Appetizers and Lessons for Mathematics & Reason Français: 26 pages
A 1100+ page site with math-free logic chapters and wordy algebra chapters.
For comprehension, study site chapters and steps. Go beyond rote learning.

Logic mastery strengthens comprehension and so improves home, work & study abilities .
 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 14+: 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
Forewords + leading chapters give original reasons, still valid, for site content & growth.

Site Review: Mathphobics, this site may ease your fears of the subject, perhaps even help you njoy it. ... unintimidating, sometimes funny and very clear. ... . Read all. Continue with Volume 2, Three Skill for Algebra.

Site Review. Math resources ... span ... arithmetic, logic, algebra, calculus, complex numbers, and Euclidean geometry. Lessons and how-tos .... provide a good foundation ... Read all. See site books as well.

Teachers & Tutors: Site material uniquely explains common troubles in terms of steps too large or missing. Plus, this December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 may focus on skills with actual or potential local 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:   Step 1 Stick diagram and fractions/
  2.    wt: 8:   11 Parallel Straight Lines and Transversals/
  3.    wt: 8:   9 Proportionality Backwards and Forwards/
  4.    wt: 8:   6 More Less Greater Than Inequalities and Comparison/
  5.    wt: 8:   Step 4 Gaussian Elimination/
  6.    wt: 8:   B Decimal Comparing and Subtracting Methods/
  7.    wt: 8:   A Decimal Counting and Adding Methods/
  8.    wt: 7:   LAMP Lean Applied Mathematics Program/
  9.    wt: 7:   5 Factored Polynomial Sign Analysis Examples/
  10.    wt: 7:   14 Degrees to Radians and Radians to Degrees/
  11.    wt: 7:   3 Cartesian and Polar Coordinates/
  12.    wt: 7:   10 Examples of Algebraic Reasoning/
  13.    wt: 7:   7 Axioms Logic and Equivalent Equations/
  14.    wt: 7:   Step 2 Algebraic solutions for one unknown/
  15.    wt: 7:   2 Formula Forward Use Evaluation/
  16.    wt: 7:   12 Webvideo Lessons on Area and Volume Calculation/
  17.    wt: 6:   Progressive Observable Motivated Mathematics Education/
  18.    wt: 6:   2 Natural Logarithms Exponentials Powers Roots/
  19.    wt: 6:   12 Function Translating and Rescaling/
  20.    wt: 6:   10 Intersecting Straight Lines and Transversals/
  21.    wt: 6:   4 Computation Rules and Function Notation/
  22.    wt: 6:   Step 3 Easy systems in 2 or more unknowns/
  23.    wt: 6:   C Decimal Multiplication Methods/
  24.    wt: 5:   3 Quadratics Geometrically/
  25.    wt: 5:   1 Five Polynomial Operations/
  26.    wt: 5:   9 Lines and Slopes Take 2 with tangent function/
  27.    wt: 5:   1 Maps Plans Measurement/
  28.    wt: 5:   A Origins of Counting and Figuring Methods/
  29.    wt: 5:   8 Unifying Theme For Algebra/
  30.    wt: 5:   3 Solving Linear Equations/
  31.    wt: 5:   11 Squares and Square Roots/
  32.    wt: 5:   9 Combinatorics Trees Tables and Products/
  33.    wt: 5:   7 Arithmetic and Fractions with Units/
  34.    wt: 5:   6 Fractions and Ratios/
  35.    wt: 5:   4 Remainder Arithmetic and Divisibility/
  36.    wt: 5:   D Decimal Long Division Methods/
  37.    wt: 5:   1 Decimal Place Value/
  38.    wt: 5:   38 Lessons on Calculating Derivatives/
  39.    wt: 5:   Volume 1A Pattern Based Reason/
  40.    wt: 4:   Mathematics Education Essays/
  41.    wt: 4:   Mathematics Skills Year by Year/
  42.    wt: 4:   5 What is Similarity/
  43.    wt: 4:   4 Lines and Slopes Take 1/
  44.    wt: 4:   2 Euclidean Geometry Constructions Theory extras/
  45.    wt: 4:   B Real Numbers Extrinsic Development/
  46.    wt: 4:   5 Real Numbers/
  47.    wt: 4:   12 Comparison of Unsigned and Signed Numbers/
  48.    wt: 4:   10 LCM GCD and Euclid GCD Algorithm/
  49.    wt: 4:   3 Prime Factorization Skills/
  50.    wt: 4:   2 Arithmetic with Decimals/
  51.    wt: 4:   Time Date Matters/
  52.    wt: 4:   Advanced Calculus Volume 3 Appendices/
  53.    wt: 4:   Mathematics 506 Lessons/
  54.    wt: 3:   Volume 1A Regles et modeles/
  55.    wt: 3:   15 Arc or Inverse Trigonometric Function/
  56.    wt: 3:   1 Working With Sets/
  57.    wt: 3:   Algebra Starter Lessons/
  58.    wt: 3:   8 Arithmetic with Signed Numbers/
  59.    wt: 3:   5 Lessons on Integration/
  60.    wt: 3:   4 Lessons on Using Derivatives/
  61.    wt: 3:   13 Lessons on Limits and Continuity/
  62.    wt: 3:   Mathematics Skill Development Framework/
  63.    wt: 2:   francais/
  64.    wt: 2:   4 Functions/
  65.    wt: 2:   More Algebra/
  66.    wt: 2:   13 Vectors/
  67.    wt: 2:   8 Unit Circle Trigonometry/
  68.    wt: 2:   7 Complex Numbers/
  69.    wt: 2:   6 Trigonometry first steps/
  70.    wt: 2:   Geometry maps plans trigonometry vectors/
  71.    wt: 2:   5 Integers/
  72.    wt: 2:   Arithmetic and Number Theory Skills/
  73.    wt: 2:   Skills with take home value/
  74.    wt: 2:   70 Calculus Starter Lessons/
  75.    wt: 2:   Volume 3 Why Slopes A Calculus Intro Etc/
  76.    wt: 2:   Volume 2 Three Skills For Algebra/
  77.    wt: 2:   Volume 1B Mathematics Curriculum Notes/
  78.    wt: 2:   Resources and Reciprocal Links/
  79.    wt: 2:   Quebec Material/
  80.    wt: 1:   Archives/
  81.    wt: 1:   Parent Center/
  82.    wt: 1:   Volume 1 Elements of Reason/
  83.    wt: 1:   Work and Study Tips/

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1044 matches:

  1.    wt: 8:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  2.    wt: 7:   Parallel Lines and Parallel Transversals
  3.    wt: 7:   9 Circle Area and Perimeter Formula Backwards Forwards
  4.    wt: 7:   4 Rectangle Area and Like Formulas Backwards
  5.    wt: 7:   11 Place Value SI Standard International way
  6.    wt: 7:   Chapter 14. Forward and Backward Use of a Formula
  7.    wt: 7:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  8.    wt: 7:   Montreal Basic and Advanced Mathematics Tutoring
  9.    wt: 6:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  10.    wt: 6:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  11.    wt: 6:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  12.    wt: 6:   8 quadratics backward use of various formulas
  13.    wt: 6:   3 Natural Logarithms and Exponentials Basic Properties
  14.    wt: 6:   7 Coordinate Addition and Scalar Multiplication
  15.    wt: 6:   Parallel Lines and Alternating Corresponding Angles
  16.    wt: 6:   29 secant cosecant and cotangent for acute angles
  17.    wt: 6:   13 Navigation Location from Angles to 2 Landmarks
  18.    wt: 6:   13 Pythagorean spatial distance formulas
  19.    wt: 6:   5 Cartesian Addition and Translation
  20.    wt: 6:   3 Lengths and Areas on Maps and Plans
  21.    wt: 6:   15 Head to Tails in place Addition Associative
  22.    wt: 6:   8 Pythagorean Relation Forwards Backwards
  23.    wt: 6:   5 Triangle Area Formula Backwards
  24.    wt: 6:   2 Another Rectangle Area Formula Example
  25.    wt: 6:   C Equality for Fractions and Two Term Ratios and Fractions
  26.    wt: 6:   8 Numerals Fractionals Quantals Take II
  27.    wt: 6:   A Decimals Modular and Remainder Arithmetic
  28.    wt: 6:   Chapter 19. Exponentials and Natural Logarithms
  29.    wt: 6:   Chapter 2 Implication Rules Forwards and Backwards
  30.    wt: 6:   Chapter 2 For and Against Mathematics
  31.    wt: 6:   Chapter 4 Implication Rules Forwards and Backwards
  32.    wt: 6:   V Reasons and Motivations for Logic and Mathematics
  33.    wt: 6:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  34.    wt: 5:   Appendix 1 primary and preschool mathematic
  35.    wt: 5:   Applied Maths Program14092009 POMME variant
  36.    wt: 5:   five decades make a difference
  37.    wt: 5:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  38.    wt: 5:   25 Mathematics Education Leaving A Good Impression
  39.    wt: 5:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  40.    wt: 5:   Objectives for Mathematics and Logic Language Skill Development
  41.    wt: 5:   25 Absolute Value greatest integer and saw tooth functions
  42.    wt: 5:   17 Function maxima minima and their location
  43.    wt: 5:   6 quadratics numerical approach
  44.    wt: 5:   5 Natural Logarithm Calculator Exercises
  45.    wt: 5:   6 Polynomial Operations and Equivalent Computation Rules
  46.    wt: 5:   9 Summary Degrees to Radians and back
  47.    wt: 5:   7 Radian Measures in special Triangles
  48.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  49.    wt: 5:   2 Radian Measure Numerical Value of one degree
  50.    wt: 5:   A Global Time and Navigation
  51.    wt: 5:   14 Why Scalar Multiplication Distributes Physical Argument
  52.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  53.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  54.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  55.    wt: 5:   35 sines and cosines of 2A 3A 4A 5A
  56.    wt: 5:   34 sines and cosines of 2A 3A 4A 5A
  57.    wt: 5:   33 sines and cosines of 2A 3A 4A 5A
  58.    wt: 5:   18 sum of sinusoidal waves as a single wave
  59.    wt: 5:   5 Trigonometric Ratios For Tangent and Special Triangles
  60.    wt: 5:   7 Translations Rotations Reflections Dilatations
  61.    wt: 5:   10 Pythagorean plane distance formula
  62.    wt: 5:   4 Angles on Maps Plans drawn to scale
  63.    wt: 5:   A Modular and Remainder Arithmetic
  64.    wt: 5:   25 Mid way Convergence to Axiomatic Approach
  65.    wt: 5:   1 Decimals Modular and Remainder Arithmetic
  66.    wt: 5:   6 Pythagorean Hypotenuse Calculation Example
  67.    wt: 5:   3 Triangle Area Formula Example
  68.    wt: 5:   A Similarities between Fractions and Two Term Ratios
  69.    wt: 5:   7 Numerals Fractionals Quantals
  70.    wt: 5:   6 Multiplication Algebraically Take II
  71.    wt: 5:   A Associative Law Theorectical Note
  72.    wt: 5:   7 Calculator Usage Notes and Cautions
  73.    wt: 5:   5 Prime Factorization and a Square Rule
  74.    wt: 5:   Long Division forwards and backwards Example 3
  75.    wt: 5:   Long Division forwards and backwards Example 2
  76.    wt: 5:   Long Division forwards and backwards Example 1
  77.    wt: 5:   3 Harder Cases Convert to Compare and Subtract
  78.    wt: 5:   1 Comparison and Subtraction Easy Direct Cases
  79.    wt: 5:   9 Place Value Review Decimal form of Avogrados number included
  80.    wt: 5:   Practical Methods Ends and Values for Arithmetic
  81.    wt: 5:   Example 1. Area Between x and x squared
  82.    wt: 5:   A Chain Rule Real Player video examples
  83.    wt: 5:   13 Limits with Parameters and Derivatives Take II
  84.    wt: 5:   12 Limits with Parameters and Derivatives Take I
  85.    wt: 5:   Chapter 17. Area Approximation
  86.    wt: 5:   Chapter 15. Algebraic Evaluation of Limits
  87.    wt: 5:   Chapter 14 Limits and Continuity with and sans Decimals
  88.    wt: 5:   Chapter 29 Contrapositive and Vacuously True Implications
  89.    wt: 5:   Chapter 25. Mathematical Induction Examples
  90.    wt: 5:   Chapter 25. Mathematical Induction Examples
  91.    wt: 5:   Chapter 10 Describing and Changing Calculations
  92.    wt: 5:   Chapter 6 Rule Based Reason in Mathematics
  93.    wt: 5:   Chapter 22 Contrapositive and Vacuously True Implications
  94.    wt: 5:   Chapter 16 Origins and Limitations of Rules and Patterns
  95.    wt: 5:   Chapter 14 Deductive and Empirical Views of Mathematics
  96.    wt: 5:   More Algebra and Slope based Calculus Preview
  97.    wt: 5:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  98.    wt: 5:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  99.    wt: 5:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  100.    wt: 4:   C LAMP Introduction Culture in Mathematics Education
  101.    wt: 4:   Ramblings Introduction Algebra Essay
  102.    wt: 4:   7 logic review and decimals an odd combination
  103.    wt: 4:   talk the algebra talk
  104.    wt: 4:   teaching tutoring algebraic reason
  105.    wt: 4:   three goals for Mathematics Education
  106.    wt: 4:   standards for course material
  107.    wt: 4:   Education in mathematics science and technology
  108.    wt: 4:   education an empirical art
  109.    wt: 4:   chapitre 07 00 Des chaines plus longues de la raison
  110.    wt: 4:   chapitre 06 00 Chaines de la raison
  111.    wt: 4:   chapitre 03 A Propos Des Prochains Chapitre
  112.    wt: 4:   A Wire Resistance Qualitative01
  113.    wt: 4:   27 Graduated Correction and Penalties for Young Offenders
  114.    wt: 4:   13 Addition and Addition Tables
  115.    wt: 4:   12 Goals and Objectives For Mathematics
  116.    wt: 4:   5 Patience Please for Yourself and Your Charges
  117.    wt: 4:   11 Function Domain Range Source and Targets
  118.    wt: 4:   4 Function notation in and beyond mathematics
  119.    wt: 4:   A Quadratics Summary
  120.    wt: 4:   9 quadratics physical and further context
  121.    wt: 4:   7 quadratic formulla derivation
  122.    wt: 4:   4 quadratics difference of two squares
  123.    wt: 4:   2 quadratics graphing in general
  124.    wt: 4:   8 Formulas for Fractional Exponents with Logarithms
  125.    wt: 4:   11 arctan left inverse of tangent Graph
  126.    wt: 4:   8 Radian Measures of Common Angles
  127.    wt: 4:   3 Circle Arclengh Proportional to Central Angle
  128.    wt: 4:   10 Parallelogram Addition Method
  129.    wt: 4:   5 Head To Tail Arrow Addition
  130.    wt: 4:   2 Graphing y=Af(x) Vertical Scaling
  131.    wt: 4:   Parallel Lines and Interior Angles
  132.    wt: 4:   14 Straight Lines Equations General Case
  133.    wt: 4:   6 Tangent Function Inclination Angle Take 2
  134.    wt: 4:   31 basic secant cosecant cotangent trig identities
  135.    wt: 4:   24 tangent Angle Difference Formula
  136.    wt: 4:   22 sine of 22.5 degrees via half angle formulas
  137.    wt: 4:   21 sine and cosine Half Angle Formulas
  138.    wt: 4:   16 Right Triangle Complementary Angle Relations
  139.    wt: 4:   14 cosine even and sine and tangent are odd
  140.    wt: 4:   1 Rectangular Polar Coordinates Review
  141.    wt: 4:   2 Similar Triangles Equality of Corresponding Side Ratios
  142.    wt: 4:   10 Similarity of Triangles Equivalent of Two Criteria
  143.    wt: 4:   9 Similarity of Triangles Usual Criteria
  144.    wt: 4:   5 Similarity of Circles Squares and Rectangles
  145.    wt: 4:   11 A Partial Summary
  146.    wt: 4:   6 Polar Multiplication and Rotation
  147.    wt: 4:   1 Cartesian Coordinates sans signs
  148.    wt: 4:   PS F Scalar Multiplication Distributes over Addition
  149.    wt: 4:   PS D Addition with Cartesian Coordinates
  150.    wt: 4:   5 Drawing to Scale Avoids Angle Distortions
  151.    wt: 4:   14 Vector Head to Tail Sums and Resultants
  152.    wt: 4:   13 Arrows and Vectors in a Plane
  153.    wt: 4:   B Decimal Comparison and Subtraction
  154.    wt: 4:   4 Fraction Operations Axiomatic Development
  155.    wt: 4:   3 Inequalities Algebraically
  156.    wt: 4:   4 Rates Ratios and Proporitionality
  157.    wt: 4:   6 Compound Interest Forward and Backwards
  158.    wt: 4:   2 Addition and Multiplication Axioms
  159.    wt: 4:   2 More and Less Than for Counts and Measures
  160.    wt: 4:   8 Coordinates for Maps and Planes
  161.    wt: 4:   5 Gaussian Elimination for 3 unknowns 2nd example
  162.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  163.    wt: 4:   3 GE III Equation Addition and Multiplication
  164.    wt: 4:   4 Circle Area Formula Example
  165.    wt: 4:   6 Three Notions of What is a Variable
  166.    wt: 4:   5 Talking about Numbers and Quantities
  167.    wt: 4:   4 A Brief Story of numbers and algebra
  168.    wt: 4:   2 What is a Variable
  169.    wt: 4:   arithmetic videos Real Player Format
  170.    wt: 4:   1 More and Less Than for Counts and Measures
  171.    wt: 4:   11 What are real lengths and numbers
  172.    wt: 4:   3 signed coordinates for maps and planes
  173.    wt: 4:   17 Efficient Ways to Add and Subtract
  174.    wt: 4:   16 Addition Subtraction Comparision Compared
  175.    wt: 4:   15 Adding and Subtracting with Unlike Denominators
  176.    wt: 4:   14 Adding and Subtracting with Like Denominators
  177.    wt: 4:   13 Fraction Comparison Algebraic View
  178.    wt: 4:   11 Simplification an Algebraic View
  179.    wt: 4:   10 Simplification of Fractions and Mixed Numerals
  180.    wt: 4:   1 What is a fraction Take II
  181.    wt: 4:   11 Adding Integers Formulas and Examples
  182.    wt: 4:   A Elementary Basis for Multiplication Methods
  183.    wt: 4:   Appendix 1 Decimals Comparison Method Take II
  184.    wt: 4:   2 Subtraction Easy Case Examples
  185.    wt: 4:   7 Adding decimal fractions using decimal point
  186.    wt: 4:   3. How to add with decimals A sans conversions
  187.    wt: 4:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  188.    wt: 4:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  189.    wt: 4:   5 More on Groups of 3 Place Value in Decimal Fractions
  190.    wt: 4:   4 Groups of 3 Place Value in Decimal Fractions
  191.    wt: 4:   Exact Arithmetic Wholes and Fractions
  192.    wt: 4:   016 Numbering Occidental Calendar Days
  193.    wt: 4:   9 Comparison and Subtraction of Time Intervals
  194.    wt: 4:   8 Addition of Time Intervals via subtotaling
  195.    wt: 4:   A Related Material in Volume 3
  196.    wt: 4:   38 Formulas and derivatives for powers and roots
  197.    wt: 4:   33 Chain Rule Real Player video examples
  198.    wt: 4:   28 Chain Rule Preparation for a Proof
  199.    wt: 4:   25 Chain Rule Animated Examples Continued
  200.    wt: 4:   24 Chain Rule Animated Examples
  201.    wt: 4:   7 Animated Differentiation Examples
  202.    wt: 4:   7 Evaluation by immediate or delayed substitution
  203.    wt: 4:   PostScript For and Against Decimal Perspectives
  204.    wt: 4:   Chapter 24 Logarithms Powers and Exponentials
  205.    wt: 4:   Chapter 18. Slopes Areas Integration
  206.    wt: 4:   Appendix E. How To Study Mathematics and Why
  207.    wt: 4:   Appendix A. Reading Guide For Next Appendices
  208.    wt: 4:   Chapter 20. Degrees and Radians
  209.    wt: 4:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  210.    wt: 4:   Postscript What is a Variable
  211.    wt: 4:   Chapter 9 Talking about Numbers or Quantities
  212.    wt: 4:   Chapter 6 Change of Language
  213.    wt: 4:   Annotated Links to Material Elsehwere
  214.    wt: 4:   Chapter 17 Objective Ways Trial and Error Discovery
  215.    wt: 4:   Chapter 11 Accidental Patterns
  216.    wt: 4:   Chapter 8 Change of Language
  217.    wt: 4:   P Exact Arithmetic With Whole Numbers and Fractions
  218.    wt: 4:   O On Learning Mathematics and Science
  219.    wt: 3:   Appendix 2 primary school Arithmetic 01
  220.    wt: 3:   E LAMP Introduction Modern Mathematics
  221.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  222.    wt: 3:   Skills Chapter 3 Algebra
  223.    wt: 3:   5 logarithms and exponentials etc
  224.    wt: 3:   Teach the teachers plus goals
  225.    wt: 3:   Math Ed if it must be short make it lean effective
  226.    wt: 3:   Mathematics Education Professors
  227.    wt: 3:   what should be learnt and When
  228.    wt: 3:   Maps Plans Drawings
  229.    wt: 3:   Secondary Three Mathematics
  230.    wt: 3:   Secondary Two Mathematics
  231.    wt: 3:   Secondary One Mathematics
  232.    wt: 3:   geometric implications for algebra
  233.    wt: 3:   02 20 mathematics education references
  234.    wt: 3:   three aims for mathematics students
  235.    wt: 3:   Operational Viewpoint to Value
  236.    wt: 3:   mathematics instruction in general
  237.    wt: 3:   three kinds of reason in mathematics
  238.    wt: 3:   need for a mixed mathematics curriculum
  239.    wt: 3:   Leaner mathematics curriculum
  240.    wt: 3:   chapitre 07 01 principle D induction mathematique
  241.    wt: 3:   chapitre 04 10 Etapes pour une meilleur raison
  242.    wt: 3:   chapitre 04 04 Parlons de la logique
  243.    wt: 3:   chapitre 02 00 La Communication des idees
  244.    wt: 3:   2 Conductance Resistance Duality02
  245.    wt: 3:   1 Conductance Resistance Duality01
  246.    wt: 3:   F Wire Resistance Calculation04
  247.    wt: 3:   E Wire Resistance Calculation03
  248.    wt: 3:   D Wire Resistance Calculation02
  249.    wt: 3:   C Wire Resistance Calculation01
  250.    wt: 3:   B Wire Resistance Qualitative02
  251.    wt: 3:   24 Standards For Skill Develoment Take II
  252.    wt: 3:   23 Modularized Skill Development Modularized Rigor Take IV
  253.    wt: 3:   23 Modularized Skill Development Modularized Rigor Take III
  254.    wt: 3:   23 Modularized Skill Development Modularized Rigor Take II
  255.    wt: 3:   19 Extending the Oral Dimension of Mathematics
  256.    wt: 3:   18 Primary School Mathematics
  257.    wt: 3:   17 Math Booklets for children and young teenagers
  258.    wt: 3:   16 Secondary Mathematics Tips
  259.    wt: 3:   14 Multiplication and Times Tables
  260.    wt: 3:   4 Learning Takes Time and Effort
  261.    wt: 3:   Ages 12 to 14 Skills with take home value
  262.    wt: 3:   sign monoticity analysis example 4
  263.    wt: 3:   sign monoticity analysis example 3
  264.    wt: 3:   sign monoticity analysis example 2
  265.    wt: 3:   sign monoticity analysis example 1
  266.    wt: 3:   22 Square Root function graphically
  267.    wt: 3:   20 Interchanging coordinates a reflection
  268.    wt: 3:   16 Increasing or decreasing on intervals
  269.    wt: 3:   6 Set Existence Formation and Notation
  270.    wt: 3:   5 Function notation for geometric transformations
  271.    wt: 3:   2 Algebraic use of function notation
  272.    wt: 3:   5 quadratics completing the square
  273.    wt: 3:   3 quadratics factoring by inspection
  274.    wt: 3:   1 quadratics graphing exercises
  275.    wt: 3:   10 Exponential Growth and Decay Models
  276.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  277.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  278.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  279.    wt: 3:   2 Square Root Simplification a prequel
  280.    wt: 3:   1 Calculator Starter Exercises
  281.    wt: 3:   3 Polynomials Multiplication Addition
  282.    wt: 3:   Rewriting algebraic substitution as function substitutions
  283.    wt: 3:   16 cotangent function Definition Graph and Inverse
  284.    wt: 3:   15 cosecant function Definition Graph and Inverse
  285.    wt: 3:   14 secant function Definition Graph and Inverse
  286.    wt: 3:   13 cosecant function Definition Graph and Inverse
  287.    wt: 3:   12 motivation for term arctan
  288.    wt: 3:   10 arctan left inverse of tangent Definition
  289.    wt: 3:   9 motivation for name arcsin
  290.    wt: 3:   5 Swapping Coordinates is a reflection
  291.    wt: 3:   6 Radian Measure to Degrees
  292.    wt: 3:   5 Degrees to Radian Measure
  293.    wt: 3:   1 Degrees and Radians Introduction
  294.    wt: 3:   12 From Applied To Pure Mathematics
  295.    wt: 3:   9 Head to Tail Coordinate View
  296.    wt: 3:   3 Navigation with Arrows or Vectors
  297.    wt: 3:   SAS Method For Isometric Or Proportional Triangle Construction
  298.    wt: 3:   Analytic View of Triangle Construction or Line Instersection More
  299.    wt: 3:   Straight Lines ASA Intersection Study More
  300.    wt: 3:   Straight Lines ASA Intersection Study
  301.    wt: 3:   D Straight Lines Slope from Coordinates Examples
  302.    wt: 3:   A Straight Line Slope Scaling Properties
  303.    wt: 3:   8 Straight Lines Equation for vertical
  304.    wt: 3:   17 tangent function angle sum formulas
  305.    wt: 3:   32 seven rows of pascals triangle
  306.    wt: 3:   25 tangent double angle formula Slope connection
  307.    wt: 3:   20 sine and cosine Double Angle Formulas
  308.    wt: 3:   19 Pythagorean Identity For sine and cosine functions
  309.    wt: 3:   17D cis formulas for sine cosines and tangent
  310.    wt: 3:   17C sine and cosine double triple angle formulas
  311.    wt: 3:   17B sine cosine Angle Sum Formulas via cis
  312.    wt: 3:   15 sine cosine Complementary Angle Relations
  313.    wt: 3:   13 Graph of tangent function many periods
  314.    wt: 3:   11 tangent function undefined when terminal side vertical
  315.    wt: 3:   10 Graphs of sines and cosines many periods
  316.    wt: 3:   2 Quadrant I reference Angles
  317.    wt: 3:   21 Logarithms Powers and Exponentials
  318.    wt: 3:   12 cis formulas for sine cosines and tangent
  319.    wt: 3:   11 sine and cosine double triple angle formulas
  320.    wt: 3:   10 sine cosine Angle Sum Formulas via cis
  321.    wt: 3:   7 Second Way to Calculate Products
  322.    wt: 3:   5 An Easy Proof of the Distributive Law
  323.    wt: 3:   Appetizer A Complex Number Applet
  324.    wt: 3:   8 Triangles Cascade Problem Solving
  325.    wt: 3:   4 Trigonometric Ratios For Two Special Triangles
  326.    wt: 3:   8 Similarity of Triangles and Polygons
  327.    wt: 3:   6 Geometric Diagrams in Class
  328.    wt: 3:   1 Early Concept of Like or Similar Shapes
  329.    wt: 3:   10 Midpoint of [a b] and [b a]
  330.    wt: 3:   1 Numerical view of lines and their equations
  331.    wt: 3:   12 Spatial Coordinates
  332.    wt: 3:   9 Pythagorean Theorem Chinese Square Proof
  333.    wt: 3:   4 Polar Coordinates to and from
  334.    wt: 3:   3 Rectangular Coordinates Review
  335.    wt: 3:   2 Cartesian Coordinates with signs
  336.    wt: 3:   PS E Multiplication with Polar Coordinates
  337.    wt: 3:   PS B Parallelogram Construction Methods
  338.    wt: 3:   21 Parallelograms
  339.    wt: 3:   18 Triangle Similarity Take 1
  340.    wt: 3:   16 Angles Subtended By Chords and Diameters
  341.    wt: 3:   14 Parallel Lines Postulate
  342.    wt: 3:   13 Angle Side Angle Failure
  343.    wt: 3:   6 Ruler and compass Angle Bisection
  344.    wt: 3:   8 More Use of Maps Not Drawn to Scale
  345.    wt: 3:   2 Measuring Area Directly
  346.    wt: 3:   26 More Less Greater Than Comparison
  347.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  348.    wt: 3:   17 Arrows Rotate to Reverse with Length Unchanged
  349.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  350.    wt: 3:   11 Signed Number Addition and Addition Properties
  351.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  352.    wt: 3:   8 Division and Mulplication of Compound Fractions
  353.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  354.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  355.    wt: 3:   4 Location of Point in Decimal Addition
  356.    wt: 3:   3 Location of Point in Decimal Multiplication
  357.    wt: 3:   1 Fractions with Finite Decimal Expansions
  358.    wt: 3:   A Decimal Addition Columm Methods
  359.    wt: 3:   7 Decimals Multiplication Methods Examples
  360.    wt: 3:   5 Areas of Rectangles Revisited
  361.    wt: 3:   2 Fraction Operations Physical Development
  362.    wt: 3:   5 Proportionality in Equivalent Fractions
  363.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  364.    wt: 3:   3 Linear Equation Literal Solution More
  365.    wt: 3:   2 Linear Equation Literal Solution
  366.    wt: 3:   1 Changing Calculations
  367.    wt: 3:   6 Equations and Systems Equivalent or Implied
  368.    wt: 3:   5 Equality in Algebra
  369.    wt: 3:   4 Subtraction and Division Axioms
  370.    wt: 3:   5 Greater More Less Than Signs in General
  371.    wt: 3:   12 Real Number Additive Inverses or Negatives
  372.    wt: 3:   7 Real Numbers as Line Cordinates
  373.    wt: 3:   1 Whole and Natural Numbers
  374.    wt: 3:   3 Geometric Formulas and Function Notation
  375.    wt: 3:   2 Computation Rules Evaluation
  376.    wt: 3:   1 Formulas Dependence and Function Notation
  377.    wt: 3:   4 GE III Animated Examples
  378.    wt: 3:   4 Solving a triangular system exercise
  379.    wt: 3:   3 Solving triangular system example
  380.    wt: 3:   6 Algebraic Solution Example
  381.    wt: 3:   4 Four Examples Fractional Coefficients
  382.    wt: 3:   Formula Usage Show Work Format
  383.    wt: 3:   8 Compound Interest Formula Evaluation
  384.    wt: 3:   9 Sets in Probability and Statistics
  385.    wt: 3:   4 Greater More Less Than Signs in General
  386.    wt: 3:   1 Squares and Square Roots Introduction
  387.    wt: 3:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  388.    wt: 3:   9 GCD of 360 110 via Primes and Euclid Algorithm
  389.    wt: 3:   7 GCD and LCM from prime factorization
  390.    wt: 3:   7 negative and additive inverse
  391.    wt: 3:   2 signed and unsigned numbers as coordinates
  392.    wt: 3:   5 Reciprocals and Division for Fractions with Units
  393.    wt: 3:   1 Addition and Subtraction with Units
  394.    wt: 3:   B Fractions and Two Term Ratios
  395.    wt: 3:   21 Reciprocals for Fractions and Wholes
  396.    wt: 3:   3 Unit fraction of a fraction
  397.    wt: 3:   1 What is a fraction
  398.    wt: 3:   6 Multiplication by Natural Numbers
  399.    wt: 3:   16 Remainder Arithmetic Modulo 9 Example 2
  400.    wt: 3:   15 Remainder Arithmetic Modulo 9 Example
  401.    wt: 3:   14 Remainder Arithmetic Modulo 9 Example
  402.    wt: 3:   13 Remainder Arithmetic Modulo 5 Example
  403.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  404.    wt: 3:   8 Remainder Arithmetic Morulo 5 Examples II
  405.    wt: 3:   7 Remainder Arithmetic Modulo 5 Examples I
  406.    wt: 3:   4 Remainder Arithmetic Modulo 10 in general
  407.    wt: 3:   18 video Count Factors given Prime Factorization
  408.    wt: 3:   15 video Factors of 20 using Prime Factorization
  409.    wt: 3:   10 video Prime Factorization upto 23 squared
  410.    wt: 3:   9 video Prime Factorization upto 19 squared
  411.    wt: 3:   6 Sieve of Eratosthenes and Square Rule
  412.    wt: 3:   1 video how Products are bigger than factor
  413.    wt: 3:   10 Division by Five Long and Short Ways
  414.    wt: 3:   5 Decimal Fraction Multiplication
  415.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  416.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  417.    wt: 3:   Video Power Notation in Decimal Expansion
  418.    wt: 3:   Appendix 2 Three Decimal Subtraction Methods
  419.    wt: 3:   7 Subtraction for Decimal Fractions with Exercises
  420.    wt: 3:   8 What skills and work habits to require
  421.    wt: 3:   6. Counting and adding units and mixed units
  422.    wt: 3:   5. How to add decimals C. Examples
  423.    wt: 3:   1. Explaining Addition Table
  424.    wt: 3:   10 Names for Big Numbers and Powers of Ten Expansion
  425.    wt: 3:   2 Groups of Three Place Value for Multidigit Decimals
  426.    wt: 3:   Quick history of numbers and algebra
  427.    wt: 3:   Formula Evaluation how to show work
  428.    wt: 3:   015 School and work day counting tables
  429.    wt: 3:   014 Counting Days with Calendars
  430.    wt: 3:   010 Repeated Addition of Time Intervals
  431.    wt: 3:   2 Time and Date Matters in School
  432.    wt: 3:   Example 1 volume of a pyramid
  433.    wt: 3:   Area Between Crossing Curves Lesson Take 2
  434.    wt: 3:   Area Between Crossing Curves Lesson Take 1
  435.    wt: 3:   Area Between Curves Lesson Take 2
  436.    wt: 3:   Area Between Curves Lesson Take 1
  437.    wt: 3:   4 Definite Integrals Evaluation Exercises
  438.    wt: 3:   36 Cube root derivative animated
  439.    wt: 3:   29 Chain Rule Optional Reading
  440.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  441.    wt: 3:   8 Four Animated Examples
  442.    wt: 3:   2 Algebraic codification
  443.    wt: 3:   Postscript One Sided and Intermediate Value Theorems
  444.    wt: 3:   .H1 First Fundamental Theorem of Calculus
  445.    wt: 3:   G.2 Differentiable Functions Mean Value Theorem
  446.    wt: 3:   Postscript Pythagorean Theorem yet another proof
  447.    wt: 3:   Chapter 21 Arrow Addition
  448.    wt: 3:   Chapter 16. Velocity Approximation
  449.    wt: 3:   Chapter 15. Slope Approximation
  450.    wt: 3:   Chapter 13. Acceleration
  451.    wt: 3:   Chapter 9 About First Courses in Calculus
  452.    wt: 3:   Chapter 6. Slopes and Vertical Shifts
  453.    wt: 3:   Chapter 4. More Slope Sign Analysis
  454.    wt: 3:   Chapter 3. Slope Sign Analysis
  455.    wt: 3:   Chapter 2. Slopes and Ski Trails
  456.    wt: 3:   Fall 1983 Calculus Appetizer
  457.    wt: 3:   Appendix D. What to do in School and Why
  458.    wt: 3:   Chapter 31 Direct and Indirect Reason
  459.    wt: 3:   Chapter 27 Shorthand Symbols as Pronouns
  460.    wt: 3:   Chapter 26 What is in chapters 27 to 31
  461.    wt: 3:   Chapter 24. Personal Investment and Pension EGS
  462.    wt: 3:   Chapter 18. Rules for Algebra
  463.    wt: 3:   Chapter 15. Solving Linear Equations
  464.    wt: 3:   Postscript Unifying Theme A Fourth Skill For Algebra
  465.    wt: 3:   Chapter 12. Shorthand Usage Guide
  466.    wt: 3:   Chapter 8 Three Skills For Algebra
  467.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  468.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  469.    wt: 3:   Chapter 4 Longer Chains of Reason
  470.    wt: 3:   Chapter 3 Chains of Reason
  471.    wt: 3:   Postscript B Mathematics Education References
  472.    wt: 3:   Chapter 3 Algebra Difficulties
  473.    wt: 3:   Postscript C Consistency as a Tool for Reason
  474.    wt: 3:   Chapter 24 Direct and Indirect Reason
  475.    wt: 3:   Chapter 20 Shorthand Symbols as Pronouns
  476.    wt: 3:   Chapter 19 What is in chapters 20 to 24
  477.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  478.    wt: 3:   Chapter 12 Islands and Divisions of Knowledge
  479.    wt: 3:   Chapter 9 What is in Chapters 10 to 18
  480.    wt: 3:   Chapter 7 Longer Chains of Reason
  481.    wt: 3:   Chapter 6 Chains of Reason
  482.    wt: 3:   Chapter 3 What is in chapters 4 to 8
  483.    wt: 3:   S Adding words to algebra
  484.    wt: 3:   R Why Learn Mathematics Skills
  485.    wt: 3:   N Mathematics Prepare for College Studies
  486.    wt: 3:   N Improving Marks on Tests and Finals
  487.    wt: 3:   I. Logic and language skills
  488.    wt: 3:   D. Check work a must with a caution
  489.    wt: 3:   Helping the Blind in Logic and Mathematics
  490.    wt: 3:   Multiple Ways to Improve Mathematics Skill Development
  491.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  492.    wt: 3:   Systematic Algebra Skill Development Missing Links
  493.    wt: 2:   K LAMP Musings Science Education
  494.    wt: 2:   I LAMP Introduction Study Habits
  495.    wt: 2:   H LAMP Introduction Instructional Concepts
  496.    wt: 2:   Skills Chapter 5 Calculus
  497.    wt: 2:   Skills Chapter 1 Arithmetic
  498.    wt: 2:   11 pure mathematics
  499.    wt: 2:   9 combinatorics probability sets
  500.    wt: 2:   8 analytic geometry etc
  501.    wt: 2:   4 algebra
  502.    wt: 2:   3 Euclidean Geometry Leanly
  503.    wt: 2:   About site lesson plans
  504.    wt: 2:   teacher certification
  505.    wt: 2:   learning takes time
  506.    wt: 2:   grouping students according to ability
  507.    wt: 2:   mathematics in context
  508.    wt: 2:   how letters appear
  509.    wt: 2:   mathematics curriculum shifts
  510.    wt: 2:   Lessening Algebra Difficulties
  511.    wt: 2:   the trouble with algebra
  512.    wt: 2:   05 13 OldSiteEntrancePage
  513.    wt: 2:   04 29 New Mathematics Curriculum
  514.    wt: 2:   04 25 when to stop or suspend mathemat
  515.    wt: 2:   formal or informal peer review
  516.    wt: 2:   Different Kinds of Reasoning in maths
  517.    wt: 2:   Four ways to improve education reform
  518.    wt: 2:   Motivation and Context Problem
  519.    wt: 2:   Prequel In For A Penny In For A Pound
  520.    wt: 2:   fairness and inductive principles for instruction
  521.    wt: 2:   words for mathematics instructor
  522.    wt: 2:   chapitre 04 09 Regles accidentelles
  523.    wt: 2:   chapitre 04 08 Limitations et benefices
  524.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  525.    wt: 2:   chapitre 04 06 engagements
  526.    wt: 2:   chapitre 04 05 Implication versus suggestion
  527.    wt: 2:   chapitre 04 00 Les regles d implication
  528.    wt: 2:   problemes algebre et arithmetique
  529.    wt: 2:   Trois Notions qui menent a algebre
  530.    wt: 2:   deux definitions pour variable
  531.    wt: 2:   3 Like resistors in parallel
  532.    wt: 2:   2 Unlike resistors in parallel01
  533.    wt: 2:   24 Standards For Skill Develoment
  534.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  535.    wt: 2:   22 Student Centered Highschool Mathematics
  536.    wt: 2:   11 Help and Defend Your Child or Teens Education
  537.    wt: 2:   9 Streaming by Student Cooperation
  538.    wt: 2:   8 The Effect of Negative Remarks
  539.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  540.    wt: 2:   2 Reading and Writing Skills
  541.    wt: 2:   Ages 12 to 14 Arithmetic
  542.    wt: 2:   Ages 10 to 12 Arithmetic
  543.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  544.    wt: 2:   19 Horizontal line rule and method
  545.    wt: 2:   18 Vertical Line Rule and Method
  546.    wt: 2:   15 Sign analysis of functions
  547.    wt: 2:   10 Interval Notation
  548.    wt: 2:   8 Set view of relations and functions
  549.    wt: 2:   3 Formula or function graphing exercise
  550.    wt: 2:   10 quadratic exercises
  551.    wt: 2:   Quadratics in 10 steps
  552.    wt: 2:   11 Growth and Decay in Biology
  553.    wt: 2:   5 Polynomials Long division Nonlinear divisor
  554.    wt: 2:   4 Polynomials Long division linear divisor
  555.    wt: 2:   1 Polynomials Distributive Law
  556.    wt: 2:   8 arcsin left inverse of sine Graph
  557.    wt: 2:   6 Graph of arccos function
  558.    wt: 2:   4 possible motivation for term arccos
  559.    wt: 2:   8 Parallel Vectors
  560.    wt: 2:   4 Resultant of a Sum of Movements
  561.    wt: 2:   Vector and Complex Number Applet
  562.    wt: 2:   4 graphing y=Asin(x c)
  563.    wt: 2:   1 graphing y=f(x a)
  564.    wt: 2:   Triangle Angles Sum To 180 Degrees
  565.    wt: 2:   Straight Lines Instersection Solving Equations
  566.    wt: 2:   C Straight Lines Slope from Coordinates
  567.    wt: 2:   B Straight Line Slope Scaling Properties More
  568.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  569.    wt: 2:   12 Straight Lines Graphing mx plus b
  570.    wt: 2:   11 Straight Lines Graphing y=mx
  571.    wt: 2:   10 Straight Lines through Origin Equations More
  572.    wt: 2:   9 Straight Lines through Origin Equations
  573.    wt: 2:   7 Tangent Function is odd on this domain
  574.    wt: 2:   5 Tangent Function Graph
  575.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  576.    wt: 2:   30 unit circle calculation of six trigonometric functions
  577.    wt: 2:   27 Logarithmic use of products of sines and cosines
  578.    wt: 2:   26 Formulas for products of sines and cosines
  579.    wt: 2:   17G Pythagorean Theorem Converse
  580.    wt: 2:   17E Trig Formulas for dot and cross Products
  581.    wt: 2:   17A The complex number valued trig function cis
  582.    wt: 2:   12 Graph of tangent function for one period
  583.    wt: 2:   9 Graphs of sine and cosine over one period
  584.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  585.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  586.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  587.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  588.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  589.    wt: 2:   16 References and Originality Question
  590.    wt: 2:   15 Pythagorean Theorem Converse
  591.    wt: 2:   13 Trig Formulas for dot and cross Products
  592.    wt: 2:   2 Complex Numbers made easier we hope
  593.    wt: 2:   6 Trigonometry Sines of Supplementary Angles
  594.    wt: 2:   3 Trigonometric Ratios sine and cosine
  595.    wt: 2:   1 Angle Measurement with Degrees
  596.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  597.    wt: 2:   12 Triangles Similarity More Problems
  598.    wt: 2:   11 Triangle Similarity Missing Side Problem
  599.    wt: 2:   4 Similarity Definition with Coordinate
  600.    wt: 2:   3 Similarity by Design with coordinates
  601.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  602.    wt: 2:   7 Exercises to test skill and concept mastery
  603.    wt: 2:   5 Algebraic View of Slopes
  604.    wt: 2:   2 point slope equation for a line
  605.    wt: 2:   What is and is not here
  606.    wt: 2:   11 Triangle Inequality
  607.    wt: 2:   8 Distance Between Points on a Line
  608.    wt: 2:   PS G Rotation Distributes over Addition
  609.    wt: 2:   19 Right Triangle Similarity
  610.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  611.    wt: 2:   12 Side Angle Side Failure
  612.    wt: 2:   11 Triangle Construction Fails
  613.    wt: 2:   10 Dropping a perpendicular to line
  614.    wt: 2:   7 Angle Side Angle
  615.    wt: 2:   1 Initial Concepts and Terms
  616.    wt: 2:   A Measurement with Ruler Proper Use
  617.    wt: 2:   6 Figuring with Maps Not to Scale
  618.    wt: 2:   A Signed Number Arithmetic Review
  619.    wt: 2:   23 Distributive Law Two Derivations
  620.    wt: 2:   21 Addition of Multiples of a Single Vector
  621.    wt: 2:   18 Geometrically Why Vector Addition Commutes
  622.    wt: 2:   12 Real Numbers Line Signed Coordinates
  623.    wt: 2:   9 Division with Digits after Decimal Point
  624.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  625.    wt: 2:   2 Counting Digits in Decimal Multiplication
  626.    wt: 2:   C Three Decimal Subtraction Methods
  627.    wt: 2:   8 Column Multiplication Methods in General
  628.    wt: 2:   6 Column Methods for Decimal Multiplication
  629.    wt: 2:   4 Commutative Law Groups Counting Form
  630.    wt: 2:   2 Combing Counts Addition Skills and Principles
  631.    wt: 2:   3 Proportionality Examples
  632.    wt: 2:   2 Algebraic View
  633.    wt: 2:   1 What is Proportionality
  634.    wt: 2:   1 Equivalent Computation Rules
  635.    wt: 2:   4 Comparison of Negative Numbers
  636.    wt: 2:   3 More and Less Than with Unlike Signs
  637.    wt: 2:   1 Real Numbers Comparison
  638.    wt: 2:   16 Real Numbers Comparison
  639.    wt: 2:   14 Real Number Multiplication
  640.    wt: 2:   13 Real Number Subtraction
  641.    wt: 2:   11 Real Number Addition
  642.    wt: 2:   10 Real Number Lengths and Signs
  643.    wt: 2:   9 Coordinates for Regions in Space
  644.    wt: 2:   5 Rational Numbers More
  645.    wt: 2:   4 Rational Numbers
  646.    wt: 2:   5 Independent versus Dependent Variables
  647.    wt: 2:   5 Algebraic Solutions Introduction
  648.    wt: 2:   1 Proper Equal Sign Usage
  649.    wt: 2:   Using Letters for Physical Quantities
  650.    wt: 2:   13 Naming Identifying Formulas with Words
  651.    wt: 2:   5 Box Volume Formula Example
  652.    wt: 2:   1 Written work formats for developing and showing skill
  653.    wt: 2:   7 Cautious or Safe Set Construction
  654.    wt: 2:   2 Venn Diagrams
  655.    wt: 2:   3 Adding Words To Arithmetic
  656.    wt: 2:   1 Three Skills For Algebra
  657.    wt: 2:   3 Comparison of Negative Numbers
  658.    wt: 2:   2 More and Less Than with Unlike Signs
  659.    wt: 2:   3 Properties of Square Roots with example
  660.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  661.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  662.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  663.    wt: 2:   13 GCD from given Prime Factorization
  664.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  665.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  666.    wt: 2:   8 GCD from Euclidean Algorithm
  667.    wt: 2:   4 LCM of 8 and 10 via Prime
  668.    wt: 2:   2 Least Common Multiple LCM intro via list method
  669.    wt: 2:   5 Counting with Tables Trees Product Rule Take II
  670.    wt: 2:   3 Counting with Tables and Trees II
  671.    wt: 2:   2 Counting with Tables and Trees I
  672.    wt: 2:   4 signed coordinates for regions in space
  673.    wt: 2:   6 Simplification of Fractions with Units
  674.    wt: 2:   2 Equality and Units
  675.    wt: 2:   12 Fraction Comparison
  676.    wt: 2:   9 Improper Fractions and Mixed Numbers
  677.    wt: 2:   5 Equivalent Fractions
  678.    wt: 2:   4 Fraction Multiplication
  679.    wt: 2:   2 Unit Fraction Multiplication
  680.    wt: 2:   D Remainders Modulo 11 Pair Rule
  681.    wt: 2:   13 Subtraction with Additive Inverse
  682.    wt: 2:   12 Adding Integers More Examples
  683.    wt: 2:   10 Integer Multiplication Formulas
  684.    wt: 2:   5 Zero Movement and Additive Inverses
  685.    wt: 2:   3 Adding Movements with same direction
  686.    wt: 2:   1 Integers as Coordinates
  687.    wt: 2:   23 Remainder Arithmetic Modulo 2
  688.    wt: 2:   22 Remainder Arithmetic Modulo 3 more
  689.    wt: 2:   21 Remainder Arithmetic Modulo 3
  690.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  691.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  692.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  693.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  694.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  695.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  696.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  697.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  698.    wt: 2:   5 Remainder Arithmetic Modulo 5
  699.    wt: 2:   3 Remainder Arithmetic Modulos 10 more still
  700.    wt: 2:   2 Remainder Arithmetic Modulo 10 more
  701.    wt: 2:   1 Remainder Arithmetic Modulo 10
  702.    wt: 2:   20 Uniqueness of Prime Factorization
  703.    wt: 2:   19 video Prime Factorization Unique
  704.    wt: 2:   17 Identify and Count Factors using Primes
  705.    wt: 2:   14 video Factors of 24 Take II
  706.    wt: 2:   8 video Prime Factorization upto 19
  707.    wt: 2:   4 video Prime Factorization Introduction
  708.    wt: 2:   3 video Primes and Composites from 9 times table
  709.    wt: 2:   2 Prime and Composites less than 16
  710.    wt: 2:   Long Division Backwards more
  711.    wt: 2:   Long Division Backward
  712.    wt: 2:   11 Another Single Digit Divisor Example
  713.    wt: 2:   7 Long Divison Mistake Catching
  714.    wt: 2:   6 Why Decimal Long Division Methods Works Take I
  715.    wt: 2:   1 Divsion Physical Examples
  716.    wt: 2:   D Decimal Multiplication Methods Derived
  717.    wt: 2:   C Counting Areas with Powers of Ten
  718.    wt: 2:   6 Multiplication Commutes Order Not Important
  719.    wt: 2:   Subtraction with J Conversions Example
  720.    wt: 2:   Subtraction Another Video Lesson
  721.    wt: 2:   8 Subtraction with Units of Measure
  722.    wt: 2:   6 Subtraction with Conversion Example with Exercises
  723.    wt: 2:   5 A Tip for Efficent Subtraction
  724.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  725.    wt: 2:   4. How to add with decimals B with conversions
  726.    wt: 2:   2 Decimal Counting Practices
  727.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  728.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  729.    wt: 2:   1 Place Value in Three Digit Whole Numbers
  730.    wt: 2:   Expression Evaluation how to show work
  731.    wt: 2:   The 12 Times Table Visually
  732.    wt: 2:   013 Travel Time Tables
  733.    wt: 2:   012 Division of Time Intervals by Time Intervals
  734.    wt: 2:   7 Addition of Time Intervals
  735.    wt: 2:   4 Mixing and Changing Units of Time
  736.    wt: 2:   Example 2 volume of a cone
  737.    wt: 2:   5 Area Under Curve Exercise
  738.    wt: 2:   1 Chain Rule in Reverse Integration Method
  739.    wt: 2:   A Related lessons in Volume 3
  740.    wt: 2:   4 Second derivative test exercise example
  741.    wt: 2:   34 Derivative of exponential function
  742.    wt: 2:   30Chain Rule A Proof
  743.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  744.    wt: 2:   23 Chain Rule in general
  745.    wt: 2:   22 Chain Rule for polynomials
  746.    wt: 2:   19 Chain Rule for linear functions
  747.    wt: 2:   17 Derivatives of quotients of sine and cosine
  748.    wt: 2:   15 sine and cosine derivatives 3rd step
  749.    wt: 2:   14 sine and cosine derivatives 2nd step
  750.    wt: 2:   13 sine and cosine derivatives 1st step
  751.    wt: 2:   8 Differentiation of polynomials
  752.    wt: 2:   3 Motivation for Limit Definition Take 2
  753.    wt: 2:   2 Motivation for Limit Definition Take 1
  754.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  755.    wt: 2:   11 Limits at infinity Three Examples
  756.    wt: 2:   6 Continuity at a point
  757.    wt: 2:   5 Jumps and absence of unlimited error control
  758.    wt: 2:   .H2 Lipshitz Conditions Integration Calculus Reform
  759.    wt: 2:   G.3 Constant Difference Theorem Proof
  760.    wt: 2:   F.3 Intermediate Value Theorem
  761.    wt: 2:   F.1 What Functions are Continuous
  762.    wt: 2:   E2 Algebraic Properties of Limits
  763.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  764.    wt: 2:   C Triangle Inequalities
  765.    wt: 2:   B3 Bolzano Weierstrass Theorem
  766.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  767.    wt: 2:   Chapter 12. Units and Slopes
  768.    wt: 2:   Chapter 11. Graphing Slope versus Position
  769.    wt: 2:   Chapter 10 Slopes and Units
  770.    wt: 2:   Chapter 8. Slope Interpretation
  771.    wt: 2:   Chapter 7 Slopes and Velocity
  772.    wt: 2:   Appendix C. How to Read
  773.    wt: 2:   Appendix B. How To Learn
  774.    wt: 2:   Chapter 30 Truth Tables
  775.    wt: 2:   Chapter 28 Occurrence Tables
  776.    wt: 2:   Chapter 23. Notation For Sums
  777.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  778.    wt: 2:   Chapter 21. Third Reading Guide
  779.    wt: 2:   Chapter 19. Functions and Sets
  780.    wt: 2:   Chapter 16. Painless Theorem Proving
  781.    wt: 2:   Chapter 13. Second Reading Guide
  782.    wt: 2:   Chapter 11. Why Shorthand
  783.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  784.    wt: 2:   Postscript A Three Remarks
  785.    wt: 2:   Chapter 12 Four Phases
  786.    wt: 2:   Chapter 11 Elementary Instruction
  787.    wt: 2:   Chapter 10 Transition
  788.    wt: 2:   Chapter 7 Two Treatments of Geometry
  789.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  790.    wt: 2:   Postscript B More on Story Telling and Reason
  791.    wt: 2:   Chapter 23 Truth Tables
  792.    wt: 2:   Chapter 21 Occurrence Tables
  793.    wt: 2:   Chapter 18 Sense and Knowledge
  794.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  795.    wt: 2:   L Skills with take home value
  796.    wt: 2:   H Jigsaw puzzles and problem solving
  797.    wt: 2:   G. Written work formats for developing and showing skill
  798.    wt: 2:   F. The student teacher tutor feedback loop
  799.    wt: 2:   A. Skill has to be seen to believed
  800.    wt: 2:   Ends Values Methods For Skill Development Framework Prequel
  801.    wt: 2:   Road Safety Questions
  802.    wt: 1:   J LAMP Introduction Extrinsic Origins
  803.    wt: 1:   G LAMP Introduction Problem Solving Skills
  804.    wt: 1:   F LAMP Introduction Prerequisites
  805.    wt: 1:   A Introduction Objectives
  806.    wt: 1:   Skills Chapter 4 Logic
  807.    wt: 1:   Ramblings Extrinsic numbers theory
  808.    wt: 1:   Skills Chapter 2 Geometry
  809.    wt: 1:   Skills Chapter 0 Introduction
  810.    wt: 1:   10 statistics
  811.    wt: 1:   6 polynomials etc
  812.    wt: 1:   2 arithmetic with signed numbers
  813.    wt: 1:   1 arithmetic with unsigned numbers
  814.    wt: 1:   What is POMME
  815.    wt: 1:   which way to go
  816.    wt: 1:   three goals to set for students
  817.    wt: 1:   permissions for teachers
  818.    wt: 1:   activities for students
  819.    wt: 1:   links Education Resources online
  820.    wt: 1:   site eurekas
  821.    wt: 1:   key notes and themes
  822.    wt: 1:   modern education
  823.    wt: 1:   Education Reform Inconsistencies
  824.    wt: 1:   teaching tips
  825.    wt: 1:   What to Tell Students
  826.    wt: 1:   02 21 words for teachers
  827.    wt: 1:   cultivating intelligence
  828.    wt: 1:   How to be a better instructor
  829.    wt: 1:   chapitre 12 00 les iles et division
  830.    wt: 1:   chapitre 05 00 Deception
  831.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  832.    wt: 1:   chapitre 04 02 Deuxieme enigme
  833.    wt: 1:   chapitre 04 01 Premiere enigme
  834.    wt: 1:   chapitre 01 00 Introduction
  835.    wt: 1:   4 Energy Power Heat09
  836.    wt: 1:   3 Energy Power Heat08
  837.    wt: 1:   2 Energy Power Heat07
  838.    wt: 1:   1 Energy Power Heat06
  839.    wt: 1:   A Energy Power01
  840.    wt: 1:   E Kirchoffs Second Law
  841.    wt: 1:   D Kirchoff First Law
  842.    wt: 1:   C Electromotive force conventional current02
  843.    wt: 1:   B Electromotive force conventional current01
  844.    wt: 1:   A Circuit Elements
  845.    wt: 1:   Home Tutoring and Home Schooling
  846.    wt: 1:   15 Counting For Parents
  847.    wt: 1:   10 Ends values for work study instruction
  848.    wt: 1:   7 Student Motivation
  849.    wt: 1:   3 Preparing for Science Studies
  850.    wt: 1:   1 Speaking Skills
  851.    wt: 1:   Ages 12 to 14 Geometry
  852.    wt: 1:   Ages 10 to 12 Geometry
  853.    wt: 1:   Ages 9 to 10
  854.    wt: 1:   Ages 8 to 9
  855.    wt: 1:   Ages 7 to 8
  856.    wt: 1:   Ages 6 to 7
  857.    wt: 1:   Ages 4 plus to 5 plus
  858.    wt: 1:   Ages 3 plus to 4 plus
  859.    wt: 1:   26 Function definitions done and coming
  860.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  861.    wt: 1:   13 From one to one to many to one
  862.    wt: 1:   12 Function Domain Recognition Exercises
  863.    wt: 1:   9 Set theory term relation possible origins
  864.    wt: 1:   7 Functions with finite domains
  865.    wt: 1:   1 Geometric Introduction of Function Notation
  866.    wt: 1:   Introduction Reading Guide
  867.    wt: 1:   2 Column Multiplication Method
  868.    wt: 1:   7 arcsin left inverse of sine Definition
  869.    wt: 1:   3 Left Inverse of cosine arccos definition
  870.    wt: 1:   15 Dot and Cross Product
  871.    wt: 1:   6 Vectors with Coordinates
  872.    wt: 1:   2 Signed Coordinates
  873.    wt: 1:   1 Unsigned Coordinates
  874.    wt: 1:   3 graphing y=f(x c) plus K
  875.    wt: 1:   Straight Lines Intersection of
  876.    wt: 1:   4 Tangent Function Properties
  877.    wt: 1:   1 Straight Lines Slope Concept
  878.    wt: 1:   28 Expressing products of sines cosines as sums
  879.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  880.    wt: 1:   17F Law of cosines
  881.    wt: 1:   8 period of tangent function
  882.    wt: 1:   7 period of sine and cosine
  883.    wt: 1:   1 Unit Points Reflections Rotations
  884.    wt: 1:   14 Law of cosines
  885.    wt: 1:   9 The complex number valued trig function cis
  886.    wt: 1:   4 Multiplication Properties
  887.    wt: 1:   3 Addition Properties
  888.    wt: 1:   7 Trignometric Ratios Unit Circle
  889.    wt: 1:   2 Similarity By Design
  890.    wt: 1:   8 Mid Point Formula
  891.    wt: 1:   6 Intersection of lines by solving linear systems
  892.    wt: 1:   4 Equations for lines three forms
  893.    wt: 1:   3 Slope product for perpendicular lines
  894.    wt: 1:   7 Complex Numbers Appetizer
  895.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  896.    wt: 1:   PS H Distributive Law For Complex Numbers
  897.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  898.    wt: 1:   PS A Kite Construction Methods
  899.    wt: 1:   17 Right Bisectors of Triangle Sides
  900.    wt: 1:   9 Construction of a right bisector
  901.    wt: 1:   8 Isoceles Triangles
  902.    wt: 1:   5 Side Angle Side
  903.    wt: 1:   3 Isometry of Triangles Congruence
  904.    wt: 1:   2 Correspondence between Triangles
  905.    wt: 1:   Short Course on Euclidean Geometry
  906.    wt: 1:   1 Length Measurement
  907.    wt: 1:   About Folder Contents
  908.    wt: 1:   musings do not puiblish real numbers
  909.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  910.    wt: 1:   22 Multiplication of Signed Numbers
  911.    wt: 1:   5 Distributive Law for Whole Numbers
  912.    wt: 1:   3 Multiplicative Counting Skills Principles
  913.    wt: 1:   3 Product Axioms Two Forms
  914.    wt: 1:   15 Real Number Division
  915.    wt: 1:   6 Unsigned Real Numbers
  916.    wt: 1:   3 Fractions
  917.    wt: 1:   4 Changing Letters
  918.    wt: 1:   2 GE II Comparison
  919.    wt: 1:   1 GE Substitution four examples
  920.    wt: 1:   2 Essentially one exercises three with solution
  921.    wt: 1:   1 Essentially One Unknown
  922.    wt: 1:   3 Four Examples
  923.    wt: 1:   2 Three Examples
  924.    wt: 1:   10 One Example
  925.    wt: 1:   9 Three Examples
  926.    wt: 1:   8 One Example
  927.    wt: 1:   7 Two Examples
  928.    wt: 1:   6 Three Examples
  929.    wt: 1:   5 Three Examples
  930.    wt: 1:   4 Two Examples
  931.    wt: 1:   3 Two Examples
  932.    wt: 1:   2 Three Examples
  933.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  934.    wt: 1:   10 Volume of Pyramid
  935.    wt: 1:   7 Compound Interest Formula Introduction
  936.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  937.    wt: 1:   6 Power Set Notation
  938.    wt: 1:   5 Product Builder Notation
  939.    wt: 1:   4 Subset Builder Notation
  940.    wt: 1:   About Folder Contents
  941.    wt: 1:   5 Square Roots with primes more still
  942.    wt: 1:   4 Square Roots with primes more
  943.    wt: 1:   2 Square Roots with Prime
  944.    wt: 1:   5 Common Divisors 60 45 via Prime
  945.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  946.    wt: 1:   1 Least Common Multiples LCM Introduction
  947.    wt: 1:   12 GCD 2700 288 via Prime
  948.    wt: 1:   4 Counting with Trees Product Rule Take I
  949.    wt: 1:   1 Counting and Counting Methods I
  950.    wt: 1:   9 subtracting signed numbers
  951.    wt: 1:   6 adding signed numbers
  952.    wt: 1:   5 lengths and signs of numbers
  953.    wt: 1:   7 Converting or Changing Units
  954.    wt: 1:   4 Fractions with Units
  955.    wt: 1:   3 Multiplying Units and Numbers
  956.    wt: 1:   D Three Term Ratios
  957.    wt: 1:   22 Complex Compound Fractions
  958.    wt: 1:   20 Dividing Fractions the Why
  959.    wt: 1:   19 Dividing Fractions How TO
  960.    wt: 1:   18 Efficient Ways to Multiply
  961.    wt: 1:   8 Multiplication by Signed Numbers Integers
  962.    wt: 1:   7 Multiplication by Signs
  963.    wt: 1:   4 Adding Movements wiht opposite directions
  964.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  965.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  966.    wt: 1:   26 Divisibility by 2 3 5 Example
  967.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  968.    wt: 1:   16 video Factors of 980 using prime
  969.    wt: 1:   13 video Factors of 24 using prime
  970.    wt: 1:   12 LCD GCD and LCM using Primes
  971.    wt: 1:   11 Efficient Square Rule Use
  972.    wt: 1:   Division with Counts and Length
  973.    wt: 1:   12 Why Long Division Works Take III
  974.    wt: 1:   9 Why Long Division Works Take II
  975.    wt: 1:   8 Correcting the Mistake
  976.    wt: 1:   3 Division Single Digit Divisor Example
  977.    wt: 1:   4 Two and Three Digit Multipliers
  978.    wt: 1:   9 22 Minute Subtraction Review Video
  979.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  980.    wt: 1:   The 20 Times Table
  981.    wt: 1:   About folder contents
  982.    wt: 1:   011 Division of Time Intervals By Numbers
  983.    wt: 1:   6 How long is a million seconds
  984.    wt: 1:   5 Conversion Arithmetic
  985.    wt: 1:   3 Units and Lengths of Time
  986.    wt: 1:   1 Intro of Kids To Time Date Skills
  987.    wt: 1:   Example 4 with x function of y
  988.    wt: 1:   Example 3
  989.    wt: 1:   Example 2
  990.    wt: 1:   Example 1
  991.    wt: 1:   Summary
  992.    wt: 1:   3 Two Chain Rule Method Exercises
  993.    wt: 1:   2 Indefinite Integrals Exercises
  994.    wt: 1:   3 Second derivative test
  995.    wt: 1:   2 Second derivative test prequel
  996.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  997.    wt: 1:   31 Derivatives of inverse functions
  998.    wt: 1:   26 Chain Rule Recognising outer inner functions
  999.    wt: 1:   21 Chain Rule for powers
  1000.    wt: 1:   20 Chain Rule for Pulley Systems
  1001.    wt: 1:   18 Chain Rule Introduction
  1002.    wt: 1:   12 Quotient rule examples
  1003.    wt: 1:   10 Power rule for negative integers
  1004.    wt: 1:   9 Reciprocal rule
  1005.    wt: 1:   10 Three one sided limits with infinite values
  1006.    wt: 1:   9 Limits Continuity and Composition
  1007.    wt: 1:   4 Numerical properties
  1008.    wt: 1:   3 Decimal insights for limits continuity convergence
  1009.    wt: 1:   1 Numerical introduction
  1010.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  1011.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  1012.    wt: 1:   F.5b Extreme Value Theorem
  1013.    wt: 1:   F.5a Equicontinuity Theorems
  1014.    wt: 1:   F.2 Closed Range Theorem
  1015.    wt: 1:   E1 Error Control Inequalities
  1016.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  1017.    wt: 1:   A1. Introduction
  1018.    wt: 1:   Chapter 23 Links To Trigonometry
  1019.    wt: 1:   Chapter 22 Complex Numbers
  1020.    wt: 1:   Chapter 5. Slope Sign Tests
  1021.    wt: 1:   Chapter 1.Introduction
  1022.    wt: 1:   Postscript More on Better Performance
  1023.    wt: 1:   Postscript For Better Performance
  1024.    wt: 1:   Solutions For Arithmetic Exercises
  1025.    wt: 1:   Chapter 9 The Two Ends
  1026.    wt: 1:   Chapter 8 Modern Instruction
  1027.    wt: 1:   Chapter 5 Four References
  1028.    wt: 1:   Chapter 1 Introduction
  1029.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  1030.    wt: 1:   Postscript A Story Telling
  1031.    wt: 1:   Chapter 15 Objective Processes
  1032.    wt: 1:   Chapter 10 Responsibility
  1033.    wt: 1:   Chapter 5 Deception
  1034.    wt: 1:   Chapter 2 Skill Development
  1035.    wt: 1:   Chapter 1 Introduction
  1036.    wt: 1:   Three Remarks
  1037.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  1038.    wt: 1:   M Words to extend arithmetic
  1039.    wt: 1:   J. More on written work and showing skill
  1040.    wt: 1:   E. When and how to correct errors
  1041.    wt: 1:   C. Domino effect of being careful
  1042.    wt: 1:   How to Build Skills and Confidence
  1043.    wt: 1:   Implementation Notes
  1044.    wt: 1:   Which Way To Go

Extended Search

1116 matches:

  1.    wt: 9:   K LAMP Musings Science Education
  2.    wt: 9:   I LAMP Introduction Study Habits
  3.    wt: 9:   H LAMP Introduction Instructional Concepts
  4.    wt: 9:   Skills Chapter 5 Calculus
  5.    wt: 9:   Skills Chapter 1 Arithmetic
  6.    wt: 9:   5 logarithms and exponentials etc
  7.    wt: 9:   Applied Maths Program14092009 POMME variant
  8.    wt: 9:   five decades make a difference
  9.    wt: 9:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  10.    wt: 9:   Objectives for Mathematics and Logic Language Skill Development
  11.    wt: 9:   A Quadratics Summary
  12.    wt: 9:   9 quadratics physical and further context
  13.    wt: 9:   7 quadratic formulla derivation
  14.    wt: 9:   4 quadratics difference of two squares
  15.    wt: 9:   2 quadratics graphing in general
  16.    wt: 9:   10 Exponential Growth and Decay Models
  17.    wt: 9:   9 Formulas for Real Exponents with Logarithms
  18.    wt: 9:   7 Formulas for Roots with Logarithms Derivation
  19.    wt: 9:   6 Formulas for Even and Odd Roots with Logarithms
  20.    wt: 9:   2 Square Root Simplification a prequel
  21.    wt: 9:   1 Calculator Starter Exercises
  22.    wt: 9:   4 graphing y=Asin(x c)
  23.    wt: 9:   1 graphing y=f(x a)
  24.    wt: 9:   SAS Method For Isometric Or Proportional Triangle Construction
  25.    wt: 9:   Analytic View of Triangle Construction or Line Instersection More
  26.    wt: 9:   Straight Lines ASA Intersection Study More
  27.    wt: 9:   Straight Lines ASA Intersection Study
  28.    wt: 9:   14 Straight Lines Equations General Case
  29.    wt: 9:   6 Tangent Function Inclination Angle Take 2
  30.    wt: 9:   7 Translations Rotations Reflections Dilatations
  31.    wt: 9:   11 Triangle Inequality
  32.    wt: 9:   8 Distance Between Points on a Line
  33.    wt: 9:   5 Drawing to Scale Avoids Angle Distortions
  34.    wt: 9:   A Modular and Remainder Arithmetic
  35.    wt: 9:   25 Mid way Convergence to Axiomatic Approach
  36.    wt: 9:   B Decimal Comparison and Subtraction
  37.    wt: 9:   6 Compound Interest Forward and Backwards
  38.    wt: 9:   1 Equivalent Computation Rules
  39.    wt: 9:   3 Geometric Formulas and Function Notation
  40.    wt: 9:   2 Computation Rules Evaluation
  41.    wt: 9:   1 Formulas Dependence and Function Notation
  42.    wt: 9:   2 GE II Comparison
  43.    wt: 9:   1 GE Substitution four examples
  44.    wt: 9:   4 Solving a triangular system exercise
  45.    wt: 9:   3 Solving triangular system example
  46.    wt: 9:   5 Algebraic Solutions Introduction
  47.    wt: 9:   1 Proper Equal Sign Usage
  48.    wt: 9:   Skill Development Notes
  49.    wt: 9:   13 Naming Identifying Formulas with Words
  50.    wt: 9:   5 Box Volume Formula Example
  51.    wt: 9:   1 Written work formats for developing and showing skill
  52.    wt: 9:   1 Squares and Square Roots Introduction
  53.    wt: 9:   17 Efficient Ways to Add and Subtract
  54.    wt: 9:   16 Addition Subtraction Comparision Compared
  55.    wt: 9:   15 Adding and Subtracting with Unlike Denominators
  56.    wt: 9:   14 Adding and Subtracting with Like Denominators
  57.    wt: 9:   13 Fraction Comparison Algebraic View
  58.    wt: 9:   11 Simplification an Algebraic View
  59.    wt: 9:   10 Simplification of Fractions and Mixed Numerals
  60.    wt: 9:   1 What is a fraction Take II
  61.    wt: 9:   16 Remainder Arithmetic Modulo 9 Example 2
  62.    wt: 9:   15 Remainder Arithmetic Modulo 9 Example
  63.    wt: 9:   14 Remainder Arithmetic Modulo 9 Example
  64.    wt: 9:   13 Remainder Arithmetic Modulo 5 Example
  65.    wt: 9:   12 Remainder Arithmetic Modulo 10 Example
  66.    wt: 9:   8 Remainder Arithmetic Morulo 5 Examples II
  67.    wt: 9:   7 Remainder Arithmetic Modulo 5 Examples I
  68.    wt: 9:   4 Remainder Arithmetic Modulo 10 in general
  69.    wt: 9:   7 Calculator Usage Notes and Cautions
  70.    wt: 9:   5 Prime Factorization and a Square Rule
  71.    wt: 9:   5 Decimal Fraction Multiplication
  72.    wt: 9:   9 22 Minute Subtraction Review Video
  73.    wt: 9:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  74.    wt: 9:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  75.    wt: 9:   5 More on Groups of 3 Place Value in Decimal Fractions
  76.    wt: 9:   4 Groups of 3 Place Value in Decimal Fractions
  77.    wt: 9:   Example 4 with x function of y
  78.    wt: 9:   Example 3
  79.    wt: 9:   Example 2
  80.    wt: 9:   Example 1
  81.    wt: 9:   38 Formulas and derivatives for powers and roots
  82.    wt: 9:   33 Chain Rule Real Player video examples
  83.    wt: 9:   28 Chain Rule Preparation for a Proof
  84.    wt: 9:   25 Chain Rule Animated Examples Continued
  85.    wt: 9:   24 Chain Rule Animated Examples
  86.    wt: 9:   7 Animated Differentiation Examples
  87.    wt: 9:   Chapter 14. Forward and Backward Use of a Formula
  88.    wt: 9:   Chapter 17 Objective Ways Trial and Error Discovery
  89.    wt: 9:   Chapter 11 Accidental Patterns
  90.    wt: 9:   Chapter 8 Change of Language
  91.    wt: 9:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  92.    wt: 8:   J LAMP Introduction Extrinsic Origins
  93.    wt: 8:   G LAMP Introduction Problem Solving Skills
  94.    wt: 8:   F LAMP Introduction Prerequisites
  95.    wt: 8:   A Introduction Objectives
  96.    wt: 8:   Skills Chapter 4 Logic
  97.    wt: 8:   Ramblings Extrinsic numbers theory
  98.    wt: 8:   Skills Chapter 2 Geometry
  99.    wt: 8:   Skills Chapter 0 Introduction
  100.    wt: 8:   11 pure mathematics
  101.    wt: 8:   9 combinatorics probability sets
  102.    wt: 8:   8 analytic geometry etc
  103.    wt: 8:   4 algebra
  104.    wt: 8:   3 Euclidean Geometry Leanly
  105.    wt: 8:   talk the algebra talk
  106.    wt: 8:   teaching tutoring algebraic reason
  107.    wt: 8:   three goals for Mathematics Education
  108.    wt: 8:   standards for course material
  109.    wt: 8:   Education in mathematics science and technology
  110.    wt: 8:   education an empirical art
  111.    wt: 8:   5 quadratics completing the square
  112.    wt: 8:   3 quadratics factoring by inspection
  113.    wt: 8:   1 quadratics graphing exercises
  114.    wt: 8:   11 Growth and Decay in Biology
  115.    wt: 8:   3 Polynomials Multiplication Addition
  116.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  117.    wt: 8:   3 graphing y=f(x c) plus K
  118.    wt: 8:   Straight Lines Instersection Solving Equations
  119.    wt: 8:   D Straight Lines Slope from Coordinates Examples
  120.    wt: 8:   A Straight Line Slope Scaling Properties
  121.    wt: 8:   8 Straight Lines Equation for vertical
  122.    wt: 8:   29 secant cosecant and cotangent for acute angles
  123.    wt: 8:   10 Similarity of Triangles Equivalent of Two Criteria
  124.    wt: 8:   9 Similarity of Triangles Usual Criteria
  125.    wt: 8:   5 Similarity of Circles Squares and Rectangles
  126.    wt: 8:   11 A Partial Summary
  127.    wt: 8:   7 Complex Numbers Appetizer
  128.    wt: 8:   PS F Scalar Multiplication Distributes over Addition
  129.    wt: 8:   PS D Addition with Cartesian Coordinates
  130.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  131.    wt: 8:   2 Measuring Area Directly
  132.    wt: 8:   14 Vector Head to Tail Sums and Resultants
  133.    wt: 8:   13 Arrows and Vectors in a Plane
  134.    wt: 8:   A Decimal Addition Columm Methods
  135.    wt: 8:   7 Decimals Multiplication Methods Examples
  136.    wt: 8:   7 Pythagorean Theorem Chinese Square Proof
  137.    wt: 8:   3 Linear Equation Literal Solution More
  138.    wt: 8:   2 Linear Equation Literal Solution
  139.    wt: 8:   1 Changing Calculations
  140.    wt: 8:   3 Product Axioms Two Forms
  141.    wt: 8:   8 Coordinates for Maps and Planes
  142.    wt: 8:   5 Independent versus Dependent Variables
  143.    wt: 8:   3 Four Examples
  144.    wt: 8:   2 Three Examples
  145.    wt: 8:   Formula Usage Show Work Format
  146.    wt: 8:   12 Cone Cylinder Sphere Lesson Idea
  147.    wt: 8:   10 Volume of Pyramid
  148.    wt: 8:   7 Compound Interest Formula Introduction
  149.    wt: 8:   1 More and Less Than for Counts and Measures
  150.    wt: 8:   3 Properties of Square Roots with example
  151.    wt: 8:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  152.    wt: 8:   9 GCD of 360 110 via Primes and Euclid Algorithm
  153.    wt: 8:   7 GCD and LCM from prime factorization
  154.    wt: 8:   5 Counting with Tables Trees Product Rule Take II
  155.    wt: 8:   3 Counting with Tables and Trees II
  156.    wt: 8:   2 Counting with Tables and Trees I
  157.    wt: 8:   5 Reciprocals and Division for Fractions with Units
  158.    wt: 8:   1 Addition and Subtraction with Units
  159.    wt: 8:   B Fractions and Two Term Ratios
  160.    wt: 8:   21 Reciprocals for Fractions and Wholes
  161.    wt: 8:   3 Unit fraction of a fraction
  162.    wt: 8:   1 What is a fraction
  163.    wt: 8:   23 Remainder Arithmetic Modulo 2
  164.    wt: 8:   22 Remainder Arithmetic Modulo 3 more
  165.    wt: 8:   21 Remainder Arithmetic Modulo 3
  166.    wt: 8:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  167.    wt: 8:   19 Remainder Arithmetic Rule of 9 for checking sums III
  168.    wt: 8:   18 Remainder Arithmetic Rule of 9 for checking sums II
  169.    wt: 8:   17 Remainder Arithmetic Rule of 9 for checking sums I
  170.    wt: 8:   11 Remainder Arithmetic Long Division by 5 Quickly more
  171.    wt: 8:   10 Remainder Arithmetic Long Division by 5 Quickly
  172.    wt: 8:   9 Remainder Arithmetic Divisibility by 5
  173.    wt: 8:   6 Remainder Arithmetic Modulo 5 Propertie
  174.    wt: 8:   5 Remainder Arithmetic Modulo 5
  175.    wt: 8:   3 Remainder Arithmetic Modulos 10 more still
  176.    wt: 8:   2 Remainder Arithmetic Modulo 10 more
  177.    wt: 8:   1 Remainder Arithmetic Modulo 10
  178.    wt: 8:   18 video Count Factors given Prime Factorization
  179.    wt: 8:   15 video Factors of 20 using Prime Factorization
  180.    wt: 8:   10 video Prime Factorization upto 23 squared
  181.    wt: 8:   9 video Prime Factorization upto 19 squared
  182.    wt: 8:   1 video how Products are bigger than factor
  183.    wt: 8:   Long Division Backwards more
  184.    wt: 8:   Long Division Backward
  185.    wt: 8:   10 Division by Five Long and Short Ways
  186.    wt: 8:   D Decimal Multiplication Methods Derived
  187.    wt: 8:   C Counting Areas with Powers of Ten
  188.    wt: 8:   6 Multiplication Commutes Order Not Important
  189.    wt: 8:   10 Names for Big Numbers and Powers of Ten Expansion
  190.    wt: 8:   2 Groups of Three Place Value for Multidigit Decimals
  191.    wt: 8:   016 Numbering Occidental Calendar Days
  192.    wt: 8:   9 Comparison and Subtraction of Time Intervals
  193.    wt: 8:   8 Addition of Time Intervals via subtotaling
  194.    wt: 8:   Volume of Solid by Cross Sections Lesson
  195.    wt: 8:   Summary
  196.    wt: 8:   36 Cube root derivative animated
  197.    wt: 8:   29 Chain Rule Optional Reading
  198.    wt: 8:   16 Derivatives of reciprocals of sine and cosine
  199.    wt: 8:   13 Limits with Parameters and Derivatives Take II
  200.    wt: 8:   12 Limits with Parameters and Derivatives Take I
  201.    wt: 8:   PostScript For and Against Decimal Perspectives
  202.    wt: 8:   Chapter 19. Exponentials and Natural Logarithms
  203.    wt: 8:   Chapter 2 Implication Rules Forwards and Backwards
  204.    wt: 8:   Chapter 2 For and Against Mathematics
  205.    wt: 8:   Postscript C Consistency as a Tool for Reason
  206.    wt: 8:   Chapter 24 Direct and Indirect Reason
  207.    wt: 8:   Chapter 20 Shorthand Symbols as Pronouns
  208.    wt: 8:   Chapter 19 What is in chapters 20 to 24
  209.    wt: 8:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  210.    wt: 8:   Chapter 12 Islands and Divisions of Knowledge
  211.    wt: 8:   Chapter 9 What is in Chapters 10 to 18
  212.    wt: 8:   Chapter 7 Longer Chains of Reason
  213.    wt: 8:   Chapter 6 Chains of Reason
  214.    wt: 8:   Chapter 3 What is in chapters 4 to 8
  215.    wt: 8:   More Algebra and Slope based Calculus Preview
  216.    wt: 8:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  217.    wt: 8:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  218.    wt: 8:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  219.    wt: 7:   10 statistics
  220.    wt: 7:   6 polynomials etc
  221.    wt: 7:   2 arithmetic with signed numbers
  222.    wt: 7:   1 arithmetic with unsigned numbers
  223.    wt: 7:   What is POMME
  224.    wt: 7:   Teach the teachers plus goals
  225.    wt: 7:   Math Ed if it must be short make it lean effective
  226.    wt: 7:   Mathematics Education Professors
  227.    wt: 7:   what should be learnt and When
  228.    wt: 7:   Maps Plans Drawings
  229.    wt: 7:   Secondary Three Mathematics
  230.    wt: 7:   Secondary Two Mathematics
  231.    wt: 7:   Secondary One Mathematics
  232.    wt: 7:   geometric implications for algebra
  233.    wt: 7:   02 20 mathematics education references
  234.    wt: 7:   three aims for mathematics students
  235.    wt: 7:   Operational Viewpoint to Value
  236.    wt: 7:   mathematics instruction in general
  237.    wt: 7:   three kinds of reason in mathematics
  238.    wt: 7:   need for a mixed mathematics curriculum
  239.    wt: 7:   Leaner mathematics curriculum
  240.    wt: 7:   chapitre 07 00 Des chaines plus longues de la raison
  241.    wt: 7:   chapitre 06 00 Chaines de la raison
  242.    wt: 7:   chapitre 03 A Propos Des Prochains Chapitre
  243.    wt: 7:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  244.    wt: 7:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  245.    wt: 7:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  246.    wt: 7:   Ages 12 to 14 Skills with take home value
  247.    wt: 7:   25 Absolute Value greatest integer and saw tooth functions
  248.    wt: 7:   17 Function maxima minima and their location
  249.    wt: 7:   10 quadratic exercises
  250.    wt: 7:   Quadratics in 10 steps
  251.    wt: 7:   5 Polynomials Long division Nonlinear divisor
  252.    wt: 7:   4 Polynomials Long division linear divisor
  253.    wt: 7:   1 Polynomials Distributive Law
  254.    wt: 7:   16 cotangent function Definition Graph and Inverse
  255.    wt: 7:   15 cosecant function Definition Graph and Inverse
  256.    wt: 7:   11 arctan left inverse of tangent Graph
  257.    wt: 7:   A Global Time and Navigation
  258.    wt: 7:   14 Why Scalar Multiplication Distributes Physical Argument
  259.    wt: 7:   Straight Lines Intersection of
  260.    wt: 7:   C Straight Lines Slope from Coordinates
  261.    wt: 7:   B Straight Line Slope Scaling Properties More
  262.    wt: 7:   13 Straight Lines Finding Equations from 2 points
  263.    wt: 7:   12 Straight Lines Graphing mx plus b
  264.    wt: 7:   11 Straight Lines Graphing y=mx
  265.    wt: 7:   10 Straight Lines through Origin Equations More
  266.    wt: 7:   9 Straight Lines through Origin Equations
  267.    wt: 7:   7 Tangent Function is odd on this domain
  268.    wt: 7:   5 Tangent Function Graph
  269.    wt: 7:   2 Straight Lines Slopes As Rise Over Run
  270.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  271.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  272.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  273.    wt: 7:   18 sum of sinusoidal waves as a single wave
  274.    wt: 7:   5 Trigonometric Ratios For Tangent and Special Triangles
  275.    wt: 7:   8 Similarity of Triangles and Polygons
  276.    wt: 7:   6 Geometric Diagrams in Class
  277.    wt: 7:   1 Early Concept of Like or Similar Shapes
  278.    wt: 7:   10 Midpoint of [a b] and [b a]
  279.    wt: 7:   1 Numerical view of lines and their equations
  280.    wt: 7:   PS E Multiplication with Polar Coordinates
  281.    wt: 7:   PS B Parallelogram Construction Methods
  282.    wt: 7:   21 Parallelograms
  283.    wt: 7:   18 Triangle Similarity Take 1
  284.    wt: 7:   16 Angles Subtended By Chords and Diameters
  285.    wt: 7:   14 Parallel Lines Postulate
  286.    wt: 7:   13 Angle Side Angle Failure
  287.    wt: 7:   6 Ruler and compass Angle Bisection
  288.    wt: 7:   A Measurement with Ruler Proper Use
  289.    wt: 7:   6 Figuring with Maps Not to Scale
  290.    wt: 7:   26 More Less Greater Than Comparison
  291.    wt: 7:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  292.    wt: 7:   17 Arrows Rotate to Reverse with Length Unchanged
  293.    wt: 7:   16 Collinear Horizontal Arrows Vectors
  294.    wt: 7:   11 Signed Number Addition and Addition Properties
  295.    wt: 7:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  296.    wt: 7:   8 Division and Mulplication of Compound Fractions
  297.    wt: 7:   7 Arithmetic with Infinite Decimal Expansions
  298.    wt: 7:   5 Fractions with Infinite Decimal Expansions
  299.    wt: 7:   4 Location of Point in Decimal Addition
  300.    wt: 7:   3 Location of Point in Decimal Multiplication
  301.    wt: 7:   1 Fractions with Finite Decimal Expansions
  302.    wt: 7:   C Three Decimal Subtraction Methods
  303.    wt: 7:   8 Column Multiplication Methods in General
  304.    wt: 7:   6 Column Methods for Decimal Multiplication
  305.    wt: 7:   4 Commutative Law Groups Counting Form
  306.    wt: 7:   2 Combing Counts Addition Skills and Principles
  307.    wt: 7:   12 Real Number Additive Inverses or Negatives
  308.    wt: 7:   7 Real Numbers as Line Cordinates
  309.    wt: 7:   1 Whole and Natural Numbers
  310.    wt: 7:   4 Changing Letters
  311.    wt: 7:   2 Essentially one exercises three with solution
  312.    wt: 7:   1 Essentially One Unknown
  313.    wt: 7:   Using Letters for Physical Quantities
  314.    wt: 7:   11 Volume of Sphere
  315.    wt: 7:   9 Volume of Cone
  316.    wt: 7:   6 Three Notions of What is a Variable
  317.    wt: 7:   5 Talking about Numbers and Quantities
  318.    wt: 7:   4 A Brief Story of numbers and algebra
  319.    wt: 7:   2 What is a Variable
  320.    wt: 7:   4 Greater More Less Than Signs in General
  321.    wt: 7:   5 Square Roots with primes more still
  322.    wt: 7:   4 Square Roots with primes more
  323.    wt: 7:   2 Square Roots with Prime
  324.    wt: 7:   17 GCD LCM of 85 and 60 via Prime
  325.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  326.    wt: 7:   14 GCD of 650 110 via Primes LCM via Product Rule
  327.    wt: 7:   13 GCD from given Prime Factorization
  328.    wt: 7:   11 GCD 2700 288 via Euclid Algorithm
  329.    wt: 7:   10 Euclid Algorithm with 129 125 and with 45 14
  330.    wt: 7:   8 GCD from Euclidean Algorithm
  331.    wt: 7:   4 LCM of 8 and 10 via Prime
  332.    wt: 7:   2 Least Common Multiple LCM intro via list method
  333.    wt: 7:   1 Least Common Multiples LCM Introduction
  334.    wt: 7:   4 Counting with Trees Product Rule Take I
  335.    wt: 7:   1 Counting and Counting Methods I
  336.    wt: 7:   11 What are real lengths and numbers
  337.    wt: 7:   3 signed coordinates for maps and planes
  338.    wt: 7:   6 Simplification of Fractions with Units
  339.    wt: 7:   2 Equality and Units
  340.    wt: 7:   12 Fraction Comparison
  341.    wt: 7:   9 Improper Fractions and Mixed Numbers
  342.    wt: 7:   5 Equivalent Fractions
  343.    wt: 7:   4 Fraction Multiplication
  344.    wt: 7:   2 Unit Fraction Multiplication
  345.    wt: 7:   A Associative Law Theorectical Note
  346.    wt: 7:   27 Divisibility by 2 3 6 5 9 10 Example
  347.    wt: 7:   26 Divisibility by 2 3 5 Example
  348.    wt: 7:   25 Divisibility Tests for 2 3 5 9 10 Example
  349.    wt: 7:   19 video Prime Factorization Unique
  350.    wt: 7:   14 video Factors of 24 Take II
  351.    wt: 7:   8 video Prime Factorization upto 19
  352.    wt: 7:   6 Sieve of Eratosthenes and Square Rule
  353.    wt: 7:   4 video Prime Factorization Introduction
  354.    wt: 7:   3 video Primes and Composites from 9 times table
  355.    wt: 7:   Division with Counts and Length
  356.    wt: 7:   11 Another Single Digit Divisor Example
  357.    wt: 7:   7 Long Divison Mistake Catching
  358.    wt: 7:   6 Why Decimal Long Division Methods Works Take I
  359.    wt: 7:   1 Divsion Physical Examples
  360.    wt: 7:   4 Two and Three Digit Multipliers
  361.    wt: 7:   8 Review Lesson 1 2 4 and 6 All in One
  362.    wt: 7:   3 More on Groups of 3 Multi Digit Place Value
  363.    wt: 7:   1 Place Value in Three Digit Whole Numbers
  364.    wt: 7:   Practical Methods Ends and Values for Arithmetic
  365.    wt: 7:   015 School and work day counting tables
  366.    wt: 7:   014 Counting Days with Calendars
  367.    wt: 7:   010 Repeated Addition of Time Intervals
  368.    wt: 7:   2 Time and Date Matters in School
  369.    wt: 7:   A Related Material in Volume 3
  370.    wt: 7:   34 Derivative of exponential function
  371.    wt: 7:   30Chain Rule A Proof
  372.    wt: 7:   27 Chain Rule sinusoidal outer inner functions EGS
  373.    wt: 7:   23 Chain Rule in general
  374.    wt: 7:   22 Chain Rule for polynomials
  375.    wt: 7:   19 Chain Rule for linear functions
  376.    wt: 7:   17 Derivatives of quotients of sine and cosine
  377.    wt: 7:   15 sine and cosine derivatives 3rd step
  378.    wt: 7:   14 sine and cosine derivatives 2nd step
  379.    wt: 7:   13 sine and cosine derivatives 1st step
  380.    wt: 7:   8 Differentiation of polynomials
  381.    wt: 7:   3 Motivation for Limit Definition Take 2
  382.    wt: 7:   2 Motivation for Limit Definition Take 1
  383.    wt: 7:   1 Fall 1983 Why Slopes Appetizer
  384.    wt: 7:   7 Evaluation by immediate or delayed substitution
  385.    wt: 7:   Postscript One Sided and Intermediate Value Theorems
  386.    wt: 7:   .H1 First Fundamental Theorem of Calculus
  387.    wt: 7:   G.2 Differentiable Functions Mean Value Theorem
  388.    wt: 7:   Chapter 17. Area Approximation
  389.    wt: 7:   Chapter 15. Algebraic Evaluation of Limits
  390.    wt: 7:   Chapter 14 Limits and Continuity with and sans Decimals
  391.    wt: 7:   Chapter 29 Contrapositive and Vacuously True Implications
  392.    wt: 7:   Chapter 25. Mathematical Induction Examples
  393.    wt: 7:   Chapter 25. Mathematical Induction Examples
  394.    wt: 7:   Chapter 10 Describing and Changing Calculations
  395.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  396.    wt: 7:   Postscript B More on Story Telling and Reason
  397.    wt: 7:   Chapter 23 Truth Tables
  398.    wt: 7:   Chapter 21 Occurrence Tables
  399.    wt: 7:   Chapter 18 Sense and Knowledge
  400.    wt: 7:   V Reasons and Motivations for Logic and Mathematics
  401.    wt: 7:   Montreal Basic and Advanced Mathematics Tutoring
  402.    wt: 6:   About site lesson plans
  403.    wt: 6:   teacher certification
  404.    wt: 6:   learning takes time
  405.    wt: 6:   grouping students according to ability
  406.    wt: 6:   mathematics in context
  407.    wt: 6:   how letters appear
  408.    wt: 6:   mathematics curriculum shifts
  409.    wt: 6:   Lessening Algebra Difficulties
  410.    wt: 6:   the trouble with algebra
  411.    wt: 6:   05 13 OldSiteEntrancePage
  412.    wt: 6:   04 29 New Mathematics Curriculum
  413.    wt: 6:   04 25 when to stop or suspend mathemat
  414.    wt: 6:   formal or informal peer review
  415.    wt: 6:   Different Kinds of Reasoning in maths
  416.    wt: 6:   Four ways to improve education reform
  417.    wt: 6:   Motivation and Context Problem
  418.    wt: 6:   Prequel In For A Penny In For A Pound
  419.    wt: 6:   fairness and inductive principles for instruction
  420.    wt: 6:   words for mathematics instructor
  421.    wt: 6:   chapitre 07 01 principle D induction mathematique
  422.    wt: 6:   chapitre 04 10 Etapes pour une meilleur raison
  423.    wt: 6:   chapitre 04 04 Parlons de la logique
  424.    wt: 6:   chapitre 02 00 La Communication des idees
  425.    wt: 6:   25 Mathematics Education Leaving A Good Impression
  426.    wt: 6:   Ages 12 to 14 Arithmetic
  427.    wt: 6:   Ages 10 to 12 Arithmetic
  428.    wt: 6:   11 Function Domain Range Source and Targets
  429.    wt: 6:   4 Function notation in and beyond mathematics
  430.    wt: 6:   2 Column Multiplication Method
  431.    wt: 6:   14 secant function Definition Graph and Inverse
  432.    wt: 6:   13 cosecant function Definition Graph and Inverse
  433.    wt: 6:   12 motivation for term arctan
  434.    wt: 6:   10 arctan left inverse of tangent Definition
  435.    wt: 6:   9 motivation for name arcsin
  436.    wt: 6:   5 Swapping Coordinates is a reflection
  437.    wt: 6:   10 Parallelogram Addition Method
  438.    wt: 6:   5 Head To Tail Arrow Addition
  439.    wt: 6:   4 Tangent Function Properties
  440.    wt: 6:   1 Straight Lines Slope Concept
  441.    wt: 6:   31 basic secant cosecant cotangent trig identities
  442.    wt: 6:   24 tangent Angle Difference Formula
  443.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  444.    wt: 6:   21 sine and cosine Half Angle Formulas
  445.    wt: 6:   16 Right Triangle Complementary Angle Relations
  446.    wt: 6:   14 cosine even and sine and tangent are odd
  447.    wt: 6:   1 Rectangular Polar Coordinates Review
  448.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  449.    wt: 6:   12 Triangles Similarity More Problems
  450.    wt: 6:   11 Triangle Similarity Missing Side Problem
  451.    wt: 6:   4 Similarity Definition with Coordinate
  452.    wt: 6:   3 Similarity by Design with coordinates
  453.    wt: 6:   9 Midpoint Coordinates Half Endpoint Sum
  454.    wt: 6:   7 Exercises to test skill and concept mastery
  455.    wt: 6:   5 Algebraic View of Slopes
  456.    wt: 6:   2 point slope equation for a line
  457.    wt: 6:   What is and is not here
  458.    wt: 6:   PS G Rotation Distributes over Addition
  459.    wt: 6:   19 Right Triangle Similarity
  460.    wt: 6:   15 Triangle Angle Sum is 180 degrees
  461.    wt: 6:   12 Side Angle Side Failure
  462.    wt: 6:   11 Triangle Construction Fails
  463.    wt: 6:   10 Dropping a perpendicular to line
  464.    wt: 6:   7 Angle Side Angle
  465.    wt: 6:   1 Initial Concepts and Terms
  466.    wt: 6:   1 Length Measurement
  467.    wt: 6:   A Signed Number Arithmetic Review
  468.    wt: 6:   23 Distributive Law Two Derivations
  469.    wt: 6:   21 Addition of Multiples of a Single Vector
  470.    wt: 6:   18 Geometrically Why Vector Addition Commutes
  471.    wt: 6:   12 Real Numbers Line Signed Coordinates
  472.    wt: 6:   9 Division with Digits after Decimal Point
  473.    wt: 6:   6 Infinite Decimals Ending in 9 repeating
  474.    wt: 6:   2 Counting Digits in Decimal Multiplication
  475.    wt: 6:   5 Distributive Law for Whole Numbers
  476.    wt: 6:   3 Multiplicative Counting Skills Principles
  477.    wt: 6:   16 Real Numbers Comparison
  478.    wt: 6:   14 Real Number Multiplication
  479.    wt: 6:   13 Real Number Subtraction
  480.    wt: 6:   11 Real Number Addition
  481.    wt: 6:   10 Real Number Lengths and Signs
  482.    wt: 6:   9 Coordinates for Regions in Space
  483.    wt: 6:   5 Rational Numbers More
  484.    wt: 6:   4 Rational Numbers
  485.    wt: 6:   9 Sets in Probability and Statistics
  486.    wt: 6:   arithmetic videos Real Player Format
  487.    wt: 6:   3 Comparison of Negative Numbers
  488.    wt: 6:   2 More and Less Than with Unlike Signs
  489.    wt: 6:   5 Common Divisors 60 45 via Prime
  490.    wt: 6:   LCM 60 45 Avoid List Method Use Prime
  491.    wt: 6:   12 GCD 2700 288 via Prime
  492.    wt: 6:   7 negative and additive inverse
  493.    wt: 6:   2 signed and unsigned numbers as coordinates
  494.    wt: 6:   7 Converting or Changing Units
  495.    wt: 6:   4 Fractions with Units
  496.    wt: 6:   3 Multiplying Units and Numbers
  497.    wt: 6:   D Three Term Ratios
  498.    wt: 6:   22 Complex Compound Fractions
  499.    wt: 6:   20 Dividing Fractions the Why
  500.    wt: 6:   19 Dividing Fractions How TO
  501.    wt: 6:   18 Efficient Ways to Multiply
  502.    wt: 6:   11 Adding Integers Formulas and Examples
  503.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  504.    wt: 6:   20 Uniqueness of Prime Factorization
  505.    wt: 6:   17 Identify and Count Factors using Primes
  506.    wt: 6:   16 video Factors of 980 using prime
  507.    wt: 6:   13 video Factors of 24 using prime
  508.    wt: 6:   2 Prime and Composites less than 16
  509.    wt: 6:   12 Why Long Division Works Take III
  510.    wt: 6:   9 Why Long Division Works Take II
  511.    wt: 6:   8 Correcting the Mistake
  512.    wt: 6:   3 Division Single Digit Divisor Example
  513.    wt: 6:   B Powers of Ten
  514.    wt: 6:   3 More One Digit Multipliers
  515.    wt: 6:   2 One Digit Multipliers
  516.    wt: 6:   1 Why 3 times 5 gives 15
  517.    wt: 6:   Exact Arithmetic Wholes and Fractions
  518.    wt: 6:   Formula Evaluation how to show work
  519.    wt: 6:   013 Travel Time Tables
  520.    wt: 6:   012 Division of Time Intervals by Time Intervals
  521.    wt: 6:   7 Addition of Time Intervals
  522.    wt: 6:   4 Mixing and Changing Units of Time
  523.    wt: 6:   4 Definite Integrals Evaluation Exercises
  524.    wt: 6:   31 Derivatives of inverse functions
  525.    wt: 6:   26 Chain Rule Recognising outer inner functions
  526.    wt: 6:   21 Chain Rule for powers
  527.    wt: 6:   20 Chain Rule for Pulley Systems
  528.    wt: 6:   18 Chain Rule Introduction
  529.    wt: 6:   12 Quotient rule examples
  530.    wt: 6:   10 Power rule for negative integers
  531.    wt: 6:   9 Reciprocal rule
  532.    wt: 6:   8 Four Animated Examples
  533.    wt: 6:   2 Algebraic codification
  534.    wt: 6:   .H2 Lipshitz Conditions Integration Calculus Reform
  535.    wt: 6:   G.3 Constant Difference Theorem Proof
  536.    wt: 6:   F.3 Intermediate Value Theorem
  537.    wt: 6:   F.1 What Functions are Continuous
  538.    wt: 6:   E2 Algebraic Properties of Limits
  539.    wt: 6:   D1 Sets and Sequences GLBs and LGBs
  540.    wt: 6:   C Triangle Inequalities
  541.    wt: 6:   B3 Bolzano Weierstrass Theorem
  542.    wt: 6:   Chapter 24 Logarithms Powers and Exponentials
  543.    wt: 6:   Chapter 18. Slopes Areas Integration
  544.    wt: 6:   Appendix E. How To Study Mathematics and Why
  545.    wt: 6:   Appendix A. Reading Guide For Next Appendices
  546.    wt: 6:   Chapter 20. Degrees and Radians
  547.    wt: 6:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  548.    wt: 6:   Postscript What is a Variable
  549.    wt: 6:   Chapter 9 Talking about Numbers or Quantities
  550.    wt: 6:   Chapter 6 Change of Language
  551.    wt: 6:   Annotated Links to Material Elsehwere
  552.    wt: 6:   Postscript D Reflections on Law of the Excluded Middle
  553.    wt: 6:   Postscript A Story Telling
  554.    wt: 6:   Chapter 15 Objective Processes
  555.    wt: 6:   Chapter 10 Responsibility
  556.    wt: 6:   Chapter 5 Deception
  557.    wt: 6:   Chapter 2 Skill Development
  558.    wt: 6:   Chapter 1 Introduction
  559.    wt: 6:   Three Remarks
  560.    wt: 6:   Helping the Blind in Logic and Mathematics
  561.    wt: 6:   Multiple Ways to Improve Mathematics Skill Development
  562.    wt: 6:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  563.    wt: 6:   Systematic Algebra Skill Development Missing Links
  564.    wt: 5:   which way to go
  565.    wt: 5:   three goals to set for students
  566.    wt: 5:   permissions for teachers
  567.    wt: 5:   activities for students
  568.    wt: 5:   links Education Resources online
  569.    wt: 5:   site eurekas
  570.    wt: 5:   key notes and themes
  571.    wt: 5:   modern education
  572.    wt: 5:   Education Reform Inconsistencies
  573.    wt: 5:   teaching tips
  574.    wt: 5:   What to Tell Students
  575.    wt: 5:   02 21 words for teachers
  576.    wt: 5:   cultivating intelligence
  577.    wt: 5:   How to be a better instructor
  578.    wt: 5:   chapitre 04 09 Regles accidentelles
  579.    wt: 5:   chapitre 04 08 Limitations et benefices
  580.    wt: 5:   chapitre 04 07 RepetablesEtReproductibles
  581.    wt: 5:   chapitre 04 06 engagements
  582.    wt: 5:   chapitre 04 05 Implication versus suggestion
  583.    wt: 5:   chapitre 04 00 Les regles d implication
  584.    wt: 5:   27 Graduated Correction and Penalties for Young Offenders
  585.    wt: 5:   13 Addition and Addition Tables
  586.    wt: 5:   12 Goals and Objectives For Mathematics
  587.    wt: 5:   5 Patience Please for Yourself and Your Charges
  588.    wt: 5:   Ages 12 to 14 Geometry
  589.    wt: 5:   Ages 10 to 12 Geometry
  590.    wt: 5:   Ages 9 to 10
  591.    wt: 5:   Ages 8 to 9
  592.    wt: 5:   Ages 7 to 8
  593.    wt: 5:   Ages 6 to 7
  594.    wt: 5:   Ages 4 plus to 5 plus
  595.    wt: 5:   Ages 3 plus to 4 plus
  596.    wt: 5:   22 Square Root function graphically
  597.    wt: 5:   20 Interchanging coordinates a reflection
  598.    wt: 5:   16 Increasing or decreasing on intervals
  599.    wt: 5:   6 Set Existence Formation and Notation
  600.    wt: 5:   5 Function notation for geometric transformations
  601.    wt: 5:   2 Algebraic use of function notation
  602.    wt: 5:   8 Notes for instructors or tutors
  603.    wt: 5:   7 Links Lessons Elsewhere
  604.    wt: 5:   Rewriting algebraic substitution as function substitutions
  605.    wt: 5:   8 arcsin left inverse of sine Graph
  606.    wt: 5:   6 Graph of arccos function
  607.    wt: 5:   4 possible motivation for term arccos
  608.    wt: 5:   12 From Applied To Pure Mathematics
  609.    wt: 5:   9 Head to Tail Coordinate View
  610.    wt: 5:   3 Navigation with Arrows or Vectors
  611.    wt: 5:   17 tangent function angle sum formulas
  612.    wt: 5:   32 seven rows of pascals triangle
  613.    wt: 5:   25 tangent double angle formula Slope connection
  614.    wt: 5:   20 sine and cosine Double Angle Formulas
  615.    wt: 5:   19 Pythagorean Identity For sine and cosine functions
  616.    wt: 5:   17D cis formulas for sine cosines and tangent
  617.    wt: 5:   17C sine and cosine double triple angle formulas
  618.    wt: 5:   17B sine cosine Angle Sum Formulas via cis
  619.    wt: 5:   15 sine cosine Complementary Angle Relations
  620.    wt: 5:   13 Graph of tangent function many periods
  621.    wt: 5:   11 tangent function undefined when terminal side vertical
  622.    wt: 5:   10 Graphs of sines and cosines many periods
  623.    wt: 5:   2 Quadrant I reference Angles
  624.    wt: 5:   21 Logarithms Powers and Exponentials
  625.    wt: 5:   12 cis formulas for sine cosines and tangent
  626.    wt: 5:   11 sine and cosine double triple angle formulas
  627.    wt: 5:   10 sine cosine Angle Sum Formulas via cis
  628.    wt: 5:   7 Second Way to Calculate Products
  629.    wt: 5:   5 An Easy Proof of the Distributive Law
  630.    wt: 5:   Appetizer A Complex Number Applet
  631.    wt: 5:   8 Triangles Cascade Problem Solving
  632.    wt: 5:   4 Trigonometric Ratios For Two Special Triangles
  633.    wt: 5:   2 Similarity By Design
  634.    wt: 5:   8 Mid Point Formula
  635.    wt: 5:   6 Intersection of lines by solving linear systems
  636.    wt: 5:   4 Equations for lines three forms
  637.    wt: 5:   3 Slope product for perpendicular lines
  638.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  639.    wt: 5:   PS H Distributive Law For Complex Numbers
  640.    wt: 5:   PS C Similarity Use Recognize it in Trigonometry
  641.    wt: 5:   PS A Kite Construction Methods
  642.    wt: 5:   17 Right Bisectors of Triangle Sides
  643.    wt: 5:   9 Construction of a right bisector
  644.    wt: 5:   8 Isoceles Triangles
  645.    wt: 5:   5 Side Angle Side
  646.    wt: 5:   3 Isometry of Triangles Congruence
  647.    wt: 5:   2 Correspondence between Triangles
  648.    wt: 5:   Short Course on Euclidean Geometry
  649.    wt: 5:   musings do not puiblish real numbers
  650.    wt: 5:   24 Signed Numbers Arithmmetic Properties
  651.    wt: 5:   22 Multiplication of Signed Numbers
  652.    wt: 5:   E Long Division Methods more
  653.    wt: 5:   D Long Division Methods
  654.    wt: 5:   1 The Counting Origins of Numbers
  655.    wt: 5:   15 Real Number Division
  656.    wt: 5:   6 Unsigned Real Numbers
  657.    wt: 5:   3 Fractions
  658.    wt: 5:   More Exercises
  659.    wt: 5:   Simple Exercises
  660.    wt: 5:   7 Cautious or Safe Set Construction
  661.    wt: 5:   2 Venn Diagrams
  662.    wt: 5:   3 Adding Words To Arithmetic
  663.    wt: 5:   1 Three Skills For Algebra
  664.    wt: 5:   6 GCD from Prime
  665.    wt: 5:   4 signed coordinates for regions in space
  666.    wt: 5:   21 Working With Signs
  667.    wt: 5:   D Remainders Modulo 11 Pair Rule
  668.    wt: 5:   13 Subtraction with Additive Inverse
  669.    wt: 5:   6 Multiplication by Natural Numbers
  670.    wt: 5:   12 LCD GCD and LCM using Primes
  671.    wt: 5:   11 Efficient Square Rule Use
  672.    wt: 5:   5 Long Division Include Zeroes or not
  673.    wt: 5:   4 Division with 2 Digit Divsors
  674.    wt: 5:   2 Division with Single Digit Divisors
  675.    wt: 5:   Quick history of numbers and algebra
  676.    wt: 5:   Expression Evaluation how to show work
  677.    wt: 5:   011 Division of Time Intervals By Numbers
  678.    wt: 5:   6 How long is a million seconds
  679.    wt: 5:   5 Conversion Arithmetic
  680.    wt: 5:   3 Units and Lengths of Time
  681.    wt: 5:   1 Intro of Kids To Time Date Skills
  682.    wt: 5:   5 Area Under Curve Exercise
  683.    wt: 5:   1 Chain Rule in Reverse Integration Method
  684.    wt: 5:   A Related lessons in Volume 3
  685.    wt: 5:   4 Second derivative test exercise example
  686.    wt: 5:   11 Quotient rule
  687.    wt: 5:   6 Power rule from product rule
  688.    wt: 5:   5 Product Rule
  689.    wt: 5:   4 Sum Rule
  690.    wt: 5:   11 Limits at infinity Three Examples
  691.    wt: 5:   6 Continuity at a point
  692.    wt: 5:   5 Jumps and absence of unlimited error control
  693.    wt: 5:   G.6 Bounded Derivatives implies Lipshitz Continuity
  694.    wt: 5:   G.1 Differentiable Functions Rolles Theorem
  695.    wt: 5:   F.5b Extreme Value Theorem
  696.    wt: 5:   F.5a Equicontinuity Theorems
  697.    wt: 5:   F.2 Closed Range Theorem
  698.    wt: 5:   E1 Error Control Inequalities
  699.    wt: 5:   B1 Pigeon Hole Principles from combinatorics
  700.    wt: 5:   A1. Introduction
  701.    wt: 5:   Postscript Pythagorean Theorem yet another proof
  702.    wt: 5:   Chapter 21 Arrow Addition
  703.    wt: 5:   Chapter 16. Velocity Approximation
  704.    wt: 5:   Chapter 15. Slope Approximation
  705.    wt: 5:   Chapter 13. Acceleration
  706.    wt: 5:   Chapter 9 About First Courses in Calculus
  707.    wt: 5:   Chapter 6. Slopes and Vertical Shifts
  708.    wt: 5:   Chapter 4. More Slope Sign Analysis
  709.    wt: 5:   Chapter 3. Slope Sign Analysis
  710.    wt: 5:   Chapter 2. Slopes and Ski Trails
  711.    wt: 5:   Fall 1983 Calculus Appetizer
  712.    wt: 5:   Appendix D. What to do in School and Why
  713.    wt: 5:   Chapter 31 Direct and Indirect Reason
  714.    wt: 5:   Chapter 27 Shorthand Symbols as Pronouns
  715.    wt: 5:   Chapter 26 What is in chapters 27 to 31
  716.    wt: 5:   Chapter 24. Personal Investment and Pension EGS
  717.    wt: 5:   Chapter 18. Rules for Algebra
  718.    wt: 5:   Chapter 15. Solving Linear Equations
  719.    wt: 5:   Postscript Unifying Theme A Fourth Skill For Algebra
  720.    wt: 5:   Chapter 12. Shorthand Usage Guide
  721.    wt: 5:   Chapter 8 Three Skills For Algebra
  722.    wt: 5:   Chapter 7 Prep for Calculus Arithmetic Exercises
  723.    wt: 5:   Chapter 5 Islands and Divisions of Knowledge
  724.    wt: 5:   Chapter 4 Longer Chains of Reason
  725.    wt: 5:   Chapter 3 Chains of Reason
  726.    wt: 5:   Postscript B Mathematics Education References
  727.    wt: 5:   Chapter 3 Algebra Difficulties
  728.    wt: 5:   Foreword
  729.    wt: 5:   P Exact Arithmetic With Whole Numbers and Fractions
  730.    wt: 5:   O On Learning Mathematics and Science
  731.    wt: 5:   Ends Values Methods For Skill Development Framework Prequel
  732.    wt: 4:   why bother
  733.    wt: 4:   website reviews
  734.    wt: 4:   site origins
  735.    wt: 4:   Postscript 2007 01 10
  736.    wt: 4:   three difficulties
  737.    wt: 4:   Theory of Knowledge
  738.    wt: 4:   chapitre 12 00 les iles et division
  739.    wt: 4:   chapitre 05 00 Deception
  740.    wt: 4:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  741.    wt: 4:   chapitre 04 02 Deuxieme enigme
  742.    wt: 4:   chapitre 04 01 Premiere enigme
  743.    wt: 4:   chapitre 01 00 Introduction
  744.    wt: 4:   problemes algebre et arithmetique
  745.    wt: 4:   Trois Notions qui menent a algebre
  746.    wt: 4:   deux definitions pour variable
  747.    wt: 4:   A Wire Resistance Qualitative01
  748.    wt: 4:   24 Standards For Skill Develoment Take II
  749.    wt: 4:   23 Modularized Skill Development Modularized Rigor Take IV
  750.    wt: 4:   23 Modularized Skill Development Modularized Rigor Take III
  751.    wt: 4:   23 Modularized Skill Development Modularized Rigor Take II
  752.    wt: 4:   19 Extending the Oral Dimension of Mathematics
  753.    wt: 4:   18 Primary School Mathematics
  754.    wt: 4:   17 Math Booklets for children and young teenagers
  755.    wt: 4:   16 Secondary Mathematics Tips
  756.    wt: 4:   14 Multiplication and Times Tables
  757.    wt: 4:   4 Learning Takes Time and Effort
  758.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  759.    wt: 4:   19 Horizontal line rule and method
  760.    wt: 4:   18 Vertical Line Rule and Method
  761.    wt: 4:   15 Sign analysis of functions
  762.    wt: 4:   10 Interval Notation
  763.    wt: 4:   8 Set view of relations and functions
  764.    wt: 4:   3 Formula or function graphing exercise
  765.    wt: 4:   7 arcsin left inverse of sine Definition
  766.    wt: 4:   3 Left Inverse of cosine arccos definition
  767.    wt: 4:   8 Parallel Vectors
  768.    wt: 4:   4 Resultant of a Sum of Movements
  769.    wt: 4:   Vector and Complex Number Applet
  770.    wt: 4:   30 unit circle calculation of six trigonometric functions
  771.    wt: 4:   27 Logarithmic use of products of sines and cosines
  772.    wt: 4:   26 Formulas for products of sines and cosines
  773.    wt: 4:   17G Pythagorean Theorem Converse
  774.    wt: 4:   17E Trig Formulas for dot and cross Products
  775.    wt: 4:   17A The complex number valued trig function cis
  776.    wt: 4:   12 Graph of tangent function for one period
  777.    wt: 4:   9 Graphs of sine and cosine over one period
  778.    wt: 4:   6 sines and cosines for reference angle 30 degrees
  779.    wt: 4:   5 sines and cosines for reference angle 60 degrees
  780.    wt: 4:   4 sines and cosines for reference angle 45 degrees
  781.    wt: 4:   3 sines and cosines for reference angle 90 degrees
  782.    wt: 4:   Right Triangle and Unit Circle Trigonometry
  783.    wt: 4:   16 References and Originality Question
  784.    wt: 4:   15 Pythagorean Theorem Converse
  785.    wt: 4:   13 Trig Formulas for dot and cross Products
  786.    wt: 4:   2 Complex Numbers made easier we hope
  787.    wt: 4:   6 Trigonometry Sines of Supplementary Angles
  788.    wt: 4:   3 Trigonometric Ratios sine and cosine
  789.    wt: 4:   1 Angle Measurement with Degrees
  790.    wt: 4:   Right Triangle and Unit Circle Trigonometry
  791.    wt: 4:   Four Simple Exercises
  792.    wt: 4:   12 Links Lessons elsewhere
  793.    wt: 4:   4 Side Side Side
  794.    wt: 4:   19 Signed Multiples of Vectors
  795.    wt: 4:   2 Integers
  796.    wt: 4:   10 Set View of Wordy Extensions To Arithmetic
  797.    wt: 4:   6 Power Set Notation
  798.    wt: 4:   5 Product Builder Notation
  799.    wt: 4:   4 Subset Builder Notation
  800.    wt: 4:   About Folder Contents
  801.    wt: 4:   9 subtracting signed numbers
  802.    wt: 4:   6 adding signed numbers
  803.    wt: 4:   5 lengths and signs of numbers
  804.    wt: 4:   12 Adding Integers More Examples
  805.    wt: 4:   10 Integer Multiplication Formulas
  806.    wt: 4:   5 Zero Movement and Additive Inverses
  807.    wt: 4:   3 Adding Movements with same direction
  808.    wt: 4:   1 Integers as Coordinates
  809.    wt: 4:   The 12 Times Table Visually
  810.    wt: 4:   3 Two Chain Rule Method Exercises
  811.    wt: 4:   2 Indefinite Integrals Exercises
  812.    wt: 4:   3 Second derivative test
  813.    wt: 4:   2 Second derivative test prequel
  814.    wt: 4:   1 Two cubic sketching exercises with 1st derivative
  815.    wt: 4:   10 Three one sided limits with infinite values
  816.    wt: 4:   9 Limits Continuity and Composition
  817.    wt: 4:   4 Numerical properties
  818.    wt: 4:   3 Decimal insights for limits continuity convergence
  819.    wt: 4:   1 Numerical introduction
  820.    wt: 4:   G.5 Motions With Bounded Velocities
  821.    wt: 4:   G.4 Lipschitz Continuity implies EquiContinuity
  822.    wt: 4:   F.4 Finite Covering Theorem
  823.    wt: 4:   D2 Limits of Monotone Sequences
  824.    wt: 4:   index
  825.    wt: 4:   Chapter 20 Vectors and Complex Numbers
  826.    wt: 4:   Chapter 12. Units and Slopes
  827.    wt: 4:   Chapter 11. Graphing Slope versus Position
  828.    wt: 4:   Chapter 10 Slopes and Units
  829.    wt: 4:   Chapter 8. Slope Interpretation
  830.    wt: 4:   Chapter 7 Slopes and Velocity
  831.    wt: 4:   Appendix C. How to Read
  832.    wt: 4:   Appendix B. How To Learn
  833.    wt: 4:   Chapter 30 Truth Tables
  834.    wt: 4:   Chapter 28 Occurrence Tables
  835.    wt: 4:   Chapter 23. Notation For Sums
  836.    wt: 4:   Chapter 22. Geometric Sums and Sequences
  837.    wt: 4:   Chapter 21. Third Reading Guide
  838.    wt: 4:   Chapter 19. Functions and Sets
  839.    wt: 4:   Chapter 16. Painless Theorem Proving
  840.    wt: 4:   Chapter 13. Second Reading Guide
  841.    wt: 4:   Chapter 11. Why Shorthand
  842.    wt: 4:   Chapter 1 Introduction to Chapters 2 to 6
  843.    wt: 4:   Postscript A Three Remarks
  844.    wt: 4:   Chapter 12 Four Phases
  845.    wt: 4:   Chapter 11 Elementary Instruction
  846.    wt: 4:   Chapter 10 Transition
  847.    wt: 4:   Chapter 7 Two Treatments of Geometry
  848.    wt: 4:   Chapter 4 Complex Numbers and Why Slopes
  849.    wt: 4:   S Adding words to algebra
  850.    wt: 4:   R Why Learn Mathematics Skills
  851.    wt: 4:   N Mathematics Prepare for College Studies
  852.    wt: 4:   N Improving Marks on Tests and Finals
  853.    wt: 4:   I. Logic and language skills
  854.    wt: 4:   D. Check work a must with a caution
  855.    wt: 4:   Implementation Notes
  856.    wt: 4:   Which Way To Go
  857.    wt: 3:   2 Conductance Resistance Duality02
  858.    wt: 3:   1 Conductance Resistance Duality01
  859.    wt: 3:   F Wire Resistance Calculation04
  860.    wt: 3:   E Wire Resistance Calculation03
  861.    wt: 3:   D Wire Resistance Calculation02
  862.    wt: 3:   C Wire Resistance Calculation01
  863.    wt: 3:   B Wire Resistance Qualitative02
  864.    wt: 3:   24 Standards For Skill Develoment
  865.    wt: 3:   23 Modularized Skill Development Modularized Rigor
  866.    wt: 3:   22 Student Centered Highschool Mathematics
  867.    wt: 3:   11 Help and Defend Your Child or Teens Education
  868.    wt: 3:   9 Streaming by Student Cooperation
  869.    wt: 3:   8 The Effect of Negative Remarks
  870.    wt: 3:   6 Discipline Who is in Charge Conserving Authority
  871.    wt: 3:   2 Reading and Writing Skills
  872.    wt: 3:   26 Function definitions done and coming
  873.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  874.    wt: 3:   13 From one to one to many to one
  875.    wt: 3:   12 Function Domain Recognition Exercises
  876.    wt: 3:   9 Set theory term relation possible origins
  877.    wt: 3:   7 Functions with finite domains
  878.    wt: 3:   1 Geometric Introduction of Function Notation
  879.    wt: 3:   Introduction Reading Guide
  880.    wt: 3:   2 cosine function more properties
  881.    wt: 3:   1 cosine function properties
  882.    wt: 3:   15 Dot and Cross Product
  883.    wt: 3:   6 Vectors with Coordinates
  884.    wt: 3:   2 Signed Coordinates
  885.    wt: 3:   1 Unsigned Coordinates
  886.    wt: 3:   28 Expressing products of sines cosines as sums
  887.    wt: 3:   23 sine and cosine of 180 plus 22.5 degrees
  888.    wt: 3:   17F Law of cosines
  889.    wt: 3:   8 period of tangent function
  890.    wt: 3:   7 period of sine and cosine
  891.    wt: 3:   1 Unit Points Reflections Rotations
  892.    wt: 3:   14 Law of cosines
  893.    wt: 3:   9 The complex number valued trig function cis
  894.    wt: 3:   4 Multiplication Properties
  895.    wt: 3:   3 Addition Properties
  896.    wt: 3:   7 Trignometric Ratios Unit Circle
  897.    wt: 3:   About Folder Contents
  898.    wt: 3:   8 Sets of Numbers
  899.    wt: 3:   3 Counting with Sets etc
  900.    wt: 3:   1 Finite Sets
  901.    wt: 3:   10 dividing signed numbers
  902.    wt: 3:   8 multiplying signed numbers
  903.    wt: 3:   8 Multiplication by Signed Numbers Integers
  904.    wt: 3:   7 Multiplication by Signs
  905.    wt: 3:   4 Adding Movements wiht opposite directions
  906.    wt: 3:   2 Integers Multiplies of a Unit Moverment
  907.    wt: 3:   The 20 Times Table
  908.    wt: 3:   About folder contents
  909.    wt: 3:   Chapter 23 Links To Trigonometry
  910.    wt: 3:   Chapter 22 Complex Numbers
  911.    wt: 3:   Chapter 5. Slope Sign Tests
  912.    wt: 3:   Chapter 1.Introduction
  913.    wt: 3:   Postscript More on Better Performance
  914.    wt: 3:   Postscript For Better Performance
  915.    wt: 3:   Solutions For Arithmetic Exercises
  916.    wt: 3:   Chapter 9 The Two Ends
  917.    wt: 3:   Chapter 8 Modern Instruction
  918.    wt: 3:   Chapter 5 Four References
  919.    wt: 3:   Chapter 1 Introduction
  920.    wt: 3:   Q How Logic and Proofs extend Show Work Practices
  921.    wt: 3:   L Skills with take home value
  922.    wt: 3:   H Jigsaw puzzles and problem solving
  923.    wt: 3:   G. Written work formats for developing and showing skill
  924.    wt: 3:   F. The student teacher tutor feedback loop
  925.    wt: 3:   A. Skill has to be seen to believed
  926.    wt: 2:   liens
  927.    wt: 2:   problemes responses
  928.    wt: 2:   logique deux enigme
  929.    wt: 2:   3 Like resistors in parallel
  930.    wt: 2:   2 Unlike resistors in parallel01
  931.    wt: 2:   Home Tutoring and Home Schooling
  932.    wt: 2:   15 Counting For Parents
  933.    wt: 2:   10 Ends values for work study instruction
  934.    wt: 2:   7 Student Motivation
  935.    wt: 2:   3 Preparing for Science Studies
  936.    wt: 2:   1 Speaking Skills
  937.    wt: 2:   23 Inverse Functions
  938.    wt: 2:   14 Surjections Injections Bijections
  939.    wt: 2:   13 Velocity Vectors in Physics
  940.    wt: 2:   11 Component Method
  941.    wt: 2:   Unit Circle Development of Trigonometry
  942.    wt: 2:   20 N th Roots of Complex Numbers
  943.    wt: 2:   19 N th Roots of Unity
  944.    wt: 2:   18 Sixth Roots of Unity
  945.    wt: 2:   17 Cube Roots of unity
  946.    wt: 2:   8 Unit Circle Development of Trigonometry
  947.    wt: 2:   6 Field Properties of Complex Number
  948.    wt: 2:   Why Trigonometry the whyslopes view
  949.    wt: 2:   C Divisibility by 11 Integer Recognition Method
  950.    wt: 2:   B Integer Long Division Multiple Choices
  951.    wt: 2:   9 Multiplying Integers
  952.    wt: 2:   Foreword
  953.    wt: 2:   Foreword
  954.    wt: 2:   Foreword
  955.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  956.    wt: 2:   M Words to extend arithmetic
  957.    wt: 2:   J. More on written work and showing skill
  958.    wt: 2:   E. When and how to correct errors
  959.    wt: 2:   C. Domino effect of being careful
  960.    wt: 2:   How to Build Skills and Confidence
  961.    wt: 2:   Road Safety Questions
  962.    wt: 1:   4 Energy Power Heat09
  963.    wt: 1:   3 Energy Power Heat08
  964.    wt: 1:   2 Energy Power Heat07
  965.    wt: 1:   1 Energy Power Heat06
  966.    wt: 1:   A Energy Power01
  967.    wt: 1:   E Kirchoffs Second Law
  968.    wt: 1:   D Kirchoff First Law
  969.    wt: 1:   C Electromotive force conventional current02
  970.    wt: 1:   B Electromotive force conventional current01
  971.    wt: 1:   A Circuit Elements
  972.    wt: 1:   H more Routine to non routine problem solving
  973.    wt: 1:   B. Domino effect of errors
  974.    wt: 15:   Parallel Lines and Parallel Transversals
  975.    wt: 14:   Parallel Lines and Alternating Corresponding Angles
  976.    wt: 13:   Proportionality of Line Segments From Parallel Transversals
  977.    wt: 13:   13 Pythagorean spatial distance formulas
  978.    wt: 13:   5 Cartesian Addition and Translation
  979.    wt: 13:   2 Another Rectangle Area Formula Example
  980.    wt: 13:   3 Harder Cases Convert to Compare and Subtract
  981.    wt: 13:   1 Comparison and Subtraction Easy Direct Cases
  982.    wt: 13:   Example 1. Area Between x and x squared
  983.    wt: 12:   Appendix 1 primary and preschool mathematic
  984.    wt: 12:   3 Natural Logarithms and Exponentials Basic Properties
  985.    wt: 12:   9 Summary Degrees to Radians and back
  986.    wt: 12:   7 Radian Measures in special Triangles
  987.    wt: 12:   4 Circle Sector Area proportional to Central Angle
  988.    wt: 12:   2 Radian Measure Numerical Value of one degree
  989.    wt: 12:   Parallel Lines and Interior Angles
  990.    wt: 12:   10 Pythagorean plane distance formula
  991.    wt: 12:   1 Decimals Modular and Remainder Arithmetic
  992.    wt: 12:   4 Rates Ratios and Proporitionality
  993.    wt: 12:   9 Circle Area and Perimeter Formula Backwards Forwards
  994.    wt: 12:   4 Rectangle Area and Like Formulas Backwards
  995.    wt: 12:   2 More and Less Than for Counts and Measures
  996.    wt: 12:   5 Gaussian Elimination for 3 unknowns 2nd example
  997.    wt: 12:   3 Gaussian Elimination 3 unknowns first example
  998.    wt: 12:   3 GE III Equation Addition and Multiplication
  999.    wt: 12:   6 Pythagorean Hypotenuse Calculation Example
  1000.    wt: 12:   3 Triangle Area Formula Example
  1001.    wt: 12:   Appendix 1 Decimals Comparison Method Take II
  1002.    wt: 12:   2 Subtraction Easy Case Examples
  1003.    wt: 12:   7 Adding decimal fractions using decimal point
  1004.    wt: 12:   3. How to add with decimals A sans conversions
  1005.    wt: 12:   11 Place Value SI Standard International way
  1006.    wt: 11:   C LAMP Introduction Culture in Mathematics Education
  1007.    wt: 11:   Ramblings Introduction Algebra Essay
  1008.    wt: 11:   8 quadratics backward use of various formulas
  1009.    wt: 11:   5 Natural Logarithm Calculator Exercises
  1010.    wt: 11:   8 Radian Measures of Common Angles
  1011.    wt: 11:   3 Circle Arclengh Proportional to Central Angle
  1012.    wt: 11:   2 Graphing y=Af(x) Vertical Scaling
  1013.    wt: 11:   Construction Methods and Criteria for Isometric and Similar Triangles
  1014.    wt: 11:   6 Polar Multiplication and Rotation
  1015.    wt: 11:   1 Cartesian Coordinates sans signs
  1016.    wt: 11:   3 Lengths and Areas on Maps and Plans
  1017.    wt: 11:   4 Fraction Operations Axiomatic Development
  1018.    wt: 11:   3 Inequalities Algebraically
  1019.    wt: 11:   5 Proportionality in Equivalent Fractions
  1020.    wt: 11:   8 Pythagorean Relation Forwards Backwards
  1021.    wt: 11:   5 Triangle Area Formula Backwards
  1022.    wt: 11:   2 Addition and Multiplication Axioms
  1023.    wt: 11:   5 Greater More Less Than Signs in General
  1024.    wt: 11:   4 GE III Animated Examples
  1025.    wt: 11:   4 Circle Area Formula Example
  1026.    wt: 11:   C Equality for Fractions and Two Term Ratios and Fractions
  1027.    wt: 11:   8 Numerals Fractionals Quantals Take II
  1028.    wt: 11:   A Decimals Modular and Remainder Arithmetic
  1029.    wt: 11:   Long Division forwards and backwards Example 3
  1030.    wt: 11:   Long Division forwards and backwards Example 2
  1031.    wt: 11:   Long Division forwards and backwards Example 1
  1032.    wt: 11:   Appendix 2 Three Decimal Subtraction Methods
  1033.    wt: 11:   Subtraction with J Conversions Example
  1034.    wt: 11:   Subtraction Another Video Lesson
  1035.    wt: 11:   7 Subtraction for Decimal Fractions with Exercises
  1036.    wt: 11:   8 What skills and work habits to require
  1037.    wt: 11:   6. Counting and adding units and mixed units
  1038.    wt: 11:   5. How to add decimals C. Examples
  1039.    wt: 11:   1. Explaining Addition Table
  1040.    wt: 11:   Example 1 volume of a pyramid
  1041.    wt: 11:   Area Between Crossing Curves Lesson Take 2
  1042.    wt: 11:   Area Between Crossing Curves Lesson Take 1
  1043.    wt: 11:   Area Between Curves Lesson Take 2
  1044.    wt: 11:   Area Between Curves Lesson Take 1
  1045.    wt: 11:   Chapter 4 Implication Rules Forwards and Backwards
  1046.    wt: 11:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  1047.    wt: 10:   Appendix 2 primary school Arithmetic 01
  1048.    wt: 10:   E LAMP Introduction Modern Mathematics
  1049.    wt: 10:   B LAMP Introduction Curriculum Development Standards
  1050.    wt: 10:   Skills Chapter 3 Algebra
  1051.    wt: 10:   7 logic review and decimals an odd combination
  1052.    wt: 10:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  1053.    wt: 10:   sign monoticity analysis example 4
  1054.    wt: 10:   sign monoticity analysis example 3
  1055.    wt: 10:   sign monoticity analysis example 2
  1056.    wt: 10:   sign monoticity analysis example 1
  1057.    wt: 10:   6 quadratics numerical approach
  1058.    wt: 10:   8 Formulas for Fractional Exponents with Logarithms
  1059.    wt: 10:   6 Polynomial Operations and Equivalent Computation Rules
  1060.    wt: 10:   6 Radian Measure to Degrees
  1061.    wt: 10:   5 Degrees to Radian Measure
  1062.    wt: 10:   1 Degrees and Radians Introduction
  1063.    wt: 10:   Triangle Angles Sum To 180 Degrees
  1064.    wt: 10:   3 Straight Lines Slope as Tangent of Inclination Angle
  1065.    wt: 10:   13 Navigation Location from Angles to 2 Landmarks
  1066.    wt: 10:   12 Spatial Coordinates
  1067.    wt: 10:   9 Pythagorean Theorem Chinese Square Proof
  1068.    wt: 10:   4 Polar Coordinates to and from
  1069.    wt: 10:   3 Rectangular Coordinates Review
  1070.    wt: 10:   2 Cartesian Coordinates with signs
  1071.    wt: 10:   4 Angles on Maps Plans drawn to scale
  1072.    wt: 10:   15 Head to Tails in place Addition Associative
  1073.    wt: 10:   5 Areas of Rectangles Revisited
  1074.    wt: 10:   2 Fraction Operations Physical Development
  1075.    wt: 10:   3 Proportionality Examples
  1076.    wt: 10:   2 Algebraic View
  1077.    wt: 10:   1 What is Proportionality
  1078.    wt: 10:   6 Equations and Systems Equivalent or Implied
  1079.    wt: 10:   5 Equality in Algebra
  1080.    wt: 10:   4 Subtraction and Division Axioms
  1081.    wt: 10:   4 Comparison of Negative Numbers
  1082.    wt: 10:   3 More and Less Than with Unlike Signs
  1083.    wt: 10:   1 Real Numbers Comparison
  1084.    wt: 10:   6 Algebraic Solution Example
  1085.    wt: 10:   4 Four Examples Fractional Coefficients
  1086.    wt: 10:   10 One Example
  1087.    wt: 10:   9 Three Examples
  1088.    wt: 10:   8 One Example
  1089.    wt: 10:   7 Two Examples
  1090.    wt: 10:   6 Three Examples
  1091.    wt: 10:   5 Three Examples
  1092.    wt: 10:   4 Two Examples
  1093.    wt: 10:   3 Two Examples
  1094.    wt: 10:   2 Three Examples
  1095.    wt: 10:   8 Compound Interest Formula Evaluation
  1096.    wt: 10:   A Similarities between Fractions and Two Term Ratios
  1097.    wt: 10:   7 Numerals Fractionals Quantals
  1098.    wt: 10:   6 Multiplication Algebraically Take II
  1099.    wt: 10:   A Elementary Basis for Multiplication Methods
  1100.    wt: 10:   Video Decimal Multiplication Geometric View Example 2
  1101.    wt: 10:   Video Decimal Multiplication Geometric View Example 2
  1102.    wt: 10:   Video Power Notation in Decimal Expansion
  1103.    wt: 10:   8 Subtraction with Units of Measure
  1104.    wt: 10:   6 Subtraction with Conversion Example with Exercises
  1105.    wt: 10:   5 A Tip for Efficent Subtraction
  1106.    wt: 10:   4 Subtraction with Conversions Borrows and Letter J
  1107.    wt: 10:   Appendix 1 Counting Revisited 15 minute video
  1108.    wt: 10:   4. How to add with decimals B with conversions
  1109.    wt: 10:   2 Decimal Counting Practices
  1110.    wt: 10:   9 Place Value Review Decimal form of Avogrados number included
  1111.    wt: 10:   Example 2 volume of a cone
  1112.    wt: 10:   A Chain Rule Real Player video examples
  1113.    wt: 10:   Chapter 22 Contrapositive and Vacuously True Implications
  1114.    wt: 10:   Chapter 16 Origins and Limitations of Rules and Patterns
  1115.    wt: 10:   Chapter 14 Deductive and Empirical Views of Mathematics
  1116.    wt: 10:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

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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.

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