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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17 matches:

  1.    wt: 8:   8 Unit Circle Trigonometry/
  2.    wt: 7:   1 Maps Plans Measurement/
  3.    wt: 6:   15 Arc or Inverse Trigonometric Function/
  4.    wt: 6:   13 Vectors/
  5.    wt: 6:   6 Trigonometry first steps/
  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:   7 Arithmetic and Fractions with Units/

Web Page Search

61 matches:

  1.    wt: 3:   30 unit circle calculation of six trigonometric functions
  2.    wt: 3:   Unit Circle Development of Trigonometry
  3.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  4.    wt: 3:   8 Unit Circle Development of Trigonometry
  5.    wt: 3:   7 Trignometric Ratios Unit Circle
  6.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  7.    wt: 2:   Maps Plans Drawings
  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:   6. Counting and adding units and mixed units
  11.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  12.    wt: 1:   About site lesson plans
  13.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  14.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  15.    wt: 1:   13 Velocity Vectors in Physics
  16.    wt: 1:   8 Parallel Vectors
  17.    wt: 1:   6 Vectors with Coordinates
  18.    wt: 1:   3 Navigation with Arrows or Vectors
  19.    wt: 1:   31 basic secant cosecant cotangent trig identities
  20.    wt: 1:   17E Trig Formulas for dot and cross Products
  21.    wt: 1:   17A The complex number valued trig function cis
  22.    wt: 1:   1 Unit Points Reflections Rotations
  23.    wt: 1:   19 N th Roots of Unity
  24.    wt: 1:   18 Sixth Roots of Unity
  25.    wt: 1:   17 Cube Roots of unity
  26.    wt: 1:   13 Trig Formulas for dot and cross Products
  27.    wt: 1:   9 The complex number valued trig function cis
  28.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  29.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  30.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  31.    wt: 1:   3 Trigonometric Ratios sine and cosine
  32.    wt: 1:   Why Trigonometry the whyslopes view
  33.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  34.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  35.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  36.    wt: 1:   6 Figuring with Maps Not to Scale
  37.    wt: 1:   19 Signed Multiples of Vectors
  38.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  39.    wt: 1:   13 Arrows and Vectors in a Plane
  40.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  41.    wt: 1:   8 Coordinates for Maps and Planes
  42.    wt: 1:   4 Circle Area Formula Example
  43.    wt: 1:   3 signed coordinates for maps and planes
  44.    wt: 1:   7 Converting or Changing Units
  45.    wt: 1:   6 Simplification of Fractions with Units
  46.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  47.    wt: 1:   4 Fractions with Units
  48.    wt: 1:   3 Multiplying Units and Numbers
  49.    wt: 1:   2 Equality and Units
  50.    wt: 1:   1 Addition and Subtraction with Units
  51.    wt: 1:   3 Unit fraction of a fraction
  52.    wt: 1:   2 Unit Fraction Multiplication
  53.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  54.    wt: 1:   8 Subtraction with Units of Measure
  55.    wt: 1:   4 Mixing and Changing Units of Time
  56.    wt: 1:   3 Units and Lengths of Time
  57.    wt: 1:   Chapter 23 Links To Trigonometry
  58.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  59.    wt: 1:   Chapter 12. Units and Slopes
  60.    wt: 1:   Chapter 10 Slopes and Units
  61.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

260 matches:

  1.    wt: 9:   31 basic secant cosecant cotangent trig identities
  2.    wt: 9:   17E Trig Formulas for dot and cross Products
  3.    wt: 9:   17A The complex number valued trig function cis
  4.    wt: 9:   1 Unit Points Reflections Rotations
  5.    wt: 9:   7 Trignometric Ratios Unit Circle
  6.    wt: 9:   Right Triangle and Unit Circle Trigonometry
  7.    wt: 9:   4 Angles on Maps Plans drawn to scale
  8.    wt: 9:   3 Lengths and Areas on Maps and Plans
  9.    wt: 8:   17 tangent function angle sum formulas
  10.    wt: 8:   35 sines and cosines of 2A 3A 4A 5A
  11.    wt: 8:   34 sines and cosines of 2A 3A 4A 5A
  12.    wt: 8:   33 sines and cosines of 2A 3A 4A 5A
  13.    wt: 8:   32 seven rows of pascals triangle
  14.    wt: 8:   29 secant cosecant and cotangent for acute angles
  15.    wt: 8:   28 Expressing products of sines cosines as sums
  16.    wt: 8:   27 Logarithmic use of products of sines and cosines
  17.    wt: 8:   26 Formulas for products of sines and cosines
  18.    wt: 8:   25 tangent double angle formula Slope connection
  19.    wt: 8:   24 tangent Angle Difference Formula
  20.    wt: 8:   23 sine and cosine of 180 plus 22.5 degrees
  21.    wt: 8:   22 sine of 22.5 degrees via half angle formulas
  22.    wt: 8:   21 sine and cosine Half Angle Formulas
  23.    wt: 8:   20 sine and cosine Double Angle Formulas
  24.    wt: 8:   19 Pythagorean Identity For sine and cosine functions
  25.    wt: 8:   18 sum of sinusoidal waves as a single wave
  26.    wt: 8:   17G Pythagorean Theorem Converse
  27.    wt: 8:   17F Law of cosines
  28.    wt: 8:   17D cis formulas for sine cosines and tangent
  29.    wt: 8:   17C sine and cosine double triple angle formulas
  30.    wt: 8:   17B sine cosine Angle Sum Formulas via cis
  31.    wt: 8:   16 Right Triangle Complementary Angle Relations
  32.    wt: 8:   15 sine cosine Complementary Angle Relations
  33.    wt: 8:   14 cosine even and sine and tangent are odd
  34.    wt: 8:   13 Graph of tangent function many periods
  35.    wt: 8:   12 Graph of tangent function for one period
  36.    wt: 8:   11 tangent function undefined when terminal side vertical
  37.    wt: 8:   10 Graphs of sines and cosines many periods
  38.    wt: 8:   9 Graphs of sine and cosine over one period
  39.    wt: 8:   8 period of tangent function
  40.    wt: 8:   7 period of sine and cosine
  41.    wt: 8:   6 sines and cosines for reference angle 30 degrees
  42.    wt: 8:   5 sines and cosines for reference angle 60 degrees
  43.    wt: 8:   4 sines and cosines for reference angle 45 degrees
  44.    wt: 8:   3 sines and cosines for reference angle 90 degrees
  45.    wt: 8:   2 Quadrant I reference Angles
  46.    wt: 8:   8 Unit Circle Development of Trigonometry
  47.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  48.    wt: 8:   6 Figuring with Maps Not to Scale
  49.    wt: 7:   13 Velocity Vectors in Physics
  50.    wt: 7:   8 Parallel Vectors
  51.    wt: 7:   6 Vectors with Coordinates
  52.    wt: 7:   3 Navigation with Arrows or Vectors
  53.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  54.    wt: 7:   5 Trigonometric Ratios For Tangent and Special Triangles
  55.    wt: 7:   4 Trigonometric Ratios For Two Special Triangles
  56.    wt: 7:   3 Trigonometric Ratios sine and cosine
  57.    wt: 7:   Why Trigonometry the whyslopes view
  58.    wt: 7:   A Measurement with Ruler Proper Use
  59.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  60.    wt: 7:   2 Measuring Area Directly
  61.    wt: 7:   1 Length Measurement
  62.    wt: 6:   16 cotangent function Definition Graph and Inverse
  63.    wt: 6:   15 cosecant function Definition Graph and Inverse
  64.    wt: 6:   14 secant function Definition Graph and Inverse
  65.    wt: 6:   13 cosecant function Definition Graph and Inverse
  66.    wt: 6:   12 motivation for term arctan
  67.    wt: 6:   11 arctan left inverse of tangent Graph
  68.    wt: 6:   10 arctan left inverse of tangent Definition
  69.    wt: 6:   9 motivation for name arcsin
  70.    wt: 6:   8 arcsin left inverse of sine Graph
  71.    wt: 6:   7 arcsin left inverse of sine Definition
  72.    wt: 6:   6 Graph of arccos function
  73.    wt: 6:   5 Swapping Coordinates is a reflection
  74.    wt: 6:   4 possible motivation for term arccos
  75.    wt: 6:   3 Left Inverse of cosine arccos definition
  76.    wt: 6:   2 cosine function more properties
  77.    wt: 6:   1 cosine function properties
  78.    wt: 6:   4 Circle Sector Area proportional to Central Angle
  79.    wt: 6:   3 Circle Arclengh Proportional to Central Angle
  80.    wt: 6:   A Global Time and Navigation
  81.    wt: 6:   15 Dot and Cross Product
  82.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  83.    wt: 6:   12 From Applied To Pure Mathematics
  84.    wt: 6:   11 Component Method
  85.    wt: 6:   10 Parallelogram Addition Method
  86.    wt: 6:   9 Head to Tail Coordinate View
  87.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  88.    wt: 6:   5 Head To Tail Arrow Addition
  89.    wt: 6:   4 Resultant of a Sum of Movements
  90.    wt: 6:   2 Signed Coordinates
  91.    wt: 6:   1 Unsigned Coordinates
  92.    wt: 6:   Vector and Complex Number Applet
  93.    wt: 6:   19 N th Roots of Unity
  94.    wt: 6:   18 Sixth Roots of Unity
  95.    wt: 6:   17 Cube Roots of unity
  96.    wt: 6:   13 Trig Formulas for dot and cross Products
  97.    wt: 6:   9 The complex number valued trig function cis
  98.    wt: 6:   8 Triangles Cascade Problem Solving
  99.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  100.    wt: 6:   1 Angle Measurement with Degrees
  101.    wt: 6:   5 Similarity of Circles Squares and Rectangles
  102.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  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:   2 Radian Measure Numerical Value of one degree
  109.    wt: 5:   1 Degrees and Radians Introduction
  110.    wt: 5:   4 graphing y=Asin(x c)
  111.    wt: 5:   3 graphing y=f(x c) plus K
  112.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  113.    wt: 5:   1 graphing y=f(x a)
  114.    wt: 5:   Parallel Lines and Parallel Transversals
  115.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  116.    wt: 5:   Triangle Angles Sum To 180 Degrees
  117.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  118.    wt: 5:   Parallel Lines and Interior Angles
  119.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  120.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  121.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  122.    wt: 5:   Straight Lines ASA Intersection Study More
  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:   B Straight Line Slope Scaling Properties More
  129.    wt: 5:   A Straight Line Slope Scaling Properties
  130.    wt: 5:   14 Straight Lines Equations General Case
  131.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  132.    wt: 5:   12 Straight Lines Graphing mx plus b
  133.    wt: 5:   11 Straight Lines Graphing y=mx
  134.    wt: 5:   10 Straight Lines through Origin Equations More
  135.    wt: 5:   9 Straight Lines through Origin Equations
  136.    wt: 5:   8 Straight Lines Equation for vertical
  137.    wt: 5:   7 Tangent Function is odd on this domain
  138.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  139.    wt: 5:   5 Tangent Function Graph
  140.    wt: 5:   4 Tangent Function Properties
  141.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  142.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  143.    wt: 5:   1 Straight Lines Slope Concept
  144.    wt: 5:   21 Logarithms Powers and Exponentials
  145.    wt: 5:   20 N th Roots of Complex Numbers
  146.    wt: 5:   16 References and Originality Question
  147.    wt: 5:   15 Pythagorean Theorem Converse
  148.    wt: 5:   14 Law of cosines
  149.    wt: 5:   12 cis formulas for sine cosines and tangent
  150.    wt: 5:   11 sine and cosine double triple angle formulas
  151.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  152.    wt: 5:   7 Second Way to Calculate Products
  153.    wt: 5:   6 Field Properties of Complex Number
  154.    wt: 5:   5 An Easy Proof of the Distributive Law
  155.    wt: 5:   4 Multiplication Properties
  156.    wt: 5:   3 Addition Properties
  157.    wt: 5:   2 Complex Numbers made easier we hope
  158.    wt: 5:   1 Rectangular Polar Coordinates Review
  159.    wt: 5:   Appetizer A Complex Number Applet
  160.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  161.    wt: 5:   12 Triangles Similarity More Problems
  162.    wt: 5:   11 Triangle Similarity Missing Side Problem
  163.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  164.    wt: 5:   9 Similarity of Triangles Usual Criteria
  165.    wt: 5:   8 Similarity of Triangles and Polygons
  166.    wt: 5:   7 Translations Rotations Reflections Dilatations
  167.    wt: 5:   6 Geometric Diagrams in Class
  168.    wt: 5:   4 Similarity Definition with Coordinate
  169.    wt: 5:   3 Similarity by Design with coordinates
  170.    wt: 5:   2 Similarity By Design
  171.    wt: 5:   1 Early Concept of Like or Similar Shapes
  172.    wt: 5:   Four Simple Exercises
  173.    wt: 5:   12 Links Lessons elsewhere
  174.    wt: 5:   11 A Partial Summary
  175.    wt: 5:   10 Midpoint of [a b] and [b a]
  176.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  177.    wt: 5:   8 Mid Point Formula
  178.    wt: 5:   7 Exercises to test skill and concept mastery
  179.    wt: 5:   6 Intersection of lines by solving linear systems
  180.    wt: 5:   5 Algebraic View of Slopes
  181.    wt: 5:   4 Equations for lines three forms
  182.    wt: 5:   3 Slope product for perpendicular lines
  183.    wt: 5:   2 point slope equation for a line
  184.    wt: 5:   1 Numerical view of lines and their equations
  185.    wt: 5:   What is and is not here
  186.    wt: 5:   13 Pythagorean spatial distance formulas
  187.    wt: 5:   12 Spatial Coordinates
  188.    wt: 5:   11 Triangle Inequality
  189.    wt: 5:   10 Pythagorean plane distance formula
  190.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  191.    wt: 5:   8 Distance Between Points on a Line
  192.    wt: 5:   7 Complex Numbers Appetizer
  193.    wt: 5:   6 Polar Multiplication and Rotation
  194.    wt: 5:   5 Cartesian Addition and Translation
  195.    wt: 5:   4 Polar Coordinates to and from
  196.    wt: 5:   3 Rectangular Coordinates Review
  197.    wt: 5:   2 Cartesian Coordinates with signs
  198.    wt: 5:   1 Cartesian Coordinates sans signs
  199.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  200.    wt: 5:   PS H Distributive Law For Complex Numbers
  201.    wt: 5:   PS G Rotation Distributes over Addition
  202.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  203.    wt: 5:   PS E Multiplication with Polar Coordinates
  204.    wt: 5:   PS D Addition with Cartesian Coordinates
  205.    wt: 5:   PS B Parallelogram Construction Methods
  206.    wt: 5:   PS A Kite Construction Methods
  207.    wt: 5:   21 Parallelograms
  208.    wt: 5:   19 Right Triangle Similarity
  209.    wt: 5:   18 Triangle Similarity Take 1
  210.    wt: 5:   17 Right Bisectors of Triangle Sides
  211.    wt: 5:   16 Angles Subtended By Chords and Diameters
  212.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  213.    wt: 5:   14 Parallel Lines Postulate
  214.    wt: 5:   13 Angle Side Angle Failure
  215.    wt: 5:   12 Side Angle Side Failure
  216.    wt: 5:   11 Triangle Construction Fails
  217.    wt: 5:   10 Dropping a perpendicular to line
  218.    wt: 5:   9 Construction of a right bisector
  219.    wt: 5:   8 Isoceles Triangles
  220.    wt: 5:   7 Angle Side Angle
  221.    wt: 5:   6 Ruler and compass Angle Bisection
  222.    wt: 5:   5 Side Angle Side
  223.    wt: 5:   4 Side Side Side
  224.    wt: 5:   3 Isometry of Triangles Congruence
  225.    wt: 5:   2 Correspondence between Triangles
  226.    wt: 5:   1 Initial Concepts and Terms
  227.    wt: 5:   Short Course on Euclidean Geometry
  228.    wt: 5:   About Folder Contents
  229.    wt: 2:   Maps Plans Drawings
  230.    wt: 2:   7 Converting or Changing Units
  231.    wt: 2:   6 Simplification of Fractions with Units
  232.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  233.    wt: 2:   4 Fractions with Units
  234.    wt: 2:   3 Multiplying Units and Numbers
  235.    wt: 2:   2 Equality and Units
  236.    wt: 2:   1 Addition and Subtraction with Units
  237.    wt: 2:   6. Counting and adding units and mixed units
  238.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  239.    wt: 1:   About site lesson plans
  240.    wt: 1:   19 Signed Multiples of Vectors
  241.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  242.    wt: 1:   13 Arrows and Vectors in a Plane
  243.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  244.    wt: 1:   8 Coordinates for Maps and Planes
  245.    wt: 1:   4 Circle Area Formula Example
  246.    wt: 1:   3 signed coordinates for maps and planes
  247.    wt: 1:   3 Unit fraction of a fraction
  248.    wt: 1:   2 Unit Fraction Multiplication
  249.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  250.    wt: 1:   8 Subtraction with Units of Measure
  251.    wt: 1:   4 Mixing and Changing Units of Time
  252.    wt: 1:   3 Units and Lengths of Time
  253.    wt: 1:   Chapter 23 Links To Trigonometry
  254.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  255.    wt: 1:   Chapter 12. Units and Slopes
  256.    wt: 1:   Chapter 10 Slopes and Units
  257.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  258.    wt: 11:   30 unit circle calculation of six trigonometric functions
  259.    wt: 11:   Unit Circle Development of Trigonometry
  260.    wt: 11:   Right Triangle and Unit Circle 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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