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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26 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: 2:   4 Functions/
  18.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  19.    wt: 1:   3 Quadratics Geometrically/
  20.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  21.    wt: 1:   1 Five Polynomial Operations/
  22.    wt: 1:   More Algebra/
  23.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  24.    wt: 1:   4 Computation Rules and Function Notation/
  25.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  26.    wt: 1:   13 Lessons on Limits and Continuity/

Web Page Search

148 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:   16 cotangent function Definition Graph and Inverse
  5.    wt: 2:   15 cosecant function Definition Graph and Inverse
  6.    wt: 2:   14 secant function Definition Graph and Inverse
  7.    wt: 2:   2 cosine function more properties
  8.    wt: 2:   13 Velocity Vectors in Physics
  9.    wt: 2:   13 Graph of tangent function many periods
  10.    wt: 2:   8 More Use of Maps Not Drawn 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:   13 Arrows and Vectors in a Plane
  14.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  15.    wt: 1:   About site lesson plans
  16.    wt: 1:   05 13 OldSiteEntrancePage
  17.    wt: 1:   Four ways to improve education reform
  18.    wt: 1:   deux definitions pour variable
  19.    wt: 1:   13 Addition and Addition Tables
  20.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  21.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  22.    wt: 1:   23 Inverse Functions
  23.    wt: 1:   22 Square Root function graphically
  24.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  25.    wt: 1:   17 Function maxima minima and their location
  26.    wt: 1:   15 Sign analysis of functions
  27.    wt: 1:   13 From one to one to many to one
  28.    wt: 1:   12 Function Domain Recognition Exercises
  29.    wt: 1:   11 Function Domain Range Source and Targets
  30.    wt: 1:   8 Set view of relations and functions
  31.    wt: 1:   7 Functions with finite domains
  32.    wt: 1:   5 Function notation for geometric transformations
  33.    wt: 1:   4 Function notation in and beyond mathematics
  34.    wt: 1:   3 Formula or function graphing exercise
  35.    wt: 1:   2 Algebraic use of function notation
  36.    wt: 1:   1 Geometric Introduction of Function Notation
  37.    wt: 1:   Rewriting algebraic substitution as function substitutions
  38.    wt: 1:   10 arctan left inverse of tangent Definition
  39.    wt: 1:   7 arcsin left inverse of sine Definition
  40.    wt: 1:   6 Graph of arccos function
  41.    wt: 1:   3 Left Inverse of cosine arccos definition
  42.    wt: 1:   1 cosine function properties
  43.    wt: 1:   8 Parallel Vectors
  44.    wt: 1:   6 Vectors with Coordinates
  45.    wt: 1:   3 Navigation with Arrows or Vectors
  46.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  47.    wt: 1:   Straight Lines ASA Intersection Study More
  48.    wt: 1:   B Straight Line Slope Scaling Properties More
  49.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  50.    wt: 1:   10 Straight Lines through Origin Equations More
  51.    wt: 1:   7 Tangent Function is odd on this domain
  52.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  53.    wt: 1:   5 Tangent Function Graph
  54.    wt: 1:   4 Tangent Function Properties
  55.    wt: 1:   17 tangent function angle sum formulas
  56.    wt: 1:   30 unit circle calculation of six trigonometric functions
  57.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  58.    wt: 1:   17A The complex number valued trig function cis
  59.    wt: 1:   12 Graph of tangent function for one period
  60.    wt: 1:   11 tangent function undefined when terminal side vertical
  61.    wt: 1:   8 period of tangent function
  62.    wt: 1:   Unit Circle Development of Trigonometry
  63.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  64.    wt: 1:   13 Trig Formulas for dot and cross Products
  65.    wt: 1:   9 The complex number valued trig function cis
  66.    wt: 1:   8 Unit Circle Development of Trigonometry
  67.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  68.    wt: 1:   Why Trigonometry the whyslopes view
  69.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  70.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  71.    wt: 1:   12 Triangles Similarity More Problems
  72.    wt: 1:   4 Similarity Definition with Coordinate
  73.    wt: 1:   13 Pythagorean spatial distance formulas
  74.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  75.    wt: 1:   13 Angle Side Angle Failure
  76.    wt: 1:   6 Figuring with Maps Not to Scale
  77.    wt: 1:   26 More Less Greater Than Comparison
  78.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  79.    wt: 1:   19 Signed Multiples of Vectors
  80.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  81.    wt: 1:   E Long Division Methods more
  82.    wt: 1:   3 Linear Equation Literal Solution More
  83.    wt: 1:   5 Greater More Less Than Signs in General
  84.    wt: 1:   3 More and Less Than with Unlike Signs
  85.    wt: 1:   2 More and Less Than for Counts and Measures
  86.    wt: 1:   13 Real Number Subtraction
  87.    wt: 1:   8 Coordinates for Maps and Planes
  88.    wt: 1:   5 Rational Numbers More
  89.    wt: 1:   3 Geometric Formulas and Function Notation
  90.    wt: 1:   1 Formulas Dependence and Function Notation
  91.    wt: 1:   More Exercises
  92.    wt: 1:   13 Naming Identifying Formulas with Words
  93.    wt: 1:   4 Greater More Less Than Signs in General
  94.    wt: 1:   2 More and Less Than with Unlike Signs
  95.    wt: 1:   1 More and Less Than for Counts and Measures
  96.    wt: 1:   5 Square Roots with primes more still
  97.    wt: 1:   4 Square Roots with primes more
  98.    wt: 1:   13 GCD from given Prime Factorization
  99.    wt: 1:   3 signed coordinates for maps and planes
  100.    wt: 1:   18 Efficient Ways to Multiply
  101.    wt: 1:   17 Efficient Ways to Add and Subtract
  102.    wt: 1:   13 Fraction Comparison Algebraic View
  103.    wt: 1:   13 Subtraction with Additive Inverse
  104.    wt: 1:   12 Adding Integers More Examples
  105.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  106.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  107.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  108.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  109.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  110.    wt: 1:   13 video Factors of 24 using prime
  111.    wt: 1:   Long Division Backwards more
  112.    wt: 1:   10 Division by Five Long and Short Ways
  113.    wt: 1:   3 More One Digit Multipliers
  114.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  115.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  116.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  117.    wt: 1:   013 Travel Time Tables
  118.    wt: 1:   Example 4 with x function of y
  119.    wt: 1:   34 Derivative of exponential function
  120.    wt: 1:   31 Derivatives of inverse functions
  121.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  122.    wt: 1:   26 Chain Rule Recognising outer inner functions
  123.    wt: 1:   19 Chain Rule for linear functions
  124.    wt: 1:   13 sine and cosine derivatives 1st step
  125.    wt: 1:   3 Motivation for Limit Definition Take 2
  126.    wt: 1:   2 Motivation for Limit Definition Take 1
  127.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  128.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  129.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  130.    wt: 1:   F.1 What Functions are Continuous
  131.    wt: 1:   Chapter 23 Links To Trigonometry
  132.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  133.    wt: 1:   Chapter 13. Acceleration
  134.    wt: 1:   Chapter 4. More Slope Sign Analysis
  135.    wt: 1:   Postscript More on Better Performance
  136.    wt: 1:   Chapter 19. Functions and Sets
  137.    wt: 1:   Chapter 13. Second Reading Guide
  138.    wt: 1:   Postscript B More on Story Telling and Reason
  139.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  140.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  141.    wt: 1:   J. More on written work and showing skill
  142.    wt: 1:   H more Routine to non routine problem solving
  143.    wt: 1:   Chapter 6 More Algebra and Geometry
  144.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  145.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  146.    wt: 1:   More Algebra and Slope based Calculus Preview
  147.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  148.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years

Extended Search

404 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:   8 More Use of Maps Not Drawn to Scale
  6.    wt: 9:   4 Angles on Maps Plans drawn to scale
  7.    wt: 9:   3 Lengths and Areas on Maps and Plans
  8.    wt: 8:   16 cotangent function Definition Graph and Inverse
  9.    wt: 8:   15 cosecant function Definition Graph and Inverse
  10.    wt: 8:   14 secant function Definition Graph and Inverse
  11.    wt: 8:   3 Left Inverse of cosine arccos definition
  12.    wt: 8:   2 cosine function more properties
  13.    wt: 8:   A Global Time and Navigation
  14.    wt: 8:   15 Dot and Cross Product
  15.    wt: 8:   14 Why Scalar Multiplication Distributes Physical Argument
  16.    wt: 8:   12 From Applied To Pure Mathematics
  17.    wt: 8:   11 Component Method
  18.    wt: 8:   10 Parallelogram Addition Method
  19.    wt: 8:   9 Head to Tail Coordinate View
  20.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  21.    wt: 8:   5 Head To Tail Arrow Addition
  22.    wt: 8:   4 Resultant of a Sum of Movements
  23.    wt: 8:   2 Signed Coordinates
  24.    wt: 8:   1 Unsigned Coordinates
  25.    wt: 8:   Vector and Complex Number Applet
  26.    wt: 8:   32 seven rows of pascals triangle
  27.    wt: 8:   13 Graph of tangent function many periods
  28.    wt: 8:   6 Figuring with Maps Not to Scale
  29.    wt: 7:   10 arctan left inverse of tangent Definition
  30.    wt: 7:   7 arcsin left inverse of sine Definition
  31.    wt: 7:   6 Graph of arccos function
  32.    wt: 7:   1 cosine function properties
  33.    wt: 7:   B Straight Line Slope Scaling Properties More
  34.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  35.    wt: 7:   10 Straight Lines through Origin Equations More
  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:   17 tangent function angle sum formulas
  41.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  42.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  43.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  44.    wt: 7:   31 basic secant cosecant cotangent trig identities
  45.    wt: 7:   30 unit circle calculation of six trigonometric functions
  46.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  47.    wt: 7:   17A The complex number valued trig function cis
  48.    wt: 7:   15 sine cosine Complementary Angle Relations
  49.    wt: 7:   12 Graph of tangent function for one period
  50.    wt: 7:   11 tangent function undefined when terminal side vertical
  51.    wt: 7:   8 period of tangent function
  52.    wt: 7:   Unit Circle Development of Trigonometry
  53.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  54.    wt: 7:   13 Trig Formulas for dot and cross Products
  55.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  56.    wt: 7:   Why Trigonometry the whyslopes view
  57.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  58.    wt: 7:   13 Navigation Location from Angles to 2 Landmarks
  59.    wt: 7:   13 Pythagorean spatial distance formulas
  60.    wt: 7:   13 Angle Side Angle Failure
  61.    wt: 7:   A Measurement with Ruler Proper Use
  62.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  63.    wt: 7:   2 Measuring Area Directly
  64.    wt: 7:   1 Length Measurement
  65.    wt: 6:   12 motivation for term arctan
  66.    wt: 6:   11 arctan left inverse of tangent Graph
  67.    wt: 6:   9 motivation for name arcsin
  68.    wt: 6:   8 arcsin left inverse of sine Graph
  69.    wt: 6:   5 Swapping Coordinates is a reflection
  70.    wt: 6:   4 possible motivation for term arccos
  71.    wt: 6:   4 graphing y=Asin(x c)
  72.    wt: 6:   3 graphing y=f(x c) plus K
  73.    wt: 6:   2 Graphing y=Af(x) Vertical Scaling
  74.    wt: 6:   1 graphing y=f(x a)
  75.    wt: 6:   Analytic View of Triangle Construction or Line Instersection More
  76.    wt: 6:   Straight Lines ASA Intersection Study More
  77.    wt: 6:   D Straight Lines Slope from Coordinates Examples
  78.    wt: 6:   C Straight Lines Slope from Coordinates
  79.    wt: 6:   A Straight Line Slope Scaling Properties
  80.    wt: 6:   14 Straight Lines Equations General Case
  81.    wt: 6:   12 Straight Lines Graphing mx plus b
  82.    wt: 6:   11 Straight Lines Graphing y=mx
  83.    wt: 6:   9 Straight Lines through Origin Equations
  84.    wt: 6:   8 Straight Lines Equation for vertical
  85.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  86.    wt: 6:   2 Straight Lines Slopes As Rise Over Run
  87.    wt: 6:   1 Straight Lines Slope Concept
  88.    wt: 6:   29 secant cosecant and cotangent for acute angles
  89.    wt: 6:   28 Expressing products of sines cosines as sums
  90.    wt: 6:   27 Logarithmic use of products of sines and cosines
  91.    wt: 6:   26 Formulas for products of sines and cosines
  92.    wt: 6:   25 tangent double angle formula Slope connection
  93.    wt: 6:   24 tangent Angle Difference Formula
  94.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  95.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  96.    wt: 6:   21 sine and cosine Half Angle Formulas
  97.    wt: 6:   20 sine and cosine Double Angle Formulas
  98.    wt: 6:   18 sum of sinusoidal waves as a single wave
  99.    wt: 6:   17G Pythagorean Theorem Converse
  100.    wt: 6:   17F Law of cosines
  101.    wt: 6:   17E Trig Formulas for dot and cross Products
  102.    wt: 6:   17D cis formulas for sine cosines and tangent
  103.    wt: 6:   17C sine and cosine double triple angle formulas
  104.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  105.    wt: 6:   16 Right Triangle Complementary Angle Relations
  106.    wt: 6:   14 cosine even and sine and tangent are odd
  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:   7 period of sine and cosine
  110.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  111.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  112.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  113.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  114.    wt: 6:   2 Quadrant I reference Angles
  115.    wt: 6:   1 Unit Points Reflections Rotations
  116.    wt: 6:   9 The complex number valued trig function cis
  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:   12 Triangles Similarity More Problems
  126.    wt: 6:   6 Geometric Diagrams in Class
  127.    wt: 6:   4 Similarity Definition with Coordinate
  128.    wt: 6:   3 Similarity by Design with coordinates
  129.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  130.    wt: 5:   9 Summary Degrees to Radians and back
  131.    wt: 5:   8 Radian Measures of Common Angles
  132.    wt: 5:   7 Radian Measures in special Triangles
  133.    wt: 5:   6 Radian Measure to Degrees
  134.    wt: 5:   5 Degrees to Radian Measure
  135.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  136.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  137.    wt: 5:   2 Radian Measure Numerical Value of one degree
  138.    wt: 5:   1 Degrees and Radians Introduction
  139.    wt: 5:   Parallel Lines and Parallel Transversals
  140.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  141.    wt: 5:   Triangle Angles Sum To 180 Degrees
  142.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  143.    wt: 5:   Parallel Lines and Interior Angles
  144.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  145.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  146.    wt: 5:   Straight Lines ASA Intersection Study
  147.    wt: 5:   Straight Lines Instersection Solving Equations
  148.    wt: 5:   Straight Lines Intersection of
  149.    wt: 5:   21 Logarithms Powers and Exponentials
  150.    wt: 5:   20 N th Roots of Complex Numbers
  151.    wt: 5:   19 N th Roots of Unity
  152.    wt: 5:   18 Sixth Roots of Unity
  153.    wt: 5:   17 Cube Roots of unity
  154.    wt: 5:   16 References and Originality Question
  155.    wt: 5:   15 Pythagorean Theorem Converse
  156.    wt: 5:   14 Law of cosines
  157.    wt: 5:   12 cis formulas for sine cosines and tangent
  158.    wt: 5:   11 sine and cosine double triple angle formulas
  159.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  160.    wt: 5:   7 Second Way to Calculate Products
  161.    wt: 5:   6 Field Properties of Complex Number
  162.    wt: 5:   5 An Easy Proof of the Distributive Law
  163.    wt: 5:   4 Multiplication Properties
  164.    wt: 5:   3 Addition Properties
  165.    wt: 5:   2 Complex Numbers made easier we hope
  166.    wt: 5:   1 Rectangular Polar Coordinates Review
  167.    wt: 5:   Appetizer A Complex Number Applet
  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: 4:   26 Function definitions done and coming
  232.    wt: 4:   13 From one to one to many to one
  233.    wt: 3:   25 Absolute Value greatest integer and saw tooth functions
  234.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  235.    wt: 3:   23 Inverse Functions
  236.    wt: 3:   22 Square Root function graphically
  237.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  238.    wt: 3:   17 Function maxima minima and their location
  239.    wt: 3:   15 Sign analysis of functions
  240.    wt: 3:   12 Function Domain Recognition Exercises
  241.    wt: 3:   11 Function Domain Range Source and Targets
  242.    wt: 3:   8 Set view of relations and functions
  243.    wt: 3:   7 Functions with finite domains
  244.    wt: 3:   5 Function notation for geometric transformations
  245.    wt: 3:   4 Function notation in and beyond mathematics
  246.    wt: 3:   3 Formula or function graphing exercise
  247.    wt: 3:   2 Algebraic use of function notation
  248.    wt: 3:   1 Geometric Introduction of Function Notation
  249.    wt: 2:   Maps Plans Drawings
  250.    wt: 2:   13 Addition and Addition Tables
  251.    wt: 2:   20 Interchanging coordinates a reflection
  252.    wt: 2:   19 Horizontal line rule and method
  253.    wt: 2:   18 Vertical Line Rule and Method
  254.    wt: 2:   16 Increasing or decreasing on intervals
  255.    wt: 2:   14 Surjections Injections Bijections
  256.    wt: 2:   10 Interval Notation
  257.    wt: 2:   9 Set theory term relation possible origins
  258.    wt: 2:   6 Set Existence Formation and Notation
  259.    wt: 2:   Introduction Reading Guide
  260.    wt: 2:   Rewriting algebraic substitution as function substitutions
  261.    wt: 2:   13 Arrows and Vectors in a Plane
  262.    wt: 2:   5 Greater More Less Than Signs in General
  263.    wt: 2:   3 More and Less Than with Unlike Signs
  264.    wt: 2:   2 More and Less Than for Counts and Measures
  265.    wt: 2:   3 Geometric Formulas and Function Notation
  266.    wt: 2:   1 Formulas Dependence and Function Notation
  267.    wt: 2:   13 video Factors of 24 using prime
  268.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  269.    wt: 2:   Chapter 13. Acceleration
  270.    wt: 2:   Chapter 13. Second Reading Guide
  271.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  272.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  273.    wt: 1:   Ramblings Extrinsic numbers theory
  274.    wt: 1:   Ramblings Introduction Algebra Essay
  275.    wt: 1:   Skills Chapter 3 Algebra
  276.    wt: 1:   About site lesson plans
  277.    wt: 1:   05 13 OldSiteEntrancePage
  278.    wt: 1:   Four ways to improve education reform
  279.    wt: 1:   deux definitions pour variable
  280.    wt: 1:   A Wire Resistance Qualitative01
  281.    wt: 1:   sign monoticity analysis example 4
  282.    wt: 1:   sign monoticity analysis example 3
  283.    wt: 1:   sign monoticity analysis example 2
  284.    wt: 1:   sign monoticity analysis example 1
  285.    wt: 1:   A Quadratics Summary
  286.    wt: 1:   10 quadratic exercises
  287.    wt: 1:   9 quadratics physical and further context
  288.    wt: 1:   8 quadratics backward use of various formulas
  289.    wt: 1:   7 quadratic formulla derivation
  290.    wt: 1:   6 quadratics numerical approach
  291.    wt: 1:   5 quadratics completing the square
  292.    wt: 1:   4 quadratics difference of two squares
  293.    wt: 1:   3 quadratics factoring by inspection
  294.    wt: 1:   2 quadratics graphing in general
  295.    wt: 1:   1 quadratics graphing exercises
  296.    wt: 1:   Quadratics in 10 steps
  297.    wt: 1:   11 Growth and Decay in Biology
  298.    wt: 1:   10 Exponential Growth and Decay Models
  299.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  300.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  301.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  302.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  303.    wt: 1:   5 Natural Logarithm Calculator Exercises
  304.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  305.    wt: 1:   2 Square Root Simplification a prequel
  306.    wt: 1:   1 Calculator Starter Exercises
  307.    wt: 1:   8 Notes for instructors or tutors
  308.    wt: 1:   7 Links Lessons Elsewhere
  309.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  310.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  311.    wt: 1:   4 Polynomials Long division linear divisor
  312.    wt: 1:   3 Polynomials Multiplication Addition
  313.    wt: 1:   2 Column Multiplication Method
  314.    wt: 1:   1 Polynomials Distributive Law
  315.    wt: 1:   26 More Less Greater Than Comparison
  316.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  317.    wt: 1:   19 Signed Multiples of Vectors
  318.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  319.    wt: 1:   E Long Division Methods more
  320.    wt: 1:   3 Linear Equation Literal Solution More
  321.    wt: 1:   4 Comparison of Negative Numbers
  322.    wt: 1:   1 Real Numbers Comparison
  323.    wt: 1:   13 Real Number Subtraction
  324.    wt: 1:   8 Coordinates for Maps and Planes
  325.    wt: 1:   5 Rational Numbers More
  326.    wt: 1:   5 Independent versus Dependent Variables
  327.    wt: 1:   4 Changing Letters
  328.    wt: 1:   2 Computation Rules Evaluation
  329.    wt: 1:   More Exercises
  330.    wt: 1:   4 Solving a triangular system exercise
  331.    wt: 1:   3 Solving triangular system example
  332.    wt: 1:   2 Essentially one exercises three with solution
  333.    wt: 1:   1 Essentially One Unknown
  334.    wt: 1:   13 Naming Identifying Formulas with Words
  335.    wt: 1:   4 Greater More Less Than Signs in General
  336.    wt: 1:   2 More and Less Than with Unlike Signs
  337.    wt: 1:   1 More and Less Than for Counts and Measures
  338.    wt: 1:   5 Square Roots with primes more still
  339.    wt: 1:   4 Square Roots with primes more
  340.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  341.    wt: 1:   13 GCD from given Prime Factorization
  342.    wt: 1:   3 signed coordinates for maps and planes
  343.    wt: 1:   18 Efficient Ways to Multiply
  344.    wt: 1:   17 Efficient Ways to Add and Subtract
  345.    wt: 1:   13 Fraction Comparison Algebraic View
  346.    wt: 1:   A Associative Law Theorectical Note
  347.    wt: 1:   13 Subtraction with Additive Inverse
  348.    wt: 1:   12 Adding Integers More Examples
  349.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  350.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  351.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  352.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  353.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  354.    wt: 1:   Long Division Backwards more
  355.    wt: 1:   10 Division by Five Long and Short Ways
  356.    wt: 1:   3 More One Digit Multipliers
  357.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  358.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  359.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  360.    wt: 1:   013 Travel Time Tables
  361.    wt: 1:   Example 4 with x function of y
  362.    wt: 1:   34 Derivative of exponential function
  363.    wt: 1:   31 Derivatives of inverse functions
  364.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  365.    wt: 1:   26 Chain Rule Recognising outer inner functions
  366.    wt: 1:   19 Chain Rule for linear functions
  367.    wt: 1:   13 sine and cosine derivatives 1st step
  368.    wt: 1:   3 Motivation for Limit Definition Take 2
  369.    wt: 1:   2 Motivation for Limit Definition Take 1
  370.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  371.    wt: 1:   11 Limits at infinity Three Examples
  372.    wt: 1:   10 Three one sided limits with infinite values
  373.    wt: 1:   9 Limits Continuity and Composition
  374.    wt: 1:   8 Four Animated Examples
  375.    wt: 1:   7 Evaluation by immediate or delayed substitution
  376.    wt: 1:   6 Continuity at a point
  377.    wt: 1:   5 Jumps and absence of unlimited error control
  378.    wt: 1:   4 Numerical properties
  379.    wt: 1:   3 Decimal insights for limits continuity convergence
  380.    wt: 1:   2 Algebraic codification
  381.    wt: 1:   1 Numerical introduction
  382.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  383.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  384.    wt: 1:   F.5a Equicontinuity Theorems
  385.    wt: 1:   F.1 What Functions are Continuous
  386.    wt: 1:   Chapter 23 Links To Trigonometry
  387.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  388.    wt: 1:   Chapter 4. More Slope Sign Analysis
  389.    wt: 1:   Postscript More on Better Performance
  390.    wt: 1:   Chapter 19. Functions and Sets
  391.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  392.    wt: 1:   Postscript A Three Remarks
  393.    wt: 1:   Postscript B More on Story Telling and Reason
  394.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  395.    wt: 1:   M Words to extend arithmetic
  396.    wt: 1:   J. More on written work and showing skill
  397.    wt: 1:   H more Routine to non routine problem solving
  398.    wt: 1:   Chapter 6 More Algebra and Geometry
  399.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  400.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  401.    wt: 1:   More Algebra and Slope based Calculus Preview
  402.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  403.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  404.    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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