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

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

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

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

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

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

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

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

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364 matches:

  1.    wt: 4:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  2.    wt: 3:   9 combinatorics probability sets
  3.    wt: 3:   Rewriting algebraic substitution as function substitutions
  4.    wt: 3:   13 Real Number Subtraction
  5.    wt: 3:   4 Subset Builder Notation
  6.    wt: 3:   4 A Brief Story of numbers and algebra
  7.    wt: 3:   012 Division of Time Intervals by Time Intervals
  8.    wt: 3:   011 Division of Time Intervals By Numbers
  9.    wt: 2:   Ramblings Extrinsic numbers theory
  10.    wt: 2:   Ramblings Introduction Algebra Essay
  11.    wt: 2:   About site lesson plans
  12.    wt: 2:   Maps Plans Drawings
  13.    wt: 2:   the trouble with algebra
  14.    wt: 2:   How to be a better instructor
  15.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  16.    wt: 2:   problemes algebre et arithmetique
  17.    wt: 2:   13 Addition and Addition Tables
  18.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  19.    wt: 2:   21 Graphs of functions given by Horizontal Line Method
  20.    wt: 2:   10 Interval Notation
  21.    wt: 2:   4 Function notation in and beyond mathematics
  22.    wt: 2:   2 Algebraic use of function notation
  23.    wt: 2:   13 Velocity Vectors in Physics
  24.    wt: 2:   10 Midpoint of [a b] and [b a]
  25.    wt: 2:   PS H Distributive Law For Complex Numbers
  26.    wt: 2:   16 Angles Subtended By Chords and Diameters
  27.    wt: 2:   4 Angles on Maps Plans drawn to scale
  28.    wt: 2:   3 Lengths and Areas on Maps and Plans
  29.    wt: 2:   musings do not puiblish real numbers
  30.    wt: 2:   13 Arrows and Vectors in a Plane
  31.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  32.    wt: 2:   B Decimal Comparison and Subtraction
  33.    wt: 2:   5 Distributive Law for Whole Numbers
  34.    wt: 2:   9 Sets in Probability and Statistics
  35.    wt: 2:   5 Product Builder Notation
  36.    wt: 2:   5 Talking about Numbers and Quantities
  37.    wt: 2:   9 subtracting signed numbers
  38.    wt: 2:   13 Fraction Comparison Algebraic View
  39.    wt: 2:   C Divisibility by 11 Integer Recognition Method
  40.    wt: 2:   13 Subtraction with Additive Inverse
  41.    wt: 2:   8 Multiplication by Signed Numbers Integers
  42.    wt: 2:   6 Multiplication by Natural Numbers
  43.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  44.    wt: 2:   26 Divisibility by 2 3 5 Example
  45.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  46.    wt: 2:   4 Subtraction with Conversions Borrows and Letter J
  47.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  48.    wt: 2:   Quick history of numbers and algebra
  49.    wt: 2:   013 Travel Time Tables
  50.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  51.    wt: 2:   8 Addition of Time Intervals via subtotaling
  52.    wt: 2:   7 Evaluation by immediate or delayed substitution
  53.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  54.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  55.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  56.    wt: 2:   B3 Bolzano Weierstrass Theorem
  57.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  58.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  59.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  60.    wt: 2:   A. Skill has to be seen to believed
  61.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  62.    wt: 2:   4 Money Matters Saving Earning Buying Selling and Budgets
  63.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  64.    wt: 2:   More Algebra and Slope based Calculus Preview
  65.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  66.    wt: 1:   I LAMP Introduction Study Habits
  67.    wt: 1:   G LAMP Introduction Problem Solving Skills
  68.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  69.    wt: 1:   A Introduction Objectives
  70.    wt: 1:   Skills Chapter 3 Algebra
  71.    wt: 1:   7 logic review and decimals an odd combination
  72.    wt: 1:   4 algebra
  73.    wt: 1:   2 arithmetic with signed numbers
  74.    wt: 1:   1 arithmetic with unsigned numbers
  75.    wt: 1:   why bother
  76.    wt: 1:   website reviews
  77.    wt: 1:   Math Ed if it must be short make it lean effective
  78.    wt: 1:   grouping students according to ability
  79.    wt: 1:   what should be learnt and When
  80.    wt: 1:   talk the algebra talk
  81.    wt: 1:   geometric implications for algebra
  82.    wt: 1:   teaching tutoring algebraic reason
  83.    wt: 1:   Lessening Algebra Difficulties
  84.    wt: 1:   05 13 OldSiteEntrancePage
  85.    wt: 1:   Motivation and Context Problem
  86.    wt: 1:   chapitre 04 08 Limitations et benefices
  87.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  88.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  89.    wt: 1:   problemes responses
  90.    wt: 1:   Trois Notions qui menent a algebre
  91.    wt: 1:   deux definitions pour variable
  92.    wt: 1:   B Energy Power02
  93.    wt: 1:   B Wire Resistance Qualitative02
  94.    wt: 1:   B Electromotive force conventional current01
  95.    wt: 1:   17 Math Booklets for children and young teenagers
  96.    wt: 1:   14 Multiplication and Times Tables
  97.    wt: 1:   12 Goals and Objectives For Mathematics
  98.    wt: 1:   9 Streaming by Student Cooperation
  99.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  100.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  101.    wt: 1:   23 Inverse Functions
  102.    wt: 1:   16 Increasing or decreasing on intervals
  103.    wt: 1:   15 Sign analysis of functions
  104.    wt: 1:   14 Surjections Injections Bijections
  105.    wt: 1:   13 From one to one to many to one
  106.    wt: 1:   9 Set theory term relation possible origins
  107.    wt: 1:   8 Set view of relations and functions
  108.    wt: 1:   7 Functions with finite domains
  109.    wt: 1:   6 Set Existence Formation and Notation
  110.    wt: 1:   5 Function notation for geometric transformations
  111.    wt: 1:   1 Geometric Introduction of Function Notation
  112.    wt: 1:   8 quadratics backward use of various formulas
  113.    wt: 1:   3 quadratics factoring by inspection
  114.    wt: 1:   11 Growth and Decay in Biology
  115.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  116.    wt: 1:   1 Polynomials Distributive Law
  117.    wt: 1:   13 cosecant function Definition Graph and Inverse
  118.    wt: 1:   4 possible motivation for term arccos
  119.    wt: 1:   9 Summary Degrees to Radians and back
  120.    wt: 1:   A Global Time and Navigation
  121.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  122.    wt: 1:   8 Parallel Vectors
  123.    wt: 1:   6 Vectors with Coordinates
  124.    wt: 1:   3 Navigation with Arrows or Vectors
  125.    wt: 1:   Vector and Complex Number Applet
  126.    wt: 1:   B Straight Line Slope Scaling Properties More
  127.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  128.    wt: 1:   12 Straight Lines Graphing mx plus b
  129.    wt: 1:   31 basic secant cosecant cotangent trig identities
  130.    wt: 1:   30 unit circle calculation of six trigonometric functions
  131.    wt: 1:   25 tangent double angle formula Slope connection
  132.    wt: 1:   20 sine and cosine Double Angle Formulas
  133.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  134.    wt: 1:   17C sine and cosine double triple angle formulas
  135.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  136.    wt: 1:   17A The complex number valued trig function cis
  137.    wt: 1:   13 Graph of tangent function many periods
  138.    wt: 1:   Unit Circle Development of Trigonometry
  139.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  140.    wt: 1:   20 N th Roots of Complex Numbers
  141.    wt: 1:   17 Cube Roots of unity
  142.    wt: 1:   13 Trig Formulas for dot and cross Products
  143.    wt: 1:   11 sine and cosine double triple angle formulas
  144.    wt: 1:   9 The complex number valued trig function cis
  145.    wt: 1:   8 Unit Circle Development of Trigonometry
  146.    wt: 1:   6 Field Properties of Complex Number
  147.    wt: 1:   5 An Easy Proof of the Distributive Law
  148.    wt: 1:   2 Complex Numbers made easier we hope
  149.    wt: 1:   Appetizer A Complex Number Applet
  150.    wt: 1:   8 Triangles Cascade Problem Solving
  151.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  152.    wt: 1:   Why Trigonometry the whyslopes view
  153.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  154.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  155.    wt: 1:   12 Triangles Similarity More Problems
  156.    wt: 1:   11 Triangle Similarity Missing Side Problem
  157.    wt: 1:   3 Similarity by Design with coordinates
  158.    wt: 1:   2 Similarity By Design
  159.    wt: 1:   6 Intersection of lines by solving linear systems
  160.    wt: 1:   5 Algebraic View of Slopes
  161.    wt: 1:   13 Pythagorean spatial distance formulas
  162.    wt: 1:   8 Distance Between Points on a Line
  163.    wt: 1:   7 Complex Numbers Appetizer
  164.    wt: 1:   PS G Rotation Distributes over Addition
  165.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  166.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  167.    wt: 1:   PS B Parallelogram Construction Methods
  168.    wt: 1:   17 Right Bisectors of Triangle Sides
  169.    wt: 1:   13 Angle Side Angle Failure
  170.    wt: 1:   9 Construction of a right bisector
  171.    wt: 1:   6 Ruler and compass Angle Bisection
  172.    wt: 1:   2 Correspondence between Triangles
  173.    wt: 1:   8 More Use of Maps Not Drawn to Scale
  174.    wt: 1:   6 Figuring with Maps Not to Scale
  175.    wt: 1:   About Folder Contents
  176.    wt: 1:   A Signed Number Arithmetic Review
  177.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  178.    wt: 1:   23 Distributive Law Two Derivations
  179.    wt: 1:   22 Multiplication of Signed Numbers
  180.    wt: 1:   19 Signed Multiples of Vectors
  181.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  182.    wt: 1:   12 Real Numbers Line Signed Coordinates
  183.    wt: 1:   11 Signed Number Addition and Addition Properties
  184.    wt: 1:   C Three Decimal Subtraction Methods
  185.    wt: 1:   2 Combing Counts Addition Skills and Principles
  186.    wt: 1:   1 The Counting Origins of Numbers
  187.    wt: 1:   3 Inequalities Algebraically
  188.    wt: 1:   2 Algebraic View
  189.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  190.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  191.    wt: 1:   6 Compound Interest Forward and Backwards
  192.    wt: 1:   5 Triangle Area Formula Backwards
  193.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  194.    wt: 1:   5 Equality in Algebra
  195.    wt: 1:   4 Subtraction and Division Axioms
  196.    wt: 1:   4 Comparison of Negative Numbers
  197.    wt: 1:   1 Real Numbers Comparison
  198.    wt: 1:   16 Real Numbers Comparison
  199.    wt: 1:   15 Real Number Division
  200.    wt: 1:   14 Real Number Multiplication
  201.    wt: 1:   12 Real Number Additive Inverses or Negatives
  202.    wt: 1:   11 Real Number Addition
  203.    wt: 1:   10 Real Number Lengths and Signs
  204.    wt: 1:   8 Coordinates for Maps and Planes
  205.    wt: 1:   7 Real Numbers as Line Cordinates
  206.    wt: 1:   6 Unsigned Real Numbers
  207.    wt: 1:   5 Rational Numbers More
  208.    wt: 1:   4 Rational Numbers
  209.    wt: 1:   1 Whole and Natural Numbers
  210.    wt: 1:   5 Independent versus Dependent Variables
  211.    wt: 1:   3 Geometric Formulas and Function Notation
  212.    wt: 1:   1 Formulas Dependence and Function Notation
  213.    wt: 1:   1 GE Substitution four examples
  214.    wt: 1:   6 Algebraic Solution Example
  215.    wt: 1:   5 Algebraic Solutions Introduction
  216.    wt: 1:   13 Naming Identifying Formulas with Words
  217.    wt: 1:   5 Box Volume Formula Example
  218.    wt: 1:   8 Sets of Numbers
  219.    wt: 1:   6 Power Set Notation
  220.    wt: 1:   6 Three Notions of What is a Variable
  221.    wt: 1:   2 What is a Variable
  222.    wt: 1:   1 Three Skills For Algebra
  223.    wt: 1:   About Folder Contents
  224.    wt: 1:   3 Comparison of Negative Numbers
  225.    wt: 1:   13 GCD from given Prime Factorization
  226.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  227.    wt: 1:   3 Counting with Tables and Trees II
  228.    wt: 1:   2 Counting with Tables and Trees I
  229.    wt: 1:   11 What are real lengths and numbers
  230.    wt: 1:   10 dividing signed numbers
  231.    wt: 1:   8 multiplying signed numbers
  232.    wt: 1:   6 adding signed numbers
  233.    wt: 1:   5 lengths and signs of numbers
  234.    wt: 1:   3 signed coordinates for maps and planes
  235.    wt: 1:   2 signed and unsigned numbers as coordinates
  236.    wt: 1:   3 Multiplying Units and Numbers
  237.    wt: 1:   1 Addition and Subtraction with Units
  238.    wt: 1:   B Fractions and Two Term Ratios
  239.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  240.    wt: 1:   17 Efficient Ways to Add and Subtract
  241.    wt: 1:   16 Addition Subtraction Comparision Compared
  242.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  243.    wt: 1:   14 Adding and Subtracting with Like Denominators
  244.    wt: 1:   11 Simplification an Algebraic View
  245.    wt: 1:   9 Improper Fractions and Mixed Numbers
  246.    wt: 1:   6 Multiplication of Mixed Numbers
  247.    wt: 1:   6 Multiplication Algebraically Take II
  248.    wt: 1:   Fraction Operations by Raising Terms A Simple Innovation
  249.    wt: 1:   B Integer Long Division Multiple Choices
  250.    wt: 1:   7 Multiplication by Signs
  251.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  252.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  253.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  254.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  255.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  256.    wt: 1:   13 video Factors of 24 using prime
  257.    wt: 1:   3 video Primes and Composites from 9 times table
  258.    wt: 1:   1 video how Products are bigger than factor
  259.    wt: 1:   Long Division Backwards more
  260.    wt: 1:   Long Division Backward
  261.    wt: 1:   Long Division forwards and backwards Example 3
  262.    wt: 1:   Long Division forwards and backwards Example 2
  263.    wt: 1:   Long Division forwards and backwards Example 1
  264.    wt: 1:   10 Division by Five Long and Short Ways
  265.    wt: 1:   B Powers of Ten
  266.    wt: 1:   A Elementary Basis for Multiplication Methods
  267.    wt: 1:   Video Power Notation in Decimal Expansion
  268.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  269.    wt: 1:   Subtraction with J Conversions Example
  270.    wt: 1:   Subtraction Another Video Lesson
  271.    wt: 1:   9 22 Minute Subtraction Review Video
  272.    wt: 1:   8 Subtraction with Units of Measure
  273.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  274.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  275.    wt: 1:   5 A Tip for Efficent Subtraction
  276.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  277.    wt: 1:   2 Subtraction Easy Case Examples
  278.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  279.    wt: 1:   8 What skills and work habits to require
  280.    wt: 1:   4. How to add with decimals B with conversions
  281.    wt: 1:   1. Explaining Addition Table
  282.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  283.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  284.    wt: 1:   The 20 Times Table
  285.    wt: 1:   The 12 Times Table Visually
  286.    wt: 1:   About folder contents
  287.    wt: 1:   016 Numbering Occidental Calendar Days
  288.    wt: 1:   015 School and work day counting tables
  289.    wt: 1:   010 Repeated Addition of Time Intervals
  290.    wt: 1:   7 Addition of Time Intervals
  291.    wt: 1:   Volume of Solid by Cross Sections Lesson
  292.    wt: 1:   Example 1. Area Between x and x squared
  293.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  294.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  295.    wt: 1:   Area Between Curves Lesson Take 2
  296.    wt: 1:   Area Between Curves Lesson Take 1
  297.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  298.    wt: 1:   36 Cube root derivative animated
  299.    wt: 1:   31 Derivatives of inverse functions
  300.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  301.    wt: 1:   26 Chain Rule Recognising outer inner functions
  302.    wt: 1:   19 Chain Rule for linear functions
  303.    wt: 1:   13 sine and cosine derivatives 1st step
  304.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  305.    wt: 1:   5 Jumps and absence of unlimited error control
  306.    wt: 1:   2 Algebraic codification
  307.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  308.    wt: 1:   G.5 Motions With Bounded Velocities
  309.    wt: 1:   F.5b Extreme Value Theorem
  310.    wt: 1:   F.1 What Functions are Continuous
  311.    wt: 1:   E2 Algebraic Properties of Limits
  312.    wt: 1:   Chapter 23 Links To Trigonometry
  313.    wt: 1:   Chapter 22 Complex Numbers
  314.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  315.    wt: 1:   Chapter 13. Acceleration
  316.    wt: 1:   Chapter 9 About First Courses in Calculus
  317.    wt: 1:   Postscript More on Better Performance
  318.    wt: 1:   Postscript For Better Performance
  319.    wt: 1:   Appendix B. How To Learn
  320.    wt: 1:   Chapter 30 Truth Tables
  321.    wt: 1:   Chapter 28 Occurrence Tables
  322.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  323.    wt: 1:   Chapter 23. Notation For Sums
  324.    wt: 1:   Chapter 19. Functions and Sets
  325.    wt: 1:   Chapter 18. Rules for Algebra
  326.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  327.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  328.    wt: 1:   Chapter 13. Second Reading Guide
  329.    wt: 1:   Chapter 10 Describing and Changing Calculations
  330.    wt: 1:   Postscript What is a Variable
  331.    wt: 1:   Chapter 8 Three Skills For Algebra
  332.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  333.    wt: 1:   Postscript B Mathematics Education References
  334.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  335.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  336.    wt: 1:   Chapter 3 Algebra Difficulties
  337.    wt: 1:   Postscript B More on Story Telling and Reason
  338.    wt: 1:   Chapter 23 Truth Tables
  339.    wt: 1:   Chapter 21 Occurrence Tables
  340.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  341.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  342.    wt: 1:   Chapter 15 Objective Processes
  343.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  344.    wt: 1:   Chapter 10 Responsibility
  345.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  346.    wt: 1:   S Adding words to algebra
  347.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  348.    wt: 1:   H more Routine to non routine problem solving
  349.    wt: 1:   H Jigsaw puzzles and problem solving
  350.    wt: 1:   F. The student teacher tutor feedback loop
  351.    wt: 1:   C. Domino effect of being careful
  352.    wt: 1:   B. Domino effect of errors
  353.    wt: 1:   How to Build Skills and Confidence
  354.    wt: 1:   Chapter 6 More Algebra and Geometry
  355.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  356.    wt: 1:   Chapter 3 Algebra Starter Lessons
  357.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  358.    wt: 1:   Helping the Blind in Logic and Mathematics
  359.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  360.    wt: 1:   Systematic Algebra Skill Development Missing Links
  361.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  362.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  363.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  364.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

899 matches:

  1.    wt: 9:   A Global Time and Navigation
  2.    wt: 9:   14 Why Scalar Multiplication Distributes Physical Argument
  3.    wt: 9:   8 Parallel Vectors
  4.    wt: 9:   6 Vectors with Coordinates
  5.    wt: 9:   3 Navigation with Arrows or Vectors
  6.    wt: 9:   Vector and Complex Number Applet
  7.    wt: 9:   4 Angles on Maps Plans drawn to scale
  8.    wt: 9:   3 Lengths and Areas on Maps and Plans
  9.    wt: 8:   15 Dot and Cross Product
  10.    wt: 8:   12 From Applied To Pure Mathematics
  11.    wt: 8:   11 Component Method
  12.    wt: 8:   10 Parallelogram Addition Method
  13.    wt: 8:   9 Head to Tail Coordinate View
  14.    wt: 8:   7 Coordinate Addition and Scalar Multiplication
  15.    wt: 8:   5 Head To Tail Arrow Addition
  16.    wt: 8:   4 Resultant of a Sum of Movements
  17.    wt: 8:   2 Signed Coordinates
  18.    wt: 8:   1 Unsigned Coordinates
  19.    wt: 8:   32 seven rows of pascals triangle
  20.    wt: 8:   31 basic secant cosecant cotangent trig identities
  21.    wt: 8:   13 Trig Formulas for dot and cross Products
  22.    wt: 8:   8 More Use of Maps Not Drawn to Scale
  23.    wt: 8:   6 Figuring with Maps Not to Scale
  24.    wt: 7:   35 sines and cosines of 2A 3A 4A 5A
  25.    wt: 7:   34 sines and cosines of 2A 3A 4A 5A
  26.    wt: 7:   33 sines and cosines of 2A 3A 4A 5A
  27.    wt: 7:   30 unit circle calculation of six trigonometric functions
  28.    wt: 7:   25 tangent double angle formula Slope connection
  29.    wt: 7:   20 sine and cosine Double Angle Formulas
  30.    wt: 7:   19 Pythagorean Identity For sine and cosine functions
  31.    wt: 7:   17C sine and cosine double triple angle formulas
  32.    wt: 7:   17B sine cosine Angle Sum Formulas via cis
  33.    wt: 7:   17A The complex number valued trig function cis
  34.    wt: 7:   15 sine cosine Complementary Angle Relations
  35.    wt: 7:   13 Graph of tangent function many periods
  36.    wt: 7:   Unit Circle Development of Trigonometry
  37.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  38.    wt: 7:   20 N th Roots of Complex Numbers
  39.    wt: 7:   17 Cube Roots of unity
  40.    wt: 7:   11 sine and cosine double triple angle formulas
  41.    wt: 7:   9 The complex number valued trig function cis
  42.    wt: 7:   8 Unit Circle Development of Trigonometry
  43.    wt: 7:   6 Field Properties of Complex Number
  44.    wt: 7:   5 An Easy Proof of the Distributive Law
  45.    wt: 7:   2 Complex Numbers made easier we hope
  46.    wt: 7:   Appetizer A Complex Number Applet
  47.    wt: 7:   8 Triangles Cascade Problem Solving
  48.    wt: 7:   6 Trigonometry Sines of Supplementary Angles
  49.    wt: 7:   Why Trigonometry the whyslopes view
  50.    wt: 7:   Right Triangle and Unit Circle Trigonometry
  51.    wt: 7:   13 Navigation Location from Angles to 2 Landmarks
  52.    wt: 7:   3 Similarity by Design with coordinates
  53.    wt: 7:   10 Midpoint of [a b] and [b a]
  54.    wt: 7:   13 Pythagorean spatial distance formulas
  55.    wt: 7:   PS H Distributive Law For Complex Numbers
  56.    wt: 7:   16 Angles Subtended By Chords and Diameters
  57.    wt: 7:   13 Angle Side Angle Failure
  58.    wt: 7:   A Measurement with Ruler Proper Use
  59.    wt: 7:   5 Drawing to Scale Avoids Angle Distortions
  60.    wt: 7:   2 Measuring Area Directly
  61.    wt: 7:   1 Length Measurement
  62.    wt: 6:   13 cosecant function Definition Graph and Inverse
  63.    wt: 6:   4 possible motivation for term arccos
  64.    wt: 6:   3 Left Inverse of cosine arccos definition
  65.    wt: 6:   9 Summary Degrees to Radians and back
  66.    wt: 6:   B Straight Line Slope Scaling Properties More
  67.    wt: 6:   13 Straight Lines Finding Equations from 2 points
  68.    wt: 6:   12 Straight Lines Graphing mx plus b
  69.    wt: 6:   17 tangent function angle sum formulas
  70.    wt: 6:   29 secant cosecant and cotangent for acute angles
  71.    wt: 6:   28 Expressing products of sines cosines as sums
  72.    wt: 6:   27 Logarithmic use of products of sines and cosines
  73.    wt: 6:   26 Formulas for products of sines and cosines
  74.    wt: 6:   24 tangent Angle Difference Formula
  75.    wt: 6:   23 sine and cosine of 180 plus 22.5 degrees
  76.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  77.    wt: 6:   21 sine and cosine Half Angle Formulas
  78.    wt: 6:   18 sum of sinusoidal waves as a single wave
  79.    wt: 6:   17G Pythagorean Theorem Converse
  80.    wt: 6:   17F Law of cosines
  81.    wt: 6:   17E Trig Formulas for dot and cross Products
  82.    wt: 6:   17D cis formulas for sine cosines and tangent
  83.    wt: 6:   16 Right Triangle Complementary Angle Relations
  84.    wt: 6:   14 cosine even and sine and tangent are odd
  85.    wt: 6:   12 Graph of tangent function for one period
  86.    wt: 6:   11 tangent function undefined when terminal side vertical
  87.    wt: 6:   10 Graphs of sines and cosines many periods
  88.    wt: 6:   9 Graphs of sine and cosine over one period
  89.    wt: 6:   8 period of tangent function
  90.    wt: 6:   7 period of sine and cosine
  91.    wt: 6:   6 sines and cosines for reference angle 30 degrees
  92.    wt: 6:   5 sines and cosines for reference angle 60 degrees
  93.    wt: 6:   4 sines and cosines for reference angle 45 degrees
  94.    wt: 6:   3 sines and cosines for reference angle 90 degrees
  95.    wt: 6:   2 Quadrant I reference Angles
  96.    wt: 6:   1 Unit Points Reflections Rotations
  97.    wt: 6:   21 Logarithms Powers and Exponentials
  98.    wt: 6:   19 N th Roots of Unity
  99.    wt: 6:   18 Sixth Roots of Unity
  100.    wt: 6:   16 References and Originality Question
  101.    wt: 6:   15 Pythagorean Theorem Converse
  102.    wt: 6:   14 Law of cosines
  103.    wt: 6:   12 cis formulas for sine cosines and tangent
  104.    wt: 6:   10 sine cosine Angle Sum Formulas via cis
  105.    wt: 6:   7 Second Way to Calculate Products
  106.    wt: 6:   4 Multiplication Properties
  107.    wt: 6:   3 Addition Properties
  108.    wt: 6:   1 Rectangular Polar Coordinates Review
  109.    wt: 6:   7 Trignometric Ratios Unit Circle
  110.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  111.    wt: 6:   4 Trigonometric Ratios For Two Special Triangles
  112.    wt: 6:   3 Trigonometric Ratios sine and cosine
  113.    wt: 6:   2 Similar Triangles Equality of Corresponding Side Ratios
  114.    wt: 6:   1 Angle Measurement with Degrees
  115.    wt: 6:   12 Triangles Similarity More Problems
  116.    wt: 6:   11 Triangle Similarity Missing Side Problem
  117.    wt: 6:   6 Geometric Diagrams in Class
  118.    wt: 6:   2 Similarity By Design
  119.    wt: 6:   6 Intersection of lines by solving linear systems
  120.    wt: 6:   5 Algebraic View of Slopes
  121.    wt: 6:   8 Distance Between Points on a Line
  122.    wt: 6:   7 Complex Numbers Appetizer
  123.    wt: 6:   PS G Rotation Distributes over Addition
  124.    wt: 6:   PS F Scalar Multiplication Distributes over Addition
  125.    wt: 6:   PS C Similarity Use Recognize it in Trigonometry
  126.    wt: 6:   PS B Parallelogram Construction Methods
  127.    wt: 6:   17 Right Bisectors of Triangle Sides
  128.    wt: 6:   9 Construction of a right bisector
  129.    wt: 6:   6 Ruler and compass Angle Bisection
  130.    wt: 6:   2 Correspondence between Triangles
  131.    wt: 6:   About Folder Contents
  132.    wt: 5:   9 combinatorics probability sets
  133.    wt: 5:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  134.    wt: 5:   16 cotangent function Definition Graph and Inverse
  135.    wt: 5:   15 cosecant function Definition Graph and Inverse
  136.    wt: 5:   14 secant function Definition Graph and Inverse
  137.    wt: 5:   12 motivation for term arctan
  138.    wt: 5:   11 arctan left inverse of tangent Graph
  139.    wt: 5:   10 arctan left inverse of tangent Definition
  140.    wt: 5:   9 motivation for name arcsin
  141.    wt: 5:   8 arcsin left inverse of sine Graph
  142.    wt: 5:   7 arcsin left inverse of sine Definition
  143.    wt: 5:   6 Graph of arccos function
  144.    wt: 5:   5 Swapping Coordinates is a reflection
  145.    wt: 5:   2 cosine function more properties
  146.    wt: 5:   1 cosine function properties
  147.    wt: 5:   8 Radian Measures of Common Angles
  148.    wt: 5:   7 Radian Measures in special Triangles
  149.    wt: 5:   6 Radian Measure to Degrees
  150.    wt: 5:   5 Degrees to Radian Measure
  151.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  152.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  153.    wt: 5:   2 Radian Measure Numerical Value of one degree
  154.    wt: 5:   1 Degrees and Radians Introduction
  155.    wt: 5:   4 graphing y=Asin(x c)
  156.    wt: 5:   3 graphing y=f(x c) plus K
  157.    wt: 5:   2 Graphing y=Af(x) Vertical Scaling
  158.    wt: 5:   1 graphing y=f(x a)
  159.    wt: 5:   Parallel Lines and Parallel Transversals
  160.    wt: 5:   Proportionality of Line Segments From Parallel Transversals
  161.    wt: 5:   Triangle Angles Sum To 180 Degrees
  162.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  163.    wt: 5:   Parallel Lines and Interior Angles
  164.    wt: 5:   Construction Methods and Criteria for Isometric and Similar Triangles
  165.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  166.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  167.    wt: 5:   Straight Lines ASA Intersection Study More
  168.    wt: 5:   Straight Lines ASA Intersection Study
  169.    wt: 5:   Straight Lines Instersection Solving Equations
  170.    wt: 5:   Straight Lines Intersection of
  171.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  172.    wt: 5:   C Straight Lines Slope from Coordinates
  173.    wt: 5:   A Straight Line Slope Scaling Properties
  174.    wt: 5:   14 Straight Lines Equations General Case
  175.    wt: 5:   11 Straight Lines Graphing y=mx
  176.    wt: 5:   10 Straight Lines through Origin Equations More
  177.    wt: 5:   9 Straight Lines through Origin Equations
  178.    wt: 5:   8 Straight Lines Equation for vertical
  179.    wt: 5:   7 Tangent Function is odd on this domain
  180.    wt: 5:   6 Tangent Function Inclination Angle Take 2
  181.    wt: 5:   5 Tangent Function Graph
  182.    wt: 5:   4 Tangent Function Properties
  183.    wt: 5:   3 Straight Lines Slope as Tangent of Inclination Angle
  184.    wt: 5:   2 Straight Lines Slopes As Rise Over Run
  185.    wt: 5:   1 Straight Lines Slope Concept
  186.    wt: 5:   10 Similarity of Triangles Equivalent of Two Criteria
  187.    wt: 5:   9 Similarity of Triangles Usual Criteria
  188.    wt: 5:   8 Similarity of Triangles and Polygons
  189.    wt: 5:   7 Translations Rotations Reflections Dilatations
  190.    wt: 5:   5 Similarity of Circles Squares and Rectangles
  191.    wt: 5:   4 Similarity Definition with Coordinate
  192.    wt: 5:   1 Early Concept of Like or Similar Shapes
  193.    wt: 5:   Four Simple Exercises
  194.    wt: 5:   12 Links Lessons elsewhere
  195.    wt: 5:   11 A Partial Summary
  196.    wt: 5:   9 Midpoint Coordinates Half Endpoint Sum
  197.    wt: 5:   8 Mid Point Formula
  198.    wt: 5:   7 Exercises to test skill and concept mastery
  199.    wt: 5:   4 Equations for lines three forms
  200.    wt: 5:   3 Slope product for perpendicular lines
  201.    wt: 5:   2 point slope equation for a line
  202.    wt: 5:   1 Numerical view of lines and their equations
  203.    wt: 5:   What is and is not here
  204.    wt: 5:   12 Spatial Coordinates
  205.    wt: 5:   11 Triangle Inequality
  206.    wt: 5:   10 Pythagorean plane distance formula
  207.    wt: 5:   9 Pythagorean Theorem Chinese Square Proof
  208.    wt: 5:   6 Polar Multiplication and Rotation
  209.    wt: 5:   5 Cartesian Addition and Translation
  210.    wt: 5:   4 Polar Coordinates to and from
  211.    wt: 5:   3 Rectangular Coordinates Review
  212.    wt: 5:   2 Cartesian Coordinates with signs
  213.    wt: 5:   1 Cartesian Coordinates sans signs
  214.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  215.    wt: 5:   PS E Multiplication with Polar Coordinates
  216.    wt: 5:   PS D Addition with Cartesian Coordinates
  217.    wt: 5:   PS A Kite Construction Methods
  218.    wt: 5:   21 Parallelograms
  219.    wt: 5:   19 Right Triangle Similarity
  220.    wt: 5:   18 Triangle Similarity Take 1
  221.    wt: 5:   15 Triangle Angle Sum is 180 degrees
  222.    wt: 5:   14 Parallel Lines Postulate
  223.    wt: 5:   12 Side Angle Side Failure
  224.    wt: 5:   11 Triangle Construction Fails
  225.    wt: 5:   10 Dropping a perpendicular to line
  226.    wt: 5:   8 Isoceles Triangles
  227.    wt: 5:   7 Angle Side Angle
  228.    wt: 5:   5 Side Angle Side
  229.    wt: 5:   4 Side Side Side
  230.    wt: 5:   3 Isometry of Triangles Congruence
  231.    wt: 5:   1 Initial Concepts and Terms
  232.    wt: 5:   Short Course on Euclidean Geometry
  233.    wt: 5:   musings do not puiblish real numbers
  234.    wt: 5:   13 Arrows and Vectors in a Plane
  235.    wt: 5:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  236.    wt: 5:   13 Real Number Subtraction
  237.    wt: 5:   4 Subtraction with Conversions Borrows and Letter J
  238.    wt: 4:   25 Absolute Value greatest integer and saw tooth functions
  239.    wt: 4:   21 Graphs of functions given by Horizontal Line Method
  240.    wt: 4:   13 From one to one to many to one
  241.    wt: 4:   10 Interval Notation
  242.    wt: 4:   4 Function notation in and beyond mathematics
  243.    wt: 4:   2 Algebraic use of function notation
  244.    wt: 4:   Rewriting algebraic substitution as function substitutions
  245.    wt: 4:   A Signed Number Arithmetic Review
  246.    wt: 4:   24 Signed Numbers Arithmmetic Properties
  247.    wt: 4:   23 Distributive Law Two Derivations
  248.    wt: 4:   22 Multiplication of Signed Numbers
  249.    wt: 4:   19 Signed Multiples of Vectors
  250.    wt: 4:   16 Collinear Horizontal Arrows Vectors
  251.    wt: 4:   12 Real Numbers Line Signed Coordinates
  252.    wt: 4:   11 Signed Number Addition and Addition Properties
  253.    wt: 4:   4 Subset Builder Notation
  254.    wt: 4:   4 A Brief Story of numbers and algebra
  255.    wt: 4:   5 Counting with Tables Trees Product Rule Take II
  256.    wt: 4:   3 Counting with Tables and Trees II
  257.    wt: 4:   2 Counting with Tables and Trees I
  258.    wt: 4:   9 subtracting signed numbers
  259.    wt: 4:   27 Divisibility by 2 3 6 5 9 10 Example
  260.    wt: 4:   26 Divisibility by 2 3 5 Example
  261.    wt: 4:   9 Remainder Arithmetic Divisibility by 5
  262.    wt: 4:   Appendix 2 Three Decimal Subtraction Methods
  263.    wt: 4:   Subtraction with J Conversions Example
  264.    wt: 4:   Subtraction Another Video Lesson
  265.    wt: 4:   9 22 Minute Subtraction Review Video
  266.    wt: 4:   8 Subtraction with Units of Measure
  267.    wt: 4:   7 Subtraction for Decimal Fractions with Exercises
  268.    wt: 4:   6 Subtraction with Conversion Example with Exercises
  269.    wt: 4:   5 A Tip for Efficent Subtraction
  270.    wt: 4:   3 Harder Cases Convert to Compare and Subtract
  271.    wt: 4:   2 Subtraction Easy Case Examples
  272.    wt: 4:   1 Comparison and Subtraction Easy Direct Cases
  273.    wt: 3:   Ramblings Extrinsic numbers theory
  274.    wt: 3:   Ramblings Introduction Algebra Essay
  275.    wt: 3:   7 logic review and decimals an odd combination
  276.    wt: 3:   4 algebra
  277.    wt: 3:   2 arithmetic with signed numbers
  278.    wt: 3:   1 arithmetic with unsigned numbers
  279.    wt: 3:   13 Addition and Addition Tables
  280.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  281.    wt: 3:   23 Inverse Functions
  282.    wt: 3:   16 Increasing or decreasing on intervals
  283.    wt: 3:   15 Sign analysis of functions
  284.    wt: 3:   14 Surjections Injections Bijections
  285.    wt: 3:   9 Set theory term relation possible origins
  286.    wt: 3:   8 Set view of relations and functions
  287.    wt: 3:   7 Functions with finite domains
  288.    wt: 3:   6 Set Existence Formation and Notation
  289.    wt: 3:   5 Function notation for geometric transformations
  290.    wt: 3:   1 Geometric Introduction of Function Notation
  291.    wt: 3:   A Modular and Remainder Arithmetic
  292.    wt: 3:   26 More Less Greater Than Comparison
  293.    wt: 3:   25 Mid way Convergence to Axiomatic Approach
  294.    wt: 3:   21 Addition of Multiples of a Single Vector
  295.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  296.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  297.    wt: 3:   17 Arrows Rotate to Reverse with Length Unchanged
  298.    wt: 3:   15 Head to Tails in place Addition Associative
  299.    wt: 3:   14 Vector Head to Tail Sums and Resultants
  300.    wt: 3:   9 Division with Digits after Decimal Point
  301.    wt: 3:   8 Division and Mulplication of Compound Fractions
  302.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  303.    wt: 3:   6 Infinite Decimals Ending in 9 repeating
  304.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  305.    wt: 3:   4 Location of Point in Decimal Addition
  306.    wt: 3:   3 Location of Point in Decimal Multiplication
  307.    wt: 3:   2 Counting Digits in Decimal Multiplication
  308.    wt: 3:   1 Fractions with Finite Decimal Expansions
  309.    wt: 3:   B Decimal Comparison and Subtraction
  310.    wt: 3:   5 Distributive Law for Whole Numbers
  311.    wt: 3:   3 Inequalities Algebraically
  312.    wt: 3:   2 Algebraic View
  313.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  314.    wt: 3:   8 Pythagorean Relation Forwards Backwards
  315.    wt: 3:   6 Compound Interest Forward and Backwards
  316.    wt: 3:   5 Triangle Area Formula Backwards
  317.    wt: 3:   4 Rectangle Area and Like Formulas Backwards
  318.    wt: 3:   16 Real Numbers Comparison
  319.    wt: 3:   15 Real Number Division
  320.    wt: 3:   14 Real Number Multiplication
  321.    wt: 3:   12 Real Number Additive Inverses or Negatives
  322.    wt: 3:   11 Real Number Addition
  323.    wt: 3:   10 Real Number Lengths and Signs
  324.    wt: 3:   8 Coordinates for Maps and Planes
  325.    wt: 3:   7 Real Numbers as Line Cordinates
  326.    wt: 3:   6 Unsigned Real Numbers
  327.    wt: 3:   5 Rational Numbers More
  328.    wt: 3:   4 Rational Numbers
  329.    wt: 3:   1 Whole and Natural Numbers
  330.    wt: 3:   5 Independent versus Dependent Variables
  331.    wt: 3:   3 Geometric Formulas and Function Notation
  332.    wt: 3:   1 Formulas Dependence and Function Notation
  333.    wt: 3:   6 Algebraic Solution Example
  334.    wt: 3:   5 Algebraic Solutions Introduction
  335.    wt: 3:   9 Sets in Probability and Statistics
  336.    wt: 3:   5 Product Builder Notation
  337.    wt: 3:   5 Talking about Numbers and Quantities
  338.    wt: 3:   3 Comparison of Negative Numbers
  339.    wt: 3:   4 Counting with Trees Product Rule Take I
  340.    wt: 3:   1 Counting and Counting Methods I
  341.    wt: 3:   11 What are real lengths and numbers
  342.    wt: 3:   10 dividing signed numbers
  343.    wt: 3:   8 multiplying signed numbers
  344.    wt: 3:   6 adding signed numbers
  345.    wt: 3:   5 lengths and signs of numbers
  346.    wt: 3:   3 signed coordinates for maps and planes
  347.    wt: 3:   2 signed and unsigned numbers as coordinates
  348.    wt: 3:   13 Fraction Comparison Algebraic View
  349.    wt: 3:   C Divisibility by 11 Integer Recognition Method
  350.    wt: 3:   13 Subtraction with Additive Inverse
  351.    wt: 3:   8 Multiplication by Signed Numbers Integers
  352.    wt: 3:   6 Multiplication by Natural Numbers
  353.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  354.    wt: 3:   24 Divisibility Tests for 2 3 5 9 10
  355.    wt: 3:   13 Remainder Arithmetic Modulo 5 Example
  356.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  357.    wt: 3:   10 Remainder Arithmetic Long Division by 5 Quickly
  358.    wt: 3:   13 video Factors of 24 using prime
  359.    wt: 3:   Appendix 1 Decimals Comparison Method Take II
  360.    wt: 3:   10 Names for Big Numbers and Powers of Ten Expansion
  361.    wt: 3:   Quick history of numbers and algebra
  362.    wt: 3:   012 Division of Time Intervals by Time Intervals
  363.    wt: 3:   011 Division of Time Intervals By Numbers
  364.    wt: 3:   7 Evaluation by immediate or delayed substitution
  365.    wt: 3:   Postscript Unifying Theme A Fourth Skill For Algebra
  366.    wt: 3:   Chapter 13. Second Reading Guide
  367.    wt: 3:   Chapter 9 Talking about Numbers or Quantities
  368.    wt: 3:   Postscript B Mathematics Education References
  369.    wt: 3:   Postscript A Three Remarks
  370.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  371.    wt: 3:   Chapter 4 Complex Numbers and Why Slopes
  372.    wt: 3:   Chapter 3 Algebra Difficulties
  373.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  374.    wt: 2:   Skills Chapter 3 Algebra
  375.    wt: 2:   11 pure mathematics
  376.    wt: 2:   10 statistics
  377.    wt: 2:   8 analytic geometry etc
  378.    wt: 2:   6 polynomials etc
  379.    wt: 2:   5 logarithms and exponentials etc
  380.    wt: 2:   3 Euclidean Geometry Leanly
  381.    wt: 2:   What is POMME
  382.    wt: 2:   About site lesson plans
  383.    wt: 2:   Maps Plans Drawings
  384.    wt: 2:   the trouble with algebra
  385.    wt: 2:   How to be a better instructor
  386.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  387.    wt: 2:   problemes algebre et arithmetique
  388.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  389.    wt: 2:   26 Function definitions done and coming
  390.    wt: 2:   22 Square Root function graphically
  391.    wt: 2:   20 Interchanging coordinates a reflection
  392.    wt: 2:   19 Horizontal line rule and method
  393.    wt: 2:   18 Vertical Line Rule and Method
  394.    wt: 2:   17 Function maxima minima and their location
  395.    wt: 2:   12 Function Domain Recognition Exercises
  396.    wt: 2:   11 Function Domain Range Source and Targets
  397.    wt: 2:   3 Formula or function graphing exercise
  398.    wt: 2:   Introduction Reading Guide
  399.    wt: 2:   8 quadratics backward use of various formulas
  400.    wt: 2:   3 quadratics factoring by inspection
  401.    wt: 2:   11 Growth and Decay in Biology
  402.    wt: 2:   3 Natural Logarithms and Exponentials Basic Properties
  403.    wt: 2:   1 Polynomials Distributive Law
  404.    wt: 2:   C Three Decimal Subtraction Methods
  405.    wt: 2:   2 Combing Counts Addition Skills and Principles
  406.    wt: 2:   1 The Counting Origins of Numbers
  407.    wt: 2:   5 Areas of Rectangles Revisited
  408.    wt: 2:   4 Fraction Operations Axiomatic Development
  409.    wt: 2:   2 Fraction Operations Physical Development
  410.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  411.    wt: 2:   5 Proportionality in Equivalent Fractions
  412.    wt: 2:   4 Rates Ratios and Proporitionality
  413.    wt: 2:   3 Proportionality Examples
  414.    wt: 2:   1 What is Proportionality
  415.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  416.    wt: 2:   3 Linear Equation Literal Solution More
  417.    wt: 2:   2 Linear Equation Literal Solution
  418.    wt: 2:   1 Changing Calculations
  419.    wt: 2:   5 Equality in Algebra
  420.    wt: 2:   4 Subtraction and Division Axioms
  421.    wt: 2:   4 Comparison of Negative Numbers
  422.    wt: 2:   1 Real Numbers Comparison
  423.    wt: 2:   9 Coordinates for Regions in Space
  424.    wt: 2:   3 Fractions
  425.    wt: 2:   2 Integers
  426.    wt: 2:   4 Changing Letters
  427.    wt: 2:   2 Computation Rules Evaluation
  428.    wt: 2:   1 GE Substitution four examples
  429.    wt: 2:   4 Four Examples Fractional Coefficients
  430.    wt: 2:   3 Four Examples
  431.    wt: 2:   2 Three Examples
  432.    wt: 2:   1 Proper Equal Sign Usage
  433.    wt: 2:   13 Naming Identifying Formulas with Words
  434.    wt: 2:   5 Box Volume Formula Example
  435.    wt: 2:   8 Sets of Numbers
  436.    wt: 2:   6 Power Set Notation
  437.    wt: 2:   6 Three Notions of What is a Variable
  438.    wt: 2:   2 What is a Variable
  439.    wt: 2:   1 Three Skills For Algebra
  440.    wt: 2:   About Folder Contents
  441.    wt: 2:   4 Greater More Less Than Signs in General
  442.    wt: 2:   2 More and Less Than with Unlike Signs
  443.    wt: 2:   1 More and Less Than for Counts and Measures
  444.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  445.    wt: 2:   13 GCD from given Prime Factorization
  446.    wt: 2:   2 Least Common Multiple LCM intro via list method
  447.    wt: 2:   7 negative and additive inverse
  448.    wt: 2:   4 signed coordinates for regions in space
  449.    wt: 2:   3 Multiplying Units and Numbers
  450.    wt: 2:   1 Addition and Subtraction with Units
  451.    wt: 2:   B Fractions and Two Term Ratios
  452.    wt: 2:   A Similarities between Fractions and Two Term Ratios
  453.    wt: 2:   17 Efficient Ways to Add and Subtract
  454.    wt: 2:   16 Addition Subtraction Comparision Compared
  455.    wt: 2:   15 Adding and Subtracting with Unlike Denominators
  456.    wt: 2:   14 Adding and Subtracting with Like Denominators
  457.    wt: 2:   11 Simplification an Algebraic View
  458.    wt: 2:   9 Improper Fractions and Mixed Numbers
  459.    wt: 2:   6 Multiplication of Mixed Numbers
  460.    wt: 2:   6 Multiplication Algebraically Take II
  461.    wt: 2:   Fraction Operations by Raising Terms A Simple Innovation
  462.    wt: 2:   B Integer Long Division Multiple Choices
  463.    wt: 2:   A Associative Law Theorectical Note
  464.    wt: 2:   7 Multiplication by Signs
  465.    wt: 2:   A Decimals Modular and Remainder Arithmetic
  466.    wt: 2:   23 Remainder Arithmetic Modulo 2
  467.    wt: 2:   22 Remainder Arithmetic Modulo 3 more
  468.    wt: 2:   21 Remainder Arithmetic Modulo 3
  469.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  470.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  471.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  472.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  473.    wt: 2:   16 Remainder Arithmetic Modulo 9 Example 2
  474.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  475.    wt: 2:   14 Remainder Arithmetic Modulo 9 Example
  476.    wt: 2:   12 Remainder Arithmetic Modulo 10 Example
  477.    wt: 2:   8 Remainder Arithmetic Morulo 5 Examples II
  478.    wt: 2:   7 Remainder Arithmetic Modulo 5 Examples I
  479.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  480.    wt: 2:   5 Remainder Arithmetic Modulo 5
  481.    wt: 2:   4 Remainder Arithmetic Modulo 10 in general
  482.    wt: 2:   3 Remainder Arithmetic Modulos 10 more still
  483.    wt: 2:   2 Remainder Arithmetic Modulo 10 more
  484.    wt: 2:   1 Remainder Arithmetic Modulo 10
  485.    wt: 2:   3 video Primes and Composites from 9 times table
  486.    wt: 2:   1 video how Products are bigger than factor
  487.    wt: 2:   Long Division Backwards more
  488.    wt: 2:   Long Division Backward
  489.    wt: 2:   Long Division forwards and backwards Example 3
  490.    wt: 2:   Long Division forwards and backwards Example 2
  491.    wt: 2:   Long Division forwards and backwards Example 1
  492.    wt: 2:   10 Division by Five Long and Short Ways
  493.    wt: 2:   B Powers of Ten
  494.    wt: 2:   A Elementary Basis for Multiplication Methods
  495.    wt: 2:   Video Power Notation in Decimal Expansion
  496.    wt: 2:   8 What skills and work habits to require
  497.    wt: 2:   4. How to add with decimals B with conversions
  498.    wt: 2:   1. Explaining Addition Table
  499.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  500.    wt: 2:   1 Place Value in Three Digit Whole Numbers
  501.    wt: 2:   The 20 Times Table
  502.    wt: 2:   The 12 Times Table Visually
  503.    wt: 2:   About folder contents
  504.    wt: 2:   013 Travel Time Tables
  505.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  506.    wt: 2:   8 Addition of Time Intervals via subtotaling
  507.    wt: 2:   Volume of Solid by Cross Sections Lesson
  508.    wt: 2:   Example 1. Area Between x and x squared
  509.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  510.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  511.    wt: 2:   Area Between Curves Lesson Take 2
  512.    wt: 2:   Area Between Curves Lesson Take 1
  513.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  514.    wt: 2:   5 Jumps and absence of unlimited error control
  515.    wt: 2:   2 Algebraic codification
  516.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  517.    wt: 2:   G.1 Differentiable Functions Rolles Theorem
  518.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  519.    wt: 2:   B3 Bolzano Weierstrass Theorem
  520.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  521.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  522.    wt: 2:   Chapter 13. Acceleration
  523.    wt: 2:   Postscript More on Better Performance
  524.    wt: 2:   Postscript For Better Performance
  525.    wt: 2:   Appendix B. How To Learn
  526.    wt: 2:   Chapter 30 Truth Tables
  527.    wt: 2:   Chapter 28 Occurrence Tables
  528.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  529.    wt: 2:   Chapter 23. Notation For Sums
  530.    wt: 2:   Chapter 19. Functions and Sets
  531.    wt: 2:   Chapter 18. Rules for Algebra
  532.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  533.    wt: 2:   Chapter 10 Describing and Changing Calculations
  534.    wt: 2:   Postscript What is a Variable
  535.    wt: 2:   Chapter 8 Three Skills For Algebra
  536.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  537.    wt: 2:   Annotated Links to Material Elsehwere
  538.    wt: 2:   Chapter 12 Four Phases
  539.    wt: 2:   Chapter 11 Elementary Instruction
  540.    wt: 2:   Chapter 10 Transition
  541.    wt: 2:   Chapter 9 The Two Ends
  542.    wt: 2:   Chapter 8 Modern Instruction
  543.    wt: 2:   Chapter 7 Two Treatments of Geometry
  544.    wt: 2:   Chapter 5 Four References
  545.    wt: 2:   Chapter 2 For and Against Mathematics
  546.    wt: 2:   Chapter 1 Introduction
  547.    wt: 2:   Foreword
  548.    wt: 2:   Postscript B More on Story Telling and Reason
  549.    wt: 2:   Chapter 23 Truth Tables
  550.    wt: 2:   Chapter 21 Occurrence Tables
  551.    wt: 2:   Chapter 20 Shorthand Symbols as Pronouns
  552.    wt: 2:   Chapter 17 Objective Ways Trial and Error Discovery
  553.    wt: 2:   Chapter 15 Objective Processes
  554.    wt: 2:   Chapter 10 Responsibility
  555.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  556.    wt: 2:   A. Skill has to be seen to believed
  557.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  558.    wt: 2:   4 Money Matters Saving Earning Buying Selling and Budgets
  559.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  560.    wt: 2:   More Algebra and Slope based Calculus Preview
  561.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  562.    wt: 1:   I LAMP Introduction Study Habits
  563.    wt: 1:   G LAMP Introduction Problem Solving Skills
  564.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  565.    wt: 1:   A Introduction Objectives
  566.    wt: 1:   why bother
  567.    wt: 1:   website reviews
  568.    wt: 1:   Math Ed if it must be short make it lean effective
  569.    wt: 1:   grouping students according to ability
  570.    wt: 1:   what should be learnt and When
  571.    wt: 1:   talk the algebra talk
  572.    wt: 1:   geometric implications for algebra
  573.    wt: 1:   teaching tutoring algebraic reason
  574.    wt: 1:   Lessening Algebra Difficulties
  575.    wt: 1:   05 13 OldSiteEntrancePage
  576.    wt: 1:   Motivation and Context Problem
  577.    wt: 1:   chapitre 04 08 Limitations et benefices
  578.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  579.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  580.    wt: 1:   problemes responses
  581.    wt: 1:   Trois Notions qui menent a algebre
  582.    wt: 1:   deux definitions pour variable
  583.    wt: 1:   B Energy Power02
  584.    wt: 1:   B Wire Resistance Qualitative02
  585.    wt: 1:   A Wire Resistance Qualitative01
  586.    wt: 1:   B Electromotive force conventional current01
  587.    wt: 1:   17 Math Booklets for children and young teenagers
  588.    wt: 1:   14 Multiplication and Times Tables
  589.    wt: 1:   12 Goals and Objectives For Mathematics
  590.    wt: 1:   9 Streaming by Student Cooperation
  591.    wt: 1:   Ages 12 to 14 Skills with take home value
  592.    wt: 1:   Ages 12 to 14 Geometry
  593.    wt: 1:   Ages 12 to 14 Arithmetic
  594.    wt: 1:   Ages 10 to 12 Geometry
  595.    wt: 1:   Ages 10 to 12 Arithmetic
  596.    wt: 1:   Ages 9 to 10
  597.    wt: 1:   Ages 8 to 9
  598.    wt: 1:   Ages 7 to 8
  599.    wt: 1:   Ages 6 to 7
  600.    wt: 1:   Ages 4 plus to 5 plus
  601.    wt: 1:   Ages 3 plus to 4 plus
  602.    wt: 1:   sign monoticity analysis example 4
  603.    wt: 1:   sign monoticity analysis example 3
  604.    wt: 1:   sign monoticity analysis example 2
  605.    wt: 1:   sign monoticity analysis example 1
  606.    wt: 1:   A Quadratics Summary
  607.    wt: 1:   10 quadratic exercises
  608.    wt: 1:   9 quadratics physical and further context
  609.    wt: 1:   7 quadratic formulla derivation
  610.    wt: 1:   6 quadratics numerical approach
  611.    wt: 1:   5 quadratics completing the square
  612.    wt: 1:   4 quadratics difference of two squares
  613.    wt: 1:   2 quadratics graphing in general
  614.    wt: 1:   1 quadratics graphing exercises
  615.    wt: 1:   Quadratics in 10 steps
  616.    wt: 1:   10 Exponential Growth and Decay Models
  617.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  618.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  619.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  620.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  621.    wt: 1:   5 Natural Logarithm Calculator Exercises
  622.    wt: 1:   2 Square Root Simplification a prequel
  623.    wt: 1:   1 Calculator Starter Exercises
  624.    wt: 1:   8 Notes for instructors or tutors
  625.    wt: 1:   7 Links Lessons Elsewhere
  626.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  627.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  628.    wt: 1:   4 Polynomials Long division linear divisor
  629.    wt: 1:   3 Polynomials Multiplication Addition
  630.    wt: 1:   2 Column Multiplication Method
  631.    wt: 1:   E Long Division Methods more
  632.    wt: 1:   D Long Division Methods
  633.    wt: 1:   A Decimal Addition Columm Methods
  634.    wt: 1:   8 Column Multiplication Methods in General
  635.    wt: 1:   7 Decimals Multiplication Methods Examples
  636.    wt: 1:   6 Column Methods for Decimal Multiplication
  637.    wt: 1:   4 Commutative Law Groups Counting Form
  638.    wt: 1:   3 Multiplicative Counting Skills Principles
  639.    wt: 1:   6 Equations and Systems Equivalent or Implied
  640.    wt: 1:   3 Product Axioms Two Forms
  641.    wt: 1:   2 Addition and Multiplication Axioms
  642.    wt: 1:   1 Equivalent Computation Rules
  643.    wt: 1:   5 Greater More Less Than Signs in General
  644.    wt: 1:   3 More and Less Than with Unlike Signs
  645.    wt: 1:   2 More and Less Than for Counts and Measures
  646.    wt: 1:   More Exercises
  647.    wt: 1:   Simple Exercises
  648.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  649.    wt: 1:   4 GE III Animated Examples
  650.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  651.    wt: 1:   3 GE III Equation Addition and Multiplication
  652.    wt: 1:   2 GE II Comparison
  653.    wt: 1:   4 Solving a triangular system exercise
  654.    wt: 1:   3 Solving triangular system example
  655.    wt: 1:   2 Essentially one exercises three with solution
  656.    wt: 1:   1 Essentially One Unknown
  657.    wt: 1:   Skill Development Notes
  658.    wt: 1:   10 One Example
  659.    wt: 1:   9 Three Examples
  660.    wt: 1:   8 One Example
  661.    wt: 1:   7 Two Examples
  662.    wt: 1:   6 Three Examples
  663.    wt: 1:   5 Three Examples
  664.    wt: 1:   4 Two Examples
  665.    wt: 1:   3 Two Examples
  666.    wt: 1:   2 Three Examples
  667.    wt: 1:   Using Letters for Physical Quantities
  668.    wt: 1:   Formula Usage Show Work Format
  669.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  670.    wt: 1:   11 Volume of Sphere
  671.    wt: 1:   10 Volume of Pyramid
  672.    wt: 1:   9 Volume of Cone
  673.    wt: 1:   8 Compound Interest Formula Evaluation
  674.    wt: 1:   7 Compound Interest Formula Introduction
  675.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  676.    wt: 1:   4 Circle Area Formula Example
  677.    wt: 1:   3 Triangle Area Formula Example
  678.    wt: 1:   2 Another Rectangle Area Formula Example
  679.    wt: 1:   1 Written work formats for developing and showing skill
  680.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  681.    wt: 1:   7 Cautious or Safe Set Construction
  682.    wt: 1:   3 Counting with Sets etc
  683.    wt: 1:   2 Venn Diagrams
  684.    wt: 1:   1 Finite Sets
  685.    wt: 1:   3 Adding Words To Arithmetic
  686.    wt: 1:   arithmetic videos Real Player Format
  687.    wt: 1:   5 Square Roots with primes more still
  688.    wt: 1:   4 Square Roots with primes more
  689.    wt: 1:   3 Properties of Square Roots with example
  690.    wt: 1:   2 Square Roots with Prime
  691.    wt: 1:   1 Squares and Square Roots Introduction
  692.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  693.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  694.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  695.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  696.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  697.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  698.    wt: 1:   8 GCD from Euclidean Algorithm
  699.    wt: 1:   7 GCD and LCM from prime factorization
  700.    wt: 1:   6 GCD from Prime
  701.    wt: 1:   5 Common Divisors 60 45 via Prime
  702.    wt: 1:   4 LCM of 8 and 10 via Prime
  703.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  704.    wt: 1:   1 Least Common Multiples LCM Introduction
  705.    wt: 1:   12 GCD 2700 288 via Prime
  706.    wt: 1:   7 Converting or Changing Units
  707.    wt: 1:   6 Simplification of Fractions with Units
  708.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  709.    wt: 1:   4 Fractions with Units
  710.    wt: 1:   2 Equality and Units
  711.    wt: 1:   D Three Term Ratios
  712.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  713.    wt: 1:   22 Complex Compound Fractions
  714.    wt: 1:   21 Working With Signs
  715.    wt: 1:   21 Reciprocals for Fractions and Wholes
  716.    wt: 1:   20 Dividing Fractions the Why
  717.    wt: 1:   19 Dividing Fractions How TO
  718.    wt: 1:   18 Efficient Ways to Multiply
  719.    wt: 1:   12 Fraction Comparison
  720.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  721.    wt: 1:   8 Numerals Fractionals Quantals Take II
  722.    wt: 1:   7 Numerals Fractionals Quantals
  723.    wt: 1:   5 Equivalent Fractions
  724.    wt: 1:   4 Fraction Multiplication
  725.    wt: 1:   3 Unit fraction of a fraction
  726.    wt: 1:   2 Unit Fraction Multiplication
  727.    wt: 1:   1 What is a fraction Take II
  728.    wt: 1:   1 What is a fraction
  729.    wt: 1:   D Remainders Modulo 11 Pair Rule
  730.    wt: 1:   12 Adding Integers More Examples
  731.    wt: 1:   11 Adding Integers Formulas and Examples
  732.    wt: 1:   10 Integer Multiplication Formulas
  733.    wt: 1:   9 Multiplying Integers
  734.    wt: 1:   5 Zero Movement and Additive Inverses
  735.    wt: 1:   4 Adding Movements wiht opposite directions
  736.    wt: 1:   3 Adding Movements with same direction
  737.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  738.    wt: 1:   1 Integers as Coordinates
  739.    wt: 1:   20 Uniqueness of Prime Factorization
  740.    wt: 1:   19 video Prime Factorization Unique
  741.    wt: 1:   18 video Count Factors given Prime Factorization
  742.    wt: 1:   17 Identify and Count Factors using Primes
  743.    wt: 1:   16 video Factors of 980 using prime
  744.    wt: 1:   15 video Factors of 20 using Prime Factorization
  745.    wt: 1:   14 video Factors of 24 Take II
  746.    wt: 1:   12 LCD GCD and LCM using Primes
  747.    wt: 1:   11 Efficient Square Rule Use
  748.    wt: 1:   10 video Prime Factorization upto 23 squared
  749.    wt: 1:   9 video Prime Factorization upto 19 squared
  750.    wt: 1:   8 video Prime Factorization upto 19
  751.    wt: 1:   7 Calculator Usage Notes and Cautions
  752.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  753.    wt: 1:   5 Prime Factorization and a Square Rule
  754.    wt: 1:   4 video Prime Factorization Introduction
  755.    wt: 1:   2 Prime and Composites less than 16
  756.    wt: 1:   Division with Counts and Length
  757.    wt: 1:   12 Why Long Division Works Take III
  758.    wt: 1:   11 Another Single Digit Divisor Example
  759.    wt: 1:   9 Why Long Division Works Take II
  760.    wt: 1:   8 Correcting the Mistake
  761.    wt: 1:   7 Long Divison Mistake Catching
  762.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  763.    wt: 1:   5 Long Division Include Zeroes or not
  764.    wt: 1:   4 Division with 2 Digit Divsors
  765.    wt: 1:   3 Division Single Digit Divisor Example
  766.    wt: 1:   2 Division with Single Digit Divisors
  767.    wt: 1:   1 Divsion Physical Examples
  768.    wt: 1:   D Decimal Multiplication Methods Derived
  769.    wt: 1:   C Counting Areas with Powers of Ten
  770.    wt: 1:   6 Multiplication Commutes Order Not Important
  771.    wt: 1:   5 Decimal Fraction Multiplication
  772.    wt: 1:   4 Two and Three Digit Multipliers
  773.    wt: 1:   3 More One Digit Multipliers
  774.    wt: 1:   2 One Digit Multipliers
  775.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  776.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  777.    wt: 1:   1 Why 3 times 5 gives 15
  778.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  779.    wt: 1:   7 Adding decimal fractions using decimal point
  780.    wt: 1:   6. Counting and adding units and mixed units
  781.    wt: 1:   5. How to add decimals C. Examples
  782.    wt: 1:   3. How to add with decimals A sans conversions
  783.    wt: 1:   2 Decimal Counting Practices
  784.    wt: 1:   11 Place Value SI Standard International way
  785.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  786.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  787.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  788.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  789.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  790.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  791.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  792.    wt: 1:   Exact Arithmetic Wholes and Fractions
  793.    wt: 1:   Formula Evaluation how to show work
  794.    wt: 1:   Expression Evaluation how to show work
  795.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  796.    wt: 1:   016 Numbering Occidental Calendar Days
  797.    wt: 1:   015 School and work day counting tables
  798.    wt: 1:   010 Repeated Addition of Time Intervals
  799.    wt: 1:   7 Addition of Time Intervals
  800.    wt: 1:   Example 2 volume of a cone
  801.    wt: 1:   Example 1 volume of a pyramid
  802.    wt: 1:   Example 4 with x function of y
  803.    wt: 1:   Example 3
  804.    wt: 1:   Example 2
  805.    wt: 1:   Example 1
  806.    wt: 1:   Summary
  807.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  808.    wt: 1:   36 Cube root derivative animated
  809.    wt: 1:   31 Derivatives of inverse functions
  810.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  811.    wt: 1:   26 Chain Rule Recognising outer inner functions
  812.    wt: 1:   19 Chain Rule for linear functions
  813.    wt: 1:   13 sine and cosine derivatives 1st step
  814.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  815.    wt: 1:   11 Limits at infinity Three Examples
  816.    wt: 1:   10 Three one sided limits with infinite values
  817.    wt: 1:   9 Limits Continuity and Composition
  818.    wt: 1:   8 Four Animated Examples
  819.    wt: 1:   6 Continuity at a point
  820.    wt: 1:   4 Numerical properties
  821.    wt: 1:   3 Decimal insights for limits continuity convergence
  822.    wt: 1:   1 Numerical introduction
  823.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  824.    wt: 1:   G.5 Motions With Bounded Velocities
  825.    wt: 1:   F.5b Extreme Value Theorem
  826.    wt: 1:   F.5a Equicontinuity Theorems
  827.    wt: 1:   F.1 What Functions are Continuous
  828.    wt: 1:   E2 Algebraic Properties of Limits
  829.    wt: 1:   Chapter 23 Links To Trigonometry
  830.    wt: 1:   Chapter 22 Complex Numbers
  831.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  832.    wt: 1:   Chapter 9 About First Courses in Calculus
  833.    wt: 1:   Appendix E. How To Study Mathematics and Why
  834.    wt: 1:   Appendix D. What to do in School and Why
  835.    wt: 1:   Appendix C. How to Read
  836.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  837.    wt: 1:   Chapter 31 Direct and Indirect Reason
  838.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  839.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  840.    wt: 1:   Chapter 25. Mathematical Induction Examples
  841.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  842.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  843.    wt: 1:   Chapter 21. Third Reading Guide
  844.    wt: 1:   Chapter 20. Degrees and Radians
  845.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  846.    wt: 1:   Chapter 16. Painless Theorem Proving
  847.    wt: 1:   Chapter 15. Solving Linear Equations
  848.    wt: 1:   Chapter 12. Shorthand Usage Guide
  849.    wt: 1:   Chapter 11. Why Shorthand
  850.    wt: 1:   Solutions For Arithmetic Exercises
  851.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  852.    wt: 1:   Chapter 6 Change of Language
  853.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  854.    wt: 1:   Chapter 4 Longer Chains of Reason
  855.    wt: 1:   Chapter 3 Chains of Reason
  856.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  857.    wt: 1:   Foreword
  858.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  859.    wt: 1:   Postscript C Consistency as a Tool for Reason
  860.    wt: 1:   Postscript A Story Telling
  861.    wt: 1:   Chapter 24 Direct and Indirect Reason
  862.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  863.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  864.    wt: 1:   Chapter 18 Sense and Knowledge
  865.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  866.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  867.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  868.    wt: 1:   Chapter 11 Accidental Patterns
  869.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  870.    wt: 1:   Chapter 8 Change of Language
  871.    wt: 1:   Chapter 7 Longer Chains of Reason
  872.    wt: 1:   Chapter 6 Chains of Reason
  873.    wt: 1:   Chapter 5 Deception
  874.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  875.    wt: 1:   Chapter 2 Skill Development
  876.    wt: 1:   Chapter 1 Introduction
  877.    wt: 1:   Three Remarks
  878.    wt: 1:   Foreword
  879.    wt: 1:   S Adding words to algebra
  880.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  881.    wt: 1:   M Words to extend arithmetic
  882.    wt: 1:   H more Routine to non routine problem solving
  883.    wt: 1:   H Jigsaw puzzles and problem solving
  884.    wt: 1:   F. The student teacher tutor feedback loop
  885.    wt: 1:   C. Domino effect of being careful
  886.    wt: 1:   B. Domino effect of errors
  887.    wt: 1:   How to Build Skills and Confidence
  888.    wt: 1:   Chapter 6 More Algebra and Geometry
  889.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  890.    wt: 1:   Chapter 3 Algebra Starter Lessons
  891.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  892.    wt: 1:   Helping the Blind in Logic and Mathematics
  893.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  894.    wt: 1:   Systematic Algebra Skill Development Missing Links
  895.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  896.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  897.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  898.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  899.    wt: 11:   13 Velocity Vectors in Physics
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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