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.

Home << Search

[1] [2] [3] [4]

Key Word Search

Folder Search

20 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   8 Unit Circle Trigonometry/
  4.    wt: 6:   7 Complex Numbers/
  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: 2:   B Real Numbers Extrinsic Development/
  18.    wt: 2:   5 Real Numbers/
  19.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  20.    wt: 1:   8 Arithmetic with Signed Numbers/

Web Page Search

82 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   4 Angles on Maps Plans drawn to scale
  3.    wt: 2:   3 Lengths and Areas on Maps and Plans
  4.    wt: 2:   musings do not puiblish real numbers
  5.    wt: 2:   12 Real Numbers Line Signed Coordinates
  6.    wt: 2:   1 Real Numbers Comparison
  7.    wt: 2:   16 Real Numbers Comparison
  8.    wt: 2:   7 Real Numbers as Line Cordinates
  9.    wt: 2:   6 Unsigned Real Numbers
  10.    wt: 2:   11 What are real lengths and numbers
  11.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  12.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  13.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  14.    wt: 1:   Ramblings Extrinsic numbers theory
  15.    wt: 1:   2 arithmetic with signed numbers
  16.    wt: 1:   1 arithmetic with unsigned numbers
  17.    wt: 1:   About site lesson plans
  18.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  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:   Unit Circle Development of Trigonometry
  24.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  25.    wt: 1:   20 N th Roots of Complex Numbers
  26.    wt: 1:   8 Unit Circle Development of Trigonometry
  27.    wt: 1:   2 Complex Numbers made easier we hope
  28.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  29.    wt: 1:   Why Trigonometry the whyslopes view
  30.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  31.    wt: 1:   7 Complex Numbers Appetizer
  32.    wt: 1:   PS H Distributive Law For Complex Numbers
  33.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  34.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  35.    wt: 1:   6 Figuring with Maps Not to Scale
  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:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  42.    wt: 1:   5 Distributive Law for Whole Numbers
  43.    wt: 1:   1 The Counting Origins of Numbers
  44.    wt: 1:   4 Comparison of Negative Numbers
  45.    wt: 1:   15 Real Number Division
  46.    wt: 1:   14 Real Number Multiplication
  47.    wt: 1:   13 Real Number Subtraction
  48.    wt: 1:   12 Real Number Additive Inverses or Negatives
  49.    wt: 1:   11 Real Number Addition
  50.    wt: 1:   10 Real Number Lengths and Signs
  51.    wt: 1:   8 Coordinates for Maps and Planes
  52.    wt: 1:   5 Rational Numbers More
  53.    wt: 1:   4 Rational Numbers
  54.    wt: 1:   1 Whole and Natural Numbers
  55.    wt: 1:   8 Sets of Numbers
  56.    wt: 1:   5 Talking about Numbers and Quantities
  57.    wt: 1:   4 A Brief Story of numbers and algebra
  58.    wt: 1:   arithmetic videos Real Player Format
  59.    wt: 1:   3 Comparison of Negative Numbers
  60.    wt: 1:   10 dividing signed numbers
  61.    wt: 1:   9 subtracting signed numbers
  62.    wt: 1:   8 multiplying signed numbers
  63.    wt: 1:   6 adding signed numbers
  64.    wt: 1:   5 lengths and signs of numbers
  65.    wt: 1:   3 signed coordinates for maps and planes
  66.    wt: 1:   2 signed and unsigned numbers as coordinates
  67.    wt: 1:   3 Multiplying Units and Numbers
  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:   A Chain Rule Real Player video examples
  77.    wt: 1:   33 Chain Rule Real Player video examples
  78.    wt: 1:   Chapter 23 Links To Trigonometry
  79.    wt: 1:   Chapter 22 Complex Numbers
  80.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  81.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  82.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions

Extended Search

323 matches:

  1.    wt: 9:   4 Angles on Maps Plans drawn to scale
  2.    wt: 9:   3 Lengths and Areas on Maps and Plans
  3.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  4.    wt: 8:   6 Figuring with Maps Not to Scale
  5.    wt: 7:   13 Velocity Vectors in Physics
  6.    wt: 7:   8 Parallel Vectors
  7.    wt: 7:   6 Vectors with Coordinates
  8.    wt: 7:   3 Navigation with Arrows or Vectors
  9.    wt: 7:   Unit Circle Development of Trigonometry
  10.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  11.    wt: 7:   20 N th Roots of Complex Numbers
  12.    wt: 7:   8 Unit Circle Development of Trigonometry
  13.    wt: 7:   2 Complex Numbers made easier we hope
  14.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  15.    wt: 7:   Why Trigonometry the whyslopes view
  16.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  17.    wt: 7:   A Measurement with Ruler Proper Use
  18.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  19.    wt: 7:   2 Measuring Area Directly
  20.    wt: 7:   1 Length Measurement
  21.    wt: 6:   A Global Time and Navigation
  22.    wt: 6:   15 Dot and Cross Product
  23.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  24.    wt: 6:   12 From Applied To Pure Mathematics
  25.    wt: 6:   11 Component Method
  26.    wt: 6:   10 Parallelogram Addition Method
  27.    wt: 6:   9 Head to Tail Coordinate View
  28.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  29.    wt: 6:   5 Head To Tail Arrow Addition
  30.    wt: 6:   4 Resultant of a Sum of Movements
  31.    wt: 6:   2 Signed Coordinates
  32.    wt: 6:   1 Unsigned Coordinates
  33.    wt: 6:   Vector and Complex Number Applet
  34.    wt: 6:   17 tangent function angle sum formulas
  35.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  36.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  37.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  38.    wt: 6:   32 seven rows of pascals triangle
  39.    wt: 6:   31 basic secant cosecant cotangent trig identities
  40.    wt: 6:   30 unit circle calculation of six trigonometric functions
  41.    wt: 6:   29 secant cosecant and cotangent for acute angles
  42.    wt: 6:   28 Expressing products of sines cosines as sums
  43.    wt: 6:   27 Logarithmic use of products of sines and cosines
  44.    wt: 6:   26 Formulas for products of sines and cosines
  45.    wt: 6:   25 tangent double angle formula Slope connection
  46.    wt: 6:   24 tangent Angle Difference Formula
  47.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  48.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  49.    wt: 6:   21 sine and cosine Half Angle Formulas
  50.    wt: 6:   20 sine and cosine Double Angle Formulas
  51.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  52.    wt: 6:   18 sum of sinusoidal waves as a single wave
  53.    wt: 6:   17G Pythagorean Theorem Converse
  54.    wt: 6:   17F Law of cosines
  55.    wt: 6:   17E Trig Formulas for dot and cross Products
  56.    wt: 6:   17D cis formulas for sine cosines and tangent
  57.    wt: 6:   17C sine and cosine double triple angle formulas
  58.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  59.    wt: 6:   17A The complex number valued trig function cis
  60.    wt: 6:   16 Right Triangle Complementary Angle Relations
  61.    wt: 6:   15 sine cosine Complementary Angle Relations
  62.    wt: 6:   14 cosine even and sine and tangent are odd
  63.    wt: 6:   13 Graph of tangent function many periods
  64.    wt: 6:   12 Graph of tangent function for one period
  65.    wt: 6:   11 tangent function undefined when terminal side vertical
  66.    wt: 6:   10 Graphs of sines and cosines many periods
  67.    wt: 6:   9 Graphs of sine and cosine over one period
  68.    wt: 6:   8 period of tangent function
  69.    wt: 6:   7 period of sine and cosine
  70.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  71.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  72.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  73.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  74.    wt: 6:   2 Quadrant I reference Angles
  75.    wt: 6:   1 Unit Points Reflections Rotations
  76.    wt: 6:   21 Logarithms Powers and Exponentials
  77.    wt: 6:   19 N th Roots of Unity
  78.    wt: 6:   18 Sixth Roots of Unity
  79.    wt: 6:   17 Cube Roots of unity
  80.    wt: 6:   16 References and Originality Question
  81.    wt: 6:   15 Pythagorean Theorem Converse
  82.    wt: 6:   14 Law of cosines
  83.    wt: 6:   13 Trig Formulas for dot and cross Products
  84.    wt: 6:   12 cis formulas for sine cosines and tangent
  85.    wt: 6:   11 sine and cosine double triple angle formulas
  86.    wt: 6:   10 sine cosine Angle Sum Formulas via cis
  87.    wt: 6:   9 The complex number valued trig function cis
  88.    wt: 6:   7 Second Way to Calculate Products
  89.    wt: 6:   6 Field Properties of Complex Number
  90.    wt: 6:   5 An Easy Proof of the Distributive Law
  91.    wt: 6:   4 Multiplication Properties
  92.    wt: 6:   3 Addition Properties
  93.    wt: 6:   1 Rectangular Polar Coordinates Review
  94.    wt: 6:   Appetizer A Complex Number Applet
  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 Complex Numbers Appetizer
  103.    wt: 6:   PS H Distributive Law For Complex Numbers
  104.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  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:   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: 4:   musings do not puiblish real numbers
  233.    wt: 4:   12 Real Numbers Line Signed Coordinates
  234.    wt: 4:   16 Real Numbers Comparison
  235.    wt: 4:   7 Real Numbers as Line Cordinates
  236.    wt: 4:   6 Unsigned Real Numbers
  237.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  238.    wt: 3:   22 Multiplication of Signed Numbers
  239.    wt: 3:   19 Signed Multiples of Vectors
  240.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  241.    wt: 3:   13 Arrows and Vectors in a Plane
  242.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  243.    wt: 3:   15 Real Number Division
  244.    wt: 3:   14 Real Number Multiplication
  245.    wt: 3:   13 Real Number Subtraction
  246.    wt: 3:   12 Real Number Additive Inverses or Negatives
  247.    wt: 3:   11 Real Number Addition
  248.    wt: 3:   10 Real Number Lengths and Signs
  249.    wt: 3:   8 Coordinates for Maps and Planes
  250.    wt: 3:   5 Rational Numbers More
  251.    wt: 3:   4 Rational Numbers
  252.    wt: 3:   1 Whole and Natural Numbers
  253.    wt: 3:   11 What are real lengths and numbers
  254.    wt: 2:   Maps Plans Drawings
  255.    wt: 2:   A Modular and Remainder Arithmetic
  256.    wt: 2:   A Signed Number Arithmetic Review
  257.    wt: 2:   26 More Less Greater Than Comparison
  258.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  259.    wt: 2:   23 Distributive Law Two Derivations
  260.    wt: 2:   21 Addition of Multiples of a Single Vector
  261.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  262.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  263.    wt: 2:   17 Arrows Rotate to Reverse with Length Unchanged
  264.    wt: 2:   15 Head to Tails in place Addition Associative
  265.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  266.    wt: 2:   11 Signed Number Addition and Addition Properties
  267.    wt: 2:   9 Division with Digits after Decimal Point
  268.    wt: 2:   8 Division and Mulplication of Compound Fractions
  269.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  270.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  271.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  272.    wt: 2:   4 Location of Point in Decimal Addition
  273.    wt: 2:   3 Location of Point in Decimal Multiplication
  274.    wt: 2:   2 Counting Digits in Decimal Multiplication
  275.    wt: 2:   1 Fractions with Finite Decimal Expansions
  276.    wt: 2:   1 Real Numbers Comparison
  277.    wt: 2:   9 Coordinates for Regions in Space
  278.    wt: 2:   3 Fractions
  279.    wt: 2:   2 Integers
  280.    wt: 2:   3 Comparison of Negative Numbers
  281.    wt: 2:   10 dividing signed numbers
  282.    wt: 2:   9 subtracting signed numbers
  283.    wt: 2:   8 multiplying signed numbers
  284.    wt: 2:   6 adding signed numbers
  285.    wt: 2:   5 lengths and signs of numbers
  286.    wt: 2:   3 signed coordinates for maps and planes
  287.    wt: 2:   2 signed and unsigned numbers as coordinates
  288.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  289.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  290.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  291.    wt: 1:   Ramblings Extrinsic numbers theory
  292.    wt: 1:   2 arithmetic with signed numbers
  293.    wt: 1:   1 arithmetic with unsigned numbers
  294.    wt: 1:   About site lesson plans
  295.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  296.    wt: 1:   5 Distributive Law for Whole Numbers
  297.    wt: 1:   1 The Counting Origins of Numbers
  298.    wt: 1:   4 Comparison of Negative Numbers
  299.    wt: 1:   8 Sets of Numbers
  300.    wt: 1:   5 Talking about Numbers and Quantities
  301.    wt: 1:   4 A Brief Story of numbers and algebra
  302.    wt: 1:   arithmetic videos Real Player Format
  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:   9 Improper Fractions and Mixed Numbers
  310.    wt: 1:   6 Multiplication of Mixed Numbers
  311.    wt: 1:   8 Multiplication by Signed Numbers Integers
  312.    wt: 1:   6 Multiplication by Natural Numbers
  313.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  314.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  315.    wt: 1:   Quick history of numbers and algebra
  316.    wt: 1:   011 Division of Time Intervals By Numbers
  317.    wt: 1:   A Chain Rule Real Player video examples
  318.    wt: 1:   33 Chain Rule Real Player video examples
  319.    wt: 1:   Chapter 23 Links To Trigonometry
  320.    wt: 1:   Chapter 22 Complex Numbers
  321.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  322.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  323.    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.

Return to Page Top

Home << Search

[1] [2] [3] [4]

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

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.