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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  1.    wt: 6:   Step 2 Algebraic solutions for one unknown/
  2.    wt: 6:   Volume 2 Three Skills For Algebra/
  3.    wt: 5:   8 Unifying Theme For Algebra/
  4.    wt: 5:   2 Formula Forward Use Evaluation/
  5.    wt: 5:   B Decimal Comparing and Subtracting Methods/
  6.    wt: 4:   12 Comparison of Unsigned and Signed Numbers/
  7.    wt: 4:   D Decimal Long Division Methods/
  8.    wt: 4:   C Decimal Multiplication Methods/
  9.    wt: 4:   A Decimal Counting and Adding Methods/
  10.    wt: 4:   2 Arithmetic with Decimals/
  11.    wt: 3:   2 Natural Logarithms Exponentials Powers Roots/
  12.    wt: 3:   2 Euclidean Geometry Constructions Theory extras/
  13.    wt: 3:   10 Examples of Algebraic Reasoning/
  14.    wt: 3:   9 Proportionality Backwards and Forwards/
  15.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  16.    wt: 3:   3 Prime Factorization Skills/
  17.    wt: 2:   Progressive Observable Motivated Mathematics Education/
  18.    wt: 2:   Mathematics Skills Year by Year/
  19.    wt: 2:   12 Function Translating and Rescaling/
  20.    wt: 2:   B Real Numbers Extrinsic Development/
  21.    wt: 2:   A Origins of Counting and Figuring Methods/
  22.    wt: 2:   7 Axioms Logic and Equivalent Equations/
  23.    wt: 2:   6 More Less Greater Than Inequalities and Comparison/
  24.    wt: 2:   5 Real Numbers/
  25.    wt: 2:   4 Computation Rules and Function Notation/
  26.    wt: 2:   Step 4 Gaussian Elimination/
  27.    wt: 2:   Step 1 Stick diagram and fractions/
  28.    wt: 2:   3 Solving Linear Equations/
  29.    wt: 2:   1 Working With Sets/
  30.    wt: 2:   Algebra Starter Lessons/
  31.    wt: 2:   11 Squares and Square Roots/
  32.    wt: 2:   10 LCM GCD and Euclid GCD Algorithm/
  33.    wt: 2:   9 Combinatorics Trees Tables and Products/
  34.    wt: 2:   8 Arithmetic with Signed Numbers/
  35.    wt: 2:   7 Arithmetic and Fractions with Units/
  36.    wt: 2:   6 Fractions and Ratios/
  37.    wt: 2:   5 Integers/
  38.    wt: 2:   4 Remainder Arithmetic and Divisibility/
  39.    wt: 2:   1 Decimal Place Value/
  40.    wt: 2:   Arithmetic and Number Theory Skills/
  41.    wt: 2:   Volume 1B Mathematics Curriculum Notes/
  42.    wt: 2:   PreSchool and Primary Mathematics or Quantitative Skills/
  43.    wt: 1:   LAMP Lean Applied Mathematics Program/
  44.    wt: 1:   Mathematics Education Essays/
  45.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  46.    wt: 1:   4 Functions/
  47.    wt: 1:   3 Quadratics Geometrically/
  48.    wt: 1:   1 Five Polynomial Operations/
  49.    wt: 1:   More Algebra/
  50.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  51.    wt: 1:   Time Date Matters/
  52.    wt: 1:   Skills with take home value/
  53.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  54.    wt: 1:   38 Lessons on Calculating Derivatives/
  55.    wt: 1:   Volume 1A Pattern Based Reason/
  56.    wt: 1:   Volume 1 Elements of Reason/
  57.    wt: 1:   Mathematics 506 Lessons/
  58.    wt: 1:   Secondary Mathematics A Practical Approach/
  59.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

494 matches:

  1.    wt: 5:   22 sine of 22.5 degrees via half angle formulas
  2.    wt: 4:   1 Three Skills For Algebra
  3.    wt: 4:   Chapter 8 Three Skills For Algebra
  4.    wt: 3:   three goals for Mathematics Education
  5.    wt: 3:   02 21 words for teachers
  6.    wt: 3:   02 20 mathematics education references
  7.    wt: 3:   three aims for mathematics students
  8.    wt: 3:   22 Student Centered Highschool Mathematics
  9.    wt: 3:   12 Goals and Objectives For Mathematics
  10.    wt: 3:   26 Formulas for products of sines and cosines
  11.    wt: 3:   23 sine and cosine of 180 plus 22.5 degrees
  12.    wt: 3:   12 cis formulas for sine cosines and tangent
  13.    wt: 3:   4 Equations for lines three forms
  14.    wt: 3:   2 Another Rectangle Area Formula Example
  15.    wt: 3:   12 GCD 2700 288 via Prime
  16.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  17.    wt: 3:   24 Divisibility Tests for 2 3 5 9 10
  18.    wt: 3:   2 Groups of Three Place Value for Multidigit Decimals
  19.    wt: 3:   22 Chain Rule for polynomials
  20.    wt: 3:   Postscript Unifying Theme A Fourth Skill For Algebra
  21.    wt: 3:   Chapter 2 For and Against Mathematics
  22.    wt: 3:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  23.    wt: 2:   Skills Chapter 3 Algebra
  24.    wt: 2:   Skills Chapter 2 Geometry
  25.    wt: 2:   three goals to set for students
  26.    wt: 2:   Secondary Three Mathematics
  27.    wt: 2:   talk the algebra talk
  28.    wt: 2:   geometric implications for algebra
  29.    wt: 2:   the trouble with algebra
  30.    wt: 2:   04 29 New Mathematics Curriculum
  31.    wt: 2:   04 25 when to stop or suspend mathemat
  32.    wt: 2:   formal or informal peer review
  33.    wt: 2:   three kinds of reason in mathematics
  34.    wt: 2:   need for a mixed mathematics curriculum
  35.    wt: 2:   Prequel In For A Penny In For A Pound
  36.    wt: 2:   words for mathematics instructor
  37.    wt: 2:   2 Conductance Resistance Duality02
  38.    wt: 2:   C Electromotive force conventional current02
  39.    wt: 2:   27 Graduated Correction and Penalties for Young Offenders
  40.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  41.    wt: 2:   24 Standards For Skill Develoment Take II
  42.    wt: 2:   24 Standards For Skill Develoment
  43.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  44.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  45.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  46.    wt: 2:   2 Reading and Writing Skills
  47.    wt: 2:   Ages 12 to 14 Skills with take home value
  48.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  49.    wt: 2:   22 Square Root function graphically
  50.    wt: 2:   5 Function notation for geometric transformations
  51.    wt: 2:   2 Algebraic use of function notation
  52.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  53.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  54.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  55.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  56.    wt: 2:   12 motivation for term arctan
  57.    wt: 2:   12 From Applied To Pure Mathematics
  58.    wt: 2:   29 secant cosecant and cotangent for acute angles
  59.    wt: 2:   25 tangent double angle formula Slope connection
  60.    wt: 2:   24 tangent Angle Difference Formula
  61.    wt: 2:   21 sine and cosine Half Angle Formulas
  62.    wt: 2:   20 sine and cosine Double Angle Formulas
  63.    wt: 2:   17E Trig Formulas for dot and cross Products
  64.    wt: 2:   17D cis formulas for sine cosines and tangent
  65.    wt: 2:   12 Graph of tangent function for one period
  66.    wt: 2:   13 Trig Formulas for dot and cross Products
  67.    wt: 2:   2 point slope equation for a line
  68.    wt: 2:   22 Multiplication of Signed Numbers
  69.    wt: 2:   2 Combing Counts Addition Skills and Principles
  70.    wt: 2:   2 Algebraic View
  71.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  72.    wt: 2:   2 More and Less Than for Counts and Measures
  73.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  74.    wt: 2:   2 Essentially one exercises three with solution
  75.    wt: 2:   2 Three Examples
  76.    wt: 2:   2 Three Examples
  77.    wt: 2:   Formula Usage Show Work Format
  78.    wt: 2:   1 Written work formats for developing and showing skill
  79.    wt: 2:   16 GCD and LCM of 650 225 via Prime
  80.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  81.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  82.    wt: 2:   10 Euclid Algorithm with 129 125 and with 45 14
  83.    wt: 2:   22 Complex Compound Fractions
  84.    wt: 2:   21 Reciprocals for Fractions and Wholes
  85.    wt: 2:   20 Dividing Fractions the Why
  86.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  87.    wt: 2:   26 Divisibility by 2 3 5 Example
  88.    wt: 2:   23 Remainder Arithmetic Modulo 2
  89.    wt: 2:   22 Remainder Arithmetic Modulo 3 more
  90.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  91.    wt: 2:   Long Division forwards and backwards Example 2
  92.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  93.    wt: 2:   9 22 Minute Subtraction Review Video
  94.    wt: 2:   The 20 Times Table
  95.    wt: 2:   The 12 Times Table Visually
  96.    wt: 2:   38 Formulas and derivatives for powers and roots
  97.    wt: 2:   28 Chain Rule Preparation for a Proof
  98.    wt: 2:   21 Chain Rule for powers
  99.    wt: 2:   20 Chain Rule for Pulley Systems
  100.    wt: 2:   3 Motivation for Limit Definition Take 2
  101.    wt: 2:   2 Motivation for Limit Definition Take 1
  102.    wt: 2:   2 Algebraic codification
  103.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  104.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  105.    wt: 2:   F.2 Closed Range Theorem
  106.    wt: 2:   E2 Algebraic Properties of Limits
  107.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  108.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  109.    wt: 2:   Chapter 22 Complex Numbers
  110.    wt: 2:   Postscript For Better Performance
  111.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  112.    wt: 2:   Chapter 25. Mathematical Induction Examples
  113.    wt: 2:   Chapter 23. Notation For Sums
  114.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  115.    wt: 2:   Chapter 18. Rules for Algebra
  116.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  117.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  118.    wt: 2:   Chapter 22 Contrapositive and Vacuously True Implications
  119.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  120.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  121.    wt: 2:   R Why Learn Mathematics Skills
  122.    wt: 2:   N Mathematics Prepare for College Studies
  123.    wt: 2:   G. Written work formats for developing and showing skill
  124.    wt: 2:   Helping the Blind in Logic and Mathematics
  125.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  126.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  127.    wt: 2:   The Math Forum and Site Content
  128.    wt: 1:   Appendix 2 primary school Arithmetic 01
  129.    wt: 1:   Appendix 1 primary and preschool mathematic
  130.    wt: 1:   G LAMP Introduction Problem Solving Skills
  131.    wt: 1:   E LAMP Introduction Modern Mathematics
  132.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  133.    wt: 1:   Skills Chapter 5 Calculus
  134.    wt: 1:   Skills Chapter 4 Logic
  135.    wt: 1:   Ramblings Extrinsic numbers theory
  136.    wt: 1:   Ramblings Introduction Algebra Essay
  137.    wt: 1:   Skills Chapter 1 Arithmetic
  138.    wt: 1:   Skills Chapter 0 Introduction
  139.    wt: 1:   11 pure mathematics
  140.    wt: 1:   4 algebra
  141.    wt: 1:   2 arithmetic with signed numbers
  142.    wt: 1:   why bother
  143.    wt: 1:   Teach the teachers plus goals
  144.    wt: 1:   permissions for teachers
  145.    wt: 1:   Applied Maths Program14092009 POMME variant
  146.    wt: 1:   activities for students
  147.    wt: 1:   key notes and themes
  148.    wt: 1:   Mathematics Education Professors
  149.    wt: 1:   mathematics in context
  150.    wt: 1:   Postscript 2007 01 10
  151.    wt: 1:   Education Reform Inconsistencies
  152.    wt: 1:   Secondary Two Mathematics
  153.    wt: 1:   Secondary One Mathematics
  154.    wt: 1:   three difficulties
  155.    wt: 1:   mathematics curriculum shifts
  156.    wt: 1:   teaching tutoring algebraic reason
  157.    wt: 1:   Lessening Algebra Difficulties
  158.    wt: 1:   standards for course material
  159.    wt: 1:   Theory of Knowledge
  160.    wt: 1:   mathematics instruction in general
  161.    wt: 1:   Education in mathematics science and technology
  162.    wt: 1:   Four ways to improve education reform
  163.    wt: 1:   Leaner mathematics curriculum
  164.    wt: 1:   fairness and inductive principles for instruction
  165.    wt: 1:   chapitre 12 00 les iles et division
  166.    wt: 1:   chapitre 07 01 principle D induction mathematique
  167.    wt: 1:   chapitre 04 02 Deuxieme enigme
  168.    wt: 1:   chapitre 02 00 La Communication des idees
  169.    wt: 1:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  170.    wt: 1:   2 Energy Power Heat07
  171.    wt: 1:   B Energy Power02
  172.    wt: 1:   D Wire Resistance Calculation02
  173.    wt: 1:   B Wire Resistance Qualitative02
  174.    wt: 1:   2 Unlike resistors in parallel01
  175.    wt: 1:   H Series Circuit02
  176.    wt: 1:   B Electromotive force conventional current01
  177.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  178.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  179.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  180.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  181.    wt: 1:   18 Primary School Mathematics
  182.    wt: 1:   17 Math Booklets for children and young teenagers
  183.    wt: 1:   16 Secondary Mathematics Tips
  184.    wt: 1:   15 Counting For Parents
  185.    wt: 1:   10 Ends values for work study instruction
  186.    wt: 1:   8 The Effect of Negative Remarks
  187.    wt: 1:   5 Patience Please for Yourself and Your Charges
  188.    wt: 1:   4 Learning Takes Time and Effort
  189.    wt: 1:   3 Preparing for Science Studies
  190.    wt: 1:   1 Speaking Skills
  191.    wt: 1:   Ages 12 to 14 Geometry
  192.    wt: 1:   Ages 12 to 14 Arithmetic
  193.    wt: 1:   Ages 10 to 12 Geometry
  194.    wt: 1:   Ages 10 to 12 Arithmetic
  195.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  196.    wt: 1:   sign monoticity analysis example 2
  197.    wt: 1:   26 Function definitions done and coming
  198.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  199.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  200.    wt: 1:   23 Inverse Functions
  201.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  202.    wt: 1:   20 Interchanging coordinates a reflection
  203.    wt: 1:   17 Function maxima minima and their location
  204.    wt: 1:   12 Function Domain Recognition Exercises
  205.    wt: 1:   9 Set theory term relation possible origins
  206.    wt: 1:   6 Set Existence Formation and Notation
  207.    wt: 1:   4 Function notation in and beyond mathematics
  208.    wt: 1:   3 Formula or function graphing exercise
  209.    wt: 1:   9 quadratics physical and further context
  210.    wt: 1:   8 quadratics backward use of various formulas
  211.    wt: 1:   7 quadratic formulla derivation
  212.    wt: 1:   5 quadratics completing the square
  213.    wt: 1:   2 quadratics graphing in general
  214.    wt: 1:   2 Square Root Simplification a prequel
  215.    wt: 1:   8 Notes for instructors or tutors
  216.    wt: 1:   2 Column Multiplication Method
  217.    wt: 1:   Rewriting algebraic substitution as function substitutions
  218.    wt: 1:   9 motivation for name arcsin
  219.    wt: 1:   4 possible motivation for term arccos
  220.    wt: 1:   2 cosine function more properties
  221.    wt: 1:   2 Radian Measure Numerical Value of one degree
  222.    wt: 1:   2 Signed Coordinates
  223.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  224.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  225.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  226.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  227.    wt: 1:   12 Straight Lines Graphing mx plus b
  228.    wt: 1:   8 Straight Lines Equation for vertical
  229.    wt: 1:   6 Tangent Function Inclination Angle Take 2
  230.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  231.    wt: 1:   17 tangent function angle sum formulas
  232.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  233.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  234.    wt: 1:   33 sines and cosines of 2A 3A 4A 5A
  235.    wt: 1:   32 seven rows of pascals triangle
  236.    wt: 1:   28 Expressing products of sines cosines as sums
  237.    wt: 1:   27 Logarithmic use of products of sines and cosines
  238.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  239.    wt: 1:   17G Pythagorean Theorem Converse
  240.    wt: 1:   17C sine and cosine double triple angle formulas
  241.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  242.    wt: 1:   17A The complex number valued trig function cis
  243.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  244.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  245.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  246.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  247.    wt: 1:   2 Quadrant I reference Angles
  248.    wt: 1:   21 Logarithms Powers and Exponentials
  249.    wt: 1:   20 N th Roots of Complex Numbers
  250.    wt: 1:   15 Pythagorean Theorem Converse
  251.    wt: 1:   11 sine and cosine double triple angle formulas
  252.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  253.    wt: 1:   9 The complex number valued trig function cis
  254.    wt: 1:   5 An Easy Proof of the Distributive Law
  255.    wt: 1:   2 Complex Numbers made easier we hope
  256.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  257.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  258.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  259.    wt: 1:   Why Trigonometry the whyslopes view
  260.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  261.    wt: 1:   12 Triangles Similarity More Problems
  262.    wt: 1:   2 Similarity By Design
  263.    wt: 1:   12 Links Lessons elsewhere
  264.    wt: 1:   8 Mid Point Formula
  265.    wt: 1:   5 Algebraic View of Slopes
  266.    wt: 1:   3 Slope product for perpendicular lines
  267.    wt: 1:   1 Numerical view of lines and their equations
  268.    wt: 1:   13 Pythagorean spatial distance formulas
  269.    wt: 1:   12 Spatial Coordinates
  270.    wt: 1:   10 Pythagorean plane distance formula
  271.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  272.    wt: 1:   2 Cartesian Coordinates with signs
  273.    wt: 1:   PS H Distributive Law For Complex Numbers
  274.    wt: 1:   21 Parallelograms
  275.    wt: 1:   12 Side Angle Side Failure
  276.    wt: 1:   2 Correspondence between Triangles
  277.    wt: 1:   2 Measuring Area Directly
  278.    wt: 1:   26 More Less Greater Than Comparison
  279.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  280.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  281.    wt: 1:   23 Distributive Law Two Derivations
  282.    wt: 1:   21 Addition of Multiples of a Single Vector
  283.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  284.    wt: 1:   12 Real Numbers Line Signed Coordinates
  285.    wt: 1:   2 Counting Digits in Decimal Multiplication
  286.    wt: 1:   C Three Decimal Subtraction Methods
  287.    wt: 1:   6 Column Methods for Decimal Multiplication
  288.    wt: 1:   5 Distributive Law for Whole Numbers
  289.    wt: 1:   4 Commutative Law Groups Counting Form
  290.    wt: 1:   3 Multiplicative Counting Skills Principles
  291.    wt: 1:   1 The Counting Origins of Numbers
  292.    wt: 1:   3 Inequalities Algebraically
  293.    wt: 1:   2 Fraction Operations Physical Development
  294.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  295.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  296.    wt: 1:   6 Compound Interest Forward and Backwards
  297.    wt: 1:   5 Triangle Area Formula Backwards
  298.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  299.    wt: 1:   2 Linear Equation Literal Solution
  300.    wt: 1:   5 Equality in Algebra
  301.    wt: 1:   3 Product Axioms Two Forms
  302.    wt: 1:   2 Addition and Multiplication Axioms
  303.    wt: 1:   12 Real Number Additive Inverses or Negatives
  304.    wt: 1:   9 Coordinates for Regions in Space
  305.    wt: 1:   8 Coordinates for Maps and Planes
  306.    wt: 1:   2 Integers
  307.    wt: 1:   3 Geometric Formulas and Function Notation
  308.    wt: 1:   2 Computation Rules Evaluation
  309.    wt: 1:   1 Formulas Dependence and Function Notation
  310.    wt: 1:   2 GE II Comparison
  311.    wt: 1:   6 Algebraic Solution Example
  312.    wt: 1:   5 Algebraic Solutions Introduction
  313.    wt: 1:   9 Three Examples
  314.    wt: 1:   6 Three Examples
  315.    wt: 1:   5 Three Examples
  316.    wt: 1:   Using Letters for Physical Quantities
  317.    wt: 1:   13 Naming Identifying Formulas with Words
  318.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  319.    wt: 1:   8 Compound Interest Formula Evaluation
  320.    wt: 1:   7 Compound Interest Formula Introduction
  321.    wt: 1:   5 Box Volume Formula Example
  322.    wt: 1:   4 Circle Area Formula Example
  323.    wt: 1:   3 Triangle Area Formula Example
  324.    wt: 1:   2 Venn Diagrams
  325.    wt: 1:   6 Three Notions of What is a Variable
  326.    wt: 1:   4 A Brief Story of numbers and algebra
  327.    wt: 1:   2 What is a Variable
  328.    wt: 1:   arithmetic videos Real Player Format
  329.    wt: 1:   2 More and Less Than with Unlike Signs
  330.    wt: 1:   1 More and Less Than for Counts and Measures
  331.    wt: 1:   2 Square Roots with Prime
  332.    wt: 1:   2 Least Common Multiple LCM intro via list method
  333.    wt: 1:   2 Counting with Tables and Trees I
  334.    wt: 1:   4 signed coordinates for regions in space
  335.    wt: 1:   3 signed coordinates for maps and planes
  336.    wt: 1:   2 signed and unsigned numbers as coordinates
  337.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  338.    wt: 1:   2 Equality and Units
  339.    wt: 1:   D Three Term Ratios
  340.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  341.    wt: 1:   21 Working With Signs
  342.    wt: 1:   13 Fraction Comparison Algebraic View
  343.    wt: 1:   12 Fraction Comparison
  344.    wt: 1:   11 Simplification an Algebraic View
  345.    wt: 1:   6 Multiplication Algebraically Take II
  346.    wt: 1:   2 Unit Fraction Multiplication
  347.    wt: 1:   A Associative Law Theorectical Note
  348.    wt: 1:   12 Adding Integers More Examples
  349.    wt: 1:   11 Adding Integers Formulas and Examples
  350.    wt: 1:   10 Integer Multiplication Formulas
  351.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  352.    wt: 1:   21 Remainder Arithmetic Modulo 3
  353.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  354.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  355.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  356.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  357.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  358.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  359.    wt: 1:   20 Uniqueness of Prime Factorization
  360.    wt: 1:   15 video Factors of 20 using Prime Factorization
  361.    wt: 1:   14 video Factors of 24 Take II
  362.    wt: 1:   13 video Factors of 24 using prime
  363.    wt: 1:   12 LCD GCD and LCM using Primes
  364.    wt: 1:   10 video Prime Factorization upto 23 squared
  365.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  366.    wt: 1:   2 Prime and Composites less than 16
  367.    wt: 1:   Long Division forwards and backwards Example 3
  368.    wt: 1:   Long Division forwards and backwards Example 1
  369.    wt: 1:   12 Why Long Division Works Take III
  370.    wt: 1:   11 Another Single Digit Divisor Example
  371.    wt: 1:   8 Correcting the Mistake
  372.    wt: 1:   4 Division with 2 Digit Divsors
  373.    wt: 1:   2 Division with Single Digit Divisors
  374.    wt: 1:   A Elementary Basis for Multiplication Methods
  375.    wt: 1:   4 Two and Three Digit Multipliers
  376.    wt: 1:   2 One Digit Multipliers
  377.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  378.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  379.    wt: 1:   Subtraction Another Video Lesson
  380.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  381.    wt: 1:   5 A Tip for Efficent Subtraction
  382.    wt: 1:   2 Subtraction Easy Case Examples
  383.    wt: 1:   8 What skills and work habits to require
  384.    wt: 1:   2 Decimal Counting Practices
  385.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  386.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  387.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  388.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  389.    wt: 1:   Quick history of numbers and algebra
  390.    wt: 1:   Formula Evaluation how to show work
  391.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  392.    wt: 1:   012 Division of Time Intervals by Time Intervals
  393.    wt: 1:   2 Time and Date Matters in School
  394.    wt: 1:   1 Intro of Kids To Time Date Skills
  395.    wt: 1:   Example 2 volume of a cone
  396.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  397.    wt: 1:   Example 2
  398.    wt: 1:   Area Between Curves Lesson Take 2
  399.    wt: 1:   2 Indefinite Integrals Exercises
  400.    wt: 1:   2 Second derivative test prequel
  401.    wt: 1:   29 Chain Rule Optional Reading
  402.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  403.    wt: 1:   26 Chain Rule Recognising outer inner functions
  404.    wt: 1:   25 Chain Rule Animated Examples Continued
  405.    wt: 1:   24 Chain Rule Animated Examples
  406.    wt: 1:   23 Chain Rule in general
  407.    wt: 1:   19 Chain Rule for linear functions
  408.    wt: 1:   14 sine and cosine derivatives 2nd step
  409.    wt: 1:   12 Quotient rule examples
  410.    wt: 1:   10 Power rule for negative integers
  411.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  412.    wt: 1:   11 Limits at infinity Three Examples
  413.    wt: 1:   10 Three one sided limits with infinite values
  414.    wt: 1:   3 Decimal insights for limits continuity convergence
  415.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  416.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  417.    wt: 1:   G.3 Constant Difference Theorem Proof
  418.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  419.    wt: 1:   F.5b Extreme Value Theorem
  420.    wt: 1:   F.5a Equicontinuity Theorems
  421.    wt: 1:   F.4 Finite Covering Theorem
  422.    wt: 1:   F.3 Intermediate Value Theorem
  423.    wt: 1:   D2 Limits of Monotone Sequences
  424.    wt: 1:   B3 Bolzano Weierstrass Theorem
  425.    wt: 1:   PostScript For and Against Decimal Perspectives
  426.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  427.    wt: 1:   Chapter 23 Links To Trigonometry
  428.    wt: 1:   Chapter 21 Arrow Addition
  429.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  430.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  431.    wt: 1:   Chapter 12. Units and Slopes
  432.    wt: 1:   Chapter 2. Slopes and Ski Trails
  433.    wt: 1:   Foreword
  434.    wt: 1:   Postscript More on Better Performance
  435.    wt: 1:   Appendix E. How To Study Mathematics and Why
  436.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  437.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  438.    wt: 1:   Chapter 28 Occurrence Tables
  439.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  440.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  441.    wt: 1:   Chapter 21. Third Reading Guide
  442.    wt: 1:   Chapter 20. Degrees and Radians
  443.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  444.    wt: 1:   Chapter 16. Painless Theorem Proving
  445.    wt: 1:   Chapter 12. Shorthand Usage Guide
  446.    wt: 1:   Solutions For Arithmetic Exercises
  447.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  448.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  449.    wt: 1:   Foreword
  450.    wt: 1:   Postscript B Mathematics Education References
  451.    wt: 1:   Postscript A Three Remarks
  452.    wt: 1:   Chapter 12 Four Phases
  453.    wt: 1:   Chapter 9 The Two Ends
  454.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  455.    wt: 1:   Chapter 3 Algebra Difficulties
  456.    wt: 1:   Foreword
  457.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  458.    wt: 1:   Postscript C Consistency as a Tool for Reason
  459.    wt: 1:   Chapter 24 Direct and Indirect Reason
  460.    wt: 1:   Chapter 23 Truth Tables
  461.    wt: 1:   Chapter 21 Occurrence Tables
  462.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  463.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  464.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  465.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  466.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  467.    wt: 1:   Chapter 2 Skill Development
  468.    wt: 1:   Three Remarks
  469.    wt: 1:   Foreword
  470.    wt: 1:   S Adding words to algebra
  471.    wt: 1:   O On Learning Mathematics and Science
  472.    wt: 1:   L Skills with take home value
  473.    wt: 1:   I. Logic and language skills
  474.    wt: 1:   F. The student teacher tutor feedback loop
  475.    wt: 1:   How to Build Skills and Confidence
  476.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  477.    wt: 1:   Chapter 6 More Algebra and Geometry
  478.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  479.    wt: 1:   Chapter 3 Algebra Starter Lessons
  480.    wt: 1:   Chapter 2 Why Sets
  481.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  482.    wt: 1:   7 Games and Activities for Instruction
  483.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  484.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  485.    wt: 1:   Mathematics Education References
  486.    wt: 1:   Mathematics Education References
  487.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  488.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  489.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  490.    wt: 1:   More Algebra and Slope based Calculus Preview
  491.    wt: 1:   Systematic Algebra Skill Development Missing Links
  492.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  493.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  494.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

957 matches:

  1.    wt: 9:   2 Three Examples
  2.    wt: 9:   Chapter 26 What is in chapters 27 to 31
  3.    wt: 9:   Chapter 25. Mathematical Induction Examples
  4.    wt: 9:   Chapter 23. Notation For Sums
  5.    wt: 9:   Postscript Unifying Theme A Fourth Skill For Algebra
  6.    wt: 9:   Chapter 2 Implication Rules Forwards and Backwards
  7.    wt: 8:   2 Another Rectangle Area Formula Example
  8.    wt: 8:   Postscript For Better Performance
  9.    wt: 8:   Chapter 29 Contrapositive and Vacuously True Implications
  10.    wt: 8:   Chapter 28 Occurrence Tables
  11.    wt: 8:   Chapter 27 Shorthand Symbols as Pronouns
  12.    wt: 8:   Chapter 24. Personal Investment and Pension EGS
  13.    wt: 8:   Chapter 21. Third Reading Guide
  14.    wt: 8:   Chapter 20. Degrees and Radians
  15.    wt: 8:   Chapter 18. Rules for Algebra
  16.    wt: 8:   Chapter 14. Forward and Backward Use of a Formula
  17.    wt: 8:   Chapter 12. Shorthand Usage Guide
  18.    wt: 7:   9 Circle Area and Perimeter Formula Backwards Forwards
  19.    wt: 7:   6 Algebraic Solution Example
  20.    wt: 7:   5 Algebraic Solutions Introduction
  21.    wt: 7:   1 Written work formats for developing and showing skill
  22.    wt: 7:   Long Division forwards and backwards Example 2
  23.    wt: 7:   Appendix 2 Three Decimal Subtraction Methods
  24.    wt: 7:   9 22 Minute Subtraction Review Video
  25.    wt: 7:   2 Subtraction Easy Case Examples
  26.    wt: 7:   Postscript More on Better Performance
  27.    wt: 7:   Appendix E. How To Study Mathematics and Why
  28.    wt: 7:   Appendix B. How To Learn
  29.    wt: 7:   Appendix A. Reading Guide For Next Appendices
  30.    wt: 7:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  31.    wt: 7:   Chapter 16. Painless Theorem Proving
  32.    wt: 7:   Solutions For Arithmetic Exercises
  33.    wt: 7:   Chapter 7 Prep for Calculus Arithmetic Exercises
  34.    wt: 7:   Chapter 1 Introduction to Chapters 2 to 6
  35.    wt: 7:   Foreword
  36.    wt: 6:   three goals for Mathematics Education
  37.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  38.    wt: 6:   2 Algebraic View
  39.    wt: 6:   8 Pythagorean Relation Forwards Backwards
  40.    wt: 6:   7 Pythagorean Theorem Chinese Square Proof
  41.    wt: 6:   6 Compound Interest Forward and Backwards
  42.    wt: 6:   5 Triangle Area Formula Backwards
  43.    wt: 6:   4 Rectangle Area and Like Formulas Backwards
  44.    wt: 6:   2 Linear Equation Literal Solution
  45.    wt: 6:   2 Essentially one exercises three with solution
  46.    wt: 6:   4 Four Examples Fractional Coefficients
  47.    wt: 6:   3 Four Examples
  48.    wt: 6:   1 Proper Equal Sign Usage
  49.    wt: 6:   13 Naming Identifying Formulas with Words
  50.    wt: 6:   12 Cone Cylinder Sphere Lesson Idea
  51.    wt: 6:   8 Compound Interest Formula Evaluation
  52.    wt: 6:   7 Compound Interest Formula Introduction
  53.    wt: 6:   5 Box Volume Formula Example
  54.    wt: 6:   4 Circle Area Formula Example
  55.    wt: 6:   3 Triangle Area Formula Example
  56.    wt: 6:   1 Three Skills For Algebra
  57.    wt: 6:   2 More and Less Than with Unlike Signs
  58.    wt: 6:   Long Division forwards and backwards Example 3
  59.    wt: 6:   12 Why Long Division Works Take III
  60.    wt: 6:   2 Division with Single Digit Divisors
  61.    wt: 6:   2 One Digit Multipliers
  62.    wt: 6:   Video Decimal Multiplication Geometric View Example 2
  63.    wt: 6:   Video Decimal Multiplication Geometric View Example 2
  64.    wt: 6:   Video Power Notation in Decimal Expansion
  65.    wt: 6:   Subtraction Another Video Lesson
  66.    wt: 6:   7 Subtraction for Decimal Fractions with Exercises
  67.    wt: 6:   5 A Tip for Efficent Subtraction
  68.    wt: 6:   2 Decimal Counting Practices
  69.    wt: 6:   2 Groups of Three Place Value for Multidigit Decimals
  70.    wt: 6:   Appendix D. What to do in School and Why
  71.    wt: 6:   Appendix C. How to Read
  72.    wt: 6:   Chapter 31 Direct and Indirect Reason
  73.    wt: 6:   Chapter 30 Truth Tables
  74.    wt: 6:   Chapter 19. Functions and Sets
  75.    wt: 6:   Chapter 15. Solving Linear Equations
  76.    wt: 6:   Chapter 13. Second Reading Guide
  77.    wt: 6:   Chapter 11. Why Shorthand
  78.    wt: 6:   Chapter 10 Describing and Changing Calculations
  79.    wt: 6:   Postscript What is a Variable
  80.    wt: 6:   Chapter 9 Talking about Numbers or Quantities
  81.    wt: 6:   Chapter 6 Change of Language
  82.    wt: 6:   Chapter 5 Islands and Divisions of Knowledge
  83.    wt: 6:   Chapter 4 Longer Chains of Reason
  84.    wt: 6:   Chapter 3 Chains of Reason
  85.    wt: 6:   Chapter 2 For and Against Mathematics
  86.    wt: 5:   the trouble with algebra
  87.    wt: 5:   02 21 words for teachers
  88.    wt: 5:   02 20 mathematics education references
  89.    wt: 5:   three aims for mathematics students
  90.    wt: 5:   22 Student Centered Highschool Mathematics
  91.    wt: 5:   Ages 12 to 14 Skills with take home value
  92.    wt: 5:   22 Square Root function graphically
  93.    wt: 5:   9 Formulas for Real Exponents with Logarithms
  94.    wt: 5:   8 Formulas for Fractional Exponents with Logarithms
  95.    wt: 5:   7 Formulas for Roots with Logarithms Derivation
  96.    wt: 5:   6 Formulas for Even and Odd Roots with Logarithms
  97.    wt: 5:   2 Square Root Simplification a prequel
  98.    wt: 5:   23 sine and cosine of 180 plus 22.5 degrees
  99.    wt: 5:   PS H Distributive Law For Complex Numbers
  100.    wt: 5:   PS B Parallelogram Construction Methods
  101.    wt: 5:   21 Parallelograms
  102.    wt: 5:   12 Side Angle Side Failure
  103.    wt: 5:   2 Correspondence between Triangles
  104.    wt: 5:   2 Combing Counts Addition Skills and Principles
  105.    wt: 5:   3 Linear Equation Literal Solution More
  106.    wt: 5:   1 Changing Calculations
  107.    wt: 5:   2 Three Examples
  108.    wt: 5:   11 Volume of Sphere
  109.    wt: 5:   10 Volume of Pyramid
  110.    wt: 5:   9 Volume of Cone
  111.    wt: 5:   6 Pythagorean Hypotenuse Calculation Example
  112.    wt: 5:   1 More and Less Than for Counts and Measures
  113.    wt: 5:   16 GCD and LCM of 650 225 via Prime
  114.    wt: 5:   12 GCD 2700 288 via Prime
  115.    wt: 5:   22 Complex Compound Fractions
  116.    wt: 5:   21 Reciprocals for Fractions and Wholes
  117.    wt: 5:   20 Dividing Fractions the Why
  118.    wt: 5:   27 Divisibility by 2 3 6 5 9 10 Example
  119.    wt: 5:   25 Divisibility Tests for 2 3 5 9 10 Example
  120.    wt: 5:   24 Divisibility Tests for 2 3 5 9 10
  121.    wt: 5:   20 Uniqueness of Prime Factorization
  122.    wt: 5:   12 LCD GCD and LCM using Primes
  123.    wt: 5:   2 Prime and Composites less than 16
  124.    wt: 5:   Long Division Backwards more
  125.    wt: 5:   Long Division Backward
  126.    wt: 5:   Long Division forwards and backwards Example 1
  127.    wt: 5:   11 Another Single Digit Divisor Example
  128.    wt: 5:   8 Correcting the Mistake
  129.    wt: 5:   4 Division with 2 Digit Divsors
  130.    wt: 5:   A Elementary Basis for Multiplication Methods
  131.    wt: 5:   4 Two and Three Digit Multipliers
  132.    wt: 5:   Appendix 1 Decimals Comparison Method Take II
  133.    wt: 5:   Subtraction with J Conversions Example
  134.    wt: 5:   8 Subtraction with Units of Measure
  135.    wt: 5:   6 Subtraction with Conversion Example with Exercises
  136.    wt: 5:   4 Subtraction with Conversions Borrows and Letter J
  137.    wt: 5:   3 Harder Cases Convert to Compare and Subtract
  138.    wt: 5:   1 Comparison and Subtraction Easy Direct Cases
  139.    wt: 5:   8 What skills and work habits to require
  140.    wt: 5:   The 20 Times Table
  141.    wt: 5:   Chapter 22 Contrapositive and Vacuously True Implications
  142.    wt: 5:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  143.    wt: 4:   Skills Chapter 2 Geometry
  144.    wt: 4:   2 arithmetic with signed numbers
  145.    wt: 4:   Secondary Three Mathematics
  146.    wt: 4:   talk the algebra talk
  147.    wt: 4:   geometric implications for algebra
  148.    wt: 4:   Lessening Algebra Difficulties
  149.    wt: 4:   04 29 New Mathematics Curriculum
  150.    wt: 4:   04 25 when to stop or suspend mathemat
  151.    wt: 4:   three kinds of reason in mathematics
  152.    wt: 4:   Prequel In For A Penny In For A Pound
  153.    wt: 4:   12 Goals and Objectives For Mathematics
  154.    wt: 4:   Ages 12 to 14 Geometry
  155.    wt: 4:   Ages 12 to 14 Arithmetic
  156.    wt: 4:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  157.    wt: 4:   2 Algebraic use of function notation
  158.    wt: 4:   26 Formulas for products of sines and cosines
  159.    wt: 4:   12 cis formulas for sine cosines and tangent
  160.    wt: 4:   PS G Rotation Distributes over Addition
  161.    wt: 4:   PS F Scalar Multiplication Distributes over Addition
  162.    wt: 4:   PS E Multiplication with Polar Coordinates
  163.    wt: 4:   PS D Addition with Cartesian Coordinates
  164.    wt: 4:   PS C Similarity Use Recognize it in Trigonometry
  165.    wt: 4:   PS A Kite Construction Methods
  166.    wt: 4:   22 Multiplication of Signed Numbers
  167.    wt: 4:   21 Addition of Multiples of a Single Vector
  168.    wt: 4:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  169.    wt: 4:   12 Real Numbers Line Signed Coordinates
  170.    wt: 4:   3 Inequalities Algebraically
  171.    wt: 4:   2 Fraction Operations Physical Development
  172.    wt: 4:   2 More and Less Than for Counts and Measures
  173.    wt: 4:   12 Real Number Additive Inverses or Negatives
  174.    wt: 4:   5 Gaussian Elimination for 3 unknowns 2nd example
  175.    wt: 4:   2 GE II Comparison
  176.    wt: 4:   Formula Usage Show Work Format
  177.    wt: 4:   4 Greater More Less Than Signs in General
  178.    wt: 4:   3 Comparison of Negative Numbers
  179.    wt: 4:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  180.    wt: 4:   11 GCD 2700 288 via Euclid Algorithm
  181.    wt: 4:   10 Euclid Algorithm with 129 125 and with 45 14
  182.    wt: 4:   3 signed coordinates for maps and planes
  183.    wt: 4:   2 signed and unsigned numbers as coordinates
  184.    wt: 4:   21 Working With Signs
  185.    wt: 4:   2 Unit Fraction Multiplication
  186.    wt: 4:   12 Adding Integers More Examples
  187.    wt: 4:   2 Integers Multiplies of a Unit Moverment
  188.    wt: 4:   26 Divisibility by 2 3 5 Example
  189.    wt: 4:   23 Remainder Arithmetic Modulo 2
  190.    wt: 4:   22 Remainder Arithmetic Modulo 3 more
  191.    wt: 4:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  192.    wt: 4:   18 Remainder Arithmetic Rule of 9 for checking sums II
  193.    wt: 4:   2 Remainder Arithmetic Modulo 10 more
  194.    wt: 4:   15 video Factors of 20 using Prime Factorization
  195.    wt: 4:   14 video Factors of 24 Take II
  196.    wt: 4:   13 video Factors of 24 using prime
  197.    wt: 4:   10 video Prime Factorization upto 23 squared
  198.    wt: 4:   6 Sieve of Eratosthenes and Square Rule
  199.    wt: 4:   Division with Counts and Length
  200.    wt: 4:   10 Division by Five Long and Short Ways
  201.    wt: 4:   9 Why Long Division Works Take II
  202.    wt: 4:   7 Long Divison Mistake Catching
  203.    wt: 4:   6 Why Decimal Long Division Methods Works Take I
  204.    wt: 4:   5 Long Division Include Zeroes or not
  205.    wt: 4:   3 Division Single Digit Divisor Example
  206.    wt: 4:   1 Divsion Physical Examples
  207.    wt: 4:   D Decimal Multiplication Methods Derived
  208.    wt: 4:   C Counting Areas with Powers of Ten
  209.    wt: 4:   B Powers of Ten
  210.    wt: 4:   6 Multiplication Commutes Order Not Important
  211.    wt: 4:   5 Decimal Fraction Multiplication
  212.    wt: 4:   3 More One Digit Multipliers
  213.    wt: 4:   1 Why 3 times 5 gives 15
  214.    wt: 4:   Appendix 1 Counting Revisited 15 minute video
  215.    wt: 4:   7 Adding decimal fractions using decimal point
  216.    wt: 4:   6. Counting and adding units and mixed units
  217.    wt: 4:   5. How to add decimals C. Examples
  218.    wt: 4:   4. How to add with decimals B with conversions
  219.    wt: 4:   3. How to add with decimals A sans conversions
  220.    wt: 4:   1. Explaining Addition Table
  221.    wt: 4:   The 12 Times Table Visually
  222.    wt: 4:   22 Chain Rule for polynomials
  223.    wt: 4:   21 Chain Rule for powers
  224.    wt: 4:   G.2 Lipshitz Conditions Integration Calculus Reform
  225.    wt: 4:   Chapter 22 Complex Numbers
  226.    wt: 4:   Chapter 12 Four Phases
  227.    wt: 4:   V Reasons and Motivations for Logic and Mathematics
  228.    wt: 4:   2 Identifying Size and Position Place and Spatial Sense
  229.    wt: 3:   Skills Chapter 3 Algebra
  230.    wt: 3:   11 pure mathematics
  231.    wt: 3:   4 algebra
  232.    wt: 3:   why bother
  233.    wt: 3:   three goals to set for students
  234.    wt: 3:   Applied Maths Program14092009 POMME variant
  235.    wt: 3:   Secondary Two Mathematics
  236.    wt: 3:   Secondary One Mathematics
  237.    wt: 3:   three difficulties
  238.    wt: 3:   mathematics curriculum shifts
  239.    wt: 3:   teaching tutoring algebraic reason
  240.    wt: 3:   formal or informal peer review
  241.    wt: 3:   need for a mixed mathematics curriculum
  242.    wt: 3:   fairness and inductive principles for instruction
  243.    wt: 3:   words for mathematics instructor
  244.    wt: 3:   B Energy Power02
  245.    wt: 3:   2 Conductance Resistance Duality02
  246.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  247.    wt: 3:   25 Mathematics Education Leaving A Good Impression
  248.    wt: 3:   24 Standards For Skill Develoment Take II
  249.    wt: 3:   24 Standards For Skill Develoment
  250.    wt: 3:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  251.    wt: 3:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  252.    wt: 3:   2 Reading and Writing Skills
  253.    wt: 3:   Ages 10 to 12 Geometry
  254.    wt: 3:   Ages 10 to 12 Arithmetic
  255.    wt: 3:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  256.    wt: 3:   sign monoticity analysis example 2
  257.    wt: 3:   26 Function definitions done and coming
  258.    wt: 3:   25 Absolute Value greatest integer and saw tooth functions
  259.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  260.    wt: 3:   23 Inverse Functions
  261.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  262.    wt: 3:   20 Interchanging coordinates a reflection
  263.    wt: 3:   12 Function Domain Recognition Exercises
  264.    wt: 3:   5 Function notation for geometric transformations
  265.    wt: 3:   11 Growth and Decay in Biology
  266.    wt: 3:   10 Exponential Growth and Decay Models
  267.    wt: 3:   5 Natural Logarithm Calculator Exercises
  268.    wt: 3:   3 Natural Logarithms and Exponentials Basic Properties
  269.    wt: 3:   1 Calculator Starter Exercises
  270.    wt: 3:   12 motivation for term arctan
  271.    wt: 3:   12 From Applied To Pure Mathematics
  272.    wt: 3:   2 Graphing y=Af(x) Vertical Scaling
  273.    wt: 3:   8 Straight Lines Equation for vertical
  274.    wt: 3:   6 Tangent Function Inclination Angle Take 2
  275.    wt: 3:   2 Straight Lines Slopes As Rise Over Run
  276.    wt: 3:   29 secant cosecant and cotangent for acute angles
  277.    wt: 3:   25 tangent double angle formula Slope connection
  278.    wt: 3:   24 tangent Angle Difference Formula
  279.    wt: 3:   21 sine and cosine Half Angle Formulas
  280.    wt: 3:   4 Equations for lines three forms
  281.    wt: 3:   2 point slope equation for a line
  282.    wt: 3:   Euclidean Geometry Elsewhere LINKS
  283.    wt: 3:   19 Right Triangle Similarity
  284.    wt: 3:   18 Triangle Similarity Take 1
  285.    wt: 3:   17 Right Bisectors of Triangle Sides
  286.    wt: 3:   16 Angles Subtended By Chords and Diameters
  287.    wt: 3:   15 Triangle Angle Sum is 180 degrees
  288.    wt: 3:   14 Parallel Lines Postulate
  289.    wt: 3:   13 Angle Side Angle Failure
  290.    wt: 3:   11 Triangle Construction Fails
  291.    wt: 3:   10 Dropping a perpendicular to line
  292.    wt: 3:   9 Construction of a right bisector
  293.    wt: 3:   8 Isoceles Triangles
  294.    wt: 3:   7 Angle Side Angle
  295.    wt: 3:   6 Ruler and compass Angle Bisection
  296.    wt: 3:   5 Side Angle Side
  297.    wt: 3:   4 Side Side Side
  298.    wt: 3:   3 Isometry of Triangles Congruence
  299.    wt: 3:   1 Initial Concepts and Terms
  300.    wt: 3:   Short Course on Euclidean Geometry
  301.    wt: 3:   26 More Less Greater Than Comparison
  302.    wt: 3:   25 Mid way Convergence to Axiomatic Approach
  303.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  304.    wt: 3:   23 Distributive Law Two Derivations
  305.    wt: 3:   19 Signed Multiples of Vectors
  306.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  307.    wt: 3:   17 Arrows Rotate to Reverse with Length Unchanged
  308.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  309.    wt: 3:   15 Head to Tails in place Addition Associative
  310.    wt: 3:   14 Vector Head to Tail Sums and Resultants
  311.    wt: 3:   13 Arrows and Vectors in a Plane
  312.    wt: 3:   11 Signed Number Addition and Addition Properties
  313.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  314.    wt: 3:   2 Counting Digits in Decimal Multiplication
  315.    wt: 3:   C Three Decimal Subtraction Methods
  316.    wt: 3:   6 Column Methods for Decimal Multiplication
  317.    wt: 3:   5 Distributive Law for Whole Numbers
  318.    wt: 3:   4 Commutative Law Groups Counting Form
  319.    wt: 3:   3 Multiplicative Counting Skills Principles
  320.    wt: 3:   1 The Counting Origins of Numbers
  321.    wt: 3:   5 Areas of Rectangles Revisited
  322.    wt: 3:   4 Fraction Operations Axiomatic Development
  323.    wt: 3:   1 Decimals Modular and Remainder Arithmetic
  324.    wt: 3:   5 Proportionality in Equivalent Fractions
  325.    wt: 3:   4 Rates Ratios and Proporitionality
  326.    wt: 3:   3 Proportionality Examples
  327.    wt: 3:   1 What is Proportionality
  328.    wt: 3:   5 Equality in Algebra
  329.    wt: 3:   3 Product Axioms Two Forms
  330.    wt: 3:   2 Addition and Multiplication Axioms
  331.    wt: 3:   16 Real Numbers Comparison
  332.    wt: 3:   15 Real Number Division
  333.    wt: 3:   14 Real Number Multiplication
  334.    wt: 3:   13 Real Number Subtraction
  335.    wt: 3:   11 Real Number Addition
  336.    wt: 3:   10 Real Number Lengths and Signs
  337.    wt: 3:   9 Coordinates for Regions in Space
  338.    wt: 3:   8 Coordinates for Maps and Planes
  339.    wt: 3:   2 Integers
  340.    wt: 3:   3 Geometric Formulas and Function Notation
  341.    wt: 3:   2 Computation Rules Evaluation
  342.    wt: 3:   1 Formulas Dependence and Function Notation
  343.    wt: 3:   4 Solving a triangular system exercise
  344.    wt: 3:   3 Solving triangular system example
  345.    wt: 3:   1 Essentially One Unknown
  346.    wt: 3:   9 Three Examples
  347.    wt: 3:   6 Three Examples
  348.    wt: 3:   5 Three Examples
  349.    wt: 3:   Using Letters for Physical Quantities
  350.    wt: 3:   2 Venn Diagrams
  351.    wt: 3:   6 Three Notions of What is a Variable
  352.    wt: 3:   4 A Brief Story of numbers and algebra
  353.    wt: 3:   2 What is a Variable
  354.    wt: 3:   arithmetic videos Real Player Format
  355.    wt: 3:   2 Square Roots with Prime
  356.    wt: 3:   8 GCD from Euclidean Algorithm
  357.    wt: 3:   2 Least Common Multiple LCM intro via list method
  358.    wt: 3:   2 Counting with Tables and Trees I
  359.    wt: 3:   4 signed coordinates for regions in space
  360.    wt: 3:   5 Reciprocals and Division for Fractions with Units
  361.    wt: 3:   2 Equality and Units
  362.    wt: 3:   D Three Term Ratios
  363.    wt: 3:   C Equality for Fractions and Two Term Ratios and Fractions
  364.    wt: 3:   19 Dividing Fractions How TO
  365.    wt: 3:   13 Fraction Comparison Algebraic View
  366.    wt: 3:   12 Fraction Comparison
  367.    wt: 3:   11 Simplification an Algebraic View
  368.    wt: 3:   6 Multiplication Algebraically Take II
  369.    wt: 3:   A Associative Law Theorectical Note
  370.    wt: 3:   13 Subtraction with Additive Inverse
  371.    wt: 3:   11 Adding Integers Formulas and Examples
  372.    wt: 3:   10 Integer Multiplication Formulas
  373.    wt: 3:   21 Remainder Arithmetic Modulo 3
  374.    wt: 3:   19 Remainder Arithmetic Rule of 9 for checking sums III
  375.    wt: 3:   17 Remainder Arithmetic Rule of 9 for checking sums I
  376.    wt: 3:   16 Remainder Arithmetic Modulo 9 Example 2
  377.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  378.    wt: 3:   8 Remainder Arithmetic Morulo 5 Examples II
  379.    wt: 3:   5 Remainder Arithmetic Modulo 5
  380.    wt: 3:   4 Remainder Arithmetic Modulo 10 in general
  381.    wt: 3:   3 Remainder Arithmetic Modulos 10 more still
  382.    wt: 3:   1 Remainder Arithmetic Modulo 10
  383.    wt: 3:   19 video Prime Factorization Unique
  384.    wt: 3:   18 video Count Factors given Prime Factorization
  385.    wt: 3:   17 Identify and Count Factors using Primes
  386.    wt: 3:   16 video Factors of 980 using prime
  387.    wt: 3:   11 Efficient Square Rule Use
  388.    wt: 3:   9 video Prime Factorization upto 19 squared
  389.    wt: 3:   8 video Prime Factorization upto 19
  390.    wt: 3:   7 Calculator Usage Notes and Cautions
  391.    wt: 3:   5 Prime Factorization and a Square Rule
  392.    wt: 3:   4 video Prime Factorization Introduction
  393.    wt: 3:   3 video Primes and Composites from 9 times table
  394.    wt: 3:   1 video how Products are bigger than factor
  395.    wt: 3:   10 Names for Big Numbers and Powers of Ten Expansion
  396.    wt: 3:   9 Place Value Review Decimal form of Avogrados number included
  397.    wt: 3:   8 Review Lesson 1 2 4 and 6 All in One
  398.    wt: 3:   1 Place Value in Three Digit Whole Numbers
  399.    wt: 3:   Quick history of numbers and algebra
  400.    wt: 3:   Formula Evaluation how to show work
  401.    wt: 3:   Practical Methods Ends and Values for Arithmetic
  402.    wt: 3:   38 Formulas and derivatives for powers and roots
  403.    wt: 3:   28 Chain Rule Preparation for a Proof
  404.    wt: 3:   20 Chain Rule for Pulley Systems
  405.    wt: 3:   10 Power rule for negative integers
  406.    wt: 3:   4 Sum Rule
  407.    wt: 3:   3 Motivation for Limit Definition Take 2
  408.    wt: 3:   2 Motivation for Limit Definition Take 1
  409.    wt: 3:   2 Algebraic codification
  410.    wt: 3:   Postscript B Mathematics Education References
  411.    wt: 3:   Postscript A Three Remarks
  412.    wt: 3:   Chapter 9 The Two Ends
  413.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  414.    wt: 3:   Chapter 3 Algebra Difficulties
  415.    wt: 3:   Foreword
  416.    wt: 3:   Postscript D Reflections on Law of the Excluded Middle
  417.    wt: 3:   Postscript C Consistency as a Tool for Reason
  418.    wt: 3:   Chapter 24 Direct and Indirect Reason
  419.    wt: 3:   Chapter 23 Truth Tables
  420.    wt: 3:   Chapter 21 Occurrence Tables
  421.    wt: 3:   Chapter 20 Shorthand Symbols as Pronouns
  422.    wt: 3:   Chapter 19 What is in chapters 20 to 24
  423.    wt: 3:   Chapter 12 Islands and Divisions of Knowledge
  424.    wt: 3:   Chapter 2 Skill Development
  425.    wt: 3:   Three Remarks
  426.    wt: 3:   Chapter 2 Why Sets
  427.    wt: 3:   Primary and Secondary Skills and Practices with Take Home Value
  428.    wt: 3:   7 Games and Activities for Instruction
  429.    wt: 3:   6 Measuring via counting or arithmetic the role of fractions
  430.    wt: 3:   Helping the Blind in Logic and Mathematics
  431.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  432.    wt: 3:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  433.    wt: 3:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  434.    wt: 2:   Appendix 2 primary school Arithmetic 01
  435.    wt: 2:   Appendix 1 primary and preschool mathematic
  436.    wt: 2:   G LAMP Introduction Problem Solving Skills
  437.    wt: 2:   E LAMP Introduction Modern Mathematics
  438.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  439.    wt: 2:   Skills Chapter 5 Calculus
  440.    wt: 2:   Skills Chapter 4 Logic
  441.    wt: 2:   Ramblings Extrinsic numbers theory
  442.    wt: 2:   Ramblings Introduction Algebra Essay
  443.    wt: 2:   Skills Chapter 1 Arithmetic
  444.    wt: 2:   Skills Chapter 0 Introduction
  445.    wt: 2:   10 statistics
  446.    wt: 2:   9 combinatorics probability sets
  447.    wt: 2:   8 analytic geometry etc
  448.    wt: 2:   7 logic review and decimals an odd combination
  449.    wt: 2:   6 polynomials etc
  450.    wt: 2:   5 logarithms and exponentials etc
  451.    wt: 2:   3 Euclidean Geometry Leanly
  452.    wt: 2:   1 arithmetic with unsigned numbers
  453.    wt: 2:   What is POMME
  454.    wt: 2:   Teach the teachers plus goals
  455.    wt: 2:   permissions for teachers
  456.    wt: 2:   activities for students
  457.    wt: 2:   About site lesson plans
  458.    wt: 2:   key notes and themes
  459.    wt: 2:   Mathematics Education Professors
  460.    wt: 2:   learning takes time
  461.    wt: 2:   mathematics in context
  462.    wt: 2:   Postscript 2007 01 10
  463.    wt: 2:   Education Reform Inconsistencies
  464.    wt: 2:   Maps Plans Drawings
  465.    wt: 2:   how letters appear
  466.    wt: 2:   teaching tips
  467.    wt: 2:   What to Tell Students
  468.    wt: 2:   05 13 OldSiteEntrancePage
  469.    wt: 2:   standards for course material
  470.    wt: 2:   Theory of Knowledge
  471.    wt: 2:   mathematics instruction in general
  472.    wt: 2:   Education in mathematics science and technology
  473.    wt: 2:   Four ways to improve education reform
  474.    wt: 2:   Leaner mathematics curriculum
  475.    wt: 2:   education an empirical art
  476.    wt: 2:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  477.    wt: 2:   2 Energy Power Heat07
  478.    wt: 2:   C Electromotive force conventional current02
  479.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  480.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  481.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  482.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  483.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  484.    wt: 2:   Ages 9 to 10
  485.    wt: 2:   Ages 8 to 9
  486.    wt: 2:   Ages 7 to 8
  487.    wt: 2:   Ages 6 to 7
  488.    wt: 2:   Ages 4 plus to 5 plus
  489.    wt: 2:   Ages 3 plus to 4 plus
  490.    wt: 2:   17 Function maxima minima and their location
  491.    wt: 2:   9 Set theory term relation possible origins
  492.    wt: 2:   6 Set Existence Formation and Notation
  493.    wt: 2:   4 Function notation in and beyond mathematics
  494.    wt: 2:   3 Formula or function graphing exercise
  495.    wt: 2:   9 quadratics physical and further context
  496.    wt: 2:   8 quadratics backward use of various formulas
  497.    wt: 2:   7 quadratic formulla derivation
  498.    wt: 2:   5 quadratics completing the square
  499.    wt: 2:   2 quadratics graphing in general
  500.    wt: 2:   8 Notes for instructors or tutors
  501.    wt: 2:   2 Column Multiplication Method
  502.    wt: 2:   Rewriting algebraic substitution as function substitutions
  503.    wt: 2:   2 Signed Coordinates
  504.    wt: 2:   4 graphing y=Asin(x c)
  505.    wt: 2:   3 graphing y=f(x c) plus K
  506.    wt: 2:   1 graphing y=f(x a)
  507.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  508.    wt: 2:   C Straight Lines Slope from Coordinates
  509.    wt: 2:   B Straight Line Slope Scaling Properties More
  510.    wt: 2:   A Straight Line Slope Scaling Properties
  511.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  512.    wt: 2:   12 Straight Lines Graphing mx plus b
  513.    wt: 2:   11 Straight Lines Graphing y=mx
  514.    wt: 2:   7 Tangent Function is odd on this domain
  515.    wt: 2:   5 Tangent Function Graph
  516.    wt: 2:   4 Tangent Function Properties
  517.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  518.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  519.    wt: 2:   28 Expressing products of sines cosines as sums
  520.    wt: 2:   27 Logarithmic use of products of sines and cosines
  521.    wt: 2:   20 sine and cosine Double Angle Formulas
  522.    wt: 2:   17E Trig Formulas for dot and cross Products
  523.    wt: 2:   17D cis formulas for sine cosines and tangent
  524.    wt: 2:   12 Graph of tangent function for one period
  525.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  526.    wt: 2:   21 Logarithms Powers and Exponentials
  527.    wt: 2:   20 N th Roots of Complex Numbers
  528.    wt: 2:   13 Trig Formulas for dot and cross Products
  529.    wt: 2:   2 Complex Numbers made easier we hope
  530.    wt: 2:   5 Trigonometric Ratios For Tangent and Special Triangles
  531.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  532.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  533.    wt: 2:   12 Triangles Similarity More Problems
  534.    wt: 2:   2 Similarity By Design
  535.    wt: 2:   12 Links Lessons elsewhere
  536.    wt: 2:   12 Spatial Coordinates
  537.    wt: 2:   2 Cartesian Coordinates with signs
  538.    wt: 2:   musings do not puiblish real numbers
  539.    wt: 2:   A Modular and Remainder Arithmetic
  540.    wt: 2:   A Signed Number Arithmetic Review
  541.    wt: 2:   9 Division with Digits after Decimal Point
  542.    wt: 2:   8 Division and Mulplication of Compound Fractions
  543.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  544.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  545.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  546.    wt: 2:   4 Location of Point in Decimal Addition
  547.    wt: 2:   3 Location of Point in Decimal Multiplication
  548.    wt: 2:   1 Fractions with Finite Decimal Expansions
  549.    wt: 2:   E Long Division Methods more
  550.    wt: 2:   D Long Division Methods
  551.    wt: 2:   B Decimal Comparison and Subtraction
  552.    wt: 2:   A Decimal Addition Columm Methods
  553.    wt: 2:   8 Column Multiplication Methods in General
  554.    wt: 2:   7 Decimals Multiplication Methods Examples
  555.    wt: 2:   6 Equations and Systems Equivalent or Implied
  556.    wt: 2:   4 Subtraction and Division Axioms
  557.    wt: 2:   1 Equivalent Computation Rules
  558.    wt: 2:   5 Greater More Less Than Signs in General
  559.    wt: 2:   4 Comparison of Negative Numbers
  560.    wt: 2:   3 More and Less Than with Unlike Signs
  561.    wt: 2:   1 Real Numbers Comparison
  562.    wt: 2:   7 Real Numbers as Line Cordinates
  563.    wt: 2:   6 Unsigned Real Numbers
  564.    wt: 2:   5 Rational Numbers More
  565.    wt: 2:   4 Rational Numbers
  566.    wt: 2:   3 Fractions
  567.    wt: 2:   1 Whole and Natural Numbers
  568.    wt: 2:   5 Independent versus Dependent Variables
  569.    wt: 2:   4 Changing Letters
  570.    wt: 2:   More Exercises
  571.    wt: 2:   Simple Exercises
  572.    wt: 2:   4 GE III Animated Examples
  573.    wt: 2:   3 Gaussian Elimination 3 unknowns first example
  574.    wt: 2:   3 GE III Equation Addition and Multiplication
  575.    wt: 2:   1 GE Substitution four examples
  576.    wt: 2:   Skill Development Notes
  577.    wt: 2:   10 One Example
  578.    wt: 2:   8 One Example
  579.    wt: 2:   7 Two Examples
  580.    wt: 2:   4 Two Examples
  581.    wt: 2:   3 Two Examples
  582.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  583.    wt: 2:   9 Sets in Probability and Statistics
  584.    wt: 2:   8 Sets of Numbers
  585.    wt: 2:   7 Cautious or Safe Set Construction
  586.    wt: 2:   6 Power Set Notation
  587.    wt: 2:   5 Product Builder Notation
  588.    wt: 2:   4 Subset Builder Notation
  589.    wt: 2:   3 Counting with Sets etc
  590.    wt: 2:   1 Finite Sets
  591.    wt: 2:   5 Talking about Numbers and Quantities
  592.    wt: 2:   3 Adding Words To Arithmetic
  593.    wt: 2:   About Folder Contents
  594.    wt: 2:   5 Square Roots with primes more still
  595.    wt: 2:   4 Square Roots with primes more
  596.    wt: 2:   3 Properties of Square Roots with example
  597.    wt: 2:   1 Squares and Square Roots Introduction
  598.    wt: 2:   17 GCD LCM of 85 and 60 via Prime
  599.    wt: 2:   14 GCD of 650 110 via Primes LCM via Product Rule
  600.    wt: 2:   13 GCD from given Prime Factorization
  601.    wt: 2:   9 GCD of 360 110 via Primes and Euclid Algorithm
  602.    wt: 2:   7 GCD and LCM from prime factorization
  603.    wt: 2:   6 GCD from Prime
  604.    wt: 2:   5 Common Divisors 60 45 via Prime
  605.    wt: 2:   4 LCM of 8 and 10 via Prime
  606.    wt: 2:   LCM 60 45 Avoid List Method Use Prime
  607.    wt: 2:   1 Least Common Multiples LCM Introduction
  608.    wt: 2:   5 Counting with Tables Trees Product Rule Take II
  609.    wt: 2:   4 Counting with Trees Product Rule Take I
  610.    wt: 2:   3 Counting with Tables and Trees II
  611.    wt: 2:   1 Counting and Counting Methods I
  612.    wt: 2:   11 What are real lengths and numbers
  613.    wt: 2:   10 dividing signed numbers
  614.    wt: 2:   9 subtracting signed numbers
  615.    wt: 2:   8 multiplying signed numbers
  616.    wt: 2:   7 negative and additive inverse
  617.    wt: 2:   6 adding signed numbers
  618.    wt: 2:   5 lengths and signs of numbers
  619.    wt: 2:   7 Converting or Changing Units
  620.    wt: 2:   6 Simplification of Fractions with Units
  621.    wt: 2:   4 Fractions with Units
  622.    wt: 2:   3 Multiplying Units and Numbers
  623.    wt: 2:   1 Addition and Subtraction with Units
  624.    wt: 2:   B Fractions and Two Term Ratios
  625.    wt: 2:   A Similarities between Fractions and Two Term Ratios
  626.    wt: 2:   18 Efficient Ways to Multiply
  627.    wt: 2:   17 Efficient Ways to Add and Subtract
  628.    wt: 2:   16 Addition Subtraction Comparision Compared
  629.    wt: 2:   15 Adding and Subtracting with Unlike Denominators
  630.    wt: 2:   14 Adding and Subtracting with Like Denominators
  631.    wt: 2:   10 Simplification of Fractions and Mixed Numerals
  632.    wt: 2:   9 Improper Fractions and Mixed Numbers
  633.    wt: 2:   8 Numerals Fractionals Quantals Take II
  634.    wt: 2:   7 Numerals Fractionals Quantals
  635.    wt: 2:   6 Multiplication of Mixed Numbers
  636.    wt: 2:   5 Equivalent Fractions
  637.    wt: 2:   4 Fraction Multiplication
  638.    wt: 2:   3 Unit fraction of a fraction
  639.    wt: 2:   1 What is a fraction Take II
  640.    wt: 2:   1 What is a fraction
  641.    wt: 2:   Fraction Operations by Raising Terms A Simple Innovation
  642.    wt: 2:   D Remainders Modulo 11 Pair Rule
  643.    wt: 2:   C Divisibility by 11 Integer Recognition Method
  644.    wt: 2:   B Integer Long Division Multiple Choices
  645.    wt: 2:   9 Multiplying Integers
  646.    wt: 2:   8 Multiplication by Signed Numbers Integers
  647.    wt: 2:   7 Multiplication by Signs
  648.    wt: 2:   6 Multiplication by Natural Numbers
  649.    wt: 2:   5 Zero Movement and Additive Inverses
  650.    wt: 2:   4 Adding Movements wiht opposite directions
  651.    wt: 2:   3 Adding Movements with same direction
  652.    wt: 2:   1 Integers as Coordinates
  653.    wt: 2:   A Decimals Modular and Remainder Arithmetic
  654.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  655.    wt: 2:   14 Remainder Arithmetic Modulo 9 Example
  656.    wt: 2:   13 Remainder Arithmetic Modulo 5 Example
  657.    wt: 2:   11 Remainder Arithmetic Long Division by 5 Quickly more
  658.    wt: 2:   10 Remainder Arithmetic Long Division by 5 Quickly
  659.    wt: 2:   9 Remainder Arithmetic Divisibility by 5
  660.    wt: 2:   7 Remainder Arithmetic Modulo 5 Examples I
  661.    wt: 2:   6 Remainder Arithmetic Modulo 5 Propertie
  662.    wt: 2:   11 Place Value SI Standard International way
  663.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  664.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  665.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  666.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  667.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  668.    wt: 2:   Exact Arithmetic Wholes and Fractions
  669.    wt: 2:   Expression Evaluation how to show work
  670.    wt: 2:   About folder contents
  671.    wt: 2:   012 Division of Time Intervals by Time Intervals
  672.    wt: 2:   2 Time and Date Matters in School
  673.    wt: 2:   1 Intro of Kids To Time Date Skills
  674.    wt: 2:   Example 2 volume of a cone
  675.    wt: 2:   Example 1. Area Between x and x squared
  676.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  677.    wt: 2:   Example 3
  678.    wt: 2:   Example 2
  679.    wt: 2:   Area Between Curves Lesson Take 2
  680.    wt: 2:   A Chain Rule Real Player video examples
  681.    wt: 2:   30Chain Rule A Proof
  682.    wt: 2:   29 Chain Rule Optional Reading
  683.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  684.    wt: 2:   26 Chain Rule Recognising outer inner functions
  685.    wt: 2:   25 Chain Rule Animated Examples Continued
  686.    wt: 2:   24 Chain Rule Animated Examples
  687.    wt: 2:   23 Chain Rule in general
  688.    wt: 2:   19 Chain Rule for linear functions
  689.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  690.    wt: 2:   14 sine and cosine derivatives 2nd step
  691.    wt: 2:   12 Quotient rule examples
  692.    wt: 2:   11 Quotient rule
  693.    wt: 2:   9 Reciprocal rule
  694.    wt: 2:   8 Differentiation of polynomials
  695.    wt: 2:   7 Animated Differentiation Examples
  696.    wt: 2:   6 Power rule from product rule
  697.    wt: 2:   5 Product Rule
  698.    wt: 2:   11 Limits at infinity Three Examples
  699.    wt: 2:   3 Decimal insights for limits continuity convergence
  700.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  701.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  702.    wt: 2:   F.4 Finite Covering Theorem
  703.    wt: 2:   F.2 Closed Range Theorem
  704.    wt: 2:   E2 Algebraic Properties of Limits
  705.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  706.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  707.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  708.    wt: 2:   Chapter 23 Links To Trigonometry
  709.    wt: 2:   Chapter 21 Arrow Addition
  710.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  711.    wt: 2:   Chapter 12. Units and Slopes
  712.    wt: 2:   Chapter 2. Slopes and Ski Trails
  713.    wt: 2:   Annotated Links to Material Elsehwere
  714.    wt: 2:   Chapter 11 Elementary Instruction
  715.    wt: 2:   Chapter 10 Transition
  716.    wt: 2:   Chapter 8 Modern Instruction
  717.    wt: 2:   Chapter 7 Two Treatments of Geometry
  718.    wt: 2:   Chapter 5 Four References
  719.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  720.    wt: 2:   Chapter 1 Introduction
  721.    wt: 2:   Postscript B More on Story Telling and Reason
  722.    wt: 2:   Postscript A Story Telling
  723.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  724.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  725.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  726.    wt: 2:   Foreword
  727.    wt: 2:   R Why Learn Mathematics Skills
  728.    wt: 2:   N Mathematics Prepare for College Studies
  729.    wt: 2:   L Skills with take home value
  730.    wt: 2:   G. Written work formats for developing and showing skill
  731.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  732.    wt: 2:   Chapter 6 More Algebra and Geometry
  733.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  734.    wt: 2:   Chapter 3 Algebra Starter Lessons
  735.    wt: 2:   5 Interpreting and Drawing Maps and Plans.
  736.    wt: 2:   4 Money Matters Saving Earning Buying Selling and Budgets
  737.    wt: 2:   3 Telling Tracking Time Temporal and More Place Sense
  738.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  739.    wt: 2:   1 From Number Recognition and Counting to Arithmetic A
  740.    wt: 2:   Mathematics Education References
  741.    wt: 2:   Mathematics Education References
  742.    wt: 2:   Ends Values Methods For Skill Development Framework Prequel
  743.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  744.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  745.    wt: 2:   More Algebra and Slope based Calculus Preview
  746.    wt: 2:   Systematic Algebra Skill Development Missing Links
  747.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  748.    wt: 2:   The Math Forum and Site Content
  749.    wt: 1:   K LAMP Musings Science Education
  750.    wt: 1:   J LAMP Introduction Extrinsic Origins
  751.    wt: 1:   I LAMP Introduction Study Habits
  752.    wt: 1:   H LAMP Introduction Instructional Concepts
  753.    wt: 1:   F LAMP Introduction Prerequisites
  754.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  755.    wt: 1:   A Introduction Objectives
  756.    wt: 1:   which way to go
  757.    wt: 1:   website reviews
  758.    wt: 1:   Math Ed if it must be short make it lean effective
  759.    wt: 1:   links Education Resources online
  760.    wt: 1:   site origins
  761.    wt: 1:   site eurekas
  762.    wt: 1:   teacher certification
  763.    wt: 1:   modern education
  764.    wt: 1:   grouping students according to ability
  765.    wt: 1:   what should be learnt and When
  766.    wt: 1:   five decades make a difference
  767.    wt: 1:   Operational Viewpoint to Value
  768.    wt: 1:   Different Kinds of Reasoning in maths
  769.    wt: 1:   cultivating intelligence
  770.    wt: 1:   How to be a better instructor
  771.    wt: 1:   Motivation and Context Problem
  772.    wt: 1:   chapitre 12 00 les iles et division
  773.    wt: 1:   chapitre 07 01 principle D induction mathematique
  774.    wt: 1:   chapitre 04 02 Deuxieme enigme
  775.    wt: 1:   chapitre 02 00 La Communication des idees
  776.    wt: 1:   4 Energy Power Heat09
  777.    wt: 1:   3 Energy Power Heat08
  778.    wt: 1:   1 Energy Power Heat06
  779.    wt: 1:   E Energy Power05
  780.    wt: 1:   D Energy Power04
  781.    wt: 1:   C Energy Power03
  782.    wt: 1:   A Energy Power01
  783.    wt: 1:   D Wire Resistance Calculation02
  784.    wt: 1:   B Wire Resistance Qualitative02
  785.    wt: 1:   3 Like resistors in parallel
  786.    wt: 1:   2 Unlike resistors in parallel01
  787.    wt: 1:   H Series Circuit02
  788.    wt: 1:   B Electromotive force conventional current01
  789.    wt: 1:   18 Primary School Mathematics
  790.    wt: 1:   17 Math Booklets for children and young teenagers
  791.    wt: 1:   16 Secondary Mathematics Tips
  792.    wt: 1:   15 Counting For Parents
  793.    wt: 1:   10 Ends values for work study instruction
  794.    wt: 1:   8 The Effect of Negative Remarks
  795.    wt: 1:   5 Patience Please for Yourself and Your Charges
  796.    wt: 1:   4 Learning Takes Time and Effort
  797.    wt: 1:   3 Preparing for Science Studies
  798.    wt: 1:   1 Speaking Skills
  799.    wt: 1:   sign monoticity analysis example 4
  800.    wt: 1:   sign monoticity analysis example 3
  801.    wt: 1:   sign monoticity analysis example 1
  802.    wt: 1:   19 Horizontal line rule and method
  803.    wt: 1:   18 Vertical Line Rule and Method
  804.    wt: 1:   16 Increasing or decreasing on intervals
  805.    wt: 1:   15 Sign analysis of functions
  806.    wt: 1:   14 Surjections Injections Bijections
  807.    wt: 1:   13 From one to one to many to one
  808.    wt: 1:   11 Function Domain Range Source and Targets
  809.    wt: 1:   10 Interval Notation
  810.    wt: 1:   8 Set view of relations and functions
  811.    wt: 1:   7 Functions with finite domains
  812.    wt: 1:   1 Geometric Introduction of Function Notation
  813.    wt: 1:   Introduction Reading Guide
  814.    wt: 1:   A Quadratics Summary
  815.    wt: 1:   10 quadratic exercises
  816.    wt: 1:   6 quadratics numerical approach
  817.    wt: 1:   4 quadratics difference of two squares
  818.    wt: 1:   3 quadratics factoring by inspection
  819.    wt: 1:   1 quadratics graphing exercises
  820.    wt: 1:   Quadratics in 10 steps
  821.    wt: 1:   7 Links Lessons Elsewhere
  822.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  823.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  824.    wt: 1:   4 Polynomials Long division linear divisor
  825.    wt: 1:   3 Polynomials Multiplication Addition
  826.    wt: 1:   1 Polynomials Distributive Law
  827.    wt: 1:   16 cotangent function Definition Graph and Inverse
  828.    wt: 1:   15 cosecant function Definition Graph and Inverse
  829.    wt: 1:   14 secant function Definition Graph and Inverse
  830.    wt: 1:   13 cosecant function Definition Graph and Inverse
  831.    wt: 1:   11 arctan left inverse of tangent Graph
  832.    wt: 1:   10 arctan left inverse of tangent Definition
  833.    wt: 1:   9 motivation for name arcsin
  834.    wt: 1:   4 possible motivation for term arccos
  835.    wt: 1:   2 cosine function more properties
  836.    wt: 1:   9 Summary Degrees to Radians and back
  837.    wt: 1:   2 Radian Measure Numerical Value of one degree
  838.    wt: 1:   Parallel Lines and Interior Angles
  839.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  840.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  841.    wt: 1:   Straight Lines ASA Intersection Study More
  842.    wt: 1:   14 Straight Lines Equations General Case
  843.    wt: 1:   10 Straight Lines through Origin Equations More
  844.    wt: 1:   9 Straight Lines through Origin Equations
  845.    wt: 1:   1 Straight Lines Slope Concept
  846.    wt: 1:   17 tangent function angle sum formulas
  847.    wt: 1:   35 sines and cosines of 2A 3A 4A 5A
  848.    wt: 1:   34 sines and cosines of 2A 3A 4A 5A
  849.    wt: 1:   32 seven rows of pascals triangle
  850.    wt: 1:   30 unit circle calculation of six trigonometric functions
  851.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  852.    wt: 1:   17G Pythagorean Theorem Converse
  853.    wt: 1:   17C sine and cosine double triple angle formulas
  854.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  855.    wt: 1:   17A The complex number valued trig function cis
  856.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  857.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  858.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  859.    wt: 1:   2 Quadrant I reference Angles
  860.    wt: 1:   15 Pythagorean Theorem Converse
  861.    wt: 1:   11 sine and cosine double triple angle formulas
  862.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  863.    wt: 1:   9 The complex number valued trig function cis
  864.    wt: 1:   5 An Easy Proof of the Distributive Law
  865.    wt: 1:   8 Triangles Cascade Problem Solving
  866.    wt: 1:   7 Trignometric Ratios Unit Circle
  867.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  868.    wt: 1:   3 Trigonometric Ratios sine and cosine
  869.    wt: 1:   Why Trigonometry the whyslopes view
  870.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  871.    wt: 1:   4 Similarity Definition with Coordinate
  872.    wt: 1:   8 Mid Point Formula
  873.    wt: 1:   5 Algebraic View of Slopes
  874.    wt: 1:   3 Slope product for perpendicular lines
  875.    wt: 1:   1 Numerical view of lines and their equations
  876.    wt: 1:   13 Pythagorean spatial distance formulas
  877.    wt: 1:   10 Pythagorean plane distance formula
  878.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  879.    wt: 1:   2 Measuring Area Directly
  880.    wt: 1:   016 Numbering Occidental Calendar Days
  881.    wt: 1:   015 School and work day counting tables
  882.    wt: 1:   014 Counting Days with Calendars
  883.    wt: 1:   013 Travel Time Tables
  884.    wt: 1:   011 Division of Time Intervals By Numbers
  885.    wt: 1:   010 Repeated Addition of Time Intervals
  886.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  887.    wt: 1:   8 Addition of Time Intervals via subtotaling
  888.    wt: 1:   7 Addition of Time Intervals
  889.    wt: 1:   6 How long is a million seconds
  890.    wt: 1:   5 Conversion Arithmetic
  891.    wt: 1:   4 Mixing and Changing Units of Time
  892.    wt: 1:   3 Units and Lengths of Time
  893.    wt: 1:   Example 1 volume of a pyramid
  894.    wt: 1:   Volume of Solid by Cross Sections Lesson
  895.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  896.    wt: 1:   Example 4 with x function of y
  897.    wt: 1:   Example 1
  898.    wt: 1:   Area Between Curves Lesson Take 1
  899.    wt: 1:   Summary
  900.    wt: 1:   2 Indefinite Integrals Exercises
  901.    wt: 1:   1 Chain Rule in Reverse Integration Method
  902.    wt: 1:   2 Second derivative test prequel
  903.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  904.    wt: 1:   36 Cube root derivative animated
  905.    wt: 1:   34 Derivative of exponential function
  906.    wt: 1:   33 Chain Rule Real Player video examples
  907.    wt: 1:   31 Derivatives of inverse functions
  908.    wt: 1:   18 Chain Rule Introduction
  909.    wt: 1:   17 Derivatives of quotients of sine and cosine
  910.    wt: 1:   15 sine and cosine derivatives 3rd step
  911.    wt: 1:   13 sine and cosine derivatives 1st step
  912.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  913.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  914.    wt: 1:   10 Three one sided limits with infinite values
  915.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  916.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  917.    wt: 1:   G.3 Constant Difference Theorem Proof
  918.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  919.    wt: 1:   F.5b Extreme Value Theorem
  920.    wt: 1:   F.5a Equicontinuity Theorems
  921.    wt: 1:   F.3 Intermediate Value Theorem
  922.    wt: 1:   D2 Limits of Monotone Sequences
  923.    wt: 1:   B3 Bolzano Weierstrass Theorem
  924.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  925.    wt: 1:   PostScript For and Against Decimal Perspectives
  926.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  927.    wt: 1:   Fall 1983 Calculus Appetizer
  928.    wt: 1:   Foreword
  929.    wt: 1:   Chapter 18 Sense and Knowledge
  930.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  931.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  932.    wt: 1:   Chapter 15 Objective Processes
  933.    wt: 1:   Chapter 11 Accidental Patterns
  934.    wt: 1:   Chapter 10 Responsibility
  935.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  936.    wt: 1:   Chapter 8 Change of Language
  937.    wt: 1:   Chapter 7 Longer Chains of Reason
  938.    wt: 1:   Chapter 6 Chains of Reason
  939.    wt: 1:   Chapter 5 Deception
  940.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  941.    wt: 1:   Chapter 1 Introduction
  942.    wt: 1:   S Adding words to algebra
  943.    wt: 1:   O On Learning Mathematics and Science
  944.    wt: 1:   I. Logic and language skills
  945.    wt: 1:   F. The student teacher tutor feedback loop
  946.    wt: 1:   B. Domino effect of errors
  947.    wt: 1:   How to Build Skills and Confidence
  948.    wt: 1:   Chapter 8 Skipped Topics and Why
  949.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  950.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  951.    wt: 1:   Chapter 1 Arithmetic
  952.    wt: 1:   Implementation Notes
  953.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  954.    wt: 1:   Which Way To Go
  955.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  956.    wt: 10:   Chapter 22. Geometric Sums and Sequences
  957.    wt: 10:   Chapter 8 Three Skills For Algebra

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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