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 Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school. See Site Map

Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits
Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles

Welcome: Site content may develop critical thinking, improve reading and writing, and build mathematics skills. See online chapters on on logic and pattern based reason.

Teachers: This December 2011, 5-phase framework offers a context for mathematics & logic instruction. Phases 1 to 3 focus on skills with actual or potential value for adult & daily life. College-oriented phases 5 & 4 focus on calculus & preparation for it. Phases 1 to 4 may also serve trades & professions not dependent on calculus.

Site Review: Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation for high school and college ... mathematics. Read more.

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22 matches:

  1.    wt: 8:   7 Complex Numbers/
  2.    wt: 7:   1 Maps Plans Measurement/
  3.    wt: 6:   13 Vectors/
  4.    wt: 6:   8 Unit Circle Trigonometry/
  5.    wt: 6:   6 Trigonometry first steps/
  6.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  7.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  8.    wt: 5:   12 Function Translating and Rescaling/
  9.    wt: 5:   11 Parallel Straight Lines and Transversals/
  10.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  11.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 1:   B Real Numbers Extrinsic Development/
  18.    wt: 1:   5 Real Numbers/
  19.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  20.    wt: 1:   8 Arithmetic with Signed Numbers/
  21.    wt: 1:   7 Arithmetic and Fractions with Units/
  22.    wt: 1:   Resources and Reciprocal Links/

Web Page Search

85 matches:

  1.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  2.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  3.    wt: 2:   Maps Plans Drawings
  4.    wt: 2:   20 N th Roots of Complex Numbers
  5.    wt: 2:   2 Complex Numbers made easier we hope
  6.    wt: 2:   7 Complex Numbers Appetizer
  7.    wt: 2:   PS H Distributive Law For Complex Numbers
  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:   Chapter 23 Links To Trigonometry
  11.    wt: 2:   Chapter 22 Complex Numbers
  12.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  13.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  14.    wt: 1:   Ramblings Extrinsic numbers theory
  15.    wt: 1:   2 arithmetic with signed numbers
  16.    wt: 1:   1 arithmetic with unsigned numbers
  17.    wt: 1:   links Education Resources online
  18.    wt: 1:   About site lesson plans
  19.    wt: 1:   7 Links Lessons Elsewhere
  20.    wt: 1:   13 Velocity Vectors in Physics
  21.    wt: 1:   8 Parallel Vectors
  22.    wt: 1:   6 Vectors with Coordinates
  23.    wt: 1:   3 Navigation with Arrows or Vectors
  24.    wt: 1:   Vector and Complex Number Applet
  25.    wt: 1:   17A The complex number valued trig function cis
  26.    wt: 1:   Unit Circle Development of Trigonometry
  27.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  28.    wt: 1:   9 The complex number valued trig function cis
  29.    wt: 1:   8 Unit Circle Development of Trigonometry
  30.    wt: 1:   6 Field Properties of Complex Number
  31.    wt: 1:   Appetizer A Complex Number Applet
  32.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  33.    wt: 1:   Why Trigonometry the whyslopes view
  34.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  35.    wt: 1:   12 Links Lessons elsewhere
  36.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  37.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  38.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  39.    wt: 1:   6 Figuring with Maps Not to Scale
  40.    wt: 1:   musings do not puiblish real numbers
  41.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  42.    wt: 1:   22 Multiplication of Signed Numbers
  43.    wt: 1:   19 Signed Multiples of Vectors
  44.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  45.    wt: 1:   13 Arrows and Vectors in a Plane
  46.    wt: 1:   12 Real Numbers Line Signed Coordinates
  47.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  48.    wt: 1:   5 Distributive Law for Whole Numbers
  49.    wt: 1:   1 The Counting Origins of Numbers
  50.    wt: 1:   4 Comparison of Negative Numbers
  51.    wt: 1:   1 Real Numbers Comparison
  52.    wt: 1:   16 Real Numbers Comparison
  53.    wt: 1:   8 Coordinates for Maps and Planes
  54.    wt: 1:   7 Real Numbers as Line Cordinates
  55.    wt: 1:   6 Unsigned Real Numbers
  56.    wt: 1:   5 Rational Numbers More
  57.    wt: 1:   4 Rational Numbers
  58.    wt: 1:   1 Whole and Natural Numbers
  59.    wt: 1:   8 Sets of Numbers
  60.    wt: 1:   5 Talking about Numbers and Quantities
  61.    wt: 1:   4 A Brief Story of numbers and algebra
  62.    wt: 1:   3 Comparison of Negative Numbers
  63.    wt: 1:   11 What are real lengths and numbers
  64.    wt: 1:   10 dividing signed numbers
  65.    wt: 1:   9 subtracting signed numbers
  66.    wt: 1:   8 multiplying signed numbers
  67.    wt: 1:   6 adding signed numbers
  68.    wt: 1:   5 lengths and signs of numbers
  69.    wt: 1:   3 signed coordinates for maps and planes
  70.    wt: 1:   2 signed and unsigned numbers as coordinates
  71.    wt: 1:   3 Multiplying Units and Numbers
  72.    wt: 1:   22 Complex Compound Fractions
  73.    wt: 1:   9 Improper Fractions and Mixed Numbers
  74.    wt: 1:   6 Multiplication of Mixed Numbers
  75.    wt: 1:   8 Multiplication by Signed Numbers Integers
  76.    wt: 1:   6 Multiplication by Natural Numbers
  77.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  78.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  79.    wt: 1:   Quick history of numbers and algebra
  80.    wt: 1:   011 Division of Time Intervals By Numbers
  81.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  82.    wt: 1:   Annotated Links to Material Elsehwere
  83.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  84.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  85.    wt: 1:   Systematic Algebra Skill Development Missing Links

Extended Search

338 matches:

  1.    wt: 9:   9 The complex number valued trig function cis
  2.    wt: 9:   8 Unit Circle Development of Trigonometry
  3.    wt: 9:   7 Second Way to Calculate Products
  4.    wt: 9:   6 Field Properties of Complex Number
  5.    wt: 9:   Appetizer A Complex Number Applet
  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:   21 Logarithms Powers and Exponentials
  9.    wt: 8:   19 N th Roots of Unity
  10.    wt: 8:   18 Sixth Roots of Unity
  11.    wt: 8:   17 Cube Roots of unity
  12.    wt: 8:   16 References and Originality Question
  13.    wt: 8:   15 Pythagorean Theorem Converse
  14.    wt: 8:   14 Law of cosines
  15.    wt: 8:   13 Trig Formulas for dot and cross Products
  16.    wt: 8:   12 cis formulas for sine cosines and tangent
  17.    wt: 8:   11 sine and cosine double triple angle formulas
  18.    wt: 8:   10 sine cosine Angle Sum Formulas via cis
  19.    wt: 8:   5 An Easy Proof of the Distributive Law
  20.    wt: 8:   4 Multiplication Properties
  21.    wt: 8:   3 Addition Properties
  22.    wt: 8:   1 Rectangular Polar Coordinates Review
  23.    wt: 8:   7 Complex Numbers Appetizer
  24.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  25.    wt: 8:   6 Figuring with Maps Not to Scale
  26.    wt: 7:   13 Velocity Vectors in Physics
  27.    wt: 7:   8 Parallel Vectors
  28.    wt: 7:   7 Coordinate Addition and Scalar Multiplication
  29.    wt: 7:   6 Vectors with Coordinates
  30.    wt: 7:   3 Navigation with Arrows or Vectors
  31.    wt: 7:   Vector and Complex Number Applet
  32.    wt: 7:   17A The complex number valued trig function cis
  33.    wt: 7:   Unit Circle Development of Trigonometry
  34.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  35.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  36.    wt: 7:   Why Trigonometry the whyslopes view
  37.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  38.    wt: 7:   PS H Distributive Law For Complex Numbers
  39.    wt: 7:   A Measurement with Ruler Proper Use
  40.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  41.    wt: 7:   2 Measuring Area Directly
  42.    wt: 7:   1 Length Measurement
  43.    wt: 6:   A Global Time and Navigation
  44.    wt: 6:   15 Dot and Cross Product
  45.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  46.    wt: 6:   12 From Applied To Pure Mathematics
  47.    wt: 6:   11 Component Method
  48.    wt: 6:   10 Parallelogram Addition Method
  49.    wt: 6:   9 Head to Tail Coordinate View
  50.    wt: 6:   5 Head To Tail Arrow Addition
  51.    wt: 6:   4 Resultant of a Sum of Movements
  52.    wt: 6:   2 Signed Coordinates
  53.    wt: 6:   1 Unsigned Coordinates
  54.    wt: 6:   17 tangent function angle sum formulas
  55.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  56.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  57.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  58.    wt: 6:   32 seven rows of pascals triangle
  59.    wt: 6:   31 basic secant cosecant cotangent trig identities
  60.    wt: 6:   30 unit circle calculation of six trigonometric functions
  61.    wt: 6:   29 secant cosecant and cotangent for acute angles
  62.    wt: 6:   28 Expressing products of sines cosines as sums
  63.    wt: 6:   27 Logarithmic use of products of sines and cosines
  64.    wt: 6:   26 Formulas for products of sines and cosines
  65.    wt: 6:   25 tangent double angle formula Slope connection
  66.    wt: 6:   24 tangent Angle Difference Formula
  67.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  68.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  69.    wt: 6:   21 sine and cosine Half Angle Formulas
  70.    wt: 6:   20 sine and cosine Double Angle Formulas
  71.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  72.    wt: 6:   18 sum of sinusoidal waves as a single wave
  73.    wt: 6:   17G Pythagorean Theorem Converse
  74.    wt: 6:   17F Law of cosines
  75.    wt: 6:   17E Trig Formulas for dot and cross Products
  76.    wt: 6:   17D cis formulas for sine cosines and tangent
  77.    wt: 6:   17C sine and cosine double triple angle formulas
  78.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  79.    wt: 6:   16 Right Triangle Complementary Angle Relations
  80.    wt: 6:   15 sine cosine Complementary Angle Relations
  81.    wt: 6:   14 cosine even and sine and tangent are odd
  82.    wt: 6:   13 Graph of tangent function many periods
  83.    wt: 6:   12 Graph of tangent function for one period
  84.    wt: 6:   11 tangent function undefined when terminal side vertical
  85.    wt: 6:   10 Graphs of sines and cosines many periods
  86.    wt: 6:   9 Graphs of sine and cosine over one period
  87.    wt: 6:   8 period of tangent function
  88.    wt: 6:   7 period of sine and cosine
  89.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  90.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  91.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  92.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  93.    wt: 6:   2 Quadrant I reference Angles
  94.    wt: 6:   1 Unit Points Reflections Rotations
  95.    wt: 6:   8 Triangles Cascade Problem Solving
  96.    wt: 6:   7 Trignometric Ratios Unit Circle
  97.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  98.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  99.    wt: 6:   3 Trigonometric Ratios sine and cosine
  100.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  101.    wt: 6:   1 Angle Measurement with Degrees
  102.    wt: 6:   12 Links Lessons elsewhere
  103.    wt: 6:   7 Exercises to test skill and concept mastery
  104.    wt: 6:   Euclidean Geometry Elsewhere LINKS
  105.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  106.    wt: 6:   7 Angle Side Angle
  107.    wt: 5:   16 cotangent function Definition Graph and Inverse
  108.    wt: 5:   15 cosecant function Definition Graph and Inverse
  109.    wt: 5:   14 secant function Definition Graph and Inverse
  110.    wt: 5:   13 cosecant function Definition Graph and Inverse
  111.    wt: 5:   12 motivation for term arctan
  112.    wt: 5:   11 arctan left inverse of tangent Graph
  113.    wt: 5:   10 arctan left inverse of tangent Definition
  114.    wt: 5:   9 motivation for name arcsin
  115.    wt: 5:   8 arcsin left inverse of sine Graph
  116.    wt: 5:   7 arcsin left inverse of sine Definition
  117.    wt: 5:   6 Graph of arccos function
  118.    wt: 5:   5 Swapping Coordinates is a reflection
  119.    wt: 5:   4 possible motivation for term arccos
  120.    wt: 5:   3 Left Inverse of cosine arccos definition
  121.    wt: 5:   2 cosine function more properties
  122.    wt: 5:   1 cosine function properties
  123.    wt: 5:   9 Summary Degrees to Radians and back
  124.    wt: 5:   8 Radian Measures of Common Angles
  125.    wt: 5:   7 Radian Measures in special Triangles
  126.    wt: 5:   6 Radian Measure to Degrees
  127.    wt: 5:   5 Degrees to Radian Measure
  128.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  129.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  130.    wt: 5:   2 Radian Measure Numerical Value of one degree
  131.    wt: 5:   1 Degrees and Radians Introduction
  132.    wt: 5:   4 graphing y=Asin(x c)
  133.    wt: 5:   3 graphing y=f(x c) plus K
  134.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  135.    wt: 5:   1 graphing y=f(x a)
  136.    wt: 5:   Parallel Lines and Parallel Transversals
  137.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  138.    wt: 5:   Triangle Angles Sum To 180 Degrees
  139.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  140.    wt: 5:   Parallel Lines and Interior Angles
  141.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  142.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  143.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  144.    wt: 5:   Straight Lines ASA Intersection Study More
  145.    wt: 5:   Straight Lines ASA Intersection Study
  146.    wt: 5:   Straight Lines Instersection Solving Equations
  147.    wt: 5:   Straight Lines Intersection of
  148.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  149.    wt: 5:   C Straight Lines Slope from Coordinates
  150.    wt: 5:   B Straight Line Slope Scaling Properties More
  151.    wt: 5:   A Straight Line Slope Scaling Properties
  152.    wt: 5:   14 Straight Lines Equations General Case
  153.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  154.    wt: 5:   12 Straight Lines Graphing mx plus b
  155.    wt: 5:   11 Straight Lines Graphing y=mx
  156.    wt: 5:   10 Straight Lines through Origin Equations More
  157.    wt: 5:   9 Straight Lines through Origin Equations
  158.    wt: 5:   8 Straight Lines Equation for vertical
  159.    wt: 5:   7 Tangent Function is odd on this domain
  160.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  161.    wt: 5:   5 Tangent Function Graph
  162.    wt: 5:   4 Tangent Function Properties
  163.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  164.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  165.    wt: 5:   1 Straight Lines Slope Concept
  166.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  167.    wt: 5:   12 Triangles Similarity More Problems
  168.    wt: 5:   11 Triangle Similarity Missing Side Problem
  169.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  170.    wt: 5:   9 Similarity of Triangles Usual Criteria
  171.    wt: 5:   8 Similarity of Triangles and Polygons
  172.    wt: 5:   7 Translations Rotations Reflections Dilatations
  173.    wt: 5:   6 Geometric Diagrams in Class
  174.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  175.    wt: 5:   4 Similarity Definition with Coordinate
  176.    wt: 5:   3 Similarity by Design with coordinates
  177.    wt: 5:   2 Similarity By Design
  178.    wt: 5:   1 Early Concept of Like or Similar Shapes
  179.    wt: 5:   Four Simple Exercises
  180.    wt: 5:   11 A Partial Summary
  181.    wt: 5:   10 Midpoint of [a b] and [b a]
  182.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  183.    wt: 5:   8 Mid Point Formula
  184.    wt: 5:   6 Intersection of lines by solving linear systems
  185.    wt: 5:   5 Algebraic View of Slopes
  186.    wt: 5:   4 Equations for lines three forms
  187.    wt: 5:   3 Slope product for perpendicular lines
  188.    wt: 5:   2 point slope equation for a line
  189.    wt: 5:   1 Numerical view of lines and their equations
  190.    wt: 5:   What is and is not here
  191.    wt: 5:   13 Pythagorean spatial distance formulas
  192.    wt: 5:   12 Spatial Coordinates
  193.    wt: 5:   11 Triangle Inequality
  194.    wt: 5:   10 Pythagorean plane distance formula
  195.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  196.    wt: 5:   8 Distance Between Points on a Line
  197.    wt: 5:   6 Polar Multiplication and Rotation
  198.    wt: 5:   5 Cartesian Addition and Translation
  199.    wt: 5:   4 Polar Coordinates to and from
  200.    wt: 5:   3 Rectangular Coordinates Review
  201.    wt: 5:   2 Cartesian Coordinates with signs
  202.    wt: 5:   1 Cartesian Coordinates sans signs
  203.    wt: 5:   PS G Rotation Distributes over Addition
  204.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  205.    wt: 5:   PS E Multiplication with Polar Coordinates
  206.    wt: 5:   PS D Addition with Cartesian Coordinates
  207.    wt: 5:   PS B Parallelogram Construction Methods
  208.    wt: 5:   PS A Kite Construction Methods
  209.    wt: 5:   21 Parallelograms
  210.    wt: 5:   19 Right Triangle Similarity
  211.    wt: 5:   18 Triangle Similarity Take 1
  212.    wt: 5:   17 Right Bisectors of Triangle Sides
  213.    wt: 5:   16 Angles Subtended By Chords and Diameters
  214.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  215.    wt: 5:   14 Parallel Lines Postulate
  216.    wt: 5:   13 Angle Side Angle Failure
  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:   6 Ruler and compass Angle Bisection
  223.    wt: 5:   5 Side Angle Side
  224.    wt: 5:   4 Side Side Side
  225.    wt: 5:   3 Isometry of Triangles Congruence
  226.    wt: 5:   2 Correspondence between Triangles
  227.    wt: 5:   1 Initial Concepts and Terms
  228.    wt: 5:   Short Course on Euclidean Geometry
  229.    wt: 5:   About Folder Contents
  230.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  231.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  232.    wt: 2:   Maps Plans Drawings
  233.    wt: 2:   musings do not puiblish real numbers
  234.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  235.    wt: 2:   22 Multiplication of Signed Numbers
  236.    wt: 2:   19 Signed Multiples of Vectors
  237.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  238.    wt: 2:   13 Arrows and Vectors in a Plane
  239.    wt: 2:   12 Real Numbers Line Signed Coordinates
  240.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  241.    wt: 2:   16 Real Numbers Comparison
  242.    wt: 2:   8 Coordinates for Maps and Planes
  243.    wt: 2:   7 Real Numbers as Line Cordinates
  244.    wt: 2:   6 Unsigned Real Numbers
  245.    wt: 2:   5 Rational Numbers More
  246.    wt: 2:   4 Rational Numbers
  247.    wt: 2:   1 Whole and Natural Numbers
  248.    wt: 2:   3 Comparison of Negative Numbers
  249.    wt: 2:   11 What are real lengths and numbers
  250.    wt: 2:   10 dividing signed numbers
  251.    wt: 2:   9 subtracting signed numbers
  252.    wt: 2:   8 multiplying signed numbers
  253.    wt: 2:   6 adding signed numbers
  254.    wt: 2:   5 lengths and signs of numbers
  255.    wt: 2:   3 signed coordinates for maps and planes
  256.    wt: 2:   2 signed and unsigned numbers as coordinates
  257.    wt: 2:   3 Multiplying Units and Numbers
  258.    wt: 2:   Chapter 23 Links To Trigonometry
  259.    wt: 2:   Chapter 22 Complex Numbers
  260.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  261.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  262.    wt: 1:   Ramblings Extrinsic numbers theory
  263.    wt: 1:   2 arithmetic with signed numbers
  264.    wt: 1:   1 arithmetic with unsigned numbers
  265.    wt: 1:   links Education Resources online
  266.    wt: 1:   About site lesson plans
  267.    wt: 1:   7 Student Motivation
  268.    wt: 1:   7 Links Lessons Elsewhere
  269.    wt: 1:   A Modular and Remainder Arithmetic
  270.    wt: 1:   A Signed Number Arithmetic Review
  271.    wt: 1:   26 More Less Greater Than Comparison
  272.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  273.    wt: 1:   23 Distributive Law Two Derivations
  274.    wt: 1:   21 Addition of Multiples of a Single Vector
  275.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  276.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  277.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  278.    wt: 1:   15 Head to Tails in place Addition Associative
  279.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  280.    wt: 1:   11 Signed Number Addition and Addition Properties
  281.    wt: 1:   9 Division with Digits after Decimal Point
  282.    wt: 1:   8 Division and Mulplication of Compound Fractions
  283.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  284.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  285.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  286.    wt: 1:   4 Location of Point in Decimal Addition
  287.    wt: 1:   3 Location of Point in Decimal Multiplication
  288.    wt: 1:   2 Counting Digits in Decimal Multiplication
  289.    wt: 1:   1 Fractions with Finite Decimal Expansions
  290.    wt: 1:   7 Decimals Multiplication Methods Examples
  291.    wt: 1:   5 Distributive Law for Whole Numbers
  292.    wt: 1:   1 The Counting Origins of Numbers
  293.    wt: 1:   4 Comparison of Negative Numbers
  294.    wt: 1:   1 Real Numbers Comparison
  295.    wt: 1:   15 Real Number Division
  296.    wt: 1:   14 Real Number Multiplication
  297.    wt: 1:   13 Real Number Subtraction
  298.    wt: 1:   12 Real Number Additive Inverses or Negatives
  299.    wt: 1:   11 Real Number Addition
  300.    wt: 1:   10 Real Number Lengths and Signs
  301.    wt: 1:   9 Coordinates for Regions in Space
  302.    wt: 1:   3 Fractions
  303.    wt: 1:   2 Integers
  304.    wt: 1:   7 Two Examples
  305.    wt: 1:   8 Sets of Numbers
  306.    wt: 1:   5 Talking about Numbers and Quantities
  307.    wt: 1:   4 A Brief Story of numbers and algebra
  308.    wt: 1:   4 Greater More Less Than Signs in General
  309.    wt: 1:   2 More and Less Than with Unlike Signs
  310.    wt: 1:   1 More and Less Than for Counts and Measures
  311.    wt: 1:   7 negative and additive inverse
  312.    wt: 1:   4 signed coordinates for regions in space
  313.    wt: 1:   7 Converting or Changing Units
  314.    wt: 1:   6 Simplification of Fractions with Units
  315.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  316.    wt: 1:   4 Fractions with Units
  317.    wt: 1:   2 Equality and Units
  318.    wt: 1:   1 Addition and Subtraction with Units
  319.    wt: 1:   22 Complex Compound Fractions
  320.    wt: 1:   9 Improper Fractions and Mixed Numbers
  321.    wt: 1:   6 Multiplication of Mixed Numbers
  322.    wt: 1:   8 Multiplication by Signed Numbers Integers
  323.    wt: 1:   7 Multiplication by Signs
  324.    wt: 1:   6 Multiplication by Natural Numbers
  325.    wt: 1:   7 Calculator Usage Notes and Cautions
  326.    wt: 1:   7 Long Divison Mistake Catching
  327.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  328.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  329.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  330.    wt: 1:   Quick history of numbers and algebra
  331.    wt: 1:   011 Division of Time Intervals By Numbers
  332.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  333.    wt: 1:   Annotated Links to Material Elsehwere
  334.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  335.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  336.    wt: 1:   Systematic Algebra Skill Development Missing Links
  337.    wt: 10:   20 N th Roots of Complex Numbers
  338.    wt: 10:   2 Complex Numbers made easier we hope

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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