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:   5 Factored Polynomial Sign Analysis Examples/
  18.    wt: 1:   10 Examples of Algebraic Reasoning/

Web Page Search

80 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  3.    wt: 2:   4 Angles on Maps Plans drawn to scale
  4.    wt: 2:   3 Lengths and Areas on Maps and Plans
  5.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  6.    wt: 1:   About site lesson plans
  7.    wt: 1:   13 Velocity Vectors in Physics
  8.    wt: 1:   8 Parallel Vectors
  9.    wt: 1:   6 Vectors with Coordinates
  10.    wt: 1:   3 Navigation with Arrows or Vectors
  11.    wt: 1:   Parallel Lines and Parallel Transversals
  12.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  13.    wt: 1:   Parallel Lines and Interior Angles
  14.    wt: 1:   Straight Lines ASA Intersection Study More
  15.    wt: 1:   Straight Lines ASA Intersection Study
  16.    wt: 1:   Straight Lines Instersection Solving Equations
  17.    wt: 1:   Straight Lines Intersection of
  18.    wt: 1:   C Straight Lines Slope from Coordinates
  19.    wt: 1:   14 Straight Lines Equations General Case
  20.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  21.    wt: 1:   12 Straight Lines Graphing mx plus b
  22.    wt: 1:   11 Straight Lines Graphing y=mx
  23.    wt: 1:   10 Straight Lines through Origin Equations More
  24.    wt: 1:   9 Straight Lines through Origin Equations
  25.    wt: 1:   8 Straight Lines Equation for vertical
  26.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  27.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  28.    wt: 1:   1 Straight Lines Slope Concept
  29.    wt: 1:   Unit Circle Development of Trigonometry
  30.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  31.    wt: 1:   8 Unit Circle Development of Trigonometry
  32.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  33.    wt: 1:   Why Trigonometry the whyslopes view
  34.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  35.    wt: 1:   6 Intersection of lines by solving linear systems
  36.    wt: 1:   4 Equations for lines three forms
  37.    wt: 1:   3 Slope product for perpendicular lines
  38.    wt: 1:   1 Numerical view of lines and their equations
  39.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  40.    wt: 1:   14 Parallel Lines Postulate
  41.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  42.    wt: 1:   6 Figuring with Maps Not to Scale
  43.    wt: 1:   19 Signed Multiples of Vectors
  44.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  45.    wt: 1:   13 Arrows and Vectors in a Plane
  46.    wt: 1:   7 Decimals Multiplication Methods Examples
  47.    wt: 1:   3 Proportionality Examples
  48.    wt: 1:   8 Coordinates for Maps and Planes
  49.    wt: 1:   4 GE III Animated Examples
  50.    wt: 1:   1 GE Substitution four examples
  51.    wt: 1:   4 Four Examples Fractional Coefficients
  52.    wt: 1:   3 Four Examples
  53.    wt: 1:   2 Three Examples
  54.    wt: 1:   9 Three Examples
  55.    wt: 1:   7 Two Examples
  56.    wt: 1:   6 Three Examples
  57.    wt: 1:   5 Three Examples
  58.    wt: 1:   4 Two Examples
  59.    wt: 1:   3 Two Examples
  60.    wt: 1:   2 Three Examples
  61.    wt: 1:   3 signed coordinates for maps and planes
  62.    wt: 1:   12 Adding Integers More Examples
  63.    wt: 1:   11 Adding Integers Formulas and Examples
  64.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  65.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  66.    wt: 1:   1 Divsion Physical Examples
  67.    wt: 1:   2 Subtraction Easy Case Examples
  68.    wt: 1:   5. How to add decimals C. Examples
  69.    wt: 1:   A Chain Rule Real Player video examples
  70.    wt: 1:   33 Chain Rule Real Player video examples
  71.    wt: 1:   25 Chain Rule Animated Examples Continued
  72.    wt: 1:   24 Chain Rule Animated Examples
  73.    wt: 1:   12 Quotient rule examples
  74.    wt: 1:   7 Animated Differentiation Examples
  75.    wt: 1:   11 Limits at infinity Three Examples
  76.    wt: 1:   8 Four Animated Examples
  77.    wt: 1:   Chapter 23 Links To Trigonometry
  78.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  79.    wt: 1:   Chapter 25. Mathematical Induction Examples
  80.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

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