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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61 matches:

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

Web Page Search

681 matches:

  1.    wt: 5:   6 Infinite Decimals Ending in 9 repeating
  2.    wt: 5:   5 Interpreting and Drawing Maps and Plans.
  3.    wt: 5:   4 Money Matters Saving Earning Buying Selling and Budgets
  4.    wt: 4:   Ramblings Extrinsic numbers theory
  5.    wt: 4:   fairness and inductive principles for instruction
  6.    wt: 4:   2 Reading and Writing Skills
  7.    wt: 4:   16 Increasing or decreasing on intervals
  8.    wt: 4:   7 arcsin left inverse of sine Definition
  9.    wt: 4:   Parallel Lines and Alternating Corresponding Angles
  10.    wt: 4:   13 Straight Lines Finding Equations from 2 points
  11.    wt: 4:   14 cosine even and sine and tangent are odd
  12.    wt: 4:   6 Intersection of lines by solving linear systems
  13.    wt: 4:   13 Arrows and Vectors in a Plane
  14.    wt: 4:   2 Combing Counts Addition Skills and Principles
  15.    wt: 4:   15 Adding and Subtracting with Unlike Denominators
  16.    wt: 4:   14 Adding and Subtracting with Like Denominators
  17.    wt: 4:   6. Counting and adding units and mixed units
  18.    wt: 4:   Helping the Blind in Logic and Mathematics
  19.    wt: 3:   J LAMP Introduction Extrinsic Origins
  20.    wt: 3:   G LAMP Introduction Problem Solving Skills
  21.    wt: 3:   Different Kinds of Reasoning in maths
  22.    wt: 3:   Home Tutoring and Home Schooling
  23.    wt: 3:   6 Discipline Who is in Charge Conserving Authority
  24.    wt: 3:   26 Function definitions done and coming
  25.    wt: 3:   24 Monotoncity Injectivity and Inverse Functions
  26.    wt: 3:   20 Interchanging coordinates a reflection
  27.    wt: 3:   16 cotangent function Definition Graph and Inverse
  28.    wt: 3:   15 cosecant function Definition Graph and Inverse
  29.    wt: 3:   14 secant function Definition Graph and Inverse
  30.    wt: 3:   13 cosecant function Definition Graph and Inverse
  31.    wt: 3:   8 arcsin left inverse of sine Graph
  32.    wt: 3:   3 Left Inverse of cosine arccos definition
  33.    wt: 3:   Parallel Lines and Interior Angles
  34.    wt: 3:   Straight Lines Instersection Solving Equations
  35.    wt: 3:   3 Straight Lines Slope as Tangent of Inclination Angle
  36.    wt: 3:   35 sines and cosines of 2A 3A 4A 5A
  37.    wt: 3:   34 sines and cosines of 2A 3A 4A 5A
  38.    wt: 3:   33 sines and cosines of 2A 3A 4A 5A
  39.    wt: 3:   28 Expressing products of sines cosines as sums
  40.    wt: 3:   27 Logarithmic use of products of sines and cosines
  41.    wt: 3:   26 Formulas for products of sines and cosines
  42.    wt: 3:   23 sine and cosine of 180 plus 22.5 degrees
  43.    wt: 3:   21 sine and cosine Half Angle Formulas
  44.    wt: 3:   20 sine and cosine Double Angle Formulas
  45.    wt: 3:   19 Pythagorean Identity For sine and cosine functions
  46.    wt: 3:   17D cis formulas for sine cosines and tangent
  47.    wt: 3:   17C sine and cosine double triple angle formulas
  48.    wt: 3:   10 Graphs of sines and cosines many periods
  49.    wt: 3:   9 Graphs of sine and cosine over one period
  50.    wt: 3:   7 period of sine and cosine
  51.    wt: 3:   6 sines and cosines for reference angle 30 degrees
  52.    wt: 3:   5 sines and cosines for reference angle 60 degrees
  53.    wt: 3:   4 sines and cosines for reference angle 45 degrees
  54.    wt: 3:   3 sines and cosines for reference angle 90 degrees
  55.    wt: 3:   12 cis formulas for sine cosines and tangent
  56.    wt: 3:   11 sine and cosine double triple angle formulas
  57.    wt: 3:   3 Trigonometric Ratios sine and cosine
  58.    wt: 3:   9 Midpoint Coordinates Half Endpoint Sum
  59.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  60.    wt: 3:   12 Real Numbers Line Signed Coordinates
  61.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  62.    wt: 3:   3 Multiplicative Counting Skills Principles
  63.    wt: 3:   1 The Counting Origins of Numbers
  64.    wt: 3:   8 Coordinates for Maps and Planes
  65.    wt: 3:   7 Real Numbers as Line Cordinates
  66.    wt: 3:   1 Written work formats for developing and showing skill
  67.    wt: 3:   5 Talking about Numbers and Quantities
  68.    wt: 3:   1 Counting and Counting Methods I
  69.    wt: 3:   3 signed coordinates for maps and planes
  70.    wt: 3:   2 signed and unsigned numbers as coordinates
  71.    wt: 3:   3 Multiplying Units and Numbers
  72.    wt: 3:   11 Adding Integers Formulas and Examples
  73.    wt: 3:   7 Adding decimal fractions using decimal point
  74.    wt: 3:   4 Mixing and Changing Units of Time
  75.    wt: 3:   2 Indefinite Integrals Exercises
  76.    wt: 3:   1 Chain Rule in Reverse Integration Method
  77.    wt: 3:   27 Chain Rule sinusoidal outer inner functions EGS
  78.    wt: 3:   26 Chain Rule Recognising outer inner functions
  79.    wt: 3:   17 Derivatives of quotients of sine and cosine
  80.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  81.    wt: 3:   15 sine and cosine derivatives 3rd step
  82.    wt: 3:   14 sine and cosine derivatives 2nd step
  83.    wt: 3:   13 sine and cosine derivatives 1st step
  84.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  85.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  86.    wt: 3:   Chapter 10 Describing and Changing Calculations
  87.    wt: 3:   Chapter 16 Origins and Limitations of Rules and Patterns
  88.    wt: 3:   N Improving Marks on Tests and Finals
  89.    wt: 3:   H more Routine to non routine problem solving
  90.    wt: 3:   G. Written work formats for developing and showing skill
  91.    wt: 3:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  92.    wt: 3:   Chapter 4 Logic for Reading Writing and Geometry etc
  93.    wt: 3:   Primary and Secondary Skills and Practices with Take Home Value
  94.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  95.    wt: 3:   2 Identifying Size and Position Place and Spatial Sense
  96.    wt: 3:   1 From Number Recognition and Counting to Arithmetic B
  97.    wt: 3:   1 From Number Recognition and Counting to Arithmetic A
  98.    wt: 3:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  99.    wt: 3:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  100.    wt: 2:   H LAMP Introduction Instructional Concepts
  101.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  102.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  103.    wt: 2:   Ramblings Introduction Algebra Essay
  104.    wt: 2:   Skills Chapter 0 Introduction
  105.    wt: 2:   7 logic review and decimals an odd combination
  106.    wt: 2:   links Education Resources online
  107.    wt: 2:   grouping students according to ability
  108.    wt: 2:   teaching tutoring algebraic reason
  109.    wt: 2:   mathematics instruction in general
  110.    wt: 2:   Education in mathematics science and technology
  111.    wt: 2:   three kinds of reason in mathematics
  112.    wt: 2:   cultivating intelligence
  113.    wt: 2:   Prequel In For A Penny In For A Pound
  114.    wt: 2:   chapitre 07 01 principle D induction mathematique
  115.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  116.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  117.    wt: 2:   4 Learning Takes Time and Effort
  118.    wt: 2:   1 Speaking Skills
  119.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  120.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  121.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  122.    wt: 2:   19 Horizontal line rule and method
  123.    wt: 2:   18 Vertical Line Rule and Method
  124.    wt: 2:   17 Function maxima minima and their location
  125.    wt: 2:   11 Function Domain Range Source and Targets
  126.    wt: 2:   9 Set theory term relation possible origins
  127.    wt: 2:   7 Functions with finite domains
  128.    wt: 2:   4 Function notation in and beyond mathematics
  129.    wt: 2:   Introduction Reading Guide
  130.    wt: 2:   3 quadratics factoring by inspection
  131.    wt: 2:   2 quadratics graphing in general
  132.    wt: 2:   11 Growth and Decay in Biology
  133.    wt: 2:   10 arctan left inverse of tangent Definition
  134.    wt: 2:   5 Swapping Coordinates is a reflection
  135.    wt: 2:   1 Degrees and Radians Introduction
  136.    wt: 2:   13 Velocity Vectors in Physics
  137.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  138.    wt: 2:   6 Vectors with Coordinates
  139.    wt: 2:   Vector and Complex Number Applet
  140.    wt: 2:   4 graphing y=Asin(x c)
  141.    wt: 2:   2 Graphing y=Af(x) Vertical Scaling
  142.    wt: 2:   Parallel Lines and Parallel Transversals
  143.    wt: 2:   Construction Methods and Criteria for Isometric and Similar Triangles
  144.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  145.    wt: 2:   Straight Lines ASA Intersection Study More
  146.    wt: 2:   Straight Lines ASA Intersection Study
  147.    wt: 2:   Straight Lines Intersection of
  148.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  149.    wt: 2:   C Straight Lines Slope from Coordinates
  150.    wt: 2:   B Straight Line Slope Scaling Properties More
  151.    wt: 2:   A Straight Line Slope Scaling Properties
  152.    wt: 2:   12 Straight Lines Graphing mx plus b
  153.    wt: 2:   11 Straight Lines Graphing y=mx
  154.    wt: 2:   10 Straight Lines through Origin Equations More
  155.    wt: 2:   9 Straight Lines through Origin Equations
  156.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  157.    wt: 2:   18 sum of sinusoidal waves as a single wave
  158.    wt: 2:   17B sine cosine Angle Sum Formulas via cis
  159.    wt: 2:   15 sine cosine Complementary Angle Relations
  160.    wt: 2:   11 tangent function undefined when terminal side vertical
  161.    wt: 2:   16 References and Originality Question
  162.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  163.    wt: 2:   4 Similarity Definition with Coordinate
  164.    wt: 2:   10 Midpoint of [a b] and [b a]
  165.    wt: 2:   2 point slope equation for a line
  166.    wt: 2:   1 Numerical view of lines and their equations
  167.    wt: 2:   8 Distance Between Points on a Line
  168.    wt: 2:   4 Polar Coordinates to and from
  169.    wt: 2:   10 Dropping a perpendicular to line
  170.    wt: 2:   1 Initial Concepts and Terms
  171.    wt: 2:   3 Lengths and Areas on Maps and Plans
  172.    wt: 2:   musings do not puiblish real numbers
  173.    wt: 2:   A Modular and Remainder Arithmetic
  174.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  175.    wt: 2:   11 Signed Number Addition and Addition Properties
  176.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  177.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  178.    wt: 2:   4 Location of Point in Decimal Addition
  179.    wt: 2:   3 Location of Point in Decimal Multiplication
  180.    wt: 2:   2 Counting Digits in Decimal Multiplication
  181.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  182.    wt: 2:   6 Compound Interest Forward and Backwards
  183.    wt: 2:   2 More and Less Than for Counts and Measures
  184.    wt: 2:   12 Real Number Additive Inverses or Negatives
  185.    wt: 2:   10 Real Number Lengths and Signs
  186.    wt: 2:   9 Coordinates for Regions in Space
  187.    wt: 2:   1 Whole and Natural Numbers
  188.    wt: 2:   13 Naming Identifying Formulas with Words
  189.    wt: 2:   7 Compound Interest Formula Introduction
  190.    wt: 2:   9 Sets in Probability and Statistics
  191.    wt: 2:   4 A Brief Story of numbers and algebra
  192.    wt: 2:   1 More and Less Than for Counts and Measures
  193.    wt: 2:   1 Squares and Square Roots Introduction
  194.    wt: 2:   3 Counting with Tables and Trees II
  195.    wt: 2:   2 Counting with Tables and Trees I
  196.    wt: 2:   11 What are real lengths and numbers
  197.    wt: 2:   10 dividing signed numbers
  198.    wt: 2:   9 subtracting signed numbers
  199.    wt: 2:   8 multiplying signed numbers
  200.    wt: 2:   7 negative and additive inverse
  201.    wt: 2:   6 adding signed numbers
  202.    wt: 2:   5 lengths and signs of numbers
  203.    wt: 2:   4 signed coordinates for regions in space
  204.    wt: 2:   7 Converting or Changing Units
  205.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  206.    wt: 2:   9 Improper Fractions and Mixed Numbers
  207.    wt: 2:   Fraction Operations by Raising Terms A Simple Innovation
  208.    wt: 2:   12 Adding Integers More Examples
  209.    wt: 2:   9 Multiplying Integers
  210.    wt: 2:   8 Multiplication by Signed Numbers Integers
  211.    wt: 2:   5 Zero Movement and Additive Inverses
  212.    wt: 2:   1 Integers as Coordinates
  213.    wt: 2:   A Decimals Modular and Remainder Arithmetic
  214.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  215.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  216.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  217.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  218.    wt: 2:   4 Remainder Arithmetic Modulo 10 in general
  219.    wt: 2:   17 Identify and Count Factors using Primes
  220.    wt: 2:   12 LCD GCD and LCM using Primes
  221.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  222.    wt: 2:   8 What skills and work habits to require
  223.    wt: 2:   1. Explaining Addition Table
  224.    wt: 2:   11 Place Value SI Standard International way
  225.    wt: 2:   10 Names for Big Numbers and Powers of Ten Expansion
  226.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  227.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  228.    wt: 2:   1 Place Value in Three Digit Whole Numbers
  229.    wt: 2:   Quick history of numbers and algebra
  230.    wt: 2:   016 Numbering Occidental Calendar Days
  231.    wt: 2:   015 School and work day counting tables
  232.    wt: 2:   012 Division of Time Intervals by Time Intervals
  233.    wt: 2:   011 Division of Time Intervals By Numbers
  234.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  235.    wt: 2:   8 Addition of Time Intervals via subtotaling
  236.    wt: 2:   2 Time and Date Matters in School
  237.    wt: 2:   1 Intro of Kids To Time Date Skills
  238.    wt: 2:   4 Definite Integrals Evaluation Exercises
  239.    wt: 2:   38 Formulas and derivatives for powers and roots
  240.    wt: 2:   29 Chain Rule Optional Reading
  241.    wt: 2:   25 Chain Rule Animated Examples Continued
  242.    wt: 2:   23 Chain Rule in general
  243.    wt: 2:   19 Chain Rule for linear functions
  244.    wt: 2:   18 Chain Rule Introduction
  245.    wt: 2:   11 Limits at infinity Three Examples
  246.    wt: 2:   10 Three one sided limits with infinite values
  247.    wt: 2:   9 Limits Continuity and Composition
  248.    wt: 2:   6 Continuity at a point
  249.    wt: 2:   3 Decimal insights for limits continuity convergence
  250.    wt: 2:   Postscript One Sided and Intermediate Value Theorems
  251.    wt: 2:   G.4 Lipschitz Continuity implies EquiContinuity
  252.    wt: 2:   F.4 Finite Covering Theorem
  253.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  254.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  255.    wt: 2:   PostScript For and Against Decimal Perspectives
  256.    wt: 2:   Appendix D. What to do in School and Why
  257.    wt: 2:   Chapter 31 Direct and Indirect Reason
  258.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  259.    wt: 2:   Chapter 16. Painless Theorem Proving
  260.    wt: 2:   Chapter 15. Solving Linear Equations
  261.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  262.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  263.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  264.    wt: 2:   Chapter 2 For and Against Mathematics
  265.    wt: 2:   Postscript B More on Story Telling and Reason
  266.    wt: 2:   Chapter 24 Direct and Indirect Reason
  267.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  268.    wt: 2:   Chapter 12 Islands and Divisions of Knowledge
  269.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  270.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  271.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  272.    wt: 2:   O On Learning Mathematics and Science
  273.    wt: 2:   J. More on written work and showing skill
  274.    wt: 2:   I. Logic and language skills
  275.    wt: 2:   H Jigsaw puzzles and problem solving
  276.    wt: 2:   C. Domino effect of being careful
  277.    wt: 2:   How to Build Skills and Confidence
  278.    wt: 2:   7 Games and Activities for Instruction
  279.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  280.    wt: 2:   Systematic Algebra Skill Development Missing Links
  281.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  282.    wt: 1:   Appendix 1 primary and preschool mathematic
  283.    wt: 1:   K LAMP Musings Science Education
  284.    wt: 1:   I LAMP Introduction Study Habits
  285.    wt: 1:   F LAMP Introduction Prerequisites
  286.    wt: 1:   E LAMP Introduction Modern Mathematics
  287.    wt: 1:   A Introduction Objectives
  288.    wt: 1:   Skills Chapter 5 Calculus
  289.    wt: 1:   Skills Chapter 4 Logic
  290.    wt: 1:   Skills Chapter 3 Algebra
  291.    wt: 1:   Skills Chapter 2 Geometry
  292.    wt: 1:   Skills Chapter 1 Arithmetic
  293.    wt: 1:   9 combinatorics probability sets
  294.    wt: 1:   5 logarithms and exponentials etc
  295.    wt: 1:   2 arithmetic with signed numbers
  296.    wt: 1:   1 arithmetic with unsigned numbers
  297.    wt: 1:   site origins
  298.    wt: 1:   key notes and themes
  299.    wt: 1:   learning takes time
  300.    wt: 1:   what should be learnt and When
  301.    wt: 1:   mathematics in context
  302.    wt: 1:   Education Reform Inconsistencies
  303.    wt: 1:   Maps Plans Drawings
  304.    wt: 1:   teaching tips
  305.    wt: 1:   Lessening Algebra Difficulties
  306.    wt: 1:   standards for course material
  307.    wt: 1:   Operational Viewpoint to Value
  308.    wt: 1:   formal or informal peer review
  309.    wt: 1:   Theory of Knowledge
  310.    wt: 1:   How to be a better instructor
  311.    wt: 1:   Motivation and Context Problem
  312.    wt: 1:   words for mathematics instructor
  313.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  314.    wt: 1:   chapitre 06 00 Chaines de la raison
  315.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  316.    wt: 1:   chapitre 01 00 Introduction
  317.    wt: 1:   deux definitions pour variable
  318.    wt: 1:   3 Like resistors in parallel
  319.    wt: 1:   2 Unlike resistors in parallel01
  320.    wt: 1:   1 Like resistors in series
  321.    wt: 1:   F Unlike Resistors in Series
  322.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  323.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  324.    wt: 1:   24 Standards For Skill Develoment Take II
  325.    wt: 1:   24 Standards For Skill Develoment
  326.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  327.    wt: 1:   17 Math Booklets for children and young teenagers
  328.    wt: 1:   15 Counting For Parents
  329.    wt: 1:   14 Multiplication and Times Tables
  330.    wt: 1:   13 Addition and Addition Tables
  331.    wt: 1:   12 Goals and Objectives For Mathematics
  332.    wt: 1:   11 Help and Defend Your Child or Teens Education
  333.    wt: 1:   10 Ends values for work study instruction
  334.    wt: 1:   9 Streaming by Student Cooperation
  335.    wt: 1:   5 Patience Please for Yourself and Your Charges
  336.    wt: 1:   3 Preparing for Science Studies
  337.    wt: 1:   Ages 12 to 14 Skills with take home value
  338.    wt: 1:   23 Inverse Functions
  339.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  340.    wt: 1:   14 Surjections Injections Bijections
  341.    wt: 1:   12 Function Domain Recognition Exercises
  342.    wt: 1:   10 Interval Notation
  343.    wt: 1:   8 Set view of relations and functions
  344.    wt: 1:   6 Set Existence Formation and Notation
  345.    wt: 1:   3 Formula or function graphing exercise
  346.    wt: 1:   1 Geometric Introduction of Function Notation
  347.    wt: 1:   9 quadratics physical and further context
  348.    wt: 1:   5 quadratics completing the square
  349.    wt: 1:   1 quadratics graphing exercises
  350.    wt: 1:   Quadratics in 10 steps
  351.    wt: 1:   10 Exponential Growth and Decay Models
  352.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  353.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  354.    wt: 1:   8 Notes for instructors or tutors
  355.    wt: 1:   7 Links Lessons Elsewhere
  356.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  357.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  358.    wt: 1:   4 Polynomials Long division linear divisor
  359.    wt: 1:   Rewriting algebraic substitution as function substitutions
  360.    wt: 1:   11 arctan left inverse of tangent Graph
  361.    wt: 1:   9 motivation for name arcsin
  362.    wt: 1:   2 cosine function more properties
  363.    wt: 1:   1 cosine function properties
  364.    wt: 1:   9 Summary Degrees to Radians and back
  365.    wt: 1:   7 Radian Measures in special Triangles
  366.    wt: 1:   A Global Time and Navigation
  367.    wt: 1:   15 Dot and Cross Product
  368.    wt: 1:   9 Head to Tail Coordinate View
  369.    wt: 1:   8 Parallel Vectors
  370.    wt: 1:   3 Navigation with Arrows or Vectors
  371.    wt: 1:   2 Signed Coordinates
  372.    wt: 1:   1 Unsigned Coordinates
  373.    wt: 1:   3 graphing y=f(x c) plus K
  374.    wt: 1:   1 graphing y=f(x a)
  375.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  376.    wt: 1:   14 Straight Lines Equations General Case
  377.    wt: 1:   8 Straight Lines Equation for vertical
  378.    wt: 1:   7 Tangent Function is odd on this domain
  379.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  380.    wt: 1:   1 Straight Lines Slope Concept
  381.    wt: 1:   29 secant cosecant and cotangent for acute angles
  382.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  383.    wt: 1:   17F Law of cosines
  384.    wt: 1:   17E Trig Formulas for dot and cross Products
  385.    wt: 1:   17A The complex number valued trig function cis
  386.    wt: 1:   1 Unit Points Reflections Rotations
  387.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  388.    wt: 1:   21 Logarithms Powers and Exponentials
  389.    wt: 1:   20 N th Roots of Complex Numbers
  390.    wt: 1:   14 Law of cosines
  391.    wt: 1:   13 Trig Formulas for dot and cross Products
  392.    wt: 1:   9 The complex number valued trig function cis
  393.    wt: 1:   6 Field Properties of Complex Number
  394.    wt: 1:   2 Complex Numbers made easier we hope
  395.    wt: 1:   1 Rectangular Polar Coordinates Review
  396.    wt: 1:   Appetizer A Complex Number Applet
  397.    wt: 1:   8 Triangles Cascade Problem Solving
  398.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  399.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  400.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  401.    wt: 1:   Right Triangle and Unit Circle Trigonometry
  402.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  403.    wt: 1:   11 Triangle Similarity Missing Side Problem
  404.    wt: 1:   8 Similarity of Triangles and Polygons
  405.    wt: 1:   6 Geometric Diagrams in Class
  406.    wt: 1:   5 Similarity of Circles Squares and Rectangles
  407.    wt: 1:   3 Similarity by Design with coordinates
  408.    wt: 1:   12 Links Lessons elsewhere
  409.    wt: 1:   8 Mid Point Formula
  410.    wt: 1:   7 Exercises to test skill and concept mastery
  411.    wt: 1:   4 Equations for lines three forms
  412.    wt: 1:   3 Slope product for perpendicular lines
  413.    wt: 1:   What is and is not here
  414.    wt: 1:   12 Spatial Coordinates
  415.    wt: 1:   11 Triangle Inequality
  416.    wt: 1:   10 Pythagorean plane distance formula
  417.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  418.    wt: 1:   7 Complex Numbers Appetizer
  419.    wt: 1:   6 Polar Multiplication and Rotation
  420.    wt: 1:   5 Cartesian Addition and Translation
  421.    wt: 1:   3 Rectangular Coordinates Review
  422.    wt: 1:   2 Cartesian Coordinates with signs
  423.    wt: 1:   1 Cartesian Coordinates sans signs
  424.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  425.    wt: 1:   PS H Distributive Law For Complex Numbers
  426.    wt: 1:   PS E Multiplication with Polar Coordinates
  427.    wt: 1:   PS D Addition with Cartesian Coordinates
  428.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  429.    wt: 1:   16 Angles Subtended By Chords and Diameters
  430.    wt: 1:   14 Parallel Lines Postulate
  431.    wt: 1:   6 Ruler and compass Angle Bisection
  432.    wt: 1:   6 Figuring with Maps Not to Scale
  433.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  434.    wt: 1:   2 Measuring Area Directly
  435.    wt: 1:   A Signed Number Arithmetic Review
  436.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  437.    wt: 1:   22 Multiplication of Signed Numbers
  438.    wt: 1:   21 Addition of Multiples of a Single Vector
  439.    wt: 1:   19 Signed Multiples of Vectors
  440.    wt: 1:   15 Head to Tails in place Addition Associative
  441.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  442.    wt: 1:   9 Division with Digits after Decimal Point
  443.    wt: 1:   8 Division and Mulplication of Compound Fractions
  444.    wt: 1:   1 Fractions with Finite Decimal Expansions
  445.    wt: 1:   B Decimal Comparison and Subtraction
  446.    wt: 1:   8 Column Multiplication Methods in General
  447.    wt: 1:   5 Distributive Law for Whole Numbers
  448.    wt: 1:   4 Commutative Law Groups Counting Form
  449.    wt: 1:   3 Inequalities Algebraically
  450.    wt: 1:   5 Proportionality in Equivalent Fractions
  451.    wt: 1:   4 Rates Ratios and Proporitionality
  452.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  453.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  454.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  455.    wt: 1:   3 Linear Equation Literal Solution More
  456.    wt: 1:   2 Linear Equation Literal Solution
  457.    wt: 1:   1 Changing Calculations
  458.    wt: 1:   6 Equations and Systems Equivalent or Implied
  459.    wt: 1:   5 Equality in Algebra
  460.    wt: 1:   4 Subtraction and Division Axioms
  461.    wt: 1:   2 Addition and Multiplication Axioms
  462.    wt: 1:   5 Greater More Less Than Signs in General
  463.    wt: 1:   4 Comparison of Negative Numbers
  464.    wt: 1:   3 More and Less Than with Unlike Signs
  465.    wt: 1:   1 Real Numbers Comparison
  466.    wt: 1:   16 Real Numbers Comparison
  467.    wt: 1:   15 Real Number Division
  468.    wt: 1:   14 Real Number Multiplication
  469.    wt: 1:   13 Real Number Subtraction
  470.    wt: 1:   11 Real Number Addition
  471.    wt: 1:   6 Unsigned Real Numbers
  472.    wt: 1:   5 Rational Numbers More
  473.    wt: 1:   4 Rational Numbers
  474.    wt: 1:   2 Integers
  475.    wt: 1:   5 Independent versus Dependent Variables
  476.    wt: 1:   4 Changing Letters
  477.    wt: 1:   3 Geometric Formulas and Function Notation
  478.    wt: 1:   1 Formulas Dependence and Function Notation
  479.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  480.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  481.    wt: 1:   3 GE III Equation Addition and Multiplication
  482.    wt: 1:   4 Solving a triangular system exercise
  483.    wt: 1:   3 Solving triangular system example
  484.    wt: 1:   5 Algebraic Solutions Introduction
  485.    wt: 1:   Using Letters for Physical Quantities
  486.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  487.    wt: 1:   8 Compound Interest Formula Evaluation
  488.    wt: 1:   8 Sets of Numbers
  489.    wt: 1:   3 Counting with Sets etc
  490.    wt: 1:   1 Finite Sets
  491.    wt: 1:   3 Adding Words To Arithmetic
  492.    wt: 1:   1 Three Skills For Algebra
  493.    wt: 1:   4 Greater More Less Than Signs in General
  494.    wt: 1:   3 Comparison of Negative Numbers
  495.    wt: 1:   2 More and Less Than with Unlike Signs
  496.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  497.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  498.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  499.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  500.    wt: 1:   7 GCD and LCM from prime factorization
  501.    wt: 1:   4 LCM of 8 and 10 via Prime
  502.    wt: 1:   2 Least Common Multiple LCM intro via list method
  503.    wt: 1:   1 Least Common Multiples LCM Introduction
  504.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  505.    wt: 1:   4 Counting with Trees Product Rule Take I
  506.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  507.    wt: 1:   2 Equality and Units
  508.    wt: 1:   1 Addition and Subtraction with Units
  509.    wt: 1:   B Fractions and Two Term Ratios
  510.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  511.    wt: 1:   21 Working With Signs
  512.    wt: 1:   21 Reciprocals for Fractions and Wholes
  513.    wt: 1:   20 Dividing Fractions the Why
  514.    wt: 1:   19 Dividing Fractions How TO
  515.    wt: 1:   17 Efficient Ways to Add and Subtract
  516.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  517.    wt: 1:   6 Multiplication of Mixed Numbers
  518.    wt: 1:   D Remainders Modulo 11 Pair Rule
  519.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  520.    wt: 1:   B Integer Long Division Multiple Choices
  521.    wt: 1:   13 Subtraction with Additive Inverse
  522.    wt: 1:   10 Integer Multiplication Formulas
  523.    wt: 1:   6 Multiplication by Natural Numbers
  524.    wt: 1:   4 Adding Movements wiht opposite directions
  525.    wt: 1:   3 Adding Movements with same direction
  526.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  527.    wt: 1:   23 Remainder Arithmetic Modulo 2
  528.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  529.    wt: 1:   21 Remainder Arithmetic Modulo 3
  530.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  531.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  532.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  533.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  534.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  535.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  536.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  537.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  538.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  539.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  540.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  541.    wt: 1:   5 Remainder Arithmetic Modulo 5
  542.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  543.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  544.    wt: 1:   1 Remainder Arithmetic Modulo 10
  545.    wt: 1:   16 video Factors of 980 using prime
  546.    wt: 1:   15 video Factors of 20 using Prime Factorization
  547.    wt: 1:   13 video Factors of 24 using prime
  548.    wt: 1:   7 Calculator Usage Notes and Cautions
  549.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  550.    wt: 1:   5 Prime Factorization and a Square Rule
  551.    wt: 1:   4 video Prime Factorization Introduction
  552.    wt: 1:   3 video Primes and Composites from 9 times table
  553.    wt: 1:   2 Prime and Composites less than 16
  554.    wt: 1:   Division with Counts and Length
  555.    wt: 1:   Long Division forwards and backwards Example 3
  556.    wt: 1:   Long Division forwards and backwards Example 2
  557.    wt: 1:   Long Division forwards and backwards Example 1
  558.    wt: 1:   11 Another Single Digit Divisor Example
  559.    wt: 1:   10 Division by Five Long and Short Ways
  560.    wt: 1:   8 Correcting the Mistake
  561.    wt: 1:   7 Long Divison Mistake Catching
  562.    wt: 1:   5 Long Division Include Zeroes or not
  563.    wt: 1:   3 Division Single Digit Divisor Example
  564.    wt: 1:   2 Division with Single Digit Divisors
  565.    wt: 1:   C Counting Areas with Powers of Ten
  566.    wt: 1:   4 Two and Three Digit Multipliers
  567.    wt: 1:   Video Power Notation in Decimal Expansion
  568.    wt: 1:   9 22 Minute Subtraction Review Video
  569.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  570.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  571.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  572.    wt: 1:   2 Decimal Counting Practices
  573.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  574.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  575.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  576.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  577.    wt: 1:   Exact Arithmetic Wholes and Fractions
  578.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  579.    wt: 1:   014 Counting Days with Calendars
  580.    wt: 1:   010 Repeated Addition of Time Intervals
  581.    wt: 1:   7 Addition of Time Intervals
  582.    wt: 1:   3 Units and Lengths of Time
  583.    wt: 1:   Example 1. Area Between x and x squared
  584.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  585.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  586.    wt: 1:   A Related Material in Volume 3
  587.    wt: 1:   3 Two Chain Rule Method Exercises
  588.    wt: 1:   A Related lessons in Volume 3
  589.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  590.    wt: 1:   A Chain Rule Real Player video examples
  591.    wt: 1:   33 Chain Rule Real Player video examples
  592.    wt: 1:   31 Derivatives of inverse functions
  593.    wt: 1:   30Chain Rule A Proof
  594.    wt: 1:   28 Chain Rule Preparation for a Proof
  595.    wt: 1:   24 Chain Rule Animated Examples
  596.    wt: 1:   22 Chain Rule for polynomials
  597.    wt: 1:   21 Chain Rule for powers
  598.    wt: 1:   20 Chain Rule for Pulley Systems
  599.    wt: 1:   10 Power rule for negative integers
  600.    wt: 1:   3 Motivation for Limit Definition Take 2
  601.    wt: 1:   2 Motivation for Limit Definition Take 1
  602.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  603.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  604.    wt: 1:   5 Jumps and absence of unlimited error control
  605.    wt: 1:   1 Numerical introduction
  606.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  607.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  608.    wt: 1:   F.5a Equicontinuity Theorems
  609.    wt: 1:   F.3 Intermediate Value Theorem
  610.    wt: 1:   F.1 What Functions are Continuous
  611.    wt: 1:   E1 Error Control Inequalities
  612.    wt: 1:   C Triangle Inequalities
  613.    wt: 1:   A1. Introduction
  614.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  615.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  616.    wt: 1:   Chapter 23 Links To Trigonometry
  617.    wt: 1:   Chapter 22 Complex Numbers
  618.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  619.    wt: 1:   Chapter 18. Slopes Areas Integration
  620.    wt: 1:   Chapter 12. Units and Slopes
  621.    wt: 1:   Chapter 11. Graphing Slope versus Position
  622.    wt: 1:   Chapter 10 Slopes and Units
  623.    wt: 1:   Chapter 9 About First Courses in Calculus
  624.    wt: 1:   Chapter 8. Slope Interpretation
  625.    wt: 1:   Chapter 7 Slopes and Velocity
  626.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  627.    wt: 1:   Chapter 2. Slopes and Ski Trails
  628.    wt: 1:   Chapter 1.Introduction
  629.    wt: 1:   Appendix E. How To Study Mathematics and Why
  630.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  631.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  632.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  633.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  634.    wt: 1:   Chapter 25. Mathematical Induction Examples
  635.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  636.    wt: 1:   Chapter 21. Third Reading Guide
  637.    wt: 1:   Chapter 20. Degrees and Radians
  638.    wt: 1:   Chapter 19. Functions and Sets
  639.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  640.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  641.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  642.    wt: 1:   Chapter 13. Second Reading Guide
  643.    wt: 1:   Chapter 12. Shorthand Usage Guide
  644.    wt: 1:   Chapter 11. Why Shorthand
  645.    wt: 1:   Chapter 8 Three Skills For Algebra
  646.    wt: 1:   Chapter 4 Longer Chains of Reason
  647.    wt: 1:   Chapter 3 Chains of Reason
  648.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  649.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  650.    wt: 1:   Annotated Links to Material Elsehwere
  651.    wt: 1:   Chapter 11 Elementary Instruction
  652.    wt: 1:   Chapter 8 Modern Instruction
  653.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  654.    wt: 1:   Chapter 1 Introduction
  655.    wt: 1:   Postscript A Story Telling
  656.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  657.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  658.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  659.    wt: 1:   Chapter 18 Sense and Knowledge
  660.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  661.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  662.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  663.    wt: 1:   Chapter 7 Longer Chains of Reason
  664.    wt: 1:   Chapter 6 Chains of Reason
  665.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  666.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  667.    wt: 1:   Chapter 1 Introduction
  668.    wt: 1:   S Adding words to algebra
  669.    wt: 1:   R Why Learn Mathematics Skills
  670.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  671.    wt: 1:   L Skills with take home value
  672.    wt: 1:   E. When and how to correct errors
  673.    wt: 1:   B. Domino effect of errors
  674.    wt: 1:   Chapter 8 Skipped Topics and Why
  675.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  676.    wt: 1:   Chapter 6 More Algebra and Geometry
  677.    wt: 1:   More Algebra and Slope based Calculus Preview
  678.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  679.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  680.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  681.    wt: 1:   The Math Forum and Site Content

Extended Search

968 matches:

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

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

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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