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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20 matches:

  1.    wt: 8:   13 Vectors/
  2.    wt: 7:   1 Maps Plans Measurement/
  3.    wt: 6:   15 Arc or Inverse Trigonometric Function/
  4.    wt: 6:   12 Function Translating and Rescaling/
  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: 5:   14 Degrees to Radians and Radians to Degrees/
  9.    wt: 5:   11 Parallel Straight Lines and Transversals/
  10.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  11.    wt: 5:   7 Complex Numbers/
  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:   4 Functions/
  18.    wt: 1:   4 Computation Rules and Function Notation/
  19.    wt: 1:   1 Working With Sets/
  20.    wt: 1:   13 Lessons on Limits and Continuity/

Web Page Search

140 matches:

  1.    wt: 3:   13 cosecant function Definition Graph and Inverse
  2.    wt: 2:   Maps Plans Drawings
  3.    wt: 2:   26 Function definitions done and coming
  4.    wt: 2:   7 Functions with finite domains
  5.    wt: 2:   16 cotangent function Definition Graph and Inverse
  6.    wt: 2:   15 cosecant function Definition Graph and Inverse
  7.    wt: 2:   14 secant function Definition Graph and Inverse
  8.    wt: 2:   13 Velocity Vectors in Physics
  9.    wt: 2:   13 Graph of tangent function many periods
  10.    wt: 2:   4 Angles on Maps Plans drawn to scale
  11.    wt: 2:   3 Lengths and Areas on Maps and Plans
  12.    wt: 2:   13 Arrows and Vectors in a Plane
  13.    wt: 2:   1 Finite Sets
  14.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  15.    wt: 2:   Chapter 19. Functions and Sets
  16.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  17.    wt: 1:   9 combinatorics probability sets
  18.    wt: 1:   About site lesson plans
  19.    wt: 1:   05 13 OldSiteEntrancePage
  20.    wt: 1:   deux definitions pour variable
  21.    wt: 1:   24 Standards For Skill Develoment Take II
  22.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  23.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  24.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  25.    wt: 1:   13 Addition and Addition Tables
  26.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  27.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  28.    wt: 1:   23 Inverse Functions
  29.    wt: 1:   22 Square Root function graphically
  30.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  31.    wt: 1:   17 Function maxima minima and their location
  32.    wt: 1:   15 Sign analysis of functions
  33.    wt: 1:   13 From one to one to many to one
  34.    wt: 1:   12 Function Domain Recognition Exercises
  35.    wt: 1:   11 Function Domain Range Source and Targets
  36.    wt: 1:   8 Set view of relations and functions
  37.    wt: 1:   5 Function notation for geometric transformations
  38.    wt: 1:   4 Function notation in and beyond mathematics
  39.    wt: 1:   3 Formula or function graphing exercise
  40.    wt: 1:   2 Algebraic use of function notation
  41.    wt: 1:   1 Geometric Introduction of Function Notation
  42.    wt: 1:   Rewriting algebraic substitution as function substitutions
  43.    wt: 1:   10 arctan left inverse of tangent Definition
  44.    wt: 1:   7 arcsin left inverse of sine Definition
  45.    wt: 1:   6 Graph of arccos function
  46.    wt: 1:   3 Left Inverse of cosine arccos definition
  47.    wt: 1:   2 cosine function more properties
  48.    wt: 1:   1 cosine function properties
  49.    wt: 1:   8 Parallel Vectors
  50.    wt: 1:   6 Vectors with Coordinates
  51.    wt: 1:   3 Navigation with Arrows or Vectors
  52.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  53.    wt: 1:   7 Tangent Function is odd on this domain
  54.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  55.    wt: 1:   5 Tangent Function Graph
  56.    wt: 1:   4 Tangent Function Properties
  57.    wt: 1:   17 tangent function angle sum formulas
  58.    wt: 1:   30 unit circle calculation of six trigonometric functions
  59.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  60.    wt: 1:   17A The complex number valued trig function cis
  61.    wt: 1:   12 Graph of tangent function for one period
  62.    wt: 1:   11 tangent function undefined when terminal side vertical
  63.    wt: 1:   8 period of tangent function
  64.    wt: 1:   Unit Circle Development of Trigonometry
  65.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  66.    wt: 1:   13 Trig Formulas for dot and cross Products
  67.    wt: 1:   9 The complex number valued trig function cis
  68.    wt: 1:   8 Unit Circle Development of Trigonometry
  69.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  70.    wt: 1:   Why Trigonometry the whyslopes view
  71.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  72.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  73.    wt: 1:   4 Similarity Definition with Coordinate
  74.    wt: 1:   13 Pythagorean spatial distance formulas
  75.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  76.    wt: 1:   13 Angle Side Angle Failure
  77.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  78.    wt: 1:   6 Figuring with Maps Not to Scale
  79.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  80.    wt: 1:   19 Signed Multiples of Vectors
  81.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  82.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  83.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  84.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  85.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  86.    wt: 1:   1 Fractions with Finite Decimal Expansions
  87.    wt: 1:   13 Real Number Subtraction
  88.    wt: 1:   8 Coordinates for Maps and Planes
  89.    wt: 1:   3 Geometric Formulas and Function Notation
  90.    wt: 1:   1 Formulas Dependence and Function Notation
  91.    wt: 1:   4 GE III Animated Examples
  92.    wt: 1:   3 GE III Equation Addition and Multiplication
  93.    wt: 1:   2 GE II Comparison
  94.    wt: 1:   13 Naming Identifying Formulas with Words
  95.    wt: 1:   9 Sets in Probability and Statistics
  96.    wt: 1:   8 Sets of Numbers
  97.    wt: 1:   3 Counting with Sets etc
  98.    wt: 1:   13 GCD from given Prime Factorization
  99.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  100.    wt: 1:   3 Counting with Tables and Trees II
  101.    wt: 1:   3 signed coordinates for maps and planes
  102.    wt: 1:   13 Fraction Comparison Algebraic View
  103.    wt: 1:   8 Numerals Fractionals Quantals Take II
  104.    wt: 1:   6 Multiplication Algebraically Take II
  105.    wt: 1:   1 What is a fraction Take II
  106.    wt: 1:   13 Subtraction with Additive Inverse
  107.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  108.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  109.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  110.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  111.    wt: 1:   14 video Factors of 24 Take II
  112.    wt: 1:   13 video Factors of 24 using prime
  113.    wt: 1:   12 Why Long Division Works Take III
  114.    wt: 1:   9 Why Long Division Works Take II
  115.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  116.    wt: 1:   013 Travel Time Tables
  117.    wt: 1:   Example 4 with x function of y
  118.    wt: 1:   4 Definite Integrals Evaluation Exercises
  119.    wt: 1:   2 Indefinite Integrals Exercises
  120.    wt: 1:   34 Derivative of exponential function
  121.    wt: 1:   31 Derivatives of inverse functions
  122.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  123.    wt: 1:   26 Chain Rule Recognising outer inner functions
  124.    wt: 1:   19 Chain Rule for linear functions
  125.    wt: 1:   13 sine and cosine derivatives 1st step
  126.    wt: 1:   3 Motivation for Limit Definition Take 2
  127.    wt: 1:   2 Motivation for Limit Definition Take 1
  128.    wt: 1:   10 Three one sided limits with infinite values
  129.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  130.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  131.    wt: 1:   F.4 Finite Covering Theorem
  132.    wt: 1:   F.1 What Functions are Continuous
  133.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  134.    wt: 1:   Chapter 23 Links To Trigonometry
  135.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  136.    wt: 1:   Chapter 13. Acceleration
  137.    wt: 1:   Chapter 13. Second Reading Guide
  138.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  139.    wt: 1:   Chapter 2 Why Sets
  140.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

366 matches:

  1.    wt: 9:   13 cosecant function Definition Graph and Inverse
  2.    wt: 9:   8 Parallel Vectors
  3.    wt: 9:   6 Vectors with Coordinates
  4.    wt: 9:   3 Navigation with Arrows or Vectors
  5.    wt: 9:   4 Angles on Maps Plans drawn to scale
  6.    wt: 9:   3 Lengths and Areas on Maps and Plans
  7.    wt: 8:   16 cotangent function Definition Graph and Inverse
  8.    wt: 8:   15 cosecant function Definition Graph and Inverse
  9.    wt: 8:   14 secant function Definition Graph and Inverse
  10.    wt: 8:   3 Left Inverse of cosine arccos definition
  11.    wt: 8:   A Global Time and Navigation
  12.    wt: 8:   15 Dot and Cross Product
  13.    wt: 8:   14 Why Scalar Multiplication Distributes Physical Argument
  14.    wt: 8:   12 From Applied To Pure Mathematics
  15.    wt: 8:   11 Component Method
  16.    wt: 8:   10 Parallelogram Addition Method
  17.    wt: 8:   9 Head to Tail Coordinate View
  18.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  19.    wt: 8:   5 Head To Tail Arrow Addition
  20.    wt: 8:   4 Resultant of a Sum of Movements
  21.    wt: 8:   2 Signed Coordinates
  22.    wt: 8:   1 Unsigned Coordinates
  23.    wt: 8:   Vector and Complex Number Applet
  24.    wt: 8:   32 seven rows of pascals triangle
  25.    wt: 8:   13 Graph of tangent function many periods
  26.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  27.    wt: 8:   6 Figuring with Maps Not to Scale
  28.    wt: 7:   10 arctan left inverse of tangent Definition
  29.    wt: 7:   7 arcsin left inverse of sine Definition
  30.    wt: 7:   6 Graph of arccos function
  31.    wt: 7:   2 cosine function more properties
  32.    wt: 7:   1 cosine function properties
  33.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  34.    wt: 7:   7 Tangent Function is odd on this domain
  35.    wt: 7:   6 Tangent Function Inclination Angle Take 2
  36.    wt: 7:   5 Tangent Function Graph
  37.    wt: 7:   4 Tangent Function Properties
  38.    wt: 7:   17 tangent function angle sum formulas
  39.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  40.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  41.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  42.    wt: 7:   31 basic secant cosecant cotangent trig identities
  43.    wt: 7:   30 unit circle calculation of six trigonometric functions
  44.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  45.    wt: 7:   17A The complex number valued trig function cis
  46.    wt: 7:   15 sine cosine Complementary Angle Relations
  47.    wt: 7:   12 Graph of tangent function for one period
  48.    wt: 7:   11 tangent function undefined when terminal side vertical
  49.    wt: 7:   8 period of tangent function
  50.    wt: 7:   Unit Circle Development of Trigonometry
  51.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  52.    wt: 7:   13 Trig Formulas for dot and cross Products
  53.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  54.    wt: 7:   Why Trigonometry the whyslopes view
  55.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  56.    wt: 7:   13 Navigation Location from Angles to 2 Landmarks
  57.    wt: 7:   13 Pythagorean spatial distance formulas
  58.    wt: 7:   13 Angle Side Angle Failure
  59.    wt: 7:   A Measurement with Ruler Proper Use
  60.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  61.    wt: 7:   2 Measuring Area Directly
  62.    wt: 7:   1 Length Measurement
  63.    wt: 6:   12 motivation for term arctan
  64.    wt: 6:   11 arctan left inverse of tangent Graph
  65.    wt: 6:   9 motivation for name arcsin
  66.    wt: 6:   8 arcsin left inverse of sine Graph
  67.    wt: 6:   5 Swapping Coordinates is a reflection
  68.    wt: 6:   4 possible motivation for term arccos
  69.    wt: 6:   4 graphing y=Asin(x c)
  70.    wt: 6:   3 graphing y=f(x c) plus K
  71.    wt: 6:   2 Graphing y=Af(x) Vertical Scaling
  72.    wt: 6:   1 graphing y=f(x a)
  73.    wt: 6:   D Straight Lines Slope from Coordinates Examples
  74.    wt: 6:   C Straight Lines Slope from Coordinates
  75.    wt: 6:   B Straight Line Slope Scaling Properties More
  76.    wt: 6:   A Straight Line Slope Scaling Properties
  77.    wt: 6:   14 Straight Lines Equations General Case
  78.    wt: 6:   12 Straight Lines Graphing mx plus b
  79.    wt: 6:   11 Straight Lines Graphing y=mx
  80.    wt: 6:   10 Straight Lines through Origin Equations More
  81.    wt: 6:   9 Straight Lines through Origin Equations
  82.    wt: 6:   8 Straight Lines Equation for vertical
  83.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  84.    wt: 6:   2 Straight Lines Slopes As Rise Over Run
  85.    wt: 6:   1 Straight Lines Slope Concept
  86.    wt: 6:   29 secant cosecant and cotangent for acute angles
  87.    wt: 6:   28 Expressing products of sines cosines as sums
  88.    wt: 6:   27 Logarithmic use of products of sines and cosines
  89.    wt: 6:   26 Formulas for products of sines and cosines
  90.    wt: 6:   25 tangent double angle formula Slope connection
  91.    wt: 6:   24 tangent Angle Difference Formula
  92.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  93.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  94.    wt: 6:   21 sine and cosine Half Angle Formulas
  95.    wt: 6:   20 sine and cosine Double Angle Formulas
  96.    wt: 6:   18 sum of sinusoidal waves as a single wave
  97.    wt: 6:   17G Pythagorean Theorem Converse
  98.    wt: 6:   17F Law of cosines
  99.    wt: 6:   17E Trig Formulas for dot and cross Products
  100.    wt: 6:   17D cis formulas for sine cosines and tangent
  101.    wt: 6:   17C sine and cosine double triple angle formulas
  102.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  103.    wt: 6:   16 Right Triangle Complementary Angle Relations
  104.    wt: 6:   14 cosine even and sine and tangent are odd
  105.    wt: 6:   10 Graphs of sines and cosines many periods
  106.    wt: 6:   9 Graphs of sine and cosine over one period
  107.    wt: 6:   7 period of sine and cosine
  108.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  109.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  110.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  111.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  112.    wt: 6:   2 Quadrant I reference Angles
  113.    wt: 6:   1 Unit Points Reflections Rotations
  114.    wt: 6:   9 The complex number valued trig function cis
  115.    wt: 6:   8 Unit Circle Development of Trigonometry
  116.    wt: 6:   8 Triangles Cascade Problem Solving
  117.    wt: 6:   7 Trignometric Ratios Unit Circle
  118.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  119.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  120.    wt: 6:   3 Trigonometric Ratios sine and cosine
  121.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  122.    wt: 6:   1 Angle Measurement with Degrees
  123.    wt: 6:   6 Geometric Diagrams in Class
  124.    wt: 6:   4 Similarity Definition with Coordinate
  125.    wt: 6:   3 Similarity by Design with coordinates
  126.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  127.    wt: 5:   9 Summary Degrees to Radians and back
  128.    wt: 5:   8 Radian Measures of Common Angles
  129.    wt: 5:   7 Radian Measures in special Triangles
  130.    wt: 5:   6 Radian Measure to Degrees
  131.    wt: 5:   5 Degrees to Radian Measure
  132.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  133.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  134.    wt: 5:   2 Radian Measure Numerical Value of one degree
  135.    wt: 5:   1 Degrees and Radians Introduction
  136.    wt: 5:   Parallel Lines and Parallel Transversals
  137.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  138.    wt: 5:   Triangle Angles Sum To 180 Degrees
  139.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  140.    wt: 5:   Parallel Lines and Interior Angles
  141.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  142.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  143.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  144.    wt: 5:   Straight Lines ASA Intersection Study More
  145.    wt: 5:   Straight Lines ASA Intersection Study
  146.    wt: 5:   Straight Lines Instersection Solving Equations
  147.    wt: 5:   Straight Lines Intersection of
  148.    wt: 5:   21 Logarithms Powers and Exponentials
  149.    wt: 5:   20 N th Roots of Complex Numbers
  150.    wt: 5:   19 N th Roots of Unity
  151.    wt: 5:   18 Sixth Roots of Unity
  152.    wt: 5:   17 Cube Roots of unity
  153.    wt: 5:   16 References and Originality Question
  154.    wt: 5:   15 Pythagorean Theorem Converse
  155.    wt: 5:   14 Law of cosines
  156.    wt: 5:   12 cis formulas for sine cosines and tangent
  157.    wt: 5:   11 sine and cosine double triple angle formulas
  158.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  159.    wt: 5:   7 Second Way to Calculate Products
  160.    wt: 5:   6 Field Properties of Complex Number
  161.    wt: 5:   5 An Easy Proof of the Distributive Law
  162.    wt: 5:   4 Multiplication Properties
  163.    wt: 5:   3 Addition Properties
  164.    wt: 5:   2 Complex Numbers made easier we hope
  165.    wt: 5:   1 Rectangular Polar Coordinates Review
  166.    wt: 5:   Appetizer A Complex Number Applet
  167.    wt: 5:   12 Triangles Similarity More Problems
  168.    wt: 5:   11 Triangle Similarity Missing Side Problem
  169.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  170.    wt: 5:   9 Similarity of Triangles Usual Criteria
  171.    wt: 5:   8 Similarity of Triangles and Polygons
  172.    wt: 5:   7 Translations Rotations Reflections Dilatations
  173.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  174.    wt: 5:   2 Similarity By Design
  175.    wt: 5:   1 Early Concept of Like or Similar Shapes
  176.    wt: 5:   Four Simple Exercises
  177.    wt: 5:   12 Links Lessons elsewhere
  178.    wt: 5:   11 A Partial Summary
  179.    wt: 5:   10 Midpoint of [a b] and [b a]
  180.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  181.    wt: 5:   8 Mid Point Formula
  182.    wt: 5:   7 Exercises to test skill and concept mastery
  183.    wt: 5:   6 Intersection of lines by solving linear systems
  184.    wt: 5:   5 Algebraic View of Slopes
  185.    wt: 5:   4 Equations for lines three forms
  186.    wt: 5:   3 Slope product for perpendicular lines
  187.    wt: 5:   2 point slope equation for a line
  188.    wt: 5:   1 Numerical view of lines and their equations
  189.    wt: 5:   What is and is not here
  190.    wt: 5:   12 Spatial Coordinates
  191.    wt: 5:   11 Triangle Inequality
  192.    wt: 5:   10 Pythagorean plane distance formula
  193.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  194.    wt: 5:   8 Distance Between Points on a Line
  195.    wt: 5:   7 Complex Numbers Appetizer
  196.    wt: 5:   6 Polar Multiplication and Rotation
  197.    wt: 5:   5 Cartesian Addition and Translation
  198.    wt: 5:   4 Polar Coordinates to and from
  199.    wt: 5:   3 Rectangular Coordinates Review
  200.    wt: 5:   2 Cartesian Coordinates with signs
  201.    wt: 5:   1 Cartesian Coordinates sans signs
  202.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  203.    wt: 5:   PS H Distributive Law For Complex Numbers
  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:   12 Side Angle Side Failure
  218.    wt: 5:   11 Triangle Construction Fails
  219.    wt: 5:   10 Dropping a perpendicular to line
  220.    wt: 5:   9 Construction of a right bisector
  221.    wt: 5:   8 Isoceles Triangles
  222.    wt: 5:   7 Angle Side Angle
  223.    wt: 5:   6 Ruler and compass Angle Bisection
  224.    wt: 5:   5 Side Angle Side
  225.    wt: 5:   4 Side Side Side
  226.    wt: 5:   3 Isometry of Triangles Congruence
  227.    wt: 5:   2 Correspondence between Triangles
  228.    wt: 5:   1 Initial Concepts and Terms
  229.    wt: 5:   Short Course on Euclidean Geometry
  230.    wt: 5:   About Folder Contents
  231.    wt: 3:   26 Function definitions done and coming
  232.    wt: 3:   13 From one to one to many to one
  233.    wt: 3:   7 Functions with finite domains
  234.    wt: 3:   1 Finite Sets
  235.    wt: 3:   13 Limits with Parameters and Derivatives Take II
  236.    wt: 2:   Maps Plans Drawings
  237.    wt: 2:   13 Addition and Addition Tables
  238.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  239.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  240.    wt: 2:   23 Inverse Functions
  241.    wt: 2:   22 Square Root function graphically
  242.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  243.    wt: 2:   17 Function maxima minima and their location
  244.    wt: 2:   15 Sign analysis of functions
  245.    wt: 2:   12 Function Domain Recognition Exercises
  246.    wt: 2:   11 Function Domain Range Source and Targets
  247.    wt: 2:   8 Set view of relations and functions
  248.    wt: 2:   5 Function notation for geometric transformations
  249.    wt: 2:   4 Function notation in and beyond mathematics
  250.    wt: 2:   3 Formula or function graphing exercise
  251.    wt: 2:   2 Algebraic use of function notation
  252.    wt: 2:   1 Geometric Introduction of Function Notation
  253.    wt: 2:   13 Arrows and Vectors in a Plane
  254.    wt: 2:   3 Geometric Formulas and Function Notation
  255.    wt: 2:   1 Formulas Dependence and Function Notation
  256.    wt: 2:   9 Sets in Probability and Statistics
  257.    wt: 2:   8 Sets of Numbers
  258.    wt: 2:   3 Counting with Sets etc
  259.    wt: 2:   13 video Factors of 24 using prime
  260.    wt: 2:   10 Three one sided limits with infinite values
  261.    wt: 2:   Chapter 13. Acceleration
  262.    wt: 2:   Chapter 19. Functions and Sets
  263.    wt: 2:   Chapter 13. Second Reading Guide
  264.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  265.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  266.    wt: 1:   Ramblings Extrinsic numbers theory
  267.    wt: 1:   Ramblings Introduction Algebra Essay
  268.    wt: 1:   Skills Chapter 3 Algebra
  269.    wt: 1:   9 combinatorics probability sets
  270.    wt: 1:   About site lesson plans
  271.    wt: 1:   05 13 OldSiteEntrancePage
  272.    wt: 1:   deux definitions pour variable
  273.    wt: 1:   A Wire Resistance Qualitative01
  274.    wt: 1:   24 Standards For Skill Develoment Take II
  275.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  276.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  277.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  278.    wt: 1:   20 Interchanging coordinates a reflection
  279.    wt: 1:   19 Horizontal line rule and method
  280.    wt: 1:   18 Vertical Line Rule and Method
  281.    wt: 1:   16 Increasing or decreasing on intervals
  282.    wt: 1:   14 Surjections Injections Bijections
  283.    wt: 1:   10 Interval Notation
  284.    wt: 1:   9 Set theory term relation possible origins
  285.    wt: 1:   6 Set Existence Formation and Notation
  286.    wt: 1:   Introduction Reading Guide
  287.    wt: 1:   Rewriting algebraic substitution as function substitutions
  288.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  289.    wt: 1:   19 Signed Multiples of Vectors
  290.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  291.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  292.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  293.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  294.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  295.    wt: 1:   1 Fractions with Finite Decimal Expansions
  296.    wt: 1:   13 Real Number Subtraction
  297.    wt: 1:   8 Coordinates for Maps and Planes
  298.    wt: 1:   5 Independent versus Dependent Variables
  299.    wt: 1:   4 Changing Letters
  300.    wt: 1:   2 Computation Rules Evaluation
  301.    wt: 1:   4 GE III Animated Examples
  302.    wt: 1:   3 GE III Equation Addition and Multiplication
  303.    wt: 1:   2 GE II Comparison
  304.    wt: 1:   13 Naming Identifying Formulas with Words
  305.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  306.    wt: 1:   7 Cautious or Safe Set Construction
  307.    wt: 1:   6 Power Set Notation
  308.    wt: 1:   5 Product Builder Notation
  309.    wt: 1:   4 Subset Builder Notation
  310.    wt: 1:   2 Venn Diagrams
  311.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  312.    wt: 1:   13 GCD from given Prime Factorization
  313.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  314.    wt: 1:   3 Counting with Tables and Trees II
  315.    wt: 1:   3 signed coordinates for maps and planes
  316.    wt: 1:   13 Fraction Comparison Algebraic View
  317.    wt: 1:   8 Numerals Fractionals Quantals Take II
  318.    wt: 1:   6 Multiplication Algebraically Take II
  319.    wt: 1:   1 What is a fraction Take II
  320.    wt: 1:   A Associative Law Theorectical Note
  321.    wt: 1:   13 Subtraction with Additive Inverse
  322.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  323.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  324.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  325.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  326.    wt: 1:   14 video Factors of 24 Take II
  327.    wt: 1:   12 Why Long Division Works Take III
  328.    wt: 1:   9 Why Long Division Works Take II
  329.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  330.    wt: 1:   013 Travel Time Tables
  331.    wt: 1:   Example 4 with x function of y
  332.    wt: 1:   4 Definite Integrals Evaluation Exercises
  333.    wt: 1:   2 Indefinite Integrals Exercises
  334.    wt: 1:   34 Derivative of exponential function
  335.    wt: 1:   31 Derivatives of inverse functions
  336.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  337.    wt: 1:   26 Chain Rule Recognising outer inner functions
  338.    wt: 1:   19 Chain Rule for linear functions
  339.    wt: 1:   13 sine and cosine derivatives 1st step
  340.    wt: 1:   3 Motivation for Limit Definition Take 2
  341.    wt: 1:   2 Motivation for Limit Definition Take 1
  342.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  343.    wt: 1:   11 Limits at infinity Three Examples
  344.    wt: 1:   9 Limits Continuity and Composition
  345.    wt: 1:   8 Four Animated Examples
  346.    wt: 1:   7 Evaluation by immediate or delayed substitution
  347.    wt: 1:   6 Continuity at a point
  348.    wt: 1:   5 Jumps and absence of unlimited error control
  349.    wt: 1:   4 Numerical properties
  350.    wt: 1:   3 Decimal insights for limits continuity convergence
  351.    wt: 1:   2 Algebraic codification
  352.    wt: 1:   1 Numerical introduction
  353.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  354.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  355.    wt: 1:   F.5a Equicontinuity Theorems
  356.    wt: 1:   F.4 Finite Covering Theorem
  357.    wt: 1:   F.1 What Functions are Continuous
  358.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  359.    wt: 1:   Chapter 23 Links To Trigonometry
  360.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  361.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  362.    wt: 1:   Postscript A Three Remarks
  363.    wt: 1:   M Words to extend arithmetic
  364.    wt: 1:   Chapter 2 Why Sets
  365.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  366.    wt: 11:   13 Velocity Vectors in Physics
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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