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

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

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

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

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

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

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

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  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 3:   10 Intersecting Straight Lines and Transversals/
  3.    wt: 3:   A Origins of Counting and Figuring Methods/
  4.    wt: 3:   Step 4 Gaussian Elimination/
  5.    wt: 3:   Step 3 Easy systems in 2 or more unknowns/
  6.    wt: 3:   B Decimal Comparing and Subtracting Methods/
  7.    wt: 3:   A Decimal Counting and Adding Methods/
  8.    wt: 2:   12 Function Translating and Rescaling/
  9.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  10.    wt: 2:   Step 1 Stick diagram and fractions/
  11.    wt: 2:   3 Solving Linear Equations/
  12.    wt: 2:   1 Working With Sets/
  13.    wt: 2:   9 Combinatorics Trees Tables and Products/
  14.    wt: 2:   5 Integers/
  15.    wt: 2:   4 Remainder Arithmetic and Divisibility/
  16.    wt: 2:   Volume 3 Why Slopes A Calculus Intro Etc/
  17.    wt: 1:   LAMP Lean Applied Mathematics Program/
  18.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  19.    wt: 1:   Mathematics Education Essays/
  20.    wt: 1:   Volume 1A Regles et modeles/
  21.    wt: 1:   Mathematics Skills Year by Year/
  22.    wt: 1:   15 Arc or Inverse Trigonometric Function/
  23.    wt: 1:   11 Parallel Straight Lines and Transversals/
  24.    wt: 1:   9 Lines and Slopes Take 2 with tangent function/
  25.    wt: 1:   4 Lines and Slopes Take 1/
  26.    wt: 1:   3 Cartesian and Polar Coordinates/
  27.    wt: 1:   2 Euclidean Geometry Constructions Theory extras/
  28.    wt: 1:   B Real Numbers Extrinsic Development/
  29.    wt: 1:   10 Examples of Algebraic Reasoning/
  30.    wt: 1:   8 Unifying Theme For Algebra/
  31.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  32.    wt: 1:   12 Comparison of Unsigned and Signed Numbers/
  33.    wt: 1:   11 Squares and Square Roots/
  34.    wt: 1:   10 LCM GCD and Euclid GCD Algorithm/
  35.    wt: 1:   8 Arithmetic with Signed Numbers/
  36.    wt: 1:   7 Arithmetic and Fractions with Units/
  37.    wt: 1:   6 Fractions and Ratios/
  38.    wt: 1:   3 Prime Factorization Skills/
  39.    wt: 1:   D Decimal Long Division Methods/
  40.    wt: 1:   C Decimal Multiplication Methods/
  41.    wt: 1:   2 Arithmetic with Decimals/
  42.    wt: 1:   1 Decimal Place Value/
  43.    wt: 1:   Arithmetic and Number Theory Skills/
  44.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  45.    wt: 1:   5 Lessons on Integration/
  46.    wt: 1:   4 Lessons on Using Derivatives/
  47.    wt: 1:   38 Lessons on Calculating Derivatives/
  48.    wt: 1:   13 Lessons on Limits and Continuity/
  49.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  50.    wt: 1:   Volume 2 Three Skills For Algebra/
  51.    wt: 1:   Volume 1A Pattern Based Reason/
  52.    wt: 1:   Volume 1 Elements of Reason/
  53.    wt: 1:   Resources and Reciprocal Links/
  54.    wt: 1:   Mathematics 506 Lessons/
  55.    wt: 1:   Secondary Mathematics A Practical Approach/
  56.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  57.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

536 matches:

  1.    wt: 5:   6 Infinite Decimals Ending in 9 repeating
  2.    wt: 4:   16 Increasing or decreasing on intervals
  3.    wt: 4:   7 arcsin left inverse of sine Definition
  4.    wt: 4:   13 Straight Lines Finding Equations from 2 points
  5.    wt: 4:   6 Intersection of lines by solving linear systems
  6.    wt: 4:   4 Money Matters Saving Earning Buying Selling and Budgets
  7.    wt: 4:   Helping the Blind in Logic and Mathematics
  8.    wt: 3:   J LAMP Introduction Extrinsic Origins
  9.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  10.    wt: 3:   Ramblings Extrinsic numbers theory
  11.    wt: 3:   mathematics instruction in general
  12.    wt: 3:   Different Kinds of Reasoning in maths
  13.    wt: 3:   three kinds of reason in mathematics
  14.    wt: 3:   fairness and inductive principles for instruction
  15.    wt: 3:   6 Discipline Who is in Charge Conserving Authority
  16.    wt: 3:   20 Interchanging coordinates a reflection
  17.    wt: 3:   9 Set theory term relation possible origins
  18.    wt: 3:   8 arcsin left inverse of sine Graph
  19.    wt: 3:   3 Left Inverse of cosine arccos definition
  20.    wt: 3:   Parallel Lines and Alternating Corresponding Angles
  21.    wt: 3:   Straight Lines Instersection Solving Equations
  22.    wt: 3:   3 Straight Lines Slope as Tangent of Inclination Angle
  23.    wt: 3:   28 Expressing products of sines cosines as sums
  24.    wt: 3:   9 Midpoint Coordinates Half Endpoint Sum
  25.    wt: 3:   15 Adding and Subtracting with Unlike Denominators
  26.    wt: 3:   14 Adding and Subtracting with Like Denominators
  27.    wt: 3:   7 Adding decimal fractions using decimal point
  28.    wt: 3:   2 Indefinite Integrals Exercises
  29.    wt: 3:   1 Chain Rule in Reverse Integration Method
  30.    wt: 3:   27 Chain Rule sinusoidal outer inner functions EGS
  31.    wt: 3:   26 Chain Rule Recognising outer inner functions
  32.    wt: 3:   H more Routine to non routine problem solving
  33.    wt: 3:   5 Interpreting and Drawing Maps and Plans.
  34.    wt: 2:   H LAMP Introduction Instructional Concepts
  35.    wt: 2:   G LAMP Introduction Problem Solving Skills
  36.    wt: 2:   E LAMP Introduction Modern Mathematics
  37.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  38.    wt: 2:   Ramblings Introduction Algebra Essay
  39.    wt: 2:   9 combinatorics probability sets
  40.    wt: 2:   links Education Resources online
  41.    wt: 2:   grouping students according to ability
  42.    wt: 2:   mathematics in context
  43.    wt: 2:   mathematics curriculum shifts
  44.    wt: 2:   teaching tutoring algebraic reason
  45.    wt: 2:   04 29 New Mathematics Curriculum
  46.    wt: 2:   Education in mathematics science and technology
  47.    wt: 2:   cultivating intelligence
  48.    wt: 2:   need for a mixed mathematics curriculum
  49.    wt: 2:   Leaner mathematics curriculum
  50.    wt: 2:   Prequel In For A Penny In For A Pound
  51.    wt: 2:   words for mathematics instructor
  52.    wt: 2:   chapitre 07 01 principle D induction mathematique
  53.    wt: 2:   Home Tutoring and Home Schooling
  54.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  55.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  56.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  57.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  58.    wt: 2:   2 Reading and Writing Skills
  59.    wt: 2:   26 Function definitions done and coming
  60.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  61.    wt: 2:   7 Functions with finite domains
  62.    wt: 2:   4 Function notation in and beyond mathematics
  63.    wt: 2:   Introduction Reading Guide
  64.    wt: 2:   3 quadratics factoring by inspection
  65.    wt: 2:   2 quadratics graphing in general
  66.    wt: 2:   8 Notes for instructors or tutors
  67.    wt: 2:   16 cotangent function Definition Graph and Inverse
  68.    wt: 2:   15 cosecant function Definition Graph and Inverse
  69.    wt: 2:   14 secant function Definition Graph and Inverse
  70.    wt: 2:   13 cosecant function Definition Graph and Inverse
  71.    wt: 2:   10 arctan left inverse of tangent Definition
  72.    wt: 2:   5 Swapping Coordinates is a reflection
  73.    wt: 2:   4 graphing y=Asin(x c)
  74.    wt: 2:   2 Graphing y=Af(x) Vertical Scaling
  75.    wt: 2:   Parallel Lines and Interior Angles
  76.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  77.    wt: 2:   Straight Lines ASA Intersection Study More
  78.    wt: 2:   Straight Lines ASA Intersection Study
  79.    wt: 2:   Straight Lines Intersection of
  80.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  81.    wt: 2:   C Straight Lines Slope from Coordinates
  82.    wt: 2:   B Straight Line Slope Scaling Properties More
  83.    wt: 2:   A Straight Line Slope Scaling Properties
  84.    wt: 2:   12 Straight Lines Graphing mx plus b
  85.    wt: 2:   11 Straight Lines Graphing y=mx
  86.    wt: 2:   10 Straight Lines through Origin Equations More
  87.    wt: 2:   9 Straight Lines through Origin Equations
  88.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  89.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  90.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  91.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  92.    wt: 2:   27 Logarithmic use of products of sines and cosines
  93.    wt: 2:   26 Formulas for products of sines and cosines
  94.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  95.    wt: 2:   21 sine and cosine Half Angle Formulas
  96.    wt: 2:   20 sine and cosine Double Angle Formulas
  97.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  98.    wt: 2:   18 sum of sinusoidal waves as a single wave
  99.    wt: 2:   17D cis formulas for sine cosines and tangent
  100.    wt: 2:   17C sine and cosine double triple angle formulas
  101.    wt: 2:   17B sine cosine Angle Sum Formulas via cis
  102.    wt: 2:   15 sine cosine Complementary Angle Relations
  103.    wt: 2:   14 cosine even and sine and tangent are odd
  104.    wt: 2:   11 tangent function undefined when terminal side vertical
  105.    wt: 2:   10 Graphs of sines and cosines many periods
  106.    wt: 2:   9 Graphs of sine and cosine over one period
  107.    wt: 2:   7 period of sine and cosine
  108.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  109.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  110.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  111.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  112.    wt: 2:   12 cis formulas for sine cosines and tangent
  113.    wt: 2:   11 sine and cosine double triple angle formulas
  114.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  115.    wt: 2:   3 Trigonometric Ratios sine and cosine
  116.    wt: 2:   4 Similarity Definition with Coordinate
  117.    wt: 2:   2 point slope equation for a line
  118.    wt: 2:   8 Distance Between Points on a Line
  119.    wt: 2:   10 Dropping a perpendicular to line
  120.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  121.    wt: 2:   12 Real Numbers Line Signed Coordinates
  122.    wt: 2:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  123.    wt: 2:   7 Arithmetic with Infinite Decimal Expansions
  124.    wt: 2:   5 Fractions with Infinite Decimal Expansions
  125.    wt: 2:   4 Location of Point in Decimal Addition
  126.    wt: 2:   3 Location of Point in Decimal Multiplication
  127.    wt: 2:   2 Counting Digits in Decimal Multiplication
  128.    wt: 2:   3 Multiplicative Counting Skills Principles
  129.    wt: 2:   2 Combing Counts Addition Skills and Principles
  130.    wt: 2:   1 The Counting Origins of Numbers
  131.    wt: 2:   9 Coordinates for Regions in Space
  132.    wt: 2:   7 Real Numbers as Line Cordinates
  133.    wt: 2:   13 Naming Identifying Formulas with Words
  134.    wt: 2:   7 Compound Interest Formula Introduction
  135.    wt: 2:   1 Written work formats for developing and showing skill
  136.    wt: 2:   9 Sets in Probability and Statistics
  137.    wt: 2:   3 Counting with Sets etc
  138.    wt: 2:   1 Finite Sets
  139.    wt: 2:   1 Counting and Counting Methods I
  140.    wt: 2:   4 signed coordinates for regions in space
  141.    wt: 2:   7 Converting or Changing Units
  142.    wt: 2:   Fraction Operations by Raising Terms A Simple Innovation
  143.    wt: 2:   12 Adding Integers More Examples
  144.    wt: 2:   11 Adding Integers Formulas and Examples
  145.    wt: 2:   9 Multiplying Integers
  146.    wt: 2:   1 Integers as Coordinates
  147.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  148.    wt: 2:   19 Remainder Arithmetic Rule of 9 for checking sums III
  149.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  150.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  151.    wt: 2:   4 Remainder Arithmetic Modulo 10 in general
  152.    wt: 2:   Appendix 1 Counting Revisited 15 minute video
  153.    wt: 2:   6. Counting and adding units and mixed units
  154.    wt: 2:   1. Explaining Addition Table
  155.    wt: 2:   012 Division of Time Intervals by Time Intervals
  156.    wt: 2:   8 Addition of Time Intervals via subtotaling
  157.    wt: 2:   4 Mixing and Changing Units of Time
  158.    wt: 2:   A Related Material in Volume 3
  159.    wt: 2:   4 Definite Integrals Evaluation Exercises
  160.    wt: 2:   A Related lessons in Volume 3
  161.    wt: 2:   29 Chain Rule Optional Reading
  162.    wt: 2:   25 Chain Rule Animated Examples Continued
  163.    wt: 2:   23 Chain Rule in general
  164.    wt: 2:   19 Chain Rule for linear functions
  165.    wt: 2:   18 Chain Rule Introduction
  166.    wt: 2:   17 Derivatives of quotients of sine and cosine
  167.    wt: 2:   16 Derivatives of reciprocals of sine and cosine
  168.    wt: 2:   15 sine and cosine derivatives 3rd step
  169.    wt: 2:   14 sine and cosine derivatives 2nd step
  170.    wt: 2:   13 sine and cosine derivatives 1st step
  171.    wt: 2:   11 Limits at infinity Three Examples
  172.    wt: 2:   10 Three one sided limits with infinite values
  173.    wt: 2:   6 Continuity at a point
  174.    wt: 2:   3 Decimal insights for limits continuity convergence
  175.    wt: 2:   G.4 Lipschitz Continuity implies EquiContinuity
  176.    wt: 2:   F.4 Finite Covering Theorem
  177.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  178.    wt: 2:   Chapter 16. Painless Theorem Proving
  179.    wt: 2:   Chapter 15. Solving Linear Equations
  180.    wt: 2:   Chapter 10 Describing and Changing Calculations
  181.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  182.    wt: 2:   Chapter 2 For and Against Mathematics
  183.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  184.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  185.    wt: 2:   O On Learning Mathematics and Science
  186.    wt: 2:   N Improving Marks on Tests and Finals
  187.    wt: 2:   G. Written work formats for developing and showing skill
  188.    wt: 2:   C. Domino effect of being careful
  189.    wt: 2:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  190.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  191.    wt: 2:   6 Measuring via counting or arithmetic the role of fractions
  192.    wt: 2:   3 Telling Tracking Time Temporal and More Place Sense
  193.    wt: 2:   Systematic Algebra Skill Development Missing Links
  194.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  195.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  196.    wt: 1:   K LAMP Musings Science Education
  197.    wt: 1:   I LAMP Introduction Study Habits
  198.    wt: 1:   F LAMP Introduction Prerequisites
  199.    wt: 1:   A Introduction Objectives
  200.    wt: 1:   Skills Chapter 0 Introduction
  201.    wt: 1:   11 pure mathematics
  202.    wt: 1:   7 logic review and decimals an odd combination
  203.    wt: 1:   three goals to set for students
  204.    wt: 1:   site origins
  205.    wt: 1:   key notes and themes
  206.    wt: 1:   Mathematics Education Professors
  207.    wt: 1:   learning takes time
  208.    wt: 1:   Education Reform Inconsistencies
  209.    wt: 1:   Maps Plans Drawings
  210.    wt: 1:   Secondary Three Mathematics
  211.    wt: 1:   Secondary Two Mathematics
  212.    wt: 1:   Secondary One Mathematics
  213.    wt: 1:   teaching tips
  214.    wt: 1:   Lessening Algebra Difficulties
  215.    wt: 1:   three goals for Mathematics Education
  216.    wt: 1:   02 20 mathematics education references
  217.    wt: 1:   three aims for mathematics students
  218.    wt: 1:   Operational Viewpoint to Value
  219.    wt: 1:   formal or informal peer review
  220.    wt: 1:   Theory of Knowledge
  221.    wt: 1:   How to be a better instructor
  222.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  223.    wt: 1:   chapitre 06 00 Chaines de la raison
  224.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  225.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  226.    wt: 1:   chapitre 01 00 Introduction
  227.    wt: 1:   deux definitions pour variable
  228.    wt: 1:   3 Like resistors in parallel
  229.    wt: 1:   2 Unlike resistors in parallel01
  230.    wt: 1:   1 Like resistors in series
  231.    wt: 1:   F Unlike Resistors in Series
  232.    wt: 1:   22 Student Centered Highschool Mathematics
  233.    wt: 1:   18 Primary School Mathematics
  234.    wt: 1:   16 Secondary Mathematics Tips
  235.    wt: 1:   15 Counting For Parents
  236.    wt: 1:   12 Goals and Objectives For Mathematics
  237.    wt: 1:   10 Ends values for work study instruction
  238.    wt: 1:   9 Streaming by Student Cooperation
  239.    wt: 1:   4 Learning Takes Time and Effort
  240.    wt: 1:   3 Preparing for Science Studies
  241.    wt: 1:   1 Speaking Skills
  242.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  243.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  244.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  245.    wt: 1:   23 Inverse Functions
  246.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  247.    wt: 1:   19 Horizontal line rule and method
  248.    wt: 1:   18 Vertical Line Rule and Method
  249.    wt: 1:   17 Function maxima minima and their location
  250.    wt: 1:   14 Surjections Injections Bijections
  251.    wt: 1:   12 Function Domain Recognition Exercises
  252.    wt: 1:   11 Function Domain Range Source and Targets
  253.    wt: 1:   10 Interval Notation
  254.    wt: 1:   8 Set view of relations and functions
  255.    wt: 1:   6 Set Existence Formation and Notation
  256.    wt: 1:   3 Formula or function graphing exercise
  257.    wt: 1:   1 Geometric Introduction of Function Notation
  258.    wt: 1:   5 quadratics completing the square
  259.    wt: 1:   1 quadratics graphing exercises
  260.    wt: 1:   Quadratics in 10 steps
  261.    wt: 1:   11 Growth and Decay in Biology
  262.    wt: 1:   7 Links Lessons Elsewhere
  263.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  264.    wt: 1:   4 Polynomials Long division linear divisor
  265.    wt: 1:   Rewriting algebraic substitution as function substitutions
  266.    wt: 1:   11 arctan left inverse of tangent Graph
  267.    wt: 1:   9 motivation for name arcsin
  268.    wt: 1:   2 cosine function more properties
  269.    wt: 1:   1 cosine function properties
  270.    wt: 1:   7 Radian Measures in special Triangles
  271.    wt: 1:   1 Degrees and Radians Introduction
  272.    wt: 1:   13 Velocity Vectors in Physics
  273.    wt: 1:   12 From Applied To Pure Mathematics
  274.    wt: 1:   9 Head to Tail Coordinate View
  275.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  276.    wt: 1:   6 Vectors with Coordinates
  277.    wt: 1:   2 Signed Coordinates
  278.    wt: 1:   1 Unsigned Coordinates
  279.    wt: 1:   3 graphing y=f(x c) plus K
  280.    wt: 1:   1 graphing y=f(x a)
  281.    wt: 1:   Parallel Lines and Parallel Transversals
  282.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  283.    wt: 1:   14 Straight Lines Equations General Case
  284.    wt: 1:   8 Straight Lines Equation for vertical
  285.    wt: 1:   7 Tangent Function is odd on this domain
  286.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  287.    wt: 1:   1 Straight Lines Slope Concept
  288.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  289.    wt: 1:   17F Law of cosines
  290.    wt: 1:   1 Unit Points Reflections Rotations
  291.    wt: 1:   16 References and Originality Question
  292.    wt: 1:   14 Law of cosines
  293.    wt: 1:   1 Rectangular Polar Coordinates Review
  294.    wt: 1:   8 Triangles Cascade Problem Solving
  295.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  296.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  297.    wt: 1:   11 Triangle Similarity Missing Side Problem
  298.    wt: 1:   6 Geometric Diagrams in Class
  299.    wt: 1:   3 Similarity by Design with coordinates
  300.    wt: 1:   12 Links Lessons elsewhere
  301.    wt: 1:   10 Midpoint of [a b] and [b a]
  302.    wt: 1:   8 Mid Point Formula
  303.    wt: 1:   4 Equations for lines three forms
  304.    wt: 1:   3 Slope product for perpendicular lines
  305.    wt: 1:   1 Numerical view of lines and their equations
  306.    wt: 1:   12 Spatial Coordinates
  307.    wt: 1:   11 Triangle Inequality
  308.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  309.    wt: 1:   4 Polar Coordinates to and from
  310.    wt: 1:   3 Rectangular Coordinates Review
  311.    wt: 1:   2 Cartesian Coordinates with signs
  312.    wt: 1:   1 Cartesian Coordinates sans signs
  313.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  314.    wt: 1:   PS E Multiplication with Polar Coordinates
  315.    wt: 1:   PS D Addition with Cartesian Coordinates
  316.    wt: 1:   PS C Similarity Use Recognize it in Trigonometry
  317.    wt: 1:   14 Parallel Lines Postulate
  318.    wt: 1:   1 Initial Concepts and Terms
  319.    wt: 1:   6 Figuring with Maps Not to Scale
  320.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  321.    wt: 1:   2 Measuring Area Directly
  322.    wt: 1:   musings do not puiblish real numbers
  323.    wt: 1:   A Modular and Remainder Arithmetic
  324.    wt: 1:   21 Addition of Multiples of a Single Vector
  325.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  326.    wt: 1:   15 Head to Tails in place Addition Associative
  327.    wt: 1:   13 Arrows and Vectors in a Plane
  328.    wt: 1:   9 Division with Digits after Decimal Point
  329.    wt: 1:   1 Fractions with Finite Decimal Expansions
  330.    wt: 1:   8 Column Multiplication Methods in General
  331.    wt: 1:   4 Commutative Law Groups Counting Form
  332.    wt: 1:   3 Inequalities Algebraically
  333.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  334.    wt: 1:   5 Proportionality in Equivalent Fractions
  335.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  336.    wt: 1:   6 Compound Interest Forward and Backwards
  337.    wt: 1:   3 Linear Equation Literal Solution More
  338.    wt: 1:   2 Linear Equation Literal Solution
  339.    wt: 1:   1 Changing Calculations
  340.    wt: 1:   5 Equality in Algebra
  341.    wt: 1:   5 Greater More Less Than Signs in General
  342.    wt: 1:   12 Real Number Additive Inverses or Negatives
  343.    wt: 1:   8 Coordinates for Maps and Planes
  344.    wt: 1:   2 Integers
  345.    wt: 1:   5 Independent versus Dependent Variables
  346.    wt: 1:   4 Changing Letters
  347.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  348.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  349.    wt: 1:   4 Solving a triangular system exercise
  350.    wt: 1:   3 Solving triangular system example
  351.    wt: 1:   5 Algebraic Solutions Introduction
  352.    wt: 1:   Skill Development Notes
  353.    wt: 1:   Using Letters for Physical Quantities
  354.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  355.    wt: 1:   11 Volume of Sphere
  356.    wt: 1:   10 Volume of Pyramid
  357.    wt: 1:   9 Volume of Cone
  358.    wt: 1:   8 Compound Interest Formula Evaluation
  359.    wt: 1:   5 Box Volume Formula Example
  360.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  361.    wt: 1:   8 Sets of Numbers
  362.    wt: 1:   7 Cautious or Safe Set Construction
  363.    wt: 1:   6 Power Set Notation
  364.    wt: 1:   4 Subset Builder Notation
  365.    wt: 1:   5 Talking about Numbers and Quantities
  366.    wt: 1:   3 Adding Words To Arithmetic
  367.    wt: 1:   4 Greater More Less Than Signs in General
  368.    wt: 1:   1 Squares and Square Roots Introduction
  369.    wt: 1:   2 Least Common Multiple LCM intro via list method
  370.    wt: 1:   1 Least Common Multiples LCM Introduction
  371.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  372.    wt: 1:   4 Counting with Trees Product Rule Take I
  373.    wt: 1:   3 Counting with Tables and Trees II
  374.    wt: 1:   2 Counting with Tables and Trees I
  375.    wt: 1:   10 dividing signed numbers
  376.    wt: 1:   9 subtracting signed numbers
  377.    wt: 1:   8 multiplying signed numbers
  378.    wt: 1:   7 negative and additive inverse
  379.    wt: 1:   6 adding signed numbers
  380.    wt: 1:   3 signed coordinates for maps and planes
  381.    wt: 1:   2 signed and unsigned numbers as coordinates
  382.    wt: 1:   3 Multiplying Units and Numbers
  383.    wt: 1:   21 Working With Signs
  384.    wt: 1:   20 Dividing Fractions the Why
  385.    wt: 1:   19 Dividing Fractions How TO
  386.    wt: 1:   D Remainders Modulo 11 Pair Rule
  387.    wt: 1:   C Divisibility by 11 Integer Recognition Method
  388.    wt: 1:   B Integer Long Division Multiple Choices
  389.    wt: 1:   13 Subtraction with Additive Inverse
  390.    wt: 1:   10 Integer Multiplication Formulas
  391.    wt: 1:   8 Multiplication by Signed Numbers Integers
  392.    wt: 1:   5 Zero Movement and Additive Inverses
  393.    wt: 1:   4 Adding Movements wiht opposite directions
  394.    wt: 1:   3 Adding Movements with same direction
  395.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  396.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  397.    wt: 1:   23 Remainder Arithmetic Modulo 2
  398.    wt: 1:   22 Remainder Arithmetic Modulo 3 more
  399.    wt: 1:   21 Remainder Arithmetic Modulo 3
  400.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  401.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  402.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  403.    wt: 1:   13 Remainder Arithmetic Modulo 5 Example
  404.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  405.    wt: 1:   11 Remainder Arithmetic Long Division by 5 Quickly more
  406.    wt: 1:   10 Remainder Arithmetic Long Division by 5 Quickly
  407.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  408.    wt: 1:   8 Remainder Arithmetic Morulo 5 Examples II
  409.    wt: 1:   7 Remainder Arithmetic Modulo 5 Examples I
  410.    wt: 1:   6 Remainder Arithmetic Modulo 5 Propertie
  411.    wt: 1:   5 Remainder Arithmetic Modulo 5
  412.    wt: 1:   3 Remainder Arithmetic Modulos 10 more still
  413.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  414.    wt: 1:   1 Remainder Arithmetic Modulo 10
  415.    wt: 1:   17 Identify and Count Factors using Primes
  416.    wt: 1:   16 video Factors of 980 using prime
  417.    wt: 1:   15 video Factors of 20 using Prime Factorization
  418.    wt: 1:   13 video Factors of 24 using prime
  419.    wt: 1:   12 LCD GCD and LCM using Primes
  420.    wt: 1:   7 Calculator Usage Notes and Cautions
  421.    wt: 1:   4 video Prime Factorization Introduction
  422.    wt: 1:   11 Another Single Digit Divisor Example
  423.    wt: 1:   8 Correcting the Mistake
  424.    wt: 1:   7 Long Divison Mistake Catching
  425.    wt: 1:   5 Long Division Include Zeroes or not
  426.    wt: 1:   3 Division Single Digit Divisor Example
  427.    wt: 1:   2 Division with Single Digit Divisors
  428.    wt: 1:   C Counting Areas with Powers of Ten
  429.    wt: 1:   Video Power Notation in Decimal Expansion
  430.    wt: 1:   9 22 Minute Subtraction Review Video
  431.    wt: 1:   2 Decimal Counting Practices
  432.    wt: 1:   11 Place Value SI Standard International way
  433.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  434.    wt: 1:   8 Review Lesson 1 2 4 and 6 All in One
  435.    wt: 1:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  436.    wt: 1:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  437.    wt: 1:   5 More on Groups of 3 Place Value in Decimal Fractions
  438.    wt: 1:   4 Groups of 3 Place Value in Decimal Fractions
  439.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  440.    wt: 1:   016 Numbering Occidental Calendar Days
  441.    wt: 1:   015 School and work day counting tables
  442.    wt: 1:   014 Counting Days with Calendars
  443.    wt: 1:   011 Division of Time Intervals By Numbers
  444.    wt: 1:   010 Repeated Addition of Time Intervals
  445.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  446.    wt: 1:   7 Addition of Time Intervals
  447.    wt: 1:   2 Time and Date Matters in School
  448.    wt: 1:   1 Intro of Kids To Time Date Skills
  449.    wt: 1:   Example 2 volume of a cone
  450.    wt: 1:   Example 1 volume of a pyramid
  451.    wt: 1:   Volume of Solid by Cross Sections Lesson
  452.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  453.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  454.    wt: 1:   3 Two Chain Rule Method Exercises
  455.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  456.    wt: 1:   A Chain Rule Real Player video examples
  457.    wt: 1:   33 Chain Rule Real Player video examples
  458.    wt: 1:   31 Derivatives of inverse functions
  459.    wt: 1:   30Chain Rule A Proof
  460.    wt: 1:   28 Chain Rule Preparation for a Proof
  461.    wt: 1:   24 Chain Rule Animated Examples
  462.    wt: 1:   22 Chain Rule for polynomials
  463.    wt: 1:   21 Chain Rule for powers
  464.    wt: 1:   20 Chain Rule for Pulley Systems
  465.    wt: 1:   10 Power rule for negative integers
  466.    wt: 1:   3 Motivation for Limit Definition Take 2
  467.    wt: 1:   2 Motivation for Limit Definition Take 1
  468.    wt: 1:   9 Limits Continuity and Composition
  469.    wt: 1:   1 Numerical introduction
  470.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  471.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  472.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  473.    wt: 1:   F.5a Equicontinuity Theorems
  474.    wt: 1:   F.3 Intermediate Value Theorem
  475.    wt: 1:   F.1 What Functions are Continuous
  476.    wt: 1:   E1 Error Control Inequalities
  477.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  478.    wt: 1:   C Triangle Inequalities
  479.    wt: 1:   PostScript For and Against Decimal Perspectives
  480.    wt: 1:   A1. Introduction
  481.    wt: 1:   Chapter 23 Links To Trigonometry
  482.    wt: 1:   Chapter 18. Slopes Areas Integration
  483.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  484.    wt: 1:   Chapter 11. Graphing Slope versus Position
  485.    wt: 1:   Chapter 9 About First Courses in Calculus
  486.    wt: 1:   Chapter 8. Slope Interpretation
  487.    wt: 1:   Chapter 1.Introduction
  488.    wt: 1:   Appendix E. How To Study Mathematics and Why
  489.    wt: 1:   Appendix D. What to do in School and Why
  490.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  491.    wt: 1:   Chapter 31 Direct and Indirect Reason
  492.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  493.    wt: 1:   Chapter 25. Mathematical Induction Examples
  494.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  495.    wt: 1:   Chapter 21. Third Reading Guide
  496.    wt: 1:   Chapter 19. Functions and Sets
  497.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  498.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  499.    wt: 1:   Chapter 13. Second Reading Guide
  500.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  501.    wt: 1:   Chapter 4 Longer Chains of Reason
  502.    wt: 1:   Chapter 3 Chains of Reason
  503.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  504.    wt: 1:   Annotated Links to Material Elsehwere
  505.    wt: 1:   Postscript B Mathematics Education References
  506.    wt: 1:   Chapter 11 Elementary Instruction
  507.    wt: 1:   Chapter 8 Modern Instruction
  508.    wt: 1:   Chapter 1 Introduction
  509.    wt: 1:   Postscript B More on Story Telling and Reason
  510.    wt: 1:   Postscript A Story Telling
  511.    wt: 1:   Chapter 24 Direct and Indirect Reason
  512.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  513.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  514.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  515.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  516.    wt: 1:   Chapter 7 Longer Chains of Reason
  517.    wt: 1:   Chapter 6 Chains of Reason
  518.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  519.    wt: 1:   Chapter 1 Introduction
  520.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  521.    wt: 1:   S Adding words to algebra
  522.    wt: 1:   R Why Learn Mathematics Skills
  523.    wt: 1:   N Mathematics Prepare for College Studies
  524.    wt: 1:   J. More on written work and showing skill
  525.    wt: 1:   H Jigsaw puzzles and problem solving
  526.    wt: 1:   B. Domino effect of errors
  527.    wt: 1:   Chapter 2 Why Sets
  528.    wt: 1:   7 Games and Activities for Instruction
  529.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  530.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  531.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  532.    wt: 1:   Mathematics Education References
  533.    wt: 1:   Mathematics Education References
  534.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  535.    wt: 1:   Implementation Notes
  536.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

Extended Search

953 matches:

  1.    wt: 8:   Chapter 6 Rule Based Reason in Mathematics
  2.    wt: 8:   Chapter 2 For and Against Mathematics
  3.    wt: 7:   Annotated Links to Material Elsehwere
  4.    wt: 7:   Postscript B Mathematics Education References
  5.    wt: 7:   Chapter 11 Elementary Instruction
  6.    wt: 7:   Chapter 8 Modern Instruction
  7.    wt: 7:   Chapter 1 Introduction
  8.    wt: 6:   Straight Lines Instersection Solving Equations
  9.    wt: 6:   6 Infinite Decimals Ending in 9 repeating
  10.    wt: 6:   7 Adding decimal fractions using decimal point
  11.    wt: 6:   Postscript A Three Remarks
  12.    wt: 6:   Chapter 12 Four Phases
  13.    wt: 6:   Chapter 10 Transition
  14.    wt: 6:   Chapter 9 The Two Ends
  15.    wt: 6:   Chapter 7 Two Treatments of Geometry
  16.    wt: 6:   Chapter 5 Four References
  17.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  18.    wt: 6:   Chapter 3 Algebra Difficulties
  19.    wt: 6:   Foreword
  20.    wt: 5:   7 arcsin left inverse of sine Definition
  21.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  22.    wt: 5:   Straight Lines ASA Intersection Study More
  23.    wt: 5:   Straight Lines ASA Intersection Study
  24.    wt: 5:   Straight Lines Intersection of
  25.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  26.    wt: 5:   6 Intersection of lines by solving linear systems
  27.    wt: 5:   3 Multiplicative Counting Skills Principles
  28.    wt: 5:   2 Combing Counts Addition Skills and Principles
  29.    wt: 5:   1 The Counting Origins of Numbers
  30.    wt: 5:   Appendix 1 Counting Revisited 15 minute video
  31.    wt: 5:   6. Counting and adding units and mixed units
  32.    wt: 5:   1. Explaining Addition Table
  33.    wt: 5:   4 Money Matters Saving Earning Buying Selling and Budgets
  34.    wt: 5:   Helping the Blind in Logic and Mathematics
  35.    wt: 4:   J LAMP Introduction Extrinsic Origins
  36.    wt: 4:   C LAMP Introduction Culture in Mathematics Education
  37.    wt: 4:   Ramblings Extrinsic numbers theory
  38.    wt: 4:   mathematics instruction in general
  39.    wt: 4:   Different Kinds of Reasoning in maths
  40.    wt: 4:   three kinds of reason in mathematics
  41.    wt: 4:   fairness and inductive principles for instruction
  42.    wt: 4:   16 Increasing or decreasing on intervals
  43.    wt: 4:   8 arcsin left inverse of sine Graph
  44.    wt: 4:   3 Left Inverse of cosine arccos definition
  45.    wt: 4:   4 graphing y=Asin(x c)
  46.    wt: 4:   2 Graphing y=Af(x) Vertical Scaling
  47.    wt: 4:   Parallel Lines and Alternating Corresponding Angles
  48.    wt: 4:   3 Straight Lines Slope as Tangent of Inclination Angle
  49.    wt: 4:   9 Midpoint Coordinates Half Endpoint Sum
  50.    wt: 4:   8 Column Multiplication Methods in General
  51.    wt: 4:   4 Commutative Law Groups Counting Form
  52.    wt: 4:   5 Gaussian Elimination for 3 unknowns 2nd example
  53.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  54.    wt: 4:   4 Solving a triangular system exercise
  55.    wt: 4:   3 Solving triangular system example
  56.    wt: 4:   9 Sets in Probability and Statistics
  57.    wt: 4:   3 Counting with Sets etc
  58.    wt: 4:   1 Finite Sets
  59.    wt: 4:   1 Counting and Counting Methods I
  60.    wt: 4:   15 Adding and Subtracting with Unlike Denominators
  61.    wt: 4:   14 Adding and Subtracting with Like Denominators
  62.    wt: 4:   12 Adding Integers More Examples
  63.    wt: 4:   11 Adding Integers Formulas and Examples
  64.    wt: 4:   9 Multiplying Integers
  65.    wt: 4:   1 Integers as Coordinates
  66.    wt: 4:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  67.    wt: 4:   19 Remainder Arithmetic Rule of 9 for checking sums III
  68.    wt: 4:   18 Remainder Arithmetic Rule of 9 for checking sums II
  69.    wt: 4:   17 Remainder Arithmetic Rule of 9 for checking sums I
  70.    wt: 4:   4 Remainder Arithmetic Modulo 10 in general
  71.    wt: 4:   9 22 Minute Subtraction Review Video
  72.    wt: 4:   2 Decimal Counting Practices
  73.    wt: 4:   2 Indefinite Integrals Exercises
  74.    wt: 4:   1 Chain Rule in Reverse Integration Method
  75.    wt: 4:   27 Chain Rule sinusoidal outer inner functions EGS
  76.    wt: 4:   26 Chain Rule Recognising outer inner functions
  77.    wt: 4:   5 Interpreting and Drawing Maps and Plans.
  78.    wt: 3:   H LAMP Introduction Instructional Concepts
  79.    wt: 3:   G LAMP Introduction Problem Solving Skills
  80.    wt: 3:   E LAMP Introduction Modern Mathematics
  81.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  82.    wt: 3:   Ramblings Introduction Algebra Essay
  83.    wt: 3:   9 combinatorics probability sets
  84.    wt: 3:   links Education Resources online
  85.    wt: 3:   grouping students according to ability
  86.    wt: 3:   mathematics in context
  87.    wt: 3:   mathematics curriculum shifts
  88.    wt: 3:   teaching tutoring algebraic reason
  89.    wt: 3:   04 29 New Mathematics Curriculum
  90.    wt: 3:   Education in mathematics science and technology
  91.    wt: 3:   cultivating intelligence
  92.    wt: 3:   need for a mixed mathematics curriculum
  93.    wt: 3:   Leaner mathematics curriculum
  94.    wt: 3:   Prequel In For A Penny In For A Pound
  95.    wt: 3:   words for mathematics instructor
  96.    wt: 3:   chapitre 07 01 principle D induction mathematique
  97.    wt: 3:   6 Discipline Who is in Charge Conserving Authority
  98.    wt: 3:   20 Interchanging coordinates a reflection
  99.    wt: 3:   9 Set theory term relation possible origins
  100.    wt: 3:   16 cotangent function Definition Graph and Inverse
  101.    wt: 3:   15 cosecant function Definition Graph and Inverse
  102.    wt: 3:   14 secant function Definition Graph and Inverse
  103.    wt: 3:   13 cosecant function Definition Graph and Inverse
  104.    wt: 3:   10 arctan left inverse of tangent Definition
  105.    wt: 3:   5 Swapping Coordinates is a reflection
  106.    wt: 3:   3 graphing y=f(x c) plus K
  107.    wt: 3:   1 graphing y=f(x a)
  108.    wt: 3:   Parallel Lines and Interior Angles
  109.    wt: 3:   Construction Methods and Criteria for Isometric and Similar Triangles
  110.    wt: 3:   SAS Method For Isometric Or Proportional Triangle Construction
  111.    wt: 3:   D Straight Lines Slope from Coordinates Examples
  112.    wt: 3:   C Straight Lines Slope from Coordinates
  113.    wt: 3:   B Straight Line Slope Scaling Properties More
  114.    wt: 3:   A Straight Line Slope Scaling Properties
  115.    wt: 3:   12 Straight Lines Graphing mx plus b
  116.    wt: 3:   11 Straight Lines Graphing y=mx
  117.    wt: 3:   10 Straight Lines through Origin Equations More
  118.    wt: 3:   9 Straight Lines through Origin Equations
  119.    wt: 3:   6 Tangent Function Inclination Angle Take 2
  120.    wt: 3:   28 Expressing products of sines cosines as sums
  121.    wt: 3:   2 point slope equation for a line
  122.    wt: 3:   8 Distance Between Points on a Line
  123.    wt: 3:   10 Dropping a perpendicular to line
  124.    wt: 3:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  125.    wt: 3:   12 Real Numbers Line Signed Coordinates
  126.    wt: 3:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  127.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  128.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  129.    wt: 3:   4 Location of Point in Decimal Addition
  130.    wt: 3:   3 Location of Point in Decimal Multiplication
  131.    wt: 3:   2 Counting Digits in Decimal Multiplication
  132.    wt: 3:   E Long Division Methods more
  133.    wt: 3:   D Long Division Methods
  134.    wt: 3:   C Three Decimal Subtraction Methods
  135.    wt: 3:   B Decimal Comparison and Subtraction
  136.    wt: 3:   A Decimal Addition Columm Methods
  137.    wt: 3:   7 Decimals Multiplication Methods Examples
  138.    wt: 3:   6 Column Methods for Decimal Multiplication
  139.    wt: 3:   5 Distributive Law for Whole Numbers
  140.    wt: 3:   4 GE III Animated Examples
  141.    wt: 3:   3 GE III Equation Addition and Multiplication
  142.    wt: 3:   2 GE II Comparison
  143.    wt: 3:   1 GE Substitution four examples
  144.    wt: 3:   2 Essentially one exercises three with solution
  145.    wt: 3:   1 Essentially One Unknown
  146.    wt: 3:   5 Algebraic Solutions Introduction
  147.    wt: 3:   Skill Development Notes
  148.    wt: 3:   Using Letters for Physical Quantities
  149.    wt: 3:   10 Set View of Wordy Extensions To Arithmetic
  150.    wt: 3:   8 Sets of Numbers
  151.    wt: 3:   7 Cautious or Safe Set Construction
  152.    wt: 3:   6 Power Set Notation
  153.    wt: 3:   4 Subset Builder Notation
  154.    wt: 3:   5 Counting with Tables Trees Product Rule Take II
  155.    wt: 3:   4 Counting with Trees Product Rule Take I
  156.    wt: 3:   3 Counting with Tables and Trees II
  157.    wt: 3:   2 Counting with Tables and Trees I
  158.    wt: 3:   4 signed coordinates for regions in space
  159.    wt: 3:   7 Converting or Changing Units
  160.    wt: 3:   Fraction Operations by Raising Terms A Simple Innovation
  161.    wt: 3:   D Remainders Modulo 11 Pair Rule
  162.    wt: 3:   C Divisibility by 11 Integer Recognition Method
  163.    wt: 3:   B Integer Long Division Multiple Choices
  164.    wt: 3:   13 Subtraction with Additive Inverse
  165.    wt: 3:   10 Integer Multiplication Formulas
  166.    wt: 3:   8 Multiplication by Signed Numbers Integers
  167.    wt: 3:   5 Zero Movement and Additive Inverses
  168.    wt: 3:   4 Adding Movements wiht opposite directions
  169.    wt: 3:   3 Adding Movements with same direction
  170.    wt: 3:   2 Integers Multiplies of a Unit Moverment
  171.    wt: 3:   A Decimals Modular and Remainder Arithmetic
  172.    wt: 3:   23 Remainder Arithmetic Modulo 2
  173.    wt: 3:   22 Remainder Arithmetic Modulo 3 more
  174.    wt: 3:   21 Remainder Arithmetic Modulo 3
  175.    wt: 3:   16 Remainder Arithmetic Modulo 9 Example 2
  176.    wt: 3:   15 Remainder Arithmetic Modulo 9 Example
  177.    wt: 3:   14 Remainder Arithmetic Modulo 9 Example
  178.    wt: 3:   13 Remainder Arithmetic Modulo 5 Example
  179.    wt: 3:   12 Remainder Arithmetic Modulo 10 Example
  180.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  181.    wt: 3:   10 Remainder Arithmetic Long Division by 5 Quickly
  182.    wt: 3:   9 Remainder Arithmetic Divisibility by 5
  183.    wt: 3:   8 Remainder Arithmetic Morulo 5 Examples II
  184.    wt: 3:   7 Remainder Arithmetic Modulo 5 Examples I
  185.    wt: 3:   6 Remainder Arithmetic Modulo 5 Propertie
  186.    wt: 3:   5 Remainder Arithmetic Modulo 5
  187.    wt: 3:   3 Remainder Arithmetic Modulos 10 more still
  188.    wt: 3:   2 Remainder Arithmetic Modulo 10 more
  189.    wt: 3:   1 Remainder Arithmetic Modulo 10
  190.    wt: 3:   Appendix 2 Three Decimal Subtraction Methods
  191.    wt: 3:   Appendix 1 Decimals Comparison Method Take II
  192.    wt: 3:   Subtraction with J Conversions Example
  193.    wt: 3:   Subtraction Another Video Lesson
  194.    wt: 3:   8 Subtraction with Units of Measure
  195.    wt: 3:   7 Subtraction for Decimal Fractions with Exercises
  196.    wt: 3:   6 Subtraction with Conversion Example with Exercises
  197.    wt: 3:   5 A Tip for Efficent Subtraction
  198.    wt: 3:   4 Subtraction with Conversions Borrows and Letter J
  199.    wt: 3:   3 Harder Cases Convert to Compare and Subtract
  200.    wt: 3:   2 Subtraction Easy Case Examples
  201.    wt: 3:   1 Comparison and Subtraction Easy Direct Cases
  202.    wt: 3:   8 What skills and work habits to require
  203.    wt: 3:   5. How to add decimals C. Examples
  204.    wt: 3:   4. How to add with decimals B with conversions
  205.    wt: 3:   3. How to add with decimals A sans conversions
  206.    wt: 3:   A Related Material in Volume 3
  207.    wt: 3:   4 Definite Integrals Evaluation Exercises
  208.    wt: 3:   A Related lessons in Volume 3
  209.    wt: 3:   29 Chain Rule Optional Reading
  210.    wt: 3:   25 Chain Rule Animated Examples Continued
  211.    wt: 3:   23 Chain Rule in general
  212.    wt: 3:   19 Chain Rule for linear functions
  213.    wt: 3:   18 Chain Rule Introduction
  214.    wt: 3:   17 Derivatives of quotients of sine and cosine
  215.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  216.    wt: 3:   15 sine and cosine derivatives 3rd step
  217.    wt: 3:   14 sine and cosine derivatives 2nd step
  218.    wt: 3:   13 sine and cosine derivatives 1st step
  219.    wt: 3:   11 Limits at infinity Three Examples
  220.    wt: 3:   10 Three one sided limits with infinite values
  221.    wt: 3:   6 Continuity at a point
  222.    wt: 3:   3 Decimal insights for limits continuity convergence
  223.    wt: 3:   G.4 Lipschitz Continuity implies EquiContinuity
  224.    wt: 3:   F.4 Finite Covering Theorem
  225.    wt: 3:   B1 Pigeon Hole Principles from combinatorics
  226.    wt: 3:   Chapter 23 Links To Trigonometry
  227.    wt: 3:   Chapter 18. Slopes Areas Integration
  228.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  229.    wt: 3:   Chapter 11. Graphing Slope versus Position
  230.    wt: 3:   Chapter 9 About First Courses in Calculus
  231.    wt: 3:   Chapter 8. Slope Interpretation
  232.    wt: 3:   Chapter 1.Introduction
  233.    wt: 3:   Chapter 16. Painless Theorem Proving
  234.    wt: 3:   Chapter 15. Solving Linear Equations
  235.    wt: 3:   Chapter 10 Describing and Changing Calculations
  236.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  237.    wt: 3:   H more Routine to non routine problem solving
  238.    wt: 3:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  239.    wt: 3:   Chapter 4 Logic for Reading Writing and Geometry etc
  240.    wt: 3:   6 Measuring via counting or arithmetic the role of fractions
  241.    wt: 3:   3 Telling Tracking Time Temporal and More Place Sense
  242.    wt: 3:   Systematic Algebra Skill Development Missing Links
  243.    wt: 3:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  244.    wt: 2:   K LAMP Musings Science Education
  245.    wt: 2:   I LAMP Introduction Study Habits
  246.    wt: 2:   F LAMP Introduction Prerequisites
  247.    wt: 2:   A Introduction Objectives
  248.    wt: 2:   Skills Chapter 0 Introduction
  249.    wt: 2:   11 pure mathematics
  250.    wt: 2:   7 logic review and decimals an odd combination
  251.    wt: 2:   three goals to set for students
  252.    wt: 2:   site origins
  253.    wt: 2:   key notes and themes
  254.    wt: 2:   Mathematics Education Professors
  255.    wt: 2:   learning takes time
  256.    wt: 2:   Education Reform Inconsistencies
  257.    wt: 2:   Maps Plans Drawings
  258.    wt: 2:   Secondary Three Mathematics
  259.    wt: 2:   Secondary Two Mathematics
  260.    wt: 2:   Secondary One Mathematics
  261.    wt: 2:   teaching tips
  262.    wt: 2:   Lessening Algebra Difficulties
  263.    wt: 2:   three goals for Mathematics Education
  264.    wt: 2:   02 20 mathematics education references
  265.    wt: 2:   three aims for mathematics students
  266.    wt: 2:   Operational Viewpoint to Value
  267.    wt: 2:   formal or informal peer review
  268.    wt: 2:   Theory of Knowledge
  269.    wt: 2:   How to be a better instructor
  270.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  271.    wt: 2:   chapitre 06 00 Chaines de la raison
  272.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  273.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  274.    wt: 2:   chapitre 01 00 Introduction
  275.    wt: 2:   Home Tutoring and Home Schooling
  276.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  277.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  278.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  279.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  280.    wt: 2:   2 Reading and Writing Skills
  281.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  282.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  283.    wt: 2:   26 Function definitions done and coming
  284.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  285.    wt: 2:   7 Functions with finite domains
  286.    wt: 2:   4 Function notation in and beyond mathematics
  287.    wt: 2:   Introduction Reading Guide
  288.    wt: 2:   3 quadratics factoring by inspection
  289.    wt: 2:   2 quadratics graphing in general
  290.    wt: 2:   8 Notes for instructors or tutors
  291.    wt: 2:   11 arctan left inverse of tangent Graph
  292.    wt: 2:   9 motivation for name arcsin
  293.    wt: 2:   2 cosine function more properties
  294.    wt: 2:   1 cosine function properties
  295.    wt: 2:   Parallel Lines and Parallel Transversals
  296.    wt: 2:   Proportionality of Line Segments From Parallel Transversals
  297.    wt: 2:   14 Straight Lines Equations General Case
  298.    wt: 2:   8 Straight Lines Equation for vertical
  299.    wt: 2:   7 Tangent Function is odd on this domain
  300.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  301.    wt: 2:   1 Straight Lines Slope Concept
  302.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  303.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  304.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  305.    wt: 2:   27 Logarithmic use of products of sines and cosines
  306.    wt: 2:   26 Formulas for products of sines and cosines
  307.    wt: 2:   23 sine and cosine of 180 plus 22.5 degrees
  308.    wt: 2:   21 sine and cosine Half Angle Formulas
  309.    wt: 2:   20 sine and cosine Double Angle Formulas
  310.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  311.    wt: 2:   18 sum of sinusoidal waves as a single wave
  312.    wt: 2:   17D cis formulas for sine cosines and tangent
  313.    wt: 2:   17C sine and cosine double triple angle formulas
  314.    wt: 2:   17B sine cosine Angle Sum Formulas via cis
  315.    wt: 2:   15 sine cosine Complementary Angle Relations
  316.    wt: 2:   14 cosine even and sine and tangent are odd
  317.    wt: 2:   11 tangent function undefined when terminal side vertical
  318.    wt: 2:   10 Graphs of sines and cosines many periods
  319.    wt: 2:   9 Graphs of sine and cosine over one period
  320.    wt: 2:   7 period of sine and cosine
  321.    wt: 2:   6 sines and cosines for reference angle 30 degrees
  322.    wt: 2:   5 sines and cosines for reference angle 60 degrees
  323.    wt: 2:   4 sines and cosines for reference angle 45 degrees
  324.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  325.    wt: 2:   12 cis formulas for sine cosines and tangent
  326.    wt: 2:   11 sine and cosine double triple angle formulas
  327.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  328.    wt: 2:   3 Trigonometric Ratios sine and cosine
  329.    wt: 2:   4 Similarity Definition with Coordinate
  330.    wt: 2:   12 Links Lessons elsewhere
  331.    wt: 2:   10 Midpoint of [a b] and [b a]
  332.    wt: 2:   8 Mid Point Formula
  333.    wt: 2:   4 Equations for lines three forms
  334.    wt: 2:   3 Slope product for perpendicular lines
  335.    wt: 2:   1 Numerical view of lines and their equations
  336.    wt: 2:   12 Spatial Coordinates
  337.    wt: 2:   11 Triangle Inequality
  338.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  339.    wt: 2:   4 Polar Coordinates to and from
  340.    wt: 2:   3 Rectangular Coordinates Review
  341.    wt: 2:   2 Cartesian Coordinates with signs
  342.    wt: 2:   1 Cartesian Coordinates sans signs
  343.    wt: 2:   Euclidean Geometry Elsewhere LINKS
  344.    wt: 2:   PS E Multiplication with Polar Coordinates
  345.    wt: 2:   PS D Addition with Cartesian Coordinates
  346.    wt: 2:   PS C Similarity Use Recognize it in Trigonometry
  347.    wt: 2:   14 Parallel Lines Postulate
  348.    wt: 2:   1 Initial Concepts and Terms
  349.    wt: 2:   musings do not puiblish real numbers
  350.    wt: 2:   A Modular and Remainder Arithmetic
  351.    wt: 2:   21 Addition of Multiples of a Single Vector
  352.    wt: 2:   16 Collinear Horizontal Arrows Vectors
  353.    wt: 2:   15 Head to Tails in place Addition Associative
  354.    wt: 2:   13 Arrows and Vectors in a Plane
  355.    wt: 2:   9 Division with Digits after Decimal Point
  356.    wt: 2:   1 Fractions with Finite Decimal Expansions
  357.    wt: 2:   3 Inequalities Algebraically
  358.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  359.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  360.    wt: 2:   6 Compound Interest Forward and Backwards
  361.    wt: 2:   3 Linear Equation Literal Solution More
  362.    wt: 2:   2 Linear Equation Literal Solution
  363.    wt: 2:   1 Changing Calculations
  364.    wt: 2:   5 Greater More Less Than Signs in General
  365.    wt: 2:   9 Coordinates for Regions in Space
  366.    wt: 2:   7 Real Numbers as Line Cordinates
  367.    wt: 2:   More Exercises
  368.    wt: 2:   Simple Exercises
  369.    wt: 2:   6 Algebraic Solution Example
  370.    wt: 2:   4 Four Examples Fractional Coefficients
  371.    wt: 2:   3 Four Examples
  372.    wt: 2:   2 Three Examples
  373.    wt: 2:   1 Proper Equal Sign Usage
  374.    wt: 2:   10 One Example
  375.    wt: 2:   9 Three Examples
  376.    wt: 2:   8 One Example
  377.    wt: 2:   7 Two Examples
  378.    wt: 2:   6 Three Examples
  379.    wt: 2:   5 Three Examples
  380.    wt: 2:   4 Two Examples
  381.    wt: 2:   3 Two Examples
  382.    wt: 2:   2 Three Examples
  383.    wt: 2:   Formula Usage Show Work Format
  384.    wt: 2:   13 Naming Identifying Formulas with Words
  385.    wt: 2:   7 Compound Interest Formula Introduction
  386.    wt: 2:   1 Written work formats for developing and showing skill
  387.    wt: 2:   5 Product Builder Notation
  388.    wt: 2:   2 Venn Diagrams
  389.    wt: 2:   4 Greater More Less Than Signs in General
  390.    wt: 2:   1 Squares and Square Roots Introduction
  391.    wt: 2:   2 Least Common Multiple LCM intro via list method
  392.    wt: 2:   1 Least Common Multiples LCM Introduction
  393.    wt: 2:   10 dividing signed numbers
  394.    wt: 2:   9 subtracting signed numbers
  395.    wt: 2:   8 multiplying signed numbers
  396.    wt: 2:   7 negative and additive inverse
  397.    wt: 2:   6 adding signed numbers
  398.    wt: 2:   3 signed coordinates for maps and planes
  399.    wt: 2:   2 signed and unsigned numbers as coordinates
  400.    wt: 2:   3 Multiplying Units and Numbers
  401.    wt: 2:   21 Working With Signs
  402.    wt: 2:   20 Dividing Fractions the Why
  403.    wt: 2:   19 Dividing Fractions How TO
  404.    wt: 2:   A Associative Law Theorectical Note
  405.    wt: 2:   7 Multiplication by Signs
  406.    wt: 2:   6 Multiplication by Natural Numbers
  407.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  408.    wt: 2:   26 Divisibility by 2 3 5 Example
  409.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  410.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  411.    wt: 2:   17 Identify and Count Factors using Primes
  412.    wt: 2:   16 video Factors of 980 using prime
  413.    wt: 2:   15 video Factors of 20 using Prime Factorization
  414.    wt: 2:   13 video Factors of 24 using prime
  415.    wt: 2:   12 LCD GCD and LCM using Primes
  416.    wt: 2:   7 Calculator Usage Notes and Cautions
  417.    wt: 2:   4 video Prime Factorization Introduction
  418.    wt: 2:   11 Another Single Digit Divisor Example
  419.    wt: 2:   8 Correcting the Mistake
  420.    wt: 2:   7 Long Divison Mistake Catching
  421.    wt: 2:   5 Long Division Include Zeroes or not
  422.    wt: 2:   3 Division Single Digit Divisor Example
  423.    wt: 2:   2 Division with Single Digit Divisors
  424.    wt: 2:   C Counting Areas with Powers of Ten
  425.    wt: 2:   Video Power Notation in Decimal Expansion
  426.    wt: 2:   11 Place Value SI Standard International way
  427.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  428.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  429.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  430.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  431.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  432.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  433.    wt: 2:   1 Place Value in Three Digit Whole Numbers
  434.    wt: 2:   012 Division of Time Intervals by Time Intervals
  435.    wt: 2:   8 Addition of Time Intervals via subtotaling
  436.    wt: 2:   4 Mixing and Changing Units of Time
  437.    wt: 2:   Example 2 volume of a cone
  438.    wt: 2:   Example 1 volume of a pyramid
  439.    wt: 2:   Volume of Solid by Cross Sections Lesson
  440.    wt: 2:   Area Between Crossing Curves Lesson Take 2
  441.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  442.    wt: 2:   3 Two Chain Rule Method Exercises
  443.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  444.    wt: 2:   A Chain Rule Real Player video examples
  445.    wt: 2:   33 Chain Rule Real Player video examples
  446.    wt: 2:   31 Derivatives of inverse functions
  447.    wt: 2:   30Chain Rule A Proof
  448.    wt: 2:   28 Chain Rule Preparation for a Proof
  449.    wt: 2:   24 Chain Rule Animated Examples
  450.    wt: 2:   22 Chain Rule for polynomials
  451.    wt: 2:   21 Chain Rule for powers
  452.    wt: 2:   20 Chain Rule for Pulley Systems
  453.    wt: 2:   10 Power rule for negative integers
  454.    wt: 2:   3 Motivation for Limit Definition Take 2
  455.    wt: 2:   2 Motivation for Limit Definition Take 1
  456.    wt: 2:   9 Limits Continuity and Composition
  457.    wt: 2:   1 Numerical introduction
  458.    wt: 2:   Postscript One Sided and Intermediate Value Theorems
  459.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  460.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  461.    wt: 2:   F.5a Equicontinuity Theorems
  462.    wt: 2:   F.3 Intermediate Value Theorem
  463.    wt: 2:   F.1 What Functions are Continuous
  464.    wt: 2:   E1 Error Control Inequalities
  465.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  466.    wt: 2:   C Triangle Inequalities
  467.    wt: 2:   PostScript For and Against Decimal Perspectives
  468.    wt: 2:   A1. Introduction
  469.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  470.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  471.    wt: 2:   Chapter 22 Complex Numbers
  472.    wt: 2:   Chapter 21 Arrow Addition
  473.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  474.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  475.    wt: 2:   Chapter 17. Area Approximation
  476.    wt: 2:   Chapter 16. Velocity Approximation
  477.    wt: 2:   Chapter 15. Slope Approximation
  478.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  479.    wt: 2:   Chapter 13. Acceleration
  480.    wt: 2:   Chapter 12. Units and Slopes
  481.    wt: 2:   Chapter 10 Slopes and Units
  482.    wt: 2:   Chapter 7 Slopes and Velocity
  483.    wt: 2:   Chapter 6. Slopes and Vertical Shifts
  484.    wt: 2:   Chapter 5. Slope Sign Tests
  485.    wt: 2:   Chapter 4. More Slope Sign Analysis
  486.    wt: 2:   Chapter 3. Slope Sign Analysis
  487.    wt: 2:   Chapter 2. Slopes and Ski Trails
  488.    wt: 2:   Fall 1983 Calculus Appetizer
  489.    wt: 2:   Foreword
  490.    wt: 2:   Appendix E. How To Study Mathematics and Why
  491.    wt: 2:   Appendix D. What to do in School and Why
  492.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  493.    wt: 2:   Chapter 31 Direct and Indirect Reason
  494.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  495.    wt: 2:   Chapter 25. Mathematical Induction Examples
  496.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  497.    wt: 2:   Chapter 21. Third Reading Guide
  498.    wt: 2:   Chapter 19. Functions and Sets
  499.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  500.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  501.    wt: 2:   Chapter 13. Second Reading Guide
  502.    wt: 2:   Chapter 9 Talking about Numbers or Quantities
  503.    wt: 2:   Chapter 4 Longer Chains of Reason
  504.    wt: 2:   Chapter 3 Chains of Reason
  505.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  506.    wt: 2:   Postscript B More on Story Telling and Reason
  507.    wt: 2:   Postscript A Story Telling
  508.    wt: 2:   Chapter 24 Direct and Indirect Reason
  509.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  510.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  511.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  512.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  513.    wt: 2:   Chapter 7 Longer Chains of Reason
  514.    wt: 2:   Chapter 6 Chains of Reason
  515.    wt: 2:   Chapter 3 What is in chapters 4 to 8
  516.    wt: 2:   Chapter 1 Introduction
  517.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  518.    wt: 2:   O On Learning Mathematics and Science
  519.    wt: 2:   N Improving Marks on Tests and Finals
  520.    wt: 2:   G. Written work formats for developing and showing skill
  521.    wt: 2:   C. Domino effect of being careful
  522.    wt: 2:   Chapter 2 Why Sets
  523.    wt: 2:   7 Games and Activities for Instruction
  524.    wt: 2:   2 Identifying Size and Position Place and Spatial Sense
  525.    wt: 2:   1 From Number Recognition and Counting to Arithmetic B
  526.    wt: 2:   1 From Number Recognition and Counting to Arithmetic A
  527.    wt: 2:   Mathematics Education References
  528.    wt: 2:   Mathematics Education References
  529.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  530.    wt: 2:   Implementation Notes
  531.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  532.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  533.    wt: 1:   Appendix 2 primary school Arithmetic 01
  534.    wt: 1:   Appendix 1 primary and preschool mathematic
  535.    wt: 1:   Skills Chapter 5 Calculus
  536.    wt: 1:   Skills Chapter 4 Logic
  537.    wt: 1:   Skills Chapter 3 Algebra
  538.    wt: 1:   Skills Chapter 2 Geometry
  539.    wt: 1:   Skills Chapter 1 Arithmetic
  540.    wt: 1:   10 statistics
  541.    wt: 1:   8 analytic geometry etc
  542.    wt: 1:   6 polynomials etc
  543.    wt: 1:   5 logarithms and exponentials etc
  544.    wt: 1:   4 algebra
  545.    wt: 1:   3 Euclidean Geometry Leanly
  546.    wt: 1:   2 arithmetic with signed numbers
  547.    wt: 1:   1 arithmetic with unsigned numbers
  548.    wt: 1:   What is POMME
  549.    wt: 1:   why bother
  550.    wt: 1:   which way to go
  551.    wt: 1:   website reviews
  552.    wt: 1:   Teach the teachers plus goals
  553.    wt: 1:   permissions for teachers
  554.    wt: 1:   Math Ed if it must be short make it lean effective
  555.    wt: 1:   Applied Maths Program14092009 POMME variant
  556.    wt: 1:   activities for students
  557.    wt: 1:   site eurekas
  558.    wt: 1:   About site lesson plans
  559.    wt: 1:   teacher certification
  560.    wt: 1:   modern education
  561.    wt: 1:   what should be learnt and When
  562.    wt: 1:   Postscript 2007 01 10
  563.    wt: 1:   five decades make a difference
  564.    wt: 1:   how letters appear
  565.    wt: 1:   talk the algebra talk
  566.    wt: 1:   three difficulties
  567.    wt: 1:   What to Tell Students
  568.    wt: 1:   geometric implications for algebra
  569.    wt: 1:   the trouble with algebra
  570.    wt: 1:   05 13 OldSiteEntrancePage
  571.    wt: 1:   04 25 when to stop or suspend mathemat
  572.    wt: 1:   02 21 words for teachers
  573.    wt: 1:   standards for course material
  574.    wt: 1:   Four ways to improve education reform
  575.    wt: 1:   Motivation and Context Problem
  576.    wt: 1:   education an empirical art
  577.    wt: 1:   chapitre 12 00 les iles et division
  578.    wt: 1:   chapitre 05 00 Deception
  579.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  580.    wt: 1:   chapitre 04 09 Regles accidentelles
  581.    wt: 1:   chapitre 04 08 Limitations et benefices
  582.    wt: 1:   chapitre 04 06 engagements
  583.    wt: 1:   chapitre 04 05 Implication versus suggestion
  584.    wt: 1:   chapitre 04 04 Parlons de la logique
  585.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  586.    wt: 1:   chapitre 04 02 Deuxieme enigme
  587.    wt: 1:   chapitre 04 01 Premiere enigme
  588.    wt: 1:   chapitre 04 00 Les regles d implication
  589.    wt: 1:   chapitre 02 00 La Communication des idees
  590.    wt: 1:   deux definitions pour variable
  591.    wt: 1:   3 Like resistors in parallel
  592.    wt: 1:   2 Unlike resistors in parallel01
  593.    wt: 1:   1 Like resistors in series
  594.    wt: 1:   F Unlike Resistors in Series
  595.    wt: 1:   22 Student Centered Highschool Mathematics
  596.    wt: 1:   18 Primary School Mathematics
  597.    wt: 1:   16 Secondary Mathematics Tips
  598.    wt: 1:   15 Counting For Parents
  599.    wt: 1:   12 Goals and Objectives For Mathematics
  600.    wt: 1:   10 Ends values for work study instruction
  601.    wt: 1:   9 Streaming by Student Cooperation
  602.    wt: 1:   4 Learning Takes Time and Effort
  603.    wt: 1:   3 Preparing for Science Studies
  604.    wt: 1:   1 Speaking Skills
  605.    wt: 1:   Ages 12 to 14 Skills with take home value
  606.    wt: 1:   Ages 12 to 14 Geometry
  607.    wt: 1:   Ages 12 to 14 Arithmetic
  608.    wt: 1:   Ages 10 to 12 Geometry
  609.    wt: 1:   Ages 10 to 12 Arithmetic
  610.    wt: 1:   Ages 9 to 10
  611.    wt: 1:   Ages 8 to 9
  612.    wt: 1:   Ages 7 to 8
  613.    wt: 1:   Ages 6 to 7
  614.    wt: 1:   Ages 4 plus to 5 plus
  615.    wt: 1:   Ages 3 plus to 4 plus
  616.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  617.    wt: 1:   23 Inverse Functions
  618.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  619.    wt: 1:   19 Horizontal line rule and method
  620.    wt: 1:   18 Vertical Line Rule and Method
  621.    wt: 1:   17 Function maxima minima and their location
  622.    wt: 1:   14 Surjections Injections Bijections
  623.    wt: 1:   12 Function Domain Recognition Exercises
  624.    wt: 1:   11 Function Domain Range Source and Targets
  625.    wt: 1:   10 Interval Notation
  626.    wt: 1:   8 Set view of relations and functions
  627.    wt: 1:   6 Set Existence Formation and Notation
  628.    wt: 1:   3 Formula or function graphing exercise
  629.    wt: 1:   1 Geometric Introduction of Function Notation
  630.    wt: 1:   5 quadratics completing the square
  631.    wt: 1:   1 quadratics graphing exercises
  632.    wt: 1:   Quadratics in 10 steps
  633.    wt: 1:   11 Growth and Decay in Biology
  634.    wt: 1:   7 Links Lessons Elsewhere
  635.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  636.    wt: 1:   4 Polynomials Long division linear divisor
  637.    wt: 1:   Rewriting algebraic substitution as function substitutions
  638.    wt: 1:   12 motivation for term arctan
  639.    wt: 1:   6 Graph of arccos function
  640.    wt: 1:   4 possible motivation for term arccos
  641.    wt: 1:   7 Radian Measures in special Triangles
  642.    wt: 1:   1 Degrees and Radians Introduction
  643.    wt: 1:   13 Velocity Vectors in Physics
  644.    wt: 1:   12 From Applied To Pure Mathematics
  645.    wt: 1:   9 Head to Tail Coordinate View
  646.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  647.    wt: 1:   6 Vectors with Coordinates
  648.    wt: 1:   2 Signed Coordinates
  649.    wt: 1:   1 Unsigned Coordinates
  650.    wt: 1:   Triangle Angles Sum To 180 Degrees
  651.    wt: 1:   5 Tangent Function Graph
  652.    wt: 1:   4 Tangent Function Properties
  653.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  654.    wt: 1:   17F Law of cosines
  655.    wt: 1:   1 Unit Points Reflections Rotations
  656.    wt: 1:   16 References and Originality Question
  657.    wt: 1:   14 Law of cosines
  658.    wt: 1:   1 Rectangular Polar Coordinates Review
  659.    wt: 1:   8 Triangles Cascade Problem Solving
  660.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  661.    wt: 1:   2 Similar Triangles Equality of Corresponding Side Ratios
  662.    wt: 1:   11 Triangle Similarity Missing Side Problem
  663.    wt: 1:   6 Geometric Diagrams in Class
  664.    wt: 1:   3 Similarity by Design with coordinates
  665.    wt: 1:   Four Simple Exercises
  666.    wt: 1:   11 A Partial Summary
  667.    wt: 1:   7 Exercises to test skill and concept mastery
  668.    wt: 1:   5 Algebraic View of Slopes
  669.    wt: 1:   What is and is not here
  670.    wt: 1:   13 Pythagorean spatial distance formulas
  671.    wt: 1:   10 Pythagorean plane distance formula
  672.    wt: 1:   7 Complex Numbers Appetizer
  673.    wt: 1:   6 Polar Multiplication and Rotation
  674.    wt: 1:   5 Cartesian Addition and Translation
  675.    wt: 1:   PS H Distributive Law For Complex Numbers
  676.    wt: 1:   PS G Rotation Distributes over Addition
  677.    wt: 1:   PS F Scalar Multiplication Distributes over Addition
  678.    wt: 1:   PS B Parallelogram Construction Methods
  679.    wt: 1:   PS A Kite Construction Methods
  680.    wt: 1:   21 Parallelograms
  681.    wt: 1:   19 Right Triangle Similarity
  682.    wt: 1:   18 Triangle Similarity Take 1
  683.    wt: 1:   17 Right Bisectors of Triangle Sides
  684.    wt: 1:   16 Angles Subtended By Chords and Diameters
  685.    wt: 1:   15 Triangle Angle Sum is 180 degrees
  686.    wt: 1:   13 Angle Side Angle Failure
  687.    wt: 1:   12 Side Angle Side Failure
  688.    wt: 1:   11 Triangle Construction Fails
  689.    wt: 1:   9 Construction of a right bisector
  690.    wt: 1:   8 Isoceles Triangles
  691.    wt: 1:   7 Angle Side Angle
  692.    wt: 1:   6 Ruler and compass Angle Bisection
  693.    wt: 1:   5 Side Angle Side
  694.    wt: 1:   4 Side Side Side
  695.    wt: 1:   3 Isometry of Triangles Congruence
  696.    wt: 1:   2 Correspondence between Triangles
  697.    wt: 1:   Short Course on Euclidean Geometry
  698.    wt: 1:   6 Figuring with Maps Not to Scale
  699.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  700.    wt: 1:   2 Measuring Area Directly
  701.    wt: 1:   A Signed Number Arithmetic Review
  702.    wt: 1:   26 More Less Greater Than Comparison
  703.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  704.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  705.    wt: 1:   23 Distributive Law Two Derivations
  706.    wt: 1:   22 Multiplication of Signed Numbers
  707.    wt: 1:   19 Signed Multiples of Vectors
  708.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  709.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  710.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  711.    wt: 1:   11 Signed Number Addition and Addition Properties
  712.    wt: 1:   8 Division and Mulplication of Compound Fractions
  713.    wt: 1:   5 Areas of Rectangles Revisited
  714.    wt: 1:   4 Fraction Operations Axiomatic Development
  715.    wt: 1:   2 Fraction Operations Physical Development
  716.    wt: 1:   5 Proportionality in Equivalent Fractions
  717.    wt: 1:   9 Circle Area and Perimeter Formula Backwards Forwards
  718.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  719.    wt: 1:   5 Triangle Area Formula Backwards
  720.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  721.    wt: 1:   5 Equality in Algebra
  722.    wt: 1:   4 Comparison of Negative Numbers
  723.    wt: 1:   3 More and Less Than with Unlike Signs
  724.    wt: 1:   2 More and Less Than for Counts and Measures
  725.    wt: 1:   1 Real Numbers Comparison
  726.    wt: 1:   12 Real Number Additive Inverses or Negatives
  727.    wt: 1:   8 Coordinates for Maps and Planes
  728.    wt: 1:   2 Integers
  729.    wt: 1:   5 Independent versus Dependent Variables
  730.    wt: 1:   4 Changing Letters
  731.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  732.    wt: 1:   11 Volume of Sphere
  733.    wt: 1:   10 Volume of Pyramid
  734.    wt: 1:   9 Volume of Cone
  735.    wt: 1:   8 Compound Interest Formula Evaluation
  736.    wt: 1:   5 Box Volume Formula Example
  737.    wt: 1:   5 Talking about Numbers and Quantities
  738.    wt: 1:   3 Adding Words To Arithmetic
  739.    wt: 1:   arithmetic videos Real Player Format
  740.    wt: 1:   3 Comparison of Negative Numbers
  741.    wt: 1:   2 More and Less Than with Unlike Signs
  742.    wt: 1:   1 More and Less Than for Counts and Measures
  743.    wt: 1:   5 Square Roots with primes more still
  744.    wt: 1:   4 Square Roots with primes more
  745.    wt: 1:   3 Properties of Square Roots with example
  746.    wt: 1:   2 Square Roots with Prime
  747.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  748.    wt: 1:   16 GCD and LCM of 650 225 via Prime
  749.    wt: 1:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  750.    wt: 1:   14 GCD of 650 110 via Primes LCM via Product Rule
  751.    wt: 1:   13 GCD from given Prime Factorization
  752.    wt: 1:   11 GCD 2700 288 via Euclid Algorithm
  753.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  754.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  755.    wt: 1:   8 GCD from Euclidean Algorithm
  756.    wt: 1:   7 GCD and LCM from prime factorization
  757.    wt: 1:   6 GCD from Prime
  758.    wt: 1:   5 Common Divisors 60 45 via Prime
  759.    wt: 1:   4 LCM of 8 and 10 via Prime
  760.    wt: 1:   LCM 60 45 Avoid List Method Use Prime
  761.    wt: 1:   12 GCD 2700 288 via Prime
  762.    wt: 1:   11 What are real lengths and numbers
  763.    wt: 1:   5 lengths and signs of numbers
  764.    wt: 1:   6 Simplification of Fractions with Units
  765.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  766.    wt: 1:   4 Fractions with Units
  767.    wt: 1:   2 Equality and Units
  768.    wt: 1:   1 Addition and Subtraction with Units
  769.    wt: 1:   D Three Term Ratios
  770.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  771.    wt: 1:   B Fractions and Two Term Ratios
  772.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  773.    wt: 1:   22 Complex Compound Fractions
  774.    wt: 1:   21 Reciprocals for Fractions and Wholes
  775.    wt: 1:   18 Efficient Ways to Multiply
  776.    wt: 1:   17 Efficient Ways to Add and Subtract
  777.    wt: 1:   16 Addition Subtraction Comparision Compared
  778.    wt: 1:   13 Fraction Comparison Algebraic View
  779.    wt: 1:   12 Fraction Comparison
  780.    wt: 1:   11 Simplification an Algebraic View
  781.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  782.    wt: 1:   9 Improper Fractions and Mixed Numbers
  783.    wt: 1:   8 Numerals Fractionals Quantals Take II
  784.    wt: 1:   7 Numerals Fractionals Quantals
  785.    wt: 1:   6 Multiplication of Mixed Numbers
  786.    wt: 1:   6 Multiplication Algebraically Take II
  787.    wt: 1:   5 Equivalent Fractions
  788.    wt: 1:   4 Fraction Multiplication
  789.    wt: 1:   3 Unit fraction of a fraction
  790.    wt: 1:   2 Unit Fraction Multiplication
  791.    wt: 1:   1 What is a fraction Take II
  792.    wt: 1:   1 What is a fraction
  793.    wt: 1:   20 Uniqueness of Prime Factorization
  794.    wt: 1:   19 video Prime Factorization Unique
  795.    wt: 1:   18 video Count Factors given Prime Factorization
  796.    wt: 1:   14 video Factors of 24 Take II
  797.    wt: 1:   11 Efficient Square Rule Use
  798.    wt: 1:   10 video Prime Factorization upto 23 squared
  799.    wt: 1:   9 video Prime Factorization upto 19 squared
  800.    wt: 1:   8 video Prime Factorization upto 19
  801.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  802.    wt: 1:   5 Prime Factorization and a Square Rule
  803.    wt: 1:   3 video Primes and Composites from 9 times table
  804.    wt: 1:   2 Prime and Composites less than 16
  805.    wt: 1:   1 video how Products are bigger than factor
  806.    wt: 1:   Long Division Backwards more
  807.    wt: 1:   Long Division Backward
  808.    wt: 1:   Division with Counts and Length
  809.    wt: 1:   Long Division forwards and backwards Example 3
  810.    wt: 1:   Long Division forwards and backwards Example 2
  811.    wt: 1:   Long Division forwards and backwards Example 1
  812.    wt: 1:   12 Why Long Division Works Take III
  813.    wt: 1:   10 Division by Five Long and Short Ways
  814.    wt: 1:   9 Why Long Division Works Take II
  815.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  816.    wt: 1:   4 Division with 2 Digit Divsors
  817.    wt: 1:   1 Divsion Physical Examples
  818.    wt: 1:   D Decimal Multiplication Methods Derived
  819.    wt: 1:   B Powers of Ten
  820.    wt: 1:   A Elementary Basis for Multiplication Methods
  821.    wt: 1:   6 Multiplication Commutes Order Not Important
  822.    wt: 1:   5 Decimal Fraction Multiplication
  823.    wt: 1:   4 Two and Three Digit Multipliers
  824.    wt: 1:   3 More One Digit Multipliers
  825.    wt: 1:   2 One Digit Multipliers
  826.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  827.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  828.    wt: 1:   1 Why 3 times 5 gives 15
  829.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  830.    wt: 1:   3 More on Groups of 3 Multi Digit Place Value
  831.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  832.    wt: 1:   Quick history of numbers and algebra
  833.    wt: 1:   Exact Arithmetic Wholes and Fractions
  834.    wt: 1:   Formula Evaluation how to show work
  835.    wt: 1:   Expression Evaluation how to show work
  836.    wt: 1:   The 20 Times Table
  837.    wt: 1:   The 12 Times Table Visually
  838.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  839.    wt: 1:   About folder contents
  840.    wt: 1:   016 Numbering Occidental Calendar Days
  841.    wt: 1:   015 School and work day counting tables
  842.    wt: 1:   014 Counting Days with Calendars
  843.    wt: 1:   011 Division of Time Intervals By Numbers
  844.    wt: 1:   010 Repeated Addition of Time Intervals
  845.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  846.    wt: 1:   7 Addition of Time Intervals
  847.    wt: 1:   2 Time and Date Matters in School
  848.    wt: 1:   1 Intro of Kids To Time Date Skills
  849.    wt: 1:   Example 1. Area Between x and x squared
  850.    wt: 1:   Example 4 with x function of y
  851.    wt: 1:   Example 3
  852.    wt: 1:   Example 2
  853.    wt: 1:   Example 1
  854.    wt: 1:   Area Between Curves Lesson Take 2
  855.    wt: 1:   Area Between Curves Lesson Take 1
  856.    wt: 1:   Summary
  857.    wt: 1:   5 Area Under Curve Exercise
  858.    wt: 1:   4 Second derivative test exercise example
  859.    wt: 1:   3 Second derivative test
  860.    wt: 1:   2 Second derivative test prequel
  861.    wt: 1:   38 Formulas and derivatives for powers and roots
  862.    wt: 1:   36 Cube root derivative animated
  863.    wt: 1:   34 Derivative of exponential function
  864.    wt: 1:   12 Quotient rule examples
  865.    wt: 1:   11 Quotient rule
  866.    wt: 1:   9 Reciprocal rule
  867.    wt: 1:   8 Differentiation of polynomials
  868.    wt: 1:   7 Animated Differentiation Examples
  869.    wt: 1:   6 Power rule from product rule
  870.    wt: 1:   5 Product Rule
  871.    wt: 1:   4 Sum Rule
  872.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  873.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  874.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  875.    wt: 1:   8 Four Animated Examples
  876.    wt: 1:   7 Evaluation by immediate or delayed substitution
  877.    wt: 1:   5 Jumps and absence of unlimited error control
  878.    wt: 1:   4 Numerical properties
  879.    wt: 1:   2 Algebraic codification
  880.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  881.    wt: 1:   G.5 Motions With Bounded Velocities
  882.    wt: 1:   G.3 Constant Difference Theorem Proof
  883.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  884.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  885.    wt: 1:   F.5b Extreme Value Theorem
  886.    wt: 1:   F.2 Closed Range Theorem
  887.    wt: 1:   E2 Algebraic Properties of Limits
  888.    wt: 1:   D2 Limits of Monotone Sequences
  889.    wt: 1:   B3 Bolzano Weierstrass Theorem
  890.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  891.    wt: 1:   Postscript More on Better Performance
  892.    wt: 1:   Postscript For Better Performance
  893.    wt: 1:   Appendix C. How to Read
  894.    wt: 1:   Appendix B. How To Learn
  895.    wt: 1:   Chapter 30 Truth Tables
  896.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  897.    wt: 1:   Chapter 28 Occurrence Tables
  898.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  899.    wt: 1:   Chapter 23. Notation For Sums
  900.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  901.    wt: 1:   Chapter 20. Degrees and Radians
  902.    wt: 1:   Chapter 18. Rules for Algebra
  903.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  904.    wt: 1:   Chapter 12. Shorthand Usage Guide
  905.    wt: 1:   Chapter 11. Why Shorthand
  906.    wt: 1:   Postscript What is a Variable
  907.    wt: 1:   Chapter 8 Three Skills For Algebra
  908.    wt: 1:   Solutions For Arithmetic Exercises
  909.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  910.    wt: 1:   Chapter 6 Change of Language
  911.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  912.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  913.    wt: 1:   Foreword
  914.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  915.    wt: 1:   Postscript C Consistency as a Tool for Reason
  916.    wt: 1:   Chapter 23 Truth Tables
  917.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  918.    wt: 1:   Chapter 21 Occurrence Tables
  919.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  920.    wt: 1:   Chapter 18 Sense and Knowledge
  921.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  922.    wt: 1:   Chapter 15 Objective Processes
  923.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  924.    wt: 1:   Chapter 11 Accidental Patterns
  925.    wt: 1:   Chapter 10 Responsibility
  926.    wt: 1:   Chapter 8 Change of Language
  927.    wt: 1:   Chapter 5 Deception
  928.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  929.    wt: 1:   Chapter 2 Skill Development
  930.    wt: 1:   Three Remarks
  931.    wt: 1:   Foreword
  932.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  933.    wt: 1:   S Adding words to algebra
  934.    wt: 1:   R Why Learn Mathematics Skills
  935.    wt: 1:   N Mathematics Prepare for College Studies
  936.    wt: 1:   J. More on written work and showing skill
  937.    wt: 1:   H Jigsaw puzzles and problem solving
  938.    wt: 1:   B. Domino effect of errors
  939.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  940.    wt: 1:   Chapter 8 Skipped Topics and Why
  941.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  942.    wt: 1:   Chapter 6 More Algebra and Geometry
  943.    wt: 1:   Chapter 3 Algebra Starter Lessons
  944.    wt: 1:   Chapter 1 Arithmetic
  945.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  946.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  947.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  948.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  949.    wt: 1:   More Algebra and Slope based Calculus Preview
  950.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  951.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  952.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  953.    wt: 1:   Which Way To Go

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

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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