Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development How-TOs Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

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

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

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

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

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

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

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18 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   8 Unit Circle Trigonometry/
  4.    wt: 6:   6 Trigonometry first steps/
  5.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  6.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  7.    wt: 5:   12 Function Translating and Rescaling/
  8.    wt: 5:   11 Parallel Straight Lines and Transversals/
  9.    wt: 5:   10 Intersecting Straight Lines and Transversals/
  10.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  11.    wt: 5:   7 Complex Numbers/
  12.    wt: 5:   5 What is Similarity/
  13.    wt: 5:   4 Lines and Slopes Take 1/
  14.    wt: 5:   3 Cartesian and Polar Coordinates/
  15.    wt: 5:   2 Euclidean Geometry Constructions Theory extras/
  16.    wt: 5:   Geometry maps plans trigonometry vectors/
  17.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  18.    wt: 1:   10 Examples of Algebraic Reasoning/

Web Page Search

62 matches:

  1.    wt: 2:   Maps Plans Drawings
  2.    wt: 2:   4 Angles on Maps Plans drawn to scale
  3.    wt: 2:   3 Lengths and Areas on Maps and Plans
  4.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  5.    wt: 1:   About site lesson plans
  6.    wt: 1:   13 Velocity Vectors in Physics
  7.    wt: 1:   8 Parallel Vectors
  8.    wt: 1:   6 Vectors with Coordinates
  9.    wt: 1:   3 Navigation with Arrows or Vectors
  10.    wt: 1:   Vector and Complex Number Applet
  11.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  12.    wt: 1:   Unit Circle Development of Trigonometry
  13.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  14.    wt: 1:   8 Unit Circle Development of Trigonometry
  15.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  16.    wt: 1:   Why Trigonometry the whyslopes view
  17.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  18.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  19.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  20.    wt: 1:   6 Figuring with Maps Not to Scale
  21.    wt: 1:   21 Addition of Multiples of a Single Vector
  22.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  23.    wt: 1:   19 Signed Multiples of Vectors
  24.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  25.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  26.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  27.    wt: 1:   13 Arrows and Vectors in a Plane
  28.    wt: 1:   7 Decimals Multiplication Methods Examples
  29.    wt: 1:   3 Proportionality Examples
  30.    wt: 1:   8 Coordinates for Maps and Planes
  31.    wt: 1:   4 GE III Animated Examples
  32.    wt: 1:   1 GE Substitution four examples
  33.    wt: 1:   4 Four Examples Fractional Coefficients
  34.    wt: 1:   3 Four Examples
  35.    wt: 1:   2 Three Examples
  36.    wt: 1:   9 Three Examples
  37.    wt: 1:   7 Two Examples
  38.    wt: 1:   6 Three Examples
  39.    wt: 1:   5 Three Examples
  40.    wt: 1:   4 Two Examples
  41.    wt: 1:   3 Two Examples
  42.    wt: 1:   2 Three Examples
  43.    wt: 1:   3 signed coordinates for maps and planes
  44.    wt: 1:   12 Adding Integers More Examples
  45.    wt: 1:   11 Adding Integers Formulas and Examples
  46.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  47.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  48.    wt: 1:   1 Divsion Physical Examples
  49.    wt: 1:   2 Subtraction Easy Case Examples
  50.    wt: 1:   5. How to add decimals C. Examples
  51.    wt: 1:   A Chain Rule Real Player video examples
  52.    wt: 1:   33 Chain Rule Real Player video examples
  53.    wt: 1:   25 Chain Rule Animated Examples Continued
  54.    wt: 1:   24 Chain Rule Animated Examples
  55.    wt: 1:   12 Quotient rule examples
  56.    wt: 1:   7 Animated Differentiation Examples
  57.    wt: 1:   11 Limits at infinity Three Examples
  58.    wt: 1:   8 Four Animated Examples
  59.    wt: 1:   Chapter 23 Links To Trigonometry
  60.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  61.    wt: 1:   Chapter 25. Mathematical Induction Examples
  62.    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:   Vector and Complex Number Applet
  10.    wt: 7:   Unit Circle Development of Trigonometry
  11.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  12.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  13.    wt: 7:   Why Trigonometry the whyslopes view
  14.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  15.    wt: 7:   A Measurement with Ruler Proper Use
  16.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  17.    wt: 7:   2 Measuring Area Directly
  18.    wt: 7:   1 Length Measurement
  19.    wt: 6:   A Global Time and Navigation
  20.    wt: 6:   15 Dot and Cross Product
  21.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  22.    wt: 6:   12 From Applied To Pure Mathematics
  23.    wt: 6:   11 Component Method
  24.    wt: 6:   10 Parallelogram Addition Method
  25.    wt: 6:   9 Head to Tail Coordinate View
  26.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  27.    wt: 6:   5 Head To Tail Arrow Addition
  28.    wt: 6:   4 Resultant of a Sum of Movements
  29.    wt: 6:   2 Signed Coordinates
  30.    wt: 6:   1 Unsigned Coordinates
  31.    wt: 6:   D Straight Lines Slope from Coordinates Examples
  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:   2 Similar Triangles Equality of Corresponding Side Ratios
  81.    wt: 6:   1 Angle Measurement with Degrees
  82.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  83.    wt: 5:   16 cotangent function Definition Graph and Inverse
  84.    wt: 5:   15 cosecant function Definition Graph and Inverse
  85.    wt: 5:   14 secant function Definition Graph and Inverse
  86.    wt: 5:   13 cosecant function Definition Graph and Inverse
  87.    wt: 5:   12 motivation for term arctan
  88.    wt: 5:   11 arctan left inverse of tangent Graph
  89.    wt: 5:   10 arctan left inverse of tangent Definition
  90.    wt: 5:   9 motivation for name arcsin
  91.    wt: 5:   8 arcsin left inverse of sine Graph
  92.    wt: 5:   7 arcsin left inverse of sine Definition
  93.    wt: 5:   6 Graph of arccos function
  94.    wt: 5:   5 Swapping Coordinates is a reflection
  95.    wt: 5:   4 possible motivation for term arccos
  96.    wt: 5:   3 Left Inverse of cosine arccos definition
  97.    wt: 5:   2 cosine function more properties
  98.    wt: 5:   1 cosine function properties
  99.    wt: 5:   9 Summary Degrees to Radians and back
  100.    wt: 5:   8 Radian Measures of Common Angles
  101.    wt: 5:   7 Radian Measures in special Triangles
  102.    wt: 5:   6 Radian Measure to Degrees
  103.    wt: 5:   5 Degrees to Radian Measure
  104.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  105.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  106.    wt: 5:   2 Radian Measure Numerical Value of one degree
  107.    wt: 5:   1 Degrees and Radians Introduction
  108.    wt: 5:   4 graphing y=Asin(x c)
  109.    wt: 5:   3 graphing y=f(x c) plus K
  110.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  111.    wt: 5:   1 graphing y=f(x a)
  112.    wt: 5:   Parallel Lines and Parallel Transversals
  113.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  114.    wt: 5:   Triangle Angles Sum To 180 Degrees
  115.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  116.    wt: 5:   Parallel Lines and Interior Angles
  117.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  118.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  119.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  120.    wt: 5:   Straight Lines ASA Intersection Study More
  121.    wt: 5:   Straight Lines ASA Intersection Study
  122.    wt: 5:   Straight Lines Instersection Solving Equations
  123.    wt: 5:   Straight Lines Intersection of
  124.    wt: 5:   C Straight Lines Slope from Coordinates
  125.    wt: 5:   B Straight Line Slope Scaling Properties More
  126.    wt: 5:   A Straight Line Slope Scaling Properties
  127.    wt: 5:   14 Straight Lines Equations General Case
  128.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  129.    wt: 5:   12 Straight Lines Graphing mx plus b
  130.    wt: 5:   11 Straight Lines Graphing y=mx
  131.    wt: 5:   10 Straight Lines through Origin Equations More
  132.    wt: 5:   9 Straight Lines through Origin Equations
  133.    wt: 5:   8 Straight Lines Equation for vertical
  134.    wt: 5:   7 Tangent Function is odd on this domain
  135.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  136.    wt: 5:   5 Tangent Function Graph
  137.    wt: 5:   4 Tangent Function Properties
  138.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  139.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  140.    wt: 5:   1 Straight Lines Slope Concept
  141.    wt: 5:   21 Logarithms Powers and Exponentials
  142.    wt: 5:   20 N th Roots of Complex Numbers
  143.    wt: 5:   19 N th Roots of Unity
  144.    wt: 5:   18 Sixth Roots of Unity
  145.    wt: 5:   17 Cube Roots of unity
  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:   13 Trig Formulas for dot and cross Products
  150.    wt: 5:   12 cis formulas for sine cosines and tangent
  151.    wt: 5:   11 sine and cosine double triple angle formulas
  152.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  153.    wt: 5:   9 The complex number valued trig function cis
  154.    wt: 5:   7 Second Way to Calculate Products
  155.    wt: 5:   6 Field Properties of Complex Number
  156.    wt: 5:   5 An Easy Proof of the Distributive Law
  157.    wt: 5:   4 Multiplication Properties
  158.    wt: 5:   3 Addition Properties
  159.    wt: 5:   2 Complex Numbers made easier we hope
  160.    wt: 5:   1 Rectangular Polar Coordinates Review
  161.    wt: 5:   Appetizer A Complex Number Applet
  162.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  163.    wt: 5:   12 Triangles Similarity More Problems
  164.    wt: 5:   11 Triangle Similarity Missing Side Problem
  165.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  166.    wt: 5:   9 Similarity of Triangles Usual Criteria
  167.    wt: 5:   8 Similarity of Triangles and Polygons
  168.    wt: 5:   7 Translations Rotations Reflections Dilatations
  169.    wt: 5:   6 Geometric Diagrams in Class
  170.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  171.    wt: 5:   4 Similarity Definition with Coordinate
  172.    wt: 5:   3 Similarity by Design with coordinates
  173.    wt: 5:   2 Similarity By Design
  174.    wt: 5:   1 Early Concept of Like or Similar Shapes
  175.    wt: 5:   Four Simple Exercises
  176.    wt: 5:   12 Links Lessons elsewhere
  177.    wt: 5:   11 A Partial Summary
  178.    wt: 5:   10 Midpoint of [a b] and [b a]
  179.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  180.    wt: 5:   8 Mid Point Formula
  181.    wt: 5:   7 Exercises to test skill and concept mastery
  182.    wt: 5:   6 Intersection of lines by solving linear systems
  183.    wt: 5:   5 Algebraic View of Slopes
  184.    wt: 5:   4 Equations for lines three forms
  185.    wt: 5:   3 Slope product for perpendicular lines
  186.    wt: 5:   2 point slope equation for a line
  187.    wt: 5:   1 Numerical view of lines and their equations
  188.    wt: 5:   What is and is not here
  189.    wt: 5:   13 Pythagorean spatial distance formulas
  190.    wt: 5:   12 Spatial Coordinates
  191.    wt: 5:   11 Triangle Inequality
  192.    wt: 5:   10 Pythagorean plane distance formula
  193.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  194.    wt: 5:   8 Distance Between Points on a Line
  195.    wt: 5:   7 Complex Numbers Appetizer
  196.    wt: 5:   6 Polar Multiplication and Rotation
  197.    wt: 5:   5 Cartesian Addition and Translation
  198.    wt: 5:   4 Polar Coordinates to and from
  199.    wt: 5:   3 Rectangular Coordinates Review
  200.    wt: 5:   2 Cartesian Coordinates with signs
  201.    wt: 5:   1 Cartesian Coordinates sans signs
  202.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  203.    wt: 5:   PS H Distributive Law For Complex Numbers
  204.    wt: 5:   PS G Rotation Distributes over Addition
  205.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  206.    wt: 5:   PS E Multiplication with Polar Coordinates
  207.    wt: 5:   PS D Addition with Cartesian Coordinates
  208.    wt: 5:   PS B Parallelogram Construction Methods
  209.    wt: 5:   PS A Kite Construction Methods
  210.    wt: 5:   21 Parallelograms
  211.    wt: 5:   19 Right Triangle Similarity
  212.    wt: 5:   18 Triangle Similarity Take 1
  213.    wt: 5:   17 Right Bisectors of Triangle Sides
  214.    wt: 5:   16 Angles Subtended By Chords and Diameters
  215.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  216.    wt: 5:   14 Parallel Lines Postulate
  217.    wt: 5:   13 Angle Side Angle Failure
  218.    wt: 5:   12 Side Angle Side Failure
  219.    wt: 5:   11 Triangle Construction Fails
  220.    wt: 5:   10 Dropping a perpendicular to line
  221.    wt: 5:   9 Construction of a right bisector
  222.    wt: 5:   8 Isoceles Triangles
  223.    wt: 5:   7 Angle Side Angle
  224.    wt: 5:   6 Ruler and compass Angle Bisection
  225.    wt: 5:   5 Side Angle Side
  226.    wt: 5:   4 Side Side Side
  227.    wt: 5:   3 Isometry of Triangles Congruence
  228.    wt: 5:   2 Correspondence between Triangles
  229.    wt: 5:   1 Initial Concepts and Terms
  230.    wt: 5:   Short Course on Euclidean Geometry
  231.    wt: 5:   About Folder Contents
  232.    wt: 2:   Maps Plans Drawings
  233.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  234.    wt: 1:   About site lesson plans
  235.    wt: 1:   sign monoticity analysis example 4
  236.    wt: 1:   sign monoticity analysis example 3
  237.    wt: 1:   sign monoticity analysis example 2
  238.    wt: 1:   sign monoticity analysis example 1
  239.    wt: 1:   21 Addition of Multiples of a Single Vector
  240.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  241.    wt: 1:   19 Signed Multiples of Vectors
  242.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  243.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  244.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  245.    wt: 1:   13 Arrows and Vectors in a Plane
  246.    wt: 1:   7 Decimals Multiplication Methods Examples
  247.    wt: 1:   5 Areas of Rectangles Revisited
  248.    wt: 1:   4 Fraction Operations Axiomatic Development
  249.    wt: 1:   3 Inequalities Algebraically
  250.    wt: 1:   2 Fraction Operations Physical Development
  251.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  252.    wt: 1:   3 Proportionality Examples
  253.    wt: 1:   8 Coordinates for Maps and Planes
  254.    wt: 1:   4 GE III Animated Examples
  255.    wt: 1:   1 GE Substitution four examples
  256.    wt: 1:   4 Four Examples Fractional Coefficients
  257.    wt: 1:   3 Four Examples
  258.    wt: 1:   2 Three Examples
  259.    wt: 1:   9 Three Examples
  260.    wt: 1:   7 Two Examples
  261.    wt: 1:   6 Three Examples
  262.    wt: 1:   5 Three Examples
  263.    wt: 1:   4 Two Examples
  264.    wt: 1:   3 Two Examples
  265.    wt: 1:   2 Three Examples
  266.    wt: 1:   3 Properties of Square Roots with example
  267.    wt: 1:   3 signed coordinates for maps and planes
  268.    wt: 1:   12 Adding Integers More Examples
  269.    wt: 1:   11 Adding Integers Formulas and Examples
  270.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  271.    wt: 1:   26 Divisibility by 2 3 5 Example
  272.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  273.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  274.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  275.    wt: 1:   1 Divsion Physical Examples
  276.    wt: 1:   Subtraction with J Conversions Example
  277.    wt: 1:   2 Subtraction Easy Case Examples
  278.    wt: 1:   5. How to add decimals C. Examples
  279.    wt: 1:   A Chain Rule Real Player video examples
  280.    wt: 1:   33 Chain Rule Real Player video examples
  281.    wt: 1:   25 Chain Rule Animated Examples Continued
  282.    wt: 1:   24 Chain Rule Animated Examples
  283.    wt: 1:   12 Quotient rule examples
  284.    wt: 1:   7 Animated Differentiation Examples
  285.    wt: 1:   11 Limits at infinity Three Examples
  286.    wt: 1:   8 Four Animated Examples
  287.    wt: 1:   Chapter 23 Links To Trigonometry
  288.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  289.    wt: 1:   Chapter 25. Mathematical Induction Examples
  290.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

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20 Times Table - the most popular site page - popular pages - unexpected.
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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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