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

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

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


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

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

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

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

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48 matches:

  1.    wt: 5:   11 Squares and Square Roots/
  2.    wt: 4:   11 Parallel Straight Lines and Transversals/
  3.    wt: 4:   10 LCM GCD and Euclid GCD Algorithm/
  4.    wt: 3:   Volume 1A Regles et modeles/
  5.    wt: 3:   12 Comparison of Unsigned and Signed Numbers/
  6.    wt: 3:   1 Decimal Place Value/
  7.    wt: 3:   13 Lessons on Limits and Continuity/
  8.    wt: 2:   1 Five Polynomial Operations/
  9.    wt: 2:   15 Arc or Inverse Trigonometric Function/
  10.    wt: 2:   14 Degrees to Radians and Radians to Degrees/
  11.    wt: 2:   13 Vectors/
  12.    wt: 2:   12 Function Translating and Rescaling/
  13.    wt: 2:   10 Intersecting Straight Lines and Transversals/
  14.    wt: 2:   1 Maps Plans Measurement/
  15.    wt: 2:   10 Examples of Algebraic Reasoning/
  16.    wt: 2:   Step 1 Stick diagram and fractions/
  17.    wt: 2:   2 Formula Forward Use Evaluation/
  18.    wt: 2:   1 Working With Sets/
  19.    wt: 2:   A Decimal Counting and Adding Methods/
  20.    wt: 2:   12 Webvideo Lessons on Area and Volume Calculation/
  21.    wt: 2:   Work and Study Tips/
  22.    wt: 1:   Mathematics Education Essays/
  23.    wt: 1:   francais/
  24.    wt: 1:   4 Lines and Slopes Take 1/
  25.    wt: 1:   9 Proportionality Backwards and Forwards/
  26.    wt: 1:   8 Unifying Theme For Algebra/
  27.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  28.    wt: 1:   9 Combinatorics Trees Tables and Products/
  29.    wt: 1:   8 Arithmetic with Signed Numbers/
  30.    wt: 1:   7 Arithmetic and Fractions with Units/
  31.    wt: 1:   6 Fractions and Ratios/
  32.    wt: 1:   5 Integers/
  33.    wt: 1:   4 Remainder Arithmetic and Divisibility/
  34.    wt: 1:   3 Prime Factorization Skills/
  35.    wt: 1:   D Decimal Long Division Methods/
  36.    wt: 1:   C Decimal Multiplication Methods/
  37.    wt: 1:   B Decimal Comparing and Subtracting Methods/
  38.    wt: 1:   2 Arithmetic with Decimals/
  39.    wt: 1:   Arithmetic and Number Theory Skills/
  40.    wt: 1:   5 Lessons on Integration/
  41.    wt: 1:   4 Lessons on Using Derivatives/
  42.    wt: 1:   38 Lessons on Calculating Derivatives/
  43.    wt: 1:   70 Calculus Starter Lessons/
  44.    wt: 1:   Volume 2 Three Skills For Algebra/
  45.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  46.    wt: 1:   Volume 1A Pattern Based Reason/
  47.    wt: 1:   Volume 1 Elements of Reason/
  48.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

511 matches:

  1.    wt: 6:   10 Ends values for work study instruction
  2.    wt: 4:   1 Written work formats for developing and showing skill
  3.    wt: 4:   10 Euclid Algorithm with 129 125 and with 45 14
  4.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  5.    wt: 3:   17E Trig Formulas for dot and cross Products
  6.    wt: 3:   17D cis formulas for sine cosines and tangent
  7.    wt: 3:   13 Trig Formulas for dot and cross Products
  8.    wt: 3:   12 cis formulas for sine cosines and tangent
  9.    wt: 3:   11 sine and cosine double triple angle formulas
  10.    wt: 3:   Formula Usage Show Work Format
  11.    wt: 3:   14 GCD of 650 110 via Primes LCM via Product Rule
  12.    wt: 3:   11 Adding Integers Formulas and Examples
  13.    wt: 3:   Practical Methods Ends and Values for Arithmetic
  14.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  15.    wt: 3:   G. Written work formats for developing and showing skill
  16.    wt: 2:   11 pure mathematics
  17.    wt: 2:   Postscript 2007 01 10
  18.    wt: 2:   02 21 words for teachers
  19.    wt: 2:   formal or informal peer review
  20.    wt: 2:   Prequel In For A Penny In For A Pound
  21.    wt: 2:   1 Conductance Resistance Duality01
  22.    wt: 2:   B Electromotive force conventional current01
  23.    wt: 2:   17 Math Booklets for children and young teenagers
  24.    wt: 2:   15 Counting For Parents
  25.    wt: 2:   12 Goals and Objectives For Mathematics
  26.    wt: 2:   11 Help and Defend Your Child or Teens Education
  27.    wt: 2:   Ages 12 to 14 Skills with take home value
  28.    wt: 2:   Ages 12 to 14 Geometry
  29.    wt: 2:   Ages 12 to 14 Arithmetic
  30.    wt: 2:   Ages 10 to 12 Geometry
  31.    wt: 2:   Ages 10 to 12 Arithmetic
  32.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  33.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  34.    wt: 2:   11 Function Domain Range Source and Targets
  35.    wt: 2:   5 Function notation for geometric transformations
  36.    wt: 2:   11 Growth and Decay in Biology
  37.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  38.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  39.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  40.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  41.    wt: 2:   12 motivation for term arctan
  42.    wt: 2:   11 arctan left inverse of tangent Graph
  43.    wt: 2:   11 Component Method
  44.    wt: 2:   11 Straight Lines Graphing y=mx
  45.    wt: 2:   17 tangent function angle sum formulas
  46.    wt: 2:   26 Formulas for products of sines and cosines
  47.    wt: 2:   21 sine and cosine Half Angle Formulas
  48.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  49.    wt: 2:   17C sine and cosine double triple angle formulas
  50.    wt: 2:   17B sine cosine Angle Sum Formulas via cis
  51.    wt: 2:   12 Graph of tangent function for one period
  52.    wt: 2:   11 tangent function undefined when terminal side vertical
  53.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  54.    wt: 2:   11 Triangle Similarity Missing Side Problem
  55.    wt: 2:   11 A Partial Summary
  56.    wt: 2:   4 Equations for lines three forms
  57.    wt: 2:   13 Pythagorean spatial distance formulas
  58.    wt: 2:   11 Triangle Inequality
  59.    wt: 2:   10 Pythagorean plane distance formula
  60.    wt: 2:   18 Triangle Similarity Take 1
  61.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  62.    wt: 2:   11 Triangle Construction Fails
  63.    wt: 2:   11 Signed Number Addition and Addition Properties
  64.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  65.    wt: 2:   11 Real Number Addition
  66.    wt: 2:   1 Formulas Dependence and Function Notation
  67.    wt: 2:   13 Naming Identifying Formulas with Words
  68.    wt: 2:   11 Volume of Sphere
  69.    wt: 2:   1 Three Skills For Algebra
  70.    wt: 2:   1 More and Less Than for Counts and Measures
  71.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  72.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  73.    wt: 2:   11 What are real lengths and numbers
  74.    wt: 2:   21 Working With Signs
  75.    wt: 2:   21 Reciprocals for Fractions and Wholes
  76.    wt: 2:   11 Simplification an Algebraic View
  77.    wt: 2:   D Remainders Modulo 11 Pair Rule
  78.    wt: 2:   C Divisibility by 11 Integer Recognition Method
  79.    wt: 2:   10 Integer Multiplication Formulas
  80.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  81.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  82.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  83.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  84.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  85.    wt: 2:   12 Remainder Arithmetic Modulo 10 Example
  86.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  87.    wt: 2:   1 Remainder Arithmetic Modulo 10
  88.    wt: 2:   11 Efficient Square Rule Use
  89.    wt: 2:   Long Division forwards and backwards Example 1
  90.    wt: 2:   12 Why Long Division Works Take III
  91.    wt: 2:   11 Another Single Digit Divisor Example
  92.    wt: 2:   1 Why 3 times 5 gives 15
  93.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  94.    wt: 2:   11 Place Value SI Standard International way
  95.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  96.    wt: 2:   Formula Evaluation how to show work
  97.    wt: 2:   015 School and work day counting tables
  98.    wt: 2:   011 Division of Time Intervals By Numbers
  99.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  100.    wt: 2:   38 Formulas and derivatives for powers and roots
  101.    wt: 2:   21 Chain Rule for powers
  102.    wt: 2:   19 Chain Rule for linear functions
  103.    wt: 2:   13 sine and cosine derivatives 1st step
  104.    wt: 2:   11 Quotient rule
  105.    wt: 2:   10 Power rule for negative integers
  106.    wt: 2:   2 Motivation for Limit Definition Take 1
  107.    wt: 2:   1 Fall 1983 Why Slopes Appetizer
  108.    wt: 2:   11 Limits at infinity Three Examples
  109.    wt: 2:   10 Three one sided limits with infinite values
  110.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  111.    wt: 2:   Chapter 11. Graphing Slope versus Position
  112.    wt: 2:   Postscript For Better Performance
  113.    wt: 2:   Chapter 18. Rules for Algebra
  114.    wt: 2:   Chapter 11. Why Shorthand
  115.    wt: 2:   Chapter 11 Elementary Instruction
  116.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  117.    wt: 2:   Chapter 11 Accidental Patterns
  118.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  119.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  120.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  121.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  122.    wt: 1:   Appendix 2 primary school Arithmetic 01
  123.    wt: 1:   Appendix 1 primary and preschool mathematic
  124.    wt: 1:   I LAMP Introduction Study Habits
  125.    wt: 1:   Skills Chapter 1 Arithmetic
  126.    wt: 1:   10 statistics
  127.    wt: 1:   1 arithmetic with unsigned numbers
  128.    wt: 1:   three goals to set for students
  129.    wt: 1:   permissions for teachers
  130.    wt: 1:   Applied Maths Program14092009 POMME variant
  131.    wt: 1:   activities for students
  132.    wt: 1:   Education Reform Inconsistencies
  133.    wt: 1:   geometric implications for algebra
  134.    wt: 1:   three goals for Mathematics Education
  135.    wt: 1:   05 13 OldSiteEntrancePage
  136.    wt: 1:   three aims for mathematics students
  137.    wt: 1:   standards for course material
  138.    wt: 1:   Four ways to improve education reform
  139.    wt: 1:   need for a mixed mathematics curriculum
  140.    wt: 1:   fairness and inductive principles for instruction
  141.    wt: 1:   words for mathematics instructor
  142.    wt: 1:   chapitre 12 00 les iles et division
  143.    wt: 1:   chapitre 07 01 principle D induction mathematique
  144.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  145.    wt: 1:   chapitre 04 01 Premiere enigme
  146.    wt: 1:   chapitre 01 00 Introduction
  147.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  148.    wt: 1:   1 Energy Power Heat06
  149.    wt: 1:   A Energy Power01
  150.    wt: 1:   C Wire Resistance Calculation01
  151.    wt: 1:   A Wire Resistance Qualitative01
  152.    wt: 1:   2 Unlike resistors in parallel01
  153.    wt: 1:   1 Like resistors in series
  154.    wt: 1:   G Series Circuit01
  155.    wt: 1:   C Electromotive force conventional current02
  156.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  157.    wt: 1:   24 Standards For Skill Develoment Take II
  158.    wt: 1:   24 Standards For Skill Develoment
  159.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  160.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  161.    wt: 1:   18 Primary School Mathematics
  162.    wt: 1:   16 Secondary Mathematics Tips
  163.    wt: 1:   14 Multiplication and Times Tables
  164.    wt: 1:   13 Addition and Addition Tables
  165.    wt: 1:   5 Patience Please for Yourself and Your Charges
  166.    wt: 1:   4 Learning Takes Time and Effort
  167.    wt: 1:   3 Preparing for Science Studies
  168.    wt: 1:   1 Speaking Skills
  169.    wt: 1:   Ages 9 to 10
  170.    wt: 1:   sign monoticity analysis example 1
  171.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  172.    wt: 1:   19 Horizontal line rule and method
  173.    wt: 1:   18 Vertical Line Rule and Method
  174.    wt: 1:   17 Function maxima minima and their location
  175.    wt: 1:   16 Increasing or decreasing on intervals
  176.    wt: 1:   15 Sign analysis of functions
  177.    wt: 1:   14 Surjections Injections Bijections
  178.    wt: 1:   13 From one to one to many to one
  179.    wt: 1:   12 Function Domain Recognition Exercises
  180.    wt: 1:   10 Interval Notation
  181.    wt: 1:   6 Set Existence Formation and Notation
  182.    wt: 1:   3 Formula or function graphing exercise
  183.    wt: 1:   1 Geometric Introduction of Function Notation
  184.    wt: 1:   10 quadratic exercises
  185.    wt: 1:   8 quadratics backward use of various formulas
  186.    wt: 1:   7 quadratic formulla derivation
  187.    wt: 1:   1 quadratics graphing exercises
  188.    wt: 1:   Quadratics in 10 steps
  189.    wt: 1:   10 Exponential Growth and Decay Models
  190.    wt: 1:   1 Calculator Starter Exercises
  191.    wt: 1:   8 Notes for instructors or tutors
  192.    wt: 1:   1 Polynomials Distributive Law
  193.    wt: 1:   16 cotangent function Definition Graph and Inverse
  194.    wt: 1:   15 cosecant function Definition Graph and Inverse
  195.    wt: 1:   14 secant function Definition Graph and Inverse
  196.    wt: 1:   13 cosecant function Definition Graph and Inverse
  197.    wt: 1:   10 arctan left inverse of tangent Definition
  198.    wt: 1:   9 motivation for name arcsin
  199.    wt: 1:   4 possible motivation for term arccos
  200.    wt: 1:   1 cosine function properties
  201.    wt: 1:   1 Degrees and Radians Introduction
  202.    wt: 1:   15 Dot and Cross Product
  203.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  204.    wt: 1:   13 Velocity Vectors in Physics
  205.    wt: 1:   12 From Applied To Pure Mathematics
  206.    wt: 1:   10 Parallelogram Addition Method
  207.    wt: 1:   1 Unsigned Coordinates
  208.    wt: 1:   1 graphing y=f(x a)
  209.    wt: 1:   Triangle Angles Sum To 180 Degrees
  210.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  211.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  212.    wt: 1:   Straight Lines ASA Intersection Study More
  213.    wt: 1:   Straight Lines ASA Intersection Study
  214.    wt: 1:   14 Straight Lines Equations General Case
  215.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  216.    wt: 1:   12 Straight Lines Graphing mx plus b
  217.    wt: 1:   10 Straight Lines through Origin Equations More
  218.    wt: 1:   8 Straight Lines Equation for vertical
  219.    wt: 1:   1 Straight Lines Slope Concept
  220.    wt: 1:   31 basic secant cosecant cotangent trig identities
  221.    wt: 1:   29 secant cosecant and cotangent for acute angles
  222.    wt: 1:   25 tangent double angle formula Slope connection
  223.    wt: 1:   24 tangent Angle Difference Formula
  224.    wt: 1:   23 sine and cosine of 180 plus 22.5 degrees
  225.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  226.    wt: 1:   20 sine and cosine Double Angle Formulas
  227.    wt: 1:   18 sum of sinusoidal waves as a single wave
  228.    wt: 1:   17G Pythagorean Theorem Converse
  229.    wt: 1:   17F Law of cosines
  230.    wt: 1:   17A The complex number valued trig function cis
  231.    wt: 1:   16 Right Triangle Complementary Angle Relations
  232.    wt: 1:   15 sine cosine Complementary Angle Relations
  233.    wt: 1:   14 cosine even and sine and tangent are odd
  234.    wt: 1:   13 Graph of tangent function many periods
  235.    wt: 1:   10 Graphs of sines and cosines many periods
  236.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  237.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  238.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  239.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  240.    wt: 1:   1 Unit Points Reflections Rotations
  241.    wt: 1:   21 Logarithms Powers and Exponentials
  242.    wt: 1:   19 N th Roots of Unity
  243.    wt: 1:   18 Sixth Roots of Unity
  244.    wt: 1:   17 Cube Roots of unity
  245.    wt: 1:   16 References and Originality Question
  246.    wt: 1:   15 Pythagorean Theorem Converse
  247.    wt: 1:   14 Law of cosines
  248.    wt: 1:   1 Rectangular Polar Coordinates Review
  249.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  250.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  251.    wt: 1:   1 Angle Measurement with Degrees
  252.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  253.    wt: 1:   12 Triangles Similarity More Problems
  254.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  255.    wt: 1:   1 Early Concept of Like or Similar Shapes
  256.    wt: 1:   12 Links Lessons elsewhere
  257.    wt: 1:   10 Midpoint of [a b] and [b a]
  258.    wt: 1:   8 Mid Point Formula
  259.    wt: 1:   3 Slope product for perpendicular lines
  260.    wt: 1:   2 point slope equation for a line
  261.    wt: 1:   1 Numerical view of lines and their equations
  262.    wt: 1:   12 Spatial Coordinates
  263.    wt: 1:   1 Cartesian Coordinates sans signs
  264.    wt: 1:   PS H Distributive Law For Complex Numbers
  265.    wt: 1:   21 Parallelograms
  266.    wt: 1:   19 Right Triangle Similarity
  267.    wt: 1:   17 Right Bisectors of Triangle Sides
  268.    wt: 1:   16 Angles Subtended By Chords and Diameters
  269.    wt: 1:   14 Parallel Lines Postulate
  270.    wt: 1:   13 Angle Side Angle Failure
  271.    wt: 1:   12 Side Angle Side Failure
  272.    wt: 1:   10 Dropping a perpendicular to line
  273.    wt: 1:   1 Initial Concepts and Terms
  274.    wt: 1:   1 Length Measurement
  275.    wt: 1:   21 Addition of Multiples of a Single Vector
  276.    wt: 1:   19 Signed Multiples of Vectors
  277.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  278.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  279.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  280.    wt: 1:   15 Head to Tails in place Addition Associative
  281.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  282.    wt: 1:   13 Arrows and Vectors in a Plane
  283.    wt: 1:   12 Real Numbers Line Signed Coordinates
  284.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  285.    wt: 1:   1 Fractions with Finite Decimal Expansions
  286.    wt: 1:   6 Column Methods for Decimal Multiplication
  287.    wt: 1:   5 Distributive Law for Whole Numbers
  288.    wt: 1:   4 Commutative Law Groups Counting Form
  289.    wt: 1:   1 The Counting Origins of Numbers
  290.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  291.    wt: 1:   1 What is Proportionality
  292.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  293.    wt: 1:   6 Compound Interest Forward and Backwards
  294.    wt: 1:   5 Triangle Area Formula Backwards
  295.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  296.    wt: 1:   1 Changing Calculations
  297.    wt: 1:   3 Product Axioms Two Forms
  298.    wt: 1:   1 Equivalent Computation Rules
  299.    wt: 1:   2 More and Less Than for Counts and Measures
  300.    wt: 1:   1 Real Numbers Comparison
  301.    wt: 1:   16 Real Numbers Comparison
  302.    wt: 1:   15 Real Number Division
  303.    wt: 1:   14 Real Number Multiplication
  304.    wt: 1:   13 Real Number Subtraction
  305.    wt: 1:   12 Real Number Additive Inverses or Negatives
  306.    wt: 1:   10 Real Number Lengths and Signs
  307.    wt: 1:   9 Coordinates for Regions in Space
  308.    wt: 1:   8 Coordinates for Maps and Planes
  309.    wt: 1:   1 Whole and Natural Numbers
  310.    wt: 1:   3 Geometric Formulas and Function Notation
  311.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  312.    wt: 1:   1 GE Substitution four examples
  313.    wt: 1:   1 Essentially One Unknown
  314.    wt: 1:   1 Proper Equal Sign Usage
  315.    wt: 1:   10 One Example
  316.    wt: 1:   Using Letters for Physical Quantities
  317.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  318.    wt: 1:   10 Volume of Pyramid
  319.    wt: 1:   8 Compound Interest Formula Evaluation
  320.    wt: 1:   7 Compound Interest Formula Introduction
  321.    wt: 1:   5 Box Volume Formula Example
  322.    wt: 1:   4 Circle Area Formula Example
  323.    wt: 1:   3 Triangle Area Formula Example
  324.    wt: 1:   2 Another Rectangle Area Formula Example
  325.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  326.    wt: 1:   1 Finite Sets
  327.    wt: 1:   arithmetic videos Real Player Format
  328.    wt: 1:   1 Squares and Square Roots Introduction
  329.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  330.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  331.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  332.    wt: 1:   13 GCD from given Prime Factorization
  333.    wt: 1:   4 LCM of 8 and 10 via Prime
  334.    wt: 1:   1 Least Common Multiples LCM Introduction
  335.    wt: 1:   12 GCD 2700 288 via Prime
  336.    wt: 1:   1 Counting and Counting Methods I
  337.    wt: 1:   10 dividing signed numbers
  338.    wt: 1:   4 signed coordinates for regions in space
  339.    wt: 1:   3 signed coordinates for maps and planes
  340.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  341.    wt: 1:   1 Addition and Subtraction with Units
  342.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  343.    wt: 1:   19 Dividing Fractions How TO
  344.    wt: 1:   18 Efficient Ways to Multiply
  345.    wt: 1:   17 Efficient Ways to Add and Subtract
  346.    wt: 1:   16 Addition Subtraction Comparision Compared
  347.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  348.    wt: 1:   14 Adding and Subtracting with Like Denominators
  349.    wt: 1:   13 Fraction Comparison Algebraic View
  350.    wt: 1:   12 Fraction Comparison
  351.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  352.    wt: 1:   1 What is a fraction Take II
  353.    wt: 1:   1 What is a fraction
  354.    wt: 1:   13 Subtraction with Additive Inverse
  355.    wt: 1:   12 Adding Integers More Examples
  356.    wt: 1:   1 Integers as Coordinates
  357.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  358.    wt: 1:   21 Remainder Arithmetic Modulo 3
  359.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  360.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  361.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  362.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  363.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  364.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  365.    wt: 1:   4 Remainder Arithmetic Modulo 10 in general
  366.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  367.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  368.    wt: 1:   19 video Prime Factorization Unique
  369.    wt: 1:   18 video Count Factors given Prime Factorization
  370.    wt: 1:   17 Identify and Count Factors using Primes
  371.    wt: 1:   16 video Factors of 980 using prime
  372.    wt: 1:   15 video Factors of 20 using Prime Factorization
  373.    wt: 1:   14 video Factors of 24 Take II
  374.    wt: 1:   13 video Factors of 24 using prime
  375.    wt: 1:   12 LCD GCD and LCM using Primes
  376.    wt: 1:   10 video Prime Factorization upto 23 squared
  377.    wt: 1:   9 video Prime Factorization upto 19 squared
  378.    wt: 1:   8 video Prime Factorization upto 19
  379.    wt: 1:   2 Prime and Composites less than 16
  380.    wt: 1:   1 video how Products are bigger than factor
  381.    wt: 1:   Long Division forwards and backwards Example 3
  382.    wt: 1:   Long Division forwards and backwards Example 2
  383.    wt: 1:   10 Division by Five Long and Short Ways
  384.    wt: 1:   9 Why Long Division Works Take II
  385.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  386.    wt: 1:   1 Divsion Physical Examples
  387.    wt: 1:   A Elementary Basis for Multiplication Methods
  388.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  389.    wt: 1:   Subtraction with J Conversions Example
  390.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  391.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  392.    wt: 1:   5 A Tip for Efficent Subtraction
  393.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  394.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  395.    wt: 1:   8 What skills and work habits to require
  396.    wt: 1:   4. How to add with decimals B with conversions
  397.    wt: 1:   3. How to add with decimals A sans conversions
  398.    wt: 1:   1. Explaining Addition Table
  399.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  400.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  401.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  402.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  403.    wt: 1:   Expression Evaluation how to show work
  404.    wt: 1:   The 12 Times Table Visually
  405.    wt: 1:   016 Numbering Occidental Calendar Days
  406.    wt: 1:   014 Counting Days with Calendars
  407.    wt: 1:   013 Travel Time Tables
  408.    wt: 1:   012 Division of Time Intervals by Time Intervals
  409.    wt: 1:   010 Repeated Addition of Time Intervals
  410.    wt: 1:   5 Conversion Arithmetic
  411.    wt: 1:   1 Intro of Kids To Time Date Skills
  412.    wt: 1:   Example 1 volume of a pyramid
  413.    wt: 1:   Example 1. Area Between x and x squared
  414.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  415.    wt: 1:   Example 1
  416.    wt: 1:   Area Between Curves Lesson Take 1
  417.    wt: 1:   1 Chain Rule in Reverse Integration Method
  418.    wt: 1:   31 Derivatives of inverse functions
  419.    wt: 1:   28 Chain Rule Preparation for a Proof
  420.    wt: 1:   22 Chain Rule for polynomials
  421.    wt: 1:   20 Chain Rule for Pulley Systems
  422.    wt: 1:   18 Chain Rule Introduction
  423.    wt: 1:   17 Derivatives of quotients of sine and cosine
  424.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  425.    wt: 1:   15 sine and cosine derivatives 3rd step
  426.    wt: 1:   14 sine and cosine derivatives 2nd step
  427.    wt: 1:   12 Quotient rule examples
  428.    wt: 1:   3 Motivation for Limit Definition Take 2
  429.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  430.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  431.    wt: 1:   3 Decimal insights for limits continuity convergence
  432.    wt: 1:   1 Numerical introduction
  433.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  434.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  435.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  436.    wt: 1:   F.1 What Functions are Continuous
  437.    wt: 1:   E1 Error Control Inequalities
  438.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  439.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  440.    wt: 1:   PostScript For and Against Decimal Perspectives
  441.    wt: 1:   A1. Introduction
  442.    wt: 1:   Chapter 21 Arrow Addition
  443.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  444.    wt: 1:   Chapter 18. Slopes Areas Integration
  445.    wt: 1:   Chapter 17. Area Approximation
  446.    wt: 1:   Chapter 16. Velocity Approximation
  447.    wt: 1:   Chapter 15. Slope Approximation
  448.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  449.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  450.    wt: 1:   Chapter 13. Acceleration
  451.    wt: 1:   Chapter 12. Units and Slopes
  452.    wt: 1:   Chapter 10 Slopes and Units
  453.    wt: 1:   Chapter 1.Introduction
  454.    wt: 1:   Fall 1983 Calculus Appetizer
  455.    wt: 1:   Foreword
  456.    wt: 1:   Postscript More on Better Performance
  457.    wt: 1:   Appendix E. How To Study Mathematics and Why
  458.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  459.    wt: 1:   Chapter 31 Direct and Indirect Reason
  460.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  461.    wt: 1:   Chapter 23. Notation For Sums
  462.    wt: 1:   Chapter 21. Third Reading Guide
  463.    wt: 1:   Chapter 19. Functions and Sets
  464.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  465.    wt: 1:   Chapter 16. Painless Theorem Proving
  466.    wt: 1:   Chapter 15. Solving Linear Equations
  467.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  468.    wt: 1:   Chapter 13. Second Reading Guide
  469.    wt: 1:   Chapter 12. Shorthand Usage Guide
  470.    wt: 1:   Chapter 10 Describing and Changing Calculations
  471.    wt: 1:   Chapter 8 Three Skills For Algebra
  472.    wt: 1:   Solutions For Arithmetic Exercises
  473.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  474.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  475.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  476.    wt: 1:   Foreword
  477.    wt: 1:   Chapter 12 Four Phases
  478.    wt: 1:   Chapter 10 Transition
  479.    wt: 1:   Chapter 9 The Two Ends
  480.    wt: 1:   Chapter 2 For and Against Mathematics
  481.    wt: 1:   Chapter 1 Introduction
  482.    wt: 1:   Foreword
  483.    wt: 1:   Postscript C Consistency as a Tool for Reason
  484.    wt: 1:   Chapter 21 Occurrence Tables
  485.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  486.    wt: 1:   Chapter 18 Sense and Knowledge
  487.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  488.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  489.    wt: 1:   Chapter 15 Objective Processes
  490.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  491.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  492.    wt: 1:   Chapter 10 Responsibility
  493.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  494.    wt: 1:   Chapter 1 Introduction
  495.    wt: 1:   Foreword
  496.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  497.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  498.    wt: 1:   N Mathematics Prepare for College Studies
  499.    wt: 1:   J. More on written work and showing skill
  500.    wt: 1:   D. Check work a must with a caution
  501.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  502.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  503.    wt: 1:   Chapter 1 Arithmetic
  504.    wt: 1:   7 Games and Activities for Instruction
  505.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  506.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  507.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  508.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  509.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  510.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  511.    wt: 1:   The Math Forum and Site Content

Extended Search

944 matches:

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

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.


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

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

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

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