Appetizers and Lessons for Mathematics & Reason Français: 26 pages
A 1100+ page site with math-free logic chapters and wordy algebra chapters.
For comprehension, study site chapters and steps. Go beyond rote learning.

Logic mastery strengthens comprehension and so improves home, work & study abilities .
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 14+: 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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

Site Review: Mathphobics, this site may ease your fears of the subject, perhaps even help you njoy it. ... unintimidating, sometimes funny and very clear. ... . Read all. Continue with Volume 2, Three Skill for Algebra.

Site Review. Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation ... Read all. See site books as well.

Teachers & Tutors: Site material uniquely explains common troubles in terms of steps too large or missing. Plus, this December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may 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.

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  5.    wt: 2:   14 Degrees to Radians and Radians to Degrees/
  6.    wt: 2:   13 Vectors/
  7.    wt: 2:   12 Function Translating and Rescaling/
  8.    wt: 2:   11 Parallel Straight Lines and Transversals/
  9.    wt: 2:   10 Intersecting Straight Lines and Transversals/
  10.    wt: 2:   9 Lines and Slopes Take 2 with tangent function/
  11.    wt: 2:   8 Unit Circle Trigonometry/
  12.    wt: 2:   7 Complex Numbers/
  13.    wt: 2:   6 Trigonometry first steps/
  14.    wt: 2:   5 What is Similarity/
  15.    wt: 2:   4 Lines and Slopes Take 1/
  16.    wt: 2:   3 Cartesian and Polar Coordinates/
  17.    wt: 2:   2 Euclidean Geometry Constructions Theory extras/
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  12.    wt: 1:   02 20 mathematics education references
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  14.    wt: 1:   Four ways to improve education reform
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  16.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  17.    wt: 1:   11 Help and Defend Your Child or Teens Education
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  22.    wt: 1:   Postscript B Mathematics Education References

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

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11 Parallel Straight Lines and Transversals
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70 Calculus Starter Lessons


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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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