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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  1.    wt: 9:   11 Parallel Straight Lines and Transversals/
  2.    wt: 9:   7 Axioms Logic and Equivalent Equations/
  3.    wt: 9:   4 Computation Rules and Function Notation/
  4.    wt: 9:   12 Comparison of Unsigned and Signed Numbers/
  5.    wt: 9:   C Decimal Multiplication Methods/
  6.    wt: 9:   12 Webvideo Lessons on Area and Volume Calculation/
  7.    wt: 8:   LAMP Lean Applied Mathematics Program/
  8.    wt: 8:   5 Factored Polynomial Sign Analysis Examples/
  9.    wt: 8:   3 Quadratics Geometrically/
  10.    wt: 8:   14 Degrees to Radians and Radians to Degrees/
  11.    wt: 8:   12 Function Translating and Rescaling/
  12.    wt: 8:   9 Lines and Slopes Take 2 with tangent function/
  13.    wt: 8:   1 Maps Plans Measurement/
  14.    wt: 8:   A Origins of Counting and Figuring Methods/
  15.    wt: 8:   10 Examples of Algebraic Reasoning/
  16.    wt: 8:   9 Proportionality Backwards and Forwards/
  17.    wt: 8:   11 Squares and Square Roots/
  18.    wt: 8:   Volume 3 Why Slopes A Calculus Intro Etc/
  19.    wt: 8:   Secondary Mathematics A Practical Approach/
  20.    wt: 7:   Progressive Observable Motivated Mathematics Education/
  21.    wt: 7:   2 Natural Logarithms Exponentials Powers Roots/
  22.    wt: 7:   10 Intersecting Straight Lines and Transversals/
  23.    wt: 7:   2 Euclidean Geometry Constructions Theory extras/
  24.    wt: 7:   3 Solving Linear Equations/
  25.    wt: 7:   9 Combinatorics Trees Tables and Products/
  26.    wt: 7:   7 Arithmetic and Fractions with Units/
  27.    wt: 7:   4 Remainder Arithmetic and Divisibility/
  28.    wt: 7:   3 Prime Factorization Skills/
  29.    wt: 7:   D Decimal Long Division Methods/
  30.    wt: 7:   1 Decimal Place Value/
  31.    wt: 7:   38 Lessons on Calculating Derivatives/
  32.    wt: 7:   PreSchool and Primary Mathematics or Quantitative Skills/
  33.    wt: 6:   Mathematics Education Essays/
  34.    wt: 6:   5 What is Similarity/
  35.    wt: 6:   4 Lines and Slopes Take 1/
  36.    wt: 6:   8 Unifying Theme For Algebra/
  37.    wt: 6:   10 LCM GCD and Euclid GCD Algorithm/
  38.    wt: 6:   6 Fractions and Ratios/
  39.    wt: 6:   Advanced Calculus Volume 3 Appendices/
  40.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  41.    wt: 6:   Volume 1A Pattern Based Reason/
  42.    wt: 5:   Volume 1A Regles et modeles/
  43.    wt: 5:   15 Arc or Inverse Trigonometric Function/
  44.    wt: 5:   13 Vectors/
  45.    wt: 5:   B Real Numbers Extrinsic Development/
  46.    wt: 5:   5 Real Numbers/
  47.    wt: 5:   8 Arithmetic with Signed Numbers/
  48.    wt: 5:   2 Arithmetic with Decimals/
  49.    wt: 5:   Time Date Matters/
  50.    wt: 5:   4 Lessons on Using Derivatives/
  51.    wt: 5:   13 Lessons on Limits and Continuity/
  52.    wt: 5:   Mathematics 506 Lessons/
  53.    wt: 4:   Mathematics Skills Year by Year/
  54.    wt: 4:   1 Five Polynomial Operations/
  55.    wt: 4:   8 Unit Circle Trigonometry/
  56.    wt: 4:   7 Complex Numbers/
  57.    wt: 4:   6 Trigonometry first steps/
  58.    wt: 4:   Mathematics Skill Development Framework/
  59.    wt: 3:   francais/
  60.    wt: 3:   4 Functions/
  61.    wt: 3:   Geometry maps plans trigonometry vectors/
  62.    wt: 3:   1 Working With Sets/
  63.    wt: 3:   Algebra Starter Lessons/
  64.    wt: 3:   5 Integers/
  65.    wt: 3:   Arithmetic and Number Theory Skills/
  66.    wt: 3:   Skills with take home value/
  67.    wt: 3:   5 Lessons on Integration/
  68.    wt: 3:   Volume 2 Three Skills For Algebra/
  69.    wt: 3:   Volume 1 Elements of Reason/
  70.    wt: 3:   Work and Study Tips/
  71.    wt: 3:   Resources and Reciprocal Links/
  72.    wt: 3:   Quebec Material/
  73.    wt: 2:   Direct Current Electric Circuits/
  74.    wt: 2:   More Algebra/
  75.    wt: 2:   70 Calculus Starter Lessons/
  76.    wt: 1:   Archives/
  77.    wt: 1:   Parent Center/
  78.    wt: 11:   Step 4 Gaussian Elimination/
  79.    wt: 11:   Step 3 Easy systems in 2 or more unknowns/
  80.    wt: 11:   Step 2 Algebraic solutions for one unknown/
  81.    wt: 11:   Step 1 Stick diagram and fractions/
  82.    wt: 10:   3 Cartesian and Polar Coordinates/
  83.    wt: 10:   6 More Less Greater Than Inequalities and Comparison/
  84.    wt: 10:   2 Formula Forward Use Evaluation/
  85.    wt: 10:   B Decimal Comparing and Subtracting Methods/
  86.    wt: 10:   A Decimal Counting and Adding Methods/

Web Page Search

1123 matches:

  1.    wt: 9:   C LAMP Introduction Culture in Mathematics Education
  2.    wt: 9:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  3.    wt: 9:   2 Radian Measure Numerical Value of one degree
  4.    wt: 9:   33 sines and cosines of 2A 3A 4A 5A
  5.    wt: 9:   13 Pythagorean spatial distance formulas
  6.    wt: 9:   9 Place Value Review Decimal form of Avogrados number included
  7.    wt: 9:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  8.    wt: 9:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  9.    wt: 9:   5 More on Groups of 3 Place Value in Decimal Fractions
  10.    wt: 9:   4 Groups of 3 Place Value in Decimal Fractions
  11.    wt: 9:   3 More on Groups of 3 Multi Digit Place Value
  12.    wt: 9:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  13.    wt: 8:   B LAMP Introduction Curriculum Development Standards
  14.    wt: 8:   25 Absolute Value greatest integer and saw tooth functions
  15.    wt: 8:   5 Natural Logarithm Calculator Exercises
  16.    wt: 8:   3 Natural Logarithms and Exponentials Basic Properties
  17.    wt: 8:   6 Polynomial Operations and Equivalent Computation Rules
  18.    wt: 8:   Rewriting algebraic substitution as function substitutions
  19.    wt: 8:   35 sines and cosines of 2A 3A 4A 5A
  20.    wt: 8:   34 sines and cosines of 2A 3A 4A 5A
  21.    wt: 8:   18 sum of sinusoidal waves as a single wave
  22.    wt: 8:   PS F Scalar Multiplication Distributes over Addition
  23.    wt: 8:   3 Lengths and Areas on Maps and Plans
  24.    wt: 8:   9 Circle Area and Perimeter Formula Backwards Forwards
  25.    wt: 8:   4 Rectangle Area and Like Formulas Backwards
  26.    wt: 8:   3 Gaussian Elimination 3 unknowns first example
  27.    wt: 8:   8 Numerals Fractionals Quantals Take II
  28.    wt: 8:   7 Calculator Usage Notes and Cautions
  29.    wt: 8:   11 Place Value SI Standard International way
  30.    wt: 8:   2 Groups of Three Place Value for Multidigit Decimals
  31.    wt: 8:   Chapter 29 Contrapositive and Vacuously True Implications
  32.    wt: 8:   Chapter 22 Contrapositive and Vacuously True Implications
  33.    wt: 8:   Primary and Secondary Skills and Practices with Take Home Value
  34.    wt: 7:   chapitre 07 00 Des chaines plus longues de la raison
  35.    wt: 7:   chapitre 04 10 Etapes pour une meilleur raison
  36.    wt: 7:   27 Graduated Correction and Penalties for Young Offenders
  37.    wt: 7:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  38.    wt: 7:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  39.    wt: 7:   6 quadratics numerical approach
  40.    wt: 7:   7 Coordinate Addition and Scalar Multiplication
  41.    wt: 7:   Parallel Lines and Parallel Transversals
  42.    wt: 7:   Construction Methods and Criteria for Isometric and Similar Triangles
  43.    wt: 7:   3 Straight Lines Slope as Tangent of Inclination Angle
  44.    wt: 7:   30 unit circle calculation of six trigonometric functions
  45.    wt: 7:   29 secant cosecant and cotangent for acute angles
  46.    wt: 7:   5 An Easy Proof of the Distributive Law
  47.    wt: 7:   13 Navigation Location from Angles to 2 Landmarks
  48.    wt: 7:   10 Similarity of Triangles Equivalent of Two Criteria
  49.    wt: 7:   9 Similarity of Triangles Usual Criteria
  50.    wt: 7:   10 Pythagorean plane distance formula
  51.    wt: 7:   8 Division and Mulplication of Compound Fractions
  52.    wt: 7:   5 Triangle Area Formula Backwards
  53.    wt: 7:   5 Gaussian Elimination for 3 unknowns 2nd example
  54.    wt: 7:   3 GE III Equation Addition and Multiplication
  55.    wt: 7:   6 Pythagorean Hypotenuse Calculation Example
  56.    wt: 7:   3 Triangle Area Formula Example
  57.    wt: 7:   2 Another Rectangle Area Formula Example
  58.    wt: 7:   5 Talking about Numbers and Quantities
  59.    wt: 7:   1 Squares and Square Roots Introduction
  60.    wt: 7:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  61.    wt: 7:   C Equality for Fractions and Two Term Ratios and Fractions
  62.    wt: 7:   7 Numerals Fractionals Quantals
  63.    wt: 7:   A Decimals Modular and Remainder Arithmetic
  64.    wt: 7:   5 Prime Factorization and a Square Rule
  65.    wt: 7:   Long Division forwards and backwards Example 3
  66.    wt: 7:   3 Harder Cases Convert to Compare and Subtract
  67.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  68.    wt: 7:   Quick history of numbers and algebra
  69.    wt: 7:   9 Comparison and Subtraction of Time Intervals
  70.    wt: 7:   33 Chain Rule Real Player video examples
  71.    wt: 7:   7 Evaluation by immediate or delayed substitution
  72.    wt: 7:   Chapter 19. Exponentials and Natural Logarithms
  73.    wt: 7:   Chapter 15. Algebraic Evaluation of Limits
  74.    wt: 7:   Chapter 9 Talking about Numbers or Quantities
  75.    wt: 7:   Chapter 2 Implication Rules Forwards and Backwards
  76.    wt: 7:   Chapter 16 Origins and Limitations of Rules and Patterns
  77.    wt: 7:   Chapter 14 Deductive and Empirical Views of Mathematics
  78.    wt: 7:   Chapter 4 Implication Rules Forwards and Backwards
  79.    wt: 7:   6 Measuring via counting or arithmetic the role of fractions
  80.    wt: 7:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  81.    wt: 7:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  82.    wt: 6:   Ramblings Introduction Algebra Essay
  83.    wt: 6:   need for a mixed mathematics curriculum
  84.    wt: 6:   Leaner mathematics curriculum
  85.    wt: 6:   2 Conductance Resistance Duality02
  86.    wt: 6:   1 Conductance Resistance Duality01
  87.    wt: 6:   E Wire Resistance Calculation03
  88.    wt: 6:   A Wire Resistance Qualitative01
  89.    wt: 6:   25 Mathematics Education Leaving A Good Impression
  90.    wt: 6:   23 Modularized Skill Development Modularized Rigor Take IV
  91.    wt: 6:   23 Modularized Skill Development Modularized Rigor Take III
  92.    wt: 6:   23 Modularized Skill Development Modularized Rigor Take II
  93.    wt: 6:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  94.    wt: 6:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  95.    wt: 6:   5 Patience Please for Yourself and Your Charges
  96.    wt: 6:   17 Function maxima minima and their location
  97.    wt: 6:   11 Function Domain Range Source and Targets
  98.    wt: 6:   3 Formula or function graphing exercise
  99.    wt: 6:   2 Algebraic use of function notation
  100.    wt: 6:   A Quadratics Summary
  101.    wt: 6:   9 quadratics physical and further context
  102.    wt: 6:   7 quadratic formulla derivation
  103.    wt: 6:   4 quadratics difference of two squares
  104.    wt: 6:   9 Summary Degrees to Radians and back
  105.    wt: 6:   8 Radian Measures of Common Angles
  106.    wt: 6:   7 Radian Measures in special Triangles
  107.    wt: 6:   4 Resultant of a Sum of Movements
  108.    wt: 6:   Proportionality of Line Segments From Parallel Transversals
  109.    wt: 6:   Parallel Lines and Alternating Corresponding Angles
  110.    wt: 6:   17 tangent function angle sum formulas
  111.    wt: 6:   27 Logarithmic use of products of sines and cosines
  112.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  113.    wt: 6:   17B sine cosine Angle Sum Formulas via cis
  114.    wt: 6:   17A The complex number valued trig function cis
  115.    wt: 6:   13 Graph of tangent function many periods
  116.    wt: 6:   10 sine cosine Angle Sum Formulas via cis
  117.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  118.    wt: 6:   5 Similarity of Circles Squares and Rectangles
  119.    wt: 6:   1 Numerical view of lines and their equations
  120.    wt: 6:   5 Cartesian Addition and Translation
  121.    wt: 6:   8 More Use of Maps Not Drawn to Scale
  122.    wt: 6:   4 Angles on Maps Plans drawn to scale
  123.    wt: 6:   A Modular and Remainder Arithmetic
  124.    wt: 6:   15 Head to Tails in place Addition Associative
  125.    wt: 6:   14 Vector Head to Tail Sums and Resultants
  126.    wt: 6:   3 Location of Point in Decimal Multiplication
  127.    wt: 6:   B Decimal Comparison and Subtraction
  128.    wt: 6:   4 Commutative Law Groups Counting Form
  129.    wt: 6:   3 Inequalities Algebraically
  130.    wt: 6:   1 Decimals Modular and Remainder Arithmetic
  131.    wt: 6:   8 Pythagorean Relation Forwards Backwards
  132.    wt: 6:   3 Linear Equation Literal Solution More
  133.    wt: 6:   2 More and Less Than for Counts and Measures
  134.    wt: 6:   3 Geometric Formulas and Function Notation
  135.    wt: 6:   2 Computation Rules Evaluation
  136.    wt: 6:   8 Compound Interest Formula Evaluation
  137.    wt: 6:   4 A Brief Story of numbers and algebra
  138.    wt: 6:   3 Comparison of Negative Numbers
  139.    wt: 6:   1 More and Less Than for Counts and Measures
  140.    wt: 6:   9 GCD of 360 110 via Primes and Euclid Algorithm
  141.    wt: 6:   3 signed coordinates for maps and planes
  142.    wt: 6:   16 Addition Subtraction Comparision Compared
  143.    wt: 6:   15 Adding and Subtracting with Unlike Denominators
  144.    wt: 6:   13 Fraction Comparison Algebraic View
  145.    wt: 6:   10 Simplification of Fractions and Mixed Numerals
  146.    wt: 6:   6 Multiplication Algebraically Take II
  147.    wt: 6:   3 Unit fraction of a fraction
  148.    wt: 6:   Fraction Operations by Raising Terms A Simple Innovation
  149.    wt: 6:   6 Multiplication by Natural Numbers
  150.    wt: 6:   10 video Prime Factorization upto 23 squared
  151.    wt: 6:   6 Sieve of Eratosthenes and Square Rule
  152.    wt: 6:   Long Division forwards and backwards Example 2
  153.    wt: 6:   Long Division forwards and backwards Example 1
  154.    wt: 6:   A Elementary Basis for Multiplication Methods
  155.    wt: 6:   8 Subtraction with Units of Measure
  156.    wt: 6:   6. Counting and adding units and mixed units
  157.    wt: 6:   Practical Methods Ends and Values for Arithmetic
  158.    wt: 6:   8 Addition of Time Intervals via subtotaling
  159.    wt: 6:   Example 1. Area Between x and x squared
  160.    wt: 6:   A Related Material in Volume 3
  161.    wt: 6:   A Chain Rule Real Player video examples
  162.    wt: 6:   38 Formulas and derivatives for powers and roots
  163.    wt: 6:   28 Chain Rule Preparation for a Proof
  164.    wt: 6:   27 Chain Rule sinusoidal outer inner functions EGS
  165.    wt: 6:   25 Chain Rule Animated Examples Continued
  166.    wt: 6:   13 Limits with Parameters and Derivatives Take II
  167.    wt: 6:   5 Jumps and absence of unlimited error control
  168.    wt: 6:   Chapter 14 Limits and Continuity with and sans Decimals
  169.    wt: 6:   Appendix E. How To Study Mathematics and Why
  170.    wt: 6:   Chapter 25. Mathematical Induction Examples
  171.    wt: 6:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  172.    wt: 6:   Chapter 10 Describing and Changing Calculations
  173.    wt: 6:   Chapter 6 Change of Language
  174.    wt: 6:   Chapter 5 Islands and Divisions of Knowledge
  175.    wt: 6:   Chapter 6 Rule Based Reason in Mathematics
  176.    wt: 6:   Chapter 2 For and Against Mathematics
  177.    wt: 6:   Chapter 12 Islands and Divisions of Knowledge
  178.    wt: 6:   Chapter 8 Change of Language
  179.    wt: 6:   V Reasons and Motivations for Logic and Mathematics
  180.    wt: 6:   5 Interpreting and Drawing Maps and Plans.
  181.    wt: 6:   4 Money Matters Saving Earning Buying Selling and Budgets
  182.    wt: 6:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  183.    wt: 6:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  184.    wt: 5:   Appendix 1 primary and preschool mathematic
  185.    wt: 5:   I LAMP Introduction Study Habits
  186.    wt: 5:   H LAMP Introduction Instructional Concepts
  187.    wt: 5:   F LAMP Introduction Prerequisites
  188.    wt: 5:   E LAMP Introduction Modern Mathematics
  189.    wt: 5:   Applied Maths Program14092009 POMME variant
  190.    wt: 5:   Mathematics Education Professors
  191.    wt: 5:   mathematics curriculum shifts
  192.    wt: 5:   teaching tutoring algebraic reason
  193.    wt: 5:   three goals for Mathematics Education
  194.    wt: 5:   04 29 New Mathematics Curriculum
  195.    wt: 5:   standards for course material
  196.    wt: 5:   Education in mathematics science and technology
  197.    wt: 5:   education an empirical art
  198.    wt: 5:   chapitre 07 01 principle D induction mathematique
  199.    wt: 5:   chapitre 06 00 Chaines de la raison
  200.    wt: 5:   chapitre 03 A Propos Des Prochains Chapitre
  201.    wt: 5:   F Wire Resistance Calculation04
  202.    wt: 5:   D Wire Resistance Calculation02
  203.    wt: 5:   C Wire Resistance Calculation01
  204.    wt: 5:   B Wire Resistance Qualitative02
  205.    wt: 5:   23 Modularized Skill Development Modularized Rigor
  206.    wt: 5:   13 Addition and Addition Tables
  207.    wt: 5:   6 Discipline Who is in Charge Conserving Authority
  208.    wt: 5:   sign monoticity analysis example 3
  209.    wt: 5:   22 Square Root function graphically
  210.    wt: 5:   15 Sign analysis of functions
  211.    wt: 5:   4 Function notation in and beyond mathematics
  212.    wt: 5:   1 Geometric Introduction of Function Notation
  213.    wt: 5:   5 quadratics completing the square
  214.    wt: 5:   3 quadratics factoring by inspection
  215.    wt: 5:   2 quadratics graphing in general
  216.    wt: 5:   1 quadratics graphing exercises
  217.    wt: 5:   8 Formulas for Fractional Exponents with Logarithms
  218.    wt: 5:   2 Square Root Simplification a prequel
  219.    wt: 5:   1 Calculator Starter Exercises
  220.    wt: 5:   3 Polynomials Multiplication Addition
  221.    wt: 5:   13 cosecant function Definition Graph and Inverse
  222.    wt: 5:   11 arctan left inverse of tangent Graph
  223.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  224.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  225.    wt: 5:   1 Degrees and Radians Introduction
  226.    wt: 5:   A Global Time and Navigation
  227.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  228.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  229.    wt: 5:   14 Straight Lines Equations General Case
  230.    wt: 5:   7 Tangent Function is odd on this domain
  231.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  232.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  233.    wt: 5:   32 seven rows of pascals triangle
  234.    wt: 5:   31 basic secant cosecant cotangent trig identities
  235.    wt: 5:   26 Formulas for products of sines and cosines
  236.    wt: 5:   25 tangent double angle formula Slope connection
  237.    wt: 5:   21 sine and cosine Half Angle Formulas
  238.    wt: 5:   20 sine and cosine Double Angle Formulas
  239.    wt: 5:   17D cis formulas for sine cosines and tangent
  240.    wt: 5:   17C sine and cosine double triple angle formulas
  241.    wt: 5:   11 tangent function undefined when terminal side vertical
  242.    wt: 5:   13 Trig Formulas for dot and cross Products
  243.    wt: 5:   12 cis formulas for sine cosines and tangent
  244.    wt: 5:   11 sine and cosine double triple angle formulas
  245.    wt: 5:   9 The complex number valued trig function cis
  246.    wt: 5:   7 Second Way to Calculate Products
  247.    wt: 5:   1 Rectangular Polar Coordinates Review
  248.    wt: 5:   5 Trigonometric Ratios For Tangent and Special Triangles
  249.    wt: 5:   7 Translations Rotations Reflections Dilatations
  250.    wt: 5:   11 A Partial Summary
  251.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  252.    wt: 5:   6 Polar Multiplication and Rotation
  253.    wt: 5:   3 Rectangular Coordinates Review
  254.    wt: 5:   PS H Distributive Law For Complex Numbers
  255.    wt: 5:   PS G Rotation Distributes over Addition
  256.    wt: 5:   PS E Multiplication with Polar Coordinates
  257.    wt: 5:   PS D Addition with Cartesian Coordinates
  258.    wt: 5:   PS B Parallelogram Construction Methods
  259.    wt: 5:   13 Angle Side Angle Failure
  260.    wt: 5:   6 Ruler and compass Angle Bisection
  261.    wt: 5:   3 Isometry of Triangles Congruence
  262.    wt: 5:   A Measurement with Ruler Proper Use
  263.    wt: 5:   5 Drawing to Scale Avoids Angle Distortions
  264.    wt: 5:   musings do not puiblish real numbers
  265.    wt: 5:   25 Mid way Convergence to Axiomatic Approach
  266.    wt: 5:   23 Distributive Law Two Derivations
  267.    wt: 5:   21 Addition of Multiples of a Single Vector
  268.    wt: 5:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  269.    wt: 5:   13 Arrows and Vectors in a Plane
  270.    wt: 5:   5 Areas of Rectangles Revisited
  271.    wt: 5:   7 Pythagorean Theorem Chinese Square Proof
  272.    wt: 5:   6 Compound Interest Forward and Backwards
  273.    wt: 5:   2 Linear Equation Literal Solution
  274.    wt: 5:   6 Equations and Systems Equivalent or Implied
  275.    wt: 5:   4 Subtraction and Division Axioms
  276.    wt: 5:   2 Addition and Multiplication Axioms
  277.    wt: 5:   1 Equivalent Computation Rules
  278.    wt: 5:   4 Comparison of Negative Numbers
  279.    wt: 5:   13 Real Number Subtraction
  280.    wt: 5:   8 Coordinates for Maps and Planes
  281.    wt: 5:   1 Whole and Natural Numbers
  282.    wt: 5:   1 Formulas Dependence and Function Notation
  283.    wt: 5:   4 Solving a triangular system exercise
  284.    wt: 5:   3 Solving triangular system example
  285.    wt: 5:   5 Algebraic Solutions Introduction
  286.    wt: 5:   Using Letters for Physical Quantities
  287.    wt: 5:   Formula Usage Show Work Format
  288.    wt: 5:   7 Compound Interest Formula Introduction
  289.    wt: 5:   4 Circle Area Formula Example
  290.    wt: 5:   7 Cautious or Safe Set Construction
  291.    wt: 5:   6 Three Notions of What is a Variable
  292.    wt: 5:   3 Properties of Square Roots with example
  293.    wt: 5:   14 GCD of 650 110 via Primes LCM via Product Rule
  294.    wt: 5:   2 Least Common Multiple LCM intro via list method
  295.    wt: 5:   5 Counting with Tables Trees Product Rule Take II
  296.    wt: 5:   11 What are real lengths and numbers
  297.    wt: 5:   2 signed and unsigned numbers as coordinates
  298.    wt: 5:   5 Reciprocals and Division for Fractions with Units
  299.    wt: 5:   3 Multiplying Units and Numbers
  300.    wt: 5:   1 Addition and Subtraction with Units
  301.    wt: 5:   A Similarities between Fractions and Two Term Ratios
  302.    wt: 5:   17 Efficient Ways to Add and Subtract
  303.    wt: 5:   14 Adding and Subtracting with Like Denominators
  304.    wt: 5:   1 What is a fraction Take II
  305.    wt: 5:   A Associative Law Theorectical Note
  306.    wt: 5:   11 Adding Integers Formulas and Examples
  307.    wt: 5:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  308.    wt: 5:   19 Remainder Arithmetic Rule of 9 for checking sums III
  309.    wt: 5:   18 Remainder Arithmetic Rule of 9 for checking sums II
  310.    wt: 5:   17 Remainder Arithmetic Rule of 9 for checking sums I
  311.    wt: 5:   13 Remainder Arithmetic Modulo 5 Example
  312.    wt: 5:   20 Uniqueness of Prime Factorization
  313.    wt: 5:   15 video Factors of 20 using Prime Factorization
  314.    wt: 5:   9 video Prime Factorization upto 19 squared
  315.    wt: 5:   Appendix 1 Decimals Comparison Method Take II
  316.    wt: 5:   7 Subtraction for Decimal Fractions with Exercises
  317.    wt: 5:   2 Subtraction Easy Case Examples
  318.    wt: 5:   7 Adding decimal fractions using decimal point
  319.    wt: 5:   3. How to add with decimals A sans conversions
  320.    wt: 5:   10 Names for Big Numbers and Powers of Ten Expansion
  321.    wt: 5:   Formula Evaluation how to show work
  322.    wt: 5:   016 Numbering Occidental Calendar Days
  323.    wt: 5:   Example 1 volume of a pyramid
  324.    wt: 5:   5 Area Under Curve Exercise
  325.    wt: 5:   4 Definite Integrals Evaluation Exercises
  326.    wt: 5:   36 Cube root derivative animated
  327.    wt: 5:   34 Derivative of exponential function
  328.    wt: 5:   30Chain Rule A Proof
  329.    wt: 5:   26 Chain Rule Recognising outer inner functions
  330.    wt: 5:   24 Chain Rule Animated Examples
  331.    wt: 5:   17 Derivatives of quotients of sine and cosine
  332.    wt: 5:   16 Derivatives of reciprocals of sine and cosine
  333.    wt: 5:   1 Fall 1983 Why Slopes Appetizer
  334.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  335.    wt: 5:   G.1 First Fundamental Theorem of Calculus
  336.    wt: 5:   G.2 Differentiable Functions Mean Value Theorem
  337.    wt: 5:   F.1 What Functions are Continuous
  338.    wt: 5:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  339.    wt: 5:   Chapter 18. Slopes Areas Integration
  340.    wt: 5:   Chapter 17. Area Approximation
  341.    wt: 5:   Chapter 9 About First Courses in Calculus
  342.    wt: 5:   Chapter 3. Slope Sign Analysis
  343.    wt: 5:   Appendix A. Reading Guide For Next Appendices
  344.    wt: 5:   Chapter 26 What is in chapters 27 to 31
  345.    wt: 5:   Postscript Unifying Theme A Fourth Skill For Algebra
  346.    wt: 5:   Chapter 12. Shorthand Usage Guide
  347.    wt: 5:   Chapter 3 Chains of Reason
  348.    wt: 5:   Chapter 4 Complex Numbers and Why Slopes
  349.    wt: 5:   Chapter 3 Algebra Difficulties
  350.    wt: 5:   Chapter 17 Objective Ways Trial and Error Discovery
  351.    wt: 5:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  352.    wt: 5:   Chapter 3 What is in chapters 4 to 8
  353.    wt: 5:   P Exact Arithmetic With Whole Numbers and Fractions
  354.    wt: 5:   D. Check work a must with a caution
  355.    wt: 5:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  356.    wt: 5:   Chapter 3 Algebra Starter Lessons
  357.    wt: 5:   3 Telling Tracking Time Temporal and More Place Sense
  358.    wt: 5:   2 Identifying Size and Position Place and Spatial Sense
  359.    wt: 5:   1 From Number Recognition and Counting to Arithmetic A
  360.    wt: 5:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  361.    wt: 5:   More Algebra and Slope based Calculus Preview
  362.    wt: 4:   K LAMP Musings Science Education
  363.    wt: 4:   Skills Chapter 3 Algebra
  364.    wt: 4:   7 logic review and decimals an odd combination
  365.    wt: 4:   5 logarithms and exponentials etc
  366.    wt: 4:   3 Euclidean Geometry Leanly
  367.    wt: 4:   Teach the teachers plus goals
  368.    wt: 4:   Math Ed if it must be short make it lean effective
  369.    wt: 4:   grouping students according to ability
  370.    wt: 4:   what should be learnt and When
  371.    wt: 4:   Maps Plans Drawings
  372.    wt: 4:   talk the algebra talk
  373.    wt: 4:   02 20 mathematics education references
  374.    wt: 4:   three aims for mathematics students
  375.    wt: 4:   Operational Viewpoint to Value
  376.    wt: 4:   mathematics instruction in general
  377.    wt: 4:   three kinds of reason in mathematics
  378.    wt: 4:   Four ways to improve education reform
  379.    wt: 4:   Prequel In For A Penny In For A Pound
  380.    wt: 4:   fairness and inductive principles for instruction
  381.    wt: 4:   chapitre 04 05 Implication versus suggestion
  382.    wt: 4:   chapitre 04 04 Parlons de la logique
  383.    wt: 4:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  384.    wt: 4:   chapitre 02 00 La Communication des idees
  385.    wt: 4:   Trois Notions qui menent a algebre
  386.    wt: 4:   3 Like resistors in parallel
  387.    wt: 4:   2 Unlike resistors in parallel01
  388.    wt: 4:   19 Extending the Oral Dimension of Mathematics
  389.    wt: 4:   17 Math Booklets for children and young teenagers
  390.    wt: 4:   16 Secondary Mathematics Tips
  391.    wt: 4:   14 Multiplication and Times Tables
  392.    wt: 4:   12 Goals and Objectives For Mathematics
  393.    wt: 4:   11 Help and Defend Your Child or Teens Education
  394.    wt: 4:   10 Ends values for work study instruction
  395.    wt: 4:   Ages 12 to 14 Skills with take home value
  396.    wt: 4:   Ages 3 plus to 4 plus
  397.    wt: 4:   sign monoticity analysis example 4
  398.    wt: 4:   sign monoticity analysis example 2
  399.    wt: 4:   sign monoticity analysis example 1
  400.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  401.    wt: 4:   8 Set view of relations and functions
  402.    wt: 4:   6 Set Existence Formation and Notation
  403.    wt: 4:   5 Function notation for geometric transformations
  404.    wt: 4:   Introduction Reading Guide
  405.    wt: 4:   10 quadratic exercises
  406.    wt: 4:   Quadratics in 10 steps
  407.    wt: 4:   9 Formulas for Real Exponents with Logarithms
  408.    wt: 4:   7 Formulas for Roots with Logarithms Derivation
  409.    wt: 4:   6 Formulas for Even and Odd Roots with Logarithms
  410.    wt: 4:   5 Polynomials Long division Nonlinear divisor
  411.    wt: 4:   4 Polynomials Long division linear divisor
  412.    wt: 4:   1 Polynomials Distributive Law
  413.    wt: 4:   16 cotangent function Definition Graph and Inverse
  414.    wt: 4:   15 cosecant function Definition Graph and Inverse
  415.    wt: 4:   14 secant function Definition Graph and Inverse
  416.    wt: 4:   10 arctan left inverse of tangent Definition
  417.    wt: 4:   6 Graph of arccos function
  418.    wt: 4:   5 Swapping Coordinates is a reflection
  419.    wt: 4:   6 Radian Measure to Degrees
  420.    wt: 4:   5 Degrees to Radian Measure
  421.    wt: 4:   12 From Applied To Pure Mathematics
  422.    wt: 4:   10 Parallelogram Addition Method
  423.    wt: 4:   5 Head To Tail Arrow Addition
  424.    wt: 4:   3 Navigation with Arrows or Vectors
  425.    wt: 4:   2 Graphing y=Af(x) Vertical Scaling
  426.    wt: 4:   Parallel Lines and Interior Angles
  427.    wt: 4:   Straight Lines ASA Intersection Study More
  428.    wt: 4:   Straight Lines ASA Intersection Study
  429.    wt: 4:   13 Straight Lines Finding Equations from 2 points
  430.    wt: 4:   10 Straight Lines through Origin Equations More
  431.    wt: 4:   9 Straight Lines through Origin Equations
  432.    wt: 4:   8 Straight Lines Equation for vertical
  433.    wt: 4:   28 Expressing products of sines cosines as sums
  434.    wt: 4:   24 tangent Angle Difference Formula
  435.    wt: 4:   23 sine and cosine of 180 plus 22.5 degrees
  436.    wt: 4:   19 Pythagorean Identity For sine and cosine functions
  437.    wt: 4:   17E Trig Formulas for dot and cross Products
  438.    wt: 4:   16 Right Triangle Complementary Angle Relations
  439.    wt: 4:   14 cosine even and sine and tangent are odd
  440.    wt: 4:   12 Graph of tangent function for one period
  441.    wt: 4:   10 Graphs of sines and cosines many periods
  442.    wt: 4:   2 Quadrant I reference Angles
  443.    wt: 4:   Appetizer A Complex Number Applet
  444.    wt: 4:   6 Trigonometry Sines of Supplementary Angles
  445.    wt: 4:   8 Similarity of Triangles and Polygons
  446.    wt: 4:   1 Early Concept of Like or Similar Shapes
  447.    wt: 4:   10 Midpoint of [a b] and [b a]
  448.    wt: 4:   5 Algebraic View of Slopes
  449.    wt: 4:   3 Slope product for perpendicular lines
  450.    wt: 4:   What is and is not here
  451.    wt: 4:   1 Cartesian Coordinates sans signs
  452.    wt: 4:   16 Angles Subtended By Chords and Diameters
  453.    wt: 4:   15 Triangle Angle Sum is 180 degrees
  454.    wt: 4:   14 Parallel Lines Postulate
  455.    wt: 4:   9 Construction of a right bisector
  456.    wt: 4:   6 Figuring with Maps Not to Scale
  457.    wt: 4:   2 Measuring Area Directly
  458.    wt: 4:   26 More Less Greater Than Comparison
  459.    wt: 4:   22 Multiplication of Signed Numbers
  460.    wt: 4:   18 Geometrically Why Vector Addition Commutes
  461.    wt: 4:   17 Arrows Rotate to Reverse with Length Unchanged
  462.    wt: 4:   11 Signed Number Addition and Addition Properties
  463.    wt: 4:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  464.    wt: 4:   4 Location of Point in Decimal Addition
  465.    wt: 4:   2 Counting Digits in Decimal Multiplication
  466.    wt: 4:   A Decimal Addition Columm Methods
  467.    wt: 4:   8 Column Multiplication Methods in General
  468.    wt: 4:   7 Decimals Multiplication Methods Examples
  469.    wt: 4:   6 Column Methods for Decimal Multiplication
  470.    wt: 4:   5 Distributive Law for Whole Numbers
  471.    wt: 4:   3 Multiplicative Counting Skills Principles
  472.    wt: 4:   4 Fraction Operations Axiomatic Development
  473.    wt: 4:   5 Proportionality in Equivalent Fractions
  474.    wt: 4:   4 Rates Ratios and Proporitionality
  475.    wt: 4:   1 Changing Calculations
  476.    wt: 4:   5 Equality in Algebra
  477.    wt: 4:   3 More and Less Than with Unlike Signs
  478.    wt: 4:   1 Real Numbers Comparison
  479.    wt: 4:   16 Real Numbers Comparison
  480.    wt: 4:   14 Real Number Multiplication
  481.    wt: 4:   12 Real Number Additive Inverses or Negatives
  482.    wt: 4:   7 Real Numbers as Line Cordinates
  483.    wt: 4:   1 GE Substitution four examples
  484.    wt: 4:   6 Algebraic Solution Example
  485.    wt: 4:   4 Four Examples Fractional Coefficients
  486.    wt: 4:   1 Proper Equal Sign Usage
  487.    wt: 4:   13 Naming Identifying Formulas with Words
  488.    wt: 4:   5 Box Volume Formula Example
  489.    wt: 4:   9 Sets in Probability and Statistics
  490.    wt: 4:   2 What is a Variable
  491.    wt: 4:   arithmetic videos Real Player Format
  492.    wt: 4:   1 Least Common Multiples LCM Introduction
  493.    wt: 4:   4 Counting with Trees Product Rule Take I
  494.    wt: 4:   3 Counting with Tables and Trees II
  495.    wt: 4:   6 Simplification of Fractions with Units
  496.    wt: 4:   2 Equality and Units
  497.    wt: 4:   11 Simplification an Algebraic View
  498.    wt: 4:   6 Multiplication of Mixed Numbers
  499.    wt: 4:   2 Unit Fraction Multiplication
  500.    wt: 4:   1 What is a fraction
  501.    wt: 4:   D Remainders Modulo 11 Pair Rule
  502.    wt: 4:   13 Subtraction with Additive Inverse
  503.    wt: 4:   10 Integer Multiplication Formulas
  504.    wt: 4:   2 Integers Multiplies of a Unit Moverment
  505.    wt: 4:   23 Remainder Arithmetic Modulo 2
  506.    wt: 4:   22 Remainder Arithmetic Modulo 3 more
  507.    wt: 4:   21 Remainder Arithmetic Modulo 3
  508.    wt: 4:   16 Remainder Arithmetic Modulo 9 Example 2
  509.    wt: 4:   15 Remainder Arithmetic Modulo 9 Example
  510.    wt: 4:   14 Remainder Arithmetic Modulo 9 Example
  511.    wt: 4:   12 Remainder Arithmetic Modulo 10 Example
  512.    wt: 4:   11 Remainder Arithmetic Long Division by 5 Quickly more
  513.    wt: 4:   10 Remainder Arithmetic Long Division by 5 Quickly
  514.    wt: 4:   8 Remainder Arithmetic Morulo 5 Examples II
  515.    wt: 4:   7 Remainder Arithmetic Modulo 5 Examples I
  516.    wt: 4:   4 Remainder Arithmetic Modulo 10 in general
  517.    wt: 4:   3 Remainder Arithmetic Modulos 10 more still
  518.    wt: 4:   19 video Prime Factorization Unique
  519.    wt: 4:   18 video Count Factors given Prime Factorization
  520.    wt: 4:   17 Identify and Count Factors using Primes
  521.    wt: 4:   13 video Factors of 24 using prime
  522.    wt: 4:   11 Efficient Square Rule Use
  523.    wt: 4:   4 video Prime Factorization Introduction
  524.    wt: 4:   1 video how Products are bigger than factor
  525.    wt: 4:   7 Long Divison Mistake Catching
  526.    wt: 4:   6 Why Decimal Long Division Methods Works Take I
  527.    wt: 4:   3 Division Single Digit Divisor Example
  528.    wt: 4:   C Counting Areas with Powers of Ten
  529.    wt: 4:   6 Multiplication Commutes Order Not Important
  530.    wt: 4:   5 Decimal Fraction Multiplication
  531.    wt: 4:   Video Decimal Multiplication Geometric View Example 2
  532.    wt: 4:   Video Decimal Multiplication Geometric View Example 2
  533.    wt: 4:   Appendix 2 Three Decimal Subtraction Methods
  534.    wt: 4:   6 Subtraction with Conversion Example with Exercises
  535.    wt: 4:   Appendix 1 Counting Revisited 15 minute video
  536.    wt: 4:   8 What skills and work habits to require
  537.    wt: 4:   1 Place Value in Three Digit Whole Numbers
  538.    wt: 4:   Exact Arithmetic Wholes and Fractions
  539.    wt: 4:   The 12 Times Table Visually
  540.    wt: 4:   015 School and work day counting tables
  541.    wt: 4:   014 Counting Days with Calendars
  542.    wt: 4:   012 Division of Time Intervals by Time Intervals
  543.    wt: 4:   011 Division of Time Intervals By Numbers
  544.    wt: 4:   010 Repeated Addition of Time Intervals
  545.    wt: 4:   4 Mixing and Changing Units of Time
  546.    wt: 4:   3 Units and Lengths of Time
  547.    wt: 4:   Example 2 volume of a cone
  548.    wt: 4:   Area Between Crossing Curves Lesson Take 2
  549.    wt: 4:   Area Between Crossing Curves Lesson Take 1
  550.    wt: 4:   Area Between Curves Lesson Take 2
  551.    wt: 4:   Area Between Curves Lesson Take 1
  552.    wt: 4:   3 Two Chain Rule Method Exercises
  553.    wt: 4:   A Related lessons in Volume 3
  554.    wt: 4:   1 Two cubic sketching exercises with 1st derivative
  555.    wt: 4:   31 Derivatives of inverse functions
  556.    wt: 4:   29 Chain Rule Optional Reading
  557.    wt: 4:   23 Chain Rule in general
  558.    wt: 4:   19 Chain Rule for linear functions
  559.    wt: 4:   18 Chain Rule Introduction
  560.    wt: 4:   7 Animated Differentiation Examples
  561.    wt: 4:   8 Four Animated Examples
  562.    wt: 4:   1 Numerical introduction
  563.    wt: 4:   Postscript One Sided and Intermediate Value Theorems
  564.    wt: 4:   G.6 Bounded Derivatives implies Lipshitz Continuity
  565.    wt: 4:   G.4 Lipschitz Continuity implies EquiContinuity
  566.    wt: 4:   F.3 Intermediate Value Theorem
  567.    wt: 4:   PostScript For and Against Decimal Perspectives
  568.    wt: 4:   Postscript Pythagorean Theorem yet another proof
  569.    wt: 4:   Chapter 24 Logarithms Powers and Exponentials
  570.    wt: 4:   Chapter 13. Acceleration
  571.    wt: 4:   Chapter 12. Units and Slopes
  572.    wt: 4:   Chapter 10 Slopes and Units
  573.    wt: 4:   Chapter 6. Slopes and Vertical Shifts
  574.    wt: 4:   Chapter 4. More Slope Sign Analysis
  575.    wt: 4:   Chapter 2. Slopes and Ski Trails
  576.    wt: 4:   Fall 1983 Calculus Appetizer
  577.    wt: 4:   Appendix D. What to do in School and Why
  578.    wt: 4:   Chapter 31 Direct and Indirect Reason
  579.    wt: 4:   Chapter 30 Truth Tables
  580.    wt: 4:   Chapter 27 Shorthand Symbols as Pronouns
  581.    wt: 4:   Chapter 23. Notation For Sums
  582.    wt: 4:   Chapter 22. Geometric Sums and Sequences
  583.    wt: 4:   Chapter 20. Degrees and Radians
  584.    wt: 4:   Chapter 18. Rules for Algebra
  585.    wt: 4:   Chapter 15. Solving Linear Equations
  586.    wt: 4:   Chapter 13. Second Reading Guide
  587.    wt: 4:   Postscript What is a Variable
  588.    wt: 4:   Chapter 7 Prep for Calculus Arithmetic Exercises
  589.    wt: 4:   Chapter 4 Longer Chains of Reason
  590.    wt: 4:   Chapter 1 Introduction to Chapters 2 to 6
  591.    wt: 4:   Annotated Links to Material Elsehwere
  592.    wt: 4:   Postscript B Mathematics Education References
  593.    wt: 4:   Postscript C Consistency as a Tool for Reason
  594.    wt: 4:   Chapter 23 Truth Tables
  595.    wt: 4:   Chapter 20 Shorthand Symbols as Pronouns
  596.    wt: 4:   Chapter 19 What is in chapters 20 to 24
  597.    wt: 4:   Chapter 11 Accidental Patterns
  598.    wt: 4:   Chapter 9 What is in Chapters 10 to 18
  599.    wt: 4:   Chapter 7 Longer Chains of Reason
  600.    wt: 4:   Chapter 6 Chains of Reason
  601.    wt: 4:   R Why Learn Mathematics Skills
  602.    wt: 4:   O On Learning Mathematics and Science
  603.    wt: 4:   N Mathematics Prepare for College Studies
  604.    wt: 4:   I. Logic and language skills
  605.    wt: 4:   F. The student teacher tutor feedback loop
  606.    wt: 4:   Appendix A Calculus with Proofs for Keen or Gifted
  607.    wt: 4:   Chapter 7 Calculus Previews and Calculus Lightly
  608.    wt: 4:   Chapter 6 More Algebra and Geometry
  609.    wt: 4:   Chapter 4 Logic for Reading Writing and Geometry etc
  610.    wt: 4:   7 Games and Activities for Instruction
  611.    wt: 4:   1 From Number Recognition and Counting to Arithmetic B
  612.    wt: 4:   Mathematics Education References
  613.    wt: 4:   Mathematics Education References
  614.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  615.    wt: 4:   Multiple Ways to Improve Mathematics Skill Development
  616.    wt: 4:   Systematic Algebra Skill Development Missing Links
  617.    wt: 4:   Talking pdf files for online lessons a webvideo alternative
  618.    wt: 3:   Appendix 2 primary school Arithmetic 01
  619.    wt: 3:   J LAMP Introduction Extrinsic Origins
  620.    wt: 3:   G LAMP Introduction Problem Solving Skills
  621.    wt: 3:   A Introduction Objectives
  622.    wt: 3:   Skills Chapter 0 Introduction
  623.    wt: 3:   11 pure mathematics
  624.    wt: 3:   8 analytic geometry etc
  625.    wt: 3:   1 arithmetic with unsigned numbers
  626.    wt: 3:   links Education Resources online
  627.    wt: 3:   About site lesson plans
  628.    wt: 3:   Education Reform Inconsistencies
  629.    wt: 3:   five decades make a difference
  630.    wt: 3:   how letters appear
  631.    wt: 3:   Secondary Three Mathematics
  632.    wt: 3:   Secondary Two Mathematics
  633.    wt: 3:   Secondary One Mathematics
  634.    wt: 3:   geometric implications for algebra
  635.    wt: 3:   Lessening Algebra Difficulties
  636.    wt: 3:   the trouble with algebra
  637.    wt: 3:   05 13 OldSiteEntrancePage
  638.    wt: 3:   04 25 when to stop or suspend mathemat
  639.    wt: 3:   Different Kinds of Reasoning in maths
  640.    wt: 3:   words for mathematics instructor
  641.    wt: 3:   chapitre 04 07 RepetablesEtReproductibles
  642.    wt: 3:   chapitre 01 00 Introduction
  643.    wt: 3:   problemes algebre et arithmetique
  644.    wt: 3:   deux definitions pour variable
  645.    wt: 3:   24 Standards For Skill Develoment Take II
  646.    wt: 3:   22 Student Centered Highschool Mathematics
  647.    wt: 3:   18 Primary School Mathematics
  648.    wt: 3:   9 Streaming by Student Cooperation
  649.    wt: 3:   8 The Effect of Negative Remarks
  650.    wt: 3:   4 Learning Takes Time and Effort
  651.    wt: 3:   3 Preparing for Science Studies
  652.    wt: 3:   Ages 4 plus to 5 plus
  653.    wt: 3:   20 Interchanging coordinates a reflection
  654.    wt: 3:   19 Horizontal line rule and method
  655.    wt: 3:   18 Vertical Line Rule and Method
  656.    wt: 3:   16 Increasing or decreasing on intervals
  657.    wt: 3:   12 Function Domain Recognition Exercises
  658.    wt: 3:   10 Exponential Growth and Decay Models
  659.    wt: 3:   2 Column Multiplication Method
  660.    wt: 3:   12 motivation for term arctan
  661.    wt: 3:   9 motivation for name arcsin
  662.    wt: 3:   8 arcsin left inverse of sine Graph
  663.    wt: 3:   3 Left Inverse of cosine arccos definition
  664.    wt: 3:   9 Head to Tail Coordinate View
  665.    wt: 3:   Vector and Complex Number Applet
  666.    wt: 3:   3 graphing y=f(x c) plus K
  667.    wt: 3:   Triangle Angles Sum To 180 Degrees
  668.    wt: 3:   Straight Lines Instersection Solving Equations
  669.    wt: 3:   D Straight Lines Slope from Coordinates Examples
  670.    wt: 3:   A Straight Line Slope Scaling Properties
  671.    wt: 3:   12 Straight Lines Graphing mx plus b
  672.    wt: 3:   5 Tangent Function Graph
  673.    wt: 3:   15 sine cosine Complementary Angle Relations
  674.    wt: 3:   9 Graphs of sine and cosine over one period
  675.    wt: 3:   8 period of tangent function
  676.    wt: 3:   6 sines and cosines for reference angle 30 degrees
  677.    wt: 3:   3 sines and cosines for reference angle 90 degrees
  678.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  679.    wt: 3:   21 Logarithms Powers and Exponentials
  680.    wt: 3:   17 Cube Roots of unity
  681.    wt: 3:   16 References and Originality Question
  682.    wt: 3:   2 Complex Numbers made easier we hope
  683.    wt: 3:   8 Triangles Cascade Problem Solving
  684.    wt: 3:   4 Trigonometric Ratios For Two Special Triangles
  685.    wt: 3:   3 Trigonometric Ratios sine and cosine
  686.    wt: 3:   1 Angle Measurement with Degrees
  687.    wt: 3:   Why Trigonometry the whyslopes view
  688.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  689.    wt: 3:   11 Triangle Similarity Missing Side Problem
  690.    wt: 3:   6 Geometric Diagrams in Class
  691.    wt: 3:   3 Similarity by Design with coordinates
  692.    wt: 3:   9 Midpoint Coordinates Half Endpoint Sum
  693.    wt: 3:   7 Exercises to test skill and concept mastery
  694.    wt: 3:   2 point slope equation for a line
  695.    wt: 3:   12 Spatial Coordinates
  696.    wt: 3:   11 Triangle Inequality
  697.    wt: 3:   8 Distance Between Points on a Line
  698.    wt: 3:   4 Polar Coordinates to and from
  699.    wt: 3:   2 Cartesian Coordinates with signs
  700.    wt: 3:   PS C Similarity Use Recognize it in Trigonometry
  701.    wt: 3:   PS A Kite Construction Methods
  702.    wt: 3:   21 Parallelograms
  703.    wt: 3:   18 Triangle Similarity Take 1
  704.    wt: 3:   17 Right Bisectors of Triangle Sides
  705.    wt: 3:   12 Side Angle Side Failure
  706.    wt: 3:   11 Triangle Construction Fails
  707.    wt: 3:   10 Dropping a perpendicular to line
  708.    wt: 3:   Short Course on Euclidean Geometry
  709.    wt: 3:   A Signed Number Arithmetic Review
  710.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  711.    wt: 3:   12 Real Numbers Line Signed Coordinates
  712.    wt: 3:   9 Division with Digits after Decimal Point
  713.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  714.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  715.    wt: 3:   1 Fractions with Finite Decimal Expansions
  716.    wt: 3:   C Three Decimal Subtraction Methods
  717.    wt: 3:   2 Combing Counts Addition Skills and Principles
  718.    wt: 3:   1 The Counting Origins of Numbers
  719.    wt: 3:   2 Fraction Operations Physical Development
  720.    wt: 3:   3 Proportionality Examples
  721.    wt: 3:   1 What is Proportionality
  722.    wt: 3:   3 Product Axioms Two Forms
  723.    wt: 3:   5 Greater More Less Than Signs in General
  724.    wt: 3:   15 Real Number Division
  725.    wt: 3:   11 Real Number Addition
  726.    wt: 3:   10 Real Number Lengths and Signs
  727.    wt: 3:   6 Unsigned Real Numbers
  728.    wt: 3:   5 Rational Numbers More
  729.    wt: 3:   4 Rational Numbers
  730.    wt: 3:   4 GE III Animated Examples
  731.    wt: 3:   2 Essentially one exercises three with solution
  732.    wt: 3:   3 Four Examples
  733.    wt: 3:   10 Volume of Pyramid
  734.    wt: 3:   5 Product Builder Notation
  735.    wt: 3:   4 Subset Builder Notation
  736.    wt: 3:   3 Counting with Sets etc
  737.    wt: 3:   3 Adding Words To Arithmetic
  738.    wt: 3:   4 Greater More Less Than Signs in General
  739.    wt: 3:   2 More and Less Than with Unlike Signs
  740.    wt: 3:   17 GCD LCM of 85 and 60 via Prime
  741.    wt: 3:   16 GCD and LCM of 650 225 via Prime
  742.    wt: 3:   13 GCD from given Prime Factorization
  743.    wt: 3:   11 GCD 2700 288 via Euclid Algorithm
  744.    wt: 3:   10 Euclid Algorithm with 129 125 and with 45 14
  745.    wt: 3:   8 GCD from Euclidean Algorithm
  746.    wt: 3:   7 GCD and LCM from prime factorization
  747.    wt: 3:   4 LCM of 8 and 10 via Prime
  748.    wt: 3:   LCM 60 45 Avoid List Method Use Prime
  749.    wt: 3:   2 Counting with Tables and Trees I
  750.    wt: 3:   1 Counting and Counting Methods I
  751.    wt: 3:   9 subtracting signed numbers
  752.    wt: 3:   7 negative and additive inverse
  753.    wt: 3:   5 lengths and signs of numbers
  754.    wt: 3:   B Fractions and Two Term Ratios
  755.    wt: 3:   21 Reciprocals for Fractions and Wholes
  756.    wt: 3:   12 Fraction Comparison
  757.    wt: 3:   9 Improper Fractions and Mixed Numbers
  758.    wt: 3:   5 Equivalent Fractions
  759.    wt: 3:   4 Fraction Multiplication
  760.    wt: 3:   8 Multiplication by Signed Numbers Integers
  761.    wt: 3:   3 Adding Movements with same direction
  762.    wt: 3:   27 Divisibility by 2 3 6 5 9 10 Example
  763.    wt: 3:   26 Divisibility by 2 3 5 Example
  764.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  765.    wt: 3:   9 Remainder Arithmetic Divisibility by 5
  766.    wt: 3:   6 Remainder Arithmetic Modulo 5 Propertie
  767.    wt: 3:   5 Remainder Arithmetic Modulo 5
  768.    wt: 3:   2 Remainder Arithmetic Modulo 10 more
  769.    wt: 3:   1 Remainder Arithmetic Modulo 10
  770.    wt: 3:   16 video Factors of 980 using prime
  771.    wt: 3:   14 video Factors of 24 Take II
  772.    wt: 3:   8 video Prime Factorization upto 19
  773.    wt: 3:   3 video Primes and Composites from 9 times table
  774.    wt: 3:   Long Division Backwards more
  775.    wt: 3:   Long Division Backward
  776.    wt: 3:   Division with Counts and Length
  777.    wt: 3:   12 Why Long Division Works Take III
  778.    wt: 3:   11 Another Single Digit Divisor Example
  779.    wt: 3:   10 Division by Five Long and Short Ways
  780.    wt: 3:   9 Why Long Division Works Take II
  781.    wt: 3:   D Decimal Multiplication Methods Derived
  782.    wt: 3:   Video Power Notation in Decimal Expansion
  783.    wt: 3:   Subtraction with J Conversions Example
  784.    wt: 3:   Subtraction Another Video Lesson
  785.    wt: 3:   9 22 Minute Subtraction Review Video
  786.    wt: 3:   5 A Tip for Efficent Subtraction
  787.    wt: 3:   4 Subtraction with Conversions Borrows and Letter J
  788.    wt: 3:   5. How to add decimals C. Examples
  789.    wt: 3:   2 Decimal Counting Practices
  790.    wt: 3:   1. Explaining Addition Table
  791.    wt: 3:   Expression Evaluation how to show work
  792.    wt: 3:   013 Travel Time Tables
  793.    wt: 3:   7 Addition of Time Intervals
  794.    wt: 3:   2 Time and Date Matters in School
  795.    wt: 3:   1 Intro of Kids To Time Date Skills
  796.    wt: 3:   Example 4 with x function of y
  797.    wt: 3:   1 Chain Rule in Reverse Integration Method
  798.    wt: 3:   4 Second derivative test exercise example
  799.    wt: 3:   22 Chain Rule for polynomials
  800.    wt: 3:   20 Chain Rule for Pulley Systems
  801.    wt: 3:   15 sine and cosine derivatives 3rd step
  802.    wt: 3:   13 sine and cosine derivatives 1st step
  803.    wt: 3:   12 Quotient rule examples
  804.    wt: 3:   8 Differentiation of polynomials
  805.    wt: 3:   6 Power rule from product rule
  806.    wt: 3:   3 Motivation for Limit Definition Take 2
  807.    wt: 3:   6 Continuity at a point
  808.    wt: 3:   3 Decimal insights for limits continuity convergence
  809.    wt: 3:   2 Algebraic codification
  810.    wt: 3:   G.2 Lipshitz Conditions Integration Calculus Reform
  811.    wt: 3:   G.3 Constant Difference Theorem Proof
  812.    wt: 3:   F.5a Equicontinuity Theorems
  813.    wt: 3:   E2 Algebraic Properties of Limits
  814.    wt: 3:   D1 Sets and Sequences GLBs and LGBs
  815.    wt: 3:   C Triangle Inequalities
  816.    wt: 3:   B3 Bolzano Weierstrass Theorem
  817.    wt: 3:   A1. Introduction
  818.    wt: 3:   Chapter 21 Arrow Addition
  819.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  820.    wt: 3:   Chapter 16. Velocity Approximation
  821.    wt: 3:   Chapter 15. Slope Approximation
  822.    wt: 3:   Chapter 11. Graphing Slope versus Position
  823.    wt: 3:   Chapter 7 Slopes and Velocity
  824.    wt: 3:   Chapter 1.Introduction
  825.    wt: 3:   Chapter 28 Occurrence Tables
  826.    wt: 3:   Chapter 24. Personal Investment and Pension EGS
  827.    wt: 3:   Chapter 21. Third Reading Guide
  828.    wt: 3:   Chapter 19. Functions and Sets
  829.    wt: 3:   Chapter 11. Why Shorthand
  830.    wt: 3:   Chapter 8 Three Skills For Algebra
  831.    wt: 3:   Solutions For Arithmetic Exercises
  832.    wt: 3:   Chapter 12 Four Phases
  833.    wt: 3:   Chapter 11 Elementary Instruction
  834.    wt: 3:   Chapter 7 Two Treatments of Geometry
  835.    wt: 3:   Chapter 1 Introduction
  836.    wt: 3:   Postscript D Reflections on Law of the Excluded Middle
  837.    wt: 3:   Chapter 24 Direct and Indirect Reason
  838.    wt: 3:   Chapter 21 Occurrence Tables
  839.    wt: 3:   Chapter 1 Introduction
  840.    wt: 3:   S Adding words to algebra
  841.    wt: 3:   Q How Logic and Proofs extend Show Work Practices
  842.    wt: 3:   L Skills with take home value
  843.    wt: 3:   N Improving Marks on Tests and Finals
  844.    wt: 3:   H Jigsaw puzzles and problem solving
  845.    wt: 3:   C. Domino effect of being careful
  846.    wt: 3:   Chapter 8 Skipped Topics and Why
  847.    wt: 3:   Helping the Blind in Logic and Mathematics
  848.    wt: 3:   Road Safety Questions
  849.    wt: 3:   The Math Forum and Site Content
  850.    wt: 2:   Skills Chapter 5 Calculus
  851.    wt: 2:   Ramblings Extrinsic numbers theory
  852.    wt: 2:   Skills Chapter 1 Arithmetic
  853.    wt: 2:   10 statistics
  854.    wt: 2:   9 combinatorics probability sets
  855.    wt: 2:   6 polynomials etc
  856.    wt: 2:   4 algebra
  857.    wt: 2:   2 arithmetic with signed numbers
  858.    wt: 2:   What is POMME
  859.    wt: 2:   three goals to set for students
  860.    wt: 2:   permissions for teachers
  861.    wt: 2:   activities for students
  862.    wt: 2:   site eurekas
  863.    wt: 2:   teacher certification
  864.    wt: 2:   modern education
  865.    wt: 2:   learning takes time
  866.    wt: 2:   mathematics in context
  867.    wt: 2:   teaching tips
  868.    wt: 2:   What to Tell Students
  869.    wt: 2:   formal or informal peer review
  870.    wt: 2:   cultivating intelligence
  871.    wt: 2:   How to be a better instructor
  872.    wt: 2:   Motivation and Context Problem
  873.    wt: 2:   chapitre 12 00 les iles et division
  874.    wt: 2:   chapitre 04 09 Regles accidentelles
  875.    wt: 2:   chapitre 04 08 Limitations et benefices
  876.    wt: 2:   chapitre 04 06 engagements
  877.    wt: 2:   chapitre 04 02 Deuxieme enigme
  878.    wt: 2:   chapitre 04 00 Les regles d implication
  879.    wt: 2:   logique deux enigme
  880.    wt: 2:   3 Energy Power Heat08
  881.    wt: 2:   F Unlike Resistors in Series
  882.    wt: 2:   E Kirchoffs Second Law
  883.    wt: 2:   D Kirchoff First Law
  884.    wt: 2:   C Electromotive force conventional current02
  885.    wt: 2:   B Electromotive force conventional current01
  886.    wt: 2:   A Circuit Elements
  887.    wt: 2:   Home Tutoring and Home Schooling
  888.    wt: 2:   24 Standards For Skill Develoment
  889.    wt: 2:   15 Counting For Parents
  890.    wt: 2:   7 Student Motivation
  891.    wt: 2:   2 Reading and Writing Skills
  892.    wt: 2:   Ages 12 to 14 Arithmetic
  893.    wt: 2:   Ages 10 to 12 Arithmetic
  894.    wt: 2:   26 Function definitions done and coming
  895.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  896.    wt: 2:   23 Inverse Functions
  897.    wt: 2:   13 From one to one to many to one
  898.    wt: 2:   10 Interval Notation
  899.    wt: 2:   7 Functions with finite domains
  900.    wt: 2:   11 Growth and Decay in Biology
  901.    wt: 2:   8 Notes for instructors or tutors
  902.    wt: 2:   7 arcsin left inverse of sine Definition
  903.    wt: 2:   4 possible motivation for term arccos
  904.    wt: 2:   15 Dot and Cross Product
  905.    wt: 2:   8 Parallel Vectors
  906.    wt: 2:   1 Unsigned Coordinates
  907.    wt: 2:   4 graphing y=Asin(x c)
  908.    wt: 2:   1 graphing y=f(x a)
  909.    wt: 2:   Straight Lines Intersection of
  910.    wt: 2:   C Straight Lines Slope from Coordinates
  911.    wt: 2:   B Straight Line Slope Scaling Properties More
  912.    wt: 2:   11 Straight Lines Graphing y=mx
  913.    wt: 2:   4 Tangent Function Properties
  914.    wt: 2:   17G Pythagorean Theorem Converse
  915.    wt: 2:   17F Law of cosines
  916.    wt: 2:   7 period of sine and cosine
  917.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  918.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  919.    wt: 2:   1 Unit Points Reflections Rotations
  920.    wt: 2:   Unit Circle Development of Trigonometry
  921.    wt: 2:   20 N th Roots of Complex Numbers
  922.    wt: 2:   19 N th Roots of Unity
  923.    wt: 2:   18 Sixth Roots of Unity
  924.    wt: 2:   15 Pythagorean Theorem Converse
  925.    wt: 2:   14 Law of cosines
  926.    wt: 2:   8 Unit Circle Development of Trigonometry
  927.    wt: 2:   6 Field Properties of Complex Number
  928.    wt: 2:   4 Multiplication Properties
  929.    wt: 2:   3 Addition Properties
  930.    wt: 2:   7 Trignometric Ratios Unit Circle
  931.    wt: 2:   12 Triangles Similarity More Problems
  932.    wt: 2:   4 Similarity Definition with Coordinate
  933.    wt: 2:   Four Simple Exercises
  934.    wt: 2:   8 Mid Point Formula
  935.    wt: 2:   6 Intersection of lines by solving linear systems
  936.    wt: 2:   4 Equations for lines three forms
  937.    wt: 2:   7 Complex Numbers Appetizer
  938.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  939.    wt: 2:   19 Right Triangle Similarity
  940.    wt: 2:   8 Isoceles Triangles
  941.    wt: 2:   7 Angle Side Angle
  942.    wt: 2:   1 Initial Concepts and Terms
  943.    wt: 2:   1 Length Measurement
  944.    wt: 2:   About Folder Contents
  945.    wt: 2:   24 Signed Numbers Arithmmetic Properties
  946.    wt: 2:   19 Signed Multiples of Vectors
  947.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  948.    wt: 2:   2 Algebraic View
  949.    wt: 2:   9 Coordinates for Regions in Space
  950.    wt: 2:   3 Fractions
  951.    wt: 2:   5 Independent versus Dependent Variables
  952.    wt: 2:   4 Changing Letters
  953.    wt: 2:   2 GE II Comparison
  954.    wt: 2:   1 Essentially One Unknown
  955.    wt: 2:   3 Two Examples
  956.    wt: 2:   11 Volume of Sphere
  957.    wt: 2:   9 Volume of Cone
  958.    wt: 2:   1 Written work formats for developing and showing skill
  959.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  960.    wt: 2:   8 Sets of Numbers
  961.    wt: 2:   2 Venn Diagrams
  962.    wt: 2:   1 Three Skills For Algebra
  963.    wt: 2:   About Folder Contents
  964.    wt: 2:   5 Square Roots with primes more still
  965.    wt: 2:   4 Square Roots with primes more
  966.    wt: 2:   2 Square Roots with Prime
  967.    wt: 2:   5 Common Divisors 60 45 via Prime
  968.    wt: 2:   8 multiplying signed numbers
  969.    wt: 2:   6 adding signed numbers
  970.    wt: 2:   4 signed coordinates for regions in space
  971.    wt: 2:   7 Converting or Changing Units
  972.    wt: 2:   4 Fractions with Units
  973.    wt: 2:   22 Complex Compound Fractions
  974.    wt: 2:   20 Dividing Fractions the Why
  975.    wt: 2:   18 Efficient Ways to Multiply
  976.    wt: 2:   B Integer Long Division Multiple Choices
  977.    wt: 2:   12 Adding Integers More Examples
  978.    wt: 2:   7 Multiplication by Signs
  979.    wt: 2:   5 Zero Movement and Additive Inverses
  980.    wt: 2:   1 Integers as Coordinates
  981.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  982.    wt: 2:   12 LCD GCD and LCM using Primes
  983.    wt: 2:   2 Prime and Composites less than 16
  984.    wt: 2:   8 Correcting the Mistake
  985.    wt: 2:   5 Long Division Include Zeroes or not
  986.    wt: 2:   2 Division with Single Digit Divisors
  987.    wt: 2:   1 Divsion Physical Examples
  988.    wt: 2:   4 Two and Three Digit Multipliers
  989.    wt: 2:   3 More One Digit Multipliers
  990.    wt: 2:   1 Why 3 times 5 gives 15
  991.    wt: 2:   4. How to add with decimals B with conversions
  992.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  993.    wt: 2:   About folder contents
  994.    wt: 2:   6 How long is a million seconds
  995.    wt: 2:   Volume of Solid by Cross Sections Lesson
  996.    wt: 2:   Example 3
  997.    wt: 2:   Summary
  998.    wt: 2:   2 Indefinite Integrals Exercises
  999.    wt: 2:   3 Second derivative test
  1000.    wt: 2:   2 Second derivative test prequel
  1001.    wt: 2:   21 Chain Rule for powers
  1002.    wt: 2:   14 sine and cosine derivatives 2nd step
  1003.    wt: 2:   11 Quotient rule
  1004.    wt: 2:   10 Power rule for negative integers
  1005.    wt: 2:   9 Reciprocal rule
  1006.    wt: 2:   5 Product Rule
  1007.    wt: 2:   4 Sum Rule
  1008.    wt: 2:   2 Motivation for Limit Definition Take 1
  1009.    wt: 2:   11 Limits at infinity Three Examples
  1010.    wt: 2:   10 Three one sided limits with infinite values
  1011.    wt: 2:   9 Limits Continuity and Composition
  1012.    wt: 2:   4 Numerical properties
  1013.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  1014.    wt: 2:   F.5b Extreme Value Theorem
  1015.    wt: 2:   E1 Error Control Inequalities
  1016.    wt: 2:   D2 Limits of Monotone Sequences
  1017.    wt: 2:   Chapter 23 Links To Trigonometry
  1018.    wt: 2:   Chapter 22 Complex Numbers
  1019.    wt: 2:   Chapter 8. Slope Interpretation
  1020.    wt: 2:   Appendix C. How to Read
  1021.    wt: 2:   Appendix B. How To Learn
  1022.    wt: 2:   Chapter 16. Painless Theorem Proving
  1023.    wt: 2:   Postscript A Three Remarks
  1024.    wt: 2:   Chapter 10 Transition
  1025.    wt: 2:   Chapter 8 Modern Instruction
  1026.    wt: 2:   Chapter 5 Four References
  1027.    wt: 2:   Postscript B More on Story Telling and Reason
  1028.    wt: 2:   Chapter 18 Sense and Knowledge
  1029.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  1030.    wt: 2:   H more Routine to non routine problem solving
  1031.    wt: 2:   G. Written work formats for developing and showing skill
  1032.    wt: 2:   A. Skill has to be seen to believed
  1033.    wt: 2:   How to Build Skills and Confidence
  1034.    wt: 2:   Chapter 2 Why Sets
  1035.    wt: 2:   Chapter 1 Arithmetic
  1036.    wt: 1:   Skills Chapter 4 Logic
  1037.    wt: 1:   Skills Chapter 2 Geometry
  1038.    wt: 1:   why bother
  1039.    wt: 1:   which way to go
  1040.    wt: 1:   key notes and themes
  1041.    wt: 1:   three difficulties
  1042.    wt: 1:   02 21 words for teachers
  1043.    wt: 1:   Theory of Knowledge
  1044.    wt: 1:   chapitre 05 00 Deception
  1045.    wt: 1:   chapitre 04 01 Premiere enigme
  1046.    wt: 1:   4 Energy Power Heat09
  1047.    wt: 1:   2 Energy Power Heat07
  1048.    wt: 1:   1 Energy Power Heat06
  1049.    wt: 1:   C Energy Power03
  1050.    wt: 1:   A Energy Power01
  1051.    wt: 1:   1 Like resistors in series
  1052.    wt: 1:   H Series Circuit02
  1053.    wt: 1:   G Series Circuit01
  1054.    wt: 1:   1 Speaking Skills
  1055.    wt: 1:   Ages 12 to 14 Geometry
  1056.    wt: 1:   Ages 10 to 12 Geometry
  1057.    wt: 1:   Ages 9 to 10
  1058.    wt: 1:   Ages 8 to 9
  1059.    wt: 1:   Ages 7 to 8
  1060.    wt: 1:   Ages 6 to 7
  1061.    wt: 1:   14 Surjections Injections Bijections
  1062.    wt: 1:   9 Set theory term relation possible origins
  1063.    wt: 1:   2 cosine function more properties
  1064.    wt: 1:   1 cosine function properties
  1065.    wt: 1:   13 Velocity Vectors in Physics
  1066.    wt: 1:   6 Vectors with Coordinates
  1067.    wt: 1:   2 Signed Coordinates
  1068.    wt: 1:   1 Straight Lines Slope Concept
  1069.    wt: 1:   2 Similarity By Design
  1070.    wt: 1:   5 Side Angle Side
  1071.    wt: 1:   2 Correspondence between Triangles
  1072.    wt: 1:   E Long Division Methods more
  1073.    wt: 1:   D Long Division Methods
  1074.    wt: 1:   More Exercises
  1075.    wt: 1:   Simple Exercises
  1076.    wt: 1:   2 Three Examples
  1077.    wt: 1:   10 One Example
  1078.    wt: 1:   9 Three Examples
  1079.    wt: 1:   8 One Example
  1080.    wt: 1:   7 Two Examples
  1081.    wt: 1:   6 Three Examples
  1082.    wt: 1:   5 Three Examples
  1083.    wt: 1:   4 Two Examples
  1084.    wt: 1:   2 Three Examples
  1085.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  1086.    wt: 1:   6 Power Set Notation
  1087.    wt: 1:   12 GCD 2700 288 via Prime
  1088.    wt: 1:   10 dividing signed numbers
  1089.    wt: 1:   D Three Term Ratios
  1090.    wt: 1:   19 Dividing Fractions How TO
  1091.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  1092.    wt: 1:   9 Multiplying Integers
  1093.    wt: 1:   4 Adding Movements wiht opposite directions
  1094.    wt: 1:   4 Division with 2 Digit Divsors
  1095.    wt: 1:   B Powers of Ten
  1096.    wt: 1:   2 One Digit Multipliers
  1097.    wt: 1:   The 20 Times Table
  1098.    wt: 1:   5 Conversion Arithmetic
  1099.    wt: 1:   Example 2
  1100.    wt: 1:   Example 1
  1101.    wt: 1:   G.5 Motions With Bounded Velocities
  1102.    wt: 1:   F.2 Closed Range Theorem
  1103.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  1104.    wt: 1:   Chapter 5. Slope Sign Tests
  1105.    wt: 1:   Postscript More on Better Performance
  1106.    wt: 1:   Postscript For Better Performance
  1107.    wt: 1:   Chapter 9 The Two Ends
  1108.    wt: 1:   Postscript A Story Telling
  1109.    wt: 1:   Chapter 15 Objective Processes
  1110.    wt: 1:   Chapter 10 Responsibility
  1111.    wt: 1:   Chapter 5 Deception
  1112.    wt: 1:   Chapter 2 Skill Development
  1113.    wt: 1:   Three Remarks
  1114.    wt: 1:   M Words to extend arithmetic
  1115.    wt: 1:   J. More on written work and showing skill
  1116.    wt: 1:   E. When and how to correct errors
  1117.    wt: 1:   B. Domino effect of errors
  1118.    wt: 1:   Implementation Notes
  1119.    wt: 1:   Which Way To Go
  1120.    wt: 12:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  1121.    wt: 11:   8 quadratics backward use of various formulas
  1122.    wt: 10:   14 Why Scalar Multiplication Distributes Physical Argument
  1123.    wt: 10:   Chapter 14. Forward and Backward Use of a Formula

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  1.    wt: 9:   Skills Chapter 4 Logic
  2.    wt: 9:   Skills Chapter 2 Geometry
  3.    wt: 9:   10 statistics
  4.    wt: 9:   9 combinatorics probability sets
  5.    wt: 9:   6 polynomials etc
  6.    wt: 9:   4 algebra
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  12.    wt: 9:   modern education
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  16.    wt: 9:   Secondary Three Mathematics
  17.    wt: 9:   Secondary Two Mathematics
  18.    wt: 9:   Secondary One Mathematics
  19.    wt: 9:   geometric implications for algebra
  20.    wt: 9:   Lessening Algebra Difficulties
  21.    wt: 9:   05 13 OldSiteEntrancePage
  22.    wt: 9:   04 25 when to stop or suspend mathemat
  23.    wt: 9:   words for mathematics instructor
  24.    wt: 9:   chapitre 04 05 Implication versus suggestion
  25.    wt: 9:   chapitre 04 04 Parlons de la logique
  26.    wt: 9:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  27.    wt: 9:   chapitre 02 00 La Communication des idees
  28.    wt: 9:   A Wire Resistance Qualitative01
  29.    wt: 9:   Ages 3 plus to 4 plus
  30.    wt: 9:   17 Function maxima minima and their location
  31.    wt: 9:   11 Function Domain Range Source and Targets
  32.    wt: 9:   2 Algebraic use of function notation
  33.    wt: 9:   11 Growth and Decay in Biology
  34.    wt: 9:   3 Polynomials Multiplication Addition
  35.    wt: 9:   14 secant function Definition Graph and Inverse
  36.    wt: 9:   10 arctan left inverse of tangent Definition
  37.    wt: 9:   6 Graph of arccos function
  38.    wt: 9:   5 Swapping Coordinates is a reflection
  39.    wt: 9:   12 From Applied To Pure Mathematics
  40.    wt: 9:   10 Parallelogram Addition Method
  41.    wt: 9:   5 Head To Tail Arrow Addition
  42.    wt: 9:   1 Straight Lines Slope Concept
  43.    wt: 9:   26 Formulas for products of sines and cosines
  44.    wt: 9:   25 tangent double angle formula Slope connection
  45.    wt: 9:   24 tangent Angle Difference Formula
  46.    wt: 9:   21 sine and cosine Half Angle Formulas
  47.    wt: 9:   20 sine and cosine Double Angle Formulas
  48.    wt: 9:   17D cis formulas for sine cosines and tangent
  49.    wt: 9:   17C sine and cosine double triple angle formulas
  50.    wt: 9:   11 tangent function undefined when terminal side vertical
  51.    wt: 9:   12 cis formulas for sine cosines and tangent
  52.    wt: 9:   11 sine and cosine double triple angle formulas
  53.    wt: 9:   9 The complex number valued trig function cis
  54.    wt: 9:   7 Second Way to Calculate Products
  55.    wt: 9:   1 Rectangular Polar Coordinates Review
  56.    wt: 9:   5 Trigonometric Ratios For Tangent and Special Triangles
  57.    wt: 9:   11 Triangle Similarity Missing Side Problem
  58.    wt: 9:   9 Midpoint Coordinates Half Endpoint Sum
  59.    wt: 9:   7 Exercises to test skill and concept mastery
  60.    wt: 9:   2 point slope equation for a line
  61.    wt: 9:   19 Right Triangle Similarity
  62.    wt: 9:   8 Isoceles Triangles
  63.    wt: 9:   7 Angle Side Angle
  64.    wt: 9:   1 Initial Concepts and Terms
  65.    wt: 9:   18 Geometrically Why Vector Addition Commutes
  66.    wt: 9:   17 Arrows Rotate to Reverse with Length Unchanged
  67.    wt: 9:   11 Signed Number Addition and Addition Properties
  68.    wt: 9:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  69.    wt: 9:   4 Location of Point in Decimal Addition
  70.    wt: 9:   2 Counting Digits in Decimal Multiplication
  71.    wt: 9:   E Long Division Methods more
  72.    wt: 9:   D Long Division Methods
  73.    wt: 9:   16 Real Numbers Comparison
  74.    wt: 9:   14 Real Number Multiplication
  75.    wt: 9:   12 Real Number Additive Inverses or Negatives
  76.    wt: 9:   7 Real Numbers as Line Cordinates
  77.    wt: 9:   4 A Brief Story of numbers and algebra
  78.    wt: 9:   5 Common Divisors 60 45 via Prime
  79.    wt: 9:   7 Converting or Changing Units
  80.    wt: 9:   4 Fractions with Units
  81.    wt: 9:   B Fractions and Two Term Ratios
  82.    wt: 9:   21 Reciprocals for Fractions and Wholes
  83.    wt: 9:   12 Fraction Comparison
  84.    wt: 9:   9 Improper Fractions and Mixed Numbers
  85.    wt: 9:   5 Equivalent Fractions
  86.    wt: 9:   4 Fraction Multiplication
  87.    wt: 9:   A Associative Law Theorectical Note
  88.    wt: 9:   6 Multiplication by Natural Numbers
  89.    wt: 9:   12 LCD GCD and LCM using Primes
  90.    wt: 9:   2 Prime and Composites less than 16
  91.    wt: 9:   8 Correcting the Mistake
  92.    wt: 9:   5 Long Division Include Zeroes or not
  93.    wt: 9:   2 Division with Single Digit Divisors
  94.    wt: 9:   1 Divsion Physical Examples
  95.    wt: 9:   8 Review Lesson 1 2 4 and 6 All in One
  96.    wt: 9:   Formula Evaluation how to show work
  97.    wt: 9:   Practical Methods Ends and Values for Arithmetic
  98.    wt: 9:   015 School and work day counting tables
  99.    wt: 9:   014 Counting Days with Calendars
  100.    wt: 9:   012 Division of Time Intervals by Time Intervals
  101.    wt: 9:   011 Division of Time Intervals By Numbers
  102.    wt: 9:   010 Repeated Addition of Time Intervals
  103.    wt: 9:   4 Mixing and Changing Units of Time
  104.    wt: 9:   3 Units and Lengths of Time
  105.    wt: 9:   A Related Material in Volume 3
  106.    wt: 9:   A Related lessons in Volume 3
  107.    wt: 9:   1 Two cubic sketching exercises with 1st derivative
  108.    wt: 9:   21 Chain Rule for powers
  109.    wt: 9:   14 sine and cosine derivatives 2nd step
  110.    wt: 9:   11 Quotient rule
  111.    wt: 9:   10 Power rule for negative integers
  112.    wt: 9:   9 Reciprocal rule
  113.    wt: 9:   4 Sum Rule
  114.    wt: 9:   2 Motivation for Limit Definition Take 1
  115.    wt: 9:   8 Four Animated Examples
  116.    wt: 9:   1 Numerical introduction
  117.    wt: 9:   G.2 Lipshitz Conditions Integration Calculus Reform
  118.    wt: 9:   G.3 Constant Difference Theorem Proof
  119.    wt: 9:   E2 Algebraic Properties of Limits
  120.    wt: 9:   D1 Sets and Sequences GLBs and LGBs
  121.    wt: 9:   C Triangle Inequalities
  122.    wt: 9:   A1. Introduction
  123.    wt: 9:   Chapter 5. Slope Sign Tests
  124.    wt: 9:   Appendix E. How To Study Mathematics and Why
  125.    wt: 9:   Chapter 25. Mathematical Induction Examples
  126.    wt: 9:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  127.    wt: 9:   Postscript Unifying Theme A Fourth Skill For Algebra
  128.    wt: 9:   Chapter 10 Describing and Changing Calculations
  129.    wt: 9:   Chapter 6 Change of Language
  130.    wt: 9:   Chapter 5 Islands and Divisions of Knowledge
  131.    wt: 9:   Chapter 3 Chains of Reason
  132.    wt: 9:   Postscript A Three Remarks
  133.    wt: 9:   Chapter 12 Four Phases
  134.    wt: 9:   Chapter 11 Elementary Instruction
  135.    wt: 9:   Chapter 7 Two Treatments of Geometry
  136.    wt: 9:   Chapter 1 Introduction
  137.    wt: 9:   Postscript D Reflections on Law of the Excluded Middle
  138.    wt: 9:   Chapter 24 Direct and Indirect Reason
  139.    wt: 9:   Chapter 21 Occurrence Tables
  140.    wt: 9:   Chapter 1 Introduction
  141.    wt: 9:   V Reasons and Motivations for Logic and Mathematics
  142.    wt: 9:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  143.    wt: 8:   three goals to set for students
  144.    wt: 8:   activities for students
  145.    wt: 8:   site eurekas
  146.    wt: 8:   teacher certification
  147.    wt: 8:   teaching tips
  148.    wt: 8:   What to Tell Students
  149.    wt: 8:   formal or informal peer review
  150.    wt: 8:   Theory of Knowledge
  151.    wt: 8:   cultivating intelligence
  152.    wt: 8:   How to be a better instructor
  153.    wt: 8:   Motivation and Context Problem
  154.    wt: 8:   chapitre 04 07 RepetablesEtReproductibles
  155.    wt: 8:   chapitre 01 00 Introduction
  156.    wt: 8:   2 Conductance Resistance Duality02
  157.    wt: 8:   1 Conductance Resistance Duality01
  158.    wt: 8:   E Wire Resistance Calculation03
  159.    wt: 8:   27 Graduated Correction and Penalties for Young Offenders
  160.    wt: 8:   23 Modularized Skill Development Modularized Rigor Take IV
  161.    wt: 8:   23 Modularized Skill Development Modularized Rigor Take III
  162.    wt: 8:   23 Modularized Skill Development Modularized Rigor Take II
  163.    wt: 8:   Ages 12 to 14 Skills with take home value
  164.    wt: 8:   22 Square Root function graphically
  165.    wt: 8:   15 Sign analysis of functions
  166.    wt: 8:   4 Function notation in and beyond mathematics
  167.    wt: 8:   1 Geometric Introduction of Function Notation
  168.    wt: 8:   5 Polynomials Long division Nonlinear divisor
  169.    wt: 8:   4 Polynomials Long division linear divisor
  170.    wt: 8:   1 Polynomials Distributive Law
  171.    wt: 8:   12 motivation for term arctan
  172.    wt: 8:   9 motivation for name arcsin
  173.    wt: 8:   8 arcsin left inverse of sine Graph
  174.    wt: 8:   3 Left Inverse of cosine arccos definition
  175.    wt: 8:   9 Head to Tail Coordinate View
  176.    wt: 8:   Vector and Complex Number Applet
  177.    wt: 8:   28 Expressing products of sines cosines as sums
  178.    wt: 8:   23 sine and cosine of 180 plus 22.5 degrees
  179.    wt: 8:   19 Pythagorean Identity For sine and cosine functions
  180.    wt: 8:   17E Trig Formulas for dot and cross Products
  181.    wt: 8:   16 Right Triangle Complementary Angle Relations
  182.    wt: 8:   15 sine cosine Complementary Angle Relations
  183.    wt: 8:   14 cosine even and sine and tangent are odd
  184.    wt: 8:   12 Graph of tangent function for one period
  185.    wt: 8:   10 Graphs of sines and cosines many periods
  186.    wt: 8:   6 sines and cosines for reference angle 30 degrees
  187.    wt: 8:   2 Quadrant I reference Angles
  188.    wt: 8:   Appetizer A Complex Number Applet
  189.    wt: 8:   6 Trigonometry Sines of Supplementary Angles
  190.    wt: 8:   12 Triangles Similarity More Problems
  191.    wt: 8:   4 Similarity Definition with Coordinate
  192.    wt: 8:   Four Simple Exercises
  193.    wt: 8:   8 Mid Point Formula
  194.    wt: 8:   6 Intersection of lines by solving linear systems
  195.    wt: 8:   4 Equations for lines three forms
  196.    wt: 8:   5 Side Angle Side
  197.    wt: 8:   2 Correspondence between Triangles
  198.    wt: 8:   A Signed Number Arithmetic Review
  199.    wt: 8:   24 Signed Numbers Arithmmetic Properties
  200.    wt: 8:   16 Collinear Horizontal Arrows Vectors
  201.    wt: 8:   12 Real Numbers Line Signed Coordinates
  202.    wt: 8:   9 Division with Digits after Decimal Point
  203.    wt: 8:   7 Arithmetic with Infinite Decimal Expansions
  204.    wt: 8:   5 Fractions with Infinite Decimal Expansions
  205.    wt: 8:   1 Fractions with Finite Decimal Expansions
  206.    wt: 8:   15 Real Number Division
  207.    wt: 8:   11 Real Number Addition
  208.    wt: 8:   10 Real Number Lengths and Signs
  209.    wt: 8:   6 Unsigned Real Numbers
  210.    wt: 8:   5 Rational Numbers More
  211.    wt: 8:   4 Rational Numbers
  212.    wt: 8:   More Exercises
  213.    wt: 8:   Simple Exercises
  214.    wt: 8:   7 Cautious or Safe Set Construction
  215.    wt: 8:   6 Three Notions of What is a Variable
  216.    wt: 8:   12 GCD 2700 288 via Prime
  217.    wt: 8:   9 subtracting signed numbers
  218.    wt: 8:   7 negative and additive inverse
  219.    wt: 8:   5 lengths and signs of numbers
  220.    wt: 8:   22 Complex Compound Fractions
  221.    wt: 8:   20 Dividing Fractions the Why
  222.    wt: 8:   18 Efficient Ways to Multiply
  223.    wt: 8:   D Remainders Modulo 11 Pair Rule
  224.    wt: 8:   13 Subtraction with Additive Inverse
  225.    wt: 8:   11 Adding Integers Formulas and Examples
  226.    wt: 8:   4 Division with 2 Digit Divsors
  227.    wt: 8:   Expression Evaluation how to show work
  228.    wt: 8:   013 Travel Time Tables
  229.    wt: 8:   7 Addition of Time Intervals
  230.    wt: 8:   2 Time and Date Matters in School
  231.    wt: 8:   1 Intro of Kids To Time Date Skills
  232.    wt: 8:   5 Area Under Curve Exercise
  233.    wt: 8:   4 Definite Integrals Evaluation Exercises
  234.    wt: 8:   4 Second derivative test exercise example
  235.    wt: 8:   2 Second derivative test prequel
  236.    wt: 8:   6 Continuity at a point
  237.    wt: 8:   4 Numerical properties
  238.    wt: 8:   3 Decimal insights for limits continuity convergence
  239.    wt: 8:   2 Algebraic codification
  240.    wt: 8:   G.1 Differentiable Functions Rolles Theorem
  241.    wt: 8:   F.5b Extreme Value Theorem
  242.    wt: 8:   E1 Error Control Inequalities
  243.    wt: 8:   D2 Limits of Monotone Sequences
  244.    wt: 8:   Foreword
  245.    wt: 8:   Appendix A. Reading Guide For Next Appendices
  246.    wt: 8:   Chapter 31 Direct and Indirect Reason
  247.    wt: 8:   Chapter 30 Truth Tables
  248.    wt: 8:   Chapter 26 What is in chapters 27 to 31
  249.    wt: 8:   Chapter 23. Notation For Sums
  250.    wt: 8:   Chapter 13. Second Reading Guide
  251.    wt: 8:   Chapter 12. Shorthand Usage Guide
  252.    wt: 8:   Chapter 10 Transition
  253.    wt: 8:   Chapter 8 Modern Instruction
  254.    wt: 8:   Chapter 5 Four References
  255.    wt: 8:   Postscript B More on Story Telling and Reason
  256.    wt: 8:   Chapter 18 Sense and Knowledge
  257.    wt: 8:   P Exact Arithmetic With Whole Numbers and Fractions
  258.    wt: 8:   D. Check work a must with a caution
  259.    wt: 8:   Mathematics Education References
  260.    wt: 8:   Mathematics Education References
  261.    wt: 8:   Ends Values Methods For Skill Development Framework Prequel
  262.    wt: 8:   Multiple Ways to Improve Mathematics Skill Development
  263.    wt: 7:   why bother
  264.    wt: 7:   which way to go
  265.    wt: 7:   key notes and themes
  266.    wt: 7:   Postscript 2007 01 10
  267.    wt: 7:   three difficulties
  268.    wt: 7:   02 21 words for teachers
  269.    wt: 7:   chapitre 12 00 les iles et division
  270.    wt: 7:   chapitre 04 09 Regles accidentelles
  271.    wt: 7:   chapitre 04 08 Limitations et benefices
  272.    wt: 7:   chapitre 04 06 engagements
  273.    wt: 7:   chapitre 04 02 Deuxieme enigme
  274.    wt: 7:   chapitre 04 00 Les regles d implication
  275.    wt: 7:   Trois Notions qui menent a algebre
  276.    wt: 7:   F Wire Resistance Calculation04
  277.    wt: 7:   D Wire Resistance Calculation02
  278.    wt: 7:   C Wire Resistance Calculation01
  279.    wt: 7:   B Wire Resistance Qualitative02
  280.    wt: 7:   25 Mathematics Education Leaving A Good Impression
  281.    wt: 7:   23 Modularized Skill Development Modularized Rigor
  282.    wt: 7:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  283.    wt: 7:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  284.    wt: 7:   13 Addition and Addition Tables
  285.    wt: 7:   5 Patience Please for Yourself and Your Charges
  286.    wt: 7:   Ages 4 plus to 5 plus
  287.    wt: 7:   21 Graphs of functions given by Horizontal Line Method
  288.    wt: 7:   8 Set view of relations and functions
  289.    wt: 7:   6 Set Existence Formation and Notation
  290.    wt: 7:   5 Function notation for geometric transformations
  291.    wt: 7:   Introduction Reading Guide
  292.    wt: 7:   2 Column Multiplication Method
  293.    wt: 7:   7 arcsin left inverse of sine Definition
  294.    wt: 7:   4 possible motivation for term arccos
  295.    wt: 7:   15 Dot and Cross Product
  296.    wt: 7:   13 Velocity Vectors in Physics
  297.    wt: 7:   8 Parallel Vectors
  298.    wt: 7:   1 Unsigned Coordinates
  299.    wt: 7:   9 Graphs of sine and cosine over one period
  300.    wt: 7:   8 period of tangent function
  301.    wt: 7:   3 sines and cosines for reference angle 90 degrees
  302.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  303.    wt: 7:   21 Logarithms Powers and Exponentials
  304.    wt: 7:   17 Cube Roots of unity
  305.    wt: 7:   16 References and Originality Question
  306.    wt: 7:   3 Addition Properties
  307.    wt: 7:   2 Complex Numbers made easier we hope
  308.    wt: 7:   8 Triangles Cascade Problem Solving
  309.    wt: 7:   4 Trigonometric Ratios For Two Special Triangles
  310.    wt: 7:   3 Trigonometric Ratios sine and cosine
  311.    wt: 7:   1 Angle Measurement with Degrees
  312.    wt: 7:   Why Trigonometry the whyslopes view
  313.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  314.    wt: 7:   2 Similarity By Design
  315.    wt: 7:   4 Side Side Side
  316.    wt: 7:   19 Signed Multiples of Vectors
  317.    wt: 7:   6 Infinite Decimals Ending in 9 repeating
  318.    wt: 7:   9 Coordinates for Regions in Space
  319.    wt: 7:   3 Fractions
  320.    wt: 7:   9 Sets in Probability and Statistics
  321.    wt: 7:   2 What is a Variable
  322.    wt: 7:   arithmetic videos Real Player Format
  323.    wt: 7:   6 GCD from Prime
  324.    wt: 7:   8 multiplying signed numbers
  325.    wt: 7:   6 adding signed numbers
  326.    wt: 7:   4 signed coordinates for regions in space
  327.    wt: 7:   D Three Term Ratios
  328.    wt: 7:   19 Dividing Fractions How TO
  329.    wt: 7:   10 Integer Multiplication Formulas
  330.    wt: 7:   3 Adding Movements with same direction
  331.    wt: 7:   2 Integers Multiplies of a Unit Moverment
  332.    wt: 7:   Exact Arithmetic Wholes and Fractions
  333.    wt: 7:   The 12 Times Table Visually
  334.    wt: 7:   6 How long is a million seconds
  335.    wt: 7:   3 Two Chain Rule Method Exercises
  336.    wt: 7:   3 Second derivative test
  337.    wt: 7:   11 Limits at infinity Three Examples
  338.    wt: 7:   10 Three one sided limits with infinite values
  339.    wt: 7:   9 Limits Continuity and Composition
  340.    wt: 7:   G.5 Motions With Bounded Velocities
  341.    wt: 7:   F.2 Closed Range Theorem
  342.    wt: 7:   B1 Pigeon Hole Principles from combinatorics
  343.    wt: 7:   Appendix D. What to do in School and Why
  344.    wt: 7:   Chapter 27 Shorthand Symbols as Pronouns
  345.    wt: 7:   Chapter 22. Geometric Sums and Sequences
  346.    wt: 7:   Chapter 20. Degrees and Radians
  347.    wt: 7:   Chapter 18. Rules for Algebra
  348.    wt: 7:   Chapter 15. Solving Linear Equations
  349.    wt: 7:   Postscript What is a Variable
  350.    wt: 7:   Chapter 7 Prep for Calculus Arithmetic Exercises
  351.    wt: 7:   Chapter 4 Longer Chains of Reason
  352.    wt: 7:   Chapter 1 Introduction to Chapters 2 to 6
  353.    wt: 7:   Chapter 9 The Two Ends
  354.    wt: 7:   Postscript A Story Telling
  355.    wt: 7:   Chapter 15 Objective Processes
  356.    wt: 7:   Chapter 10 Responsibility
  357.    wt: 7:   Chapter 5 Deception
  358.    wt: 7:   Chapter 2 Skill Development
  359.    wt: 7:   Three Remarks
  360.    wt: 7:   R Why Learn Mathematics Skills
  361.    wt: 7:   O On Learning Mathematics and Science
  362.    wt: 7:   N Mathematics Prepare for College Studies
  363.    wt: 7:   I. Logic and language skills
  364.    wt: 7:   F. The student teacher tutor feedback loop
  365.    wt: 7:   C. Domino effect of being careful
  366.    wt: 7:   Helping the Blind in Logic and Mathematics
  367.    wt: 6:   website reviews
  368.    wt: 6:   site origins
  369.    wt: 6:   chapitre 05 00 Deception
  370.    wt: 6:   chapitre 04 01 Premiere enigme
  371.    wt: 6:   problemes algebre et arithmetique
  372.    wt: 6:   deux definitions pour variable
  373.    wt: 6:   3 Like resistors in parallel
  374.    wt: 6:   2 Unlike resistors in parallel01
  375.    wt: 6:   6 Discipline Who is in Charge Conserving Authority
  376.    wt: 6:   Ages 12 to 14 Arithmetic
  377.    wt: 6:   Ages 10 to 12 Arithmetic
  378.    wt: 6:   23 Inverse Functions
  379.    wt: 6:   20 Interchanging coordinates a reflection
  380.    wt: 6:   19 Horizontal line rule and method
  381.    wt: 6:   18 Vertical Line Rule and Method
  382.    wt: 6:   16 Increasing or decreasing on intervals
  383.    wt: 6:   13 From one to one to many to one
  384.    wt: 6:   12 Function Domain Recognition Exercises
  385.    wt: 6:   8 Notes for instructors or tutors
  386.    wt: 6:   2 cosine function more properties
  387.    wt: 6:   1 cosine function properties
  388.    wt: 6:   6 Vectors with Coordinates
  389.    wt: 6:   2 Signed Coordinates
  390.    wt: 6:   17G Pythagorean Theorem Converse
  391.    wt: 6:   17F Law of cosines
  392.    wt: 6:   7 period of sine and cosine
  393.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  394.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  395.    wt: 6:   1 Unit Points Reflections Rotations
  396.    wt: 6:   Unit Circle Development of Trigonometry
  397.    wt: 6:   20 N th Roots of Complex Numbers
  398.    wt: 6:   19 N th Roots of Unity
  399.    wt: 6:   18 Sixth Roots of Unity
  400.    wt: 6:   15 Pythagorean Theorem Converse
  401.    wt: 6:   14 Law of cosines
  402.    wt: 6:   8 Unit Circle Development of Trigonometry
  403.    wt: 6:   6 Field Properties of Complex Number
  404.    wt: 6:   4 Multiplication Properties
  405.    wt: 6:   7 Trignometric Ratios Unit Circle
  406.    wt: 6:   12 Links Lessons elsewhere
  407.    wt: 6:   5 Product Builder Notation
  408.    wt: 6:   4 Subset Builder Notation
  409.    wt: 6:   3 Counting with Sets etc
  410.    wt: 6:   3 Adding Words To Arithmetic
  411.    wt: 6:   10 dividing signed numbers
  412.    wt: 6:   21 Working With Signs
  413.    wt: 6:   8 Multiplication by Signed Numbers Integers
  414.    wt: 6:   5 Conversion Arithmetic
  415.    wt: 6:   1 Chain Rule in Reverse Integration Method
  416.    wt: 6:   F.4 Finite Covering Theorem
  417.    wt: 6:   Appendix C. How to Read
  418.    wt: 6:   Chapter 28 Occurrence Tables
  419.    wt: 6:   Chapter 24. Personal Investment and Pension EGS
  420.    wt: 6:   Chapter 21. Third Reading Guide
  421.    wt: 6:   Chapter 19. Functions and Sets
  422.    wt: 6:   Chapter 11. Why Shorthand
  423.    wt: 6:   Chapter 8 Three Skills For Algebra
  424.    wt: 6:   Solutions For Arithmetic Exercises
  425.    wt: 6:   Foreword
  426.    wt: 6:   Foreword
  427.    wt: 6:   S Adding words to algebra
  428.    wt: 6:   Q How Logic and Proofs extend Show Work Practices
  429.    wt: 6:   L Skills with take home value
  430.    wt: 6:   N Improving Marks on Tests and Finals
  431.    wt: 6:   H Jigsaw puzzles and problem solving
  432.    wt: 6:   Implementation Notes
  433.    wt: 5:   logique deux enigme
  434.    wt: 5:   B Electromotive force conventional current01
  435.    wt: 5:   19 Extending the Oral Dimension of Mathematics
  436.    wt: 5:   17 Math Booklets for children and young teenagers
  437.    wt: 5:   16 Secondary Mathematics Tips
  438.    wt: 5:   14 Multiplication and Times Tables
  439.    wt: 5:   12 Goals and Objectives For Mathematics
  440.    wt: 5:   11 Help and Defend Your Child or Teens Education
  441.    wt: 5:   10 Ends values for work study instruction
  442.    wt: 5:   3 Preparing for Science Studies
  443.    wt: 5:   Ages 12 to 14 Geometry
  444.    wt: 5:   Ages 10 to 12 Geometry
  445.    wt: 5:   Ages 9 to 10
  446.    wt: 5:   Ages 8 to 9
  447.    wt: 5:   Ages 7 to 8
  448.    wt: 5:   Ages 6 to 7
  449.    wt: 5:   26 Function definitions done and coming
  450.    wt: 5:   24 Monotoncity Injectivity and Inverse Functions
  451.    wt: 5:   10 Interval Notation
  452.    wt: 5:   7 Functions with finite domains
  453.    wt: 5:   11 Component Method
  454.    wt: 5:   About Folder Contents
  455.    wt: 5:   2 Integers
  456.    wt: 5:   10 Set View of Wordy Extensions To Arithmetic
  457.    wt: 5:   8 Sets of Numbers
  458.    wt: 5:   2 Venn Diagrams
  459.    wt: 5:   1 Three Skills For Algebra
  460.    wt: 5:   About Folder Contents
  461.    wt: 5:   B Integer Long Division Multiple Choices
  462.    wt: 5:   12 Adding Integers More Examples
  463.    wt: 5:   7 Multiplication by Signs
  464.    wt: 5:   5 Zero Movement and Additive Inverses
  465.    wt: 5:   1 Integers as Coordinates
  466.    wt: 5:   About folder contents
  467.    wt: 5:   2 Indefinite Integrals Exercises
  468.    wt: 5:   Appendix B. How To Learn
  469.    wt: 5:   Chapter 16. Painless Theorem Proving
  470.    wt: 5:   1 Links to Online Resources Elsewhere Take 1
  471.    wt: 5:   M Words to extend arithmetic
  472.    wt: 5:   H more Routine to non routine problem solving
  473.    wt: 5:   G. Written work formats for developing and showing skill
  474.    wt: 5:   A. Skill has to be seen to believed
  475.    wt: 5:   How to Build Skills and Confidence
  476.    wt: 5:   Which Way To Go
  477.    wt: 4:   liens
  478.    wt: 4:   3 Energy Power Heat08
  479.    wt: 4:   C Energy Power03
  480.    wt: 4:   F Unlike Resistors in Series
  481.    wt: 4:   E Kirchoffs Second Law
  482.    wt: 4:   D Kirchoff First Law
  483.    wt: 4:   C Electromotive force conventional current02
  484.    wt: 4:   A Circuit Elements
  485.    wt: 4:   24 Standards For Skill Develoment Take II
  486.    wt: 4:   22 Student Centered Highschool Mathematics
  487.    wt: 4:   18 Primary School Mathematics
  488.    wt: 4:   9 Streaming by Student Cooperation
  489.    wt: 4:   8 The Effect of Negative Remarks
  490.    wt: 4:   4 Learning Takes Time and Effort
  491.    wt: 4:   14 Surjections Injections Bijections
  492.    wt: 4:   9 Set theory term relation possible origins
  493.    wt: 4:   7 Links Lessons Elsewhere
  494.    wt: 4:   6 Power Set Notation
  495.    wt: 4:   C Divisibility by 11 Integer Recognition Method
  496.    wt: 4:   9 Multiplying Integers
  497.    wt: 4:   4 Adding Movements wiht opposite directions
  498.    wt: 4:   The 20 Times Table
  499.    wt: 4:   Postscript More on Better Performance
  500.    wt: 4:   Postscript For Better Performance
  501.    wt: 4:   J. More on written work and showing skill
  502.    wt: 4:   E. When and how to correct errors
  503.    wt: 4:   B. Domino effect of errors
  504.    wt: 4:   Talking pdf files for online lessons a webvideo alternative
  505.    wt: 3:   problemes responses
  506.    wt: 3:   4 Energy Power Heat09
  507.    wt: 3:   2 Energy Power Heat07
  508.    wt: 3:   1 Energy Power Heat06
  509.    wt: 3:   A Energy Power01
  510.    wt: 3:   1 Like resistors in series
  511.    wt: 3:   H Series Circuit02
  512.    wt: 3:   G Series Circuit01
  513.    wt: 3:   Home Tutoring and Home Schooling
  514.    wt: 3:   24 Standards For Skill Develoment
  515.    wt: 3:   15 Counting For Parents
  516.    wt: 3:   7 Student Motivation
  517.    wt: 3:   2 Reading and Writing Skills
  518.    wt: 3:   1 Finite Sets
  519.    wt: 3:   Foreword
  520.    wt: 3:   Road Safety Questions
  521.    wt: 3:   The Math Forum and Site Content
  522.    wt: 2:   E Energy Power05
  523.    wt: 2:   D Energy Power04
  524.    wt: 2:   B Energy Power02
  525.    wt: 2:   1 Speaking Skills
  526.    wt: 20:   13 Pythagorean spatial distance formulas
  527.    wt: 20:   3 Gaussian Elimination 3 unknowns first example
  528.    wt: 19:   8 quadratics backward use of various formulas
  529.    wt: 19:   3 GE III Equation Addition and Multiplication
  530.    wt: 18:   5 Gaussian Elimination for 3 unknowns 2nd example
  531.    wt: 18:   3 Harder Cases Convert to Compare and Subtract
  532.    wt: 17:   C LAMP Introduction Culture in Mathematics Education
  533.    wt: 17:   2 Radian Measure Numerical Value of one degree
  534.    wt: 17:   10 Pythagorean plane distance formula
  535.    wt: 17:   3 Solving triangular system example
  536.    wt: 17:   6 Pythagorean Hypotenuse Calculation Example
  537.    wt: 17:   3 Triangle Area Formula Example
  538.    wt: 17:   2 Another Rectangle Area Formula Example
  539.    wt: 17:   1 Comparison and Subtraction Easy Direct Cases
  540.    wt: 17:   3 More on Groups of 3 Multi Digit Place Value
  541.    wt: 16:   B LAMP Introduction Curriculum Development Standards
  542.    wt: 16:   3 Natural Logarithms and Exponentials Basic Properties
  543.    wt: 16:   Parallel Lines and Parallel Transversals
  544.    wt: 16:   Parallel Lines and Alternating Corresponding Angles
  545.    wt: 16:   5 Cartesian Addition and Translation
  546.    wt: 16:   3 Rectangular Coordinates Review
  547.    wt: 16:   3 Lengths and Areas on Maps and Plans
  548.    wt: 16:   2 More and Less Than for Counts and Measures
  549.    wt: 16:   4 Solving a triangular system exercise
  550.    wt: 16:   5 Algebraic Solutions Introduction
  551.    wt: 16:   8 Compound Interest Formula Evaluation
  552.    wt: 16:   3 Comparison of Negative Numbers
  553.    wt: 16:   1 Squares and Square Roots Introduction
  554.    wt: 16:   8 Subtraction with Units of Measure
  555.    wt: 16:   6. Counting and adding units and mixed units
  556.    wt: 16:   3. How to add with decimals A sans conversions
  557.    wt: 16:   9 Place Value Review Decimal form of Avogrados number included
  558.    wt: 16:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  559.    wt: 16:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  560.    wt: 16:   5 More on Groups of 3 Place Value in Decimal Fractions
  561.    wt: 16:   4 Groups of 3 Place Value in Decimal Fractions
  562.    wt: 16:   Example 1. Area Between x and x squared
  563.    wt: 16:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  564.    wt: 15:   Ramblings Introduction Algebra Essay
  565.    wt: 15:   6 quadratics numerical approach
  566.    wt: 15:   5 Natural Logarithm Calculator Exercises
  567.    wt: 15:   14 Why Scalar Multiplication Distributes Physical Argument
  568.    wt: 15:   Proportionality of Line Segments From Parallel Transversals
  569.    wt: 15:   3 Straight Lines Slope as Tangent of Inclination Angle
  570.    wt: 15:   9 Pythagorean Theorem Chinese Square Proof
  571.    wt: 15:   6 Polar Multiplication and Rotation
  572.    wt: 15:   PS F Scalar Multiplication Distributes over Addition
  573.    wt: 15:   4 Comparison of Negative Numbers
  574.    wt: 15:   3 Geometric Formulas and Function Notation
  575.    wt: 15:   2 Computation Rules Evaluation
  576.    wt: 15:   1 GE Substitution four examples
  577.    wt: 15:   6 Algebraic Solution Example
  578.    wt: 15:   4 Four Examples Fractional Coefficients
  579.    wt: 15:   3 Four Examples
  580.    wt: 15:   1 Proper Equal Sign Usage
  581.    wt: 15:   7 Compound Interest Formula Introduction
  582.    wt: 15:   4 Circle Area Formula Example
  583.    wt: 15:   1 More and Less Than for Counts and Measures
  584.    wt: 15:   A Decimals Modular and Remainder Arithmetic
  585.    wt: 15:   7 Calculator Usage Notes and Cautions
  586.    wt: 15:   Long Division forwards and backwards Example 3
  587.    wt: 15:   A Elementary Basis for Multiplication Methods
  588.    wt: 15:   Video Decimal Multiplication Geometric View Example 2
  589.    wt: 15:   Appendix 1 Decimals Comparison Method Take II
  590.    wt: 15:   Subtraction Another Video Lesson
  591.    wt: 15:   7 Subtraction for Decimal Fractions with Exercises
  592.    wt: 15:   2 Subtraction Easy Case Examples
  593.    wt: 15:   Appendix 1 Counting Revisited 15 minute video
  594.    wt: 15:   7 Adding decimal fractions using decimal point
  595.    wt: 15:   11 Place Value SI Standard International way
  596.    wt: 15:   2 Groups of Three Place Value for Multidigit Decimals
  597.    wt: 15:   Example 1 volume of a pyramid
  598.    wt: 15:   Chapter 19. Exponentials and Natural Logarithms
  599.    wt: 15:   Chapter 15. Algebraic Evaluation of Limits
  600.    wt: 15:   Primary and Secondary Skills and Practices with Take Home Value
  601.    wt: 14:   sign monoticity analysis example 3
  602.    wt: 14:   A Quadratics Summary
  603.    wt: 14:   9 quadratics physical and further context
  604.    wt: 14:   7 quadratic formulla derivation
  605.    wt: 14:   4 quadratics difference of two squares
  606.    wt: 14:   9 Summary Degrees to Radians and back
  607.    wt: 14:   8 Radian Measures of Common Angles
  608.    wt: 14:   7 Radian Measures in special Triangles
  609.    wt: 14:   3 Circle Arclengh Proportional to Central Angle
  610.    wt: 14:   Construction Methods and Criteria for Isometric and Similar Triangles
  611.    wt: 14:   14 Straight Lines Equations General Case
  612.    wt: 14:   34 sines and cosines of 2A 3A 4A 5A
  613.    wt: 14:   33 sines and cosines of 2A 3A 4A 5A
  614.    wt: 14:   13 Navigation Location from Angles to 2 Landmarks
  615.    wt: 14:   1 Cartesian Coordinates sans signs
  616.    wt: 14:   8 More Use of Maps Not Drawn to Scale
  617.    wt: 14:   4 Angles on Maps Plans drawn to scale
  618.    wt: 14:   B Decimal Comparison and Subtraction
  619.    wt: 14:   4 Commutative Law Groups Counting Form
  620.    wt: 14:   3 Inequalities Algebraically
  621.    wt: 14:   1 Decimals Modular and Remainder Arithmetic
  622.    wt: 14:   9 Circle Area and Perimeter Formula Backwards Forwards
  623.    wt: 14:   4 Rectangle Area and Like Formulas Backwards
  624.    wt: 14:   6 Equations and Systems Equivalent or Implied
  625.    wt: 14:   4 Subtraction and Division Axioms
  626.    wt: 14:   2 Addition and Multiplication Axioms
  627.    wt: 14:   1 Equivalent Computation Rules
  628.    wt: 14:   3 More and Less Than with Unlike Signs
  629.    wt: 14:   1 Real Numbers Comparison
  630.    wt: 14:   1 Formulas Dependence and Function Notation
  631.    wt: 14:   4 GE III Animated Examples
  632.    wt: 14:   2 Essentially one exercises three with solution
  633.    wt: 14:   3 Two Examples
  634.    wt: 14:   13 Naming Identifying Formulas with Words
  635.    wt: 14:   5 Box Volume Formula Example
  636.    wt: 14:   3 Properties of Square Roots with example
  637.    wt: 14:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  638.    wt: 14:   9 GCD of 360 110 via Primes and Euclid Algorithm
  639.    wt: 14:   8 Numerals Fractionals Quantals Take II
  640.    wt: 14:   19 Remainder Arithmetic Rule of 9 for checking sums III
  641.    wt: 14:   13 Remainder Arithmetic Modulo 5 Example
  642.    wt: 14:   10 video Prime Factorization upto 23 squared
  643.    wt: 14:   5 Prime Factorization and a Square Rule
  644.    wt: 14:   Long Division forwards and backwards Example 2
  645.    wt: 14:   Long Division forwards and backwards Example 1
  646.    wt: 14:   Video Decimal Multiplication Geometric View Example 2
  647.    wt: 14:   Appendix 2 Three Decimal Subtraction Methods
  648.    wt: 14:   Subtraction with J Conversions Example
  649.    wt: 14:   6 Subtraction with Conversion Example with Exercises
  650.    wt: 14:   8 What skills and work habits to require
  651.    wt: 14:   Example 2 volume of a cone
  652.    wt: 14:   Area Between Crossing Curves Lesson Take 2
  653.    wt: 14:   Area Between Crossing Curves Lesson Take 1
  654.    wt: 14:   Example 4 with x function of y
  655.    wt: 14:   Area Between Curves Lesson Take 2
  656.    wt: 14:   Area Between Curves Lesson Take 1
  657.    wt: 14:   33 Chain Rule Real Player video examples
  658.    wt: 14:   Chapter 14 Limits and Continuity with and sans Decimals
  659.    wt: 14:   Chapter 3. Slope Sign Analysis
  660.    wt: 14:   Chapter 22 Contrapositive and Vacuously True Implications
  661.    wt: 14:   Chapter 3 Algebra Starter Lessons
  662.    wt: 14:   6 Measuring via counting or arithmetic the role of fractions
  663.    wt: 14:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  664.    wt: 13:   Appendix 1 primary and preschool mathematic
  665.    wt: 13:   I LAMP Introduction Study Habits
  666.    wt: 13:   H LAMP Introduction Instructional Concepts
  667.    wt: 13:   F LAMP Introduction Prerequisites
  668.    wt: 13:   E LAMP Introduction Modern Mathematics
  669.    wt: 13:   Skills Chapter 3 Algebra
  670.    wt: 13:   5 quadratics completing the square
  671.    wt: 13:   3 quadratics factoring by inspection
  672.    wt: 13:   2 quadratics graphing in general
  673.    wt: 13:   1 quadratics graphing exercises
  674.    wt: 13:   4 Circle Sector Area proportional to Central Angle
  675.    wt: 13:   1 Degrees and Radians Introduction
  676.    wt: 13:   2 Graphing y=Af(x) Vertical Scaling
  677.    wt: 13:   Parallel Lines and Interior Angles
  678.    wt: 13:   13 Straight Lines Finding Equations from 2 points
  679.    wt: 13:   12 Straight Lines Graphing mx plus b
  680.    wt: 13:   10 Straight Lines through Origin Equations More
  681.    wt: 13:   9 Straight Lines through Origin Equations
  682.    wt: 13:   7 Tangent Function is odd on this domain
  683.    wt: 13:   6 Tangent Function Inclination Angle Take 2
  684.    wt: 13:   2 Straight Lines Slopes As Rise Over Run
  685.    wt: 13:   35 sines and cosines of 2A 3A 4A 5A
  686.    wt: 13:   10 Similarity of Triangles Equivalent of Two Criteria
  687.    wt: 13:   9 Similarity of Triangles Usual Criteria
  688.    wt: 13:   12 Spatial Coordinates
  689.    wt: 13:   11 Triangle Inequality
  690.    wt: 13:   8 Distance Between Points on a Line
  691.    wt: 13:   4 Polar Coordinates to and from
  692.    wt: 13:   2 Cartesian Coordinates with signs
  693.    wt: 13:   13 Angle Side Angle Failure
  694.    wt: 13:   3 Isometry of Triangles Congruence
  695.    wt: 13:   A Measurement with Ruler Proper Use
  696.    wt: 13:   5 Drawing to Scale Avoids Angle Distortions
  697.    wt: 13:   3 Multiplicative Counting Skills Principles
  698.    wt: 13:   5 Areas of Rectangles Revisited
  699.    wt: 13:   5 Triangle Area Formula Backwards
  700.    wt: 13:   5 Equality in Algebra
  701.    wt: 13:   5 Greater More Less Than Signs in General
  702.    wt: 13:   2 GE II Comparison
  703.    wt: 13:   1 Essentially One Unknown
  704.    wt: 13:   10 Volume of Pyramid
  705.    wt: 13:   2 Least Common Multiple LCM intro via list method
  706.    wt: 13:   5 Counting with Tables Trees Product Rule Take II
  707.    wt: 13:   C Equality for Fractions and Two Term Ratios and Fractions
  708.    wt: 13:   7 Numerals Fractionals Quantals
  709.    wt: 13:   3 Unit fraction of a fraction
  710.    wt: 13:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  711.    wt: 13:   18 Remainder Arithmetic Rule of 9 for checking sums II
  712.    wt: 13:   17 Remainder Arithmetic Rule of 9 for checking sums I
  713.    wt: 13:   15 Remainder Arithmetic Modulo 9 Example
  714.    wt: 13:   14 Remainder Arithmetic Modulo 9 Example
  715.    wt: 13:   12 Remainder Arithmetic Modulo 10 Example
  716.    wt: 13:   11 Remainder Arithmetic Long Division by 5 Quickly more
  717.    wt: 13:   10 Remainder Arithmetic Long Division by 5 Quickly
  718.    wt: 13:   9 Remainder Arithmetic Divisibility by 5
  719.    wt: 13:   8 Remainder Arithmetic Morulo 5 Examples II
  720.    wt: 13:   7 Remainder Arithmetic Modulo 5 Examples I
  721.    wt: 13:   15 video Factors of 20 using Prime Factorization
  722.    wt: 13:   13 video Factors of 24 using prime
  723.    wt: 13:   9 video Prime Factorization upto 19 squared
  724.    wt: 13:   6 Sieve of Eratosthenes and Square Rule
  725.    wt: 13:   C Counting Areas with Powers of Ten
  726.    wt: 13:   6 Multiplication Commutes Order Not Important
  727.    wt: 13:   5 Decimal Fraction Multiplication
  728.    wt: 13:   Video Power Notation in Decimal Expansion
  729.    wt: 13:   9 22 Minute Subtraction Review Video
  730.    wt: 13:   5 A Tip for Efficent Subtraction
  731.    wt: 13:   4 Subtraction with Conversions Borrows and Letter J
  732.    wt: 13:   5. How to add decimals C. Examples
  733.    wt: 13:   2 Decimal Counting Practices
  734.    wt: 13:   1. Explaining Addition Table
  735.    wt: 13:   Example 3
  736.    wt: 13:   A Chain Rule Real Player video examples
  737.    wt: 13:   38 Formulas and derivatives for powers and roots
  738.    wt: 13:   28 Chain Rule Preparation for a Proof
  739.    wt: 13:   27 Chain Rule sinusoidal outer inner functions EGS
  740.    wt: 13:   25 Chain Rule Animated Examples Continued
  741.    wt: 13:   Chapter 18. Slopes Areas Integration
  742.    wt: 13:   Chapter 17. Area Approximation
  743.    wt: 13:   Chapter 13. Acceleration
  744.    wt: 13:   Chapter 9 About First Courses in Calculus
  745.    wt: 13:   Chapter 14. Forward and Backward Use of a Formula
  746.    wt: 13:   Chapter 16 Origins and Limitations of Rules and Patterns
  747.    wt: 13:   Chapter 14 Deductive and Empirical Views of Mathematics
  748.    wt: 13:   Chapter 4 Implication Rules Forwards and Backwards
  749.    wt: 13:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  750.    wt: 13:   5 Interpreting and Drawing Maps and Plans.
  751.    wt: 13:   4 Money Matters Saving Earning Buying Selling and Budgets
  752.    wt: 13:   3 Telling Tracking Time Temporal and More Place Sense
  753.    wt: 12:   K LAMP Musings Science Education
  754.    wt: 12:   3 Euclidean Geometry Leanly
  755.    wt: 12:   teaching tutoring algebraic reason
  756.    wt: 12:   need for a mixed mathematics curriculum
  757.    wt: 12:   Leaner mathematics curriculum
  758.    wt: 12:   chapitre 07 00 Des chaines plus longues de la raison
  759.    wt: 12:   chapitre 04 10 Etapes pour une meilleur raison
  760.    wt: 12:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  761.    wt: 12:   sign monoticity analysis example 4
  762.    wt: 12:   sign monoticity analysis example 2
  763.    wt: 12:   sign monoticity analysis example 1
  764.    wt: 12:   10 quadratic exercises
  765.    wt: 12:   Quadratics in 10 steps
  766.    wt: 12:   8 Formulas for Fractional Exponents with Logarithms
  767.    wt: 12:   2 Square Root Simplification a prequel
  768.    wt: 12:   1 Calculator Starter Exercises
  769.    wt: 12:   6 Polynomial Operations and Equivalent Computation Rules
  770.    wt: 12:   6 Radian Measure to Degrees
  771.    wt: 12:   5 Degrees to Radian Measure
  772.    wt: 12:   7 Coordinate Addition and Scalar Multiplication
  773.    wt: 12:   3 graphing y=f(x c) plus K
  774.    wt: 12:   Triangle Angles Sum To 180 Degrees
  775.    wt: 12:   SAS Method For Isometric Or Proportional Triangle Construction
  776.    wt: 12:   Analytic View of Triangle Construction or Line Instersection More
  777.    wt: 12:   8 Straight Lines Equation for vertical
  778.    wt: 12:   18 sum of sinusoidal waves as a single wave
  779.    wt: 12:   5 Similarity of Circles Squares and Rectangles
  780.    wt: 12:   1 Numerical view of lines and their equations
  781.    wt: 12:   7 Complex Numbers Appetizer
  782.    wt: 12:   PS H Distributive Law For Complex Numbers
  783.    wt: 12:   PS G Rotation Distributes over Addition
  784.    wt: 12:   PS E Multiplication with Polar Coordinates
  785.    wt: 12:   PS D Addition with Cartesian Coordinates
  786.    wt: 12:   PS B Parallelogram Construction Methods
  787.    wt: 12:   6 Ruler and compass Angle Bisection
  788.    wt: 12:   6 Figuring with Maps Not to Scale
  789.    wt: 12:   2 Measuring Area Directly
  790.    wt: 12:   8 Division and Mulplication of Compound Fractions
  791.    wt: 12:   A Decimal Addition Columm Methods
  792.    wt: 12:   8 Column Multiplication Methods in General
  793.    wt: 12:   7 Decimals Multiplication Methods Examples
  794.    wt: 12:   6 Column Methods for Decimal Multiplication
  795.    wt: 12:   5 Distributive Law for Whole Numbers
  796.    wt: 12:   4 Fraction Operations Axiomatic Development
  797.    wt: 12:   5 Proportionality in Equivalent Fractions
  798.    wt: 12:   4 Rates Ratios and Proporitionality
  799.    wt: 12:   3 Proportionality Examples
  800.    wt: 12:   8 Pythagorean Relation Forwards Backwards
  801.    wt: 12:   3 Linear Equation Literal Solution More
  802.    wt: 12:   3 Product Axioms Two Forms
  803.    wt: 12:   2 Three Examples
  804.    wt: 12:   10 One Example
  805.    wt: 12:   9 Three Examples
  806.    wt: 12:   8 One Example
  807.    wt: 12:   7 Two Examples
  808.    wt: 12:   6 Three Examples
  809.    wt: 12:   5 Three Examples
  810.    wt: 12:   4 Two Examples
  811.    wt: 12:   2 Three Examples
  812.    wt: 12:   Using Letters for Physical Quantities
  813.    wt: 12:   Formula Usage Show Work Format
  814.    wt: 12:   11 Volume of Sphere
  815.    wt: 12:   9 Volume of Cone
  816.    wt: 12:   1 Written work formats for developing and showing skill
  817.    wt: 12:   4 Greater More Less Than Signs in General
  818.    wt: 12:   2 More and Less Than with Unlike Signs
  819.    wt: 12:   14 GCD of 650 110 via Primes LCM via Product Rule
  820.    wt: 12:   1 Least Common Multiples LCM Introduction
  821.    wt: 12:   4 Counting with Trees Product Rule Take I
  822.    wt: 12:   3 Counting with Tables and Trees II
  823.    wt: 12:   5 Reciprocals and Division for Fractions with Units
  824.    wt: 12:   3 Multiplying Units and Numbers
  825.    wt: 12:   1 Addition and Subtraction with Units
  826.    wt: 12:   16 Addition Subtraction Comparision Compared
  827.    wt: 12:   15 Adding and Subtracting with Unlike Denominators
  828.    wt: 12:   13 Fraction Comparison Algebraic View
  829.    wt: 12:   10 Simplification of Fractions and Mixed Numerals
  830.    wt: 12:   6 Multiplication Algebraically Take II
  831.    wt: 12:   Fraction Operations by Raising Terms A Simple Innovation
  832.    wt: 12:   23 Remainder Arithmetic Modulo 2
  833.    wt: 12:   22 Remainder Arithmetic Modulo 3 more
  834.    wt: 12:   21 Remainder Arithmetic Modulo 3
  835.    wt: 12:   16 Remainder Arithmetic Modulo 9 Example 2
  836.    wt: 12:   6 Remainder Arithmetic Modulo 5 Propertie
  837.    wt: 12:   4 Remainder Arithmetic Modulo 10 in general
  838.    wt: 12:   3 Remainder Arithmetic Modulos 10 more still
  839.    wt: 12:   20 Uniqueness of Prime Factorization
  840.    wt: 12:   19 video Prime Factorization Unique
  841.    wt: 12:   18 video Count Factors given Prime Factorization
  842.    wt: 12:   4 video Prime Factorization Introduction
  843.    wt: 12:   3 video Primes and Composites from 9 times table
  844.    wt: 12:   1 video how Products are bigger than factor
  845.    wt: 12:   Long Division Backward
  846.    wt: 12:   3 Division Single Digit Divisor Example
  847.    wt: 12:   D Decimal Multiplication Methods Derived
  848.    wt: 12:   3 More One Digit Multipliers
  849.    wt: 12:   4. How to add with decimals B with conversions
  850.    wt: 12:   10 Names for Big Numbers and Powers of Ten Expansion
  851.    wt: 12:   9 Comparison and Subtraction of Time Intervals
  852.    wt: 12:   Volume of Solid by Cross Sections Lesson
  853.    wt: 12:   Example 2
  854.    wt: 12:   Example 1
  855.    wt: 12:   36 Cube root derivative animated
  856.    wt: 12:   34 Derivative of exponential function
  857.    wt: 12:   31 Derivatives of inverse functions
  858.    wt: 12:   30Chain Rule A Proof
  859.    wt: 12:   26 Chain Rule Recognising outer inner functions
  860.    wt: 12:   24 Chain Rule Animated Examples
  861.    wt: 12:   17 Derivatives of quotients of sine and cosine
  862.    wt: 12:   16 Derivatives of reciprocals of sine and cosine
  863.    wt: 12:   1 Fall 1983 Why Slopes Appetizer
  864.    wt: 12:   7 Evaluation by immediate or delayed substitution
  865.    wt: 12:   Postscript Pythagorean Theorem yet another proof
  866.    wt: 12:   Chapter 24 Logarithms Powers and Exponentials
  867.    wt: 12:   Chapter 12. Units and Slopes
  868.    wt: 12:   Chapter 10 Slopes and Units
  869.    wt: 12:   Chapter 6. Slopes and Vertical Shifts
  870.    wt: 12:   Chapter 4. More Slope Sign Analysis
  871.    wt: 12:   Chapter 2. Slopes and Ski Trails
  872.    wt: 12:   Fall 1983 Calculus Appetizer
  873.    wt: 12:   Chapter 6 Rule Based Reason in Mathematics
  874.    wt: 12:   Chapter 3 Algebra Difficulties
  875.    wt: 12:   Chapter 2 For and Against Mathematics
  876.    wt: 12:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  877.    wt: 12:   Chapter 12 Islands and Divisions of Knowledge
  878.    wt: 12:   Chapter 8 Change of Language
  879.    wt: 12:   Chapter 3 What is in chapters 4 to 8
  880.    wt: 12:   Appendix A Calculus with Proofs for Keen or Gifted
  881.    wt: 12:   Chapter 7 Calculus Previews and Calculus Lightly
  882.    wt: 12:   Chapter 6 More Algebra and Geometry
  883.    wt: 12:   Chapter 4 Logic for Reading Writing and Geometry etc
  884.    wt: 12:   2 Identifying Size and Position Place and Spatial Sense
  885.    wt: 12:   1 From Number Recognition and Counting to Arithmetic A
  886.    wt: 12:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  887.    wt: 11:   Appendix 2 primary school Arithmetic 01
  888.    wt: 11:   J LAMP Introduction Extrinsic Origins
  889.    wt: 11:   G LAMP Introduction Problem Solving Skills
  890.    wt: 11:   A Introduction Objectives
  891.    wt: 11:   Ramblings Extrinsic numbers theory
  892.    wt: 11:   Skills Chapter 0 Introduction
  893.    wt: 11:   7 logic review and decimals an odd combination
  894.    wt: 11:   5 logarithms and exponentials etc
  895.    wt: 11:   Math Ed if it must be short make it lean effective
  896.    wt: 11:   Applied Maths Program14092009 POMME variant
  897.    wt: 11:   Mathematics Education Professors
  898.    wt: 11:   grouping students according to ability
  899.    wt: 11:   what should be learnt and When
  900.    wt: 11:   Education Reform Inconsistencies
  901.    wt: 11:   mathematics curriculum shifts
  902.    wt: 11:   three goals for Mathematics Education
  903.    wt: 11:   04 29 New Mathematics Curriculum
  904.    wt: 11:   standards for course material
  905.    wt: 11:   Education in mathematics science and technology
  906.    wt: 11:   education an empirical art
  907.    wt: 11:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  908.    wt: 11:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  909.    wt: 11:   25 Absolute Value greatest integer and saw tooth functions
  910.    wt: 11:   9 Formulas for Real Exponents with Logarithms
  911.    wt: 11:   7 Formulas for Roots with Logarithms Derivation
  912.    wt: 11:   6 Formulas for Even and Odd Roots with Logarithms
  913.    wt: 11:   4 Resultant of a Sum of Movements
  914.    wt: 11:   4 graphing y=Asin(x c)
  915.    wt: 11:   1 graphing y=f(x a)
  916.    wt: 11:   Straight Lines ASA Intersection Study More
  917.    wt: 11:   Straight Lines ASA Intersection Study
  918.    wt: 11:   D Straight Lines Slope from Coordinates Examples
  919.    wt: 11:   A Straight Line Slope Scaling Properties
  920.    wt: 11:   11 Straight Lines Graphing y=mx
  921.    wt: 11:   5 Tangent Function Graph
  922.    wt: 11:   30 unit circle calculation of six trigonometric functions
  923.    wt: 11:   29 secant cosecant and cotangent for acute angles
  924.    wt: 11:   5 An Easy Proof of the Distributive Law
  925.    wt: 11:   7 Translations Rotations Reflections Dilatations
  926.    wt: 11:   11 A Partial Summary
  927.    wt: 11:   3 Slope product for perpendicular lines
  928.    wt: 11:   PS C Similarity Use Recognize it in Trigonometry
  929.    wt: 11:   16 Angles Subtended By Chords and Diameters
  930.    wt: 11:   15 Triangle Angle Sum is 180 degrees
  931.    wt: 11:   14 Parallel Lines Postulate
  932.    wt: 11:   9 Construction of a right bisector
  933.    wt: 11:   A Modular and Remainder Arithmetic
  934.    wt: 11:   25 Mid way Convergence to Axiomatic Approach
  935.    wt: 11:   23 Distributive Law Two Derivations
  936.    wt: 11:   15 Head to Tails in place Addition Associative
  937.    wt: 11:   14 Vector Head to Tail Sums and Resultants
  938.    wt: 11:   3 Location of Point in Decimal Multiplication
  939.    wt: 11:   C Three Decimal Subtraction Methods
  940.    wt: 11:   2 Combing Counts Addition Skills and Principles
  941.    wt: 11:   1 The Counting Origins of Numbers
  942.    wt: 11:   2 Fraction Operations Physical Development
  943.    wt: 11:   1 What is Proportionality
  944.    wt: 11:   7 Pythagorean Theorem Chinese Square Proof
  945.    wt: 11:   6 Compound Interest Forward and Backwards
  946.    wt: 11:   2 Linear Equation Literal Solution
  947.    wt: 11:   5 Independent versus Dependent Variables
  948.    wt: 11:   4 Changing Letters
  949.    wt: 11:   Skill Development Notes
  950.    wt: 11:   12 Cone Cylinder Sphere Lesson Idea
  951.    wt: 11:   5 Square Roots with primes more still
  952.    wt: 11:   4 Square Roots with primes more
  953.    wt: 11:   2 Square Roots with Prime
  954.    wt: 11:   17 GCD LCM of 85 and 60 via Prime
  955.    wt: 11:   LCM 60 45 Avoid List Method Use Prime
  956.    wt: 11:   2 Counting with Tables and Trees I
  957.    wt: 11:   1 Counting and Counting Methods I
  958.    wt: 11:   3 signed coordinates for maps and planes
  959.    wt: 11:   6 Simplification of Fractions with Units
  960.    wt: 11:   2 Equality and Units
  961.    wt: 11:   A Similarities between Fractions and Two Term Ratios
  962.    wt: 11:   17 Efficient Ways to Add and Subtract
  963.    wt: 11:   14 Adding and Subtracting with Like Denominators
  964.    wt: 11:   1 What is a fraction Take II
  965.    wt: 11:   27 Divisibility by 2 3 6 5 9 10 Example
  966.    wt: 11:   26 Divisibility by 2 3 5 Example
  967.    wt: 11:   25 Divisibility Tests for 2 3 5 9 10 Example
  968.    wt: 11:   5 Remainder Arithmetic Modulo 5
  969.    wt: 11:   2 Remainder Arithmetic Modulo 10 more
  970.    wt: 11:   1 Remainder Arithmetic Modulo 10
  971.    wt: 11:   17 Identify and Count Factors using Primes
  972.    wt: 11:   16 video Factors of 980 using prime
  973.    wt: 11:   14 video Factors of 24 Take II
  974.    wt: 11:   11 Efficient Square Rule Use
  975.    wt: 11:   8 video Prime Factorization upto 19
  976.    wt: 11:   Long Division Backwards more
  977.    wt: 11:   Division with Counts and Length
  978.    wt: 11:   7 Long Divison Mistake Catching
  979.    wt: 11:   6 Why Decimal Long Division Methods Works Take I
  980.    wt: 11:   4 Two and Three Digit Multipliers
  981.    wt: 11:   1 Why 3 times 5 gives 15
  982.    wt: 11:   1 Place Value in Three Digit Whole Numbers
  983.    wt: 11:   8 Addition of Time Intervals via subtotaling
  984.    wt: 11:   Summary
  985.    wt: 11:   29 Chain Rule Optional Reading
  986.    wt: 11:   23 Chain Rule in general
  987.    wt: 11:   22 Chain Rule for polynomials
  988.    wt: 11:   19 Chain Rule for linear functions
  989.    wt: 11:   18 Chain Rule Introduction
  990.    wt: 11:   12 Quotient rule examples
  991.    wt: 11:   7 Animated Differentiation Examples
  992.    wt: 11:   13 Limits with Parameters and Derivatives Take II
  993.    wt: 11:   5 Jumps and absence of unlimited error control
  994.    wt: 11:   G.1 First Fundamental Theorem of Calculus
  995.    wt: 11:   G.2 Differentiable Functions Mean Value Theorem
  996.    wt: 11:   F.1 What Functions are Continuous
  997.    wt: 11:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  998.    wt: 11:   Chapter 23 Links To Trigonometry
  999.    wt: 11:   Chapter 21 Arrow Addition
  1000.    wt: 11:   Chapter 20 Vectors and Complex Numbers
  1001.    wt: 11:   Chapter 16. Velocity Approximation
  1002.    wt: 11:   Chapter 15. Slope Approximation
  1003.    wt: 11:   Chapter 11. Graphing Slope versus Position
  1004.    wt: 11:   Chapter 7 Slopes and Velocity
  1005.    wt: 11:   Chapter 1.Introduction
  1006.    wt: 11:   Chapter 29 Contrapositive and Vacuously True Implications
  1007.    wt: 11:   Chapter 4 Complex Numbers and Why Slopes
  1008.    wt: 11:   Chapter 23 Truth Tables
  1009.    wt: 11:   Chapter 17 Objective Ways Trial and Error Discovery
  1010.    wt: 11:   Chapter 8 Skipped Topics and Why
  1011.    wt: 11:   7 Games and Activities for Instruction
  1012.    wt: 11:   1 From Number Recognition and Counting to Arithmetic B
  1013.    wt: 11:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  1014.    wt: 11:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  1015.    wt: 10:   Skills Chapter 5 Calculus
  1016.    wt: 10:   Skills Chapter 1 Arithmetic
  1017.    wt: 10:   11 pure mathematics
  1018.    wt: 10:   8 analytic geometry etc
  1019.    wt: 10:   1 arithmetic with unsigned numbers
  1020.    wt: 10:   Teach the teachers plus goals
  1021.    wt: 10:   five decades make a difference
  1022.    wt: 10:   Maps Plans Drawings
  1023.    wt: 10:   talk the algebra talk
  1024.    wt: 10:   the trouble with algebra
  1025.    wt: 10:   02 20 mathematics education references
  1026.    wt: 10:   three aims for mathematics students
  1027.    wt: 10:   Operational Viewpoint to Value
  1028.    wt: 10:   mathematics instruction in general
  1029.    wt: 10:   Different Kinds of Reasoning in maths
  1030.    wt: 10:   three kinds of reason in mathematics
  1031.    wt: 10:   Four ways to improve education reform
  1032.    wt: 10:   Prequel In For A Penny In For A Pound
  1033.    wt: 10:   fairness and inductive principles for instruction
  1034.    wt: 10:   chapitre 07 01 principle D induction mathematique
  1035.    wt: 10:   chapitre 06 00 Chaines de la raison
  1036.    wt: 10:   chapitre 03 A Propos Des Prochains Chapitre
  1037.    wt: 10:   3 Formula or function graphing exercise
  1038.    wt: 10:   10 Exponential Growth and Decay Models
  1039.    wt: 10:   Rewriting algebraic substitution as function substitutions
  1040.    wt: 10:   16 cotangent function Definition Graph and Inverse
  1041.    wt: 10:   15 cosecant function Definition Graph and Inverse
  1042.    wt: 10:   13 cosecant function Definition Graph and Inverse
  1043.    wt: 10:   11 arctan left inverse of tangent Graph
  1044.    wt: 10:   A Global Time and Navigation
  1045.    wt: 10:   3 Navigation with Arrows or Vectors
  1046.    wt: 10:   Straight Lines Instersection Solving Equations
  1047.    wt: 10:   Straight Lines Intersection of
  1048.    wt: 10:   C Straight Lines Slope from Coordinates
  1049.    wt: 10:   B Straight Line Slope Scaling Properties More
  1050.    wt: 10:   4 Tangent Function Properties
  1051.    wt: 10:   17 tangent function angle sum formulas
  1052.    wt: 10:   32 seven rows of pascals triangle
  1053.    wt: 10:   31 basic secant cosecant cotangent trig identities
  1054.    wt: 10:   27 Logarithmic use of products of sines and cosines
  1055.    wt: 10:   22 sine of 22.5 degrees via half angle formulas
  1056.    wt: 10:   17B sine cosine Angle Sum Formulas via cis
  1057.    wt: 10:   17A The complex number valued trig function cis
  1058.    wt: 10:   13 Graph of tangent function many periods
  1059.    wt: 10:   13 Trig Formulas for dot and cross Products
  1060.    wt: 10:   10 sine cosine Angle Sum Formulas via cis
  1061.    wt: 10:   2 Similar Triangles Equality of Corresponding Side Ratios
  1062.    wt: 10:   8 Similarity of Triangles and Polygons
  1063.    wt: 10:   6 Geometric Diagrams in Class
  1064.    wt: 10:   3 Similarity by Design with coordinates
  1065.    wt: 10:   1 Early Concept of Like or Similar Shapes
  1066.    wt: 10:   10 Midpoint of [a b] and [b a]
  1067.    wt: 10:   5 Algebraic View of Slopes
  1068.    wt: 10:   What is and is not here
  1069.    wt: 10:   Euclidean Geometry Elsewhere LINKS
  1070.    wt: 10:   PS A Kite Construction Methods
  1071.    wt: 10:   21 Parallelograms
  1072.    wt: 10:   18 Triangle Similarity Take 1
  1073.    wt: 10:   17 Right Bisectors of Triangle Sides
  1074.    wt: 10:   12 Side Angle Side Failure
  1075.    wt: 10:   11 Triangle Construction Fails
  1076.    wt: 10:   10 Dropping a perpendicular to line
  1077.    wt: 10:   Short Course on Euclidean Geometry
  1078.    wt: 10:   1 Length Measurement
  1079.    wt: 10:   musings do not puiblish real numbers
  1080.    wt: 10:   26 More Less Greater Than Comparison
  1081.    wt: 10:   22 Multiplication of Signed Numbers
  1082.    wt: 10:   21 Addition of Multiples of a Single Vector
  1083.    wt: 10:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  1084.    wt: 10:   13 Arrows and Vectors in a Plane
  1085.    wt: 10:   2 Algebraic View
  1086.    wt: 10:   1 Changing Calculations
  1087.    wt: 10:   13 Real Number Subtraction
  1088.    wt: 10:   8 Coordinates for Maps and Planes
  1089.    wt: 10:   1 Whole and Natural Numbers
  1090.    wt: 10:   5 Talking about Numbers and Quantities
  1091.    wt: 10:   16 GCD and LCM of 650 225 via Prime
  1092.    wt: 10:   13 GCD from given Prime Factorization
  1093.    wt: 10:   11 GCD 2700 288 via Euclid Algorithm
  1094.    wt: 10:   10 Euclid Algorithm with 129 125 and with 45 14
  1095.    wt: 10:   8 GCD from Euclidean Algorithm
  1096.    wt: 10:   7 GCD and LCM from prime factorization
  1097.    wt: 10:   4 LCM of 8 and 10 via Prime
  1098.    wt: 10:   11 What are real lengths and numbers
  1099.    wt: 10:   2 signed and unsigned numbers as coordinates
  1100.    wt: 10:   11 Simplification an Algebraic View
  1101.    wt: 10:   6 Multiplication of Mixed Numbers
  1102.    wt: 10:   2 Unit Fraction Multiplication
  1103.    wt: 10:   1 What is a fraction
  1104.    wt: 10:   24 Divisibility Tests for 2 3 5 9 10
  1105.    wt: 10:   12 Why Long Division Works Take III
  1106.    wt: 10:   11 Another Single Digit Divisor Example
  1107.    wt: 10:   10 Division by Five Long and Short Ways
  1108.    wt: 10:   9 Why Long Division Works Take II
  1109.    wt: 10:   B Powers of Ten
  1110.    wt: 10:   2 One Digit Multipliers
  1111.    wt: 10:   Quick history of numbers and algebra
  1112.    wt: 10:   016 Numbering Occidental Calendar Days
  1113.    wt: 10:   20 Chain Rule for Pulley Systems
  1114.    wt: 10:   15 sine and cosine derivatives 3rd step
  1115.    wt: 10:   13 sine and cosine derivatives 1st step
  1116.    wt: 10:   8 Differentiation of polynomials
  1117.    wt: 10:   6 Power rule from product rule
  1118.    wt: 10:   5 Product Rule
  1119.    wt: 10:   3 Motivation for Limit Definition Take 2
  1120.    wt: 10:   12 Limits with Parameters and Derivatives Take I
  1121.    wt: 10:   Postscript One Sided and Intermediate Value Theorems
  1122.    wt: 10:   G.6 Bounded Derivatives implies Lipshitz Continuity
  1123.    wt: 10:   G.4 Lipschitz Continuity implies EquiContinuity
  1124.    wt: 10:   F.5a Equicontinuity Theorems
  1125.    wt: 10:   F.3 Intermediate Value Theorem
  1126.    wt: 10:   B3 Bolzano Weierstrass Theorem
  1127.    wt: 10:   PostScript For and Against Decimal Perspectives
  1128.    wt: 10:   Chapter 22 Complex Numbers
  1129.    wt: 10:   Chapter 8. Slope Interpretation
  1130.    wt: 10:   Chapter 9 Talking about Numbers or Quantities
  1131.    wt: 10:   Chapter 2 Implication Rules Forwards and Backwards
  1132.    wt: 10:   Annotated Links to Material Elsehwere
  1133.    wt: 10:   Postscript B Mathematics Education References
  1134.    wt: 10:   Postscript C Consistency as a Tool for Reason
  1135.    wt: 10:   Chapter 20 Shorthand Symbols as Pronouns
  1136.    wt: 10:   Chapter 19 What is in chapters 20 to 24
  1137.    wt: 10:   Chapter 11 Accidental Patterns
  1138.    wt: 10:   Chapter 9 What is in Chapters 10 to 18
  1139.    wt: 10:   Chapter 7 Longer Chains of Reason
  1140.    wt: 10:   Chapter 6 Chains of Reason
  1141.    wt: 10:   Chapter 2 Why Sets
  1142.    wt: 10:   Chapter 1 Arithmetic
  1143.    wt: 10:   More Algebra and Slope based Calculus Preview
  1144.    wt: 10:   Systematic Algebra Skill Development Missing Links
  1145.    wt: 10:   Phase 2. More Basic Skills with likely take home value 1 to 2 years

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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