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

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

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

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

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

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

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

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74 matches:

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

Web Page Search

814 matches:

  1.    wt: 5:   5 Function notation for geometric transformations
  2.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  3.    wt: 5:   22 sine of 22.5 degrees via half angle formulas
  4.    wt: 5:   Appendix 2 Three Decimal Subtraction Methods
  5.    wt: 5:   G.2 Lipshitz Conditions Integration Calculus Reform
  6.    wt: 4:   C Electromotive force conventional current02
  7.    wt: 4:   26 Function definitions done and coming
  8.    wt: 4:   24 Monotoncity Injectivity and Inverse Functions
  9.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  10.    wt: 4:   2 Algebraic use of function notation
  11.    wt: 4:   8 Formulas for Fractional Exponents with Logarithms
  12.    wt: 4:   Rewriting algebraic substitution as function substitutions
  13.    wt: 4:   Construction Methods and Criteria for Isometric and Similar Triangles
  14.    wt: 4:   25 tangent double angle formula Slope connection
  15.    wt: 4:   12 Graph of tangent function for one period
  16.    wt: 4:   7 Translations Rotations Reflections Dilatations
  17.    wt: 4:   4 Equations for lines three forms
  18.    wt: 4:   C Three Decimal Subtraction Methods
  19.    wt: 4:   6 Column Methods for Decimal Multiplication
  20.    wt: 4:   2 Essentially one exercises three with solution
  21.    wt: 4:   1 Three Skills For Algebra
  22.    wt: 4:   Long Division forwards and backwards Example 2
  23.    wt: 4:   6 Why Decimal Long Division Methods Works Take I
  24.    wt: 4:   7 Subtraction for Decimal Fractions with Exercises
  25.    wt: 4:   2 Groups of Three Place Value for Multidigit Decimals
  26.    wt: 4:   3 Motivation for Limit Definition Take 2
  27.    wt: 4:   2 Motivation for Limit Definition Take 1
  28.    wt: 4:   3 Decimal insights for limits continuity convergence
  29.    wt: 4:   Chapter 8 Three Skills For Algebra
  30.    wt: 4:   Chapter 22 Contrapositive and Vacuously True Implications
  31.    wt: 3:   H LAMP Introduction Instructional Concepts
  32.    wt: 3:   Education Reform Inconsistencies
  33.    wt: 3:   geometric implications for algebra
  34.    wt: 3:   three goals for Mathematics Education
  35.    wt: 3:   02 21 words for teachers
  36.    wt: 3:   02 20 mathematics education references
  37.    wt: 3:   2 Conductance Resistance Duality02
  38.    wt: 3:   B Electromotive force conventional current01
  39.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  40.    wt: 3:   25 Mathematics Education Leaving A Good Impression
  41.    wt: 3:   22 Square Root function graphically
  42.    wt: 3:   14 Surjections Injections Bijections
  43.    wt: 3:   13 From one to one to many to one
  44.    wt: 3:   12 Function Domain Recognition Exercises
  45.    wt: 3:   6 Set Existence Formation and Notation
  46.    wt: 3:   4 Function notation in and beyond mathematics
  47.    wt: 3:   1 Geometric Introduction of Function Notation
  48.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  49.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  50.    wt: 3:   5 Polynomials Long division Nonlinear divisor
  51.    wt: 3:   2 Column Multiplication Method
  52.    wt: 3:   12 motivation for term arctan
  53.    wt: 3:   Analytic View of Triangle Construction or Line Instersection More
  54.    wt: 3:   6 Tangent Function Inclination Angle Take 2
  55.    wt: 3:   30 unit circle calculation of six trigonometric functions
  56.    wt: 3:   26 Formulas for products of sines and cosines
  57.    wt: 3:   23 sine and cosine of 180 plus 22.5 degrees
  58.    wt: 3:   12 cis formulas for sine cosines and tangent
  59.    wt: 3:   13 Navigation Location from Angles to 2 Landmarks
  60.    wt: 3:   2 point slope equation for a line
  61.    wt: 3:   PS B Parallelogram Construction Methods
  62.    wt: 3:   PS A Kite Construction Methods
  63.    wt: 3:   22 Multiplication of Signed Numbers
  64.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  65.    wt: 3:   8 Division and Mulplication of Compound Fractions
  66.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  67.    wt: 3:   4 Location of Point in Decimal Addition
  68.    wt: 3:   3 Location of Point in Decimal Multiplication
  69.    wt: 3:   2 Counting Digits in Decimal Multiplication
  70.    wt: 3:   1 Fractions with Finite Decimal Expansions
  71.    wt: 3:   E Long Division Methods more
  72.    wt: 3:   D Long Division Methods
  73.    wt: 3:   B Decimal Comparison and Subtraction
  74.    wt: 3:   A Decimal Addition Columm Methods
  75.    wt: 3:   7 Decimals Multiplication Methods Examples
  76.    wt: 3:   2 Combing Counts Addition Skills and Principles
  77.    wt: 3:   2 Fraction Operations Physical Development
  78.    wt: 3:   2 Linear Equation Literal Solution
  79.    wt: 3:   2 Addition and Multiplication Axioms
  80.    wt: 3:   3 Geometric Formulas and Function Notation
  81.    wt: 3:   2 Computation Rules Evaluation
  82.    wt: 3:   1 Formulas Dependence and Function Notation
  83.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  84.    wt: 3:   3 GE III Equation Addition and Multiplication
  85.    wt: 3:   5 Algebraic Solutions Introduction
  86.    wt: 3:   12 Cone Cylinder Sphere Lesson Idea
  87.    wt: 3:   2 Least Common Multiple LCM intro via list method
  88.    wt: 3:   12 GCD 2700 288 via Prime
  89.    wt: 3:   5 Reciprocals and Division for Fractions with Units
  90.    wt: 3:   C Equality for Fractions and Two Term Ratios and Fractions
  91.    wt: 3:   22 Complex Compound Fractions
  92.    wt: 3:   21 Reciprocals for Fractions and Wholes
  93.    wt: 3:   16 Addition Subtraction Comparision Compared
  94.    wt: 3:   13 Fraction Comparison Algebraic View
  95.    wt: 3:   12 Fraction Comparison
  96.    wt: 3:   2 Unit Fraction Multiplication
  97.    wt: 3:   Fraction Operations by Raising Terms A Simple Innovation
  98.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  99.    wt: 3:   24 Divisibility Tests for 2 3 5 9 10
  100.    wt: 3:   Long Division forwards and backwards Example 3
  101.    wt: 3:   Long Division forwards and backwards Example 1
  102.    wt: 3:   12 Why Long Division Works Take III
  103.    wt: 3:   D Decimal Multiplication Methods Derived
  104.    wt: 3:   A Elementary Basis for Multiplication Methods
  105.    wt: 3:   5 Decimal Fraction Multiplication
  106.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  107.    wt: 3:   Video Decimal Multiplication Geometric View Example 2
  108.    wt: 3:   Video Power Notation in Decimal Expansion
  109.    wt: 3:   Appendix 1 Decimals Comparison Method Take II
  110.    wt: 3:   Subtraction with J Conversions Example
  111.    wt: 3:   9 22 Minute Subtraction Review Video
  112.    wt: 3:   6 Subtraction with Conversion Example with Exercises
  113.    wt: 3:   4 Subtraction with Conversions Borrows and Letter J
  114.    wt: 3:   7 Adding decimal fractions using decimal point
  115.    wt: 3:   4. How to add with decimals B with conversions
  116.    wt: 3:   3. How to add with decimals A sans conversions
  117.    wt: 3:   8 Review Lesson 1 2 4 and 6 All in One
  118.    wt: 3:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  119.    wt: 3:   5 More on Groups of 3 Place Value in Decimal Fractions
  120.    wt: 3:   6 How long is a million seconds
  121.    wt: 3:   28 Chain Rule Preparation for a Proof
  122.    wt: 3:   22 Chain Rule for polynomials
  123.    wt: 3:   2 Algebraic codification
  124.    wt: 3:   D2 Limits of Monotone Sequences
  125.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  126.    wt: 3:   Chapter 29 Contrapositive and Vacuously True Implications
  127.    wt: 3:   Chapter 24. Personal Investment and Pension EGS
  128.    wt: 3:   Chapter 23. Notation For Sums
  129.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  130.    wt: 3:   Postscript C Consistency as a Tool for Reason
  131.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  132.    wt: 3:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  133.    wt: 3:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  134.    wt: 3:   Talking pdf files for online lessons a webvideo alternative
  135.    wt: 2:   G LAMP Introduction Problem Solving Skills
  136.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  137.    wt: 2:   Ramblings Introduction Algebra Essay
  138.    wt: 2:   Skills Chapter 3 Algebra
  139.    wt: 2:   Skills Chapter 2 Geometry
  140.    wt: 2:   Skills Chapter 0 Introduction
  141.    wt: 2:   7 logic review and decimals an odd combination
  142.    wt: 2:   three goals to set for students
  143.    wt: 2:   permissions for teachers
  144.    wt: 2:   links Education Resources online
  145.    wt: 2:   Secondary Three Mathematics
  146.    wt: 2:   Secondary One Mathematics
  147.    wt: 2:   teaching tutoring algebraic reason
  148.    wt: 2:   three aims for mathematics students
  149.    wt: 2:   formal or informal peer review
  150.    wt: 2:   three kinds of reason in mathematics
  151.    wt: 2:   Four ways to improve education reform
  152.    wt: 2:   Motivation and Context Problem
  153.    wt: 2:   Prequel In For A Penny In For A Pound
  154.    wt: 2:   fairness and inductive principles for instruction
  155.    wt: 2:   chapitre 12 00 les iles et division
  156.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  157.    wt: 2:   chapitre 04 05 Implication versus suggestion
  158.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  159.    wt: 2:   chapitre 02 00 La Communication des idees
  160.    wt: 2:   D Wire Resistance Calculation02
  161.    wt: 2:   24 Standards For Skill Develoment Take II
  162.    wt: 2:   24 Standards For Skill Develoment
  163.    wt: 2:   22 Student Centered Highschool Mathematics
  164.    wt: 2:   13 Addition and Addition Tables
  165.    wt: 2:   12 Goals and Objectives For Mathematics
  166.    wt: 2:   10 Ends values for work study instruction
  167.    wt: 2:   2 Reading and Writing Skills
  168.    wt: 2:   Ages 12 to 14 Skills with take home value
  169.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  170.    wt: 2:   sign monoticity analysis example 2
  171.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  172.    wt: 2:   23 Inverse Functions
  173.    wt: 2:   20 Interchanging coordinates a reflection
  174.    wt: 2:   19 Horizontal line rule and method
  175.    wt: 2:   17 Function maxima minima and their location
  176.    wt: 2:   8 Set view of relations and functions
  177.    wt: 2:   3 Formula or function graphing exercise
  178.    wt: 2:   7 quadratic formulla derivation
  179.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  180.    wt: 2:   2 Square Root Simplification a prequel
  181.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  182.    wt: 2:   4 Polynomials Long division linear divisor
  183.    wt: 2:   3 Polynomials Multiplication Addition
  184.    wt: 2:   16 cotangent function Definition Graph and Inverse
  185.    wt: 2:   15 cosecant function Definition Graph and Inverse
  186.    wt: 2:   14 secant function Definition Graph and Inverse
  187.    wt: 2:   13 cosecant function Definition Graph and Inverse
  188.    wt: 2:   9 motivation for name arcsin
  189.    wt: 2:   4 possible motivation for term arccos
  190.    wt: 2:   2 cosine function more properties
  191.    wt: 2:   2 Radian Measure Numerical Value of one degree
  192.    wt: 2:   11 Component Method
  193.    wt: 2:   10 Parallelogram Addition Method
  194.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  195.    wt: 2:   Straight Lines Instersection Solving Equations
  196.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  197.    wt: 2:   8 Straight Lines Equation for vertical
  198.    wt: 2:   7 Tangent Function is odd on this domain
  199.    wt: 2:   17 tangent function angle sum formulas
  200.    wt: 2:   29 secant cosecant and cotangent for acute angles
  201.    wt: 2:   24 tangent Angle Difference Formula
  202.    wt: 2:   21 sine and cosine Half Angle Formulas
  203.    wt: 2:   20 sine and cosine Double Angle Formulas
  204.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  205.    wt: 2:   17E Trig Formulas for dot and cross Products
  206.    wt: 2:   17D cis formulas for sine cosines and tangent
  207.    wt: 2:   1 Unit Points Reflections Rotations
  208.    wt: 2:   21 Logarithms Powers and Exponentials
  209.    wt: 2:   13 Trig Formulas for dot and cross Products
  210.    wt: 2:   5 Trigonometric Ratios For Tangent and Special Triangles
  211.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  212.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  213.    wt: 2:   12 Links Lessons elsewhere
  214.    wt: 2:   6 Polar Multiplication and Rotation
  215.    wt: 2:   5 Cartesian Addition and Translation
  216.    wt: 2:   PS G Rotation Distributes over Addition
  217.    wt: 2:   PS F Scalar Multiplication Distributes over Addition
  218.    wt: 2:   11 Triangle Construction Fails
  219.    wt: 2:   9 Construction of a right bisector
  220.    wt: 2:   2 Correspondence between Triangles
  221.    wt: 2:   26 More Less Greater Than Comparison
  222.    wt: 2:   25 Mid way Convergence to Axiomatic Approach
  223.    wt: 2:   23 Distributive Law Two Derivations
  224.    wt: 2:   21 Addition of Multiples of a Single Vector
  225.    wt: 2:   11 Signed Number Addition and Addition Properties
  226.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  227.    wt: 2:   9 Division with Digits after Decimal Point
  228.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  229.    wt: 2:   8 Column Multiplication Methods in General
  230.    wt: 2:   4 Fraction Operations Axiomatic Development
  231.    wt: 2:   5 Proportionality in Equivalent Fractions
  232.    wt: 2:   2 Algebraic View
  233.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  234.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  235.    wt: 2:   3 Linear Equation Literal Solution More
  236.    wt: 2:   4 Subtraction and Division Axioms
  237.    wt: 2:   2 More and Less Than for Counts and Measures
  238.    wt: 2:   9 Coordinates for Regions in Space
  239.    wt: 2:   2 GE II Comparison
  240.    wt: 2:   6 Algebraic Solution Example
  241.    wt: 2:   2 Three Examples
  242.    wt: 2:   2 Three Examples
  243.    wt: 2:   Formula Usage Show Work Format
  244.    wt: 2:   8 Compound Interest Formula Evaluation
  245.    wt: 2:   7 Compound Interest Formula Introduction
  246.    wt: 2:   2 Another Rectangle Area Formula Example
  247.    wt: 2:   1 Written work formats for developing and showing skill
  248.    wt: 2:   7 Cautious or Safe Set Construction
  249.    wt: 2:   6 Three Notions of What is a Variable
  250.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  251.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  252.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  253.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  254.    wt: 2:   1 Least Common Multiples LCM Introduction
  255.    wt: 2:   4 signed coordinates for regions in space
  256.    wt: 2:   6 Simplification of Fractions with Units
  257.    wt: 2:   1 Addition and Subtraction with Units
  258.    wt: 2:   20 Dividing Fractions the Why
  259.    wt: 2:   11 Simplification an Algebraic View
  260.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  261.    wt: 2:   6 Multiplication Algebraically Take II
  262.    wt: 2:   4 Fraction Multiplication
  263.    wt: 2:   3 Unit fraction of a fraction
  264.    wt: 2:   C Divisibility by 11 Integer Recognition Method
  265.    wt: 2:   B Integer Long Division Multiple Choices
  266.    wt: 2:   10 Integer Multiplication Formulas
  267.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  268.    wt: 2:   26 Divisibility by 2 3 5 Example
  269.    wt: 2:   23 Remainder Arithmetic Modulo 2
  270.    wt: 2:   22 Remainder Arithmetic Modulo 3 more
  271.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  272.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  273.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  274.    wt: 2:   20 Uniqueness of Prime Factorization
  275.    wt: 2:   15 video Factors of 20 using Prime Factorization
  276.    wt: 2:   10 video Prime Factorization upto 23 squared
  277.    wt: 2:   4 video Prime Factorization Introduction
  278.    wt: 2:   Long Division Backwards more
  279.    wt: 2:   Long Division Backward
  280.    wt: 2:   10 Division by Five Long and Short Ways
  281.    wt: 2:   9 Why Long Division Works Take II
  282.    wt: 2:   7 Long Divison Mistake Catching
  283.    wt: 2:   5 Long Division Include Zeroes or not
  284.    wt: 2:   4 Division with 2 Digit Divsors
  285.    wt: 2:   2 Division with Single Digit Divisors
  286.    wt: 2:   2 One Digit Multipliers
  287.    wt: 2:   Subtraction Another Video Lesson
  288.    wt: 2:   5 A Tip for Efficent Subtraction
  289.    wt: 2:   2 Subtraction Easy Case Examples
  290.    wt: 2:   1 Comparison and Subtraction Easy Direct Cases
  291.    wt: 2:   2 Decimal Counting Practices
  292.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  293.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  294.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  295.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  296.    wt: 2:   Formula Evaluation how to show work
  297.    wt: 2:   Expression Evaluation how to show work
  298.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  299.    wt: 2:   012 Division of Time Intervals by Time Intervals
  300.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  301.    wt: 2:   5 Conversion Arithmetic
  302.    wt: 2:   Example 2 volume of a cone
  303.    wt: 2:   Volume of Solid by Cross Sections Lesson
  304.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  305.    wt: 2:   Area Between Curves Lesson Take 2
  306.    wt: 2:   1 Chain Rule in Reverse Integration Method
  307.    wt: 2:   2 Second derivative test prequel
  308.    wt: 2:   38 Formulas and derivatives for powers and roots
  309.    wt: 2:   34 Derivative of exponential function
  310.    wt: 2:   29 Chain Rule Optional Reading
  311.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  312.    wt: 2:   26 Chain Rule Recognising outer inner functions
  313.    wt: 2:   25 Chain Rule Animated Examples Continued
  314.    wt: 2:   21 Chain Rule for powers
  315.    wt: 2:   20 Chain Rule for Pulley Systems
  316.    wt: 2:   19 Chain Rule for linear functions
  317.    wt: 2:   10 Three one sided limits with infinite values
  318.    wt: 2:   9 Limits Continuity and Composition
  319.    wt: 2:   7 Evaluation by immediate or delayed substitution
  320.    wt: 2:   G.4 Lipschitz Continuity implies EquiContinuity
  321.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  322.    wt: 2:   F.1 What Functions are Continuous
  323.    wt: 2:   E2 Algebraic Properties of Limits
  324.    wt: 2:   PostScript For and Against Decimal Perspectives
  325.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  326.    wt: 2:   Chapter 23 Links To Trigonometry
  327.    wt: 2:   Chapter 22 Complex Numbers
  328.    wt: 2:   Chapter 21 Arrow Addition
  329.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  330.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  331.    wt: 2:   Postscript More on Better Performance
  332.    wt: 2:   Postscript For Better Performance
  333.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  334.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  335.    wt: 2:   Chapter 25. Mathematical Induction Examples
  336.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  337.    wt: 2:   Chapter 18. Rules for Algebra
  338.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  339.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  340.    wt: 2:   Solutions For Arithmetic Exercises
  341.    wt: 2:   Chapter 4 Longer Chains of Reason
  342.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  343.    wt: 2:   Chapter 2 For and Against Mathematics
  344.    wt: 2:   Postscript D Reflections on Law of the Excluded Middle
  345.    wt: 2:   Postscript B More on Story Telling and Reason
  346.    wt: 2:   Chapter 24 Direct and Indirect Reason
  347.    wt: 2:   Chapter 20 Shorthand Symbols as Pronouns
  348.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  349.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  350.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  351.    wt: 2:   Chapter 7 Longer Chains of Reason
  352.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  353.    wt: 2:   G. Written work formats for developing and showing skill
  354.    wt: 2:   How to Build Skills and Confidence
  355.    wt: 2:   Chapter 3 Algebra Starter Lessons
  356.    wt: 2:   Primary and Secondary Skills and Practices with Take Home Value
  357.    wt: 2:   7 Games and Activities for Instruction
  358.    wt: 2:   2 Identifying Size and Position Place and Spatial Sense
  359.    wt: 2:   Ends Values Methods For Skill Development Framework Prequel
  360.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  361.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  362.    wt: 2:   The Math Forum and Site Content
  363.    wt: 1:   Appendix 2 primary school Arithmetic 01
  364.    wt: 1:   K LAMP Musings Science Education
  365.    wt: 1:   J LAMP Introduction Extrinsic Origins
  366.    wt: 1:   I LAMP Introduction Study Habits
  367.    wt: 1:   F LAMP Introduction Prerequisites
  368.    wt: 1:   E LAMP Introduction Modern Mathematics
  369.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  370.    wt: 1:   A Introduction Objectives
  371.    wt: 1:   Skills Chapter 5 Calculus
  372.    wt: 1:   Skills Chapter 4 Logic
  373.    wt: 1:   Skills Chapter 1 Arithmetic
  374.    wt: 1:   5 logarithms and exponentials etc
  375.    wt: 1:   4 algebra
  376.    wt: 1:   2 arithmetic with signed numbers
  377.    wt: 1:   Applied Maths Program14092009 POMME variant
  378.    wt: 1:   activities for students
  379.    wt: 1:   About site lesson plans
  380.    wt: 1:   Mathematics Education Professors
  381.    wt: 1:   teacher certification
  382.    wt: 1:   modern education
  383.    wt: 1:   mathematics in context
  384.    wt: 1:   Postscript 2007 01 10
  385.    wt: 1:   Secondary Two Mathematics
  386.    wt: 1:   talk the algebra talk
  387.    wt: 1:   three difficulties
  388.    wt: 1:   Lessening Algebra Difficulties
  389.    wt: 1:   the trouble with algebra
  390.    wt: 1:   04 29 New Mathematics Curriculum
  391.    wt: 1:   04 25 when to stop or suspend mathemat
  392.    wt: 1:   standards for course material
  393.    wt: 1:   Operational Viewpoint to Value
  394.    wt: 1:   mathematics instruction in general
  395.    wt: 1:   Education in mathematics science and technology
  396.    wt: 1:   Different Kinds of Reasoning in maths
  397.    wt: 1:   need for a mixed mathematics curriculum
  398.    wt: 1:   education an empirical art
  399.    wt: 1:   words for mathematics instructor
  400.    wt: 1:   chapitre 07 01 principle D induction mathematique
  401.    wt: 1:   chapitre 06 00 Chaines de la raison
  402.    wt: 1:   chapitre 05 00 Deception
  403.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  404.    wt: 1:   chapitre 04 08 Limitations et benefices
  405.    wt: 1:   chapitre 04 04 Parlons de la logique
  406.    wt: 1:   chapitre 04 02 Deuxieme enigme
  407.    wt: 1:   chapitre 04 00 Les regles d implication
  408.    wt: 1:   chapitre 01 00 Introduction
  409.    wt: 1:   problemes responses
  410.    wt: 1:   Trois Notions qui menent a algebre
  411.    wt: 1:   deux definitions pour variable
  412.    wt: 1:   2 Energy Power Heat07
  413.    wt: 1:   B Energy Power02
  414.    wt: 1:   1 Conductance Resistance Duality01
  415.    wt: 1:   F Wire Resistance Calculation04
  416.    wt: 1:   E Wire Resistance Calculation03
  417.    wt: 1:   C Wire Resistance Calculation01
  418.    wt: 1:   B Wire Resistance Qualitative02
  419.    wt: 1:   2 Unlike resistors in parallel01
  420.    wt: 1:   H Series Circuit02
  421.    wt: 1:   E Kirchoffs Second Law
  422.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  423.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  424.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  425.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  426.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  427.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  428.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  429.    wt: 1:   17 Math Booklets for children and young teenagers
  430.    wt: 1:   16 Secondary Mathematics Tips
  431.    wt: 1:   15 Counting For Parents
  432.    wt: 1:   14 Multiplication and Times Tables
  433.    wt: 1:   11 Help and Defend Your Child or Teens Education
  434.    wt: 1:   9 Streaming by Student Cooperation
  435.    wt: 1:   7 Student Motivation
  436.    wt: 1:   6 Discipline Who is in Charge Conserving Authority
  437.    wt: 1:   5 Patience Please for Yourself and Your Charges
  438.    wt: 1:   4 Learning Takes Time and Effort
  439.    wt: 1:   3 Preparing for Science Studies
  440.    wt: 1:   1 Speaking Skills
  441.    wt: 1:   Ages 12 to 14 Geometry
  442.    wt: 1:   Ages 12 to 14 Arithmetic
  443.    wt: 1:   Ages 10 to 12 Geometry
  444.    wt: 1:   Ages 10 to 12 Arithmetic
  445.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  446.    wt: 1:   sign monoticity analysis example 4
  447.    wt: 1:   sign monoticity analysis example 3
  448.    wt: 1:   sign monoticity analysis example 1
  449.    wt: 1:   18 Vertical Line Rule and Method
  450.    wt: 1:   16 Increasing or decreasing on intervals
  451.    wt: 1:   15 Sign analysis of functions
  452.    wt: 1:   11 Function Domain Range Source and Targets
  453.    wt: 1:   10 Interval Notation
  454.    wt: 1:   9 Set theory term relation possible origins
  455.    wt: 1:   7 Functions with finite domains
  456.    wt: 1:   Introduction Reading Guide
  457.    wt: 1:   9 quadratics physical and further context
  458.    wt: 1:   8 quadratics backward use of various formulas
  459.    wt: 1:   3 quadratics factoring by inspection
  460.    wt: 1:   2 quadratics graphing in general
  461.    wt: 1:   10 Exponential Growth and Decay Models
  462.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  463.    wt: 1:   8 Notes for instructors or tutors
  464.    wt: 1:   7 Links Lessons Elsewhere
  465.    wt: 1:   10 arctan left inverse of tangent Definition
  466.    wt: 1:   7 arcsin left inverse of sine Definition
  467.    wt: 1:   6 Graph of arccos function
  468.    wt: 1:   5 Swapping Coordinates is a reflection
  469.    wt: 1:   3 Left Inverse of cosine arccos definition
  470.    wt: 1:   1 cosine function properties
  471.    wt: 1:   8 Radian Measures of Common Angles
  472.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  473.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  474.    wt: 1:   1 Degrees and Radians Introduction
  475.    wt: 1:   A Global Time and Navigation
  476.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  477.    wt: 1:   12 From Applied To Pure Mathematics
  478.    wt: 1:   5 Head To Tail Arrow Addition
  479.    wt: 1:   3 Navigation with Arrows or Vectors
  480.    wt: 1:   2 Signed Coordinates
  481.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  482.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  483.    wt: 1:   Parallel Lines and Alternating Corresponding Angles
  484.    wt: 1:   Straight Lines ASA Intersection Study More
  485.    wt: 1:   Straight Lines ASA Intersection Study
  486.    wt: 1:   Straight Lines Intersection of
  487.    wt: 1:   14 Straight Lines Equations General Case
  488.    wt: 1:   12 Straight Lines Graphing mx plus b
  489.    wt: 1:   10 Straight Lines through Origin Equations More
  490.    wt: 1:   9 Straight Lines through Origin Equations
  491.    wt: 1:   5 Tangent Function Graph
  492.    wt: 1:   4 Tangent Function Properties
  493.    wt: 1:   3 Straight Lines Slope as Tangent of Inclination Angle
  494.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  495.    wt: 1:   1 Straight Lines Slope Concept
  496.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  497.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  498.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  499.    wt: 1:   32 seven rows of pascals triangle
  500.    wt: 1:   28 Expressing products of sines cosines as sums
  501.    wt: 1:   27 Logarithmic use of products of sines and cosines
  502.    wt: 1:   17G Pythagorean Theorem Converse
  503.    wt: 1:   17C sine and cosine double triple angle formulas
  504.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  505.    wt: 1:   17A The complex number valued trig function cis
  506.    wt: 1:   16 Right Triangle Complementary Angle Relations
  507.    wt: 1:   15 sine cosine Complementary Angle Relations
  508.    wt: 1:   13 Graph of tangent function many periods
  509.    wt: 1:   11 tangent function undefined when terminal side vertical
  510.    wt: 1:   9 Graphs of sine and cosine over one period
  511.    wt: 1:   8 period of tangent function
  512.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  513.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  514.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  515.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  516.    wt: 1:   2 Quadrant I reference Angles
  517.    wt: 1:   Unit Circle Development of Trigonometry
  518.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  519.    wt: 1:   20 N th Roots of Complex Numbers
  520.    wt: 1:   16 References and Originality Question
  521.    wt: 1:   15 Pythagorean Theorem Converse
  522.    wt: 1:   11 sine and cosine double triple angle formulas
  523.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  524.    wt: 1:   9 The complex number valued trig function cis
  525.    wt: 1:   8 Unit Circle Development of Trigonometry
  526.    wt: 1:   7 Second Way to Calculate Products
  527.    wt: 1:   4 Multiplication Properties
  528.    wt: 1:   3 Addition Properties
  529.    wt: 1:   2 Complex Numbers made easier we hope
  530.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  531.    wt: 1:   3 Trigonometric Ratios sine and cosine
  532.    wt: 1:   Why Trigonometry the whyslopes view
  533.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  534.    wt: 1:   12 Triangles Similarity More Problems
  535.    wt: 1:   8 Similarity of Triangles and Polygons
  536.    wt: 1:   4 Similarity Definition with Coordinate
  537.    wt: 1:   2 Similarity By Design
  538.    wt: 1:   1 Early Concept of Like or Similar Shapes
  539.    wt: 1:   8 Mid Point Formula
  540.    wt: 1:   7 Exercises to test skill and concept mastery
  541.    wt: 1:   6 Intersection of lines by solving linear systems
  542.    wt: 1:   5 Algebraic View of Slopes
  543.    wt: 1:   3 Slope product for perpendicular lines
  544.    wt: 1:   1 Numerical view of lines and their equations
  545.    wt: 1:   13 Pythagorean spatial distance formulas
  546.    wt: 1:   12 Spatial Coordinates
  547.    wt: 1:   10 Pythagorean plane distance formula
  548.    wt: 1:   8 Distance Between Points on a Line
  549.    wt: 1:   2 Cartesian Coordinates with signs
  550.    wt: 1:   PS H Distributive Law For Complex Numbers
  551.    wt: 1:   PS E Multiplication with Polar Coordinates
  552.    wt: 1:   PS D Addition with Cartesian Coordinates
  553.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  554.    wt: 1:   21 Parallelograms
  555.    wt: 1:   12 Side Angle Side Failure
  556.    wt: 1:   6 Ruler and compass Angle Bisection
  557.    wt: 1:   3 Isometry of Triangles Congruence
  558.    wt: 1:   1 Initial Concepts and Terms
  559.    wt: 1:   Short Course on Euclidean Geometry
  560.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  561.    wt: 1:   4 Angles on Maps Plans drawn to scale
  562.    wt: 1:   3 Lengths and Areas on Maps and Plans
  563.    wt: 1:   2 Measuring Area Directly
  564.    wt: 1:   About Folder Contents
  565.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  566.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  567.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  568.    wt: 1:   15 Head to Tails in place Addition Associative
  569.    wt: 1:   12 Real Numbers Line Signed Coordinates
  570.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  571.    wt: 1:   5 Distributive Law for Whole Numbers
  572.    wt: 1:   4 Commutative Law Groups Counting Form
  573.    wt: 1:   3 Multiplicative Counting Skills Principles
  574.    wt: 1:   3 Inequalities Algebraically
  575.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  576.    wt: 1:   4 Rates Ratios and Proporitionality
  577.    wt: 1:   3 Proportionality Examples
  578.    wt: 1:   1 What is Proportionality
  579.    wt: 1:   6 Compound Interest Forward and Backwards
  580.    wt: 1:   5 Triangle Area Formula Backwards
  581.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  582.    wt: 1:   1 Changing Calculations
  583.    wt: 1:   6 Equations and Systems Equivalent or Implied
  584.    wt: 1:   5 Equality in Algebra
  585.    wt: 1:   3 Product Axioms Two Forms
  586.    wt: 1:   1 Equivalent Computation Rules
  587.    wt: 1:   4 Comparison of Negative Numbers
  588.    wt: 1:   1 Real Numbers Comparison
  589.    wt: 1:   16 Real Numbers Comparison
  590.    wt: 1:   15 Real Number Division
  591.    wt: 1:   14 Real Number Multiplication
  592.    wt: 1:   13 Real Number Subtraction
  593.    wt: 1:   12 Real Number Additive Inverses or Negatives
  594.    wt: 1:   11 Real Number Addition
  595.    wt: 1:   8 Coordinates for Maps and Planes
  596.    wt: 1:   5 Rational Numbers More
  597.    wt: 1:   4 Rational Numbers
  598.    wt: 1:   3 Fractions
  599.    wt: 1:   2 Integers
  600.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  601.    wt: 1:   1 GE Substitution four examples
  602.    wt: 1:   1 Essentially One Unknown
  603.    wt: 1:   4 Four Examples Fractional Coefficients
  604.    wt: 1:   10 One Example
  605.    wt: 1:   9 Three Examples
  606.    wt: 1:   8 One Example
  607.    wt: 1:   6 Three Examples
  608.    wt: 1:   5 Three Examples
  609.    wt: 1:   Using Letters for Physical Quantities
  610.    wt: 1:   13 Naming Identifying Formulas with Words
  611.    wt: 1:   9 Volume of Cone
  612.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  613.    wt: 1:   5 Box Volume Formula Example
  614.    wt: 1:   4 Circle Area Formula Example
  615.    wt: 1:   3 Triangle Area Formula Example
  616.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  617.    wt: 1:   6 Power Set Notation
  618.    wt: 1:   5 Product Builder Notation
  619.    wt: 1:   4 Subset Builder Notation
  620.    wt: 1:   2 Venn Diagrams
  621.    wt: 1:   4 A Brief Story of numbers and algebra
  622.    wt: 1:   2 What is a Variable
  623.    wt: 1:   About Folder Contents
  624.    wt: 1:   arithmetic videos Real Player Format
  625.    wt: 1:   3 Comparison of Negative Numbers
  626.    wt: 1:   2 More and Less Than with Unlike Signs
  627.    wt: 1:   1 More and Less Than for Counts and Measures
  628.    wt: 1:   2 Square Roots with Prime
  629.    wt: 1:   1 Squares and Square Roots Introduction
  630.    wt: 1:   13 GCD from given Prime Factorization
  631.    wt: 1:   7 GCD and LCM from prime factorization
  632.    wt: 1:   5 Common Divisors 60 45 via Prime
  633.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  634.    wt: 1:   2 Counting with Tables and Trees I
  635.    wt: 1:   1 Counting and Counting Methods I
  636.    wt: 1:   3 signed coordinates for maps and planes
  637.    wt: 1:   2 signed and unsigned numbers as coordinates
  638.    wt: 1:   7 Converting or Changing Units
  639.    wt: 1:   4 Fractions with Units
  640.    wt: 1:   2 Equality and Units
  641.    wt: 1:   D Three Term Ratios
  642.    wt: 1:   B Fractions and Two Term Ratios
  643.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  644.    wt: 1:   21 Working With Signs
  645.    wt: 1:   19 Dividing Fractions How TO
  646.    wt: 1:   9 Improper Fractions and Mixed Numbers
  647.    wt: 1:   8 Numerals Fractionals Quantals Take II
  648.    wt: 1:   7 Numerals Fractionals Quantals
  649.    wt: 1:   6 Multiplication of Mixed Numbers
  650.    wt: 1:   5 Equivalent Fractions
  651.    wt: 1:   1 What is a fraction Take II
  652.    wt: 1:   1 What is a fraction
  653.    wt: 1:   13 Subtraction with Additive Inverse
  654.    wt: 1:   12 Adding Integers More Examples
  655.    wt: 1:   11 Adding Integers Formulas and Examples
  656.    wt: 1:   8 Multiplication by Signed Numbers Integers
  657.    wt: 1:   7 Multiplication by Signs
  658.    wt: 1:   6 Multiplication by Natural Numbers
  659.    wt: 1:   4 Adding Movements wiht opposite directions
  660.    wt: 1:   3 Adding Movements with same direction
  661.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  662.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  663.    wt: 1:   21 Remainder Arithmetic Modulo 3
  664.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  665.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  666.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  667.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  668.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  669.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  670.    wt: 1:   19 video Prime Factorization Unique
  671.    wt: 1:   18 video Count Factors given Prime Factorization
  672.    wt: 1:   14 video Factors of 24 Take II
  673.    wt: 1:   13 video Factors of 24 using prime
  674.    wt: 1:   12 LCD GCD and LCM using Primes
  675.    wt: 1:   9 video Prime Factorization upto 19 squared
  676.    wt: 1:   8 video Prime Factorization upto 19
  677.    wt: 1:   7 Calculator Usage Notes and Cautions
  678.    wt: 1:   5 Prime Factorization and a Square Rule
  679.    wt: 1:   2 Prime and Composites less than 16
  680.    wt: 1:   Division with Counts and Length
  681.    wt: 1:   3 Division Single Digit Divisor Example
  682.    wt: 1:   1 Divsion Physical Examples
  683.    wt: 1:   6 Multiplication Commutes Order Not Important
  684.    wt: 1:   4 Two and Three Digit Multipliers
  685.    wt: 1:   3 More One Digit Multipliers
  686.    wt: 1:   8 Subtraction with Units of Measure
  687.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  688.    wt: 1:   8 What skills and work habits to require
  689.    wt: 1:   5. How to add decimals C. Examples
  690.    wt: 1:   1. Explaining Addition Table
  691.    wt: 1:   11 Place Value SI Standard International way
  692.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  693.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  694.    wt: 1:   Quick history of numbers and algebra
  695.    wt: 1:   Exact Arithmetic Wholes and Fractions
  696.    wt: 1:   The 20 Times Table
  697.    wt: 1:   The 12 Times Table Visually
  698.    wt: 1:   About folder contents
  699.    wt: 1:   011 Division of Time Intervals By Numbers
  700.    wt: 1:   010 Repeated Addition of Time Intervals
  701.    wt: 1:   8 Addition of Time Intervals via subtotaling
  702.    wt: 1:   7 Addition of Time Intervals
  703.    wt: 1:   2 Time and Date Matters in School
  704.    wt: 1:   1 Intro of Kids To Time Date Skills
  705.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  706.    wt: 1:   Example 4 with x function of y
  707.    wt: 1:   Example 2
  708.    wt: 1:   Area Between Curves Lesson Take 1
  709.    wt: 1:   4 Definite Integrals Evaluation Exercises
  710.    wt: 1:   3 Two Chain Rule Method Exercises
  711.    wt: 1:   2 Indefinite Integrals Exercises
  712.    wt: 1:   A Related lessons in Volume 3
  713.    wt: 1:   4 Second derivative test exercise example
  714.    wt: 1:   3 Second derivative test
  715.    wt: 1:   31 Derivatives of inverse functions
  716.    wt: 1:   24 Chain Rule Animated Examples
  717.    wt: 1:   23 Chain Rule in general
  718.    wt: 1:   18 Chain Rule Introduction
  719.    wt: 1:   14 sine and cosine derivatives 2nd step
  720.    wt: 1:   12 Quotient rule examples
  721.    wt: 1:   10 Power rule for negative integers
  722.    wt: 1:   8 Differentiation of polynomials
  723.    wt: 1:   7 Animated Differentiation Examples
  724.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  725.    wt: 1:   11 Limits at infinity Three Examples
  726.    wt: 1:   6 Continuity at a point
  727.    wt: 1:   5 Jumps and absence of unlimited error control
  728.    wt: 1:   1 Numerical introduction
  729.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  730.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  731.    wt: 1:   G.5 Motions With Bounded Velocities
  732.    wt: 1:   G.3 Constant Difference Theorem Proof
  733.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  734.    wt: 1:   F.5a Equicontinuity Theorems
  735.    wt: 1:   F.2 Closed Range Theorem
  736.    wt: 1:   E1 Error Control Inequalities
  737.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  738.    wt: 1:   A1. Introduction
  739.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  740.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  741.    wt: 1:   Chapter 18. Slopes Areas Integration
  742.    wt: 1:   Chapter 17. Area Approximation
  743.    wt: 1:   Chapter 16. Velocity Approximation
  744.    wt: 1:   Chapter 15. Slope Approximation
  745.    wt: 1:   Chapter 13. Acceleration
  746.    wt: 1:   Chapter 12. Units and Slopes
  747.    wt: 1:   Chapter 11. Graphing Slope versus Position
  748.    wt: 1:   Chapter 8. Slope Interpretation
  749.    wt: 1:   Chapter 2. Slopes and Ski Trails
  750.    wt: 1:   Chapter 1.Introduction
  751.    wt: 1:   Foreword
  752.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  753.    wt: 1:   Chapter 31 Direct and Indirect Reason
  754.    wt: 1:   Chapter 28 Occurrence Tables
  755.    wt: 1:   Chapter 21. Third Reading Guide
  756.    wt: 1:   Chapter 20. Degrees and Radians
  757.    wt: 1:   Chapter 19. Functions and Sets
  758.    wt: 1:   Chapter 15. Solving Linear Equations
  759.    wt: 1:   Chapter 13. Second Reading Guide
  760.    wt: 1:   Chapter 12. Shorthand Usage Guide
  761.    wt: 1:   Chapter 10 Describing and Changing Calculations
  762.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  763.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  764.    wt: 1:   Chapter 3 Chains of Reason
  765.    wt: 1:   Foreword
  766.    wt: 1:   Postscript B Mathematics Education References
  767.    wt: 1:   Postscript A Three Remarks
  768.    wt: 1:   Chapter 12 Four Phases
  769.    wt: 1:   Chapter 11 Elementary Instruction
  770.    wt: 1:   Chapter 10 Transition
  771.    wt: 1:   Chapter 8 Modern Instruction
  772.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  773.    wt: 1:   Chapter 3 Algebra Difficulties
  774.    wt: 1:   Chapter 1 Introduction
  775.    wt: 1:   Foreword
  776.    wt: 1:   Chapter 23 Truth Tables
  777.    wt: 1:   Chapter 21 Occurrence Tables
  778.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  779.    wt: 1:   Chapter 10 Responsibility
  780.    wt: 1:   Chapter 6 Chains of Reason
  781.    wt: 1:   Chapter 5 Deception
  782.    wt: 1:   Chapter 2 Skill Development
  783.    wt: 1:   Chapter 1 Introduction
  784.    wt: 1:   Three Remarks
  785.    wt: 1:   Foreword
  786.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  787.    wt: 1:   S Adding words to algebra
  788.    wt: 1:   R Why Learn Mathematics Skills
  789.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  790.    wt: 1:   O On Learning Mathematics and Science
  791.    wt: 1:   N Mathematics Prepare for College Studies
  792.    wt: 1:   L Skills with take home value
  793.    wt: 1:   N Improving Marks on Tests and Finals
  794.    wt: 1:   J. More on written work and showing skill
  795.    wt: 1:   I. Logic and language skills
  796.    wt: 1:   H more Routine to non routine problem solving
  797.    wt: 1:   D. Check work a must with a caution
  798.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  799.    wt: 1:   Chapter 6 More Algebra and Geometry
  800.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  801.    wt: 1:   Chapter 2 Why Sets
  802.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  803.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  804.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  805.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  806.    wt: 1:   Mathematics Education References
  807.    wt: 1:   Mathematics Education References
  808.    wt: 1:   Implementation Notes
  809.    wt: 1:   More Algebra and Slope based Calculus Preview
  810.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  811.    wt: 1:   Systematic Algebra Skill Development Missing Links
  812.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  813.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  814.    wt: 1:   Road Safety Questions

Extended Search

1103 matches:

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

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

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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