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.

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38 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:   2 Formula Forward Use Evaluation/
  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:   9 Proportionality Backwards and Forwards/
  23.    wt: 1:   8 Unifying Theme For Algebra/
  24.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  25.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  26.    wt: 1:   11 Squares and Square Roots/
  27.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  28.    wt: 1:   9 Combinatorics Trees Tables and Products/
  29.    wt: 1:   8 Arithmetic with Signed Numbers/
  30.    wt: 1:   7 Arithmetic and Fractions with Units/
  31.    wt: 1:   6 Fractions and Ratios/
  32.    wt: 1:   5 Integers/
  33.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  34.    wt: 1:   3 Prime Factorization Skills/
  35.    wt: 1:   1 Decimal Place Value/
  36.    wt: 1:   Arithmetic and Number Theory Skills/
  37.    wt: 1:   Volume 2 Three Skills For Algebra/
  38.    wt: 11:   2 Euclidean Geometry Constructions Theory extras/

Web Page Search

221 matches:

  1.    wt: 3:   PS H Distributive Law For Complex Numbers
  2.    wt: 3:   5 Distributive Law for Whole Numbers
  3.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  4.    wt: 2:   3 Euclidean Geometry Leanly
  5.    wt: 2:   Maps Plans Drawings
  6.    wt: 2:   formal or informal peer review
  7.    wt: 2:   Prequel In For A Penny In For A Pound
  8.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  9.    wt: 2:   5 Function notation for geometric transformations
  10.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  11.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  12.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  13.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  14.    wt: 2:   1 Polynomials Distributive Law
  15.    wt: 2:   26 Formulas for products of sines and cosines
  16.    wt: 2:   17E Trig Formulas for dot and cross Products
  17.    wt: 2:   17D cis formulas for sine cosines and tangent
  18.    wt: 2:   13 Trig Formulas for dot and cross Products
  19.    wt: 2:   12 cis formulas for sine cosines and tangent
  20.    wt: 2:   5 An Easy Proof of the Distributive Law
  21.    wt: 2:   4 Equations for lines three forms
  22.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  23.    wt: 2:   Short Course on Euclidean Geometry
  24.    wt: 2:   4 Angles on Maps Plans drawn to scale
  25.    wt: 2:   3 Lengths and Areas on Maps and Plans
  26.    wt: 2:   23 Distributive Law Two Derivations
  27.    wt: 2:   4 Commutative Law Groups Counting Form
  28.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  29.    wt: 2:   8 Coordinates for Maps and Planes
  30.    wt: 2:   Formula Usage Show Work Format
  31.    wt: 2:   1 Written work formats for developing and showing skill
  32.    wt: 2:   3 signed coordinates for maps and planes
  33.    wt: 2:   38 Formulas and derivatives for powers and roots
  34.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  35.    wt: 2:   Postscript For Better Performance
  36.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  37.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  38.    wt: 2:   G. Written work formats for developing and showing skill
  39.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  40.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  41.    wt: 1:   Ramblings Extrinsic numbers theory
  42.    wt: 1:   Skills Chapter 2 Geometry
  43.    wt: 1:   8 analytic geometry etc
  44.    wt: 1:   three goals to set for students
  45.    wt: 1:   permissions for teachers
  46.    wt: 1:   activities for students
  47.    wt: 1:   About site lesson plans
  48.    wt: 1:   Education Reform Inconsistencies
  49.    wt: 1:   geometric implications for algebra
  50.    wt: 1:   three goals for Mathematics Education
  51.    wt: 1:   02 21 words for teachers
  52.    wt: 1:   three aims for mathematics students
  53.    wt: 1:   standards for course material
  54.    wt: 1:   Theory of Knowledge
  55.    wt: 1:   Four ways to improve education reform
  56.    wt: 1:   need for a mixed mathematics curriculum
  57.    wt: 1:   fairness and inductive principles for instruction
  58.    wt: 1:   words for mathematics instructor
  59.    wt: 1:   E Kirchoffs Second Law
  60.    wt: 1:   D Kirchoff First Law
  61.    wt: 1:   C Electromotive force conventional current02
  62.    wt: 1:   B Electromotive force conventional current01
  63.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  64.    wt: 1:   24 Standards For Skill Develoment Take II
  65.    wt: 1:   24 Standards For Skill Develoment
  66.    wt: 1:   17 Math Booklets for children and young teenagers
  67.    wt: 1:   15 Counting For Parents
  68.    wt: 1:   12 Goals and Objectives For Mathematics
  69.    wt: 1:   10 Ends values for work study instruction
  70.    wt: 1:   5 Patience Please for Yourself and Your Charges
  71.    wt: 1:   4 Learning Takes Time and Effort
  72.    wt: 1:   3 Preparing for Science Studies
  73.    wt: 1:   Ages 12 to 14 Geometry
  74.    wt: 1:   Ages 10 to 12 Geometry
  75.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  76.    wt: 1:   9 Set theory term relation possible origins
  77.    wt: 1:   6 Set Existence Formation and Notation
  78.    wt: 1:   3 Formula or function graphing exercise
  79.    wt: 1:   8 quadratics backward use of various formulas
  80.    wt: 1:   7 quadratic formulla derivation
  81.    wt: 1:   8 Notes for instructors or tutors
  82.    wt: 1:   12 motivation for term arctan
  83.    wt: 1:   9 motivation for name arcsin
  84.    wt: 1:   4 possible motivation for term arccos
  85.    wt: 1:   13 Velocity Vectors in Physics
  86.    wt: 1:   8 Parallel Vectors
  87.    wt: 1:   6 Vectors with Coordinates
  88.    wt: 1:   3 Navigation with Arrows or Vectors
  89.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  90.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  91.    wt: 1:   8 Straight Lines Equation for vertical
  92.    wt: 1:   17 tangent function angle sum formulas
  93.    wt: 1:   29 secant cosecant and cotangent for acute angles
  94.    wt: 1:   25 tangent double angle formula Slope connection
  95.    wt: 1:   24 tangent Angle Difference Formula
  96.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  97.    wt: 1:   21 sine and cosine Half Angle Formulas
  98.    wt: 1:   20 sine and cosine Double Angle Formulas
  99.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  100.    wt: 1:   17F Law of cosines
  101.    wt: 1:   17C sine and cosine double triple angle formulas
  102.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  103.    wt: 1:   12 Graph of tangent function for one period
  104.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  105.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  106.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  107.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  108.    wt: 1:   1 Unit Points Reflections Rotations
  109.    wt: 1:   Unit Circle Development of Trigonometry
  110.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  111.    wt: 1:   14 Law of cosines
  112.    wt: 1:   11 sine and cosine double triple angle formulas
  113.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  114.    wt: 1:   8 Unit Circle Development of Trigonometry
  115.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  116.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  117.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  118.    wt: 1:   Why Trigonometry the whyslopes view
  119.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  120.    wt: 1:   7 Translations Rotations Reflections Dilatations
  121.    wt: 1:   8 Mid Point Formula
  122.    wt: 1:   3 Slope product for perpendicular lines
  123.    wt: 1:   2 point slope equation for a line
  124.    wt: 1:   13 Pythagorean spatial distance formulas
  125.    wt: 1:   10 Pythagorean plane distance formula
  126.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  127.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  128.    wt: 1:   6 Figuring with Maps Not to Scale
  129.    wt: 1:   19 Signed Multiples of Vectors
  130.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  131.    wt: 1:   13 Arrows and Vectors in a Plane
  132.    wt: 1:   6 Column Methods for Decimal Multiplication
  133.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  134.    wt: 1:   6 Compound Interest Forward and Backwards
  135.    wt: 1:   5 Triangle Area Formula Backwards
  136.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  137.    wt: 1:   3 Product Axioms Two Forms
  138.    wt: 1:   2 More and Less Than for Counts and Measures
  139.    wt: 1:   9 Coordinates for Regions in Space
  140.    wt: 1:   3 Geometric Formulas and Function Notation
  141.    wt: 1:   1 Formulas Dependence and Function Notation
  142.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  143.    wt: 1:   Using Letters for Physical Quantities
  144.    wt: 1:   13 Naming Identifying Formulas with Words
  145.    wt: 1:   8 Compound Interest Formula Evaluation
  146.    wt: 1:   7 Compound Interest Formula Introduction
  147.    wt: 1:   5 Box Volume Formula Example
  148.    wt: 1:   4 Circle Area Formula Example
  149.    wt: 1:   3 Triangle Area Formula Example
  150.    wt: 1:   2 Another Rectangle Area Formula Example
  151.    wt: 1:   1 Three Skills For Algebra
  152.    wt: 1:   arithmetic videos Real Player Format
  153.    wt: 1:   1 More and Less Than for Counts and Measures
  154.    wt: 1:   8 GCD from Euclidean Algorithm
  155.    wt: 1:   4 signed coordinates for regions in space
  156.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  157.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  158.    wt: 1:   21 Reciprocals for Fractions and Wholes
  159.    wt: 1:   A Associative Law Theorectical Note
  160.    wt: 1:   11 Adding Integers Formulas and Examples
  161.    wt: 1:   10 Integer Multiplication Formulas
  162.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  163.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  164.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  165.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  166.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  167.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  168.    wt: 1:   Long Division forwards and backwards Example 3
  169.    wt: 1:   Long Division forwards and backwards Example 2
  170.    wt: 1:   Long Division forwards and backwards Example 1
  171.    wt: 1:   A Elementary Basis for Multiplication Methods
  172.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  173.    wt: 1:   5 A Tip for Efficent Subtraction
  174.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  175.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  176.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  177.    wt: 1:   Formula Evaluation how to show work
  178.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  179.    wt: 1:   28 Chain Rule Preparation for a Proof
  180.    wt: 1:   22 Chain Rule for polynomials
  181.    wt: 1:   21 Chain Rule for powers
  182.    wt: 1:   20 Chain Rule for Pulley Systems
  183.    wt: 1:   19 Chain Rule for linear functions
  184.    wt: 1:   10 Power rule for negative integers
  185.    wt: 1:   3 Motivation for Limit Definition Take 2
  186.    wt: 1:   2 Motivation for Limit Definition Take 1
  187.    wt: 1:   3 Decimal insights for limits continuity convergence
  188.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  189.    wt: 1:   PostScript For and Against Decimal Perspectives
  190.    wt: 1:   Chapter 23 Links To Trigonometry
  191.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  192.    wt: 1:   Foreword
  193.    wt: 1:   Postscript More on Better Performance
  194.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  195.    wt: 1:   Chapter 23. Notation For Sums
  196.    wt: 1:   Chapter 18. Rules for Algebra
  197.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  198.    wt: 1:   Chapter 8 Three Skills For Algebra
  199.    wt: 1:   Solutions For Arithmetic Exercises
  200.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  201.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  202.    wt: 1:   Foreword
  203.    wt: 1:   Chapter 7 Two Treatments of Geometry
  204.    wt: 1:   Chapter 2 For and Against Mathematics
  205.    wt: 1:   Foreword
  206.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  207.    wt: 1:   Postscript C Consistency as a Tool for Reason
  208.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  209.    wt: 1:   Foreword
  210.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  211.    wt: 1:   N Mathematics Prepare for College Studies
  212.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  213.    wt: 1:   Chapter 6 More Algebra and Geometry
  214.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  215.    wt: 1:   7 Games and Activities for Instruction
  216.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  217.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  218.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  219.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  220.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  221.    wt: 1:   The Math Forum and Site Content

Extended Search

638 matches:

  1.    wt: 9:   4 Angles on Maps Plans drawn to scale
  2.    wt: 9:   3 Lengths and Areas on Maps and Plans
  3.    wt: 8:   26 Formulas for products of sines and cosines
  4.    wt: 8:   17E Trig Formulas for dot and cross Products
  5.    wt: 8:   17D cis formulas for sine cosines and tangent
  6.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  7.    wt: 8:   6 Figuring with Maps Not to Scale
  8.    wt: 7:   13 Velocity Vectors in Physics
  9.    wt: 7:   8 Parallel Vectors
  10.    wt: 7:   6 Vectors with Coordinates
  11.    wt: 7:   3 Navigation with Arrows or Vectors
  12.    wt: 7:   2 Signed Coordinates
  13.    wt: 7:   17 tangent function angle sum formulas
  14.    wt: 7:   29 secant cosecant and cotangent for acute angles
  15.    wt: 7:   25 tangent double angle formula Slope connection
  16.    wt: 7:   24 tangent Angle Difference Formula
  17.    wt: 7:   22 sine of 22.5 degrees via half angle formulas
  18.    wt: 7:   21 sine and cosine Half Angle Formulas
  19.    wt: 7:   20 sine and cosine Double Angle Formulas
  20.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  21.    wt: 7:   17F Law of cosines
  22.    wt: 7:   17C sine and cosine double triple angle formulas
  23.    wt: 7:   17B sine cosine Angle Sum Formulas via cis
  24.    wt: 7:   12 Graph of tangent function for one period
  25.    wt: 7:   6 sines and cosines for reference angle 30 degrees
  26.    wt: 7:   5 sines and cosines for reference angle 60 degrees
  27.    wt: 7:   4 sines and cosines for reference angle 45 degrees
  28.    wt: 7:   3 sines and cosines for reference angle 90 degrees
  29.    wt: 7:   1 Unit Points Reflections Rotations
  30.    wt: 7:   Unit Circle Development of Trigonometry
  31.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  32.    wt: 7:   13 Trig Formulas for dot and cross Products
  33.    wt: 7:   12 cis formulas for sine cosines and tangent
  34.    wt: 7:   5 An Easy Proof of the Distributive Law
  35.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  36.    wt: 7:   5 Trigonometric Ratios For Tangent and Special Triangles
  37.    wt: 7:   4 Trigonometric Ratios For Two Special Triangles
  38.    wt: 7:   2 Similar Triangles Equality of Corresponding Side Ratios
  39.    wt: 7:   Why Trigonometry the whyslopes view
  40.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  41.    wt: 7:   4 Equations for lines three forms
  42.    wt: 7:   2 point slope equation for a line
  43.    wt: 7:   A Measurement with Ruler Proper Use
  44.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  45.    wt: 7:   2 Measuring Area Directly
  46.    wt: 7:   1 Length Measurement
  47.    wt: 6:   12 motivation for term arctan
  48.    wt: 6:   9 motivation for name arcsin
  49.    wt: 6:   4 possible motivation for term arccos
  50.    wt: 6:   A Global Time and Navigation
  51.    wt: 6:   15 Dot and Cross Product
  52.    wt: 6:   14 Why Scalar Multiplication Distributes Physical Argument
  53.    wt: 6:   12 From Applied To Pure Mathematics
  54.    wt: 6:   11 Component Method
  55.    wt: 6:   10 Parallelogram Addition Method
  56.    wt: 6:   9 Head to Tail Coordinate View
  57.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  58.    wt: 6:   5 Head To Tail Arrow Addition
  59.    wt: 6:   4 Resultant of a Sum of Movements
  60.    wt: 6:   1 Unsigned Coordinates
  61.    wt: 6:   Vector and Complex Number Applet
  62.    wt: 6:   Construction Methods and Criteria for Isometric and Similar Triangles
  63.    wt: 6:   SAS Method For Isometric Or Proportional Triangle Construction
  64.    wt: 6:   8 Straight Lines Equation for vertical
  65.    wt: 6:   35 sines and cosines of 2A 3A 4A 5A
  66.    wt: 6:   34 sines and cosines of 2A 3A 4A 5A
  67.    wt: 6:   33 sines and cosines of 2A 3A 4A 5A
  68.    wt: 6:   32 seven rows of pascals triangle
  69.    wt: 6:   31 basic secant cosecant cotangent trig identities
  70.    wt: 6:   30 unit circle calculation of six trigonometric functions
  71.    wt: 6:   28 Expressing products of sines cosines as sums
  72.    wt: 6:   27 Logarithmic use of products of sines and cosines
  73.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  74.    wt: 6:   18 sum of sinusoidal waves as a single wave
  75.    wt: 6:   17G Pythagorean Theorem Converse
  76.    wt: 6:   17A The complex number valued trig function cis
  77.    wt: 6:   16 Right Triangle Complementary Angle Relations
  78.    wt: 6:   15 sine cosine Complementary Angle Relations
  79.    wt: 6:   14 cosine even and sine and tangent are odd
  80.    wt: 6:   13 Graph of tangent function many periods
  81.    wt: 6:   11 tangent function undefined when terminal side vertical
  82.    wt: 6:   10 Graphs of sines and cosines many periods
  83.    wt: 6:   9 Graphs of sine and cosine over one period
  84.    wt: 6:   8 period of tangent function
  85.    wt: 6:   7 period of sine and cosine
  86.    wt: 6:   2 Quadrant I reference Angles
  87.    wt: 6:   14 Law of cosines
  88.    wt: 6:   11 sine and cosine double triple angle formulas
  89.    wt: 6:   10 sine cosine Angle Sum Formulas via cis
  90.    wt: 6:   8 Unit Circle Development of Trigonometry
  91.    wt: 6:   2 Complex Numbers made easier we hope
  92.    wt: 6:   8 Triangles Cascade Problem Solving
  93.    wt: 6:   7 Trignometric Ratios Unit Circle
  94.    wt: 6:   3 Trigonometric Ratios sine and cosine
  95.    wt: 6:   1 Angle Measurement with Degrees
  96.    wt: 6:   7 Translations Rotations Reflections Dilatations
  97.    wt: 6:   8 Mid Point Formula
  98.    wt: 6:   3 Slope product for perpendicular lines
  99.    wt: 6:   13 Pythagorean spatial distance formulas
  100.    wt: 6:   10 Pythagorean plane distance formula
  101.    wt: 6:   2 Cartesian Coordinates with signs
  102.    wt: 5:   16 cotangent function Definition Graph and Inverse
  103.    wt: 5:   15 cosecant function Definition Graph and Inverse
  104.    wt: 5:   14 secant function Definition Graph and Inverse
  105.    wt: 5:   13 cosecant function Definition Graph and Inverse
  106.    wt: 5:   11 arctan left inverse of tangent Graph
  107.    wt: 5:   10 arctan left inverse of tangent Definition
  108.    wt: 5:   8 arcsin left inverse of sine Graph
  109.    wt: 5:   7 arcsin left inverse of sine Definition
  110.    wt: 5:   6 Graph of arccos function
  111.    wt: 5:   5 Swapping Coordinates is a reflection
  112.    wt: 5:   3 Left Inverse of cosine arccos definition
  113.    wt: 5:   2 cosine function more properties
  114.    wt: 5:   1 cosine function properties
  115.    wt: 5:   9 Summary Degrees to Radians and back
  116.    wt: 5:   8 Radian Measures of Common Angles
  117.    wt: 5:   7 Radian Measures in special Triangles
  118.    wt: 5:   6 Radian Measure to Degrees
  119.    wt: 5:   5 Degrees to Radian Measure
  120.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  121.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  122.    wt: 5:   2 Radian Measure Numerical Value of one degree
  123.    wt: 5:   1 Degrees and Radians Introduction
  124.    wt: 5:   4 graphing y=Asin(x c)
  125.    wt: 5:   3 graphing y=f(x c) plus K
  126.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  127.    wt: 5:   1 graphing y=f(x a)
  128.    wt: 5:   Parallel Lines and Parallel Transversals
  129.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  130.    wt: 5:   Triangle Angles Sum To 180 Degrees
  131.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  132.    wt: 5:   Parallel Lines and Interior Angles
  133.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  134.    wt: 5:   Straight Lines ASA Intersection Study More
  135.    wt: 5:   Straight Lines ASA Intersection Study
  136.    wt: 5:   Straight Lines Instersection Solving Equations
  137.    wt: 5:   Straight Lines Intersection of
  138.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  139.    wt: 5:   C Straight Lines Slope from Coordinates
  140.    wt: 5:   B Straight Line Slope Scaling Properties More
  141.    wt: 5:   A Straight Line Slope Scaling Properties
  142.    wt: 5:   14 Straight Lines Equations General Case
  143.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  144.    wt: 5:   12 Straight Lines Graphing mx plus b
  145.    wt: 5:   11 Straight Lines Graphing y=mx
  146.    wt: 5:   10 Straight Lines through Origin Equations More
  147.    wt: 5:   9 Straight Lines through Origin Equations
  148.    wt: 5:   7 Tangent Function is odd on this domain
  149.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  150.    wt: 5:   5 Tangent Function Graph
  151.    wt: 5:   4 Tangent Function Properties
  152.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  153.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  154.    wt: 5:   1 Straight Lines Slope Concept
  155.    wt: 5:   21 Logarithms Powers and Exponentials
  156.    wt: 5:   20 N th Roots of Complex Numbers
  157.    wt: 5:   19 N th Roots of Unity
  158.    wt: 5:   18 Sixth Roots of Unity
  159.    wt: 5:   17 Cube Roots of unity
  160.    wt: 5:   16 References and Originality Question
  161.    wt: 5:   15 Pythagorean Theorem Converse
  162.    wt: 5:   9 The complex number valued trig function cis
  163.    wt: 5:   7 Second Way to Calculate Products
  164.    wt: 5:   6 Field Properties of Complex Number
  165.    wt: 5:   4 Multiplication Properties
  166.    wt: 5:   3 Addition Properties
  167.    wt: 5:   1 Rectangular Polar Coordinates Review
  168.    wt: 5:   Appetizer A Complex Number Applet
  169.    wt: 5:   13 Navigation Location from Angles to 2 Landmarks
  170.    wt: 5:   12 Triangles Similarity More Problems
  171.    wt: 5:   11 Triangle Similarity Missing Side Problem
  172.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  173.    wt: 5:   9 Similarity of Triangles Usual Criteria
  174.    wt: 5:   8 Similarity of Triangles and Polygons
  175.    wt: 5:   6 Geometric Diagrams in Class
  176.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  177.    wt: 5:   4 Similarity Definition with Coordinate
  178.    wt: 5:   3 Similarity by Design with coordinates
  179.    wt: 5:   2 Similarity By Design
  180.    wt: 5:   1 Early Concept of Like or Similar Shapes
  181.    wt: 5:   Four Simple Exercises
  182.    wt: 5:   12 Links Lessons elsewhere
  183.    wt: 5:   11 A Partial Summary
  184.    wt: 5:   10 Midpoint of [a b] and [b a]
  185.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  186.    wt: 5:   7 Exercises to test skill and concept mastery
  187.    wt: 5:   6 Intersection of lines by solving linear systems
  188.    wt: 5:   5 Algebraic View of Slopes
  189.    wt: 5:   1 Numerical view of lines and their equations
  190.    wt: 5:   What is and is not here
  191.    wt: 5:   12 Spatial Coordinates
  192.    wt: 5:   11 Triangle Inequality
  193.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  194.    wt: 5:   8 Distance Between Points on a Line
  195.    wt: 5:   7 Complex Numbers Appetizer
  196.    wt: 5:   6 Polar Multiplication and Rotation
  197.    wt: 5:   5 Cartesian Addition and Translation
  198.    wt: 5:   4 Polar Coordinates to and from
  199.    wt: 5:   3 Rectangular Coordinates Review
  200.    wt: 5:   1 Cartesian Coordinates sans signs
  201.    wt: 5:   About Folder Contents
  202.    wt: 4:   1 Written work formats for developing and showing skill
  203.    wt: 3:   5 Distributive Law for Whole Numbers
  204.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  205.    wt: 3:   13 Naming Identifying Formulas with Words
  206.    wt: 3:   8 Compound Interest Formula Evaluation
  207.    wt: 3:   7 Compound Interest Formula Introduction
  208.    wt: 3:   5 Box Volume Formula Example
  209.    wt: 3:   4 Circle Area Formula Example
  210.    wt: 3:   3 Triangle Area Formula Example
  211.    wt: 3:   2 Another Rectangle Area Formula Example
  212.    wt: 3:   3 signed coordinates for maps and planes
  213.    wt: 3:   Long Division forwards and backwards Example 3
  214.    wt: 3:   Long Division forwards and backwards Example 2
  215.    wt: 3:   Long Division forwards and backwards Example 1
  216.    wt: 3:   2 Division with Single Digit Divisors
  217.    wt: 3:   A Elementary Basis for Multiplication Methods
  218.    wt: 3:   2 One Digit Multipliers
  219.    wt: 3:   7 Subtraction for Decimal Fractions with Exercises
  220.    wt: 3:   5 A Tip for Efficent Subtraction
  221.    wt: 3:   2 Subtraction Easy Case Examples
  222.    wt: 3:   Postscript For Better Performance
  223.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  224.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  225.    wt: 2:   3 Euclidean Geometry Leanly
  226.    wt: 2:   Maps Plans Drawings
  227.    wt: 2:   formal or informal peer review
  228.    wt: 2:   Prequel In For A Penny In For A Pound
  229.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  230.    wt: 2:   5 Function notation for geometric transformations
  231.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  232.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  233.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  234.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  235.    wt: 2:   1 Polynomials Distributive Law
  236.    wt: 2:   23 Distributive Law Two Derivations
  237.    wt: 2:   4 Commutative Law Groups Counting Form
  238.    wt: 2:   2 Algebraic View
  239.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  240.    wt: 2:   6 Compound Interest Forward and Backwards
  241.    wt: 2:   5 Triangle Area Formula Backwards
  242.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  243.    wt: 2:   8 Coordinates for Maps and Planes
  244.    wt: 2:   2 Three Examples
  245.    wt: 2:   Formula Usage Show Work Format
  246.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  247.    wt: 2:   11 Volume of Sphere
  248.    wt: 2:   10 Volume of Pyramid
  249.    wt: 2:   9 Volume of Cone
  250.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  251.    wt: 2:   arithmetic videos Real Player Format
  252.    wt: 2:   2 More and Less Than with Unlike Signs
  253.    wt: 2:   1 More and Less Than for Counts and Measures
  254.    wt: 2:   8 GCD from Euclidean Algorithm
  255.    wt: 2:   4 signed coordinates for regions in space
  256.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  257.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  258.    wt: 2:   21 Reciprocals for Fractions and Wholes
  259.    wt: 2:   A Associative Law Theorectical Note
  260.    wt: 2:   11 Adding Integers Formulas and Examples
  261.    wt: 2:   10 Integer Multiplication Formulas
  262.    wt: 2:   2 Integers Multiplies of a Unit Moverment
  263.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  264.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  265.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  266.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  267.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  268.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  269.    wt: 2:   2 Prime and Composites less than 16
  270.    wt: 2:   Long Division Backwards more
  271.    wt: 2:   Long Division Backward
  272.    wt: 2:   Division with Counts and Length
  273.    wt: 2:   12 Why Long Division Works Take III
  274.    wt: 2:   11 Another Single Digit Divisor Example
  275.    wt: 2:   10 Division by Five Long and Short Ways
  276.    wt: 2:   9 Why Long Division Works Take II
  277.    wt: 2:   8 Correcting the Mistake
  278.    wt: 2:   7 Long Divison Mistake Catching
  279.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  280.    wt: 2:   5 Long Division Include Zeroes or not
  281.    wt: 2:   4 Division with 2 Digit Divsors
  282.    wt: 2:   3 Division Single Digit Divisor Example
  283.    wt: 2:   1 Divsion Physical Examples
  284.    wt: 2:   D Decimal Multiplication Methods Derived
  285.    wt: 2:   C Counting Areas with Powers of Ten
  286.    wt: 2:   B Powers of Ten
  287.    wt: 2:   6 Multiplication Commutes Order Not Important
  288.    wt: 2:   5 Decimal Fraction Multiplication
  289.    wt: 2:   4 Two and Three Digit Multipliers
  290.    wt: 2:   3 More One Digit Multipliers
  291.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  292.    wt: 2:   Video Decimal Multiplication Geometric View Example 2
  293.    wt: 2:   Video Power Notation in Decimal Expansion
  294.    wt: 2:   1 Why 3 times 5 gives 15
  295.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  296.    wt: 2:   Appendix 1 Decimals Comparison Method Take II
  297.    wt: 2:   Subtraction with J Conversions Example
  298.    wt: 2:   Subtraction Another Video Lesson
  299.    wt: 2:   9 22 Minute Subtraction Review Video
  300.    wt: 2:   8 Subtraction with Units of Measure
  301.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  302.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  303.    wt: 2:   3 Harder Cases Convert to Compare and Subtract
  304.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  305.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  306.    wt: 2:   8 What skills and work habits to require
  307.    wt: 2:   7 Adding decimal fractions using decimal point
  308.    wt: 2:   6. Counting and adding units and mixed units
  309.    wt: 2:   5. How to add decimals C. Examples
  310.    wt: 2:   4. How to add with decimals B with conversions
  311.    wt: 2:   3. How to add with decimals A sans conversions
  312.    wt: 2:   2 Decimal Counting Practices
  313.    wt: 2:   1. Explaining Addition Table
  314.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  315.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  316.    wt: 2:   2 Groups of Three Place Value for Multidigit Decimals
  317.    wt: 2:   Formula Evaluation how to show work
  318.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  319.    wt: 2:   38 Formulas and derivatives for powers and roots
  320.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  321.    wt: 2:   Postscript More on Better Performance
  322.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  323.    wt: 2:   Chapter 23. Notation For Sums
  324.    wt: 2:   Chapter 18. Rules for Algebra
  325.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  326.    wt: 2:   Chapter 8 Three Skills For Algebra
  327.    wt: 2:   Solutions For Arithmetic Exercises
  328.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  329.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  330.    wt: 2:   Foreword
  331.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  332.    wt: 2:   G. Written work formats for developing and showing skill
  333.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  334.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  335.    wt: 1:   Ramblings Extrinsic numbers theory
  336.    wt: 1:   Skills Chapter 2 Geometry
  337.    wt: 1:   8 analytic geometry etc
  338.    wt: 1:   three goals to set for students
  339.    wt: 1:   permissions for teachers
  340.    wt: 1:   activities for students
  341.    wt: 1:   About site lesson plans
  342.    wt: 1:   Education Reform Inconsistencies
  343.    wt: 1:   geometric implications for algebra
  344.    wt: 1:   three goals for Mathematics Education
  345.    wt: 1:   02 21 words for teachers
  346.    wt: 1:   three aims for mathematics students
  347.    wt: 1:   standards for course material
  348.    wt: 1:   Theory of Knowledge
  349.    wt: 1:   Four ways to improve education reform
  350.    wt: 1:   need for a mixed mathematics curriculum
  351.    wt: 1:   fairness and inductive principles for instruction
  352.    wt: 1:   words for mathematics instructor
  353.    wt: 1:   2 Conductance Resistance Duality02
  354.    wt: 1:   E Kirchoffs Second Law
  355.    wt: 1:   D Kirchoff First Law
  356.    wt: 1:   C Electromotive force conventional current02
  357.    wt: 1:   B Electromotive force conventional current01
  358.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  359.    wt: 1:   24 Standards For Skill Develoment Take II
  360.    wt: 1:   24 Standards For Skill Develoment
  361.    wt: 1:   17 Math Booklets for children and young teenagers
  362.    wt: 1:   15 Counting For Parents
  363.    wt: 1:   12 Goals and Objectives For Mathematics
  364.    wt: 1:   10 Ends values for work study instruction
  365.    wt: 1:   5 Patience Please for Yourself and Your Charges
  366.    wt: 1:   4 Learning Takes Time and Effort
  367.    wt: 1:   3 Preparing for Science Studies
  368.    wt: 1:   2 Reading and Writing Skills
  369.    wt: 1:   Ages 12 to 14 Geometry
  370.    wt: 1:   Ages 10 to 12 Geometry
  371.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  372.    wt: 1:   20 Interchanging coordinates a reflection
  373.    wt: 1:   9 Set theory term relation possible origins
  374.    wt: 1:   6 Set Existence Formation and Notation
  375.    wt: 1:   3 Formula or function graphing exercise
  376.    wt: 1:   8 quadratics backward use of various formulas
  377.    wt: 1:   7 quadratic formulla derivation
  378.    wt: 1:   8 Notes for instructors or tutors
  379.    wt: 1:   19 Signed Multiples of Vectors
  380.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  381.    wt: 1:   13 Arrows and Vectors in a Plane
  382.    wt: 1:   6 Column Methods for Decimal Multiplication
  383.    wt: 1:   2 Combing Counts Addition Skills and Principles
  384.    wt: 1:   5 Proportionality in Equivalent Fractions
  385.    wt: 1:   4 Rates Ratios and Proporitionality
  386.    wt: 1:   3 Proportionality Examples
  387.    wt: 1:   1 What is Proportionality
  388.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  389.    wt: 1:   3 Linear Equation Literal Solution More
  390.    wt: 1:   2 Linear Equation Literal Solution
  391.    wt: 1:   1 Changing Calculations
  392.    wt: 1:   3 Product Axioms Two Forms
  393.    wt: 1:   2 More and Less Than for Counts and Measures
  394.    wt: 1:   9 Coordinates for Regions in Space
  395.    wt: 1:   3 Geometric Formulas and Function Notation
  396.    wt: 1:   1 Formulas Dependence and Function Notation
  397.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  398.    wt: 1:   2 GE II Comparison
  399.    wt: 1:   2 Essentially one exercises three with solution
  400.    wt: 1:   6 Algebraic Solution Example
  401.    wt: 1:   5 Algebraic Solutions Introduction
  402.    wt: 1:   4 Four Examples Fractional Coefficients
  403.    wt: 1:   3 Four Examples
  404.    wt: 1:   1 Proper Equal Sign Usage
  405.    wt: 1:   2 Three Examples
  406.    wt: 1:   Using Letters for Physical Quantities
  407.    wt: 1:   1 Three Skills For Algebra
  408.    wt: 1:   4 Greater More Less Than Signs in General
  409.    wt: 1:   3 Comparison of Negative Numbers
  410.    wt: 1:   5 Square Roots with primes more still
  411.    wt: 1:   4 Square Roots with primes more
  412.    wt: 1:   3 Properties of Square Roots with example
  413.    wt: 1:   2 Square Roots with Prime
  414.    wt: 1:   1 Squares and Square Roots Introduction
  415.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  416.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  417.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  418.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  419.    wt: 1:   13 GCD from given Prime Factorization
  420.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  421.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  422.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  423.    wt: 1:   7 GCD and LCM from prime factorization
  424.    wt: 1:   6 GCD from Prime
  425.    wt: 1:   5 Common Divisors 60 45 via Prime
  426.    wt: 1:   4 LCM of 8 and 10 via Prime
  427.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  428.    wt: 1:   2 Least Common Multiple LCM intro via list method
  429.    wt: 1:   1 Least Common Multiples LCM Introduction
  430.    wt: 1:   12 GCD 2700 288 via Prime
  431.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  432.    wt: 1:   4 Counting with Trees Product Rule Take I
  433.    wt: 1:   3 Counting with Tables and Trees II
  434.    wt: 1:   2 Counting with Tables and Trees I
  435.    wt: 1:   1 Counting and Counting Methods I
  436.    wt: 1:   11 What are real lengths and numbers
  437.    wt: 1:   10 dividing signed numbers
  438.    wt: 1:   9 subtracting signed numbers
  439.    wt: 1:   8 multiplying signed numbers
  440.    wt: 1:   7 negative and additive inverse
  441.    wt: 1:   6 adding signed numbers
  442.    wt: 1:   5 lengths and signs of numbers
  443.    wt: 1:   2 signed and unsigned numbers as coordinates
  444.    wt: 1:   7 Converting or Changing Units
  445.    wt: 1:   6 Simplification of Fractions with Units
  446.    wt: 1:   4 Fractions with Units
  447.    wt: 1:   3 Multiplying Units and Numbers
  448.    wt: 1:   2 Equality and Units
  449.    wt: 1:   1 Addition and Subtraction with Units
  450.    wt: 1:   D Three Term Ratios
  451.    wt: 1:   B Fractions and Two Term Ratios
  452.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  453.    wt: 1:   22 Complex Compound Fractions
  454.    wt: 1:   21 Working With Signs
  455.    wt: 1:   20 Dividing Fractions the Why
  456.    wt: 1:   19 Dividing Fractions How TO
  457.    wt: 1:   18 Efficient Ways to Multiply
  458.    wt: 1:   17 Efficient Ways to Add and Subtract
  459.    wt: 1:   16 Addition Subtraction Comparision Compared
  460.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  461.    wt: 1:   14 Adding and Subtracting with Like Denominators
  462.    wt: 1:   13 Fraction Comparison Algebraic View
  463.    wt: 1:   12 Fraction Comparison
  464.    wt: 1:   11 Simplification an Algebraic View
  465.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  466.    wt: 1:   9 Improper Fractions and Mixed Numbers
  467.    wt: 1:   8 Numerals Fractionals Quantals Take II
  468.    wt: 1:   7 Numerals Fractionals Quantals
  469.    wt: 1:   6 Multiplication of Mixed Numbers
  470.    wt: 1:   6 Multiplication Algebraically Take II
  471.    wt: 1:   5 Equivalent Fractions
  472.    wt: 1:   4 Fraction Multiplication
  473.    wt: 1:   3 Unit fraction of a fraction
  474.    wt: 1:   2 Unit Fraction Multiplication
  475.    wt: 1:   1 What is a fraction Take II
  476.    wt: 1:   1 What is a fraction
  477.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  478.    wt: 1:   D Remainders Modulo 11 Pair Rule
  479.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  480.    wt: 1:   B Integer Long Division Multiple Choices
  481.    wt: 1:   13 Subtraction with Additive Inverse
  482.    wt: 1:   12 Adding Integers More Examples
  483.    wt: 1:   9 Multiplying Integers
  484.    wt: 1:   8 Multiplication by Signed Numbers Integers
  485.    wt: 1:   7 Multiplication by Signs
  486.    wt: 1:   6 Multiplication by Natural Numbers
  487.    wt: 1:   5 Zero Movement and Additive Inverses
  488.    wt: 1:   4 Adding Movements wiht opposite directions
  489.    wt: 1:   3 Adding Movements with same direction
  490.    wt: 1:   1 Integers as Coordinates
  491.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  492.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  493.    wt: 1:   26 Divisibility by 2 3 5 Example
  494.    wt: 1:   23 Remainder Arithmetic Modulo 2
  495.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  496.    wt: 1:   21 Remainder Arithmetic Modulo 3
  497.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  498.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  499.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  500.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  501.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  502.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  503.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  504.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  505.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  506.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  507.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  508.    wt: 1:   5 Remainder Arithmetic Modulo 5
  509.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  510.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  511.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  512.    wt: 1:   1 Remainder Arithmetic Modulo 10
  513.    wt: 1:   20 Uniqueness of Prime Factorization
  514.    wt: 1:   19 video Prime Factorization Unique
  515.    wt: 1:   18 video Count Factors given Prime Factorization
  516.    wt: 1:   17 Identify and Count Factors using Primes
  517.    wt: 1:   16 video Factors of 980 using prime
  518.    wt: 1:   15 video Factors of 20 using Prime Factorization
  519.    wt: 1:   14 video Factors of 24 Take II
  520.    wt: 1:   13 video Factors of 24 using prime
  521.    wt: 1:   12 LCD GCD and LCM using Primes
  522.    wt: 1:   11 Efficient Square Rule Use
  523.    wt: 1:   10 video Prime Factorization upto 23 squared
  524.    wt: 1:   9 video Prime Factorization upto 19 squared
  525.    wt: 1:   8 video Prime Factorization upto 19
  526.    wt: 1:   7 Calculator Usage Notes and Cautions
  527.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  528.    wt: 1:   5 Prime Factorization and a Square Rule
  529.    wt: 1:   4 video Prime Factorization Introduction
  530.    wt: 1:   3 video Primes and Composites from 9 times table
  531.    wt: 1:   1 video how Products are bigger than factor
  532.    wt: 1:   11 Place Value SI Standard International way
  533.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  534.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  535.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  536.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  537.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  538.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  539.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  540.    wt: 1:   Quick history of numbers and algebra
  541.    wt: 1:   Exact Arithmetic Wholes and Fractions
  542.    wt: 1:   Expression Evaluation how to show work
  543.    wt: 1:   The 20 Times Table
  544.    wt: 1:   The 12 Times Table Visually
  545.    wt: 1:   About folder contents
  546.    wt: 1:   28 Chain Rule Preparation for a Proof
  547.    wt: 1:   22 Chain Rule for polynomials
  548.    wt: 1:   21 Chain Rule for powers
  549.    wt: 1:   20 Chain Rule for Pulley Systems
  550.    wt: 1:   19 Chain Rule for linear functions
  551.    wt: 1:   10 Power rule for negative integers
  552.    wt: 1:   3 Motivation for Limit Definition Take 2
  553.    wt: 1:   2 Motivation for Limit Definition Take 1
  554.    wt: 1:   3 Decimal insights for limits continuity convergence
  555.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  556.    wt: 1:   PostScript For and Against Decimal Perspectives
  557.    wt: 1:   Chapter 23 Links To Trigonometry
  558.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  559.    wt: 1:   Foreword
  560.    wt: 1:   Appendix E. How To Study Mathematics and Why
  561.    wt: 1:   Appendix D. What to do in School and Why
  562.    wt: 1:   Appendix C. How to Read
  563.    wt: 1:   Appendix B. How To Learn
  564.    wt: 1:   Chapter 31 Direct and Indirect Reason
  565.    wt: 1:   Chapter 30 Truth Tables
  566.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  567.    wt: 1:   Chapter 28 Occurrence Tables
  568.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  569.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  570.    wt: 1:   Chapter 25. Mathematical Induction Examples
  571.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  572.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  573.    wt: 1:   Chapter 21. Third Reading Guide
  574.    wt: 1:   Chapter 20. Degrees and Radians
  575.    wt: 1:   Chapter 19. Functions and Sets
  576.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  577.    wt: 1:   Chapter 16. Painless Theorem Proving
  578.    wt: 1:   Chapter 15. Solving Linear Equations
  579.    wt: 1:   Chapter 13. Second Reading Guide
  580.    wt: 1:   Chapter 12. Shorthand Usage Guide
  581.    wt: 1:   Chapter 11. Why Shorthand
  582.    wt: 1:   Chapter 10 Describing and Changing Calculations
  583.    wt: 1:   Postscript What is a Variable
  584.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  585.    wt: 1:   Chapter 6 Change of Language
  586.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  587.    wt: 1:   Chapter 4 Longer Chains of Reason
  588.    wt: 1:   Chapter 3 Chains of Reason
  589.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  590.    wt: 1:   Chapter 7 Two Treatments of Geometry
  591.    wt: 1:   Chapter 2 For and Against Mathematics
  592.    wt: 1:   Foreword
  593.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  594.    wt: 1:   Postscript C Consistency as a Tool for Reason
  595.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  596.    wt: 1:   Foreword
  597.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  598.    wt: 1:   N Mathematics Prepare for College Studies
  599.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  600.    wt: 1:   Chapter 6 More Algebra and Geometry
  601.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  602.    wt: 1:   7 Games and Activities for Instruction
  603.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  604.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  605.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  606.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  607.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  608.    wt: 1:   The Math Forum and Site Content
  609.    wt: 14:   PS H Distributive Law For Complex Numbers
  610.    wt: 13:   Euclidean Geometry Elsewhere LINKS
  611.    wt: 13:   Short Course on Euclidean Geometry
  612.    wt: 12:   PS C Similarity Use Recognize it in Trigonometry
  613.    wt: 12:   2 Correspondence between Triangles
  614.    wt: 11:   PS G Rotation Distributes over Addition
  615.    wt: 11:   PS F Scalar Multiplication Distributes over Addition
  616.    wt: 11:   PS E Multiplication with Polar Coordinates
  617.    wt: 11:   PS D Addition with Cartesian Coordinates
  618.    wt: 11:   PS B Parallelogram Construction Methods
  619.    wt: 11:   PS A Kite Construction Methods
  620.    wt: 11:   21 Parallelograms
  621.    wt: 11:   19 Right Triangle Similarity
  622.    wt: 11:   18 Triangle Similarity Take 1
  623.    wt: 11:   17 Right Bisectors of Triangle Sides
  624.    wt: 11:   16 Angles Subtended By Chords and Diameters
  625.    wt: 11:   15 Triangle Angle Sum is 180 degrees
  626.    wt: 11:   14 Parallel Lines Postulate
  627.    wt: 11:   13 Angle Side Angle Failure
  628.    wt: 11:   12 Side Angle Side Failure
  629.    wt: 11:   11 Triangle Construction Fails
  630.    wt: 11:   10 Dropping a perpendicular to line
  631.    wt: 11:   9 Construction of a right bisector
  632.    wt: 11:   8 Isoceles Triangles
  633.    wt: 11:   7 Angle Side Angle
  634.    wt: 11:   6 Ruler and compass Angle Bisection
  635.    wt: 11:   5 Side Angle Side
  636.    wt: 11:   4 Side Side Side
  637.    wt: 11:   3 Isometry of Triangles Congruence
  638.    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.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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