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

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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