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

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

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

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

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

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

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

Home << Search

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

Key Word Search

Folder Search

36 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:   Geometry maps plans trigonometry vectors/
  16.    wt: 2:   12 Comparison of Unsigned and Signed Numbers/
  17.    wt: 2:   D Decimal Long Division Methods/
  18.    wt: 2:   C Decimal Multiplication Methods/
  19.    wt: 2:   B Decimal Comparing and Subtracting Methods/
  20.    wt: 2:   A Decimal Counting and Adding Methods/
  21.    wt: 2:   2 Arithmetic with Decimals/
  22.    wt: 1:   A Origins of Counting and Figuring Methods/
  23.    wt: 1:   10 Examples of Algebraic Reasoning/
  24.    wt: 1:   11 Squares and Square Roots/
  25.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  26.    wt: 1:   9 Combinatorics Trees Tables and Products/
  27.    wt: 1:   8 Arithmetic with Signed Numbers/
  28.    wt: 1:   7 Arithmetic and Fractions with Units/
  29.    wt: 1:   6 Fractions and Ratios/
  30.    wt: 1:   5 Integers/
  31.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  32.    wt: 1:   3 Prime Factorization Skills/
  33.    wt: 1:   1 Decimal Place Value/
  34.    wt: 1:   Arithmetic and Number Theory Skills/
  35.    wt: 1:   Volume 1 Elements of Reason/
  36.    wt: 11:   2 Euclidean Geometry Constructions Theory extras/

Web Page Search

230 matches:

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

Extended Search

577 matches:

  1.    wt: 9:   Right Triangle and Unit Circle Trigonometry
  2.    wt: 9:   2 Similar Triangles Equality of Corresponding Side Ratios
  3.    wt: 9:   Right Triangle and Unit Circle Trigonometry
  4.    wt: 9:   8 More Use of Maps Not Drawn to Scale
  5.    wt: 9:   4 Angles on Maps Plans drawn to scale
  6.    wt: 9:   3 Lengths and Areas on Maps and Plans
  7.    wt: 8:   4 Resultant of a Sum of Movements
  8.    wt: 8:   32 seven rows of pascals triangle
  9.    wt: 8:   27 Logarithmic use of products of sines and cosines
  10.    wt: 8:   16 Right Triangle Complementary Angle Relations
  11.    wt: 8:   Unit Circle Development of Trigonometry
  12.    wt: 8:   6 Trigonometry Sines of Supplementary Angles
  13.    wt: 8:   10 Similarity of Triangles Equivalent of Two Criteria
  14.    wt: 8:   6 Figuring with Maps Not to Scale
  15.    wt: 7:   13 Velocity Vectors in Physics
  16.    wt: 7:   8 Parallel Vectors
  17.    wt: 7:   6 Vectors with Coordinates
  18.    wt: 7:   3 Navigation with Arrows or Vectors
  19.    wt: 7:   2 Signed Coordinates
  20.    wt: 7:   Analytic View of Triangle Construction or Line Instersection More
  21.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  22.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  23.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  24.    wt: 7:   30 unit circle calculation of six trigonometric functions
  25.    wt: 7:   28 Expressing products of sines cosines as sums
  26.    wt: 7:   26 Formulas for products of sines and cosines
  27.    wt: 7:   23 sine and cosine of 180 plus 22.5 degrees
  28.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  29.    wt: 7:   18 sum of sinusoidal waves as a single wave
  30.    wt: 7:   17F Law of cosines
  31.    wt: 7:   13 Graph of tangent function many periods
  32.    wt: 7:   12 Graph of tangent function for one period
  33.    wt: 7:   10 Graphs of sines and cosines many periods
  34.    wt: 7:   9 Graphs of sine and cosine over one period
  35.    wt: 7:   8 period of tangent function
  36.    wt: 7:   7 period of sine and cosine
  37.    wt: 7:   8 Unit Circle Development of Trigonometry
  38.    wt: 7:   5 An Easy Proof of the Distributive Law
  39.    wt: 7:   8 Triangles Cascade Problem Solving
  40.    wt: 7:   5 Trigonometric Ratios For Tangent and Special Triangles
  41.    wt: 7:   4 Trigonometric Ratios For Two Special Triangles
  42.    wt: 7:   Why Trigonometry the whyslopes view
  43.    wt: 7:   9 Similarity of Triangles Usual Criteria
  44.    wt: 7:   8 Similarity of Triangles and Polygons
  45.    wt: 7:   A Measurement with Ruler Proper Use
  46.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  47.    wt: 7:   2 Measuring Area Directly
  48.    wt: 7:   1 Length Measurement
  49.    wt: 6:   11 arctan left inverse of tangent Graph
  50.    wt: 6:   10 arctan left inverse of tangent Definition
  51.    wt: 6:   8 arcsin left inverse of sine Graph
  52.    wt: 6:   7 arcsin left inverse of sine Definition
  53.    wt: 6:   6 Graph of arccos function
  54.    wt: 6:   3 Left Inverse of cosine arccos definition
  55.    wt: 6:   8 Radian Measures of Common Angles
  56.    wt: 6:   7 Radian Measures in special Triangles
  57.    wt: 6:   2 Radian Measure Numerical Value of one degree
  58.    wt: 6:   A Global Time and Navigation
  59.    wt: 6:   15 Dot and Cross Product
  60.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  61.    wt: 6:   12 From Applied To Pure Mathematics
  62.    wt: 6:   11 Component Method
  63.    wt: 6:   10 Parallelogram Addition Method
  64.    wt: 6:   9 Head to Tail Coordinate View
  65.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  66.    wt: 6:   5 Head To Tail Arrow Addition
  67.    wt: 6:   1 Unsigned Coordinates
  68.    wt: 6:   Vector and Complex Number Applet
  69.    wt: 6:   Proportionality of Line Segments From Parallel Transversals
  70.    wt: 6:   Triangle Angles Sum To 180 Degrees
  71.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  72.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  73.    wt: 6:   Straight Lines Intersection of
  74.    wt: 6:   3 Straight Lines Slope as Tangent of Inclination Angle
  75.    wt: 6:   17 tangent function angle sum formulas
  76.    wt: 6:   31 basic secant cosecant cotangent trig identities
  77.    wt: 6:   29 secant cosecant and cotangent for acute angles
  78.    wt: 6:   25 tangent double angle formula Slope connection
  79.    wt: 6:   24 tangent Angle Difference Formula
  80.    wt: 6:   21 sine and cosine Half Angle Formulas
  81.    wt: 6:   20 sine and cosine Double Angle Formulas
  82.    wt: 6:   19 Pythagorean Identity For sine and cosine functions
  83.    wt: 6:   17G Pythagorean Theorem Converse
  84.    wt: 6:   17E Trig Formulas for dot and cross Products
  85.    wt: 6:   17D cis formulas for sine cosines and tangent
  86.    wt: 6:   17C sine and cosine double triple angle formulas
  87.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  88.    wt: 6:   17A The complex number valued trig function cis
  89.    wt: 6:   15 sine cosine Complementary Angle Relations
  90.    wt: 6:   14 cosine even and sine and tangent are odd
  91.    wt: 6:   11 tangent function undefined when terminal side vertical
  92.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  93.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  94.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  95.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  96.    wt: 6:   2 Quadrant I reference Angles
  97.    wt: 6:   1 Unit Points Reflections Rotations
  98.    wt: 6:   20 N th Roots of Complex Numbers
  99.    wt: 6:   19 N th Roots of Unity
  100.    wt: 6:   18 Sixth Roots of Unity
  101.    wt: 6:   17 Cube Roots of unity
  102.    wt: 6:   14 Law of cosines
  103.    wt: 6:   6 Field Properties of Complex Number
  104.    wt: 6:   2 Complex Numbers made easier we hope
  105.    wt: 6:   7 Trignometric Ratios Unit Circle
  106.    wt: 6:   3 Trigonometric Ratios sine and cosine
  107.    wt: 6:   1 Angle Measurement with Degrees
  108.    wt: 6:   12 Triangles Similarity More Problems
  109.    wt: 6:   11 Triangle Similarity Missing Side Problem
  110.    wt: 6:   5 Similarity of Circles Squares and Rectangles
  111.    wt: 6:   1 Early Concept of Like or Similar Shapes
  112.    wt: 6:   10 Midpoint of [a b] and [b a]
  113.    wt: 6:   6 Intersection of lines by solving linear systems
  114.    wt: 6:   5 Algebraic View of Slopes
  115.    wt: 6:   2 point slope equation for a line
  116.    wt: 6:   1 Numerical view of lines and their equations
  117.    wt: 6:   11 Triangle Inequality
  118.    wt: 6:   9 Pythagorean Theorem Chinese Square Proof
  119.    wt: 6:   2 Cartesian Coordinates with signs
  120.    wt: 5:   16 cotangent function Definition Graph and Inverse
  121.    wt: 5:   15 cosecant function Definition Graph and Inverse
  122.    wt: 5:   14 secant function Definition Graph and Inverse
  123.    wt: 5:   13 cosecant function Definition Graph and Inverse
  124.    wt: 5:   12 motivation for term arctan
  125.    wt: 5:   9 motivation for name arcsin
  126.    wt: 5:   5 Swapping Coordinates is a reflection
  127.    wt: 5:   4 possible motivation for term arccos
  128.    wt: 5:   2 cosine function more properties
  129.    wt: 5:   1 cosine function properties
  130.    wt: 5:   9 Summary Degrees to Radians and back
  131.    wt: 5:   6 Radian Measure to Degrees
  132.    wt: 5:   5 Degrees to Radian Measure
  133.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  134.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  135.    wt: 5:   1 Degrees and Radians Introduction
  136.    wt: 5:   4 graphing y=Asin(x c)
  137.    wt: 5:   3 graphing y=f(x c) plus K
  138.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  139.    wt: 5:   1 graphing y=f(x a)
  140.    wt: 5:   Parallel Lines and Parallel Transversals
  141.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  142.    wt: 5:   Parallel Lines and Interior Angles
  143.    wt: 5:   Straight Lines ASA Intersection Study More
  144.    wt: 5:   Straight Lines ASA Intersection Study
  145.    wt: 5:   Straight Lines Instersection Solving Equations
  146.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  147.    wt: 5:   C Straight Lines Slope from Coordinates
  148.    wt: 5:   B Straight Line Slope Scaling Properties More
  149.    wt: 5:   A Straight Line Slope Scaling Properties
  150.    wt: 5:   14 Straight Lines Equations General Case
  151.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  152.    wt: 5:   12 Straight Lines Graphing mx plus b
  153.    wt: 5:   11 Straight Lines Graphing y=mx
  154.    wt: 5:   10 Straight Lines through Origin Equations More
  155.    wt: 5:   9 Straight Lines through Origin Equations
  156.    wt: 5:   8 Straight Lines Equation for vertical
  157.    wt: 5:   7 Tangent Function is odd on this domain
  158.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  159.    wt: 5:   5 Tangent Function Graph
  160.    wt: 5:   4 Tangent Function Properties
  161.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  162.    wt: 5:   1 Straight Lines Slope Concept
  163.    wt: 5:   21 Logarithms Powers and Exponentials
  164.    wt: 5:   16 References and Originality Question
  165.    wt: 5:   15 Pythagorean Theorem Converse
  166.    wt: 5:   13 Trig Formulas for dot and cross Products
  167.    wt: 5:   12 cis formulas for sine cosines and tangent
  168.    wt: 5:   11 sine and cosine double triple angle formulas
  169.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  170.    wt: 5:   9 The complex number valued trig function cis
  171.    wt: 5:   7 Second Way to Calculate Products
  172.    wt: 5:   4 Multiplication Properties
  173.    wt: 5:   3 Addition Properties
  174.    wt: 5:   1 Rectangular Polar Coordinates Review
  175.    wt: 5:   Appetizer A Complex Number Applet
  176.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  177.    wt: 5:   7 Translations Rotations Reflections Dilatations
  178.    wt: 5:   6 Geometric Diagrams in Class
  179.    wt: 5:   4 Similarity Definition with Coordinate
  180.    wt: 5:   3 Similarity by Design with coordinates
  181.    wt: 5:   2 Similarity By Design
  182.    wt: 5:   Four Simple Exercises
  183.    wt: 5:   12 Links Lessons elsewhere
  184.    wt: 5:   11 A Partial Summary
  185.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  186.    wt: 5:   8 Mid Point Formula
  187.    wt: 5:   7 Exercises to test skill and concept mastery
  188.    wt: 5:   4 Equations for lines three forms
  189.    wt: 5:   3 Slope product for perpendicular lines
  190.    wt: 5:   What is and is not here
  191.    wt: 5:   13 Pythagorean spatial distance formulas
  192.    wt: 5:   12 Spatial Coordinates
  193.    wt: 5:   10 Pythagorean plane distance formula
  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:   1 Cartesian Coordinates sans signs
  201.    wt: 5:   About Folder Contents
  202.    wt: 3:   3 Comparison of Negative Numbers
  203.    wt: 3:   2 More and Less Than with Unlike Signs
  204.    wt: 3:   2 Integers Multiplies of a Unit Moverment
  205.    wt: 3:   2 Division with Single Digit Divisors
  206.    wt: 3:   C Counting Areas with Powers of Ten
  207.    wt: 3:   B Powers of Ten
  208.    wt: 3:   2 One Digit Multipliers
  209.    wt: 3:   8 Subtraction with Units of Measure
  210.    wt: 3:   2 Subtraction Easy Case Examples
  211.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  212.    wt: 2:   3 Euclidean Geometry Leanly
  213.    wt: 2:   Maps Plans Drawings
  214.    wt: 2:   Theory of Knowledge
  215.    wt: 2:   21 Addition of Multiples of a Single Vector
  216.    wt: 2:   19 Signed Multiples of Vectors
  217.    wt: 2:   2 Combing Counts Addition Skills and Principles
  218.    wt: 2:   1 The Counting Origins of Numbers
  219.    wt: 2:   5 Areas of Rectangles Revisited
  220.    wt: 2:   4 Greater More Less Than Signs in General
  221.    wt: 2:   1 More and Less Than for Counts and Measures
  222.    wt: 2:   3 Properties of Square Roots with example
  223.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  224.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  225.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  226.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  227.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  228.    wt: 2:   8 GCD from Euclidean Algorithm
  229.    wt: 2:   4 LCM of 8 and 10 via Prime
  230.    wt: 2:   5 lengths and signs of numbers
  231.    wt: 2:   3 signed coordinates for maps and planes
  232.    wt: 2:   6 Simplification of Fractions with Units
  233.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  234.    wt: 2:   6 Multiplication of Mixed Numbers
  235.    wt: 2:   3 Unit fraction of a fraction
  236.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  237.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  238.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  239.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  240.    wt: 2:   20 Uniqueness of Prime Factorization
  241.    wt: 2:   16 video Factors of 980 using prime
  242.    wt: 2:   15 video Factors of 20 using Prime Factorization
  243.    wt: 2:   14 video Factors of 24 Take II
  244.    wt: 2:   13 video Factors of 24 using prime
  245.    wt: 2:   6 Sieve of Eratosthenes and Square Rule
  246.    wt: 2:   2 Prime and Composites less than 16
  247.    wt: 2:   Long Division Backwards more
  248.    wt: 2:   Long Division Backward
  249.    wt: 2:   Division with Counts and Length
  250.    wt: 2:   Long Division forwards and backwards Example 3
  251.    wt: 2:   Long Division forwards and backwards Example 2
  252.    wt: 2:   Long Division forwards and backwards Example 1
  253.    wt: 2:   12 Why Long Division Works Take III
  254.    wt: 2:   11 Another Single Digit Divisor Example
  255.    wt: 2:   10 Division by Five Long and Short Ways
  256.    wt: 2:   9 Why Long Division Works Take II
  257.    wt: 2:   8 Correcting the Mistake
  258.    wt: 2:   7 Long Divison Mistake Catching
  259.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  260.    wt: 2:   5 Long Division Include Zeroes or not
  261.    wt: 2:   4 Division with 2 Digit Divsors
  262.    wt: 2:   3 Division Single Digit Divisor Example
  263.    wt: 2:   1 Divsion Physical Examples
  264.    wt: 2:   D Decimal Multiplication Methods Derived
  265.    wt: 2:   A Elementary Basis for Multiplication Methods
  266.    wt: 2:   6 Multiplication Commutes Order Not Important
  267.    wt: 2:   5 Decimal Fraction Multiplication
  268.    wt: 2:   4 Two and Three Digit Multipliers
  269.    wt: 2:   3 More One Digit Multipliers
  270.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  271.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  272.    wt: 2:   Video Power Notation in Decimal Expansion
  273.    wt: 2:   1 Why 3 times 5 gives 15
  274.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  275.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  276.    wt: 2:   Subtraction with J Conversions Example
  277.    wt: 2:   Subtraction Another Video Lesson
  278.    wt: 2:   9 22 Minute Subtraction Review Video
  279.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  280.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  281.    wt: 2:   5 A Tip for Efficent Subtraction
  282.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  283.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  284.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  285.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  286.    wt: 2:   8 What skills and work habits to require
  287.    wt: 2:   7 Adding decimal fractions using decimal point
  288.    wt: 2:   6. Counting and adding units and mixed units
  289.    wt: 2:   5. How to add decimals C. Examples
  290.    wt: 2:   4. How to add with decimals B with conversions
  291.    wt: 2:   3. How to add with decimals A sans conversions
  292.    wt: 2:   2 Decimal Counting Practices
  293.    wt: 2:   1. Explaining Addition Table
  294.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  295.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  296.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  297.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  298.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  299.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  300.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  301.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  302.    wt: 2:   Quick history of numbers and algebra
  303.    wt: 2:   17 Derivatives of quotients of sine and cosine
  304.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  305.    wt: 2:   Chapter 7 Two Treatments of Geometry
  306.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  307.    wt: 1:   Ramblings Extrinsic numbers theory
  308.    wt: 1:   Skills Chapter 2 Geometry
  309.    wt: 1:   8 analytic geometry etc
  310.    wt: 1:   About site lesson plans
  311.    wt: 1:   Mathematics Education Professors
  312.    wt: 1:   Different Kinds of Reasoning in maths
  313.    wt: 1:   three kinds of reason in mathematics
  314.    wt: 1:   2 Conductance Resistance Duality02
  315.    wt: 1:   E Kirchoffs Second Law
  316.    wt: 1:   D Kirchoff First Law
  317.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  318.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  319.    wt: 1:   8 The Effect of Negative Remarks
  320.    wt: 1:   2 Reading and Writing Skills
  321.    wt: 1:   Ages 12 to 14 Geometry
  322.    wt: 1:   Ages 10 to 12 Geometry
  323.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  324.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  325.    wt: 1:   20 Interchanging coordinates a reflection
  326.    wt: 1:   15 Sign analysis of functions
  327.    wt: 1:   9 Set theory term relation possible origins
  328.    wt: 1:   8 Set view of relations and functions
  329.    wt: 1:   2 Algebraic use of function notation
  330.    wt: 1:   1 Geometric Introduction of Function Notation
  331.    wt: 1:   8 quadratics backward use of various formulas
  332.    wt: 1:   4 quadratics difference of two squares
  333.    wt: 1:   22 Multiplication of Signed Numbers
  334.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  335.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  336.    wt: 1:   13 Arrows and Vectors in a Plane
  337.    wt: 1:   8 Division and Mulplication of Compound Fractions
  338.    wt: 1:   4 Location of Point in Decimal Addition
  339.    wt: 1:   3 Location of Point in Decimal Multiplication
  340.    wt: 1:   E Long Division Methods more
  341.    wt: 1:   D Long Division Methods
  342.    wt: 1:   C Three Decimal Subtraction Methods
  343.    wt: 1:   B Decimal Comparison and Subtraction
  344.    wt: 1:   A Decimal Addition Columm Methods
  345.    wt: 1:   8 Column Multiplication Methods in General
  346.    wt: 1:   7 Decimals Multiplication Methods Examples
  347.    wt: 1:   6 Column Methods for Decimal Multiplication
  348.    wt: 1:   5 Distributive Law for Whole Numbers
  349.    wt: 1:   4 Commutative Law Groups Counting Form
  350.    wt: 1:   3 Multiplicative Counting Skills Principles
  351.    wt: 1:   4 Fraction Operations Axiomatic Development
  352.    wt: 1:   3 Inequalities Algebraically
  353.    wt: 1:   2 Fraction Operations Physical Development
  354.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  355.    wt: 1:   2 Algebraic View
  356.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  357.    wt: 1:   5 Triangle Area Formula Backwards
  358.    wt: 1:   4 Comparison of Negative Numbers
  359.    wt: 1:   8 Coordinates for Maps and Planes
  360.    wt: 1:   2 GE II Comparison
  361.    wt: 1:   2 Essentially one exercises three with solution
  362.    wt: 1:   2 Three Examples
  363.    wt: 1:   2 Three Examples
  364.    wt: 1:   11 Volume of Sphere
  365.    wt: 1:   10 Volume of Pyramid
  366.    wt: 1:   9 Volume of Cone
  367.    wt: 1:   3 Triangle Area Formula Example
  368.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  369.    wt: 1:   8 Sets of Numbers
  370.    wt: 1:   6 Three Notions of What is a Variable
  371.    wt: 1:   4 A Brief Story of numbers and algebra
  372.    wt: 1:   arithmetic videos Real Player Format
  373.    wt: 1:   5 Square Roots with primes more still
  374.    wt: 1:   4 Square Roots with primes more
  375.    wt: 1:   2 Square Roots with Prime
  376.    wt: 1:   1 Squares and Square Roots Introduction
  377.    wt: 1:   13 GCD from given Prime Factorization
  378.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  379.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  380.    wt: 1:   7 GCD and LCM from prime factorization
  381.    wt: 1:   6 GCD from Prime
  382.    wt: 1:   5 Common Divisors 60 45 via Prime
  383.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  384.    wt: 1:   2 Least Common Multiple LCM intro via list method
  385.    wt: 1:   1 Least Common Multiples LCM Introduction
  386.    wt: 1:   12 GCD 2700 288 via Prime
  387.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  388.    wt: 1:   4 Counting with Trees Product Rule Take I
  389.    wt: 1:   3 Counting with Tables and Trees II
  390.    wt: 1:   2 Counting with Tables and Trees I
  391.    wt: 1:   1 Counting and Counting Methods I
  392.    wt: 1:   11 What are real lengths and numbers
  393.    wt: 1:   10 dividing signed numbers
  394.    wt: 1:   9 subtracting signed numbers
  395.    wt: 1:   8 multiplying signed numbers
  396.    wt: 1:   7 negative and additive inverse
  397.    wt: 1:   6 adding signed numbers
  398.    wt: 1:   4 signed coordinates for regions in space
  399.    wt: 1:   2 signed and unsigned numbers as coordinates
  400.    wt: 1:   7 Converting or Changing Units
  401.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  402.    wt: 1:   4 Fractions with Units
  403.    wt: 1:   3 Multiplying Units and Numbers
  404.    wt: 1:   2 Equality and Units
  405.    wt: 1:   1 Addition and Subtraction with Units
  406.    wt: 1:   D Three Term Ratios
  407.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  408.    wt: 1:   B Fractions and Two Term Ratios
  409.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  410.    wt: 1:   22 Complex Compound Fractions
  411.    wt: 1:   21 Working With Signs
  412.    wt: 1:   21 Reciprocals for Fractions and Wholes
  413.    wt: 1:   20 Dividing Fractions the Why
  414.    wt: 1:   19 Dividing Fractions How TO
  415.    wt: 1:   18 Efficient Ways to Multiply
  416.    wt: 1:   17 Efficient Ways to Add and Subtract
  417.    wt: 1:   16 Addition Subtraction Comparision Compared
  418.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  419.    wt: 1:   14 Adding and Subtracting with Like Denominators
  420.    wt: 1:   13 Fraction Comparison Algebraic View
  421.    wt: 1:   12 Fraction Comparison
  422.    wt: 1:   11 Simplification an Algebraic View
  423.    wt: 1:   9 Improper Fractions and Mixed Numbers
  424.    wt: 1:   8 Numerals Fractionals Quantals Take II
  425.    wt: 1:   7 Numerals Fractionals Quantals
  426.    wt: 1:   6 Multiplication Algebraically Take II
  427.    wt: 1:   5 Equivalent Fractions
  428.    wt: 1:   4 Fraction Multiplication
  429.    wt: 1:   2 Unit Fraction Multiplication
  430.    wt: 1:   1 What is a fraction Take II
  431.    wt: 1:   1 What is a fraction
  432.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  433.    wt: 1:   D Remainders Modulo 11 Pair Rule
  434.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  435.    wt: 1:   B Integer Long Division Multiple Choices
  436.    wt: 1:   A Associative Law Theorectical Note
  437.    wt: 1:   13 Subtraction with Additive Inverse
  438.    wt: 1:   12 Adding Integers More Examples
  439.    wt: 1:   11 Adding Integers Formulas and Examples
  440.    wt: 1:   10 Integer Multiplication Formulas
  441.    wt: 1:   9 Multiplying Integers
  442.    wt: 1:   8 Multiplication by Signed Numbers Integers
  443.    wt: 1:   7 Multiplication by Signs
  444.    wt: 1:   6 Multiplication by Natural Numbers
  445.    wt: 1:   5 Zero Movement and Additive Inverses
  446.    wt: 1:   4 Adding Movements wiht opposite directions
  447.    wt: 1:   3 Adding Movements with same direction
  448.    wt: 1:   1 Integers as Coordinates
  449.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  450.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  451.    wt: 1:   26 Divisibility by 2 3 5 Example
  452.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  453.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  454.    wt: 1:   23 Remainder Arithmetic Modulo 2
  455.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  456.    wt: 1:   21 Remainder Arithmetic Modulo 3
  457.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  458.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  459.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  460.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  461.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  462.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  463.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  464.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  465.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  466.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  467.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  468.    wt: 1:   5 Remainder Arithmetic Modulo 5
  469.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  470.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  471.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  472.    wt: 1:   1 Remainder Arithmetic Modulo 10
  473.    wt: 1:   19 video Prime Factorization Unique
  474.    wt: 1:   18 video Count Factors given Prime Factorization
  475.    wt: 1:   17 Identify and Count Factors using Primes
  476.    wt: 1:   12 LCD GCD and LCM using Primes
  477.    wt: 1:   11 Efficient Square Rule Use
  478.    wt: 1:   10 video Prime Factorization upto 23 squared
  479.    wt: 1:   9 video Prime Factorization upto 19 squared
  480.    wt: 1:   8 video Prime Factorization upto 19
  481.    wt: 1:   7 Calculator Usage Notes and Cautions
  482.    wt: 1:   5 Prime Factorization and a Square Rule
  483.    wt: 1:   4 video Prime Factorization Introduction
  484.    wt: 1:   3 video Primes and Composites from 9 times table
  485.    wt: 1:   1 video how Products are bigger than factor
  486.    wt: 1:   11 Place Value SI Standard International way
  487.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  488.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  489.    wt: 1:   Exact Arithmetic Wholes and Fractions
  490.    wt: 1:   Formula Evaluation how to show work
  491.    wt: 1:   Expression Evaluation how to show work
  492.    wt: 1:   The 20 Times Table
  493.    wt: 1:   The 12 Times Table Visually
  494.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  495.    wt: 1:   About folder contents
  496.    wt: 1:   012 Division of Time Intervals by Time Intervals
  497.    wt: 1:   011 Division of Time Intervals By Numbers
  498.    wt: 1:   010 Repeated Addition of Time Intervals
  499.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  500.    wt: 1:   8 Addition of Time Intervals via subtotaling
  501.    wt: 1:   7 Addition of Time Intervals
  502.    wt: 1:   4 Mixing and Changing Units of Time
  503.    wt: 1:   3 Units and Lengths of Time
  504.    wt: 1:   1 Intro of Kids To Time Date Skills
  505.    wt: 1:   Example 2 volume of a cone
  506.    wt: 1:   Example 1 volume of a pyramid
  507.    wt: 1:   Volume of Solid by Cross Sections Lesson
  508.    wt: 1:   Example 4 with x function of y
  509.    wt: 1:   34 Derivative of exponential function
  510.    wt: 1:   31 Derivatives of inverse functions
  511.    wt: 1:   30Chain Rule A Proof
  512.    wt: 1:   28 Chain Rule Preparation for a Proof
  513.    wt: 1:   8 Differentiation of polynomials
  514.    wt: 1:   5 Jumps and absence of unlimited error control
  515.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  516.    wt: 1:   G.3 Constant Difference Theorem Proof
  517.    wt: 1:   E2 Algebraic Properties of Limits
  518.    wt: 1:   D2 Limits of Monotone Sequences
  519.    wt: 1:   C Triangle Inequalities
  520.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  521.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  522.    wt: 1:   Chapter 23 Links To Trigonometry
  523.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  524.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  525.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  526.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  527.    wt: 1:   Chapter 6 Change of Language
  528.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  529.    wt: 1:   Chapter 4 Longer Chains of Reason
  530.    wt: 1:   Chapter 3 Chains of Reason
  531.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  532.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  533.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  534.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  535.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  536.    wt: 1:   Chapter 8 Change of Language
  537.    wt: 1:   Chapter 7 Longer Chains of Reason
  538.    wt: 1:   Chapter 6 Chains of Reason
  539.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  540.    wt: 1:   C. Domino effect of being careful
  541.    wt: 1:   B. Domino effect of errors
  542.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  543.    wt: 1:   Chapter 6 More Algebra and Geometry
  544.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  545.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  546.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  547.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  548.    wt: 16:   17 Right Bisectors of Triangle Sides
  549.    wt: 13:   Euclidean Geometry Elsewhere LINKS
  550.    wt: 13:   19 Right Triangle Similarity
  551.    wt: 13:   9 Construction of a right bisector
  552.    wt: 13:   3 Isometry of Triangles Congruence
  553.    wt: 13:   2 Correspondence between Triangles
  554.    wt: 13:   Short Course on Euclidean Geometry
  555.    wt: 12:   PS C Similarity Use Recognize it in Trigonometry
  556.    wt: 12:   18 Triangle Similarity Take 1
  557.    wt: 12:   15 Triangle Angle Sum is 180 degrees
  558.    wt: 12:   11 Triangle Construction Fails
  559.    wt: 12:   8 Isoceles Triangles
  560.    wt: 11:   PS H Distributive Law For Complex Numbers
  561.    wt: 11:   PS G Rotation Distributes over Addition
  562.    wt: 11:   PS F Scalar Multiplication Distributes over Addition
  563.    wt: 11:   PS E Multiplication with Polar Coordinates
  564.    wt: 11:   PS D Addition with Cartesian Coordinates
  565.    wt: 11:   PS B Parallelogram Construction Methods
  566.    wt: 11:   PS A Kite Construction Methods
  567.    wt: 11:   21 Parallelograms
  568.    wt: 11:   16 Angles Subtended By Chords and Diameters
  569.    wt: 11:   14 Parallel Lines Postulate
  570.    wt: 11:   13 Angle Side Angle Failure
  571.    wt: 11:   12 Side Angle Side Failure
  572.    wt: 11:   10 Dropping a perpendicular to line
  573.    wt: 11:   7 Angle Side Angle
  574.    wt: 11:   6 Ruler and compass Angle Bisection
  575.    wt: 11:   5 Side Angle Side
  576.    wt: 11:   4 Side Side Side
  577.    wt: 11:   1 Initial Concepts and Terms

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

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.