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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  1.    wt: 4:   Mathematics Education Essays/
  2.    wt: 4:   1 Maps Plans Measurement/
  3.    wt: 2:   Progressive Observable Motivated Mathematics Education/
  4.    wt: 2:   15 Arc or Inverse Trigonometric Function/
  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/
  18.    wt: 2:   Geometry maps plans trigonometry vectors/
  19.    wt: 1:   LAMP Lean Applied Mathematics Program/
  20.    wt: 1:   Archives/

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  1.    wt: 3:   Maps Plans Drawings
  2.    wt: 2:   4 Angles on Maps Plans drawn to scale
  3.    wt: 2:   3 Lengths and Areas on Maps and Plans
  4.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  5.    wt: 1:   K LAMP Musings Science Education
  6.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  7.    wt: 1:   links Education Resources online
  8.    wt: 1:   About site lesson plans
  9.    wt: 1:   Mathematics Education Professors
  10.    wt: 1:   modern education
  11.    wt: 1:   Education Reform Inconsistencies
  12.    wt: 1:   three goals for Mathematics Education
  13.    wt: 1:   02 20 mathematics education references
  14.    wt: 1:   Education in mathematics science and technology
  15.    wt: 1:   Four ways to improve education reform
  16.    wt: 1:   education an empirical art
  17.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  18.    wt: 1:   11 Help and Defend Your Child or Teens Education
  19.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  20.    wt: 1:   6 Figuring with Maps Not to Scale
  21.    wt: 1:   8 Coordinates for Maps and Planes
  22.    wt: 1:   3 signed coordinates for maps and planes
  23.    wt: 1:   Postscript B Mathematics Education References
  24.    wt: 1:   Mathematics Education References
  25.    wt: 1:   Mathematics Education References

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334 matches:

  1.    wt: 7:   Maps Plans Drawings
  2.    wt: 6:   4 Angles on Maps Plans drawn to scale
  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
  8.    wt: 5:   Education Reform Inconsistencies
  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
  15.    wt: 5:   6 Figuring with Maps Not to Scale
  16.    wt: 4:   why bother
  17.    wt: 4:   which way to go
  18.    wt: 4:   website reviews
  19.    wt: 4:   three goals to set for students
  20.    wt: 4:   Teach the teachers plus goals
  21.    wt: 4:   permissions for teachers
  22.    wt: 4:   Math Ed if it must be short make it lean effective
  23.    wt: 4:   Applied Maths Program14092009 POMME variant
  24.    wt: 4:   activities for students
  25.    wt: 4:   site origins
  26.    wt: 4:   site eurekas
  27.    wt: 4:   key notes and themes
  28.    wt: 4:   teacher certification
  29.    wt: 4:   learning takes time
  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
  37.    wt: 4:   Secondary Two Mathematics
  38.    wt: 4:   Secondary One Mathematics
  39.    wt: 4:   talk the algebra talk
  40.    wt: 4:   three difficulties
  41.    wt: 4:   teaching tips
  42.    wt: 4:   What to Tell Students
  43.    wt: 4:   mathematics curriculum shifts
  44.    wt: 4:   geometric implications for algebra
  45.    wt: 4:   teaching tutoring algebraic reason
  46.    wt: 4:   Lessening Algebra Difficulties
  47.    wt: 4:   the trouble with algebra
  48.    wt: 4:   05 13 OldSiteEntrancePage
  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
  53.    wt: 4:   standards for course material
  54.    wt: 4:   Operational Viewpoint to Value
  55.    wt: 4:   formal or informal peer review
  56.    wt: 4:   Theory of Knowledge
  57.    wt: 4:   mathematics instruction in general
  58.    wt: 4:   Different Kinds of Reasoning in maths
  59.    wt: 4:   three kinds of reason in mathematics
  60.    wt: 4:   cultivating intelligence
  61.    wt: 4:   How to be a better instructor
  62.    wt: 4:   Motivation and Context Problem
  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: 2:   5 Interpreting and Drawing Maps and Plans.
  310.    wt: 1:   Appendix 2 primary school Arithmetic 01
  311.    wt: 1:   Appendix 1 primary and preschool mathematic
  312.    wt: 1:   J LAMP Introduction Extrinsic Origins
  313.    wt: 1:   I LAMP Introduction Study Habits
  314.    wt: 1:   H LAMP Introduction Instructional Concepts
  315.    wt: 1:   G LAMP Introduction Problem Solving Skills
  316.    wt: 1:   F LAMP Introduction Prerequisites
  317.    wt: 1:   E LAMP Introduction Modern Mathematics
  318.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  319.    wt: 1:   A Introduction Objectives
  320.    wt: 1:   Skills Chapter 5 Calculus
  321.    wt: 1:   Skills Chapter 4 Logic
  322.    wt: 1:   Ramblings Extrinsic numbers theory
  323.    wt: 1:   Ramblings Introduction Algebra Essay
  324.    wt: 1:   Skills Chapter 3 Algebra
  325.    wt: 1:   Skills Chapter 2 Geometry
  326.    wt: 1:   Skills Chapter 1 Arithmetic
  327.    wt: 1:   Skills Chapter 0 Introduction
  328.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  329.    wt: 1:   11 Help and Defend Your Child or Teens Education
  330.    wt: 1:   8 Coordinates for Maps and Planes
  331.    wt: 1:   3 signed coordinates for maps and planes
  332.    wt: 1:   Postscript B Mathematics Education References
  333.    wt: 1:   Mathematics Education References
  334.    wt: 1:   Mathematics Education References
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.
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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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