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.

Home << Search

[1] [2] [3] [4]

Key Word Search

Folder Search

26 matches:

  1.    wt: 7:   1 Maps Plans Measurement/
  2.    wt: 6:   13 Vectors/
  3.    wt: 6:   11 Parallel Straight Lines and Transversals/
  4.    wt: 6:   10 Intersecting Straight Lines and Transversals/
  5.    wt: 6:   9 Lines and Slopes Take 2 with tangent function/
  6.    wt: 6:   8 Unit Circle Trigonometry/
  7.    wt: 6:   6 Trigonometry first steps/
  8.    wt: 6:   4 Lines and Slopes Take 1/
  9.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  10.    wt: 5:   14 Degrees to Radians and Radians to Degrees/
  11.    wt: 5:   12 Function Translating and Rescaling/
  12.    wt: 5:   7 Complex Numbers/
  13.    wt: 5:   5 What is Similarity/
  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:   Step 3 Easy systems in 2 or more unknowns/
  18.    wt: 1:   A Origins of Counting and Figuring Methods/
  19.    wt: 1:   10 Examples of Algebraic Reasoning/
  20.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  21.    wt: 1:   Step 4 Gaussian Elimination/
  22.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  23.    wt: 1:   Step 1 Stick diagram and fractions/
  24.    wt: 1:   3 Solving Linear Equations/
  25.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  26.    wt: 1:   Volume 1 Elements of Reason/

Web Page Search

217 matches:

  1.    wt: 3:   6 Intersection of lines by solving linear systems
  2.    wt: 3:   1 Numerical view of lines and their equations
  3.    wt: 2:   Maps Plans Drawings
  4.    wt: 2:   4 Resultant of a Sum of Movements
  5.    wt: 2:   Straight Lines Instersection Solving Equations
  6.    wt: 2:   Straight Lines Intersection of
  7.    wt: 2:   14 Straight Lines Equations General Case
  8.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  9.    wt: 2:   10 Straight Lines through Origin Equations More
  10.    wt: 2:   9 Straight Lines through Origin Equations
  11.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  12.    wt: 2:   27 Logarithmic use of products of sines and cosines
  13.    wt: 2:   Unit Circle Development of Trigonometry
  14.    wt: 2:   8 Unit Circle Development of Trigonometry
  15.    wt: 2:   5 An Easy Proof of the Distributive Law
  16.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  17.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  18.    wt: 2:   4 Equations for lines three forms
  19.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  20.    wt: 2:   4 Angles on Maps Plans drawn to scale
  21.    wt: 2:   3 Lengths and Areas on Maps and Plans
  22.    wt: 2:   21 Addition of Multiples of a Single Vector
  23.    wt: 2:   19 Signed Multiples of Vectors
  24.    wt: 2:   6 Equations and Systems Equivalent or Implied
  25.    wt: 2:   17 Derivatives of quotients of sine and cosine
  26.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  27.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  28.    wt: 1:   About site lesson plans
  29.    wt: 1:   Mathematics Education Professors
  30.    wt: 1:   Theory of Knowledge
  31.    wt: 1:   Different Kinds of Reasoning in maths
  32.    wt: 1:   three kinds of reason in mathematics
  33.    wt: 1:   E Kirchoffs Second Law
  34.    wt: 1:   D Kirchoff First Law
  35.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  36.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  37.    wt: 1:   8 The Effect of Negative Remarks
  38.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  39.    wt: 1:   15 Sign analysis of functions
  40.    wt: 1:   8 Set view of relations and functions
  41.    wt: 1:   2 Algebraic use of function notation
  42.    wt: 1:   1 Geometric Introduction of Function Notation
  43.    wt: 1:   8 quadratics backward use of various formulas
  44.    wt: 1:   4 quadratics difference of two squares
  45.    wt: 1:   11 arctan left inverse of tangent Graph
  46.    wt: 1:   10 arctan left inverse of tangent Definition
  47.    wt: 1:   8 arcsin left inverse of sine Graph
  48.    wt: 1:   7 arcsin left inverse of sine Definition
  49.    wt: 1:   6 Graph of arccos function
  50.    wt: 1:   3 Left Inverse of cosine arccos definition
  51.    wt: 1:   8 Radian Measures of Common Angles
  52.    wt: 1:   2 Radian Measure Numerical Value of one degree
  53.    wt: 1:   13 Velocity Vectors in Physics
  54.    wt: 1:   8 Parallel Vectors
  55.    wt: 1:   6 Vectors with Coordinates
  56.    wt: 1:   3 Navigation with Arrows or Vectors
  57.    wt: 1:   Parallel Lines and Parallel Transversals
  58.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  59.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  60.    wt: 1:   Parallel Lines and Interior Angles
  61.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  62.    wt: 1:   Straight Lines ASA Intersection Study More
  63.    wt: 1:   Straight Lines ASA Intersection Study
  64.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  65.    wt: 1:   C Straight Lines Slope from Coordinates
  66.    wt: 1:   12 Straight Lines Graphing mx plus b
  67.    wt: 1:   11 Straight Lines Graphing y=mx
  68.    wt: 1:   8 Straight Lines Equation for vertical
  69.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  70.    wt: 1:   1 Straight Lines Slope Concept
  71.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  72.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  73.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  74.    wt: 1:   32 seven rows of pascals triangle
  75.    wt: 1:   30 unit circle calculation of six trigonometric functions
  76.    wt: 1:   28 Expressing products of sines cosines as sums
  77.    wt: 1:   26 Formulas for products of sines and cosines
  78.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  79.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  80.    wt: 1:   18 sum of sinusoidal waves as a single wave
  81.    wt: 1:   17F Law of cosines
  82.    wt: 1:   13 Graph of tangent function many periods
  83.    wt: 1:   12 Graph of tangent function for one period
  84.    wt: 1:   10 Graphs of sines and cosines many periods
  85.    wt: 1:   9 Graphs of sine and cosine over one period
  86.    wt: 1:   8 period of tangent function
  87.    wt: 1:   7 period of sine and cosine
  88.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  89.    wt: 1:   20 N th Roots of Complex Numbers
  90.    wt: 1:   19 N th Roots of Unity
  91.    wt: 1:   18 Sixth Roots of Unity
  92.    wt: 1:   17 Cube Roots of unity
  93.    wt: 1:   14 Law of cosines
  94.    wt: 1:   6 Field Properties of Complex Number
  95.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  96.    wt: 1:   Why Trigonometry the whyslopes view
  97.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  98.    wt: 1:   9 Similarity of Triangles Usual Criteria
  99.    wt: 1:   8 Similarity of Triangles and Polygons
  100.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  101.    wt: 1:   1 Early Concept of Like or Similar Shapes
  102.    wt: 1:   10 Midpoint of [a b] and [b a]
  103.    wt: 1:   5 Algebraic View of Slopes
  104.    wt: 1:   3 Slope product for perpendicular lines
  105.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  106.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  107.    wt: 1:   17 Right Bisectors of Triangle Sides
  108.    wt: 1:   14 Parallel Lines Postulate
  109.    wt: 1:   9 Construction of a right bisector
  110.    wt: 1:   3 Isometry of Triangles Congruence
  111.    wt: 1:   6 Figuring with Maps Not to Scale
  112.    wt: 1:   22 Multiplication of Signed Numbers
  113.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  114.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  115.    wt: 1:   13 Arrows and Vectors in a Plane
  116.    wt: 1:   8 Division and Mulplication of Compound Fractions
  117.    wt: 1:   4 Location of Point in Decimal Addition
  118.    wt: 1:   3 Location of Point in Decimal Multiplication
  119.    wt: 1:   1 The Counting Origins of Numbers
  120.    wt: 1:   5 Areas of Rectangles Revisited
  121.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  122.    wt: 1:   4 Comparison of Negative Numbers
  123.    wt: 1:   8 Coordinates for Maps and Planes
  124.    wt: 1:   11 Volume of Sphere
  125.    wt: 1:   10 Volume of Pyramid
  126.    wt: 1:   9 Volume of Cone
  127.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  128.    wt: 1:   8 Sets of Numbers
  129.    wt: 1:   6 Three Notions of What is a Variable
  130.    wt: 1:   4 A Brief Story of numbers and algebra
  131.    wt: 1:   3 Comparison of Negative Numbers
  132.    wt: 1:   3 Properties of Square Roots with example
  133.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  134.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  135.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  136.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  137.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  138.    wt: 1:   4 LCM of 8 and 10 via Prime
  139.    wt: 1:   5 lengths and signs of numbers
  140.    wt: 1:   3 signed coordinates for maps and planes
  141.    wt: 1:   6 Simplification of Fractions with Units
  142.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  143.    wt: 1:   6 Multiplication of Mixed Numbers
  144.    wt: 1:   3 Unit fraction of a fraction
  145.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  146.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  147.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  148.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  149.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  150.    wt: 1:   20 Uniqueness of Prime Factorization
  151.    wt: 1:   16 video Factors of 980 using prime
  152.    wt: 1:   15 video Factors of 20 using Prime Factorization
  153.    wt: 1:   14 video Factors of 24 Take II
  154.    wt: 1:   13 video Factors of 24 using prime
  155.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  156.    wt: 1:   C Counting Areas with Powers of Ten
  157.    wt: 1:   B Powers of Ten
  158.    wt: 1:   8 Subtraction with Units of Measure
  159.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  160.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  161.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  162.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  163.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  164.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  165.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  166.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  167.    wt: 1:   Quick history of numbers and algebra
  168.    wt: 1:   012 Division of Time Intervals by Time Intervals
  169.    wt: 1:   011 Division of Time Intervals By Numbers
  170.    wt: 1:   010 Repeated Addition of Time Intervals
  171.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  172.    wt: 1:   8 Addition of Time Intervals via subtotaling
  173.    wt: 1:   7 Addition of Time Intervals
  174.    wt: 1:   4 Mixing and Changing Units of Time
  175.    wt: 1:   3 Units and Lengths of Time
  176.    wt: 1:   1 Intro of Kids To Time Date Skills
  177.    wt: 1:   Example 2 volume of a cone
  178.    wt: 1:   Example 1 volume of a pyramid
  179.    wt: 1:   Volume of Solid by Cross Sections Lesson
  180.    wt: 1:   Example 4 with x function of y
  181.    wt: 1:   34 Derivative of exponential function
  182.    wt: 1:   31 Derivatives of inverse functions
  183.    wt: 1:   30Chain Rule A Proof
  184.    wt: 1:   28 Chain Rule Preparation for a Proof
  185.    wt: 1:   20 Chain Rule for Pulley Systems
  186.    wt: 1:   8 Differentiation of polynomials
  187.    wt: 1:   5 Jumps and absence of unlimited error control
  188.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  189.    wt: 1:   G.3 Constant Difference Theorem Proof
  190.    wt: 1:   E2 Algebraic Properties of Limits
  191.    wt: 1:   D2 Limits of Monotone Sequences
  192.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  193.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  194.    wt: 1:   Chapter 23 Links To Trigonometry
  195.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  196.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  197.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  198.    wt: 1:   Chapter 15. Solving Linear Equations
  199.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  200.    wt: 1:   Chapter 6 Change of Language
  201.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  202.    wt: 1:   Chapter 4 Longer Chains of Reason
  203.    wt: 1:   Chapter 3 Chains of Reason
  204.    wt: 1:   Chapter 7 Two Treatments of Geometry
  205.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  206.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  207.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  208.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  209.    wt: 1:   Chapter 8 Change of Language
  210.    wt: 1:   Chapter 7 Longer Chains of Reason
  211.    wt: 1:   Chapter 6 Chains of Reason
  212.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  213.    wt: 1:   C. Domino effect of being careful
  214.    wt: 1:   B. Domino effect of errors
  215.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  216.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  217.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry

Extended Search

415 matches:

  1.    wt: 9:   6 Intersection of lines by solving linear systems
  2.    wt: 9:   1 Numerical view of lines and their equations
  3.    wt: 9:   8 More Use of Maps Not Drawn to Scale
  4.    wt: 9:   4 Angles on Maps Plans drawn to scale
  5.    wt: 9:   3 Lengths and Areas on Maps and Plans
  6.    wt: 8:   4 Resultant of a Sum of Movements
  7.    wt: 8:   Straight Lines Instersection Solving Equations
  8.    wt: 8:   Straight Lines Intersection of
  9.    wt: 8:   14 Straight Lines Equations General Case
  10.    wt: 8:   13 Straight Lines Finding Equations from 2 points
  11.    wt: 8:   10 Straight Lines through Origin Equations More
  12.    wt: 8:   9 Straight Lines through Origin Equations
  13.    wt: 8:   3 Straight Lines Slope as Tangent of Inclination Angle
  14.    wt: 8:   27 Logarithmic use of products of sines and cosines
  15.    wt: 8:   Unit Circle Development of Trigonometry
  16.    wt: 8:   6 Trigonometry Sines of Supplementary Angles
  17.    wt: 8:   4 Equations for lines three forms
  18.    wt: 8:   6 Figuring with Maps Not to Scale
  19.    wt: 7:   13 Velocity Vectors in Physics
  20.    wt: 7:   8 Parallel Vectors
  21.    wt: 7:   6 Vectors with Coordinates
  22.    wt: 7:   3 Navigation with Arrows or Vectors
  23.    wt: 7:   Parallel Lines and Parallel Transversals
  24.    wt: 7:   Proportionality of Line Segments From Parallel Transversals
  25.    wt: 7:   Parallel Lines and Alternating Corresponding Angles
  26.    wt: 7:   Parallel Lines and Interior Angles
  27.    wt: 7:   Analytic View of Triangle Construction or Line Instersection More
  28.    wt: 7:   Straight Lines ASA Intersection Study More
  29.    wt: 7:   Straight Lines ASA Intersection Study
  30.    wt: 7:   D Straight Lines Slope from Coordinates Examples
  31.    wt: 7:   C Straight Lines Slope from Coordinates
  32.    wt: 7:   12 Straight Lines Graphing mx plus b
  33.    wt: 7:   11 Straight Lines Graphing y=mx
  34.    wt: 7:   8 Straight Lines Equation for vertical
  35.    wt: 7:   2 Straight Lines Slopes As Rise Over Run
  36.    wt: 7:   1 Straight Lines Slope Concept
  37.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  38.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  39.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  40.    wt: 7:   32 seven rows of pascals triangle
  41.    wt: 7:   30 unit circle calculation of six trigonometric functions
  42.    wt: 7:   28 Expressing products of sines cosines as sums
  43.    wt: 7:   26 Formulas for products of sines and cosines
  44.    wt: 7:   23 sine and cosine of 180 plus 22.5 degrees
  45.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  46.    wt: 7:   18 sum of sinusoidal waves as a single wave
  47.    wt: 7:   17F Law of cosines
  48.    wt: 7:   13 Graph of tangent function many periods
  49.    wt: 7:   12 Graph of tangent function for one period
  50.    wt: 7:   10 Graphs of sines and cosines many periods
  51.    wt: 7:   9 Graphs of sine and cosine over one period
  52.    wt: 7:   8 period of tangent function
  53.    wt: 7:   7 period of sine and cosine
  54.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  55.    wt: 7:   8 Unit Circle Development of Trigonometry
  56.    wt: 7:   5 An Easy Proof of the Distributive Law
  57.    wt: 7:   2 Similar Triangles Equality of Corresponding Side Ratios
  58.    wt: 7:   Why Trigonometry the whyslopes view
  59.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  60.    wt: 7:   10 Similarity of Triangles Equivalent of Two Criteria
  61.    wt: 7:   10 Midpoint of [a b] and [b a]
  62.    wt: 7:   5 Algebraic View of Slopes
  63.    wt: 7:   3 Slope product for perpendicular lines
  64.    wt: 7:   A Measurement with Ruler Proper Use
  65.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  66.    wt: 7:   2 Measuring Area Directly
  67.    wt: 7:   1 Length Measurement
  68.    wt: 6:   11 arctan left inverse of tangent Graph
  69.    wt: 6:   10 arctan left inverse of tangent Definition
  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:   3 Left Inverse of cosine arccos definition
  74.    wt: 6:   8 Radian Measures of Common Angles
  75.    wt: 6:   2 Radian Measure Numerical Value of one degree
  76.    wt: 6:   A Global Time and Navigation
  77.    wt: 6:   15 Dot and Cross Product
  78.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  79.    wt: 6:   12 From Applied To Pure Mathematics
  80.    wt: 6:   11 Component Method
  81.    wt: 6:   10 Parallelogram Addition Method
  82.    wt: 6:   9 Head to Tail Coordinate View
  83.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  84.    wt: 6:   5 Head To Tail Arrow Addition
  85.    wt: 6:   2 Signed Coordinates
  86.    wt: 6:   1 Unsigned Coordinates
  87.    wt: 6:   Vector and Complex Number Applet
  88.    wt: 6:   Triangle Angles Sum To 180 Degrees
  89.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  90.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  91.    wt: 6:   B Straight Line Slope Scaling Properties More
  92.    wt: 6:   A Straight Line Slope Scaling Properties
  93.    wt: 6:   7 Tangent Function is odd on this domain
  94.    wt: 6:   6 Tangent Function Inclination Angle Take 2
  95.    wt: 6:   5 Tangent Function Graph
  96.    wt: 6:   4 Tangent Function Properties
  97.    wt: 6:   17 tangent function angle sum formulas
  98.    wt: 6:   31 basic secant cosecant cotangent trig identities
  99.    wt: 6:   29 secant cosecant and cotangent for acute angles
  100.    wt: 6:   25 tangent double angle formula Slope connection
  101.    wt: 6:   24 tangent Angle Difference Formula
  102.    wt: 6:   21 sine and cosine Half Angle Formulas
  103.    wt: 6:   20 sine and cosine Double Angle Formulas
  104.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  105.    wt: 6:   17G Pythagorean Theorem Converse
  106.    wt: 6:   17E Trig Formulas for dot and cross Products
  107.    wt: 6:   17D cis formulas for sine cosines and tangent
  108.    wt: 6:   17C sine and cosine double triple angle formulas
  109.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  110.    wt: 6:   17A The complex number valued trig function cis
  111.    wt: 6:   16 Right Triangle Complementary Angle Relations
  112.    wt: 6:   15 sine cosine Complementary Angle Relations
  113.    wt: 6:   14 cosine even and sine and tangent are odd
  114.    wt: 6:   11 tangent function undefined when terminal side vertical
  115.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  116.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  117.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  118.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  119.    wt: 6:   2 Quadrant I reference Angles
  120.    wt: 6:   1 Unit Points Reflections Rotations
  121.    wt: 6:   20 N th Roots of Complex Numbers
  122.    wt: 6:   19 N th Roots of Unity
  123.    wt: 6:   18 Sixth Roots of Unity
  124.    wt: 6:   17 Cube Roots of unity
  125.    wt: 6:   14 Law of cosines
  126.    wt: 6:   6 Field Properties of Complex Number
  127.    wt: 6:   8 Triangles Cascade Problem Solving
  128.    wt: 6:   7 Trignometric Ratios Unit Circle
  129.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  130.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  131.    wt: 6:   3 Trigonometric Ratios sine and cosine
  132.    wt: 6:   1 Angle Measurement with Degrees
  133.    wt: 6:   9 Similarity of Triangles Usual Criteria
  134.    wt: 6:   8 Similarity of Triangles and Polygons
  135.    wt: 6:   5 Similarity of Circles Squares and Rectangles
  136.    wt: 6:   1 Early Concept of Like or Similar Shapes
  137.    wt: 6:   Four Simple Exercises
  138.    wt: 6:   12 Links Lessons elsewhere
  139.    wt: 6:   11 A Partial Summary
  140.    wt: 6:   9 Midpoint Coordinates Half Endpoint Sum
  141.    wt: 6:   8 Mid Point Formula
  142.    wt: 6:   7 Exercises to test skill and concept mastery
  143.    wt: 6:   2 point slope equation for a line
  144.    wt: 6:   What is and is not here
  145.    wt: 6:   9 Pythagorean Theorem Chinese Square Proof
  146.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  147.    wt: 6:   17 Right Bisectors of Triangle Sides
  148.    wt: 6:   14 Parallel Lines Postulate
  149.    wt: 6:   9 Construction of a right bisector
  150.    wt: 6:   3 Isometry of Triangles Congruence
  151.    wt: 5:   16 cotangent function Definition Graph and Inverse
  152.    wt: 5:   15 cosecant function Definition Graph and Inverse
  153.    wt: 5:   14 secant function Definition Graph and Inverse
  154.    wt: 5:   13 cosecant function Definition Graph and Inverse
  155.    wt: 5:   12 motivation for term arctan
  156.    wt: 5:   9 motivation for name arcsin
  157.    wt: 5:   5 Swapping Coordinates is a reflection
  158.    wt: 5:   4 possible motivation for term arccos
  159.    wt: 5:   2 cosine function more properties
  160.    wt: 5:   1 cosine function properties
  161.    wt: 5:   9 Summary Degrees to Radians and back
  162.    wt: 5:   7 Radian Measures in special Triangles
  163.    wt: 5:   6 Radian Measure to Degrees
  164.    wt: 5:   5 Degrees to Radian Measure
  165.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  166.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  167.    wt: 5:   1 Degrees and Radians Introduction
  168.    wt: 5:   4 graphing y=Asin(x c)
  169.    wt: 5:   3 graphing y=f(x c) plus K
  170.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  171.    wt: 5:   1 graphing y=f(x a)
  172.    wt: 5:   21 Logarithms Powers and Exponentials
  173.    wt: 5:   16 References and Originality Question
  174.    wt: 5:   15 Pythagorean Theorem Converse
  175.    wt: 5:   13 Trig Formulas for dot and cross Products
  176.    wt: 5:   12 cis formulas for sine cosines and tangent
  177.    wt: 5:   11 sine and cosine double triple angle formulas
  178.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  179.    wt: 5:   9 The complex number valued trig function cis
  180.    wt: 5:   7 Second Way to Calculate Products
  181.    wt: 5:   4 Multiplication Properties
  182.    wt: 5:   3 Addition Properties
  183.    wt: 5:   2 Complex Numbers made easier we hope
  184.    wt: 5:   1 Rectangular Polar Coordinates Review
  185.    wt: 5:   Appetizer A Complex Number Applet
  186.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  187.    wt: 5:   12 Triangles Similarity More Problems
  188.    wt: 5:   11 Triangle Similarity Missing Side Problem
  189.    wt: 5:   7 Translations Rotations Reflections Dilatations
  190.    wt: 5:   6 Geometric Diagrams in Class
  191.    wt: 5:   4 Similarity Definition with Coordinate
  192.    wt: 5:   3 Similarity by Design with coordinates
  193.    wt: 5:   2 Similarity By Design
  194.    wt: 5:   13 Pythagorean spatial distance formulas
  195.    wt: 5:   12 Spatial Coordinates
  196.    wt: 5:   11 Triangle Inequality
  197.    wt: 5:   10 Pythagorean plane distance formula
  198.    wt: 5:   8 Distance Between Points on a Line
  199.    wt: 5:   7 Complex Numbers Appetizer
  200.    wt: 5:   6 Polar Multiplication and Rotation
  201.    wt: 5:   5 Cartesian Addition and Translation
  202.    wt: 5:   4 Polar Coordinates to and from
  203.    wt: 5:   3 Rectangular Coordinates Review
  204.    wt: 5:   2 Cartesian Coordinates with signs
  205.    wt: 5:   1 Cartesian Coordinates sans signs
  206.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  207.    wt: 5:   PS H Distributive Law For Complex Numbers
  208.    wt: 5:   PS G Rotation Distributes over Addition
  209.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  210.    wt: 5:   PS E Multiplication with Polar Coordinates
  211.    wt: 5:   PS D Addition with Cartesian Coordinates
  212.    wt: 5:   PS B Parallelogram Construction Methods
  213.    wt: 5:   PS A Kite Construction Methods
  214.    wt: 5:   21 Parallelograms
  215.    wt: 5:   19 Right Triangle Similarity
  216.    wt: 5:   18 Triangle Similarity Take 1
  217.    wt: 5:   16 Angles Subtended By Chords and Diameters
  218.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  219.    wt: 5:   13 Angle Side Angle Failure
  220.    wt: 5:   12 Side Angle Side Failure
  221.    wt: 5:   11 Triangle Construction Fails
  222.    wt: 5:   10 Dropping a perpendicular to line
  223.    wt: 5:   8 Isoceles Triangles
  224.    wt: 5:   7 Angle Side Angle
  225.    wt: 5:   6 Ruler and compass Angle Bisection
  226.    wt: 5:   5 Side Angle Side
  227.    wt: 5:   4 Side Side Side
  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:   6 Equations and Systems Equivalent or Implied
  233.    wt: 2:   Maps Plans Drawings
  234.    wt: 2:   21 Addition of Multiples of a Single Vector
  235.    wt: 2:   19 Signed Multiples of Vectors
  236.    wt: 2:   1 The Counting Origins of Numbers
  237.    wt: 2:   5 Areas of Rectangles Revisited
  238.    wt: 2:   4 Solving a triangular system exercise
  239.    wt: 2:   3 Solving triangular system example
  240.    wt: 2:   2 Essentially one exercises three with solution
  241.    wt: 2:   1 Essentially One Unknown
  242.    wt: 2:   3 Comparison of Negative Numbers
  243.    wt: 2:   17 Derivatives of quotients of sine and cosine
  244.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  245.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  246.    wt: 1:   About site lesson plans
  247.    wt: 1:   Mathematics Education Professors
  248.    wt: 1:   Theory of Knowledge
  249.    wt: 1:   Different Kinds of Reasoning in maths
  250.    wt: 1:   three kinds of reason in mathematics
  251.    wt: 1:   E Kirchoffs Second Law
  252.    wt: 1:   D Kirchoff First Law
  253.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  254.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  255.    wt: 1:   8 The Effect of Negative Remarks
  256.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  257.    wt: 1:   15 Sign analysis of functions
  258.    wt: 1:   8 Set view of relations and functions
  259.    wt: 1:   2 Algebraic use of function notation
  260.    wt: 1:   1 Geometric Introduction of Function Notation
  261.    wt: 1:   8 quadratics backward use of various formulas
  262.    wt: 1:   4 quadratics difference of two squares
  263.    wt: 1:   22 Multiplication of Signed Numbers
  264.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  265.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  266.    wt: 1:   13 Arrows and Vectors in a Plane
  267.    wt: 1:   8 Division and Mulplication of Compound Fractions
  268.    wt: 1:   4 Location of Point in Decimal Addition
  269.    wt: 1:   3 Location of Point in Decimal Multiplication
  270.    wt: 1:   E Long Division Methods more
  271.    wt: 1:   D Long Division Methods
  272.    wt: 1:   C Three Decimal Subtraction Methods
  273.    wt: 1:   B Decimal Comparison and Subtraction
  274.    wt: 1:   A Decimal Addition Columm Methods
  275.    wt: 1:   8 Column Multiplication Methods in General
  276.    wt: 1:   7 Decimals Multiplication Methods Examples
  277.    wt: 1:   6 Column Methods for Decimal Multiplication
  278.    wt: 1:   5 Distributive Law for Whole Numbers
  279.    wt: 1:   4 Commutative Law Groups Counting Form
  280.    wt: 1:   3 Multiplicative Counting Skills Principles
  281.    wt: 1:   2 Combing Counts Addition Skills and Principles
  282.    wt: 1:   4 Fraction Operations Axiomatic Development
  283.    wt: 1:   3 Inequalities Algebraically
  284.    wt: 1:   2 Fraction Operations Physical Development
  285.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  286.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  287.    wt: 1:   5 Equality in Algebra
  288.    wt: 1:   4 Subtraction and Division Axioms
  289.    wt: 1:   3 Product Axioms Two Forms
  290.    wt: 1:   2 Addition and Multiplication Axioms
  291.    wt: 1:   1 Equivalent Computation Rules
  292.    wt: 1:   4 Comparison of Negative Numbers
  293.    wt: 1:   8 Coordinates for Maps and Planes
  294.    wt: 1:   More Exercises
  295.    wt: 1:   Simple Exercises
  296.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  297.    wt: 1:   4 GE III Animated Examples
  298.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  299.    wt: 1:   3 GE III Equation Addition and Multiplication
  300.    wt: 1:   2 GE II Comparison
  301.    wt: 1:   1 GE Substitution four examples
  302.    wt: 1:   6 Algebraic Solution Example
  303.    wt: 1:   5 Algebraic Solutions Introduction
  304.    wt: 1:   4 Four Examples Fractional Coefficients
  305.    wt: 1:   3 Four Examples
  306.    wt: 1:   2 Three Examples
  307.    wt: 1:   1 Proper Equal Sign Usage
  308.    wt: 1:   Skill Development Notes
  309.    wt: 1:   10 One Example
  310.    wt: 1:   9 Three Examples
  311.    wt: 1:   8 One Example
  312.    wt: 1:   7 Two Examples
  313.    wt: 1:   6 Three Examples
  314.    wt: 1:   5 Three Examples
  315.    wt: 1:   4 Two Examples
  316.    wt: 1:   3 Two Examples
  317.    wt: 1:   2 Three Examples
  318.    wt: 1:   Using Letters for Physical Quantities
  319.    wt: 1:   Formula Usage Show Work Format
  320.    wt: 1:   11 Volume of Sphere
  321.    wt: 1:   10 Volume of Pyramid
  322.    wt: 1:   9 Volume of Cone
  323.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  324.    wt: 1:   8 Sets of Numbers
  325.    wt: 1:   6 Three Notions of What is a Variable
  326.    wt: 1:   4 A Brief Story of numbers and algebra
  327.    wt: 1:   4 Greater More Less Than Signs in General
  328.    wt: 1:   2 More and Less Than with Unlike Signs
  329.    wt: 1:   1 More and Less Than for Counts and Measures
  330.    wt: 1:   3 Properties of Square Roots with example
  331.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  332.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  333.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  334.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  335.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  336.    wt: 1:   4 LCM of 8 and 10 via Prime
  337.    wt: 1:   5 lengths and signs of numbers
  338.    wt: 1:   3 signed coordinates for maps and planes
  339.    wt: 1:   6 Simplification of Fractions with Units
  340.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  341.    wt: 1:   6 Multiplication of Mixed Numbers
  342.    wt: 1:   3 Unit fraction of a fraction
  343.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  344.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  345.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  346.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  347.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  348.    wt: 1:   20 Uniqueness of Prime Factorization
  349.    wt: 1:   16 video Factors of 980 using prime
  350.    wt: 1:   15 video Factors of 20 using Prime Factorization
  351.    wt: 1:   14 video Factors of 24 Take II
  352.    wt: 1:   13 video Factors of 24 using prime
  353.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  354.    wt: 1:   C Counting Areas with Powers of Ten
  355.    wt: 1:   B Powers of Ten
  356.    wt: 1:   8 Subtraction with Units of Measure
  357.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  358.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  359.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  360.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  361.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  362.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  363.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  364.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  365.    wt: 1:   Quick history of numbers and algebra
  366.    wt: 1:   012 Division of Time Intervals by Time Intervals
  367.    wt: 1:   011 Division of Time Intervals By Numbers
  368.    wt: 1:   010 Repeated Addition of Time Intervals
  369.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  370.    wt: 1:   8 Addition of Time Intervals via subtotaling
  371.    wt: 1:   7 Addition of Time Intervals
  372.    wt: 1:   4 Mixing and Changing Units of Time
  373.    wt: 1:   3 Units and Lengths of Time
  374.    wt: 1:   1 Intro of Kids To Time Date Skills
  375.    wt: 1:   Example 2 volume of a cone
  376.    wt: 1:   Example 1 volume of a pyramid
  377.    wt: 1:   Volume of Solid by Cross Sections Lesson
  378.    wt: 1:   Example 4 with x function of y
  379.    wt: 1:   34 Derivative of exponential function
  380.    wt: 1:   31 Derivatives of inverse functions
  381.    wt: 1:   30Chain Rule A Proof
  382.    wt: 1:   28 Chain Rule Preparation for a Proof
  383.    wt: 1:   20 Chain Rule for Pulley Systems
  384.    wt: 1:   8 Differentiation of polynomials
  385.    wt: 1:   5 Jumps and absence of unlimited error control
  386.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  387.    wt: 1:   G.3 Constant Difference Theorem Proof
  388.    wt: 1:   E2 Algebraic Properties of Limits
  389.    wt: 1:   D2 Limits of Monotone Sequences
  390.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  391.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  392.    wt: 1:   Chapter 23 Links To Trigonometry
  393.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  394.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  395.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  396.    wt: 1:   Chapter 15. Solving Linear Equations
  397.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  398.    wt: 1:   Chapter 6 Change of Language
  399.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  400.    wt: 1:   Chapter 4 Longer Chains of Reason
  401.    wt: 1:   Chapter 3 Chains of Reason
  402.    wt: 1:   Chapter 7 Two Treatments of Geometry
  403.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  404.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  405.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  406.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  407.    wt: 1:   Chapter 8 Change of Language
  408.    wt: 1:   Chapter 7 Longer Chains of Reason
  409.    wt: 1:   Chapter 6 Chains of Reason
  410.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  411.    wt: 1:   C. Domino effect of being careful
  412.    wt: 1:   B. Domino effect of errors
  413.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  414.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  415.    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:

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.

Return to Page Top

Home << Search

[1] [2] [3] [4]

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

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.