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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40 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: 2:   12 Webvideo Lessons on Area and Volume Calculation/
  18.    wt: 2:   5 Lessons on Integration/
  19.    wt: 2:   4 Lessons on Using Derivatives/
  20.    wt: 2:   38 Lessons on Calculating Derivatives/
  21.    wt: 2:   13 Lessons on Limits and Continuity/
  22.    wt: 1:   B Real Numbers Extrinsic Development/
  23.    wt: 1:   A Origins of Counting and Figuring Methods/
  24.    wt: 1:   10 Examples of Algebraic Reasoning/
  25.    wt: 1:   9 Proportionality Backwards and Forwards/
  26.    wt: 1:   8 Unifying Theme For Algebra/
  27.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  28.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  29.    wt: 1:   5 Real Numbers/
  30.    wt: 1:   4 Computation Rules and Function Notation/
  31.    wt: 1:   Step 4 Gaussian Elimination/
  32.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  33.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  34.    wt: 1:   Step 1 Stick diagram and fractions/
  35.    wt: 1:   3 Solving Linear Equations/
  36.    wt: 1:   2 Formula Forward Use Evaluation/
  37.    wt: 1:   1 Working With Sets/
  38.    wt: 1:   Algebra Starter Lessons/
  39.    wt: 1:   70 Calculus Starter Lessons/
  40.    wt: 1:   Mathematics 506 Lessons/

Web Page Search

57 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   7 Links Lessons Elsewhere
  3.    wt: 2:   12 Links Lessons elsewhere
  4.    wt: 2:   4 Angles on Maps Plans drawn to scale
  5.    wt: 2:   3 Lengths and Areas on Maps and Plans
  6.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  7.    wt: 1:   About site lesson plans
  8.    wt: 1:   13 Velocity Vectors in Physics
  9.    wt: 1:   8 Parallel Vectors
  10.    wt: 1:   6 Vectors with Coordinates
  11.    wt: 1:   3 Navigation with Arrows or Vectors
  12.    wt: 1:   Parallel Lines and Parallel Transversals
  13.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  14.    wt: 1:   Parallel Lines and Interior Angles
  15.    wt: 1:   Straight Lines ASA Intersection Study More
  16.    wt: 1:   Straight Lines ASA Intersection Study
  17.    wt: 1:   Straight Lines Instersection Solving Equations
  18.    wt: 1:   Straight Lines Intersection of
  19.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  20.    wt: 1:   C Straight Lines Slope from Coordinates
  21.    wt: 1:   14 Straight Lines Equations General Case
  22.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  23.    wt: 1:   12 Straight Lines Graphing mx plus b
  24.    wt: 1:   11 Straight Lines Graphing y=mx
  25.    wt: 1:   10 Straight Lines through Origin Equations More
  26.    wt: 1:   9 Straight Lines through Origin Equations
  27.    wt: 1:   8 Straight Lines Equation for vertical
  28.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  29.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  30.    wt: 1:   1 Straight Lines Slope Concept
  31.    wt: 1:   Unit Circle Development of Trigonometry
  32.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  33.    wt: 1:   8 Unit Circle Development of Trigonometry
  34.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  35.    wt: 1:   Why Trigonometry the whyslopes view
  36.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  37.    wt: 1:   6 Intersection of lines by solving linear systems
  38.    wt: 1:   4 Equations for lines three forms
  39.    wt: 1:   3 Slope product for perpendicular lines
  40.    wt: 1:   1 Numerical view of lines and their equations
  41.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  42.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  43.    wt: 1:   14 Parallel Lines Postulate
  44.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  45.    wt: 1:   6 Figuring with Maps Not to Scale
  46.    wt: 1:   19 Signed Multiples of Vectors
  47.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  48.    wt: 1:   13 Arrows and Vectors in a Plane
  49.    wt: 1:   8 Coordinates for Maps and Planes
  50.    wt: 1:   3 signed coordinates for maps and planes
  51.    wt: 1:   A Related lessons in Volume 3
  52.    wt: 1:   Chapter 23 Links To Trigonometry
  53.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  54.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  55.    wt: 1:   Chapter 3 Algebra Starter Lessons
  56.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  57.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

468 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:   12 Links Lessons elsewhere
  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:   D Straight Lines Slope from Coordinates Examples
  18.    wt: 7:   C Straight Lines Slope from Coordinates
  19.    wt: 7:   14 Straight Lines Equations General Case
  20.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  21.    wt: 7:   12 Straight Lines Graphing mx plus b
  22.    wt: 7:   11 Straight Lines Graphing y=mx
  23.    wt: 7:   10 Straight Lines through Origin Equations More
  24.    wt: 7:   9 Straight Lines through Origin Equations
  25.    wt: 7:   8 Straight Lines Equation for vertical
  26.    wt: 7:   3 Straight Lines Slope as Tangent of Inclination Angle
  27.    wt: 7:   2 Straight Lines Slopes As Rise Over Run
  28.    wt: 7:   1 Straight Lines Slope Concept
  29.    wt: 7:   Unit Circle Development of Trigonometry
  30.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  31.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  32.    wt: 7:   Why Trigonometry the whyslopes view
  33.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  34.    wt: 7:   6 Intersection of lines by solving linear systems
  35.    wt: 7:   4 Equations for lines three forms
  36.    wt: 7:   3 Slope product for perpendicular lines
  37.    wt: 7:   1 Numerical view of lines and their equations
  38.    wt: 7:   A Measurement with Ruler Proper Use
  39.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  40.    wt: 7:   2 Measuring Area Directly
  41.    wt: 7:   1 Length Measurement
  42.    wt: 6:   A Global Time and Navigation
  43.    wt: 6:   15 Dot and Cross Product
  44.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  45.    wt: 6:   12 From Applied To Pure Mathematics
  46.    wt: 6:   11 Component Method
  47.    wt: 6:   10 Parallelogram Addition Method
  48.    wt: 6:   9 Head to Tail Coordinate View
  49.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  50.    wt: 6:   5 Head To Tail Arrow Addition
  51.    wt: 6:   4 Resultant of a Sum of Movements
  52.    wt: 6:   2 Signed Coordinates
  53.    wt: 6:   1 Unsigned Coordinates
  54.    wt: 6:   Vector and Complex Number Applet
  55.    wt: 6:   Proportionality of Line Segments From Parallel Transversals
  56.    wt: 6:   Triangle Angles Sum To 180 Degrees
  57.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  58.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  59.    wt: 6:   Analytic View of Triangle Construction or Line Instersection More
  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:   8 Triangles Cascade Problem Solving
  110.    wt: 6:   7 Trignometric Ratios Unit Circle
  111.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  112.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  113.    wt: 6:   3 Trigonometric Ratios sine and cosine
  114.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  115.    wt: 6:   1 Angle Measurement with Degrees
  116.    wt: 6:   Four Simple Exercises
  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:   Euclidean Geometry Elsewhere LINKS
  126.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  127.    wt: 6:   14 Parallel Lines Postulate
  128.    wt: 5:   16 cotangent function Definition Graph and Inverse
  129.    wt: 5:   15 cosecant function Definition Graph and Inverse
  130.    wt: 5:   14 secant function Definition Graph and Inverse
  131.    wt: 5:   13 cosecant function Definition Graph and Inverse
  132.    wt: 5:   12 motivation for term arctan
  133.    wt: 5:   11 arctan left inverse of tangent Graph
  134.    wt: 5:   10 arctan left inverse of tangent Definition
  135.    wt: 5:   9 motivation for name arcsin
  136.    wt: 5:   8 arcsin left inverse of sine Graph
  137.    wt: 5:   7 arcsin left inverse of sine Definition
  138.    wt: 5:   6 Graph of arccos function
  139.    wt: 5:   5 Swapping Coordinates is a reflection
  140.    wt: 5:   4 possible motivation for term arccos
  141.    wt: 5:   3 Left Inverse of cosine arccos definition
  142.    wt: 5:   2 cosine function more properties
  143.    wt: 5:   1 cosine function properties
  144.    wt: 5:   9 Summary Degrees to Radians and back
  145.    wt: 5:   8 Radian Measures of Common Angles
  146.    wt: 5:   7 Radian Measures in special Triangles
  147.    wt: 5:   6 Radian Measure to Degrees
  148.    wt: 5:   5 Degrees to Radian Measure
  149.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  150.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  151.    wt: 5:   2 Radian Measure Numerical Value of one degree
  152.    wt: 5:   1 Degrees and Radians Introduction
  153.    wt: 5:   4 graphing y=Asin(x c)
  154.    wt: 5:   3 graphing y=f(x c) plus K
  155.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  156.    wt: 5:   1 graphing y=f(x a)
  157.    wt: 5:   21 Logarithms Powers and Exponentials
  158.    wt: 5:   20 N th Roots of Complex Numbers
  159.    wt: 5:   19 N th Roots of Unity
  160.    wt: 5:   18 Sixth Roots of Unity
  161.    wt: 5:   17 Cube Roots of unity
  162.    wt: 5:   16 References and Originality Question
  163.    wt: 5:   15 Pythagorean Theorem Converse
  164.    wt: 5:   14 Law of cosines
  165.    wt: 5:   13 Trig Formulas for dot and cross Products
  166.    wt: 5:   12 cis formulas for sine cosines and tangent
  167.    wt: 5:   11 sine and cosine double triple angle formulas
  168.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  169.    wt: 5:   9 The complex number valued trig function cis
  170.    wt: 5:   7 Second Way to Calculate Products
  171.    wt: 5:   6 Field Properties of Complex Number
  172.    wt: 5:   5 An Easy Proof of the Distributive Law
  173.    wt: 5:   4 Multiplication Properties
  174.    wt: 5:   3 Addition Properties
  175.    wt: 5:   2 Complex Numbers made easier we hope
  176.    wt: 5:   1 Rectangular Polar Coordinates Review
  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:   3 Rectangular Coordinates Review
  202.    wt: 5:   2 Cartesian Coordinates with signs
  203.    wt: 5:   1 Cartesian Coordinates sans signs
  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: 3:   A Related lessons in Volume 3
  233.    wt: 2:   Maps Plans Drawings
  234.    wt: 2:   7 Links Lessons Elsewhere
  235.    wt: 2:   19 Signed Multiples of Vectors
  236.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  237.    wt: 2:   13 Arrows and Vectors in a Plane
  238.    wt: 2:   8 Coordinates for Maps and Planes
  239.    wt: 2:   Example 2 volume of a cone
  240.    wt: 2:   Example 1 volume of a pyramid
  241.    wt: 2:   Volume of Solid by Cross Sections Lesson
  242.    wt: 2:   Example 1. Area Between x and x squared
  243.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  244.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  245.    wt: 2:   Example 4 with x function of y
  246.    wt: 2:   Example 3
  247.    wt: 2:   Example 2
  248.    wt: 2:   Example 1
  249.    wt: 2:   Area Between Curves Lesson Take 2
  250.    wt: 2:   Area Between Curves Lesson Take 1
  251.    wt: 2:   Summary
  252.    wt: 2:   A Related Material in Volume 3
  253.    wt: 2:   5 Area Under Curve Exercise
  254.    wt: 2:   4 Definite Integrals Evaluation Exercises
  255.    wt: 2:   3 Two Chain Rule Method Exercises
  256.    wt: 2:   2 Indefinite Integrals Exercises
  257.    wt: 2:   1 Chain Rule in Reverse Integration Method
  258.    wt: 2:   4 Second derivative test exercise example
  259.    wt: 2:   3 Second derivative test
  260.    wt: 2:   2 Second derivative test prequel
  261.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  262.    wt: 2:   A Chain Rule Real Player video examples
  263.    wt: 2:   38 Formulas and derivatives for powers and roots
  264.    wt: 2:   36 Cube root derivative animated
  265.    wt: 2:   34 Derivative of exponential function
  266.    wt: 2:   33 Chain Rule Real Player video examples
  267.    wt: 2:   31 Derivatives of inverse functions
  268.    wt: 2:   30Chain Rule A Proof
  269.    wt: 2:   29 Chain Rule Optional Reading
  270.    wt: 2:   28 Chain Rule Preparation for a Proof
  271.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  272.    wt: 2:   26 Chain Rule Recognising outer inner functions
  273.    wt: 2:   25 Chain Rule Animated Examples Continued
  274.    wt: 2:   24 Chain Rule Animated Examples
  275.    wt: 2:   23 Chain Rule in general
  276.    wt: 2:   22 Chain Rule for polynomials
  277.    wt: 2:   21 Chain Rule for powers
  278.    wt: 2:   20 Chain Rule for Pulley Systems
  279.    wt: 2:   19 Chain Rule for linear functions
  280.    wt: 2:   18 Chain Rule Introduction
  281.    wt: 2:   17 Derivatives of quotients of sine and cosine
  282.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  283.    wt: 2:   15 sine and cosine derivatives 3rd step
  284.    wt: 2:   14 sine and cosine derivatives 2nd step
  285.    wt: 2:   13 sine and cosine derivatives 1st step
  286.    wt: 2:   12 Quotient rule examples
  287.    wt: 2:   11 Quotient rule
  288.    wt: 2:   10 Power rule for negative integers
  289.    wt: 2:   9 Reciprocal rule
  290.    wt: 2:   8 Differentiation of polynomials
  291.    wt: 2:   7 Animated Differentiation Examples
  292.    wt: 2:   6 Power rule from product rule
  293.    wt: 2:   5 Product Rule
  294.    wt: 2:   4 Sum Rule
  295.    wt: 2:   3 Motivation for Limit Definition Take 2
  296.    wt: 2:   2 Motivation for Limit Definition Take 1
  297.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  298.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  299.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  300.    wt: 2:   11 Limits at infinity Three Examples
  301.    wt: 2:   10 Three one sided limits with infinite values
  302.    wt: 2:   9 Limits Continuity and Composition
  303.    wt: 2:   8 Four Animated Examples
  304.    wt: 2:   7 Evaluation by immediate or delayed substitution
  305.    wt: 2:   6 Continuity at a point
  306.    wt: 2:   5 Jumps and absence of unlimited error control
  307.    wt: 2:   4 Numerical properties
  308.    wt: 2:   3 Decimal insights for limits continuity convergence
  309.    wt: 2:   2 Algebraic codification
  310.    wt: 2:   1 Numerical introduction
  311.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  312.    wt: 1:   About site lesson plans
  313.    wt: 1:   musings do not puiblish real numbers
  314.    wt: 1:   A Modular and Remainder Arithmetic
  315.    wt: 1:   A Signed Number Arithmetic Review
  316.    wt: 1:   26 More Less Greater Than Comparison
  317.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  318.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  319.    wt: 1:   23 Distributive Law Two Derivations
  320.    wt: 1:   22 Multiplication of Signed Numbers
  321.    wt: 1:   21 Addition of Multiples of a Single Vector
  322.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  323.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  324.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  325.    wt: 1:   15 Head to Tails in place Addition Associative
  326.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  327.    wt: 1:   12 Real Numbers Line Signed Coordinates
  328.    wt: 1:   11 Signed Number Addition and Addition Properties
  329.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  330.    wt: 1:   9 Division with Digits after Decimal Point
  331.    wt: 1:   8 Division and Mulplication of Compound Fractions
  332.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  333.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  334.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  335.    wt: 1:   4 Location of Point in Decimal Addition
  336.    wt: 1:   3 Location of Point in Decimal Multiplication
  337.    wt: 1:   2 Counting Digits in Decimal Multiplication
  338.    wt: 1:   1 Fractions with Finite Decimal Expansions
  339.    wt: 1:   E Long Division Methods more
  340.    wt: 1:   D Long Division Methods
  341.    wt: 1:   C Three Decimal Subtraction Methods
  342.    wt: 1:   B Decimal Comparison and Subtraction
  343.    wt: 1:   A Decimal Addition Columm Methods
  344.    wt: 1:   8 Column Multiplication Methods in General
  345.    wt: 1:   7 Decimals Multiplication Methods Examples
  346.    wt: 1:   6 Column Methods for Decimal Multiplication
  347.    wt: 1:   5 Distributive Law for Whole Numbers
  348.    wt: 1:   4 Commutative Law Groups Counting Form
  349.    wt: 1:   3 Multiplicative Counting Skills Principles
  350.    wt: 1:   2 Combing Counts Addition Skills and Principles
  351.    wt: 1:   1 The Counting Origins of Numbers
  352.    wt: 1:   5 Areas of Rectangles Revisited
  353.    wt: 1:   4 Fraction Operations Axiomatic Development
  354.    wt: 1:   3 Inequalities Algebraically
  355.    wt: 1:   2 Fraction Operations Physical Development
  356.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  357.    wt: 1:   5 Proportionality in Equivalent Fractions
  358.    wt: 1:   4 Rates Ratios and Proporitionality
  359.    wt: 1:   3 Proportionality Examples
  360.    wt: 1:   2 Algebraic View
  361.    wt: 1:   1 What is Proportionality
  362.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  363.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  364.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  365.    wt: 1:   6 Compound Interest Forward and Backwards
  366.    wt: 1:   5 Triangle Area Formula Backwards
  367.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  368.    wt: 1:   3 Linear Equation Literal Solution More
  369.    wt: 1:   2 Linear Equation Literal Solution
  370.    wt: 1:   1 Changing Calculations
  371.    wt: 1:   6 Equations and Systems Equivalent or Implied
  372.    wt: 1:   5 Equality in Algebra
  373.    wt: 1:   4 Subtraction and Division Axioms
  374.    wt: 1:   3 Product Axioms Two Forms
  375.    wt: 1:   2 Addition and Multiplication Axioms
  376.    wt: 1:   1 Equivalent Computation Rules
  377.    wt: 1:   5 Greater More Less Than Signs in General
  378.    wt: 1:   4 Comparison of Negative Numbers
  379.    wt: 1:   3 More and Less Than with Unlike Signs
  380.    wt: 1:   2 More and Less Than for Counts and Measures
  381.    wt: 1:   1 Real Numbers Comparison
  382.    wt: 1:   16 Real Numbers Comparison
  383.    wt: 1:   15 Real Number Division
  384.    wt: 1:   14 Real Number Multiplication
  385.    wt: 1:   13 Real Number Subtraction
  386.    wt: 1:   12 Real Number Additive Inverses or Negatives
  387.    wt: 1:   11 Real Number Addition
  388.    wt: 1:   10 Real Number Lengths and Signs
  389.    wt: 1:   9 Coordinates for Regions in Space
  390.    wt: 1:   7 Real Numbers as Line Cordinates
  391.    wt: 1:   6 Unsigned Real Numbers
  392.    wt: 1:   5 Rational Numbers More
  393.    wt: 1:   4 Rational Numbers
  394.    wt: 1:   3 Fractions
  395.    wt: 1:   2 Integers
  396.    wt: 1:   1 Whole and Natural Numbers
  397.    wt: 1:   5 Independent versus Dependent Variables
  398.    wt: 1:   4 Changing Letters
  399.    wt: 1:   3 Geometric Formulas and Function Notation
  400.    wt: 1:   2 Computation Rules Evaluation
  401.    wt: 1:   1 Formulas Dependence and Function Notation
  402.    wt: 1:   More Exercises
  403.    wt: 1:   Simple Exercises
  404.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  405.    wt: 1:   4 GE III Animated Examples
  406.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  407.    wt: 1:   3 GE III Equation Addition and Multiplication
  408.    wt: 1:   2 GE II Comparison
  409.    wt: 1:   1 GE Substitution four examples
  410.    wt: 1:   4 Solving a triangular system exercise
  411.    wt: 1:   3 Solving triangular system example
  412.    wt: 1:   2 Essentially one exercises three with solution
  413.    wt: 1:   1 Essentially One Unknown
  414.    wt: 1:   6 Algebraic Solution Example
  415.    wt: 1:   5 Algebraic Solutions Introduction
  416.    wt: 1:   4 Four Examples Fractional Coefficients
  417.    wt: 1:   3 Four Examples
  418.    wt: 1:   2 Three Examples
  419.    wt: 1:   1 Proper Equal Sign Usage
  420.    wt: 1:   Skill Development Notes
  421.    wt: 1:   10 One Example
  422.    wt: 1:   9 Three Examples
  423.    wt: 1:   8 One Example
  424.    wt: 1:   7 Two Examples
  425.    wt: 1:   6 Three Examples
  426.    wt: 1:   5 Three Examples
  427.    wt: 1:   4 Two Examples
  428.    wt: 1:   3 Two Examples
  429.    wt: 1:   2 Three Examples
  430.    wt: 1:   Using Letters for Physical Quantities
  431.    wt: 1:   Formula Usage Show Work Format
  432.    wt: 1:   13 Naming Identifying Formulas with Words
  433.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  434.    wt: 1:   11 Volume of Sphere
  435.    wt: 1:   10 Volume of Pyramid
  436.    wt: 1:   9 Volume of Cone
  437.    wt: 1:   8 Compound Interest Formula Evaluation
  438.    wt: 1:   7 Compound Interest Formula Introduction
  439.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  440.    wt: 1:   5 Box Volume Formula Example
  441.    wt: 1:   4 Circle Area Formula Example
  442.    wt: 1:   3 Triangle Area Formula Example
  443.    wt: 1:   2 Another Rectangle Area Formula Example
  444.    wt: 1:   1 Written work formats for developing and showing skill
  445.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  446.    wt: 1:   9 Sets in Probability and Statistics
  447.    wt: 1:   8 Sets of Numbers
  448.    wt: 1:   7 Cautious or Safe Set Construction
  449.    wt: 1:   6 Power Set Notation
  450.    wt: 1:   5 Product Builder Notation
  451.    wt: 1:   4 Subset Builder Notation
  452.    wt: 1:   3 Counting with Sets etc
  453.    wt: 1:   2 Venn Diagrams
  454.    wt: 1:   1 Finite Sets
  455.    wt: 1:   6 Three Notions of What is a Variable
  456.    wt: 1:   5 Talking about Numbers and Quantities
  457.    wt: 1:   4 A Brief Story of numbers and algebra
  458.    wt: 1:   3 Adding Words To Arithmetic
  459.    wt: 1:   2 What is a Variable
  460.    wt: 1:   1 Three Skills For Algebra
  461.    wt: 1:   About Folder Contents
  462.    wt: 1:   3 signed coordinates for maps and planes
  463.    wt: 1:   Chapter 23 Links To Trigonometry
  464.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  465.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  466.    wt: 1:   Chapter 3 Algebra Starter Lessons
  467.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  468.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
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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