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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24 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   8 Unit Circle Trigonometry/
  4.    wt: 6:   6 Trigonometry first steps/
  5.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  6.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  7.    wt: 5:   12 Function Translating and Rescaling/
  8.    wt: 5:   11 Parallel Straight Lines and Transversals/
  9.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  10.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  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:   5 Factored Polynomial Sign Analysis Examples/
  18.    wt: 1:   4 Functions/
  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:   Step 3 Easy systems in 2 or more unknowns/

Web Page Search

70 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  3.    wt: 2:   4 Angles on Maps Plans drawn to scale
  4.    wt: 2:   3 Lengths and Areas on Maps and Plans
  5.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  6.    wt: 1:   About site lesson plans
  7.    wt: 1:   learning takes time
  8.    wt: 1:   what should be learnt and When
  9.    wt: 1:   4 Learning Takes Time and Effort
  10.    wt: 1:   2 cosine function more properties
  11.    wt: 1:   13 Velocity Vectors in Physics
  12.    wt: 1:   8 Parallel Vectors
  13.    wt: 1:   6 Vectors with Coordinates
  14.    wt: 1:   3 Navigation with Arrows or Vectors
  15.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  16.    wt: 1:   Straight Lines ASA Intersection Study More
  17.    wt: 1:   B Straight Line Slope Scaling Properties More
  18.    wt: 1:   10 Straight Lines through Origin Equations More
  19.    wt: 1:   Unit Circle Development of Trigonometry
  20.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  21.    wt: 1:   8 Unit Circle Development of Trigonometry
  22.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  23.    wt: 1:   Why Trigonometry the whyslopes view
  24.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  25.    wt: 1:   12 Triangles Similarity More Problems
  26.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  27.    wt: 1:   6 Figuring with Maps Not to Scale
  28.    wt: 1:   26 More Less Greater Than Comparison
  29.    wt: 1:   19 Signed Multiples of Vectors
  30.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  31.    wt: 1:   13 Arrows and Vectors in a Plane
  32.    wt: 1:   E Long Division Methods more
  33.    wt: 1:   3 Linear Equation Literal Solution More
  34.    wt: 1:   5 Greater More Less Than Signs in General
  35.    wt: 1:   3 More and Less Than with Unlike Signs
  36.    wt: 1:   2 More and Less Than for Counts and Measures
  37.    wt: 1:   8 Coordinates for Maps and Planes
  38.    wt: 1:   5 Rational Numbers More
  39.    wt: 1:   More Exercises
  40.    wt: 1:   4 Greater More Less Than Signs in General
  41.    wt: 1:   2 More and Less Than with Unlike Signs
  42.    wt: 1:   1 More and Less Than for Counts and Measures
  43.    wt: 1:   5 Square Roots with primes more still
  44.    wt: 1:   4 Square Roots with primes more
  45.    wt: 1:   3 signed coordinates for maps and planes
  46.    wt: 1:   12 Adding Integers More Examples
  47.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  48.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  49.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  50.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  51.    wt: 1:   Long Division Backwards more
  52.    wt: 1:   3 More One Digit Multipliers
  53.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  54.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  55.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  56.    wt: 1:   Chapter 23 Links To Trigonometry
  57.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  58.    wt: 1:   Chapter 4. More Slope Sign Analysis
  59.    wt: 1:   Postscript More on Better Performance
  60.    wt: 1:   Appendix B. How To Learn
  61.    wt: 1:   Postscript B More on Story Telling and Reason
  62.    wt: 1:   R Why Learn Mathematics Skills
  63.    wt: 1:   O On Learning Mathematics and Science
  64.    wt: 1:   J. More on written work and showing skill
  65.    wt: 1:   H more Routine to non routine problem solving
  66.    wt: 1:   Chapter 6 More Algebra and Geometry
  67.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  68.    wt: 1:   More Algebra and Slope based Calculus Preview
  69.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  70.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years

Extended Search

348 matches:

  1.    wt: 9:   8 More Use of Maps Not Drawn to Scale
  2.    wt: 9:   4 Angles on Maps Plans drawn to scale
  3.    wt: 9:   3 Lengths and Areas on Maps and Plans
  4.    wt: 8:   6 Figuring with Maps Not to Scale
  5.    wt: 7:   13 Velocity Vectors in Physics
  6.    wt: 7:   8 Parallel Vectors
  7.    wt: 7:   6 Vectors with Coordinates
  8.    wt: 7:   3 Navigation with Arrows or Vectors
  9.    wt: 7:   Unit Circle Development of Trigonometry
  10.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  11.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  12.    wt: 7:   Why Trigonometry the whyslopes view
  13.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  14.    wt: 7:   A Measurement with Ruler Proper Use
  15.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  16.    wt: 7:   2 Measuring Area Directly
  17.    wt: 7:   1 Length Measurement
  18.    wt: 6:   2 cosine function more properties
  19.    wt: 6:   A Global Time and Navigation
  20.    wt: 6:   15 Dot and Cross Product
  21.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  22.    wt: 6:   12 From Applied To Pure Mathematics
  23.    wt: 6:   11 Component Method
  24.    wt: 6:   10 Parallelogram Addition Method
  25.    wt: 6:   9 Head to Tail Coordinate View
  26.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  27.    wt: 6:   5 Head To Tail Arrow Addition
  28.    wt: 6:   4 Resultant of a Sum of Movements
  29.    wt: 6:   2 Signed Coordinates
  30.    wt: 6:   1 Unsigned Coordinates
  31.    wt: 6:   Vector and Complex Number Applet
  32.    wt: 6:   Analytic View of Triangle Construction or Line Instersection More
  33.    wt: 6:   Straight Lines ASA Intersection Study More
  34.    wt: 6:   B Straight Line Slope Scaling Properties More
  35.    wt: 6:   10 Straight Lines through Origin Equations More
  36.    wt: 6:   17 tangent function angle sum formulas
  37.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  38.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  39.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  40.    wt: 6:   32 seven rows of pascals triangle
  41.    wt: 6:   31 basic secant cosecant cotangent trig identities
  42.    wt: 6:   30 unit circle calculation of six trigonometric functions
  43.    wt: 6:   29 secant cosecant and cotangent for acute angles
  44.    wt: 6:   28 Expressing products of sines cosines as sums
  45.    wt: 6:   27 Logarithmic use of products of sines and cosines
  46.    wt: 6:   26 Formulas for products of sines and cosines
  47.    wt: 6:   25 tangent double angle formula Slope connection
  48.    wt: 6:   24 tangent Angle Difference Formula
  49.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  50.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  51.    wt: 6:   21 sine and cosine Half Angle Formulas
  52.    wt: 6:   20 sine and cosine Double Angle Formulas
  53.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  54.    wt: 6:   18 sum of sinusoidal waves as a single wave
  55.    wt: 6:   17G Pythagorean Theorem Converse
  56.    wt: 6:   17F Law of cosines
  57.    wt: 6:   17E Trig Formulas for dot and cross Products
  58.    wt: 6:   17D cis formulas for sine cosines and tangent
  59.    wt: 6:   17C sine and cosine double triple angle formulas
  60.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  61.    wt: 6:   17A The complex number valued trig function cis
  62.    wt: 6:   16 Right Triangle Complementary Angle Relations
  63.    wt: 6:   15 sine cosine Complementary Angle Relations
  64.    wt: 6:   14 cosine even and sine and tangent are odd
  65.    wt: 6:   13 Graph of tangent function many periods
  66.    wt: 6:   12 Graph of tangent function for one period
  67.    wt: 6:   11 tangent function undefined when terminal side vertical
  68.    wt: 6:   10 Graphs of sines and cosines many periods
  69.    wt: 6:   9 Graphs of sine and cosine over one period
  70.    wt: 6:   8 period of tangent function
  71.    wt: 6:   7 period of sine and cosine
  72.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  73.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  74.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  75.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  76.    wt: 6:   2 Quadrant I reference Angles
  77.    wt: 6:   1 Unit Points Reflections Rotations
  78.    wt: 6:   8 Unit Circle Development of Trigonometry
  79.    wt: 6:   8 Triangles Cascade Problem Solving
  80.    wt: 6:   7 Trignometric Ratios Unit Circle
  81.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  82.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  83.    wt: 6:   3 Trigonometric Ratios sine and cosine
  84.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  85.    wt: 6:   1 Angle Measurement with Degrees
  86.    wt: 6:   12 Triangles Similarity More Problems
  87.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  88.    wt: 5:   16 cotangent function Definition Graph and Inverse
  89.    wt: 5:   15 cosecant function Definition Graph and Inverse
  90.    wt: 5:   14 secant function Definition Graph and Inverse
  91.    wt: 5:   13 cosecant function Definition Graph and Inverse
  92.    wt: 5:   12 motivation for term arctan
  93.    wt: 5:   11 arctan left inverse of tangent Graph
  94.    wt: 5:   10 arctan left inverse of tangent Definition
  95.    wt: 5:   9 motivation for name arcsin
  96.    wt: 5:   8 arcsin left inverse of sine Graph
  97.    wt: 5:   7 arcsin left inverse of sine Definition
  98.    wt: 5:   6 Graph of arccos function
  99.    wt: 5:   5 Swapping Coordinates is a reflection
  100.    wt: 5:   4 possible motivation for term arccos
  101.    wt: 5:   3 Left Inverse of cosine arccos definition
  102.    wt: 5:   1 cosine function properties
  103.    wt: 5:   9 Summary Degrees to Radians and back
  104.    wt: 5:   8 Radian Measures of Common Angles
  105.    wt: 5:   7 Radian Measures in special Triangles
  106.    wt: 5:   6 Radian Measure to Degrees
  107.    wt: 5:   5 Degrees to Radian Measure
  108.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  109.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  110.    wt: 5:   2 Radian Measure Numerical Value of one degree
  111.    wt: 5:   1 Degrees and Radians Introduction
  112.    wt: 5:   4 graphing y=Asin(x c)
  113.    wt: 5:   3 graphing y=f(x c) plus K
  114.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  115.    wt: 5:   1 graphing y=f(x a)
  116.    wt: 5:   Parallel Lines and Parallel Transversals
  117.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  118.    wt: 5:   Triangle Angles Sum To 180 Degrees
  119.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  120.    wt: 5:   Parallel Lines and Interior Angles
  121.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  122.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  123.    wt: 5:   Straight Lines ASA Intersection Study
  124.    wt: 5:   Straight Lines Instersection Solving Equations
  125.    wt: 5:   Straight Lines Intersection of
  126.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  127.    wt: 5:   C Straight Lines Slope from Coordinates
  128.    wt: 5:   A Straight Line Slope Scaling Properties
  129.    wt: 5:   14 Straight Lines Equations General Case
  130.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  131.    wt: 5:   12 Straight Lines Graphing mx plus b
  132.    wt: 5:   11 Straight Lines Graphing y=mx
  133.    wt: 5:   9 Straight Lines through Origin Equations
  134.    wt: 5:   8 Straight Lines Equation for vertical
  135.    wt: 5:   7 Tangent Function is odd on this domain
  136.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  137.    wt: 5:   5 Tangent Function Graph
  138.    wt: 5:   4 Tangent Function Properties
  139.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  140.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  141.    wt: 5:   1 Straight Lines Slope Concept
  142.    wt: 5:   21 Logarithms Powers and Exponentials
  143.    wt: 5:   20 N th Roots of Complex Numbers
  144.    wt: 5:   19 N th Roots of Unity
  145.    wt: 5:   18 Sixth Roots of Unity
  146.    wt: 5:   17 Cube Roots of unity
  147.    wt: 5:   16 References and Originality Question
  148.    wt: 5:   15 Pythagorean Theorem Converse
  149.    wt: 5:   14 Law of cosines
  150.    wt: 5:   13 Trig Formulas for dot and cross Products
  151.    wt: 5:   12 cis formulas for sine cosines and tangent
  152.    wt: 5:   11 sine and cosine double triple angle formulas
  153.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  154.    wt: 5:   9 The complex number valued trig function 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:   11 Triangle Similarity Missing Side Problem
  165.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  166.    wt: 5:   9 Similarity of Triangles Usual Criteria
  167.    wt: 5:   8 Similarity of Triangles and Polygons
  168.    wt: 5:   7 Translations Rotations Reflections Dilatations
  169.    wt: 5:   6 Geometric Diagrams in Class
  170.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  171.    wt: 5:   4 Similarity Definition with Coordinate
  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: 2:   Maps Plans Drawings
  233.    wt: 2:   5 Greater More Less Than Signs in General
  234.    wt: 2:   3 More and Less Than with Unlike Signs
  235.    wt: 2:   2 More and Less Than for Counts and Measures
  236.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  237.    wt: 1:   About site lesson plans
  238.    wt: 1:   learning takes time
  239.    wt: 1:   what should be learnt and When
  240.    wt: 1:   4 Learning Takes Time and Effort
  241.    wt: 1:   sign monoticity analysis example 4
  242.    wt: 1:   sign monoticity analysis example 3
  243.    wt: 1:   sign monoticity analysis example 2
  244.    wt: 1:   sign monoticity analysis example 1
  245.    wt: 1:   26 Function definitions done and coming
  246.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  247.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  248.    wt: 1:   23 Inverse Functions
  249.    wt: 1:   22 Square Root function graphically
  250.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  251.    wt: 1:   20 Interchanging coordinates a reflection
  252.    wt: 1:   19 Horizontal line rule and method
  253.    wt: 1:   18 Vertical Line Rule and Method
  254.    wt: 1:   17 Function maxima minima and their location
  255.    wt: 1:   16 Increasing or decreasing on intervals
  256.    wt: 1:   15 Sign analysis of functions
  257.    wt: 1:   14 Surjections Injections Bijections
  258.    wt: 1:   13 From one to one to many to one
  259.    wt: 1:   12 Function Domain Recognition Exercises
  260.    wt: 1:   11 Function Domain Range Source and Targets
  261.    wt: 1:   10 Interval Notation
  262.    wt: 1:   9 Set theory term relation possible origins
  263.    wt: 1:   8 Set view of relations and functions
  264.    wt: 1:   7 Functions with finite domains
  265.    wt: 1:   6 Set Existence Formation and Notation
  266.    wt: 1:   5 Function notation for geometric transformations
  267.    wt: 1:   4 Function notation in and beyond mathematics
  268.    wt: 1:   3 Formula or function graphing exercise
  269.    wt: 1:   2 Algebraic use of function notation
  270.    wt: 1:   1 Geometric Introduction of Function Notation
  271.    wt: 1:   Introduction Reading Guide
  272.    wt: 1:   A Quadratics Summary
  273.    wt: 1:   10 quadratic exercises
  274.    wt: 1:   9 quadratics physical and further context
  275.    wt: 1:   8 quadratics backward use of various formulas
  276.    wt: 1:   7 quadratic formulla derivation
  277.    wt: 1:   6 quadratics numerical approach
  278.    wt: 1:   5 quadratics completing the square
  279.    wt: 1:   4 quadratics difference of two squares
  280.    wt: 1:   3 quadratics factoring by inspection
  281.    wt: 1:   2 quadratics graphing in general
  282.    wt: 1:   1 quadratics graphing exercises
  283.    wt: 1:   Quadratics in 10 steps
  284.    wt: 1:   11 Growth and Decay in Biology
  285.    wt: 1:   10 Exponential Growth and Decay Models
  286.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  287.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  288.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  289.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  290.    wt: 1:   5 Natural Logarithm Calculator Exercises
  291.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  292.    wt: 1:   2 Square Root Simplification a prequel
  293.    wt: 1:   1 Calculator Starter Exercises
  294.    wt: 1:   8 Notes for instructors or tutors
  295.    wt: 1:   7 Links Lessons Elsewhere
  296.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  297.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  298.    wt: 1:   4 Polynomials Long division linear divisor
  299.    wt: 1:   3 Polynomials Multiplication Addition
  300.    wt: 1:   2 Column Multiplication Method
  301.    wt: 1:   1 Polynomials Distributive Law
  302.    wt: 1:   Rewriting algebraic substitution as function substitutions
  303.    wt: 1:   26 More Less Greater Than Comparison
  304.    wt: 1:   19 Signed Multiples of Vectors
  305.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  306.    wt: 1:   13 Arrows and Vectors in a Plane
  307.    wt: 1:   E Long Division Methods more
  308.    wt: 1:   3 Linear Equation Literal Solution More
  309.    wt: 1:   4 Comparison of Negative Numbers
  310.    wt: 1:   1 Real Numbers Comparison
  311.    wt: 1:   8 Coordinates for Maps and Planes
  312.    wt: 1:   5 Rational Numbers More
  313.    wt: 1:   More Exercises
  314.    wt: 1:   4 Solving a triangular system exercise
  315.    wt: 1:   3 Solving triangular system example
  316.    wt: 1:   2 Essentially one exercises three with solution
  317.    wt: 1:   1 Essentially One Unknown
  318.    wt: 1:   4 Greater More Less Than Signs in General
  319.    wt: 1:   2 More and Less Than with Unlike Signs
  320.    wt: 1:   1 More and Less Than for Counts and Measures
  321.    wt: 1:   5 Square Roots with primes more still
  322.    wt: 1:   4 Square Roots with primes more
  323.    wt: 1:   3 signed coordinates for maps and planes
  324.    wt: 1:   12 Adding Integers More Examples
  325.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  326.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  327.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  328.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  329.    wt: 1:   Long Division Backwards more
  330.    wt: 1:   3 More One Digit Multipliers
  331.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  332.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  333.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  334.    wt: 1:   Chapter 23 Links To Trigonometry
  335.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  336.    wt: 1:   Chapter 4. More Slope Sign Analysis
  337.    wt: 1:   Postscript More on Better Performance
  338.    wt: 1:   Appendix B. How To Learn
  339.    wt: 1:   Postscript B More on Story Telling and Reason
  340.    wt: 1:   R Why Learn Mathematics Skills
  341.    wt: 1:   O On Learning Mathematics and Science
  342.    wt: 1:   J. More on written work and showing skill
  343.    wt: 1:   H more Routine to non routine problem solving
  344.    wt: 1:   Chapter 6 More Algebra and Geometry
  345.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  346.    wt: 1:   More Algebra and Slope based Calculus Preview
  347.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  348.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
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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