Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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20 matches:

  1.    wt: 7:   7 Complex Numbers/
  2.    wt: 7:   1 Maps Plans Measurement/
  3.    wt: 6:   15 Arc or Inverse Trigonometric Function/
  4.    wt: 6:   13 Vectors/
  5.    wt: 6:   8 Unit Circle Trigonometry/
  6.    wt: 6:   6 Trigonometry first steps/
  7.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  8.    wt: 5:   12 Function Translating and Rescaling/
  9.    wt: 5:   11 Parallel Straight Lines and Transversals/
  10.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  11.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 1:   B Real Numbers Extrinsic Development/
  18.    wt: 1:   5 Real Numbers/
  19.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  20.    wt: 1:   8 Arithmetic with Signed Numbers/

Web Page Search

86 matches:

  1.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  2.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  3.    wt: 2:   Maps Plans Drawings
  4.    wt: 2:   17A The complex number valued trig function cis
  5.    wt: 2:   20 N th Roots of Complex Numbers
  6.    wt: 2:   9 The complex number valued trig function cis
  7.    wt: 2:   2 Complex Numbers made easier we hope
  8.    wt: 2:   7 Complex Numbers Appetizer
  9.    wt: 2:   PS H Distributive Law For Complex Numbers
  10.    wt: 2:   4 Angles on Maps Plans drawn to scale
  11.    wt: 2:   3 Lengths and Areas on Maps and Plans
  12.    wt: 2:   Chapter 22 Complex Numbers
  13.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  14.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  15.    wt: 1:   Ramblings Extrinsic numbers theory
  16.    wt: 1:   2 arithmetic with signed numbers
  17.    wt: 1:   1 arithmetic with unsigned numbers
  18.    wt: 1:   About site lesson plans
  19.    wt: 1:   13 Velocity Vectors in Physics
  20.    wt: 1:   8 Parallel Vectors
  21.    wt: 1:   6 Vectors with Coordinates
  22.    wt: 1:   3 Navigation with Arrows or Vectors
  23.    wt: 1:   Vector and Complex Number Applet
  24.    wt: 1:   31 basic secant cosecant cotangent trig identities
  25.    wt: 1:   30 unit circle calculation of six trigonometric functions
  26.    wt: 1:   17E Trig Formulas for dot and cross Products
  27.    wt: 1:   Unit Circle Development of Trigonometry
  28.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  29.    wt: 1:   13 Trig Formulas for dot and cross Products
  30.    wt: 1:   8 Unit Circle Development of Trigonometry
  31.    wt: 1:   6 Field Properties of Complex Number
  32.    wt: 1:   Appetizer A Complex Number Applet
  33.    wt: 1:   7 Trignometric Ratios Unit Circle
  34.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  35.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  36.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  37.    wt: 1:   3 Trigonometric Ratios sine and cosine
  38.    wt: 1:   Why Trigonometry the whyslopes view
  39.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  40.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  41.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  42.    wt: 1:   6 Figuring with Maps Not to Scale
  43.    wt: 1:   musings do not puiblish real numbers
  44.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  45.    wt: 1:   22 Multiplication of Signed Numbers
  46.    wt: 1:   19 Signed Multiples of Vectors
  47.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  48.    wt: 1:   13 Arrows and Vectors in a Plane
  49.    wt: 1:   12 Real Numbers Line Signed Coordinates
  50.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  51.    wt: 1:   5 Distributive Law for Whole Numbers
  52.    wt: 1:   1 The Counting Origins of Numbers
  53.    wt: 1:   4 Comparison of Negative Numbers
  54.    wt: 1:   1 Real Numbers Comparison
  55.    wt: 1:   16 Real Numbers Comparison
  56.    wt: 1:   8 Coordinates for Maps and Planes
  57.    wt: 1:   7 Real Numbers as Line Cordinates
  58.    wt: 1:   6 Unsigned Real Numbers
  59.    wt: 1:   5 Rational Numbers More
  60.    wt: 1:   4 Rational Numbers
  61.    wt: 1:   1 Whole and Natural Numbers
  62.    wt: 1:   8 Sets of Numbers
  63.    wt: 1:   5 Talking about Numbers and Quantities
  64.    wt: 1:   4 A Brief Story of numbers and algebra
  65.    wt: 1:   3 Comparison of Negative Numbers
  66.    wt: 1:   11 What are real lengths and numbers
  67.    wt: 1:   10 dividing signed numbers
  68.    wt: 1:   9 subtracting signed numbers
  69.    wt: 1:   8 multiplying signed numbers
  70.    wt: 1:   6 adding signed numbers
  71.    wt: 1:   5 lengths and signs of numbers
  72.    wt: 1:   3 signed coordinates for maps and planes
  73.    wt: 1:   2 signed and unsigned numbers as coordinates
  74.    wt: 1:   3 Multiplying Units and Numbers
  75.    wt: 1:   22 Complex Compound Fractions
  76.    wt: 1:   9 Improper Fractions and Mixed Numbers
  77.    wt: 1:   6 Multiplication of Mixed Numbers
  78.    wt: 1:   8 Multiplication by Signed Numbers Integers
  79.    wt: 1:   6 Multiplication by Natural Numbers
  80.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  81.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  82.    wt: 1:   Quick history of numbers and algebra
  83.    wt: 1:   011 Division of Time Intervals By Numbers
  84.    wt: 1:   Chapter 23 Links To Trigonometry
  85.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  86.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions

Extended Search

320 matches:

  1.    wt: 9:   20 N th Roots of Complex Numbers
  2.    wt: 9:   9 The complex number valued trig function cis
  3.    wt: 9:   2 Complex Numbers made easier we hope
  4.    wt: 9:   4 Angles on Maps Plans drawn to scale
  5.    wt: 9:   3 Lengths and Areas on Maps and Plans
  6.    wt: 8:   17A The complex number valued trig function cis
  7.    wt: 8:   13 Trig Formulas for dot and cross Products
  8.    wt: 8:   8 Unit Circle Development of Trigonometry
  9.    wt: 8:   6 Field Properties of Complex Number
  10.    wt: 8:   Appetizer A Complex Number Applet
  11.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  12.    wt: 8:   6 Figuring with Maps Not to Scale
  13.    wt: 7:   13 Velocity Vectors in Physics
  14.    wt: 7:   8 Parallel Vectors
  15.    wt: 7:   6 Vectors with Coordinates
  16.    wt: 7:   3 Navigation with Arrows or Vectors
  17.    wt: 7:   Vector and Complex Number Applet
  18.    wt: 7:   31 basic secant cosecant cotangent trig identities
  19.    wt: 7:   30 unit circle calculation of six trigonometric functions
  20.    wt: 7:   17E Trig Formulas for dot and cross Products
  21.    wt: 7:   Unit Circle Development of Trigonometry
  22.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  23.    wt: 7:   21 Logarithms Powers and Exponentials
  24.    wt: 7:   19 N th Roots of Unity
  25.    wt: 7:   18 Sixth Roots of Unity
  26.    wt: 7:   17 Cube Roots of unity
  27.    wt: 7:   16 References and Originality Question
  28.    wt: 7:   15 Pythagorean Theorem Converse
  29.    wt: 7:   14 Law of cosines
  30.    wt: 7:   12 cis formulas for sine cosines and tangent
  31.    wt: 7:   11 sine and cosine double triple angle formulas
  32.    wt: 7:   10 sine cosine Angle Sum Formulas via cis
  33.    wt: 7:   7 Second Way to Calculate Products
  34.    wt: 7:   5 An Easy Proof of the Distributive Law
  35.    wt: 7:   4 Multiplication Properties
  36.    wt: 7:   3 Addition Properties
  37.    wt: 7:   1 Rectangular Polar Coordinates Review
  38.    wt: 7:   7 Trignometric Ratios Unit Circle
  39.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  40.    wt: 7:   5 Trigonometric Ratios For Tangent and Special Triangles
  41.    wt: 7:   4 Trigonometric Ratios For Two Special Triangles
  42.    wt: 7:   3 Trigonometric Ratios sine and cosine
  43.    wt: 7:   Why Trigonometry the whyslopes view
  44.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  45.    wt: 7:   7 Complex Numbers Appetizer
  46.    wt: 7:   PS H Distributive Law For Complex Numbers
  47.    wt: 7:   A Measurement with Ruler Proper Use
  48.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  49.    wt: 7:   2 Measuring Area Directly
  50.    wt: 7:   1 Length Measurement
  51.    wt: 6:   16 cotangent function Definition Graph and Inverse
  52.    wt: 6:   15 cosecant function Definition Graph and Inverse
  53.    wt: 6:   14 secant function Definition Graph and Inverse
  54.    wt: 6:   13 cosecant function Definition Graph and Inverse
  55.    wt: 6:   12 motivation for term arctan
  56.    wt: 6:   11 arctan left inverse of tangent Graph
  57.    wt: 6:   10 arctan left inverse of tangent Definition
  58.    wt: 6:   9 motivation for name arcsin
  59.    wt: 6:   8 arcsin left inverse of sine Graph
  60.    wt: 6:   7 arcsin left inverse of sine Definition
  61.    wt: 6:   6 Graph of arccos function
  62.    wt: 6:   5 Swapping Coordinates is a reflection
  63.    wt: 6:   4 possible motivation for term arccos
  64.    wt: 6:   3 Left Inverse of cosine arccos definition
  65.    wt: 6:   2 cosine function more properties
  66.    wt: 6:   1 cosine function properties
  67.    wt: 6:   A Global Time and Navigation
  68.    wt: 6:   15 Dot and Cross Product
  69.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  70.    wt: 6:   12 From Applied To Pure Mathematics
  71.    wt: 6:   11 Component Method
  72.    wt: 6:   10 Parallelogram Addition Method
  73.    wt: 6:   9 Head to Tail Coordinate View
  74.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  75.    wt: 6:   5 Head To Tail Arrow Addition
  76.    wt: 6:   4 Resultant of a Sum of Movements
  77.    wt: 6:   2 Signed Coordinates
  78.    wt: 6:   1 Unsigned Coordinates
  79.    wt: 6:   17 tangent function angle sum formulas
  80.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  81.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  82.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  83.    wt: 6:   32 seven rows of pascals triangle
  84.    wt: 6:   29 secant cosecant and cotangent for acute angles
  85.    wt: 6:   28 Expressing products of sines cosines as sums
  86.    wt: 6:   27 Logarithmic use of products of sines and cosines
  87.    wt: 6:   26 Formulas for products of sines and cosines
  88.    wt: 6:   25 tangent double angle formula Slope connection
  89.    wt: 6:   24 tangent Angle Difference Formula
  90.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  91.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  92.    wt: 6:   21 sine and cosine Half Angle Formulas
  93.    wt: 6:   20 sine and cosine Double Angle Formulas
  94.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  95.    wt: 6:   18 sum of sinusoidal waves as a single wave
  96.    wt: 6:   17G Pythagorean Theorem Converse
  97.    wt: 6:   17F Law of cosines
  98.    wt: 6:   17D cis formulas for sine cosines and tangent
  99.    wt: 6:   17C sine and cosine double triple angle formulas
  100.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  101.    wt: 6:   16 Right Triangle Complementary Angle Relations
  102.    wt: 6:   15 sine cosine Complementary Angle Relations
  103.    wt: 6:   14 cosine even and sine and tangent are odd
  104.    wt: 6:   13 Graph of tangent function many periods
  105.    wt: 6:   12 Graph of tangent function for one period
  106.    wt: 6:   11 tangent function undefined when terminal side vertical
  107.    wt: 6:   10 Graphs of sines and cosines many periods
  108.    wt: 6:   9 Graphs of sine and cosine over one period
  109.    wt: 6:   8 period of tangent function
  110.    wt: 6:   7 period of sine and cosine
  111.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  112.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  113.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  114.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  115.    wt: 6:   2 Quadrant I reference Angles
  116.    wt: 6:   1 Unit Points Reflections Rotations
  117.    wt: 6:   8 Triangles Cascade Problem Solving
  118.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  119.    wt: 6:   1 Angle Measurement with Degrees
  120.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  121.    wt: 5:   9 Summary Degrees to Radians and back
  122.    wt: 5:   8 Radian Measures of Common Angles
  123.    wt: 5:   7 Radian Measures in special Triangles
  124.    wt: 5:   6 Radian Measure to Degrees
  125.    wt: 5:   5 Degrees to Radian Measure
  126.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  127.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  128.    wt: 5:   2 Radian Measure Numerical Value of one degree
  129.    wt: 5:   1 Degrees and Radians Introduction
  130.    wt: 5:   4 graphing y=Asin(x c)
  131.    wt: 5:   3 graphing y=f(x c) plus K
  132.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  133.    wt: 5:   1 graphing y=f(x a)
  134.    wt: 5:   Parallel Lines and Parallel Transversals
  135.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  136.    wt: 5:   Triangle Angles Sum To 180 Degrees
  137.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  138.    wt: 5:   Parallel Lines and Interior Angles
  139.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  140.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  141.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  142.    wt: 5:   Straight Lines ASA Intersection Study More
  143.    wt: 5:   Straight Lines ASA Intersection Study
  144.    wt: 5:   Straight Lines Instersection Solving Equations
  145.    wt: 5:   Straight Lines Intersection of
  146.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  147.    wt: 5:   C Straight Lines Slope from Coordinates
  148.    wt: 5:   B Straight Line Slope Scaling Properties More
  149.    wt: 5:   A Straight Line Slope Scaling Properties
  150.    wt: 5:   14 Straight Lines Equations General Case
  151.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  152.    wt: 5:   12 Straight Lines Graphing mx plus b
  153.    wt: 5:   11 Straight Lines Graphing y=mx
  154.    wt: 5:   10 Straight Lines through Origin Equations More
  155.    wt: 5:   9 Straight Lines through Origin Equations
  156.    wt: 5:   8 Straight Lines Equation for vertical
  157.    wt: 5:   7 Tangent Function is odd on this domain
  158.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  159.    wt: 5:   5 Tangent Function Graph
  160.    wt: 5:   4 Tangent Function Properties
  161.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  162.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  163.    wt: 5:   1 Straight Lines Slope Concept
  164.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  165.    wt: 5:   12 Triangles Similarity More Problems
  166.    wt: 5:   11 Triangle Similarity Missing Side Problem
  167.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  168.    wt: 5:   9 Similarity of Triangles Usual Criteria
  169.    wt: 5:   8 Similarity of Triangles and Polygons
  170.    wt: 5:   7 Translations Rotations Reflections Dilatations
  171.    wt: 5:   6 Geometric Diagrams in Class
  172.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  173.    wt: 5:   4 Similarity Definition with Coordinate
  174.    wt: 5:   3 Similarity by Design with coordinates
  175.    wt: 5:   2 Similarity By Design
  176.    wt: 5:   1 Early Concept of Like or Similar Shapes
  177.    wt: 5:   Four Simple Exercises
  178.    wt: 5:   12 Links Lessons elsewhere
  179.    wt: 5:   11 A Partial Summary
  180.    wt: 5:   10 Midpoint of [a b] and [b a]
  181.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  182.    wt: 5:   8 Mid Point Formula
  183.    wt: 5:   7 Exercises to test skill and concept mastery
  184.    wt: 5:   6 Intersection of lines by solving linear systems
  185.    wt: 5:   5 Algebraic View of Slopes
  186.    wt: 5:   4 Equations for lines three forms
  187.    wt: 5:   3 Slope product for perpendicular lines
  188.    wt: 5:   2 point slope equation for a line
  189.    wt: 5:   1 Numerical view of lines and their equations
  190.    wt: 5:   What is and is not here
  191.    wt: 5:   13 Pythagorean spatial distance formulas
  192.    wt: 5:   12 Spatial Coordinates
  193.    wt: 5:   11 Triangle Inequality
  194.    wt: 5:   10 Pythagorean plane distance formula
  195.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  196.    wt: 5:   8 Distance Between Points on a Line
  197.    wt: 5:   6 Polar Multiplication and Rotation
  198.    wt: 5:   5 Cartesian Addition and Translation
  199.    wt: 5:   4 Polar Coordinates to and from
  200.    wt: 5:   3 Rectangular Coordinates Review
  201.    wt: 5:   2 Cartesian Coordinates with signs
  202.    wt: 5:   1 Cartesian Coordinates sans signs
  203.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  204.    wt: 5:   PS G Rotation Distributes over Addition
  205.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  206.    wt: 5:   PS E Multiplication with Polar Coordinates
  207.    wt: 5:   PS D Addition with Cartesian Coordinates
  208.    wt: 5:   PS B Parallelogram Construction Methods
  209.    wt: 5:   PS A Kite Construction Methods
  210.    wt: 5:   21 Parallelograms
  211.    wt: 5:   19 Right Triangle Similarity
  212.    wt: 5:   18 Triangle Similarity Take 1
  213.    wt: 5:   17 Right Bisectors of Triangle Sides
  214.    wt: 5:   16 Angles Subtended By Chords and Diameters
  215.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  216.    wt: 5:   14 Parallel Lines Postulate
  217.    wt: 5:   13 Angle Side Angle Failure
  218.    wt: 5:   12 Side Angle Side Failure
  219.    wt: 5:   11 Triangle Construction Fails
  220.    wt: 5:   10 Dropping a perpendicular to line
  221.    wt: 5:   9 Construction of a right bisector
  222.    wt: 5:   8 Isoceles Triangles
  223.    wt: 5:   7 Angle Side Angle
  224.    wt: 5:   6 Ruler and compass Angle Bisection
  225.    wt: 5:   5 Side Angle Side
  226.    wt: 5:   4 Side Side Side
  227.    wt: 5:   3 Isometry of Triangles Congruence
  228.    wt: 5:   2 Correspondence between Triangles
  229.    wt: 5:   1 Initial Concepts and Terms
  230.    wt: 5:   Short Course on Euclidean Geometry
  231.    wt: 5:   About Folder Contents
  232.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  233.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  234.    wt: 2:   Maps Plans Drawings
  235.    wt: 2:   musings do not puiblish real numbers
  236.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  237.    wt: 2:   22 Multiplication of Signed Numbers
  238.    wt: 2:   19 Signed Multiples of Vectors
  239.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  240.    wt: 2:   13 Arrows and Vectors in a Plane
  241.    wt: 2:   12 Real Numbers Line Signed Coordinates
  242.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  243.    wt: 2:   16 Real Numbers Comparison
  244.    wt: 2:   8 Coordinates for Maps and Planes
  245.    wt: 2:   7 Real Numbers as Line Cordinates
  246.    wt: 2:   6 Unsigned Real Numbers
  247.    wt: 2:   5 Rational Numbers More
  248.    wt: 2:   4 Rational Numbers
  249.    wt: 2:   1 Whole and Natural Numbers
  250.    wt: 2:   3 Comparison of Negative Numbers
  251.    wt: 2:   11 What are real lengths and numbers
  252.    wt: 2:   10 dividing signed numbers
  253.    wt: 2:   9 subtracting signed numbers
  254.    wt: 2:   8 multiplying signed numbers
  255.    wt: 2:   6 adding signed numbers
  256.    wt: 2:   5 lengths and signs of numbers
  257.    wt: 2:   3 signed coordinates for maps and planes
  258.    wt: 2:   2 signed and unsigned numbers as coordinates
  259.    wt: 2:   Chapter 22 Complex Numbers
  260.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  261.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  262.    wt: 1:   Ramblings Extrinsic numbers theory
  263.    wt: 1:   2 arithmetic with signed numbers
  264.    wt: 1:   1 arithmetic with unsigned numbers
  265.    wt: 1:   About site lesson plans
  266.    wt: 1:   A Modular and Remainder Arithmetic
  267.    wt: 1:   A Signed Number Arithmetic Review
  268.    wt: 1:   26 More Less Greater Than Comparison
  269.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  270.    wt: 1:   23 Distributive Law Two Derivations
  271.    wt: 1:   21 Addition of Multiples of a Single Vector
  272.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  273.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  274.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  275.    wt: 1:   15 Head to Tails in place Addition Associative
  276.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  277.    wt: 1:   11 Signed Number Addition and Addition Properties
  278.    wt: 1:   9 Division with Digits after Decimal Point
  279.    wt: 1:   8 Division and Mulplication of Compound Fractions
  280.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  281.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  282.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  283.    wt: 1:   4 Location of Point in Decimal Addition
  284.    wt: 1:   3 Location of Point in Decimal Multiplication
  285.    wt: 1:   2 Counting Digits in Decimal Multiplication
  286.    wt: 1:   1 Fractions with Finite Decimal Expansions
  287.    wt: 1:   5 Distributive Law for Whole Numbers
  288.    wt: 1:   1 The Counting Origins of Numbers
  289.    wt: 1:   4 Comparison of Negative Numbers
  290.    wt: 1:   1 Real Numbers Comparison
  291.    wt: 1:   15 Real Number Division
  292.    wt: 1:   14 Real Number Multiplication
  293.    wt: 1:   13 Real Number Subtraction
  294.    wt: 1:   12 Real Number Additive Inverses or Negatives
  295.    wt: 1:   11 Real Number Addition
  296.    wt: 1:   10 Real Number Lengths and Signs
  297.    wt: 1:   9 Coordinates for Regions in Space
  298.    wt: 1:   3 Fractions
  299.    wt: 1:   2 Integers
  300.    wt: 1:   8 Sets of Numbers
  301.    wt: 1:   5 Talking about Numbers and Quantities
  302.    wt: 1:   4 A Brief Story of numbers and algebra
  303.    wt: 1:   4 Greater More Less Than Signs in General
  304.    wt: 1:   2 More and Less Than with Unlike Signs
  305.    wt: 1:   1 More and Less Than for Counts and Measures
  306.    wt: 1:   7 negative and additive inverse
  307.    wt: 1:   4 signed coordinates for regions in space
  308.    wt: 1:   3 Multiplying Units and Numbers
  309.    wt: 1:   22 Complex Compound Fractions
  310.    wt: 1:   9 Improper Fractions and Mixed Numbers
  311.    wt: 1:   6 Multiplication of Mixed Numbers
  312.    wt: 1:   8 Multiplication by Signed Numbers Integers
  313.    wt: 1:   6 Multiplication by Natural Numbers
  314.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  315.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  316.    wt: 1:   Quick history of numbers and algebra
  317.    wt: 1:   011 Division of Time Intervals By Numbers
  318.    wt: 1:   Chapter 23 Links To Trigonometry
  319.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  320.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
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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