Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic
and Pattern Based Reason to inform and amuse thinkers and avid readers, studying or not. Enjoy.

Logic mastery strengthens comprehension and improve home, work & study habits.
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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

About: Site material shows how common troubles stem from steps too large or missing. Site material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin. If one site element is not to your liking, try another. Each is different. Many are unique

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local 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. Reform: look before you leap - plan all in detail first.

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

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20 matches:

  1.    wt: 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: 2:   12 Comparison of Unsigned and Signed Numbers/
  18.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  19.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  20.    wt: 1:   8 Arithmetic with Signed Numbers/

Web Page Search

75 matches:

  1.    wt: 3:   1 Proper Equal Sign Usage
  2.    wt: 2:   Maps Plans Drawings
  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:   19 Signed Multiples of Vectors
  6.    wt: 2:   3 signed coordinates for maps and planes
  7.    wt: 2:   2 signed and unsigned numbers as coordinates
  8.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  9.    wt: 1:   2 arithmetic with signed numbers
  10.    wt: 1:   1 arithmetic with unsigned numbers
  11.    wt: 1:   About site lesson plans
  12.    wt: 1:   sign monoticity analysis example 4
  13.    wt: 1:   sign monoticity analysis example 3
  14.    wt: 1:   sign monoticity analysis example 2
  15.    wt: 1:   sign monoticity analysis example 1
  16.    wt: 1:   15 Sign analysis of functions
  17.    wt: 1:   13 Velocity Vectors in Physics
  18.    wt: 1:   8 Parallel Vectors
  19.    wt: 1:   6 Vectors with Coordinates
  20.    wt: 1:   3 Navigation with Arrows or Vectors
  21.    wt: 1:   2 Signed Coordinates
  22.    wt: 1:   1 Unsigned Coordinates
  23.    wt: 1:   Unit Circle Development of Trigonometry
  24.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  25.    wt: 1:   8 Unit Circle Development of Trigonometry
  26.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  27.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  28.    wt: 1:   Why Trigonometry the whyslopes view
  29.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  30.    wt: 1:   3 Similarity by Design with coordinates
  31.    wt: 1:   2 Similarity By Design
  32.    wt: 1:   11 Triangle Inequality
  33.    wt: 1:   2 Cartesian Coordinates with signs
  34.    wt: 1:   1 Cartesian Coordinates sans signs
  35.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  36.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  37.    wt: 1:   6 Figuring with Maps Not to Scale
  38.    wt: 1:   A Signed Number Arithmetic Review
  39.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  40.    wt: 1:   22 Multiplication of Signed Numbers
  41.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  42.    wt: 1:   13 Arrows and Vectors in a Plane
  43.    wt: 1:   12 Real Numbers Line Signed Coordinates
  44.    wt: 1:   11 Signed Number Addition and Addition Properties
  45.    wt: 1:   3 Inequalities Algebraically
  46.    wt: 1:   5 Equality in Algebra
  47.    wt: 1:   5 Greater More Less Than Signs in General
  48.    wt: 1:   3 More and Less Than with Unlike Signs
  49.    wt: 1:   10 Real Number Lengths and Signs
  50.    wt: 1:   8 Coordinates for Maps and Planes
  51.    wt: 1:   6 Unsigned Real Numbers
  52.    wt: 1:   Formula Usage Show Work Format
  53.    wt: 1:   4 Greater More Less Than Signs in General
  54.    wt: 1:   2 More and Less Than with Unlike Signs
  55.    wt: 1:   10 dividing signed numbers
  56.    wt: 1:   9 subtracting signed numbers
  57.    wt: 1:   8 multiplying signed numbers
  58.    wt: 1:   6 adding signed numbers
  59.    wt: 1:   5 lengths and signs of numbers
  60.    wt: 1:   4 signed coordinates for regions in space
  61.    wt: 1:   2 Equality and Units
  62.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  63.    wt: 1:   21 Working With Signs
  64.    wt: 1:   8 Multiplication by Signed Numbers Integers
  65.    wt: 1:   7 Multiplication by Signs
  66.    wt: 1:   7 Calculator Usage Notes and Cautions
  67.    wt: 1:   E1 Error Control Inequalities
  68.    wt: 1:   C Triangle Inequalities
  69.    wt: 1:   Chapter 23 Links To Trigonometry
  70.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  71.    wt: 1:   Chapter 5. Slope Sign Tests
  72.    wt: 1:   Chapter 4. More Slope Sign Analysis
  73.    wt: 1:   Chapter 3. Slope Sign Analysis
  74.    wt: 1:   Chapter 12. Shorthand Usage Guide
  75.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

290 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:   8 More Use of Maps Not Drawn to Scale
  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:   2 Signed Coordinates
  10.    wt: 7:   1 Unsigned Coordinates
  11.    wt: 7:   Unit Circle Development of Trigonometry
  12.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  13.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  14.    wt: 7:   2 Similar Triangles Equality of Corresponding Side Ratios
  15.    wt: 7:   Why Trigonometry the whyslopes view
  16.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  17.    wt: 7:   A Measurement with Ruler Proper Use
  18.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  19.    wt: 7:   2 Measuring Area Directly
  20.    wt: 7:   1 Length Measurement
  21.    wt: 6:   A Global Time and Navigation
  22.    wt: 6:   15 Dot and Cross Product
  23.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  24.    wt: 6:   12 From Applied To Pure Mathematics
  25.    wt: 6:   11 Component Method
  26.    wt: 6:   10 Parallelogram Addition Method
  27.    wt: 6:   9 Head to Tail Coordinate View
  28.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  29.    wt: 6:   5 Head To Tail Arrow Addition
  30.    wt: 6:   4 Resultant of a Sum of Movements
  31.    wt: 6:   Vector and Complex Number Applet
  32.    wt: 6:   17 tangent function angle sum formulas
  33.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  34.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  35.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  36.    wt: 6:   32 seven rows of pascals triangle
  37.    wt: 6:   31 basic secant cosecant cotangent trig identities
  38.    wt: 6:   30 unit circle calculation of six trigonometric functions
  39.    wt: 6:   29 secant cosecant and cotangent for acute angles
  40.    wt: 6:   28 Expressing products of sines cosines as sums
  41.    wt: 6:   27 Logarithmic use of products of sines and cosines
  42.    wt: 6:   26 Formulas for products of sines and cosines
  43.    wt: 6:   25 tangent double angle formula Slope connection
  44.    wt: 6:   24 tangent Angle Difference Formula
  45.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  46.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  47.    wt: 6:   21 sine and cosine Half Angle Formulas
  48.    wt: 6:   20 sine and cosine Double Angle Formulas
  49.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  50.    wt: 6:   18 sum of sinusoidal waves as a single wave
  51.    wt: 6:   17G Pythagorean Theorem Converse
  52.    wt: 6:   17F Law of cosines
  53.    wt: 6:   17E Trig Formulas for dot and cross Products
  54.    wt: 6:   17D cis formulas for sine cosines and tangent
  55.    wt: 6:   17C sine and cosine double triple angle formulas
  56.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  57.    wt: 6:   17A The complex number valued trig function cis
  58.    wt: 6:   16 Right Triangle Complementary Angle Relations
  59.    wt: 6:   15 sine cosine Complementary Angle Relations
  60.    wt: 6:   14 cosine even and sine and tangent are odd
  61.    wt: 6:   13 Graph of tangent function many periods
  62.    wt: 6:   12 Graph of tangent function for one period
  63.    wt: 6:   11 tangent function undefined when terminal side vertical
  64.    wt: 6:   10 Graphs of sines and cosines many periods
  65.    wt: 6:   9 Graphs of sine and cosine over one period
  66.    wt: 6:   8 period of tangent function
  67.    wt: 6:   7 period of sine and cosine
  68.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  69.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  70.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  71.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  72.    wt: 6:   2 Quadrant I reference Angles
  73.    wt: 6:   1 Unit Points Reflections Rotations
  74.    wt: 6:   8 Unit Circle Development of Trigonometry
  75.    wt: 6:   8 Triangles Cascade Problem Solving
  76.    wt: 6:   7 Trignometric Ratios Unit Circle
  77.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  78.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  79.    wt: 6:   3 Trigonometric Ratios sine and cosine
  80.    wt: 6:   1 Angle Measurement with Degrees
  81.    wt: 6:   3 Similarity by Design with coordinates
  82.    wt: 6:   2 Similarity By Design
  83.    wt: 6:   11 Triangle Inequality
  84.    wt: 6:   2 Cartesian Coordinates with signs
  85.    wt: 6:   1 Cartesian Coordinates sans signs
  86.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  87.    wt: 5:   16 cotangent function Definition Graph and Inverse
  88.    wt: 5:   15 cosecant function Definition Graph and Inverse
  89.    wt: 5:   14 secant function Definition Graph and Inverse
  90.    wt: 5:   13 cosecant function Definition Graph and Inverse
  91.    wt: 5:   12 motivation for term arctan
  92.    wt: 5:   11 arctan left inverse of tangent Graph
  93.    wt: 5:   10 arctan left inverse of tangent Definition
  94.    wt: 5:   9 motivation for name arcsin
  95.    wt: 5:   8 arcsin left inverse of sine Graph
  96.    wt: 5:   7 arcsin left inverse of sine Definition
  97.    wt: 5:   6 Graph of arccos function
  98.    wt: 5:   5 Swapping Coordinates is a reflection
  99.    wt: 5:   4 possible motivation for term arccos
  100.    wt: 5:   3 Left Inverse of cosine arccos definition
  101.    wt: 5:   2 cosine function more properties
  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:   Analytic View of Triangle Construction or Line Instersection More
  124.    wt: 5:   Straight Lines ASA Intersection Study More
  125.    wt: 5:   Straight Lines ASA Intersection Study
  126.    wt: 5:   Straight Lines Instersection Solving Equations
  127.    wt: 5:   Straight Lines Intersection of
  128.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  129.    wt: 5:   C Straight Lines Slope from Coordinates
  130.    wt: 5:   B Straight Line Slope Scaling Properties More
  131.    wt: 5:   A Straight Line Slope Scaling Properties
  132.    wt: 5:   14 Straight Lines Equations General Case
  133.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  134.    wt: 5:   12 Straight Lines Graphing mx plus b
  135.    wt: 5:   11 Straight Lines Graphing y=mx
  136.    wt: 5:   10 Straight Lines through Origin Equations More
  137.    wt: 5:   9 Straight Lines through Origin Equations
  138.    wt: 5:   8 Straight Lines Equation for vertical
  139.    wt: 5:   7 Tangent Function is odd on this domain
  140.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  141.    wt: 5:   5 Tangent Function Graph
  142.    wt: 5:   4 Tangent Function Properties
  143.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  144.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  145.    wt: 5:   1 Straight Lines Slope Concept
  146.    wt: 5:   21 Logarithms Powers and Exponentials
  147.    wt: 5:   20 N th Roots of Complex Numbers
  148.    wt: 5:   19 N th Roots of Unity
  149.    wt: 5:   18 Sixth Roots of Unity
  150.    wt: 5:   17 Cube Roots of unity
  151.    wt: 5:   16 References and Originality Question
  152.    wt: 5:   15 Pythagorean Theorem Converse
  153.    wt: 5:   14 Law of cosines
  154.    wt: 5:   13 Trig Formulas for dot and cross Products
  155.    wt: 5:   12 cis formulas for sine cosines and tangent
  156.    wt: 5:   11 sine and cosine double triple angle formulas
  157.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  158.    wt: 5:   9 The complex number valued trig function cis
  159.    wt: 5:   7 Second Way to Calculate Products
  160.    wt: 5:   6 Field Properties of Complex Number
  161.    wt: 5:   5 An Easy Proof of the Distributive Law
  162.    wt: 5:   4 Multiplication Properties
  163.    wt: 5:   3 Addition Properties
  164.    wt: 5:   2 Complex Numbers made easier we hope
  165.    wt: 5:   1 Rectangular Polar Coordinates Review
  166.    wt: 5:   Appetizer A Complex Number Applet
  167.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  168.    wt: 5:   12 Triangles Similarity More Problems
  169.    wt: 5:   11 Triangle Similarity Missing Side Problem
  170.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  171.    wt: 5:   9 Similarity of Triangles Usual Criteria
  172.    wt: 5:   8 Similarity of Triangles and Polygons
  173.    wt: 5:   7 Translations Rotations Reflections Dilatations
  174.    wt: 5:   6 Geometric Diagrams in Class
  175.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  176.    wt: 5:   4 Similarity Definition with Coordinate
  177.    wt: 5:   1 Early Concept of Like or Similar Shapes
  178.    wt: 5:   Four Simple Exercises
  179.    wt: 5:   12 Links Lessons elsewhere
  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:   7 Exercises to test skill and concept mastery
  185.    wt: 5:   6 Intersection of lines by solving linear systems
  186.    wt: 5:   5 Algebraic View of Slopes
  187.    wt: 5:   4 Equations for lines three forms
  188.    wt: 5:   3 Slope product for perpendicular lines
  189.    wt: 5:   2 point slope equation for a line
  190.    wt: 5:   1 Numerical view of lines and their equations
  191.    wt: 5:   What is and is not here
  192.    wt: 5:   13 Pythagorean spatial distance formulas
  193.    wt: 5:   12 Spatial Coordinates
  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:   7 Complex Numbers Appetizer
  198.    wt: 5:   6 Polar Multiplication and Rotation
  199.    wt: 5:   5 Cartesian Addition and Translation
  200.    wt: 5:   4 Polar Coordinates to and from
  201.    wt: 5:   3 Rectangular Coordinates Review
  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:   1 Proper Equal Sign Usage
  233.    wt: 3:   4 Greater More Less Than Signs in General
  234.    wt: 3:   2 More and Less Than with Unlike Signs
  235.    wt: 3:   3 signed coordinates for maps and planes
  236.    wt: 3:   2 signed and unsigned numbers as coordinates
  237.    wt: 2:   Maps Plans Drawings
  238.    wt: 2:   sign monoticity analysis example 4
  239.    wt: 2:   sign monoticity analysis example 3
  240.    wt: 2:   sign monoticity analysis example 2
  241.    wt: 2:   sign monoticity analysis example 1
  242.    wt: 2:   19 Signed Multiples of Vectors
  243.    wt: 2:   5 Greater More Less Than Signs in General
  244.    wt: 2:   3 More and Less Than with Unlike Signs
  245.    wt: 2:   3 Comparison of Negative Numbers
  246.    wt: 2:   1 More and Less Than for Counts and Measures
  247.    wt: 2:   10 dividing signed numbers
  248.    wt: 2:   9 subtracting signed numbers
  249.    wt: 2:   8 multiplying signed numbers
  250.    wt: 2:   6 adding signed numbers
  251.    wt: 2:   5 lengths and signs of numbers
  252.    wt: 2:   4 signed coordinates for regions in space
  253.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  254.    wt: 1:   2 arithmetic with signed numbers
  255.    wt: 1:   1 arithmetic with unsigned numbers
  256.    wt: 1:   About site lesson plans
  257.    wt: 1:   15 Sign analysis of functions
  258.    wt: 1:   A Signed Number Arithmetic Review
  259.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  260.    wt: 1:   22 Multiplication of Signed Numbers
  261.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  262.    wt: 1:   13 Arrows and Vectors in a Plane
  263.    wt: 1:   12 Real Numbers Line Signed Coordinates
  264.    wt: 1:   11 Signed Number Addition and Addition Properties
  265.    wt: 1:   3 Inequalities Algebraically
  266.    wt: 1:   5 Equality in Algebra
  267.    wt: 1:   4 Comparison of Negative Numbers
  268.    wt: 1:   2 More and Less Than for Counts and Measures
  269.    wt: 1:   1 Real Numbers Comparison
  270.    wt: 1:   10 Real Number Lengths and Signs
  271.    wt: 1:   8 Coordinates for Maps and Planes
  272.    wt: 1:   6 Unsigned Real Numbers
  273.    wt: 1:   Formula Usage Show Work Format
  274.    wt: 1:   11 What are real lengths and numbers
  275.    wt: 1:   7 negative and additive inverse
  276.    wt: 1:   2 Equality and Units
  277.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  278.    wt: 1:   21 Working With Signs
  279.    wt: 1:   8 Multiplication by Signed Numbers Integers
  280.    wt: 1:   7 Multiplication by Signs
  281.    wt: 1:   7 Calculator Usage Notes and Cautions
  282.    wt: 1:   E1 Error Control Inequalities
  283.    wt: 1:   C Triangle Inequalities
  284.    wt: 1:   Chapter 23 Links To Trigonometry
  285.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  286.    wt: 1:   Chapter 5. Slope Sign Tests
  287.    wt: 1:   Chapter 4. More Slope Sign Analysis
  288.    wt: 1:   Chapter 3. Slope Sign Analysis
  289.    wt: 1:   Chapter 12. Shorthand Usage Guide
  290.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

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 bicylce?

Death Penalty: How Texas sent an innocent man to his death - The wrong Carlos.

For home-tutoring or -schooling, or for schools or colleges with course content control: Secondary Mathematics for Ages 11+, A Practical Approach.

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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