Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic and Pattern Based Reason to inform and amuse.

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 material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin.

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 focus on skills with actual or potential local 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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  6.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  7.    wt: 1:   14 Degrees to Radians and Radians to Degrees/
  8.    wt: 1:   13 Vectors/
  9.    wt: 1:   12 Function Translating and Rescaling/
  10.    wt: 1:   11 Parallel Straight Lines and Transversals/
  11.    wt: 1:   10 Intersecting Straight Lines and Transversals/
  12.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
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  1.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  2.    wt: 2:   3 Euclidean Geometry Leanly
  3.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  4.    wt: 2:   Short Course on Euclidean Geometry
  5.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  6.    wt: 1:   K LAMP Musings Science Education
  7.    wt: 1:   J LAMP Introduction Extrinsic Origins
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  9.    wt: 1:   H LAMP Introduction Instructional Concepts
  10.    wt: 1:   G LAMP Introduction Problem Solving Skills
  11.    wt: 1:   F LAMP Introduction Prerequisites
  12.    wt: 1:   E LAMP Introduction Modern Mathematics
  13.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  14.    wt: 1:   A Introduction Objectives
  15.    wt: 1:   Ramblings Introduction Algebra Essay
  16.    wt: 1:   Skills Chapter 2 Geometry
  17.    wt: 1:   Skills Chapter 0 Introduction
  18.    wt: 1:   8 analytic geometry etc
  19.    wt: 1:   links Education Resources online
  20.    wt: 1:   Mathematics Education Professors
  21.    wt: 1:   modern education
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  23.    wt: 1:   three goals for Mathematics Education
  24.    wt: 1:   02 20 mathematics education references
  25.    wt: 1:   Education in mathematics science and technology
  26.    wt: 1:   Four ways to improve education reform
  27.    wt: 1:   education an empirical art
  28.    wt: 1:   chapitre 01 00 Introduction
  29.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  30.    wt: 1:   11 Help and Defend Your Child or Teens Education
  31.    wt: 1:   Ages 12 to 14 Geometry
  32.    wt: 1:   Ages 10 to 12 Geometry
  33.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  34.    wt: 1:   1 Geometric Introduction of Function Notation
  35.    wt: 1:   Introduction Reading Guide
  36.    wt: 1:   1 Degrees and Radians Introduction
  37.    wt: 1:   2 Correspondence between Triangles
  38.    wt: 1:   5 Algebraic Solutions Introduction
  39.    wt: 1:   7 Compound Interest Formula Introduction
  40.    wt: 1:   1 Squares and Square Roots Introduction
  41.    wt: 1:   8 GCD from Euclidean Algorithm
  42.    wt: 1:   1 Least Common Multiples LCM Introduction
  43.    wt: 1:   4 video Prime Factorization Introduction
  44.    wt: 1:   18 Chain Rule Introduction
  45.    wt: 1:   1 Numerical introduction
  46.    wt: 1:   A1. Introduction
  47.    wt: 1:   Chapter 1.Introduction
  48.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  49.    wt: 1:   Postscript B Mathematics Education References
  50.    wt: 1:   Chapter 7 Two Treatments of Geometry
  51.    wt: 1:   Chapter 1 Introduction
  52.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  53.    wt: 1:   Chapter 1 Introduction
  54.    wt: 1:   Chapter 6 More Algebra and Geometry
  55.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  56.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  57.    wt: 1:   Mathematics Education References
  58.    wt: 1:   Mathematics Education References
  59.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics

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  3.    wt: 5:   modern education
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  5.    wt: 5:   three goals for Mathematics Education
  6.    wt: 5:   02 20 mathematics education references
  7.    wt: 5:   Education in mathematics science and technology
  8.    wt: 5:   Four ways to improve education reform
  9.    wt: 5:   education an empirical art
  10.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  11.    wt: 5:   Short Course on Euclidean Geometry
  12.    wt: 4:   3 Euclidean Geometry Leanly
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  27.    wt: 4:   learning takes time
  28.    wt: 4:   grouping students according to ability
  29.    wt: 4:   what should be learnt and When
  30.    wt: 4:   mathematics in context
  31.    wt: 4:   Postscript 2007 01 10
  32.    wt: 4:   five decades make a difference
  33.    wt: 4:   Maps Plans Drawings
  34.    wt: 4:   how letters appear
  35.    wt: 4:   Secondary Three Mathematics
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  37.    wt: 4:   Secondary One Mathematics
  38.    wt: 4:   talk the algebra talk
  39.    wt: 4:   three difficulties
  40.    wt: 4:   teaching tips
  41.    wt: 4:   What to Tell Students
  42.    wt: 4:   mathematics curriculum shifts
  43.    wt: 4:   geometric implications for algebra
  44.    wt: 4:   teaching tutoring algebraic reason
  45.    wt: 4:   Lessening Algebra Difficulties
  46.    wt: 4:   the trouble with algebra
  47.    wt: 4:   05 13 OldSiteEntrancePage
  48.    wt: 4:   04 29 New Mathematics Curriculum
  49.    wt: 4:   04 25 when to stop or suspend mathemat
  50.    wt: 4:   02 21 words for teachers
  51.    wt: 4:   three aims for mathematics students
  52.    wt: 4:   standards for course material
  53.    wt: 4:   Operational Viewpoint to Value
  54.    wt: 4:   formal or informal peer review
  55.    wt: 4:   Theory of Knowledge
  56.    wt: 4:   mathematics instruction in general
  57.    wt: 4:   Different Kinds of Reasoning in maths
  58.    wt: 4:   three kinds of reason in mathematics
  59.    wt: 4:   cultivating intelligence
  60.    wt: 4:   How to be a better instructor
  61.    wt: 4:   Motivation and Context Problem
  62.    wt: 4:   need for a mixed mathematics curriculum
  63.    wt: 4:   Leaner mathematics curriculum
  64.    wt: 4:   Prequel In For A Penny In For A Pound
  65.    wt: 4:   fairness and inductive principles for instruction
  66.    wt: 4:   words for mathematics instructor
  67.    wt: 4:   2 Correspondence between Triangles
  68.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  69.    wt: 3:   8 analytic geometry etc
  70.    wt: 3:   PS H Distributive Law For Complex Numbers
  71.    wt: 3:   PS G Rotation Distributes over Addition
  72.    wt: 3:   PS F Scalar Multiplication Distributes over Addition
  73.    wt: 3:   PS E Multiplication with Polar Coordinates
  74.    wt: 3:   PS D Addition with Cartesian Coordinates
  75.    wt: 3:   PS C Similarity Use Recognize it in Trigonometry
  76.    wt: 3:   PS B Parallelogram Construction Methods
  77.    wt: 3:   PS A Kite Construction Methods
  78.    wt: 3:   21 Parallelograms
  79.    wt: 3:   19 Right Triangle Similarity
  80.    wt: 3:   18 Triangle Similarity Take 1
  81.    wt: 3:   17 Right Bisectors of Triangle Sides
  82.    wt: 3:   16 Angles Subtended By Chords and Diameters
  83.    wt: 3:   15 Triangle Angle Sum is 180 degrees
  84.    wt: 3:   14 Parallel Lines Postulate
  85.    wt: 3:   13 Angle Side Angle Failure
  86.    wt: 3:   12 Side Angle Side Failure
  87.    wt: 3:   11 Triangle Construction Fails
  88.    wt: 3:   10 Dropping a perpendicular to line
  89.    wt: 3:   9 Construction of a right bisector
  90.    wt: 3:   8 Isoceles Triangles
  91.    wt: 3:   7 Angle Side Angle
  92.    wt: 3:   6 Ruler and compass Angle Bisection
  93.    wt: 3:   5 Side Angle Side
  94.    wt: 3:   4 Side Side Side
  95.    wt: 3:   3 Isometry of Triangles Congruence
  96.    wt: 3:   1 Initial Concepts and Terms
  97.    wt: 2:   K LAMP Musings Science Education
  98.    wt: 2:   J LAMP Introduction Extrinsic Origins
  99.    wt: 2:   I LAMP Introduction Study Habits
  100.    wt: 2:   H LAMP Introduction Instructional Concepts
  101.    wt: 2:   G LAMP Introduction Problem Solving Skills
  102.    wt: 2:   F LAMP Introduction Prerequisites
  103.    wt: 2:   E LAMP Introduction Modern Mathematics
  104.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  105.    wt: 2:   A Introduction Objectives
  106.    wt: 2:   Ramblings Introduction Algebra Essay
  107.    wt: 2:   Skills Chapter 2 Geometry
  108.    wt: 2:   Skills Chapter 0 Introduction
  109.    wt: 2:   11 pure mathematics
  110.    wt: 2:   10 statistics
  111.    wt: 2:   9 combinatorics probability sets
  112.    wt: 2:   7 logic review and decimals an odd combination
  113.    wt: 2:   6 polynomials etc
  114.    wt: 2:   5 logarithms and exponentials etc
  115.    wt: 2:   4 algebra
  116.    wt: 2:   2 arithmetic with signed numbers
  117.    wt: 2:   1 arithmetic with unsigned numbers
  118.    wt: 2:   What is POMME
  119.    wt: 2:   1 Degrees and Radians Introduction
  120.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  121.    wt: 1:   Appendix 2 primary school Arithmetic 01
  122.    wt: 1:   Appendix 1 primary and preschool mathematic
  123.    wt: 1:   Skills Chapter 5 Calculus
  124.    wt: 1:   Skills Chapter 4 Logic
  125.    wt: 1:   Ramblings Extrinsic numbers theory
  126.    wt: 1:   Skills Chapter 3 Algebra
  127.    wt: 1:   Skills Chapter 1 Arithmetic
  128.    wt: 1:   chapitre 01 00 Introduction
  129.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  130.    wt: 1:   11 Help and Defend Your Child or Teens Education
  131.    wt: 1:   Ages 12 to 14 Geometry
  132.    wt: 1:   Ages 10 to 12 Geometry
  133.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  134.    wt: 1:   1 Geometric Introduction of Function Notation
  135.    wt: 1:   Introduction Reading Guide
  136.    wt: 1:   16 cotangent function Definition Graph and Inverse
  137.    wt: 1:   15 cosecant function Definition Graph and Inverse
  138.    wt: 1:   14 secant function Definition Graph and Inverse
  139.    wt: 1:   13 cosecant function Definition Graph and Inverse
  140.    wt: 1:   12 motivation for term arctan
  141.    wt: 1:   11 arctan left inverse of tangent Graph
  142.    wt: 1:   10 arctan left inverse of tangent Definition
  143.    wt: 1:   9 motivation for name arcsin
  144.    wt: 1:   8 arcsin left inverse of sine Graph
  145.    wt: 1:   7 arcsin left inverse of sine Definition
  146.    wt: 1:   6 Graph of arccos function
  147.    wt: 1:   5 Swapping Coordinates is a reflection
  148.    wt: 1:   4 possible motivation for term arccos
  149.    wt: 1:   3 Left Inverse of cosine arccos definition
  150.    wt: 1:   2 cosine function more properties
  151.    wt: 1:   1 cosine function properties
  152.    wt: 1:   9 Summary Degrees to Radians and back
  153.    wt: 1:   8 Radian Measures of Common Angles
  154.    wt: 1:   7 Radian Measures in special Triangles
  155.    wt: 1:   6 Radian Measure to Degrees
  156.    wt: 1:   5 Degrees to Radian Measure
  157.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  158.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  159.    wt: 1:   2 Radian Measure Numerical Value of one degree
  160.    wt: 1:   A Global Time and Navigation
  161.    wt: 1:   15 Dot and Cross Product
  162.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  163.    wt: 1:   13 Velocity Vectors in Physics
  164.    wt: 1:   12 From Applied To Pure Mathematics
  165.    wt: 1:   11 Component Method
  166.    wt: 1:   10 Parallelogram Addition Method
  167.    wt: 1:   9 Head to Tail Coordinate View
  168.    wt: 1:   8 Parallel Vectors
  169.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  170.    wt: 1:   6 Vectors with Coordinates
  171.    wt: 1:   5 Head To Tail Arrow Addition
  172.    wt: 1:   4 Resultant of a Sum of Movements
  173.    wt: 1:   3 Navigation with Arrows or Vectors
  174.    wt: 1:   2 Signed Coordinates
  175.    wt: 1:   1 Unsigned Coordinates
  176.    wt: 1:   Vector and Complex Number Applet
  177.    wt: 1:   4 graphing y=Asin(x c)
  178.    wt: 1:   3 graphing y=f(x c) plus K
  179.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  180.    wt: 1:   1 graphing y=f(x a)
  181.    wt: 1:   Parallel Lines and Parallel Transversals
  182.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  183.    wt: 1:   Triangle Angles Sum To 180 Degrees
  184.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  185.    wt: 1:   Parallel Lines and Interior Angles
  186.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  187.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  188.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  189.    wt: 1:   Straight Lines ASA Intersection Study More
  190.    wt: 1:   Straight Lines ASA Intersection Study
  191.    wt: 1:   Straight Lines Instersection Solving Equations
  192.    wt: 1:   Straight Lines Intersection of
  193.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  194.    wt: 1:   C Straight Lines Slope from Coordinates
  195.    wt: 1:   B Straight Line Slope Scaling Properties More
  196.    wt: 1:   A Straight Line Slope Scaling Properties
  197.    wt: 1:   14 Straight Lines Equations General Case
  198.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  199.    wt: 1:   12 Straight Lines Graphing mx plus b
  200.    wt: 1:   11 Straight Lines Graphing y=mx
  201.    wt: 1:   10 Straight Lines through Origin Equations More
  202.    wt: 1:   9 Straight Lines through Origin Equations
  203.    wt: 1:   8 Straight Lines Equation for vertical
  204.    wt: 1:   7 Tangent Function is odd on this domain
  205.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  206.    wt: 1:   5 Tangent Function Graph
  207.    wt: 1:   4 Tangent Function Properties
  208.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  209.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  210.    wt: 1:   1 Straight Lines Slope Concept
  211.    wt: 1:   17 tangent function angle sum formulas
  212.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  213.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  214.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  215.    wt: 1:   32 seven rows of pascals triangle
  216.    wt: 1:   31 basic secant cosecant cotangent trig identities
  217.    wt: 1:   30 unit circle calculation of six trigonometric functions
  218.    wt: 1:   29 secant cosecant and cotangent for acute angles
  219.    wt: 1:   28 Expressing products of sines cosines as sums
  220.    wt: 1:   27 Logarithmic use of products of sines and cosines
  221.    wt: 1:   26 Formulas for products of sines and cosines
  222.    wt: 1:   25 tangent double angle formula Slope connection
  223.    wt: 1:   24 tangent Angle Difference Formula
  224.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  225.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  226.    wt: 1:   21 sine and cosine Half Angle Formulas
  227.    wt: 1:   20 sine and cosine Double Angle Formulas
  228.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  229.    wt: 1:   18 sum of sinusoidal waves as a single wave
  230.    wt: 1:   17G Pythagorean Theorem Converse
  231.    wt: 1:   17F Law of cosines
  232.    wt: 1:   17E Trig Formulas for dot and cross Products
  233.    wt: 1:   17D cis formulas for sine cosines and tangent
  234.    wt: 1:   17C sine and cosine double triple angle formulas
  235.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  236.    wt: 1:   17A The complex number valued trig function cis
  237.    wt: 1:   16 Right Triangle Complementary Angle Relations
  238.    wt: 1:   15 sine cosine Complementary Angle Relations
  239.    wt: 1:   14 cosine even and sine and tangent are odd
  240.    wt: 1:   13 Graph of tangent function many periods
  241.    wt: 1:   12 Graph of tangent function for one period
  242.    wt: 1:   11 tangent function undefined when terminal side vertical
  243.    wt: 1:   10 Graphs of sines and cosines many periods
  244.    wt: 1:   9 Graphs of sine and cosine over one period
  245.    wt: 1:   8 period of tangent function
  246.    wt: 1:   7 period of sine and cosine
  247.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  248.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  249.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  250.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  251.    wt: 1:   2 Quadrant I reference Angles
  252.    wt: 1:   1 Unit Points Reflections Rotations
  253.    wt: 1:   Unit Circle Development of Trigonometry
  254.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  255.    wt: 1:   21 Logarithms Powers and Exponentials
  256.    wt: 1:   20 N th Roots of Complex Numbers
  257.    wt: 1:   19 N th Roots of Unity
  258.    wt: 1:   18 Sixth Roots of Unity
  259.    wt: 1:   17 Cube Roots of unity
  260.    wt: 1:   16 References and Originality Question
  261.    wt: 1:   15 Pythagorean Theorem Converse
  262.    wt: 1:   14 Law of cosines
  263.    wt: 1:   13 Trig Formulas for dot and cross Products
  264.    wt: 1:   12 cis formulas for sine cosines and tangent
  265.    wt: 1:   11 sine and cosine double triple angle formulas
  266.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  267.    wt: 1:   9 The complex number valued trig function cis
  268.    wt: 1:   8 Unit Circle Development of Trigonometry
  269.    wt: 1:   7 Second Way to Calculate Products
  270.    wt: 1:   6 Field Properties of Complex Number
  271.    wt: 1:   5 An Easy Proof of the Distributive Law
  272.    wt: 1:   4 Multiplication Properties
  273.    wt: 1:   3 Addition Properties
  274.    wt: 1:   2 Complex Numbers made easier we hope
  275.    wt: 1:   1 Rectangular Polar Coordinates Review
  276.    wt: 1:   Appetizer A Complex Number Applet
  277.    wt: 1:   8 Triangles Cascade Problem Solving
  278.    wt: 1:   7 Trignometric Ratios Unit Circle
  279.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  280.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  281.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  282.    wt: 1:   3 Trigonometric Ratios sine and cosine
  283.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  284.    wt: 1:   1 Angle Measurement with Degrees
  285.    wt: 1:   Why Trigonometry the whyslopes view
  286.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  287.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  288.    wt: 1:   12 Triangles Similarity More Problems
  289.    wt: 1:   11 Triangle Similarity Missing Side Problem
  290.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  291.    wt: 1:   9 Similarity of Triangles Usual Criteria
  292.    wt: 1:   8 Similarity of Triangles and Polygons
  293.    wt: 1:   7 Translations Rotations Reflections Dilatations
  294.    wt: 1:   6 Geometric Diagrams in Class
  295.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  296.    wt: 1:   4 Similarity Definition with Coordinate
  297.    wt: 1:   3 Similarity by Design with coordinates
  298.    wt: 1:   2 Similarity By Design
  299.    wt: 1:   1 Early Concept of Like or Similar Shapes
  300.    wt: 1:   Four Simple Exercises
  301.    wt: 1:   12 Links Lessons elsewhere
  302.    wt: 1:   11 A Partial Summary
  303.    wt: 1:   10 Midpoint of [a b] and [b a]
  304.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  305.    wt: 1:   8 Mid Point Formula
  306.    wt: 1:   7 Exercises to test skill and concept mastery
  307.    wt: 1:   6 Intersection of lines by solving linear systems
  308.    wt: 1:   5 Algebraic View of Slopes
  309.    wt: 1:   4 Equations for lines three forms
  310.    wt: 1:   3 Slope product for perpendicular lines
  311.    wt: 1:   2 point slope equation for a line
  312.    wt: 1:   1 Numerical view of lines and their equations
  313.    wt: 1:   What is and is not here
  314.    wt: 1:   13 Pythagorean spatial distance formulas
  315.    wt: 1:   12 Spatial Coordinates
  316.    wt: 1:   11 Triangle Inequality
  317.    wt: 1:   10 Pythagorean plane distance formula
  318.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  319.    wt: 1:   8 Distance Between Points on a Line
  320.    wt: 1:   7 Complex Numbers Appetizer
  321.    wt: 1:   6 Polar Multiplication and Rotation
  322.    wt: 1:   5 Cartesian Addition and Translation
  323.    wt: 1:   4 Polar Coordinates to and from
  324.    wt: 1:   3 Rectangular Coordinates Review
  325.    wt: 1:   2 Cartesian Coordinates with signs
  326.    wt: 1:   1 Cartesian Coordinates sans signs
  327.    wt: 1:   A Measurement with Ruler Proper Use
  328.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  329.    wt: 1:   6 Figuring with Maps Not to Scale
  330.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  331.    wt: 1:   4 Angles on Maps Plans drawn to scale
  332.    wt: 1:   3 Lengths and Areas on Maps and Plans
  333.    wt: 1:   2 Measuring Area Directly
  334.    wt: 1:   1 Length Measurement
  335.    wt: 1:   About Folder Contents
  336.    wt: 1:   5 Algebraic Solutions Introduction
  337.    wt: 1:   7 Compound Interest Formula Introduction
  338.    wt: 1:   1 Squares and Square Roots Introduction
  339.    wt: 1:   8 GCD from Euclidean Algorithm
  340.    wt: 1:   1 Least Common Multiples LCM Introduction
  341.    wt: 1:   4 video Prime Factorization Introduction
  342.    wt: 1:   18 Chain Rule Introduction
  343.    wt: 1:   1 Numerical introduction
  344.    wt: 1:   A1. Introduction
  345.    wt: 1:   Chapter 1.Introduction
  346.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  347.    wt: 1:   Postscript B Mathematics Education References
  348.    wt: 1:   Chapter 7 Two Treatments of Geometry
  349.    wt: 1:   Chapter 1 Introduction
  350.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  351.    wt: 1:   Chapter 1 Introduction
  352.    wt: 1:   Chapter 6 More Algebra and Geometry
  353.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  354.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  355.    wt: 1:   Mathematics Education References
  356.    wt: 1:   Mathematics Education References
  357.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
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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