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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21 matches:

  1.    wt: 8:   7 Complex Numbers/
  2.    wt: 7:   1 Maps Plans Measurement/
  3.    wt: 6:   13 Vectors/
  4.    wt: 6:   8 Unit Circle Trigonometry/
  5.    wt: 6:   6 Trigonometry first steps/
  6.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  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/
  21.    wt: 1:   7 Arithmetic and Fractions with Units/

Web Page Search

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

Extended Search

333 matches:

  1.    wt: 9:   9 The complex number valued trig function cis
  2.    wt: 9:   8 Unit Circle Development of Trigonometry
  3.    wt: 9:   7 Second Way to Calculate Products
  4.    wt: 9:   6 Field Properties of Complex Number
  5.    wt: 9:   Appetizer A Complex Number Applet
  6.    wt: 9:   4 Angles on Maps Plans drawn to scale
  7.    wt: 9:   3 Lengths and Areas on Maps and Plans
  8.    wt: 8:   21 Logarithms Powers and Exponentials
  9.    wt: 8:   19 N th Roots of Unity
  10.    wt: 8:   18 Sixth Roots of Unity
  11.    wt: 8:   17 Cube Roots of unity
  12.    wt: 8:   16 References and Originality Question
  13.    wt: 8:   15 Pythagorean Theorem Converse
  14.    wt: 8:   14 Law of cosines
  15.    wt: 8:   13 Trig Formulas for dot and cross Products
  16.    wt: 8:   12 cis formulas for sine cosines and tangent
  17.    wt: 8:   11 sine and cosine double triple angle formulas
  18.    wt: 8:   10 sine cosine Angle Sum Formulas via cis
  19.    wt: 8:   5 An Easy Proof of the Distributive Law
  20.    wt: 8:   4 Multiplication Properties
  21.    wt: 8:   3 Addition Properties
  22.    wt: 8:   1 Rectangular Polar Coordinates Review
  23.    wt: 8:   7 Complex Numbers Appetizer
  24.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  25.    wt: 8:   6 Figuring with Maps Not to Scale
  26.    wt: 7:   13 Velocity Vectors in Physics
  27.    wt: 7:   8 Parallel Vectors
  28.    wt: 7:   7 Coordinate Addition and Scalar Multiplication
  29.    wt: 7:   6 Vectors with Coordinates
  30.    wt: 7:   3 Navigation with Arrows or Vectors
  31.    wt: 7:   Vector and Complex Number Applet
  32.    wt: 7:   17A The complex number valued trig function cis
  33.    wt: 7:   Unit Circle Development of Trigonometry
  34.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  35.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  36.    wt: 7:   Why Trigonometry the whyslopes view
  37.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  38.    wt: 7:   PS H Distributive Law For Complex Numbers
  39.    wt: 7:   A Measurement with Ruler Proper Use
  40.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  41.    wt: 7:   2 Measuring Area Directly
  42.    wt: 7:   1 Length Measurement
  43.    wt: 6:   A Global Time and Navigation
  44.    wt: 6:   15 Dot and Cross Product
  45.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  46.    wt: 6:   12 From Applied To Pure Mathematics
  47.    wt: 6:   11 Component Method
  48.    wt: 6:   10 Parallelogram Addition Method
  49.    wt: 6:   9 Head to Tail Coordinate View
  50.    wt: 6:   5 Head To Tail Arrow Addition
  51.    wt: 6:   4 Resultant of a Sum of Movements
  52.    wt: 6:   2 Signed Coordinates
  53.    wt: 6:   1 Unsigned Coordinates
  54.    wt: 6:   17 tangent function angle sum formulas
  55.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  56.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  57.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  58.    wt: 6:   32 seven rows of pascals triangle
  59.    wt: 6:   31 basic secant cosecant cotangent trig identities
  60.    wt: 6:   30 unit circle calculation of six trigonometric functions
  61.    wt: 6:   29 secant cosecant and cotangent for acute angles
  62.    wt: 6:   28 Expressing products of sines cosines as sums
  63.    wt: 6:   27 Logarithmic use of products of sines and cosines
  64.    wt: 6:   26 Formulas for products of sines and cosines
  65.    wt: 6:   25 tangent double angle formula Slope connection
  66.    wt: 6:   24 tangent Angle Difference Formula
  67.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  68.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  69.    wt: 6:   21 sine and cosine Half Angle Formulas
  70.    wt: 6:   20 sine and cosine Double Angle Formulas
  71.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  72.    wt: 6:   18 sum of sinusoidal waves as a single wave
  73.    wt: 6:   17G Pythagorean Theorem Converse
  74.    wt: 6:   17F Law of cosines
  75.    wt: 6:   17E Trig Formulas for dot and cross Products
  76.    wt: 6:   17D cis formulas for sine cosines and tangent
  77.    wt: 6:   17C sine and cosine double triple angle formulas
  78.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  79.    wt: 6:   16 Right Triangle Complementary Angle Relations
  80.    wt: 6:   15 sine cosine Complementary Angle Relations
  81.    wt: 6:   14 cosine even and sine and tangent are odd
  82.    wt: 6:   13 Graph of tangent function many periods
  83.    wt: 6:   12 Graph of tangent function for one period
  84.    wt: 6:   11 tangent function undefined when terminal side vertical
  85.    wt: 6:   10 Graphs of sines and cosines many periods
  86.    wt: 6:   9 Graphs of sine and cosine over one period
  87.    wt: 6:   8 period of tangent function
  88.    wt: 6:   7 period of sine and cosine
  89.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  90.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  91.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  92.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  93.    wt: 6:   2 Quadrant I reference Angles
  94.    wt: 6:   1 Unit Points Reflections Rotations
  95.    wt: 6:   8 Triangles Cascade Problem Solving
  96.    wt: 6:   7 Trignometric Ratios Unit Circle
  97.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  98.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  99.    wt: 6:   3 Trigonometric Ratios sine and cosine
  100.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  101.    wt: 6:   1 Angle Measurement with Degrees
  102.    wt: 6:   7 Exercises to test skill and concept mastery
  103.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  104.    wt: 6:   7 Angle Side Angle
  105.    wt: 5:   16 cotangent function Definition Graph and Inverse
  106.    wt: 5:   15 cosecant function Definition Graph and Inverse
  107.    wt: 5:   14 secant function Definition Graph and Inverse
  108.    wt: 5:   13 cosecant function Definition Graph and Inverse
  109.    wt: 5:   12 motivation for term arctan
  110.    wt: 5:   11 arctan left inverse of tangent Graph
  111.    wt: 5:   10 arctan left inverse of tangent Definition
  112.    wt: 5:   9 motivation for name arcsin
  113.    wt: 5:   8 arcsin left inverse of sine Graph
  114.    wt: 5:   7 arcsin left inverse of sine Definition
  115.    wt: 5:   6 Graph of arccos function
  116.    wt: 5:   5 Swapping Coordinates is a reflection
  117.    wt: 5:   4 possible motivation for term arccos
  118.    wt: 5:   3 Left Inverse of cosine arccos definition
  119.    wt: 5:   2 cosine function more properties
  120.    wt: 5:   1 cosine function properties
  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:   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:   2 point slope equation for a line
  188.    wt: 5:   1 Numerical view of lines and their equations
  189.    wt: 5:   What is and is not here
  190.    wt: 5:   13 Pythagorean spatial distance formulas
  191.    wt: 5:   12 Spatial Coordinates
  192.    wt: 5:   11 Triangle Inequality
  193.    wt: 5:   10 Pythagorean plane distance formula
  194.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  195.    wt: 5:   8 Distance Between Points on a Line
  196.    wt: 5:   6 Polar Multiplication and Rotation
  197.    wt: 5:   5 Cartesian Addition and Translation
  198.    wt: 5:   4 Polar Coordinates to and from
  199.    wt: 5:   3 Rectangular Coordinates Review
  200.    wt: 5:   2 Cartesian Coordinates with signs
  201.    wt: 5:   1 Cartesian Coordinates sans signs
  202.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  203.    wt: 5:   PS G Rotation Distributes over Addition
  204.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  205.    wt: 5:   PS E Multiplication with Polar Coordinates
  206.    wt: 5:   PS D Addition with Cartesian Coordinates
  207.    wt: 5:   PS B Parallelogram Construction Methods
  208.    wt: 5:   PS A Kite Construction Methods
  209.    wt: 5:   21 Parallelograms
  210.    wt: 5:   19 Right Triangle Similarity
  211.    wt: 5:   18 Triangle Similarity Take 1
  212.    wt: 5:   17 Right Bisectors of Triangle Sides
  213.    wt: 5:   16 Angles Subtended By Chords and Diameters
  214.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  215.    wt: 5:   14 Parallel Lines Postulate
  216.    wt: 5:   13 Angle Side Angle Failure
  217.    wt: 5:   12 Side Angle Side Failure
  218.    wt: 5:   11 Triangle Construction Fails
  219.    wt: 5:   10 Dropping a perpendicular to line
  220.    wt: 5:   9 Construction of a right bisector
  221.    wt: 5:   8 Isoceles Triangles
  222.    wt: 5:   6 Ruler and compass Angle Bisection
  223.    wt: 5:   5 Side Angle Side
  224.    wt: 5:   4 Side Side Side
  225.    wt: 5:   3 Isometry of Triangles Congruence
  226.    wt: 5:   2 Correspondence between Triangles
  227.    wt: 5:   1 Initial Concepts and Terms
  228.    wt: 5:   Short Course on Euclidean Geometry
  229.    wt: 5:   About Folder Contents
  230.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  231.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  232.    wt: 2:   Maps Plans Drawings
  233.    wt: 2:   musings do not puiblish real numbers
  234.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  235.    wt: 2:   22 Multiplication of Signed Numbers
  236.    wt: 2:   19 Signed Multiples of Vectors
  237.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  238.    wt: 2:   13 Arrows and Vectors in a Plane
  239.    wt: 2:   12 Real Numbers Line Signed Coordinates
  240.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  241.    wt: 2:   16 Real Numbers Comparison
  242.    wt: 2:   8 Coordinates for Maps and Planes
  243.    wt: 2:   7 Real Numbers as Line Cordinates
  244.    wt: 2:   6 Unsigned Real Numbers
  245.    wt: 2:   5 Rational Numbers More
  246.    wt: 2:   4 Rational Numbers
  247.    wt: 2:   1 Whole and Natural Numbers
  248.    wt: 2:   3 Comparison of Negative Numbers
  249.    wt: 2:   11 What are real lengths and numbers
  250.    wt: 2:   10 dividing signed numbers
  251.    wt: 2:   9 subtracting signed numbers
  252.    wt: 2:   8 multiplying signed numbers
  253.    wt: 2:   6 adding signed numbers
  254.    wt: 2:   5 lengths and signs of numbers
  255.    wt: 2:   3 signed coordinates for maps and planes
  256.    wt: 2:   2 signed and unsigned numbers as coordinates
  257.    wt: 2:   3 Multiplying Units and Numbers
  258.    wt: 2:   Chapter 22 Complex Numbers
  259.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  260.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  261.    wt: 1:   Ramblings Extrinsic numbers theory
  262.    wt: 1:   2 arithmetic with signed numbers
  263.    wt: 1:   1 arithmetic with unsigned numbers
  264.    wt: 1:   About site lesson plans
  265.    wt: 1:   7 Student Motivation
  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:   7 Decimals Multiplication Methods Examples
  288.    wt: 1:   5 Distributive Law for Whole Numbers
  289.    wt: 1:   1 The Counting Origins of Numbers
  290.    wt: 1:   4 Comparison of Negative Numbers
  291.    wt: 1:   1 Real Numbers Comparison
  292.    wt: 1:   15 Real Number Division
  293.    wt: 1:   14 Real Number Multiplication
  294.    wt: 1:   13 Real Number Subtraction
  295.    wt: 1:   12 Real Number Additive Inverses or Negatives
  296.    wt: 1:   11 Real Number Addition
  297.    wt: 1:   10 Real Number Lengths and Signs
  298.    wt: 1:   9 Coordinates for Regions in Space
  299.    wt: 1:   3 Fractions
  300.    wt: 1:   2 Integers
  301.    wt: 1:   7 Two Examples
  302.    wt: 1:   8 Sets of Numbers
  303.    wt: 1:   5 Talking about Numbers and Quantities
  304.    wt: 1:   4 A Brief Story of numbers and algebra
  305.    wt: 1:   4 Greater More Less Than Signs in General
  306.    wt: 1:   2 More and Less Than with Unlike Signs
  307.    wt: 1:   1 More and Less Than for Counts and Measures
  308.    wt: 1:   7 negative and additive inverse
  309.    wt: 1:   4 signed coordinates for regions in space
  310.    wt: 1:   7 Converting or Changing Units
  311.    wt: 1:   6 Simplification of Fractions with Units
  312.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  313.    wt: 1:   4 Fractions with Units
  314.    wt: 1:   2 Equality and Units
  315.    wt: 1:   1 Addition and Subtraction with Units
  316.    wt: 1:   22 Complex Compound Fractions
  317.    wt: 1:   9 Improper Fractions and Mixed Numbers
  318.    wt: 1:   6 Multiplication of Mixed Numbers
  319.    wt: 1:   8 Multiplication by Signed Numbers Integers
  320.    wt: 1:   7 Multiplication by Signs
  321.    wt: 1:   6 Multiplication by Natural Numbers
  322.    wt: 1:   7 Calculator Usage Notes and Cautions
  323.    wt: 1:   7 Long Divison Mistake Catching
  324.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  325.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  326.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  327.    wt: 1:   Quick history of numbers and algebra
  328.    wt: 1:   011 Division of Time Intervals By Numbers
  329.    wt: 1:   Chapter 23 Links To Trigonometry
  330.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  331.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  332.    wt: 10:   20 N th Roots of Complex Numbers
  333.    wt: 10:   2 Complex Numbers made easier we hope

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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