Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic
and Pattern Based Reason to inform and amuse thinkers and avid readers, studying or not. Enjoy.

Logic mastery strengthens comprehension and improve home, work & study habits.
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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

About: Site material shows how common troubles stem from steps too large or missing. Site material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin. If one site element is not to your liking, try another. Each is different. Many are unique

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local 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. Reform: look before you leap - plan all in detail first.

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:   9 Lines and Slopes Take 2 with tangent function/
  2.    wt: 7:   4 Lines and Slopes Take 1/
  3.    wt: 7:   1 Maps Plans Measurement/
  4.    wt: 6:   13 Vectors/
  5.    wt: 6:   11 Parallel Straight Lines and Transversals/
  6.    wt: 6:   10 Intersecting Straight Lines and Transversals/
  7.    wt: 6:   8 Unit Circle Trigonometry/
  8.    wt: 6:   6 Trigonometry first steps/
  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:   7 Axioms Logic and Equivalent Equations/
  18.    wt: 2:   Step 4 Gaussian Elimination/
  19.    wt: 2:   Step 3 Easy systems in 2 or more unknowns/
  20.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  21.    wt: 2:   Step 1 Stick diagram and fractions/
  22.    wt: 2:   3 Solving Linear Equations/
  23.    wt: 1:   B Real Numbers Extrinsic Development/
  24.    wt: 1:   A Origins of Counting and Figuring Methods/
  25.    wt: 1:   10 Examples of Algebraic Reasoning/
  26.    wt: 1:   9 Proportionality Backwards and Forwards/
  27.    wt: 1:   8 Unifying Theme For Algebra/
  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:   2 Formula Forward Use Evaluation/
  32.    wt: 1:   1 Working With Sets/
  33.    wt: 1:   Algebra Starter Lessons/
  34.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  35.    wt: 1:   5 Lessons on Integration/
  36.    wt: 1:   4 Lessons on Using Derivatives/
  37.    wt: 1:   38 Lessons on Calculating Derivatives/
  38.    wt: 1:   13 Lessons on Limits and Continuity/
  39.    wt: 1:   70 Calculus Starter Lessons/
  40.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/

Web Page Search

63 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   Straight Lines Instersection Solving Equations
  3.    wt: 2:   14 Straight Lines Equations General Case
  4.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  5.    wt: 2:   10 Straight Lines through Origin Equations More
  6.    wt: 2:   9 Straight Lines through Origin Equations
  7.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  8.    wt: 2:   Why Trigonometry the whyslopes view
  9.    wt: 2:   4 Equations for lines three forms
  10.    wt: 2:   1 Numerical view of lines and their equations
  11.    wt: 2:   4 Angles on Maps Plans drawn to scale
  12.    wt: 2:   3 Lengths and Areas on Maps and Plans
  13.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  14.    wt: 1:   About site lesson plans
  15.    wt: 1:   1 Calculator Starter Exercises
  16.    wt: 1:   13 Velocity Vectors in Physics
  17.    wt: 1:   8 Parallel Vectors
  18.    wt: 1:   6 Vectors with Coordinates
  19.    wt: 1:   3 Navigation with Arrows or Vectors
  20.    wt: 1:   Parallel Lines and Parallel Transversals
  21.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  22.    wt: 1:   Parallel Lines and Interior Angles
  23.    wt: 1:   Straight Lines ASA Intersection Study More
  24.    wt: 1:   Straight Lines ASA Intersection Study
  25.    wt: 1:   Straight Lines Intersection of
  26.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  27.    wt: 1:   C Straight Lines Slope from Coordinates
  28.    wt: 1:   12 Straight Lines Graphing mx plus b
  29.    wt: 1:   11 Straight Lines Graphing y=mx
  30.    wt: 1:   8 Straight Lines Equation for vertical
  31.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  32.    wt: 1:   1 Straight Lines Slope Concept
  33.    wt: 1:   Unit Circle Development of Trigonometry
  34.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  35.    wt: 1:   8 Unit Circle Development of Trigonometry
  36.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  37.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  38.    wt: 1:   6 Intersection of lines by solving linear systems
  39.    wt: 1:   5 Algebraic View of Slopes
  40.    wt: 1:   3 Slope product for perpendicular lines
  41.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  42.    wt: 1:   14 Parallel Lines Postulate
  43.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  44.    wt: 1:   6 Figuring with Maps Not to Scale
  45.    wt: 1:   19 Signed Multiples of Vectors
  46.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  47.    wt: 1:   13 Arrows and Vectors in a Plane
  48.    wt: 1:   6 Equations and Systems Equivalent or Implied
  49.    wt: 1:   8 Coordinates for Maps and Planes
  50.    wt: 1:   3 signed coordinates for maps and planes
  51.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  52.    wt: 1:   Chapter 23 Links To Trigonometry
  53.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  54.    wt: 1:   Chapter 18. Slopes Areas Integration
  55.    wt: 1:   Chapter 12. Units and Slopes
  56.    wt: 1:   Chapter 10 Slopes and Units
  57.    wt: 1:   Chapter 7 Slopes and Velocity
  58.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  59.    wt: 1:   Chapter 2. Slopes and Ski Trails
  60.    wt: 1:   Chapter 15. Solving Linear Equations
  61.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  62.    wt: 1:   Chapter 3 Algebra Starter Lessons
  63.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

494 matches:

  1.    wt: 9:   14 Straight Lines Equations General Case
  2.    wt: 9:   13 Straight Lines Finding Equations from 2 points
  3.    wt: 9:   10 Straight Lines through Origin Equations More
  4.    wt: 9:   9 Straight Lines through Origin Equations
  5.    wt: 9:   2 Straight Lines Slopes As Rise Over Run
  6.    wt: 9:   4 Equations for lines three forms
  7.    wt: 9:   1 Numerical view of lines and their equations
  8.    wt: 9:   4 Angles on Maps Plans drawn to scale
  9.    wt: 9:   3 Lengths and Areas on Maps and Plans
  10.    wt: 8:   Straight Lines Instersection Solving Equations
  11.    wt: 8:   D Straight Lines Slope from Coordinates Examples
  12.    wt: 8:   C Straight Lines Slope from Coordinates
  13.    wt: 8:   12 Straight Lines Graphing mx plus b
  14.    wt: 8:   11 Straight Lines Graphing y=mx
  15.    wt: 8:   8 Straight Lines Equation for vertical
  16.    wt: 8:   3 Straight Lines Slope as Tangent of Inclination Angle
  17.    wt: 8:   1 Straight Lines Slope Concept
  18.    wt: 8:   Why Trigonometry the whyslopes view
  19.    wt: 8:   6 Intersection of lines by solving linear systems
  20.    wt: 8:   5 Algebraic View of Slopes
  21.    wt: 8:   3 Slope product for perpendicular lines
  22.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  23.    wt: 8:   6 Figuring with Maps Not to Scale
  24.    wt: 7:   13 Velocity Vectors in Physics
  25.    wt: 7:   8 Parallel Vectors
  26.    wt: 7:   6 Vectors with Coordinates
  27.    wt: 7:   3 Navigation with Arrows or Vectors
  28.    wt: 7:   Parallel Lines and Parallel Transversals
  29.    wt: 7:   Parallel Lines and Alternating Corresponding Angles
  30.    wt: 7:   Parallel Lines and Interior Angles
  31.    wt: 7:   Straight Lines ASA Intersection Study More
  32.    wt: 7:   Straight Lines ASA Intersection Study
  33.    wt: 7:   Straight Lines Intersection of
  34.    wt: 7:   B Straight Line Slope Scaling Properties More
  35.    wt: 7:   A Straight Line Slope Scaling Properties
  36.    wt: 7:   7 Tangent Function is odd on this domain
  37.    wt: 7:   6 Tangent Function Inclination Angle Take 2
  38.    wt: 7:   5 Tangent Function Graph
  39.    wt: 7:   4 Tangent Function Properties
  40.    wt: 7:   Unit Circle Development of Trigonometry
  41.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  42.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  43.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  44.    wt: 7:   Four Simple Exercises
  45.    wt: 7:   12 Links Lessons elsewhere
  46.    wt: 7:   11 A Partial Summary
  47.    wt: 7:   10 Midpoint of [a b] and [b a]
  48.    wt: 7:   9 Midpoint Coordinates Half Endpoint Sum
  49.    wt: 7:   8 Mid Point Formula
  50.    wt: 7:   7 Exercises to test skill and concept mastery
  51.    wt: 7:   2 point slope equation for a line
  52.    wt: 7:   What is and is not here
  53.    wt: 7:   A Measurement with Ruler Proper Use
  54.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  55.    wt: 7:   2 Measuring Area Directly
  56.    wt: 7:   1 Length Measurement
  57.    wt: 6:   A Global Time and Navigation
  58.    wt: 6:   15 Dot and Cross Product
  59.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  60.    wt: 6:   12 From Applied To Pure Mathematics
  61.    wt: 6:   11 Component Method
  62.    wt: 6:   10 Parallelogram Addition Method
  63.    wt: 6:   9 Head to Tail Coordinate View
  64.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  65.    wt: 6:   5 Head To Tail Arrow Addition
  66.    wt: 6:   4 Resultant of a Sum of Movements
  67.    wt: 6:   2 Signed Coordinates
  68.    wt: 6:   1 Unsigned Coordinates
  69.    wt: 6:   Vector and Complex Number Applet
  70.    wt: 6:   Proportionality of Line Segments From Parallel Transversals
  71.    wt: 6:   Triangle Angles Sum To 180 Degrees
  72.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  73.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  74.    wt: 6:   Analytic View of Triangle Construction or Line Instersection More
  75.    wt: 6:   17 tangent function angle sum formulas
  76.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  77.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  78.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  79.    wt: 6:   32 seven rows of pascals triangle
  80.    wt: 6:   31 basic secant cosecant cotangent trig identities
  81.    wt: 6:   30 unit circle calculation of six trigonometric functions
  82.    wt: 6:   29 secant cosecant and cotangent for acute angles
  83.    wt: 6:   28 Expressing products of sines cosines as sums
  84.    wt: 6:   27 Logarithmic use of products of sines and cosines
  85.    wt: 6:   26 Formulas for products of sines and cosines
  86.    wt: 6:   25 tangent double angle formula Slope connection
  87.    wt: 6:   24 tangent Angle Difference Formula
  88.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  89.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  90.    wt: 6:   21 sine and cosine Half Angle Formulas
  91.    wt: 6:   20 sine and cosine Double Angle Formulas
  92.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  93.    wt: 6:   18 sum of sinusoidal waves as a single wave
  94.    wt: 6:   17G Pythagorean Theorem Converse
  95.    wt: 6:   17F Law of cosines
  96.    wt: 6:   17E Trig Formulas for dot and cross Products
  97.    wt: 6:   17D cis formulas for sine cosines and tangent
  98.    wt: 6:   17C sine and cosine double triple angle formulas
  99.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  100.    wt: 6:   17A The complex number valued trig function cis
  101.    wt: 6:   16 Right Triangle Complementary Angle Relations
  102.    wt: 6:   15 sine cosine Complementary Angle Relations
  103.    wt: 6:   14 cosine even and sine and tangent are odd
  104.    wt: 6:   13 Graph of tangent function many periods
  105.    wt: 6:   12 Graph of tangent function for one period
  106.    wt: 6:   11 tangent function undefined when terminal side vertical
  107.    wt: 6:   10 Graphs of sines and cosines many periods
  108.    wt: 6:   9 Graphs of sine and cosine over one period
  109.    wt: 6:   8 period of tangent function
  110.    wt: 6:   7 period of sine and cosine
  111.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  112.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  113.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  114.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  115.    wt: 6:   2 Quadrant I reference Angles
  116.    wt: 6:   1 Unit Points Reflections Rotations
  117.    wt: 6:   8 Unit Circle Development of Trigonometry
  118.    wt: 6:   8 Triangles Cascade Problem Solving
  119.    wt: 6:   7 Trignometric Ratios Unit Circle
  120.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  121.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  122.    wt: 6:   3 Trigonometric Ratios sine and cosine
  123.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  124.    wt: 6:   1 Angle Measurement with Degrees
  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: 3:   6 Equations and Systems Equivalent or Implied
  233.    wt: 2:   Maps Plans Drawings
  234.    wt: 2:   19 Signed Multiples of Vectors
  235.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  236.    wt: 2:   13 Arrows and Vectors in a Plane
  237.    wt: 2:   5 Equality in Algebra
  238.    wt: 2:   4 Subtraction and Division Axioms
  239.    wt: 2:   3 Product Axioms Two Forms
  240.    wt: 2:   2 Addition and Multiplication Axioms
  241.    wt: 2:   1 Equivalent Computation Rules
  242.    wt: 2:   8 Coordinates for Maps and Planes
  243.    wt: 2:   More Exercises
  244.    wt: 2:   Simple Exercises
  245.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  246.    wt: 2:   4 GE III Animated Examples
  247.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  248.    wt: 2:   3 GE III Equation Addition and Multiplication
  249.    wt: 2:   2 GE II Comparison
  250.    wt: 2:   1 GE Substitution four examples
  251.    wt: 2:   4 Solving a triangular system exercise
  252.    wt: 2:   3 Solving triangular system example
  253.    wt: 2:   2 Essentially one exercises three with solution
  254.    wt: 2:   1 Essentially One Unknown
  255.    wt: 2:   6 Algebraic Solution Example
  256.    wt: 2:   5 Algebraic Solutions Introduction
  257.    wt: 2:   4 Four Examples Fractional Coefficients
  258.    wt: 2:   3 Four Examples
  259.    wt: 2:   2 Three Examples
  260.    wt: 2:   1 Proper Equal Sign Usage
  261.    wt: 2:   Skill Development Notes
  262.    wt: 2:   10 One Example
  263.    wt: 2:   9 Three Examples
  264.    wt: 2:   8 One Example
  265.    wt: 2:   7 Two Examples
  266.    wt: 2:   6 Three Examples
  267.    wt: 2:   5 Three Examples
  268.    wt: 2:   4 Two Examples
  269.    wt: 2:   3 Two Examples
  270.    wt: 2:   2 Three Examples
  271.    wt: 2:   Using Letters for Physical Quantities
  272.    wt: 2:   Formula Usage Show Work Format
  273.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  274.    wt: 2:   Chapter 23 Links To Trigonometry
  275.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  276.    wt: 2:   Chapter 18. Slopes Areas Integration
  277.    wt: 2:   Chapter 12. Units and Slopes
  278.    wt: 2:   Chapter 10 Slopes and Units
  279.    wt: 2:   Chapter 7 Slopes and Velocity
  280.    wt: 2:   Chapter 6. Slopes and Vertical Shifts
  281.    wt: 2:   Chapter 2. Slopes and Ski Trails
  282.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  283.    wt: 1:   About site lesson plans
  284.    wt: 1:   1 Calculator Starter Exercises
  285.    wt: 1:   musings do not puiblish real numbers
  286.    wt: 1:   A Modular and Remainder Arithmetic
  287.    wt: 1:   A Signed Number Arithmetic Review
  288.    wt: 1:   26 More Less Greater Than Comparison
  289.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  290.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  291.    wt: 1:   23 Distributive Law Two Derivations
  292.    wt: 1:   22 Multiplication of Signed Numbers
  293.    wt: 1:   21 Addition of Multiples of a Single Vector
  294.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  295.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  296.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  297.    wt: 1:   15 Head to Tails in place Addition Associative
  298.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  299.    wt: 1:   12 Real Numbers Line Signed Coordinates
  300.    wt: 1:   11 Signed Number Addition and Addition Properties
  301.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  302.    wt: 1:   9 Division with Digits after Decimal Point
  303.    wt: 1:   8 Division and Mulplication of Compound Fractions
  304.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  305.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  306.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  307.    wt: 1:   4 Location of Point in Decimal Addition
  308.    wt: 1:   3 Location of Point in Decimal Multiplication
  309.    wt: 1:   2 Counting Digits in Decimal Multiplication
  310.    wt: 1:   1 Fractions with Finite Decimal Expansions
  311.    wt: 1:   E Long Division Methods more
  312.    wt: 1:   D Long Division Methods
  313.    wt: 1:   C Three Decimal Subtraction Methods
  314.    wt: 1:   B Decimal Comparison and Subtraction
  315.    wt: 1:   A Decimal Addition Columm Methods
  316.    wt: 1:   8 Column Multiplication Methods in General
  317.    wt: 1:   7 Decimals Multiplication Methods Examples
  318.    wt: 1:   6 Column Methods for Decimal Multiplication
  319.    wt: 1:   5 Distributive Law for Whole Numbers
  320.    wt: 1:   4 Commutative Law Groups Counting Form
  321.    wt: 1:   3 Multiplicative Counting Skills Principles
  322.    wt: 1:   2 Combing Counts Addition Skills and Principles
  323.    wt: 1:   1 The Counting Origins of Numbers
  324.    wt: 1:   5 Areas of Rectangles Revisited
  325.    wt: 1:   4 Fraction Operations Axiomatic Development
  326.    wt: 1:   3 Inequalities Algebraically
  327.    wt: 1:   2 Fraction Operations Physical Development
  328.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  329.    wt: 1:   5 Proportionality in Equivalent Fractions
  330.    wt: 1:   4 Rates Ratios and Proporitionality
  331.    wt: 1:   3 Proportionality Examples
  332.    wt: 1:   2 Algebraic View
  333.    wt: 1:   1 What is Proportionality
  334.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  335.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  336.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  337.    wt: 1:   6 Compound Interest Forward and Backwards
  338.    wt: 1:   5 Triangle Area Formula Backwards
  339.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  340.    wt: 1:   3 Linear Equation Literal Solution More
  341.    wt: 1:   2 Linear Equation Literal Solution
  342.    wt: 1:   1 Changing Calculations
  343.    wt: 1:   5 Greater More Less Than Signs in General
  344.    wt: 1:   4 Comparison of Negative Numbers
  345.    wt: 1:   3 More and Less Than with Unlike Signs
  346.    wt: 1:   2 More and Less Than for Counts and Measures
  347.    wt: 1:   1 Real Numbers Comparison
  348.    wt: 1:   16 Real Numbers Comparison
  349.    wt: 1:   15 Real Number Division
  350.    wt: 1:   14 Real Number Multiplication
  351.    wt: 1:   13 Real Number Subtraction
  352.    wt: 1:   12 Real Number Additive Inverses or Negatives
  353.    wt: 1:   11 Real Number Addition
  354.    wt: 1:   10 Real Number Lengths and Signs
  355.    wt: 1:   9 Coordinates for Regions in Space
  356.    wt: 1:   7 Real Numbers as Line Cordinates
  357.    wt: 1:   6 Unsigned Real Numbers
  358.    wt: 1:   5 Rational Numbers More
  359.    wt: 1:   4 Rational Numbers
  360.    wt: 1:   3 Fractions
  361.    wt: 1:   2 Integers
  362.    wt: 1:   1 Whole and Natural Numbers
  363.    wt: 1:   5 Independent versus Dependent Variables
  364.    wt: 1:   4 Changing Letters
  365.    wt: 1:   3 Geometric Formulas and Function Notation
  366.    wt: 1:   2 Computation Rules Evaluation
  367.    wt: 1:   1 Formulas Dependence and Function Notation
  368.    wt: 1:   13 Naming Identifying Formulas with Words
  369.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  370.    wt: 1:   11 Volume of Sphere
  371.    wt: 1:   10 Volume of Pyramid
  372.    wt: 1:   9 Volume of Cone
  373.    wt: 1:   8 Compound Interest Formula Evaluation
  374.    wt: 1:   7 Compound Interest Formula Introduction
  375.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  376.    wt: 1:   5 Box Volume Formula Example
  377.    wt: 1:   4 Circle Area Formula Example
  378.    wt: 1:   3 Triangle Area Formula Example
  379.    wt: 1:   2 Another Rectangle Area Formula Example
  380.    wt: 1:   1 Written work formats for developing and showing skill
  381.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  382.    wt: 1:   9 Sets in Probability and Statistics
  383.    wt: 1:   8 Sets of Numbers
  384.    wt: 1:   7 Cautious or Safe Set Construction
  385.    wt: 1:   6 Power Set Notation
  386.    wt: 1:   5 Product Builder Notation
  387.    wt: 1:   4 Subset Builder Notation
  388.    wt: 1:   3 Counting with Sets etc
  389.    wt: 1:   2 Venn Diagrams
  390.    wt: 1:   1 Finite Sets
  391.    wt: 1:   6 Three Notions of What is a Variable
  392.    wt: 1:   5 Talking about Numbers and Quantities
  393.    wt: 1:   4 A Brief Story of numbers and algebra
  394.    wt: 1:   3 Adding Words To Arithmetic
  395.    wt: 1:   2 What is a Variable
  396.    wt: 1:   1 Three Skills For Algebra
  397.    wt: 1:   About Folder Contents
  398.    wt: 1:   3 signed coordinates for maps and planes
  399.    wt: 1:   Example 2 volume of a cone
  400.    wt: 1:   Example 1 volume of a pyramid
  401.    wt: 1:   Volume of Solid by Cross Sections Lesson
  402.    wt: 1:   Example 1. Area Between x and x squared
  403.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  404.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  405.    wt: 1:   Example 4 with x function of y
  406.    wt: 1:   Example 3
  407.    wt: 1:   Example 2
  408.    wt: 1:   Example 1
  409.    wt: 1:   Area Between Curves Lesson Take 2
  410.    wt: 1:   Area Between Curves Lesson Take 1
  411.    wt: 1:   Summary
  412.    wt: 1:   A Related Material in Volume 3
  413.    wt: 1:   5 Area Under Curve Exercise
  414.    wt: 1:   4 Definite Integrals Evaluation Exercises
  415.    wt: 1:   3 Two Chain Rule Method Exercises
  416.    wt: 1:   2 Indefinite Integrals Exercises
  417.    wt: 1:   1 Chain Rule in Reverse Integration Method
  418.    wt: 1:   A Related lessons in Volume 3
  419.    wt: 1:   4 Second derivative test exercise example
  420.    wt: 1:   3 Second derivative test
  421.    wt: 1:   2 Second derivative test prequel
  422.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  423.    wt: 1:   A Chain Rule Real Player video examples
  424.    wt: 1:   38 Formulas and derivatives for powers and roots
  425.    wt: 1:   36 Cube root derivative animated
  426.    wt: 1:   34 Derivative of exponential function
  427.    wt: 1:   33 Chain Rule Real Player video examples
  428.    wt: 1:   31 Derivatives of inverse functions
  429.    wt: 1:   30Chain Rule A Proof
  430.    wt: 1:   29 Chain Rule Optional Reading
  431.    wt: 1:   28 Chain Rule Preparation for a Proof
  432.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  433.    wt: 1:   26 Chain Rule Recognising outer inner functions
  434.    wt: 1:   25 Chain Rule Animated Examples Continued
  435.    wt: 1:   24 Chain Rule Animated Examples
  436.    wt: 1:   23 Chain Rule in general
  437.    wt: 1:   22 Chain Rule for polynomials
  438.    wt: 1:   21 Chain Rule for powers
  439.    wt: 1:   20 Chain Rule for Pulley Systems
  440.    wt: 1:   19 Chain Rule for linear functions
  441.    wt: 1:   18 Chain Rule Introduction
  442.    wt: 1:   17 Derivatives of quotients of sine and cosine
  443.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  444.    wt: 1:   15 sine and cosine derivatives 3rd step
  445.    wt: 1:   14 sine and cosine derivatives 2nd step
  446.    wt: 1:   13 sine and cosine derivatives 1st step
  447.    wt: 1:   12 Quotient rule examples
  448.    wt: 1:   11 Quotient rule
  449.    wt: 1:   10 Power rule for negative integers
  450.    wt: 1:   9 Reciprocal rule
  451.    wt: 1:   8 Differentiation of polynomials
  452.    wt: 1:   7 Animated Differentiation Examples
  453.    wt: 1:   6 Power rule from product rule
  454.    wt: 1:   5 Product Rule
  455.    wt: 1:   4 Sum Rule
  456.    wt: 1:   3 Motivation for Limit Definition Take 2
  457.    wt: 1:   2 Motivation for Limit Definition Take 1
  458.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  459.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  460.    wt: 1:   11 Limits at infinity Three Examples
  461.    wt: 1:   10 Three one sided limits with infinite values
  462.    wt: 1:   9 Limits Continuity and Composition
  463.    wt: 1:   8 Four Animated Examples
  464.    wt: 1:   7 Evaluation by immediate or delayed substitution
  465.    wt: 1:   6 Continuity at a point
  466.    wt: 1:   5 Jumps and absence of unlimited error control
  467.    wt: 1:   4 Numerical properties
  468.    wt: 1:   3 Decimal insights for limits continuity convergence
  469.    wt: 1:   2 Algebraic codification
  470.    wt: 1:   1 Numerical introduction
  471.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  472.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  473.    wt: 1:   Chapter 22 Complex Numbers
  474.    wt: 1:   Chapter 21 Arrow Addition
  475.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  476.    wt: 1:   Chapter 17. Area Approximation
  477.    wt: 1:   Chapter 16. Velocity Approximation
  478.    wt: 1:   Chapter 15. Slope Approximation
  479.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  480.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  481.    wt: 1:   Chapter 13. Acceleration
  482.    wt: 1:   Chapter 11. Graphing Slope versus Position
  483.    wt: 1:   Chapter 9 About First Courses in Calculus
  484.    wt: 1:   Chapter 8. Slope Interpretation
  485.    wt: 1:   Chapter 5. Slope Sign Tests
  486.    wt: 1:   Chapter 4. More Slope Sign Analysis
  487.    wt: 1:   Chapter 3. Slope Sign Analysis
  488.    wt: 1:   Chapter 1.Introduction
  489.    wt: 1:   Fall 1983 Calculus Appetizer
  490.    wt: 1:   Foreword
  491.    wt: 1:   Chapter 15. Solving Linear Equations
  492.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  493.    wt: 1:   Chapter 3 Algebra Starter Lessons
  494.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

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 bicylce?

Death Penalty: How Texas sent an innocent man to his death - The wrong Carlos.

For home-tutoring or -schooling, or for schools or colleges with course content control: Secondary Mathematics for Ages 11+, A Practical Approach.

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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