formulas and Function Notation
  449.    wt: 1:   More Exercises
  450.    wt: 1:   Simple Exercises
  451.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  452.    wt: 1:   4 GE III Animated Examples
  453.    wt: 1:   2 GE II Comparison
  454.    wt: 1:   1 GE Substitution four examples
  455.    wt: 1:   6 Algebraic Solution Example
  456.    wt: 1:   5 Algebraic Solutions Introduction
  457.    wt: 1:   4 Four Examples Fractional Coefficients
  458.    wt: 1:   2 Three Examples
  459.    wt: 1:   1 Proper Equal Sign Usage
  460.    wt: 1:   Skill Development Notes
  461.    wt: 1:   10 One Example
  462.    wt: 1:   9 Three Examples
  463.    wt: 1:   7 Two Examples
  464.    wt: 1:   6 Three Examples
  465.    wt: 1:   5 Three Examples
  466.    wt: 1:   4 Two Examples
  467.    wt: 1:   2 Three Examples
  468.    wt: 1:   Using Letters for Physical Quantities
  469.    wt: 1:   Formula Usage Show Work Format
  470.    wt: 1:   8 Compound Interest Formula Evaluation
  471.    wt: 1:   3 Triangle Area Formula Example
  472.    wt: 1:   8 Sets of Numbers
  473.    wt: 1:   3 Counting with Sets etc
  474.    wt: 1:   3 Adding Words To Arithmetic
  475.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  476.    wt: 1:   1 Least Common Multiples LCM Introduction
  477.    wt: 1:   1 Addition and Subtraction with Units
  478.    wt: 1:   16 Addition Subtraction Comparision Compared
  479.    wt: 1:   14 Adding and Subtracting with Like Denominators
  480.    wt: 1:   6 Multiplication of Mixed Numbers
  481.    wt: 1:   6 Multiplication Algebraically Take II
  482.    wt: 1:   4 Fraction Multiplication
  483.    wt: 1:   3 Unit fraction of a fraction
  484.    wt: 1:   2 Unit Fraction Multiplication
  485.    wt: 1:   10 Integer Multiplication Formulas
  486.    wt: 1:   7 Multiplication by Signs
  487.    wt: 1:   6 Multiplication by Natural Numbers
  488.    wt: 1:   26 Divisibility by 2 3 5 Example
  489.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  490.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  491.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  492.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  493.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  494.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  495.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  496.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  497.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  498.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  499.    wt: 1:   8 What skills and work habits to require
  500.    wt: 1:   3. How to add with decimals A sans conversions
  501.    wt: 1:   1. Explaining Addition Table
  502.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  503.    wt: 1:   010 Repeated Addition of Time Intervals
  504.    wt: 1:   7 Addition of Time Intervals
  505.    wt: 1:   3 Units and Lengths of Time
  506.    wt: 1:   Example 4 with x function of y
  507.    wt: 1:   Example 3
  508.    wt: 1:   Example 2
  509.    wt: 1:   Example 1
  510.    wt: 1:   A Related Material in Volume 3
  511.    wt: 1:   3 Two Chain Rule Method Exercises
  512.    wt: 1:   A Related lessons in Volume 3
  513.    wt: 1:   4 Second derivative test exercise example
  514.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  515.    wt: 1:   A Chain Rule Real Player video examples
  516.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  517.    wt: 1:   26 Chain Rule Recognising outer inner functions
  518.    wt: 1:   25 Chain Rule Animated Examples Continued
  519.    wt: 1:   24 Chain Rule Animated Examples
  520.    wt: 1:   23 Chain Rule in general
  521.    wt: 1:   21 Chain Rule for powers
  522.    wt: 1:   20 Chain Rule for Pulley Systems
  523.    wt: 1:   19 Chain Rule for linear functions
  524.    wt: 1:   18 Chain Rule Introduction
  525.    wt: 1:   17 Derivatives of quotients of sine and cosine
  526.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  527.    wt: 1:   15 sine and cosine derivatives 3rd step
  528.    wt: 1:   14 sine and cosine derivatives 2nd step
  529.    wt: 1:   13 sine and cosine derivatives 1st step
  530.    wt: 1:   11 Quotient rule
  531.    wt: 1:   10 Power rule for negative integers
  532.    wt: 1:   9 Reciprocal rule
  533.    wt: 1:   7 Animated Differentiation Examples
  534.    wt: 1:   6 Power rule from product rule
  535.    wt: 1:   5 Product Rule
  536.    wt: 1:   4 Sum Rule
  537.    wt: 1:   2 Motivation for Limit Definition Take 1
  538.    wt: 1:   4 Numerical properties
  539.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  540.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  541.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  542.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  543.    wt: 1:   G.5 Motions With Bounded Velocities
  544.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  545.    wt: 1:   G.3 Constant Difference Theorem Proof
  546.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  547.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  548.    wt: 1:   F.5b Extreme Value Theorem
  549.    wt: 1:   F.5a Equicontinuity Theorems
  550.    wt: 1:   F.4 Finite Covering Theorem
  551.    wt: 1:   F.3 Intermediate Value Theorem
  552.    wt: 1:   F.2 Closed Range Theorem
  553.    wt: 1:   F.1 What Functions are Continuous
  554.    wt: 1:   E1 Error Control Inequalities
  555.    wt: 1:   D2 Limits of Monotone Sequences
  556.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  557.    wt: 1:   C Triangle Inequalities
  558.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  559.    wt: 1:   PostScript For and Against Decimal Perspectives
  560.    wt: 1:   A1. Introduction
  561.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  562.    wt: 1:   Chapter 23 Links To Trigonometry
  563.    wt: 1:   Chapter 21 Arrow Addition
  564.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  565.    wt: 1:   Chapter 8. Slope Interpretation
  566.    wt: 1:   Chapter 3. Slope Sign Analysis
  567.    wt: 1:   Chapter 8 Three Skills For Algebra
  568.    wt: 1:   Chapter 3 Chains of Reason
  569.    wt: 1:   Chapter 8 Modern Instruction
  570.    wt: 1:   Chapter 3 Algebra Difficulties
  571.    wt: 1:   Chapter 8 Change of Language
  572.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  573.    wt: 1:   H more Routine to non routine problem solving
  574.    wt: 1:   H Jigsaw puzzles and problem solving
  575.    wt: 1:   C. Domino effect of being careful
  576.    wt: 1:   Chapter 8 Skipped Topics and Why
  577.    wt: 1:   Chapter 3 Algebra Starter Lessons
  578.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  579.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  580.    wt: 1:   Helping the Blind in Logic and Mathematics
  581.    wt: 1:   Mathematics Education References
  582.    wt: 1:   Mathematics Education References
  583.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  584.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  585.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  586.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  587.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  588.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  589.    wt: 1:   Which Way To Go
  590.    wt: 1:   Road Safety Questions
  591.    wt: 1:   The Math Forum and Site Content
  592.    wt: 1:   Site Reviews
  593.    wt: 10:   3 Lengths and Areas on Maps and Plans
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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