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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.

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

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1088 matches:

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

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