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 Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

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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33 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   8 Unit Circle Trigonometry/
  4.    wt: 6:   6 Trigonometry first steps/
  5.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  6.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  7.    wt: 5:   12 Function Translating and Rescaling/
  8.    wt: 5:   11 Parallel Straight Lines and Transversals/
  9.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  10.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  11.    wt: 5:   7 Complex Numbers/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   Geometry maps plans trigonometry vectors/
  16.    wt: 2:   D Decimal Long Division Methods/
  17.    wt: 2:   C Decimal Multiplication Methods/
  18.    wt: 2:   B Decimal Comparing and Subtracting Methods/
  19.    wt: 2:   A Decimal Counting and Adding Methods/
  20.    wt: 2:   2 Arithmetic with Decimals/
  21.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  22.    wt: 1:   11 Squares and Square Roots/
  23.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  24.    wt: 1:   9 Combinatorics Trees Tables and Products/
  25.    wt: 1:   8 Arithmetic with Signed Numbers/
  26.    wt: 1:   7 Arithmetic and Fractions with Units/
  27.    wt: 1:   6 Fractions and Ratios/
  28.    wt: 1:   5 Integers/
  29.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  30.    wt: 1:   3 Prime Factorization Skills/
  31.    wt: 1:   1 Decimal Place Value/
  32.    wt: 1:   Arithmetic and Number Theory Skills/
  33.    wt: 11:   2 Euclidean Geometry Constructions Theory extras/

Web Page Search

126 matches:

  1.    wt: 3:   Triangle Angles Sum To 180 Degrees
  2.    wt: 3:   15 Triangle Angle Sum is 180 degrees
  3.    wt: 3:   4 Angles on Maps Plans drawn to scale
  4.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  5.    wt: 2:   3 Euclidean Geometry Leanly
  6.    wt: 2:   Maps Plans Drawings
  7.    wt: 2:   17 tangent function angle sum formulas
  8.    wt: 2:   17B sine cosine Angle Sum Formulas via cis
  9.    wt: 2:   16 Right Triangle Complementary Angle Relations
  10.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  11.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  12.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  13.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  14.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  15.    wt: 2:   13 Angle Side Angle Failure
  16.    wt: 2:   7 Angle Side Angle
  17.    wt: 2:   Short Course on Euclidean Geometry
  18.    wt: 2:   3 Lengths and Areas on Maps and Plans
  19.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  20.    wt: 1:   Ramblings Extrinsic numbers theory
  21.    wt: 1:   Skills Chapter 2 Geometry
  22.    wt: 1:   8 analytic geometry etc
  23.    wt: 1:   About site lesson plans
  24.    wt: 1:   Theory of Knowledge
  25.    wt: 1:   Ages 12 to 14 Geometry
  26.    wt: 1:   Ages 10 to 12 Geometry
  27.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  28.    wt: 1:   9 Set theory term relation possible origins
  29.    wt: 1:   A Quadratics Summary
  30.    wt: 1:   9 Summary Degrees to Radians and back
  31.    wt: 1:   8 Radian Measures of Common Angles
  32.    wt: 1:   7 Radian Measures in special Triangles
  33.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  34.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  35.    wt: 1:   13 Velocity Vectors in Physics
  36.    wt: 1:   8 Parallel Vectors
  37.    wt: 1:   6 Vectors with Coordinates
  38.    wt: 1:   4 Resultant of a Sum of Movements
  39.    wt: 1:   3 Navigation with Arrows or Vectors
  40.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  41.    wt: 1:   Parallel Lines and Interior Angles
  42.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  43.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  44.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  45.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  46.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  47.    wt: 1:   32 seven rows of pascals triangle
  48.    wt: 1:   29 secant cosecant and cotangent for acute angles
  49.    wt: 1:   28 Expressing products of sines cosines as sums
  50.    wt: 1:   25 tangent double angle formula Slope connection
  51.    wt: 1:   24 tangent Angle Difference Formula
  52.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  53.    wt: 1:   21 sine and cosine Half Angle Formulas
  54.    wt: 1:   20 sine and cosine Double Angle Formulas
  55.    wt: 1:   18 sum of sinusoidal waves as a single wave
  56.    wt: 1:   17C sine and cosine double triple angle formulas
  57.    wt: 1:   15 sine cosine Complementary Angle Relations
  58.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  59.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  60.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  61.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  62.    wt: 1:   2 Quadrant I reference Angles
  63.    wt: 1:   Unit Circle Development of Trigonometry
  64.    wt: 1:   11 sine and cosine double triple angle formulas
  65.    wt: 1:   8 Unit Circle Development of Trigonometry
  66.    wt: 1:   8 Triangles Cascade Problem Solving
  67.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  68.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  69.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  70.    wt: 1:   1 Angle Measurement with Degrees
  71.    wt: 1:   Why Trigonometry the whyslopes view
  72.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  73.    wt: 1:   12 Triangles Similarity More Problems
  74.    wt: 1:   11 Triangle Similarity Missing Side Problem
  75.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  76.    wt: 1:   9 Similarity of Triangles Usual Criteria
  77.    wt: 1:   8 Similarity of Triangles and Polygons
  78.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  79.    wt: 1:   11 A Partial Summary
  80.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  81.    wt: 1:   11 Triangle Inequality
  82.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  83.    wt: 1:   19 Right Triangle Similarity
  84.    wt: 1:   18 Triangle Similarity Take 1
  85.    wt: 1:   17 Right Bisectors of Triangle Sides
  86.    wt: 1:   16 Angles Subtended By Chords and Diameters
  87.    wt: 1:   12 Side Angle Side Failure
  88.    wt: 1:   11 Triangle Construction Fails
  89.    wt: 1:   8 Isoceles Triangles
  90.    wt: 1:   6 Ruler and compass Angle Bisection
  91.    wt: 1:   5 Side Angle Side
  92.    wt: 1:   3 Isometry of Triangles Congruence
  93.    wt: 1:   2 Correspondence between Triangles
  94.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  95.    wt: 1:   6 Figuring with Maps Not to Scale
  96.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  97.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  98.    wt: 1:   19 Signed Multiples of Vectors
  99.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  100.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  101.    wt: 1:   13 Arrows and Vectors in a Plane
  102.    wt: 1:   5 Areas of Rectangles Revisited
  103.    wt: 1:   5 Triangle Area Formula Backwards
  104.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  105.    wt: 1:   8 Coordinates for Maps and Planes
  106.    wt: 1:   3 Triangle Area Formula Example
  107.    wt: 1:   2 Another Rectangle Area Formula Example
  108.    wt: 1:   8 GCD from Euclidean Algorithm
  109.    wt: 1:   3 signed coordinates for maps and planes
  110.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  111.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  112.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  113.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  114.    wt: 1:   Summary
  115.    wt: 1:   4 Sum Rule
  116.    wt: 1:   C Triangle Inequalities
  117.    wt: 1:   Chapter 23 Links To Trigonometry
  118.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  119.    wt: 1:   Chapter 23. Notation For Sums
  120.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  121.    wt: 1:   Chapter 7 Two Treatments of Geometry
  122.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  123.    wt: 1:   Chapter 6 More Algebra and Geometry
  124.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  125.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  126.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics

Extended Search

494 matches:

  1.    wt: 9:   3 Lengths and Areas on Maps and Plans
  2.    wt: 8:   Triangle Angles Sum To 180 Degrees
  3.    wt: 8:   17 tangent function angle sum formulas
  4.    wt: 8:   17B sine cosine Angle Sum Formulas via cis
  5.    wt: 8:   16 Right Triangle Complementary Angle Relations
  6.    wt: 8:   Right Triangle and Unit Circle Trigonometry
  7.    wt: 8:   6 Trigonometry Sines of Supplementary Angles
  8.    wt: 8:   2 Similar Triangles Equality of Corresponding Side Ratios
  9.    wt: 8:   Right Triangle and Unit Circle Trigonometry
  10.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  11.    wt: 8:   6 Figuring with Maps Not to Scale
  12.    wt: 8:   5 Drawing to Scale Avoids Angle Distortions
  13.    wt: 7:   13 Velocity Vectors in Physics
  14.    wt: 7:   8 Parallel Vectors
  15.    wt: 7:   6 Vectors with Coordinates
  16.    wt: 7:   4 Resultant of a Sum of Movements
  17.    wt: 7:   3 Navigation with Arrows or Vectors
  18.    wt: 7:   2 Signed Coordinates
  19.    wt: 7:   32 seven rows of pascals triangle
  20.    wt: 7:   29 secant cosecant and cotangent for acute angles
  21.    wt: 7:   28 Expressing products of sines cosines as sums
  22.    wt: 7:   25 tangent double angle formula Slope connection
  23.    wt: 7:   24 tangent Angle Difference Formula
  24.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  25.    wt: 7:   21 sine and cosine Half Angle Formulas
  26.    wt: 7:   20 sine and cosine Double Angle Formulas
  27.    wt: 7:   18 sum of sinusoidal waves as a single wave
  28.    wt: 7:   17C sine and cosine double triple angle formulas
  29.    wt: 7:   15 sine cosine Complementary Angle Relations
  30.    wt: 7:   6 sines and cosines for reference angle 30 degrees
  31.    wt: 7:   5 sines and cosines for reference angle 60 degrees
  32.    wt: 7:   4 sines and cosines for reference angle 45 degrees
  33.    wt: 7:   3 sines and cosines for reference angle 90 degrees
  34.    wt: 7:   2 Quadrant I reference Angles
  35.    wt: 7:   Unit Circle Development of Trigonometry
  36.    wt: 7:   10 sine cosine Angle Sum Formulas via cis
  37.    wt: 7:   8 Triangles Cascade Problem Solving
  38.    wt: 7:   5 Trigonometric Ratios For Tangent and Special Triangles
  39.    wt: 7:   4 Trigonometric Ratios For Two Special Triangles
  40.    wt: 7:   1 Angle Measurement with Degrees
  41.    wt: 7:   Why Trigonometry the whyslopes view
  42.    wt: 7:   A Measurement with Ruler Proper Use
  43.    wt: 7:   2 Measuring Area Directly
  44.    wt: 7:   1 Length Measurement
  45.    wt: 6:   9 Summary Degrees to Radians and back
  46.    wt: 6:   8 Radian Measures of Common Angles
  47.    wt: 6:   7 Radian Measures in special Triangles
  48.    wt: 6:   4 Circle Sector Area proportional to Central Angle
  49.    wt: 6:   3 Circle Arclengh Proportional to Central Angle
  50.    wt: 6:   A Global Time and Navigation
  51.    wt: 6:   15 Dot and Cross Product
  52.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  53.    wt: 6:   12 From Applied To Pure Mathematics
  54.    wt: 6:   11 Component Method
  55.    wt: 6:   10 Parallelogram Addition Method
  56.    wt: 6:   9 Head to Tail Coordinate View
  57.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  58.    wt: 6:   5 Head To Tail Arrow Addition
  59.    wt: 6:   1 Unsigned Coordinates
  60.    wt: 6:   Vector and Complex Number Applet
  61.    wt: 6:   Parallel Lines and Alternating Corresponding Angles
  62.    wt: 6:   Parallel Lines and Interior Angles
  63.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  64.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  65.    wt: 6:   Analytic View of Triangle Construction or Line Instersection More
  66.    wt: 6:   6 Tangent Function Inclination Angle Take 2
  67.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  68.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  69.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  70.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  71.    wt: 6:   31 basic secant cosecant cotangent trig identities
  72.    wt: 6:   30 unit circle calculation of six trigonometric functions
  73.    wt: 6:   27 Logarithmic use of products of sines and cosines
  74.    wt: 6:   26 Formulas for products of sines and cosines
  75.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  76.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  77.    wt: 6:   17G Pythagorean Theorem Converse
  78.    wt: 6:   17F Law of cosines
  79.    wt: 6:   17E Trig Formulas for dot and cross Products
  80.    wt: 6:   17D cis formulas for sine cosines and tangent
  81.    wt: 6:   17A The complex number valued trig function cis
  82.    wt: 6:   14 cosine even and sine and tangent are odd
  83.    wt: 6:   13 Graph of tangent function many periods
  84.    wt: 6:   12 Graph of tangent function for one period
  85.    wt: 6:   11 tangent function undefined when terminal side vertical
  86.    wt: 6:   10 Graphs of sines and cosines many periods
  87.    wt: 6:   9 Graphs of sine and cosine over one period
  88.    wt: 6:   8 period of tangent function
  89.    wt: 6:   7 period of sine and cosine
  90.    wt: 6:   1 Unit Points Reflections Rotations
  91.    wt: 6:   11 sine and cosine double triple angle formulas
  92.    wt: 6:   8 Unit Circle Development of Trigonometry
  93.    wt: 6:   2 Complex Numbers made easier we hope
  94.    wt: 6:   7 Trignometric Ratios Unit Circle
  95.    wt: 6:   3 Trigonometric Ratios sine and cosine
  96.    wt: 6:   13 Navigation Location from Angles to 2 Landmarks
  97.    wt: 6:   12 Triangles Similarity More Problems
  98.    wt: 6:   11 Triangle Similarity Missing Side Problem
  99.    wt: 6:   10 Similarity of Triangles Equivalent of Two Criteria
  100.    wt: 6:   9 Similarity of Triangles Usual Criteria
  101.    wt: 6:   8 Similarity of Triangles and Polygons
  102.    wt: 6:   5 Similarity of Circles Squares and Rectangles
  103.    wt: 6:   11 A Partial Summary
  104.    wt: 6:   9 Midpoint Coordinates Half Endpoint Sum
  105.    wt: 6:   2 point slope equation for a line
  106.    wt: 6:   11 Triangle Inequality
  107.    wt: 6:   2 Cartesian Coordinates with signs
  108.    wt: 5:   16 cotangent function Definition Graph and Inverse
  109.    wt: 5:   15 cosecant function Definition Graph and Inverse
  110.    wt: 5:   14 secant function Definition Graph and Inverse
  111.    wt: 5:   13 cosecant function Definition Graph and Inverse
  112.    wt: 5:   12 motivation for term arctan
  113.    wt: 5:   11 arctan left inverse of tangent Graph
  114.    wt: 5:   10 arctan left inverse of tangent Definition
  115.    wt: 5:   9 motivation for name arcsin
  116.    wt: 5:   8 arcsin left inverse of sine Graph
  117.    wt: 5:   7 arcsin left inverse of sine Definition
  118.    wt: 5:   6 Graph of arccos function
  119.    wt: 5:   5 Swapping Coordinates is a reflection
  120.    wt: 5:   4 possible motivation for term arccos
  121.    wt: 5:   3 Left Inverse of cosine arccos definition
  122.    wt: 5:   2 cosine function more properties
  123.    wt: 5:   1 cosine function properties
  124.    wt: 5:   6 Radian Measure to Degrees
  125.    wt: 5:   5 Degrees to Radian Measure
  126.    wt: 5:   2 Radian Measure Numerical Value of one degree
  127.    wt: 5:   1 Degrees and Radians Introduction
  128.    wt: 5:   4 graphing y=Asin(x c)
  129.    wt: 5:   3 graphing y=f(x c) plus K
  130.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  131.    wt: 5:   1 graphing y=f(x a)
  132.    wt: 5:   Parallel Lines and Parallel Transversals
  133.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  134.    wt: 5:   Straight Lines ASA Intersection Study More
  135.    wt: 5:   Straight Lines ASA Intersection Study
  136.    wt: 5:   Straight Lines Instersection Solving Equations
  137.    wt: 5:   Straight Lines Intersection of
  138.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  139.    wt: 5:   C Straight Lines Slope from Coordinates
  140.    wt: 5:   B Straight Line Slope Scaling Properties More
  141.    wt: 5:   A Straight Line Slope Scaling Properties
  142.    wt: 5:   14 Straight Lines Equations General Case
  143.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  144.    wt: 5:   12 Straight Lines Graphing mx plus b
  145.    wt: 5:   11 Straight Lines Graphing y=mx
  146.    wt: 5:   10 Straight Lines through Origin Equations More
  147.    wt: 5:   9 Straight Lines through Origin Equations
  148.    wt: 5:   8 Straight Lines Equation for vertical
  149.    wt: 5:   7 Tangent Function is odd on this domain
  150.    wt: 5:   5 Tangent Function Graph
  151.    wt: 5:   4 Tangent Function Properties
  152.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  153.    wt: 5:   1 Straight Lines Slope Concept
  154.    wt: 5:   21 Logarithms Powers and Exponentials
  155.    wt: 5:   20 N th Roots of Complex Numbers
  156.    wt: 5:   19 N th Roots of Unity
  157.    wt: 5:   18 Sixth Roots of Unity
  158.    wt: 5:   17 Cube Roots of unity
  159.    wt: 5:   16 References and Originality Question
  160.    wt: 5:   15 Pythagorean Theorem Converse
  161.    wt: 5:   14 Law of cosines
  162.    wt: 5:   13 Trig Formulas for dot and cross Products
  163.    wt: 5:   12 cis formulas for sine cosines and tangent
  164.    wt: 5:   9 The complex number valued trig function cis
  165.    wt: 5:   7 Second Way to Calculate Products
  166.    wt: 5:   6 Field Properties of Complex Number
  167.    wt: 5:   5 An Easy Proof of the Distributive Law
  168.    wt: 5:   4 Multiplication Properties
  169.    wt: 5:   3 Addition Properties
  170.    wt: 5:   1 Rectangular Polar Coordinates Review
  171.    wt: 5:   Appetizer A Complex Number Applet
  172.    wt: 5:   7 Translations Rotations Reflections Dilatations
  173.    wt: 5:   6 Geometric Diagrams in Class
  174.    wt: 5:   4 Similarity Definition with Coordinate
  175.    wt: 5:   3 Similarity by Design with coordinates
  176.    wt: 5:   2 Similarity By Design
  177.    wt: 5:   1 Early Concept of Like or Similar Shapes
  178.    wt: 5:   Four Simple Exercises
  179.    wt: 5:   12 Links Lessons elsewhere
  180.    wt: 5:   10 Midpoint of [a b] and [b a]
  181.    wt: 5:   8 Mid Point Formula
  182.    wt: 5:   7 Exercises to test skill and concept mastery
  183.    wt: 5:   6 Intersection of lines by solving linear systems
  184.    wt: 5:   5 Algebraic View of Slopes
  185.    wt: 5:   4 Equations for lines three forms
  186.    wt: 5:   3 Slope product for perpendicular lines
  187.    wt: 5:   1 Numerical view of lines and their equations
  188.    wt: 5:   What is and is not here
  189.    wt: 5:   13 Pythagorean spatial distance formulas
  190.    wt: 5:   12 Spatial Coordinates
  191.    wt: 5:   10 Pythagorean plane distance formula
  192.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  193.    wt: 5:   8 Distance Between Points on a Line
  194.    wt: 5:   7 Complex Numbers Appetizer
  195.    wt: 5:   6 Polar Multiplication and Rotation
  196.    wt: 5:   5 Cartesian Addition and Translation
  197.    wt: 5:   4 Polar Coordinates to and from
  198.    wt: 5:   3 Rectangular Coordinates Review
  199.    wt: 5:   1 Cartesian Coordinates sans signs
  200.    wt: 5:   About Folder Contents
  201.    wt: 3:   2 Division with Single Digit Divisors
  202.    wt: 3:   2 One Digit Multipliers
  203.    wt: 3:   2 Subtraction Easy Case Examples
  204.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  205.    wt: 2:   3 Euclidean Geometry Leanly
  206.    wt: 2:   Maps Plans Drawings
  207.    wt: 2:   2 More and Less Than with Unlike Signs
  208.    wt: 2:   8 GCD from Euclidean Algorithm
  209.    wt: 2:   3 signed coordinates for maps and planes
  210.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  211.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  212.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  213.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  214.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  215.    wt: 2:   2 Prime and Composites less than 16
  216.    wt: 2:   Long Division Backwards more
  217.    wt: 2:   Long Division Backward
  218.    wt: 2:   Division with Counts and Length
  219.    wt: 2:   Long Division forwards and backwards Example 3
  220.    wt: 2:   Long Division forwards and backwards Example 2
  221.    wt: 2:   Long Division forwards and backwards Example 1
  222.    wt: 2:   12 Why Long Division Works Take III
  223.    wt: 2:   11 Another Single Digit Divisor Example
  224.    wt: 2:   10 Division by Five Long and Short Ways
  225.    wt: 2:   9 Why Long Division Works Take II
  226.    wt: 2:   8 Correcting the Mistake
  227.    wt: 2:   7 Long Divison Mistake Catching
  228.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  229.    wt: 2:   5 Long Division Include Zeroes or not
  230.    wt: 2:   4 Division with 2 Digit Divsors
  231.    wt: 2:   3 Division Single Digit Divisor Example
  232.    wt: 2:   1 Divsion Physical Examples
  233.    wt: 2:   D Decimal Multiplication Methods Derived
  234.    wt: 2:   C Counting Areas with Powers of Ten
  235.    wt: 2:   B Powers of Ten
  236.    wt: 2:   A Elementary Basis for Multiplication Methods
  237.    wt: 2:   6 Multiplication Commutes Order Not Important
  238.    wt: 2:   5 Decimal Fraction Multiplication
  239.    wt: 2:   4 Two and Three Digit Multipliers
  240.    wt: 2:   3 More One Digit Multipliers
  241.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  242.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  243.    wt: 2:   Video Power Notation in Decimal Expansion
  244.    wt: 2:   1 Why 3 times 5 gives 15
  245.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  246.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  247.    wt: 2:   Subtraction with J Conversions Example
  248.    wt: 2:   Subtraction Another Video Lesson
  249.    wt: 2:   9 22 Minute Subtraction Review Video
  250.    wt: 2:   8 Subtraction with Units of Measure
  251.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  252.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  253.    wt: 2:   5 A Tip for Efficent Subtraction
  254.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  255.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  256.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  257.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  258.    wt: 2:   8 What skills and work habits to require
  259.    wt: 2:   7 Adding decimal fractions using decimal point
  260.    wt: 2:   6. Counting and adding units and mixed units
  261.    wt: 2:   5. How to add decimals C. Examples
  262.    wt: 2:   4. How to add with decimals B with conversions
  263.    wt: 2:   3. How to add with decimals A sans conversions
  264.    wt: 2:   2 Decimal Counting Practices
  265.    wt: 2:   1. Explaining Addition Table
  266.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  267.    wt: 1:   Ramblings Extrinsic numbers theory
  268.    wt: 1:   Skills Chapter 2 Geometry
  269.    wt: 1:   8 analytic geometry etc
  270.    wt: 1:   About site lesson plans
  271.    wt: 1:   Theory of Knowledge
  272.    wt: 1:   2 Conductance Resistance Duality02
  273.    wt: 1:   2 Reading and Writing Skills
  274.    wt: 1:   Ages 12 to 14 Geometry
  275.    wt: 1:   Ages 10 to 12 Geometry
  276.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  277.    wt: 1:   20 Interchanging coordinates a reflection
  278.    wt: 1:   9 Set theory term relation possible origins
  279.    wt: 1:   A Quadratics Summary
  280.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  281.    wt: 1:   19 Signed Multiples of Vectors
  282.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  283.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  284.    wt: 1:   13 Arrows and Vectors in a Plane
  285.    wt: 1:   2 Combing Counts Addition Skills and Principles
  286.    wt: 1:   5 Areas of Rectangles Revisited
  287.    wt: 1:   2 Algebraic View
  288.    wt: 1:   5 Triangle Area Formula Backwards
  289.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  290.    wt: 1:   8 Coordinates for Maps and Planes
  291.    wt: 1:   2 GE II Comparison
  292.    wt: 1:   2 Essentially one exercises three with solution
  293.    wt: 1:   2 Three Examples
  294.    wt: 1:   2 Three Examples
  295.    wt: 1:   3 Triangle Area Formula Example
  296.    wt: 1:   2 Another Rectangle Area Formula Example
  297.    wt: 1:   arithmetic videos Real Player Format
  298.    wt: 1:   4 Greater More Less Than Signs in General
  299.    wt: 1:   3 Comparison of Negative Numbers
  300.    wt: 1:   1 More and Less Than for Counts and Measures
  301.    wt: 1:   5 Square Roots with primes more still
  302.    wt: 1:   4 Square Roots with primes more
  303.    wt: 1:   3 Properties of Square Roots with example
  304.    wt: 1:   2 Square Roots with Prime
  305.    wt: 1:   1 Squares and Square Roots Introduction
  306.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  307.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  308.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  309.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  310.    wt: 1:   13 GCD from given Prime Factorization
  311.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  312.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  313.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  314.    wt: 1:   7 GCD and LCM from prime factorization
  315.    wt: 1:   6 GCD from Prime
  316.    wt: 1:   5 Common Divisors 60 45 via Prime
  317.    wt: 1:   4 LCM of 8 and 10 via Prime
  318.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  319.    wt: 1:   2 Least Common Multiple LCM intro via list method
  320.    wt: 1:   1 Least Common Multiples LCM Introduction
  321.    wt: 1:   12 GCD 2700 288 via Prime
  322.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  323.    wt: 1:   4 Counting with Trees Product Rule Take I
  324.    wt: 1:   3 Counting with Tables and Trees II
  325.    wt: 1:   2 Counting with Tables and Trees I
  326.    wt: 1:   1 Counting and Counting Methods I
  327.    wt: 1:   11 What are real lengths and numbers
  328.    wt: 1:   10 dividing signed numbers
  329.    wt: 1:   9 subtracting signed numbers
  330.    wt: 1:   8 multiplying signed numbers
  331.    wt: 1:   7 negative and additive inverse
  332.    wt: 1:   6 adding signed numbers
  333.    wt: 1:   5 lengths and signs of numbers
  334.    wt: 1:   4 signed coordinates for regions in space
  335.    wt: 1:   2 signed and unsigned numbers as coordinates
  336.    wt: 1:   7 Converting or Changing Units
  337.    wt: 1:   6 Simplification of Fractions with Units
  338.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  339.    wt: 1:   4 Fractions with Units
  340.    wt: 1:   3 Multiplying Units and Numbers
  341.    wt: 1:   2 Equality and Units
  342.    wt: 1:   1 Addition and Subtraction with Units
  343.    wt: 1:   D Three Term Ratios
  344.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  345.    wt: 1:   B Fractions and Two Term Ratios
  346.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  347.    wt: 1:   22 Complex Compound Fractions
  348.    wt: 1:   21 Working With Signs
  349.    wt: 1:   21 Reciprocals for Fractions and Wholes
  350.    wt: 1:   20 Dividing Fractions the Why
  351.    wt: 1:   19 Dividing Fractions How TO
  352.    wt: 1:   18 Efficient Ways to Multiply
  353.    wt: 1:   17 Efficient Ways to Add and Subtract
  354.    wt: 1:   16 Addition Subtraction Comparision Compared
  355.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  356.    wt: 1:   14 Adding and Subtracting with Like Denominators
  357.    wt: 1:   13 Fraction Comparison Algebraic View
  358.    wt: 1:   12 Fraction Comparison
  359.    wt: 1:   11 Simplification an Algebraic View
  360.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  361.    wt: 1:   9 Improper Fractions and Mixed Numbers
  362.    wt: 1:   8 Numerals Fractionals Quantals Take II
  363.    wt: 1:   7 Numerals Fractionals Quantals
  364.    wt: 1:   6 Multiplication of Mixed Numbers
  365.    wt: 1:   6 Multiplication Algebraically Take II
  366.    wt: 1:   5 Equivalent Fractions
  367.    wt: 1:   4 Fraction Multiplication
  368.    wt: 1:   3 Unit fraction of a fraction
  369.    wt: 1:   2 Unit Fraction Multiplication
  370.    wt: 1:   1 What is a fraction Take II
  371.    wt: 1:   1 What is a fraction
  372.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  373.    wt: 1:   D Remainders Modulo 11 Pair Rule
  374.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  375.    wt: 1:   B Integer Long Division Multiple Choices
  376.    wt: 1:   A Associative Law Theorectical Note
  377.    wt: 1:   13 Subtraction with Additive Inverse
  378.    wt: 1:   12 Adding Integers More Examples
  379.    wt: 1:   11 Adding Integers Formulas and Examples
  380.    wt: 1:   10 Integer Multiplication Formulas
  381.    wt: 1:   9 Multiplying Integers
  382.    wt: 1:   8 Multiplication by Signed Numbers Integers
  383.    wt: 1:   7 Multiplication by Signs
  384.    wt: 1:   6 Multiplication by Natural Numbers
  385.    wt: 1:   5 Zero Movement and Additive Inverses
  386.    wt: 1:   4 Adding Movements wiht opposite directions
  387.    wt: 1:   3 Adding Movements with same direction
  388.    wt: 1:   1 Integers as Coordinates
  389.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  390.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  391.    wt: 1:   26 Divisibility by 2 3 5 Example
  392.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  393.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  394.    wt: 1:   23 Remainder Arithmetic Modulo 2
  395.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  396.    wt: 1:   21 Remainder Arithmetic Modulo 3
  397.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  398.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  399.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  400.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  401.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  402.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  403.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  404.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  405.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  406.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  407.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  408.    wt: 1:   5 Remainder Arithmetic Modulo 5
  409.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  410.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  411.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  412.    wt: 1:   1 Remainder Arithmetic Modulo 10
  413.    wt: 1:   20 Uniqueness of Prime Factorization
  414.    wt: 1:   19 video Prime Factorization Unique
  415.    wt: 1:   18 video Count Factors given Prime Factorization
  416.    wt: 1:   17 Identify and Count Factors using Primes
  417.    wt: 1:   16 video Factors of 980 using prime
  418.    wt: 1:   15 video Factors of 20 using Prime Factorization
  419.    wt: 1:   14 video Factors of 24 Take II
  420.    wt: 1:   13 video Factors of 24 using prime
  421.    wt: 1:   12 LCD GCD and LCM using Primes
  422.    wt: 1:   11 Efficient Square Rule Use
  423.    wt: 1:   10 video Prime Factorization upto 23 squared
  424.    wt: 1:   9 video Prime Factorization upto 19 squared
  425.    wt: 1:   8 video Prime Factorization upto 19
  426.    wt: 1:   7 Calculator Usage Notes and Cautions
  427.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  428.    wt: 1:   5 Prime Factorization and a Square Rule
  429.    wt: 1:   4 video Prime Factorization Introduction
  430.    wt: 1:   3 video Primes and Composites from 9 times table
  431.    wt: 1:   1 video how Products are bigger than factor
  432.    wt: 1:   11 Place Value SI Standard International way
  433.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  434.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  435.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  436.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  437.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  438.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  439.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  440.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  441.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  442.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  443.    wt: 1:   Quick history of numbers and algebra
  444.    wt: 1:   Exact Arithmetic Wholes and Fractions
  445.    wt: 1:   Formula Evaluation how to show work
  446.    wt: 1:   Expression Evaluation how to show work
  447.    wt: 1:   The 20 Times Table
  448.    wt: 1:   The 12 Times Table Visually
  449.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  450.    wt: 1:   About folder contents
  451.    wt: 1:   Summary
  452.    wt: 1:   4 Sum Rule
  453.    wt: 1:   C Triangle Inequalities
  454.    wt: 1:   Chapter 23 Links To Trigonometry
  455.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  456.    wt: 1:   Chapter 23. Notation For Sums
  457.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  458.    wt: 1:   Chapter 7 Two Treatments of Geometry
  459.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  460.    wt: 1:   Chapter 6 More Algebra and Geometry
  461.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  462.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  463.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  464.    wt: 14:   15 Triangle Angle Sum is 180 degrees
  465.    wt: 13:   Euclidean Geometry Elsewhere LINKS
  466.    wt: 13:   13 Angle Side Angle Failure
  467.    wt: 13:   7 Angle Side Angle
  468.    wt: 13:   2 Correspondence between Triangles
  469.    wt: 13:   Short Course on Euclidean Geometry
  470.    wt: 12:   PS C Similarity Use Recognize it in Trigonometry
  471.    wt: 12:   19 Right Triangle Similarity
  472.    wt: 12:   18 Triangle Similarity Take 1
  473.    wt: 12:   17 Right Bisectors of Triangle Sides
  474.    wt: 12:   16 Angles Subtended By Chords and Diameters
  475.    wt: 12:   12 Side Angle Side Failure
  476.    wt: 12:   11 Triangle Construction Fails
  477.    wt: 12:   8 Isoceles Triangles
  478.    wt: 12:   6 Ruler and compass Angle Bisection
  479.    wt: 12:   5 Side Angle Side
  480.    wt: 12:   3 Isometry of Triangles Congruence
  481.    wt: 11:   PS H Distributive Law For Complex Numbers
  482.    wt: 11:   PS G Rotation Distributes over Addition
  483.    wt: 11:   PS F Scalar Multiplication Distributes over Addition
  484.    wt: 11:   PS E Multiplication with Polar Coordinates
  485.    wt: 11:   PS D Addition with Cartesian Coordinates
  486.    wt: 11:   PS B Parallelogram Construction Methods
  487.    wt: 11:   PS A Kite Construction Methods
  488.    wt: 11:   21 Parallelograms
  489.    wt: 11:   14 Parallel Lines Postulate
  490.    wt: 11:   10 Dropping a perpendicular to line
  491.    wt: 11:   9 Construction of a right bisector
  492.    wt: 11:   4 Side Side Side
  493.    wt: 11:   1 Initial Concepts and Terms
  494.    wt: 10:   4 Angles on Maps Plans drawn to scale

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

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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