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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22 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   15 Arc or Inverse Trigonometric Function/
  3.    wt: 6:   13 Vectors/
  4.    wt: 6:   8 Unit Circle Trigonometry/
  5.    wt: 6:   7 Complex Numbers/
  6.    wt: 6:   6 Trigonometry first steps/
  7.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  8.    wt: 5:   12 Function Translating and Rescaling/
  9.    wt: 5:   11 Parallel Straight Lines and Transversals/
  10.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  11.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  18.    wt: 1:   1 Five Polynomial Operations/
  19.    wt: 1:   4 Computation Rules and Function Notation/
  20.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  21.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  22.    wt: 1:   Volume 1B Mathematics Curriculum Notes/

Web Page Search

133 matches:

  1.    wt: 4:   Postscript Pythagorean Theorem yet another proof
  2.    wt: 3:   9 Pythagorean Theorem Chinese Square Proof
  3.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  4.    wt: 3:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  5.    wt: 2:   Maps Plans Drawings
  6.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  7.    wt: 2:   17G Pythagorean Theorem Converse
  8.    wt: 2:   15 Pythagorean Theorem Converse
  9.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  10.    wt: 2:   6 Figuring with Maps Not to Scale
  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:   G.3 Constant Difference Theorem Proof
  14.    wt: 2:   B3 Bolzano Weierstrass Theorem
  15.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  16.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  17.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  18.    wt: 1:   6 polynomials etc
  19.    wt: 1:   About site lesson plans
  20.    wt: 1:   key notes and themes
  21.    wt: 1:   Theory of Knowledge
  22.    wt: 1:   Education in mathematics science and technology
  23.    wt: 1:   Trois Notions qui menent a algebre
  24.    wt: 1:   sign monoticity analysis example 4
  25.    wt: 1:   sign monoticity analysis example 3
  26.    wt: 1:   sign monoticity analysis example 2
  27.    wt: 1:   sign monoticity analysis example 1
  28.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  29.    wt: 1:   10 Interval Notation
  30.    wt: 1:   6 Set Existence Formation and Notation
  31.    wt: 1:   5 Function notation for geometric transformations
  32.    wt: 1:   4 Function notation in and beyond mathematics
  33.    wt: 1:   2 Algebraic use of function notation
  34.    wt: 1:   1 Geometric Introduction of Function Notation
  35.    wt: 1:   8 Notes for instructors or tutors
  36.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  37.    wt: 1:   4 Polynomials Long division linear divisor
  38.    wt: 1:   3 Polynomials Multiplication Addition
  39.    wt: 1:   1 Polynomials Distributive Law
  40.    wt: 1:   13 Velocity Vectors in Physics
  41.    wt: 1:   8 Parallel Vectors
  42.    wt: 1:   6 Vectors with Coordinates
  43.    wt: 1:   3 Navigation with Arrows or Vectors
  44.    wt: 1:   Vector and Complex Number Applet
  45.    wt: 1:   30 unit circle calculation of six trigonometric functions
  46.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  47.    wt: 1:   17A The complex number valued trig function cis
  48.    wt: 1:   Unit Circle Development of Trigonometry
  49.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  50.    wt: 1:   20 N th Roots of Complex Numbers
  51.    wt: 1:   9 The complex number valued trig function cis
  52.    wt: 1:   8 Unit Circle Development of Trigonometry
  53.    wt: 1:   6 Field Properties of Complex Number
  54.    wt: 1:   5 An Easy Proof of the Distributive Law
  55.    wt: 1:   2 Complex Numbers made easier we hope
  56.    wt: 1:   Appetizer A Complex Number Applet
  57.    wt: 1:   7 Trignometric Ratios Unit Circle
  58.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  59.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  60.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  61.    wt: 1:   3 Trigonometric Ratios sine and cosine
  62.    wt: 1:   Why Trigonometry the whyslopes view
  63.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  64.    wt: 1:   What is and is not here
  65.    wt: 1:   13 Pythagorean spatial distance formulas
  66.    wt: 1:   10 Pythagorean plane distance formula
  67.    wt: 1:   7 Complex Numbers Appetizer
  68.    wt: 1:   PS H Distributive Law For Complex Numbers
  69.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  70.    wt: 1:   musings do not puiblish real numbers
  71.    wt: 1:   19 Signed Multiples of Vectors
  72.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  73.    wt: 1:   13 Arrows and Vectors in a Plane
  74.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  75.    wt: 1:   8 Coordinates for Maps and Planes
  76.    wt: 1:   3 Geometric Formulas and Function Notation
  77.    wt: 1:   1 Formulas Dependence and Function Notation
  78.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  79.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  80.    wt: 1:   1 Essentially One Unknown
  81.    wt: 1:   Skill Development Notes
  82.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  83.    wt: 1:   2 Another Rectangle Area Formula Example
  84.    wt: 1:   6 Power Set Notation
  85.    wt: 1:   5 Product Builder Notation
  86.    wt: 1:   4 Subset Builder Notation
  87.    wt: 1:   6 Three Notions of What is a Variable
  88.    wt: 1:   3 signed coordinates for maps and planes
  89.    wt: 1:   22 Complex Compound Fractions
  90.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  91.    wt: 1:   14 Adding and Subtracting with Like Denominators
  92.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  93.    wt: 1:   A Associative Law Theorectical Note
  94.    wt: 1:   7 Calculator Usage Notes and Cautions
  95.    wt: 1:   11 Another Single Digit Divisor Example
  96.    wt: 1:   5 Long Division Include Zeroes or not
  97.    wt: 1:   6 Multiplication Commutes Order Not Important
  98.    wt: 1:   Video Power Notation in Decimal Expansion
  99.    wt: 1:   Subtraction Another Video Lesson
  100.    wt: 1:   30Chain Rule A Proof
  101.    wt: 1:   28 Chain Rule Preparation for a Proof
  102.    wt: 1:   22 Chain Rule for polynomials
  103.    wt: 1:   8 Differentiation of polynomials
  104.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  105.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  106.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  107.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  108.    wt: 1:   F.5b Extreme Value Theorem
  109.    wt: 1:   F.5a Equicontinuity Theorems
  110.    wt: 1:   F.4 Finite Covering Theorem
  111.    wt: 1:   F.3 Intermediate Value Theorem
  112.    wt: 1:   F.2 Closed Range Theorem
  113.    wt: 1:   D2 Limits of Monotone Sequences
  114.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  115.    wt: 1:   Chapter 23 Links To Trigonometry
  116.    wt: 1:   Chapter 22 Complex Numbers
  117.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  118.    wt: 1:   Chapter 23. Notation For Sums
  119.    wt: 1:   Chapter 16. Painless Theorem Proving
  120.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  121.    wt: 1:   Annotated Links to Material Elsehwere
  122.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  123.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  124.    wt: 1:   Chapter 18 Sense and Knowledge
  125.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  126.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  127.    wt: 1:   H more Routine to non routine problem solving
  128.    wt: 1:   C. Domino effect of being careful
  129.    wt: 1:   B. Domino effect of errors
  130.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  131.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  132.    wt: 1:   Implementation Notes
  133.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics

Extended Search

355 matches:

  1.    wt: 9:   8 More Use of Maps Not Drawn to Scale
  2.    wt: 9:   6 Figuring with Maps Not to Scale
  3.    wt: 9:   4 Angles on Maps Plans drawn to scale
  4.    wt: 9:   3 Lengths and Areas on Maps and Plans
  5.    wt: 8:   17G Pythagorean Theorem Converse
  6.    wt: 8:   15 Pythagorean Theorem Converse
  7.    wt: 8:   9 Pythagorean Theorem Chinese Square Proof
  8.    wt: 7:   13 Velocity Vectors in Physics
  9.    wt: 7:   8 Parallel Vectors
  10.    wt: 7:   6 Vectors with Coordinates
  11.    wt: 7:   3 Navigation with Arrows or Vectors
  12.    wt: 7:   Vector and Complex Number Applet
  13.    wt: 7:   30 unit circle calculation of six trigonometric functions
  14.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  15.    wt: 7:   17A The complex number valued trig function cis
  16.    wt: 7:   Unit Circle Development of Trigonometry
  17.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  18.    wt: 7:   20 N th Roots of Complex Numbers
  19.    wt: 7:   9 The complex number valued trig function cis
  20.    wt: 7:   8 Unit Circle Development of Trigonometry
  21.    wt: 7:   6 Field Properties of Complex Number
  22.    wt: 7:   5 An Easy Proof of the Distributive Law
  23.    wt: 7:   2 Complex Numbers made easier we hope
  24.    wt: 7:   Appetizer A Complex Number Applet
  25.    wt: 7:   7 Trignometric Ratios Unit Circle
  26.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  27.    wt: 7:   5 Trigonometric Ratios For Tangent and Special Triangles
  28.    wt: 7:   4 Trigonometric Ratios For Two Special Triangles
  29.    wt: 7:   3 Trigonometric Ratios sine and cosine
  30.    wt: 7:   Why Trigonometry the whyslopes view
  31.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  32.    wt: 7:   A Measurement with Ruler Proper Use
  33.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  34.    wt: 7:   2 Measuring Area Directly
  35.    wt: 7:   1 Length Measurement
  36.    wt: 6:   16 cotangent function Definition Graph and Inverse
  37.    wt: 6:   15 cosecant function Definition Graph and Inverse
  38.    wt: 6:   14 secant function Definition Graph and Inverse
  39.    wt: 6:   13 cosecant function Definition Graph and Inverse
  40.    wt: 6:   12 motivation for term arctan
  41.    wt: 6:   11 arctan left inverse of tangent Graph
  42.    wt: 6:   10 arctan left inverse of tangent Definition
  43.    wt: 6:   9 motivation for name arcsin
  44.    wt: 6:   8 arcsin left inverse of sine Graph
  45.    wt: 6:   7 arcsin left inverse of sine Definition
  46.    wt: 6:   6 Graph of arccos function
  47.    wt: 6:   5 Swapping Coordinates is a reflection
  48.    wt: 6:   4 possible motivation for term arccos
  49.    wt: 6:   3 Left Inverse of cosine arccos definition
  50.    wt: 6:   2 cosine function more properties
  51.    wt: 6:   1 cosine function properties
  52.    wt: 6:   A Global Time and Navigation
  53.    wt: 6:   15 Dot and Cross Product
  54.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  55.    wt: 6:   12 From Applied To Pure Mathematics
  56.    wt: 6:   11 Component Method
  57.    wt: 6:   10 Parallelogram Addition Method
  58.    wt: 6:   9 Head to Tail Coordinate View
  59.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  60.    wt: 6:   5 Head To Tail Arrow Addition
  61.    wt: 6:   4 Resultant of a Sum of Movements
  62.    wt: 6:   2 Signed Coordinates
  63.    wt: 6:   1 Unsigned Coordinates
  64.    wt: 6:   17 tangent function angle sum formulas
  65.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  66.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  67.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  68.    wt: 6:   32 seven rows of pascals triangle
  69.    wt: 6:   31 basic secant cosecant cotangent trig identities
  70.    wt: 6:   29 secant cosecant and cotangent for acute angles
  71.    wt: 6:   28 Expressing products of sines cosines as sums
  72.    wt: 6:   27 Logarithmic use of products of sines and cosines
  73.    wt: 6:   26 Formulas for products of sines and cosines
  74.    wt: 6:   25 tangent double angle formula Slope connection
  75.    wt: 6:   24 tangent Angle Difference Formula
  76.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  77.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  78.    wt: 6:   21 sine and cosine Half Angle Formulas
  79.    wt: 6:   20 sine and cosine Double Angle Formulas
  80.    wt: 6:   18 sum of sinusoidal waves as a single wave
  81.    wt: 6:   17F Law of cosines
  82.    wt: 6:   17E Trig Formulas for dot and cross Products
  83.    wt: 6:   17D cis formulas for sine cosines and tangent
  84.    wt: 6:   17C sine and cosine double triple angle formulas
  85.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  86.    wt: 6:   16 Right Triangle Complementary Angle Relations
  87.    wt: 6:   15 sine cosine Complementary Angle Relations
  88.    wt: 6:   14 cosine even and sine and tangent are odd
  89.    wt: 6:   13 Graph of tangent function many periods
  90.    wt: 6:   12 Graph of tangent function for one period
  91.    wt: 6:   11 tangent function undefined when terminal side vertical
  92.    wt: 6:   10 Graphs of sines and cosines many periods
  93.    wt: 6:   9 Graphs of sine and cosine over one period
  94.    wt: 6:   8 period of tangent function
  95.    wt: 6:   7 period of sine and cosine
  96.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  97.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  98.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  99.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  100.    wt: 6:   2 Quadrant I reference Angles
  101.    wt: 6:   1 Unit Points Reflections Rotations
  102.    wt: 6:   21 Logarithms Powers and Exponentials
  103.    wt: 6:   19 N th Roots of Unity
  104.    wt: 6:   18 Sixth Roots of Unity
  105.    wt: 6:   17 Cube Roots of unity
  106.    wt: 6:   16 References and Originality Question
  107.    wt: 6:   14 Law of cosines
  108.    wt: 6:   13 Trig Formulas for dot and cross Products
  109.    wt: 6:   12 cis formulas for sine cosines and tangent
  110.    wt: 6:   11 sine and cosine double triple angle formulas
  111.    wt: 6:   10 sine cosine Angle Sum Formulas via cis
  112.    wt: 6:   7 Second Way to Calculate Products
  113.    wt: 6:   4 Multiplication Properties
  114.    wt: 6:   3 Addition Properties
  115.    wt: 6:   1 Rectangular Polar Coordinates Review
  116.    wt: 6:   8 Triangles Cascade Problem Solving
  117.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  118.    wt: 6:   1 Angle Measurement with Degrees
  119.    wt: 6:   What is and is not here
  120.    wt: 6:   13 Pythagorean spatial distance formulas
  121.    wt: 6:   10 Pythagorean plane distance formula
  122.    wt: 6:   7 Complex Numbers Appetizer
  123.    wt: 6:   PS H Distributive Law For Complex Numbers
  124.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  125.    wt: 5:   9 Summary Degrees to Radians and back
  126.    wt: 5:   8 Radian Measures of Common Angles
  127.    wt: 5:   7 Radian Measures in special Triangles
  128.    wt: 5:   6 Radian Measure to Degrees
  129.    wt: 5:   5 Degrees to Radian Measure
  130.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  131.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  132.    wt: 5:   2 Radian Measure Numerical Value of one degree
  133.    wt: 5:   1 Degrees and Radians Introduction
  134.    wt: 5:   4 graphing y=Asin(x c)
  135.    wt: 5:   3 graphing y=f(x c) plus K
  136.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  137.    wt: 5:   1 graphing y=f(x a)
  138.    wt: 5:   Parallel Lines and Parallel Transversals
  139.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  140.    wt: 5:   Triangle Angles Sum To 180 Degrees
  141.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  142.    wt: 5:   Parallel Lines and Interior Angles
  143.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  144.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  145.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  146.    wt: 5:   Straight Lines ASA Intersection Study More
  147.    wt: 5:   Straight Lines ASA Intersection Study
  148.    wt: 5:   Straight Lines Instersection Solving Equations
  149.    wt: 5:   Straight Lines Intersection of
  150.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  151.    wt: 5:   C Straight Lines Slope from Coordinates
  152.    wt: 5:   B Straight Line Slope Scaling Properties More
  153.    wt: 5:   A Straight Line Slope Scaling Properties
  154.    wt: 5:   14 Straight Lines Equations General Case
  155.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  156.    wt: 5:   12 Straight Lines Graphing mx plus b
  157.    wt: 5:   11 Straight Lines Graphing y=mx
  158.    wt: 5:   10 Straight Lines through Origin Equations More
  159.    wt: 5:   9 Straight Lines through Origin Equations
  160.    wt: 5:   8 Straight Lines Equation for vertical
  161.    wt: 5:   7 Tangent Function is odd on this domain
  162.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  163.    wt: 5:   5 Tangent Function Graph
  164.    wt: 5:   4 Tangent Function Properties
  165.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  166.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  167.    wt: 5:   1 Straight Lines Slope Concept
  168.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  169.    wt: 5:   12 Triangles Similarity More Problems
  170.    wt: 5:   11 Triangle Similarity Missing Side Problem
  171.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  172.    wt: 5:   9 Similarity of Triangles Usual Criteria
  173.    wt: 5:   8 Similarity of Triangles and Polygons
  174.    wt: 5:   7 Translations Rotations Reflections Dilatations
  175.    wt: 5:   6 Geometric Diagrams in Class
  176.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  177.    wt: 5:   4 Similarity Definition with Coordinate
  178.    wt: 5:   3 Similarity by Design with coordinates
  179.    wt: 5:   2 Similarity By Design
  180.    wt: 5:   1 Early Concept of Like or Similar Shapes
  181.    wt: 5:   Four Simple Exercises
  182.    wt: 5:   12 Links Lessons elsewhere
  183.    wt: 5:   11 A Partial Summary
  184.    wt: 5:   10 Midpoint of [a b] and [b a]
  185.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  186.    wt: 5:   8 Mid Point Formula
  187.    wt: 5:   7 Exercises to test skill and concept mastery
  188.    wt: 5:   6 Intersection of lines by solving linear systems
  189.    wt: 5:   5 Algebraic View of Slopes
  190.    wt: 5:   4 Equations for lines three forms
  191.    wt: 5:   3 Slope product for perpendicular lines
  192.    wt: 5:   2 point slope equation for a line
  193.    wt: 5:   1 Numerical view of lines and their equations
  194.    wt: 5:   12 Spatial Coordinates
  195.    wt: 5:   11 Triangle Inequality
  196.    wt: 5:   8 Distance Between Points on a Line
  197.    wt: 5:   6 Polar Multiplication and Rotation
  198.    wt: 5:   5 Cartesian Addition and Translation
  199.    wt: 5:   4 Polar Coordinates to and from
  200.    wt: 5:   3 Rectangular Coordinates Review
  201.    wt: 5:   2 Cartesian Coordinates with signs
  202.    wt: 5:   1 Cartesian Coordinates sans signs
  203.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  204.    wt: 5:   PS G Rotation Distributes over Addition
  205.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  206.    wt: 5:   PS E Multiplication with Polar Coordinates
  207.    wt: 5:   PS D Addition with Cartesian Coordinates
  208.    wt: 5:   PS B Parallelogram Construction Methods
  209.    wt: 5:   PS A Kite Construction Methods
  210.    wt: 5:   21 Parallelograms
  211.    wt: 5:   19 Right Triangle Similarity
  212.    wt: 5:   18 Triangle Similarity Take 1
  213.    wt: 5:   17 Right Bisectors of Triangle Sides
  214.    wt: 5:   16 Angles Subtended By Chords and Diameters
  215.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  216.    wt: 5:   14 Parallel Lines Postulate
  217.    wt: 5:   13 Angle Side Angle Failure
  218.    wt: 5:   12 Side Angle Side Failure
  219.    wt: 5:   11 Triangle Construction Fails
  220.    wt: 5:   10 Dropping a perpendicular to line
  221.    wt: 5:   9 Construction of a right bisector
  222.    wt: 5:   8 Isoceles Triangles
  223.    wt: 5:   7 Angle Side Angle
  224.    wt: 5:   6 Ruler and compass Angle Bisection
  225.    wt: 5:   5 Side Angle Side
  226.    wt: 5:   4 Side Side Side
  227.    wt: 5:   3 Isometry of Triangles Congruence
  228.    wt: 5:   2 Correspondence between Triangles
  229.    wt: 5:   1 Initial Concepts and Terms
  230.    wt: 5:   Short Course on Euclidean Geometry
  231.    wt: 5:   About Folder Contents
  232.    wt: 4:   Postscript Pythagorean Theorem yet another proof
  233.    wt: 3:   5 Polynomials Long division Nonlinear divisor
  234.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  235.    wt: 3:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  236.    wt: 2:   Maps Plans Drawings
  237.    wt: 2:   sign monoticity analysis example 4
  238.    wt: 2:   sign monoticity analysis example 3
  239.    wt: 2:   sign monoticity analysis example 2
  240.    wt: 2:   sign monoticity analysis example 1
  241.    wt: 2:   8 Notes for instructors or tutors
  242.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  243.    wt: 2:   4 Polynomials Long division linear divisor
  244.    wt: 2:   3 Polynomials Multiplication Addition
  245.    wt: 2:   1 Polynomials Distributive Law
  246.    wt: 2:   3 Geometric Formulas and Function Notation
  247.    wt: 2:   1 Formulas Dependence and Function Notation
  248.    wt: 2:   1 Essentially One Unknown
  249.    wt: 2:   G.3 Constant Difference Theorem Proof
  250.    wt: 2:   B3 Bolzano Weierstrass Theorem
  251.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  252.    wt: 2:   Annotated Links to Material Elsehwere
  253.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  254.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  255.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  256.    wt: 1:   6 polynomials etc
  257.    wt: 1:   About site lesson plans
  258.    wt: 1:   key notes and themes
  259.    wt: 1:   Theory of Knowledge
  260.    wt: 1:   Education in mathematics science and technology
  261.    wt: 1:   Trois Notions qui menent a algebre
  262.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  263.    wt: 1:   10 Interval Notation
  264.    wt: 1:   6 Set Existence Formation and Notation
  265.    wt: 1:   5 Function notation for geometric transformations
  266.    wt: 1:   4 Function notation in and beyond mathematics
  267.    wt: 1:   2 Algebraic use of function notation
  268.    wt: 1:   1 Geometric Introduction of Function Notation
  269.    wt: 1:   7 Links Lessons Elsewhere
  270.    wt: 1:   2 Column Multiplication Method
  271.    wt: 1:   musings do not puiblish real numbers
  272.    wt: 1:   19 Signed Multiples of Vectors
  273.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  274.    wt: 1:   13 Arrows and Vectors in a Plane
  275.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  276.    wt: 1:   8 Coordinates for Maps and Planes
  277.    wt: 1:   5 Independent versus Dependent Variables
  278.    wt: 1:   4 Changing Letters
  279.    wt: 1:   2 Computation Rules Evaluation
  280.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  281.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  282.    wt: 1:   4 Solving a triangular system exercise
  283.    wt: 1:   3 Solving triangular system example
  284.    wt: 1:   2 Essentially one exercises three with solution
  285.    wt: 1:   6 Algebraic Solution Example
  286.    wt: 1:   5 Algebraic Solutions Introduction
  287.    wt: 1:   4 Four Examples Fractional Coefficients
  288.    wt: 1:   3 Four Examples
  289.    wt: 1:   2 Three Examples
  290.    wt: 1:   1 Proper Equal Sign Usage
  291.    wt: 1:   Skill Development Notes
  292.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  293.    wt: 1:   2 Another Rectangle Area Formula Example
  294.    wt: 1:   6 Power Set Notation
  295.    wt: 1:   5 Product Builder Notation
  296.    wt: 1:   4 Subset Builder Notation
  297.    wt: 1:   6 Three Notions of What is a Variable
  298.    wt: 1:   3 signed coordinates for maps and planes
  299.    wt: 1:   22 Complex Compound Fractions
  300.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  301.    wt: 1:   14 Adding and Subtracting with Like Denominators
  302.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  303.    wt: 1:   A Associative Law Theorectical Note
  304.    wt: 1:   7 Calculator Usage Notes and Cautions
  305.    wt: 1:   11 Another Single Digit Divisor Example
  306.    wt: 1:   5 Long Division Include Zeroes or not
  307.    wt: 1:   6 Multiplication Commutes Order Not Important
  308.    wt: 1:   Video Power Notation in Decimal Expansion
  309.    wt: 1:   Subtraction Another Video Lesson
  310.    wt: 1:   30Chain Rule A Proof
  311.    wt: 1:   28 Chain Rule Preparation for a Proof
  312.    wt: 1:   22 Chain Rule for polynomials
  313.    wt: 1:   8 Differentiation of polynomials
  314.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  315.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  316.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  317.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  318.    wt: 1:   F.5b Extreme Value Theorem
  319.    wt: 1:   F.5a Equicontinuity Theorems
  320.    wt: 1:   F.4 Finite Covering Theorem
  321.    wt: 1:   F.3 Intermediate Value Theorem
  322.    wt: 1:   F.2 Closed Range Theorem
  323.    wt: 1:   D2 Limits of Monotone Sequences
  324.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  325.    wt: 1:   Chapter 23 Links To Trigonometry
  326.    wt: 1:   Chapter 22 Complex Numbers
  327.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  328.    wt: 1:   Chapter 23. Notation For Sums
  329.    wt: 1:   Chapter 16. Painless Theorem Proving
  330.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  331.    wt: 1:   Postscript B Mathematics Education References
  332.    wt: 1:   Postscript A Three Remarks
  333.    wt: 1:   Chapter 12 Four Phases
  334.    wt: 1:   Chapter 11 Elementary Instruction
  335.    wt: 1:   Chapter 10 Transition
  336.    wt: 1:   Chapter 9 The Two Ends
  337.    wt: 1:   Chapter 8 Modern Instruction
  338.    wt: 1:   Chapter 7 Two Treatments of Geometry
  339.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  340.    wt: 1:   Chapter 5 Four References
  341.    wt: 1:   Chapter 3 Algebra Difficulties
  342.    wt: 1:   Chapter 2 For and Against Mathematics
  343.    wt: 1:   Chapter 1 Introduction
  344.    wt: 1:   Foreword
  345.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  346.    wt: 1:   Chapter 18 Sense and Knowledge
  347.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  348.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  349.    wt: 1:   H more Routine to non routine problem solving
  350.    wt: 1:   C. Domino effect of being careful
  351.    wt: 1:   B. Domino effect of errors
  352.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  353.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  354.    wt: 1:   Implementation Notes
  355.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
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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