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

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

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

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

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

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

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

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18 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   11 Parallel Straight Lines and Transversals/
  4.    wt: 6:   10 Intersecting Straight Lines and Transversals/
  5.    wt: 6:   9 Lines and Slopes Take 2 with tangent function/
  6.    wt: 6:   8 Unit Circle Trigonometry/
  7.    wt: 6:   6 Trigonometry first steps/
  8.    wt: 6:   4 Lines and Slopes Take 1/
  9.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  10.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  11.    wt: 5:   12 Function Translating and Rescaling/
  12.    wt: 5:   7 Complex Numbers/
  13.    wt: 5:   5 What is Similarity/
  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:   10 Examples of Algebraic Reasoning/
  18.    wt: 1:   Step 2 Algebraic solutions for one unknown/

Web Page Search

84 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   Why Trigonometry the whyslopes view
  3.    wt: 2:   5 Algebraic View of Slopes
  4.    wt: 2:   1 Numerical view of lines and their equations
  5.    wt: 2:   4 Angles on Maps Plans drawn to scale
  6.    wt: 2:   3 Lengths and Areas on Maps and Plans
  7.    wt: 2:   2 Algebraic View
  8.    wt: 2:   13 Fraction Comparison Algebraic View
  9.    wt: 2:   11 Simplification an Algebraic View
  10.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  11.    wt: 1:   7 logic review and decimals an odd combination
  12.    wt: 1:   website reviews
  13.    wt: 1:   About site lesson plans
  14.    wt: 1:   teaching tutoring algebraic reason
  15.    wt: 1:   Operational Viewpoint to Value
  16.    wt: 1:   formal or informal peer review
  17.    wt: 1:   8 Set view of relations and functions
  18.    wt: 1:   2 Algebraic use of function notation
  19.    wt: 1:   Rewriting algebraic substitution as function substitutions
  20.    wt: 1:   13 Velocity Vectors in Physics
  21.    wt: 1:   9 Head to Tail Coordinate View
  22.    wt: 1:   8 Parallel Vectors
  23.    wt: 1:   6 Vectors with Coordinates
  24.    wt: 1:   3 Navigation with Arrows or Vectors
  25.    wt: 1:   Parallel Lines and Parallel Transversals
  26.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  27.    wt: 1:   Parallel Lines and Interior Angles
  28.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  29.    wt: 1:   Straight Lines ASA Intersection Study More
  30.    wt: 1:   Straight Lines ASA Intersection Study
  31.    wt: 1:   Straight Lines Instersection Solving Equations
  32.    wt: 1:   Straight Lines Intersection of
  33.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  34.    wt: 1:   C Straight Lines Slope from Coordinates
  35.    wt: 1:   14 Straight Lines Equations General Case
  36.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  37.    wt: 1:   12 Straight Lines Graphing mx plus b
  38.    wt: 1:   11 Straight Lines Graphing y=mx
  39.    wt: 1:   10 Straight Lines through Origin Equations More
  40.    wt: 1:   9 Straight Lines through Origin Equations
  41.    wt: 1:   8 Straight Lines Equation for vertical
  42.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  43.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  44.    wt: 1:   1 Straight Lines Slope Concept
  45.    wt: 1:   Unit Circle Development of Trigonometry
  46.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  47.    wt: 1:   8 Unit Circle Development of Trigonometry
  48.    wt: 1:   1 Rectangular Polar Coordinates Review
  49.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  50.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  51.    wt: 1:   6 Intersection of lines by solving linear systems
  52.    wt: 1:   4 Equations for lines three forms
  53.    wt: 1:   3 Slope product for perpendicular lines
  54.    wt: 1:   3 Rectangular Coordinates Review
  55.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  56.    wt: 1:   14 Parallel Lines Postulate
  57.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  58.    wt: 1:   6 Figuring with Maps Not to Scale
  59.    wt: 1:   A Signed Number Arithmetic Review
  60.    wt: 1:   19 Signed Multiples of Vectors
  61.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  62.    wt: 1:   13 Arrows and Vectors in a Plane
  63.    wt: 1:   3 Inequalities Algebraically
  64.    wt: 1:   8 Coordinates for Maps and Planes
  65.    wt: 1:   6 Algebraic Solution Example
  66.    wt: 1:   5 Algebraic Solutions Introduction
  67.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  68.    wt: 1:   3 signed coordinates for maps and planes
  69.    wt: 1:   6 Multiplication Algebraically Take II
  70.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  71.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  72.    wt: 1:   9 22 Minute Subtraction Review Video
  73.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  74.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  75.    wt: 1:   2 Algebraic codification
  76.    wt: 1:   E2 Algebraic Properties of Limits
  77.    wt: 1:   Chapter 23 Links To Trigonometry
  78.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  79.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  80.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  81.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  82.    wt: 1:   More Algebra and Slope based Calculus Preview
  83.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  84.    wt: 1:   Site Reviews

Extended Search

279 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:   Why Trigonometry the whyslopes view
  4.    wt: 8:   5 Algebraic View of Slopes
  5.    wt: 8:   1 Numerical view of lines and their equations
  6.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  7.    wt: 8:   6 Figuring with Maps Not to Scale
  8.    wt: 7:   13 Velocity Vectors in Physics
  9.    wt: 7:   9 Head to Tail Coordinate View
  10.    wt: 7:   8 Parallel Vectors
  11.    wt: 7:   6 Vectors with Coordinates
  12.    wt: 7:   3 Navigation with Arrows or Vectors
  13.    wt: 7:   Parallel Lines and Parallel Transversals
  14.    wt: 7:   Parallel Lines and Alternating Corresponding Angles
  15.    wt: 7:   Parallel Lines and Interior Angles
  16.    wt: 7:   Analytic View of Triangle Construction or Line Instersection More
  17.    wt: 7:   Straight Lines ASA Intersection Study More
  18.    wt: 7:   Straight Lines ASA Intersection Study
  19.    wt: 7:   Straight Lines Instersection Solving Equations
  20.    wt: 7:   Straight Lines Intersection of
  21.    wt: 7:   D Straight Lines Slope from Coordinates Examples
  22.    wt: 7:   C Straight Lines Slope from Coordinates
  23.    wt: 7:   14 Straight Lines Equations General Case
  24.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  25.    wt: 7:   12 Straight Lines Graphing mx plus b
  26.    wt: 7:   11 Straight Lines Graphing y=mx
  27.    wt: 7:   10 Straight Lines through Origin Equations More
  28.    wt: 7:   9 Straight Lines through Origin Equations
  29.    wt: 7:   8 Straight Lines Equation for vertical
  30.    wt: 7:   3 Straight Lines Slope as Tangent of Inclination Angle
  31.    wt: 7:   2 Straight Lines Slopes As Rise Over Run
  32.    wt: 7:   1 Straight Lines Slope Concept
  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:   Right Triangle and Unit Circle Trigonometry
  37.    wt: 7:   6 Intersection of lines by solving linear systems
  38.    wt: 7:   4 Equations for lines three forms
  39.    wt: 7:   3 Slope product for perpendicular lines
  40.    wt: 7:   A Measurement with Ruler Proper Use
  41.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  42.    wt: 7:   2 Measuring Area Directly
  43.    wt: 7:   1 Length Measurement
  44.    wt: 6:   A Global Time and Navigation
  45.    wt: 6:   15 Dot and Cross Product
  46.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  47.    wt: 6:   12 From Applied To Pure Mathematics
  48.    wt: 6:   11 Component Method
  49.    wt: 6:   10 Parallelogram Addition Method
  50.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  51.    wt: 6:   5 Head To Tail Arrow Addition
  52.    wt: 6:   4 Resultant of a Sum of Movements
  53.    wt: 6:   2 Signed Coordinates
  54.    wt: 6:   1 Unsigned Coordinates
  55.    wt: 6:   Vector and Complex Number Applet
  56.    wt: 6:   Proportionality of Line Segments From Parallel Transversals
  57.    wt: 6:   Triangle Angles Sum To 180 Degrees
  58.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  59.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  60.    wt: 6:   B Straight Line Slope Scaling Properties More
  61.    wt: 6:   A Straight Line Slope Scaling Properties
  62.    wt: 6:   7 Tangent Function is odd on this domain
  63.    wt: 6:   6 Tangent Function Inclination Angle Take 2
  64.    wt: 6:   5 Tangent Function Graph
  65.    wt: 6:   4 Tangent Function Properties
  66.    wt: 6:   17 tangent function angle sum formulas
  67.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  68.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  69.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  70.    wt: 6:   32 seven rows of pascals triangle
  71.    wt: 6:   31 basic secant cosecant cotangent trig identities
  72.    wt: 6:   30 unit circle calculation of six trigonometric functions
  73.    wt: 6:   29 secant cosecant and cotangent for acute angles
  74.    wt: 6:   28 Expressing products of sines cosines as sums
  75.    wt: 6:   27 Logarithmic use of products of sines and cosines
  76.    wt: 6:   26 Formulas for products of sines and cosines
  77.    wt: 6:   25 tangent double angle formula Slope connection
  78.    wt: 6:   24 tangent Angle Difference Formula
  79.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  80.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  81.    wt: 6:   21 sine and cosine Half Angle Formulas
  82.    wt: 6:   20 sine and cosine Double Angle Formulas
  83.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  84.    wt: 6:   18 sum of sinusoidal waves as a single wave
  85.    wt: 6:   17G Pythagorean Theorem Converse
  86.    wt: 6:   17F Law of cosines
  87.    wt: 6:   17E Trig Formulas for dot and cross Products
  88.    wt: 6:   17D cis formulas for sine cosines and tangent
  89.    wt: 6:   17C sine and cosine double triple angle formulas
  90.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  91.    wt: 6:   17A The complex number valued trig function cis
  92.    wt: 6:   16 Right Triangle Complementary Angle Relations
  93.    wt: 6:   15 sine cosine Complementary Angle Relations
  94.    wt: 6:   14 cosine even and sine and tangent are odd
  95.    wt: 6:   13 Graph of tangent function many periods
  96.    wt: 6:   12 Graph of tangent function for one period
  97.    wt: 6:   11 tangent function undefined when terminal side vertical
  98.    wt: 6:   10 Graphs of sines and cosines many periods
  99.    wt: 6:   9 Graphs of sine and cosine over one period
  100.    wt: 6:   8 period of tangent function
  101.    wt: 6:   7 period of sine and cosine
  102.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  103.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  104.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  105.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  106.    wt: 6:   2 Quadrant I reference Angles
  107.    wt: 6:   1 Unit Points Reflections Rotations
  108.    wt: 6:   8 Unit Circle Development of Trigonometry
  109.    wt: 6:   1 Rectangular Polar Coordinates Review
  110.    wt: 6:   8 Triangles Cascade Problem Solving
  111.    wt: 6:   7 Trignometric Ratios Unit Circle
  112.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  113.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  114.    wt: 6:   3 Trigonometric Ratios sine and cosine
  115.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  116.    wt: 6:   1 Angle Measurement with Degrees
  117.    wt: 6:   Four Simple Exercises
  118.    wt: 6:   12 Links Lessons elsewhere
  119.    wt: 6:   11 A Partial Summary
  120.    wt: 6:   10 Midpoint of [a b] and [b a]
  121.    wt: 6:   9 Midpoint Coordinates Half Endpoint Sum
  122.    wt: 6:   8 Mid Point Formula
  123.    wt: 6:   7 Exercises to test skill and concept mastery
  124.    wt: 6:   2 point slope equation for a line
  125.    wt: 6:   What is and is not here
  126.    wt: 6:   3 Rectangular Coordinates Review
  127.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  128.    wt: 6:   14 Parallel Lines Postulate
  129.    wt: 5:   16 cotangent function Definition Graph and Inverse
  130.    wt: 5:   15 cosecant function Definition Graph and Inverse
  131.    wt: 5:   14 secant function Definition Graph and Inverse
  132.    wt: 5:   13 cosecant function Definition Graph and Inverse
  133.    wt: 5:   12 motivation for term arctan
  134.    wt: 5:   11 arctan left inverse of tangent Graph
  135.    wt: 5:   10 arctan left inverse of tangent Definition
  136.    wt: 5:   9 motivation for name arcsin
  137.    wt: 5:   8 arcsin left inverse of sine Graph
  138.    wt: 5:   7 arcsin left inverse of sine Definition
  139.    wt: 5:   6 Graph of arccos function
  140.    wt: 5:   5 Swapping Coordinates is a reflection
  141.    wt: 5:   4 possible motivation for term arccos
  142.    wt: 5:   3 Left Inverse of cosine arccos definition
  143.    wt: 5:   2 cosine function more properties
  144.    wt: 5:   1 cosine function properties
  145.    wt: 5:   9 Summary Degrees to Radians and back
  146.    wt: 5:   8 Radian Measures of Common Angles
  147.    wt: 5:   7 Radian Measures in special Triangles
  148.    wt: 5:   6 Radian Measure to Degrees
  149.    wt: 5:   5 Degrees to Radian Measure
  150.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  151.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  152.    wt: 5:   2 Radian Measure Numerical Value of one degree
  153.    wt: 5:   1 Degrees and Radians Introduction
  154.    wt: 5:   4 graphing y=Asin(x c)
  155.    wt: 5:   3 graphing y=f(x c) plus K
  156.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  157.    wt: 5:   1 graphing y=f(x a)
  158.    wt: 5:   21 Logarithms Powers and Exponentials
  159.    wt: 5:   20 N th Roots of Complex Numbers
  160.    wt: 5:   19 N th Roots of Unity
  161.    wt: 5:   18 Sixth Roots of Unity
  162.    wt: 5:   17 Cube Roots of unity
  163.    wt: 5:   16 References and Originality Question
  164.    wt: 5:   15 Pythagorean Theorem Converse
  165.    wt: 5:   14 Law of cosines
  166.    wt: 5:   13 Trig Formulas for dot and cross Products
  167.    wt: 5:   12 cis formulas for sine cosines and tangent
  168.    wt: 5:   11 sine and cosine double triple angle formulas
  169.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  170.    wt: 5:   9 The complex number valued trig function cis
  171.    wt: 5:   7 Second Way to Calculate Products
  172.    wt: 5:   6 Field Properties of Complex Number
  173.    wt: 5:   5 An Easy Proof of the Distributive Law
  174.    wt: 5:   4 Multiplication Properties
  175.    wt: 5:   3 Addition Properties
  176.    wt: 5:   2 Complex Numbers made easier we hope
  177.    wt: 5:   Appetizer A Complex Number Applet
  178.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  179.    wt: 5:   12 Triangles Similarity More Problems
  180.    wt: 5:   11 Triangle Similarity Missing Side Problem
  181.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  182.    wt: 5:   9 Similarity of Triangles Usual Criteria
  183.    wt: 5:   8 Similarity of Triangles and Polygons
  184.    wt: 5:   7 Translations Rotations Reflections Dilatations
  185.    wt: 5:   6 Geometric Diagrams in Class
  186.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  187.    wt: 5:   4 Similarity Definition with Coordinate
  188.    wt: 5:   3 Similarity by Design with coordinates
  189.    wt: 5:   2 Similarity By Design
  190.    wt: 5:   1 Early Concept of Like or Similar Shapes
  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:   7 Complex Numbers Appetizer
  198.    wt: 5:   6 Polar Multiplication and Rotation
  199.    wt: 5:   5 Cartesian Addition and Translation
  200.    wt: 5:   4 Polar Coordinates to and from
  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 H Distributive Law For Complex Numbers
  205.    wt: 5:   PS G Rotation Distributes over Addition
  206.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  207.    wt: 5:   PS E Multiplication with Polar Coordinates
  208.    wt: 5:   PS D Addition with Cartesian Coordinates
  209.    wt: 5:   PS B Parallelogram Construction Methods
  210.    wt: 5:   PS A Kite Construction Methods
  211.    wt: 5:   21 Parallelograms
  212.    wt: 5:   19 Right Triangle Similarity
  213.    wt: 5:   18 Triangle Similarity Take 1
  214.    wt: 5:   17 Right Bisectors of Triangle Sides
  215.    wt: 5:   16 Angles Subtended By Chords and Diameters
  216.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  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: 2:   Maps Plans Drawings
  233.    wt: 2:   3 Inequalities Algebraically
  234.    wt: 2:   2 Algebraic View
  235.    wt: 2:   6 Algebraic Solution Example
  236.    wt: 2:   5 Algebraic Solutions Introduction
  237.    wt: 2:   13 Fraction Comparison Algebraic View
  238.    wt: 2:   11 Simplification an Algebraic View
  239.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  240.    wt: 1:   7 logic review and decimals an odd combination
  241.    wt: 1:   website reviews
  242.    wt: 1:   About site lesson plans
  243.    wt: 1:   teaching tutoring algebraic reason
  244.    wt: 1:   Operational Viewpoint to Value
  245.    wt: 1:   formal or informal peer review
  246.    wt: 1:   8 Set view of relations and functions
  247.    wt: 1:   2 Algebraic use of function notation
  248.    wt: 1:   Rewriting algebraic substitution as function substitutions
  249.    wt: 1:   A Signed Number Arithmetic Review
  250.    wt: 1:   19 Signed Multiples of Vectors
  251.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  252.    wt: 1:   13 Arrows and Vectors in a Plane
  253.    wt: 1:   5 Areas of Rectangles Revisited
  254.    wt: 1:   4 Fraction Operations Axiomatic Development
  255.    wt: 1:   2 Fraction Operations Physical Development
  256.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  257.    wt: 1:   8 Coordinates for Maps and Planes
  258.    wt: 1:   4 Four Examples Fractional Coefficients
  259.    wt: 1:   3 Four Examples
  260.    wt: 1:   2 Three Examples
  261.    wt: 1:   1 Proper Equal Sign Usage
  262.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  263.    wt: 1:   3 signed coordinates for maps and planes
  264.    wt: 1:   6 Multiplication Algebraically Take II
  265.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  266.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  267.    wt: 1:   9 22 Minute Subtraction Review Video
  268.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  269.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  270.    wt: 1:   2 Algebraic codification
  271.    wt: 1:   E2 Algebraic Properties of Limits
  272.    wt: 1:   Chapter 23 Links To Trigonometry
  273.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  274.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  275.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  276.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  277.    wt: 1:   More Algebra and Slope based Calculus Preview
  278.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  279.    wt: 1:   Site Reviews
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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