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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18 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:   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/

Web Page Search

92 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   26 Function definitions done and coming
  3.    wt: 2:   16 cotangent function Definition Graph and Inverse
  4.    wt: 2:   15 cosecant function Definition Graph and Inverse
  5.    wt: 2:   14 secant function Definition Graph and Inverse
  6.    wt: 2:   13 cosecant function Definition Graph and Inverse
  7.    wt: 2:   13 Graph of tangent function many periods
  8.    wt: 2:   4 Angles on Maps Plans drawn to scale
  9.    wt: 2:   3 Lengths and Areas on Maps and Plans
  10.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  11.    wt: 1:   About site lesson plans
  12.    wt: 1:   Four ways to improve education reform
  13.    wt: 1:   deux definitions pour variable
  14.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  15.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  16.    wt: 1:   23 Inverse Functions
  17.    wt: 1:   22 Square Root function graphically
  18.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  19.    wt: 1:   17 Function maxima minima and their location
  20.    wt: 1:   15 Sign analysis of functions
  21.    wt: 1:   13 From one to one to many to one
  22.    wt: 1:   12 Function Domain Recognition Exercises
  23.    wt: 1:   11 Function Domain Range Source and Targets
  24.    wt: 1:   8 Set view of relations and functions
  25.    wt: 1:   7 Functions with finite domains
  26.    wt: 1:   5 Function notation for geometric transformations
  27.    wt: 1:   4 Function notation in and beyond mathematics
  28.    wt: 1:   3 Formula or function graphing exercise
  29.    wt: 1:   2 Algebraic use of function notation
  30.    wt: 1:   1 Geometric Introduction of Function Notation
  31.    wt: 1:   Rewriting algebraic substitution as function substitutions
  32.    wt: 1:   10 arctan left inverse of tangent Definition
  33.    wt: 1:   7 arcsin left inverse of sine Definition
  34.    wt: 1:   6 Graph of arccos function
  35.    wt: 1:   3 Left Inverse of cosine arccos definition
  36.    wt: 1:   2 cosine function more properties
  37.    wt: 1:   1 cosine function properties
  38.    wt: 1:   13 Velocity Vectors in Physics
  39.    wt: 1:   8 Parallel Vectors
  40.    wt: 1:   6 Vectors with Coordinates
  41.    wt: 1:   3 Navigation with Arrows or Vectors
  42.    wt: 1:   7 Tangent Function is odd on this domain
  43.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  44.    wt: 1:   5 Tangent Function Graph
  45.    wt: 1:   4 Tangent Function Properties
  46.    wt: 1:   17 tangent function angle sum formulas
  47.    wt: 1:   30 unit circle calculation of six trigonometric functions
  48.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  49.    wt: 1:   17A The complex number valued trig function cis
  50.    wt: 1:   12 Graph of tangent function for one period
  51.    wt: 1:   11 tangent function undefined when terminal side vertical
  52.    wt: 1:   10 Graphs of sines and cosines many periods
  53.    wt: 1:   8 period of tangent function
  54.    wt: 1:   Unit Circle Development of Trigonometry
  55.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  56.    wt: 1:   9 The complex number valued trig function cis
  57.    wt: 1:   8 Unit Circle Development of Trigonometry
  58.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  59.    wt: 1:   Why Trigonometry the whyslopes view
  60.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  61.    wt: 1:   4 Similarity Definition with Coordinate
  62.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  63.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  64.    wt: 1:   6 Figuring with Maps Not to Scale
  65.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  66.    wt: 1:   19 Signed Multiples of Vectors
  67.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  68.    wt: 1:   13 Arrows and Vectors in a Plane
  69.    wt: 1:   8 Coordinates for Maps and Planes
  70.    wt: 1:   3 Geometric Formulas and Function Notation
  71.    wt: 1:   1 Formulas Dependence and Function Notation
  72.    wt: 1:   3 signed coordinates for maps and planes
  73.    wt: 1:   18 Efficient Ways to Multiply
  74.    wt: 1:   17 Efficient Ways to Add and Subtract
  75.    wt: 1:   10 Division by Five Long and Short Ways
  76.    wt: 1:   Example 4 with x function of y
  77.    wt: 1:   34 Derivative of exponential function
  78.    wt: 1:   31 Derivatives of inverse functions
  79.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  80.    wt: 1:   26 Chain Rule Recognising outer inner functions
  81.    wt: 1:   19 Chain Rule for linear functions
  82.    wt: 1:   3 Motivation for Limit Definition Take 2
  83.    wt: 1:   2 Motivation for Limit Definition Take 1
  84.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  85.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  86.    wt: 1:   F.1 What Functions are Continuous
  87.    wt: 1:   Chapter 23 Links To Trigonometry
  88.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  89.    wt: 1:   Chapter 19. Functions and Sets
  90.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  91.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  92.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

295 matches:

  1.    wt: 9:   4 Angles on Maps Plans drawn to scale
  2.    wt: 9:   3 Lengths and Areas on Maps and Plans
  3.    wt: 8:   16 cotangent function Definition Graph and Inverse
  4.    wt: 8:   15 cosecant function Definition Graph and Inverse
  5.    wt: 8:   14 secant function Definition Graph and Inverse
  6.    wt: 8:   13 cosecant function Definition Graph and Inverse
  7.    wt: 8:   13 Graph of tangent function many periods
  8.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  9.    wt: 8:   6 Figuring with Maps Not to Scale
  10.    wt: 7:   10 arctan left inverse of tangent Definition
  11.    wt: 7:   7 arcsin left inverse of sine Definition
  12.    wt: 7:   6 Graph of arccos function
  13.    wt: 7:   3 Left Inverse of cosine arccos definition
  14.    wt: 7:   2 cosine function more properties
  15.    wt: 7:   1 cosine function properties
  16.    wt: 7:   13 Velocity Vectors in Physics
  17.    wt: 7:   8 Parallel Vectors
  18.    wt: 7:   6 Vectors with Coordinates
  19.    wt: 7:   3 Navigation with Arrows or Vectors
  20.    wt: 7:   7 Tangent Function is odd on this domain
  21.    wt: 7:   6 Tangent Function Inclination Angle Take 2
  22.    wt: 7:   5 Tangent Function Graph
  23.    wt: 7:   4 Tangent Function Properties
  24.    wt: 7:   17 tangent function angle sum formulas
  25.    wt: 7:   30 unit circle calculation of six trigonometric functions
  26.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  27.    wt: 7:   17A The complex number valued trig function cis
  28.    wt: 7:   12 Graph of tangent function for one period
  29.    wt: 7:   11 tangent function undefined when terminal side vertical
  30.    wt: 7:   10 Graphs of sines and cosines many periods
  31.    wt: 7:   8 period of tangent function
  32.    wt: 7:   Unit Circle Development of Trigonometry
  33.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  34.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  35.    wt: 7:   Why Trigonometry the whyslopes view
  36.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  37.    wt: 7:   A Measurement with Ruler Proper Use
  38.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  39.    wt: 7:   2 Measuring Area Directly
  40.    wt: 7:   1 Length Measurement
  41.    wt: 6:   12 motivation for term arctan
  42.    wt: 6:   11 arctan left inverse of tangent Graph
  43.    wt: 6:   9 motivation for name arcsin
  44.    wt: 6:   8 arcsin left inverse of sine Graph
  45.    wt: 6:   5 Swapping Coordinates is a reflection
  46.    wt: 6:   4 possible motivation for term arccos
  47.    wt: 6:   A Global Time and Navigation
  48.    wt: 6:   15 Dot and Cross Product
  49.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  50.    wt: 6:   12 From Applied To Pure Mathematics
  51.    wt: 6:   11 Component Method
  52.    wt: 6:   10 Parallelogram Addition Method
  53.    wt: 6:   9 Head to Tail Coordinate View
  54.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  55.    wt: 6:   5 Head To Tail Arrow Addition
  56.    wt: 6:   4 Resultant of a Sum of Movements
  57.    wt: 6:   2 Signed Coordinates
  58.    wt: 6:   1 Unsigned Coordinates
  59.    wt: 6:   Vector and Complex Number Applet
  60.    wt: 6:   4 graphing y=Asin(x c)
  61.    wt: 6:   3 graphing y=f(x c) plus K
  62.    wt: 6:   2 Graphing y=Af(x) Vertical Scaling
  63.    wt: 6:   1 graphing y=f(x a)
  64.    wt: 6:   D Straight Lines Slope from Coordinates Examples
  65.    wt: 6:   C Straight Lines Slope from Coordinates
  66.    wt: 6:   B Straight Line Slope Scaling Properties More
  67.    wt: 6:   A Straight Line Slope Scaling Properties
  68.    wt: 6:   14 Straight Lines Equations General Case
  69.    wt: 6:   13 Straight Lines Finding Equations from 2 points
  70.    wt: 6:   12 Straight Lines Graphing mx plus b
  71.    wt: 6:   11 Straight Lines Graphing y=mx
  72.    wt: 6:   10 Straight Lines through Origin Equations More
  73.    wt: 6:   9 Straight Lines through Origin Equations
  74.    wt: 6:   8 Straight Lines Equation for vertical
  75.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  76.    wt: 6:   2 Straight Lines Slopes As Rise Over Run
  77.    wt: 6:   1 Straight Lines Slope Concept
  78.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  79.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  80.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  81.    wt: 6:   32 seven rows of pascals triangle
  82.    wt: 6:   31 basic secant cosecant cotangent trig identities
  83.    wt: 6:   29 secant cosecant and cotangent for acute angles
  84.    wt: 6:   28 Expressing products of sines cosines as sums
  85.    wt: 6:   27 Logarithmic use of products of sines and cosines
  86.    wt: 6:   26 Formulas for products of sines and cosines
  87.    wt: 6:   25 tangent double angle formula Slope connection
  88.    wt: 6:   24 tangent Angle Difference Formula
  89.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  90.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  91.    wt: 6:   21 sine and cosine Half Angle Formulas
  92.    wt: 6:   20 sine and cosine Double Angle Formulas
  93.    wt: 6:   18 sum of sinusoidal waves as a single wave
  94.    wt: 6:   17G Pythagorean Theorem Converse
  95.    wt: 6:   17F Law of cosines
  96.    wt: 6:   17E Trig Formulas for dot and cross Products
  97.    wt: 6:   17D cis formulas for sine cosines and tangent
  98.    wt: 6:   17C sine and cosine double triple angle formulas
  99.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  100.    wt: 6:   16 Right Triangle Complementary Angle Relations
  101.    wt: 6:   15 sine cosine Complementary Angle Relations
  102.    wt: 6:   14 cosine even and sine and tangent are odd
  103.    wt: 6:   9 Graphs of sine and cosine over one period
  104.    wt: 6:   7 period of sine and cosine
  105.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  106.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  107.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  108.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  109.    wt: 6:   2 Quadrant I reference Angles
  110.    wt: 6:   1 Unit Points Reflections Rotations
  111.    wt: 6:   9 The complex number valued trig function cis
  112.    wt: 6:   8 Unit Circle Development of Trigonometry
  113.    wt: 6:   8 Triangles Cascade Problem Solving
  114.    wt: 6:   7 Trignometric Ratios Unit Circle
  115.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  116.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  117.    wt: 6:   3 Trigonometric Ratios sine and cosine
  118.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  119.    wt: 6:   1 Angle Measurement with Degrees
  120.    wt: 6:   4 Similarity Definition with Coordinate
  121.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  122.    wt: 5:   9 Summary Degrees to Radians and back
  123.    wt: 5:   8 Radian Measures of Common Angles
  124.    wt: 5:   7 Radian Measures in special Triangles
  125.    wt: 5:   6 Radian Measure to Degrees
  126.    wt: 5:   5 Degrees to Radian Measure
  127.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  128.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  129.    wt: 5:   2 Radian Measure Numerical Value of one degree
  130.    wt: 5:   1 Degrees and Radians Introduction
  131.    wt: 5:   Parallel Lines and Parallel Transversals
  132.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  133.    wt: 5:   Triangle Angles Sum To 180 Degrees
  134.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  135.    wt: 5:   Parallel Lines and Interior Angles
  136.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  137.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  138.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  139.    wt: 5:   Straight Lines ASA Intersection Study More
  140.    wt: 5:   Straight Lines ASA Intersection Study
  141.    wt: 5:   Straight Lines Instersection Solving Equations
  142.    wt: 5:   Straight Lines Intersection of
  143.    wt: 5:   21 Logarithms Powers and Exponentials
  144.    wt: 5:   20 N th Roots of Complex Numbers
  145.    wt: 5:   19 N th Roots of Unity
  146.    wt: 5:   18 Sixth Roots of Unity
  147.    wt: 5:   17 Cube Roots of unity
  148.    wt: 5:   16 References and Originality Question
  149.    wt: 5:   15 Pythagorean Theorem Converse
  150.    wt: 5:   14 Law of cosines
  151.    wt: 5:   13 Trig Formulas for dot and cross Products
  152.    wt: 5:   12 cis formulas for sine cosines and tangent
  153.    wt: 5:   11 sine and cosine double triple angle formulas
  154.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  155.    wt: 5:   7 Second Way to Calculate Products
  156.    wt: 5:   6 Field Properties of Complex Number
  157.    wt: 5:   5 An Easy Proof of the Distributive Law
  158.    wt: 5:   4 Multiplication Properties
  159.    wt: 5:   3 Addition Properties
  160.    wt: 5:   2 Complex Numbers made easier we hope
  161.    wt: 5:   1 Rectangular Polar Coordinates Review
  162.    wt: 5:   Appetizer A Complex Number Applet
  163.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  164.    wt: 5:   12 Triangles Similarity More Problems
  165.    wt: 5:   11 Triangle Similarity Missing Side Problem
  166.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  167.    wt: 5:   9 Similarity of Triangles Usual Criteria
  168.    wt: 5:   8 Similarity of Triangles and Polygons
  169.    wt: 5:   7 Translations Rotations Reflections Dilatations
  170.    wt: 5:   6 Geometric Diagrams in Class
  171.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  172.    wt: 5:   3 Similarity by Design with coordinates
  173.    wt: 5:   2 Similarity By Design
  174.    wt: 5:   1 Early Concept of Like or Similar Shapes
  175.    wt: 5:   Four Simple Exercises
  176.    wt: 5:   12 Links Lessons elsewhere
  177.    wt: 5:   11 A Partial Summary
  178.    wt: 5:   10 Midpoint of [a b] and [b a]
  179.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  180.    wt: 5:   8 Mid Point Formula
  181.    wt: 5:   7 Exercises to test skill and concept mastery
  182.    wt: 5:   6 Intersection of lines by solving linear systems
  183.    wt: 5:   5 Algebraic View of Slopes
  184.    wt: 5:   4 Equations for lines three forms
  185.    wt: 5:   3 Slope product for perpendicular lines
  186.    wt: 5:   2 point slope equation for a line
  187.    wt: 5:   1 Numerical view of lines and their equations
  188.    wt: 5:   What is and is not here
  189.    wt: 5:   13 Pythagorean spatial distance formulas
  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:   13 Angle Side Angle Failure
  218.    wt: 5:   12 Side Angle Side Failure
  219.    wt: 5:   11 Triangle Construction Fails
  220.    wt: 5:   10 Dropping a perpendicular to line
  221.    wt: 5:   9 Construction of a right bisector
  222.    wt: 5:   8 Isoceles Triangles
  223.    wt: 5:   7 Angle Side Angle
  224.    wt: 5:   6 Ruler and compass Angle Bisection
  225.    wt: 5:   5 Side Angle Side
  226.    wt: 5:   4 Side Side Side
  227.    wt: 5:   3 Isometry of Triangles Congruence
  228.    wt: 5:   2 Correspondence between Triangles
  229.    wt: 5:   1 Initial Concepts and Terms
  230.    wt: 5:   Short Course on Euclidean Geometry
  231.    wt: 5:   About Folder Contents
  232.    wt: 3:   26 Function definitions done and coming
  233.    wt: 2:   Maps Plans Drawings
  234.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  235.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  236.    wt: 2:   23 Inverse Functions
  237.    wt: 2:   22 Square Root function graphically
  238.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  239.    wt: 2:   17 Function maxima minima and their location
  240.    wt: 2:   15 Sign analysis of functions
  241.    wt: 2:   13 From one to one to many to one
  242.    wt: 2:   12 Function Domain Recognition Exercises
  243.    wt: 2:   11 Function Domain Range Source and Targets
  244.    wt: 2:   8 Set view of relations and functions
  245.    wt: 2:   7 Functions with finite domains
  246.    wt: 2:   5 Function notation for geometric transformations
  247.    wt: 2:   4 Function notation in and beyond mathematics
  248.    wt: 2:   3 Formula or function graphing exercise
  249.    wt: 2:   2 Algebraic use of function notation
  250.    wt: 2:   1 Geometric Introduction of Function Notation
  251.    wt: 2:   3 Geometric Formulas and Function Notation
  252.    wt: 2:   1 Formulas Dependence and Function Notation
  253.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  254.    wt: 1:   About site lesson plans
  255.    wt: 1:   Four ways to improve education reform
  256.    wt: 1:   deux definitions pour variable
  257.    wt: 1:   20 Interchanging coordinates a reflection
  258.    wt: 1:   19 Horizontal line rule and method
  259.    wt: 1:   18 Vertical Line Rule and Method
  260.    wt: 1:   16 Increasing or decreasing on intervals
  261.    wt: 1:   14 Surjections Injections Bijections
  262.    wt: 1:   10 Interval Notation
  263.    wt: 1:   9 Set theory term relation possible origins
  264.    wt: 1:   6 Set Existence Formation and Notation
  265.    wt: 1:   Introduction Reading Guide
  266.    wt: 1:   Rewriting algebraic substitution as function substitutions
  267.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  268.    wt: 1:   19 Signed Multiples of Vectors
  269.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  270.    wt: 1:   13 Arrows and Vectors in a Plane
  271.    wt: 1:   8 Coordinates for Maps and Planes
  272.    wt: 1:   5 Independent versus Dependent Variables
  273.    wt: 1:   4 Changing Letters
  274.    wt: 1:   2 Computation Rules Evaluation
  275.    wt: 1:   3 signed coordinates for maps and planes
  276.    wt: 1:   18 Efficient Ways to Multiply
  277.    wt: 1:   17 Efficient Ways to Add and Subtract
  278.    wt: 1:   10 Division by Five Long and Short Ways
  279.    wt: 1:   Example 4 with x function of y
  280.    wt: 1:   34 Derivative of exponential function
  281.    wt: 1:   31 Derivatives of inverse functions
  282.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  283.    wt: 1:   26 Chain Rule Recognising outer inner functions
  284.    wt: 1:   19 Chain Rule for linear functions
  285.    wt: 1:   3 Motivation for Limit Definition Take 2
  286.    wt: 1:   2 Motivation for Limit Definition Take 1
  287.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  288.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  289.    wt: 1:   F.1 What Functions are Continuous
  290.    wt: 1:   Chapter 23 Links To Trigonometry
  291.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  292.    wt: 1:   Chapter 19. Functions and Sets
  293.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  294.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  295.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
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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