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

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

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

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

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

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

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

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74 matches:

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

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707 matches:

  1.    wt: 7:   29 secant cosecant and cotangent for acute angles
  2.    wt: 6:   22 sine of 22.5 degrees via half angle formulas
  3.    wt: 5:   12 cis formulas for sine cosines and tangent
  4.    wt: 5:   2 More and Less Than for Counts and Measures
  5.    wt: 4:   2 Conductance Resistance Duality02
  6.    wt: 4:   Construction Methods and Criteria for Isometric and Similar Triangles
  7.    wt: 4:   26 Formulas for products of sines and cosines
  8.    wt: 4:   25 tangent double angle formula Slope connection
  9.    wt: 4:   24 tangent Angle Difference Formula
  10.    wt: 4:   23 sine and cosine of 180 plus 22.5 degrees
  11.    wt: 4:   21 sine and cosine Half Angle Formulas
  12.    wt: 4:   20 sine and cosine Double Angle Formulas
  13.    wt: 4:   17D cis formulas for sine cosines and tangent
  14.    wt: 4:   5 Trigonometric Ratios For Tangent and Special Triangles
  15.    wt: 4:   10 Pythagorean plane distance formula
  16.    wt: 4:   2 Another Rectangle Area Formula Example
  17.    wt: 4:   1 Three Skills For Algebra
  18.    wt: 4:   1 More and Less Than for Counts and Measures
  19.    wt: 4:   38 Formulas and derivatives for powers and roots
  20.    wt: 4:   Chapter 8 Three Skills For Algebra
  21.    wt: 4:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  22.    wt: 3:   02 21 words for teachers
  23.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  24.    wt: 3:   24 Standards For Skill Develoment Take II
  25.    wt: 3:   24 Standards For Skill Develoment
  26.    wt: 3:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  27.    wt: 3:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  28.    wt: 3:   12 Goals and Objectives For Mathematics
  29.    wt: 3:   2 Reading and Writing Skills
  30.    wt: 3:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  31.    wt: 3:   5 Function notation for geometric transformations
  32.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  33.    wt: 3:   12 motivation for term arctan
  34.    wt: 3:   6 Tangent Function Inclination Angle Take 2
  35.    wt: 3:   17 tangent function angle sum formulas
  36.    wt: 3:   31 basic secant cosecant cotangent trig identities
  37.    wt: 3:   19 Pythagorean Identity For sine and cosine functions
  38.    wt: 3:   17E Trig Formulas for dot and cross Products
  39.    wt: 3:   17C sine and cosine double triple angle formulas
  40.    wt: 3:   14 cosine even and sine and tangent are odd
  41.    wt: 3:   12 Graph of tangent function for one period
  42.    wt: 3:   6 sines and cosines for reference angle 30 degrees
  43.    wt: 3:   5 sines and cosines for reference angle 60 degrees
  44.    wt: 3:   4 sines and cosines for reference angle 45 degrees
  45.    wt: 3:   3 sines and cosines for reference angle 90 degrees
  46.    wt: 3:   2 Quadrant I reference Angles
  47.    wt: 3:   13 Trig Formulas for dot and cross Products
  48.    wt: 3:   11 sine and cosine double triple angle formulas
  49.    wt: 3:   13 Navigation Location from Angles to 2 Landmarks
  50.    wt: 3:   4 Equations for lines three forms
  51.    wt: 3:   13 Pythagorean spatial distance formulas
  52.    wt: 3:   5 Cartesian Addition and Translation
  53.    wt: 3:   3 Lengths and Areas on Maps and Plans
  54.    wt: 3:   2 Combing Counts Addition Skills and Principles
  55.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  56.    wt: 3:   4 Rectangle Area and Like Formulas Backwards
  57.    wt: 3:   8 Coordinates for Maps and Planes
  58.    wt: 3:   5 Gaussian Elimination for 3 unknowns 2nd example
  59.    wt: 3:   2 Essentially one exercises three with solution
  60.    wt: 3:   1 Written work formats for developing and showing skill
  61.    wt: 3:   2 More and Less Than with Unlike Signs
  62.    wt: 3:   16 GCD and LCM of 650 225 via Prime
  63.    wt: 3:   10 Euclid Algorithm with 129 125 and with 45 14
  64.    wt: 3:   12 GCD 2700 288 via Prime
  65.    wt: 3:   3 signed coordinates for maps and planes
  66.    wt: 3:   C Equality for Fractions and Two Term Ratios and Fractions
  67.    wt: 3:   21 Reciprocals for Fractions and Wholes
  68.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  69.    wt: 3:   24 Divisibility Tests for 2 3 5 9 10
  70.    wt: 3:   2 Prime and Composites less than 16
  71.    wt: 3:   Long Division forwards and backwards Example 2
  72.    wt: 3:   10 Names for Big Numbers and Powers of Ten Expansion
  73.    wt: 3:   2 Groups of Three Place Value for Multidigit Decimals
  74.    wt: 3:   22 Chain Rule for polynomials
  75.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  76.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  77.    wt: 3:   Postscript For Better Performance
  78.    wt: 3:   Chapter 22. Geometric Sums and Sequences
  79.    wt: 3:   Chapter 20. Degrees and Radians
  80.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  81.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  82.    wt: 3:   Chapter 2 For and Against Mathematics
  83.    wt: 3:   Chapter 22 Contrapositive and Vacuously True Implications
  84.    wt: 3:   Chapter 12 Islands and Divisions of Knowledge
  85.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  86.    wt: 3:   I. Logic and language skills
  87.    wt: 3:   G. Written work formats for developing and showing skill
  88.    wt: 3:   Primary and Secondary Skills and Practices with Take Home Value
  89.    wt: 3:   5 Interpreting and Drawing Maps and Plans.
  90.    wt: 3:   2 Identifying Size and Position Place and Spatial Sense
  91.    wt: 3:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  92.    wt: 3:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  93.    wt: 2:   Skills Chapter 3 Algebra
  94.    wt: 2:   Skills Chapter 2 Geometry
  95.    wt: 2:   7 logic review and decimals an odd combination
  96.    wt: 2:   3 Euclidean Geometry Leanly
  97.    wt: 2:   three goals to set for students
  98.    wt: 2:   Applied Maths Program14092009 POMME variant
  99.    wt: 2:   geometric implications for algebra
  100.    wt: 2:   three goals for Mathematics Education
  101.    wt: 2:   02 20 mathematics education references
  102.    wt: 2:   three aims for mathematics students
  103.    wt: 2:   standards for course material
  104.    wt: 2:   formal or informal peer review
  105.    wt: 2:   Prequel In For A Penny In For A Pound
  106.    wt: 2:   fairness and inductive principles for instruction
  107.    wt: 2:   1 Conductance Resistance Duality01
  108.    wt: 2:   D Wire Resistance Calculation02
  109.    wt: 2:   B Wire Resistance Qualitative02
  110.    wt: 2:   C Electromotive force conventional current02
  111.    wt: 2:   22 Student Centered Highschool Mathematics
  112.    wt: 2:   17 Math Booklets for children and young teenagers
  113.    wt: 2:   5 Patience Please for Yourself and Your Charges
  114.    wt: 2:   4 Learning Takes Time and Effort
  115.    wt: 2:   Ages 12 to 14 Skills with take home value
  116.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  117.    wt: 2:   sign monoticity analysis example 2
  118.    wt: 2:   26 Function definitions done and coming
  119.    wt: 2:   25 Absolute Value greatest integer and saw tooth functions
  120.    wt: 2:   24 Monotoncity Injectivity and Inverse Functions
  121.    wt: 2:   22 Square Root function graphically
  122.    wt: 2:   20 Interchanging coordinates a reflection
  123.    wt: 2:   12 Function Domain Recognition Exercises
  124.    wt: 2:   11 Function Domain Range Source and Targets
  125.    wt: 2:   6 Set Existence Formation and Notation
  126.    wt: 2:   3 Formula or function graphing exercise
  127.    wt: 2:   2 Algebraic use of function notation
  128.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  129.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  130.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  131.    wt: 2:   16 cotangent function Definition Graph and Inverse
  132.    wt: 2:   15 cosecant function Definition Graph and Inverse
  133.    wt: 2:   14 secant function Definition Graph and Inverse
  134.    wt: 2:   13 cosecant function Definition Graph and Inverse
  135.    wt: 2:   11 arctan left inverse of tangent Graph
  136.    wt: 2:   10 arctan left inverse of tangent Definition
  137.    wt: 2:   9 Summary Degrees to Radians and back
  138.    wt: 2:   8 Radian Measures of Common Angles
  139.    wt: 2:   7 Radian Measures in special Triangles
  140.    wt: 2:   2 Radian Measure Numerical Value of one degree
  141.    wt: 2:   1 Degrees and Radians Introduction
  142.    wt: 2:   Parallel Lines and Parallel Transversals
  143.    wt: 2:   Triangle Angles Sum To 180 Degrees
  144.    wt: 2:   Parallel Lines and Alternating Corresponding Angles
  145.    wt: 2:   Parallel Lines and Interior Angles
  146.    wt: 2:   SAS Method For Isometric Or Proportional Triangle Construction
  147.    wt: 2:   Analytic View of Triangle Construction or Line Instersection More
  148.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  149.    wt: 2:   35 sines and cosines of 2A 3A 4A 5A
  150.    wt: 2:   34 sines and cosines of 2A 3A 4A 5A
  151.    wt: 2:   33 sines and cosines of 2A 3A 4A 5A
  152.    wt: 2:   32 seven rows of pascals triangle
  153.    wt: 2:   27 Logarithmic use of products of sines and cosines
  154.    wt: 2:   17B sine cosine Angle Sum Formulas via cis
  155.    wt: 2:   16 Right Triangle Complementary Angle Relations
  156.    wt: 2:   13 Graph of tangent function many periods
  157.    wt: 2:   10 Graphs of sines and cosines many periods
  158.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  159.    wt: 2:   21 Logarithms Powers and Exponentials
  160.    wt: 2:   10 sine cosine Angle Sum Formulas via cis
  161.    wt: 2:   4 Trigonometric Ratios For Two Special Triangles
  162.    wt: 2:   2 Similar Triangles Equality of Corresponding Side Ratios
  163.    wt: 2:   Right Triangle and Unit Circle Trigonometry
  164.    wt: 2:   12 Triangles Similarity More Problems
  165.    wt: 2:   8 Similarity of Triangles and Polygons
  166.    wt: 2:   5 Similarity of Circles Squares and Rectangles
  167.    wt: 2:   7 Exercises to test skill and concept mastery
  168.    wt: 2:   2 point slope equation for a line
  169.    wt: 2:   2 Cartesian Coordinates with signs
  170.    wt: 2:   1 Cartesian Coordinates sans signs
  171.    wt: 2:   16 Angles Subtended By Chords and Diameters
  172.    wt: 2:   15 Triangle Angle Sum is 180 degrees
  173.    wt: 2:   13 Angle Side Angle Failure
  174.    wt: 2:   12 Side Angle Side Failure
  175.    wt: 2:   7 Angle Side Angle
  176.    wt: 2:   6 Ruler and compass Angle Bisection
  177.    wt: 2:   2 Correspondence between Triangles
  178.    wt: 2:   4 Angles on Maps Plans drawn to scale
  179.    wt: 2:   26 More Less Greater Than Comparison
  180.    wt: 2:   22 Multiplication of Signed Numbers
  181.    wt: 2:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  182.    wt: 2:   14 Vector Head to Tail Sums and Resultants
  183.    wt: 2:   13 Arrows and Vectors in a Plane
  184.    wt: 2:   2 Algebraic View
  185.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  186.    wt: 2:   6 Compound Interest Forward and Backwards
  187.    wt: 2:   5 Triangle Area Formula Backwards
  188.    wt: 2:   2 Addition and Multiplication Axioms
  189.    wt: 2:   3 More and Less Than with Unlike Signs
  190.    wt: 2:   3 Geometric Formulas and Function Notation
  191.    wt: 2:   1 Formulas Dependence and Function Notation
  192.    wt: 2:   4 Solving a triangular system exercise
  193.    wt: 2:   2 Three Examples
  194.    wt: 2:   2 Three Examples
  195.    wt: 2:   Using Letters for Physical Quantities
  196.    wt: 2:   Formula Usage Show Work Format
  197.    wt: 2:   3 Triangle Area Formula Example
  198.    wt: 2:   5 Talking about Numbers and Quantities
  199.    wt: 2:   4 A Brief Story of numbers and algebra
  200.    wt: 2:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  201.    wt: 2:   11 GCD 2700 288 via Euclid Algorithm
  202.    wt: 2:   2 Counting with Tables and Trees I
  203.    wt: 2:   2 signed and unsigned numbers as coordinates
  204.    wt: 2:   5 Reciprocals and Division for Fractions with Units
  205.    wt: 2:   2 Equality and Units
  206.    wt: 2:   22 Complex Compound Fractions
  207.    wt: 2:   11 Simplification an Algebraic View
  208.    wt: 2:   11 Adding Integers Formulas and Examples
  209.    wt: 2:   27 Divisibility by 2 3 6 5 9 10 Example
  210.    wt: 2:   26 Divisibility by 2 3 5 Example
  211.    wt: 2:   23 Remainder Arithmetic Modulo 2
  212.    wt: 2:   22 Remainder Arithmetic Modulo 3 more
  213.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  214.    wt: 2:   12 LCD GCD and LCM using Primes
  215.    wt: 2:   Long Division forwards and backwards Example 3
  216.    wt: 2:   Long Division forwards and backwards Example 1
  217.    wt: 2:   4 Two and Three Digit Multipliers
  218.    wt: 2:   Appendix 2 Three Decimal Subtraction Methods
  219.    wt: 2:   9 22 Minute Subtraction Review Video
  220.    wt: 2:   7 Subtraction for Decimal Fractions with Exercises
  221.    wt: 2:   8 What skills and work habits to require
  222.    wt: 2:   6. Counting and adding units and mixed units
  223.    wt: 2:   8 Review Lesson 1 2 4 and 6 All in One
  224.    wt: 2:   Quick history of numbers and algebra
  225.    wt: 2:   Practical Methods Ends and Values for Arithmetic
  226.    wt: 2:   4 Mixing and Changing Units of Time
  227.    wt: 2:   2 Time and Date Matters in School
  228.    wt: 2:   2 Indefinite Integrals Exercises
  229.    wt: 2:   28 Chain Rule Preparation for a Proof
  230.    wt: 2:   25 Chain Rule Animated Examples Continued
  231.    wt: 2:   24 Chain Rule Animated Examples
  232.    wt: 2:   21 Chain Rule for powers
  233.    wt: 2:   20 Chain Rule for Pulley Systems
  234.    wt: 2:   14 sine and cosine derivatives 2nd step
  235.    wt: 2:   3 Motivation for Limit Definition Take 2
  236.    wt: 2:   2 Motivation for Limit Definition Take 1
  237.    wt: 2:   12 Limits with Parameters and Derivatives Take I
  238.    wt: 2:   2 Algebraic codification
  239.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  240.    wt: 2:   G.2 Differentiable Functions Mean Value Theorem
  241.    wt: 2:   F.2 Closed Range Theorem
  242.    wt: 2:   E2 Algebraic Properties of Limits
  243.    wt: 2:   D1 Sets and Sequences GLBs and LGBs
  244.    wt: 2:   PostScript For and Against Decimal Perspectives
  245.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  246.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  247.    wt: 2:   Chapter 22 Complex Numbers
  248.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  249.    wt: 2:   Chapter 12. Units and Slopes
  250.    wt: 2:   Chapter 2. Slopes and Ski Trails
  251.    wt: 2:   Postscript More on Better Performance
  252.    wt: 2:   Chapter 29 Contrapositive and Vacuously True Implications
  253.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  254.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  255.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  256.    wt: 2:   Chapter 23. Notation For Sums
  257.    wt: 2:   Chapter 18. Rules for Algebra
  258.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  259.    wt: 2:   Chapter 12. Shorthand Usage Guide
  260.    wt: 2:   Chapter 10 Describing and Changing Calculations
  261.    wt: 2:   Solutions For Arithmetic Exercises
  262.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  263.    wt: 2:   Chapter 6 Change of Language
  264.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  265.    wt: 2:   Chapter 24 Direct and Indirect Reason
  266.    wt: 2:   Chapter 20 Shorthand Symbols as Pronouns
  267.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  268.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  269.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  270.    wt: 2:   Chapter 8 Change of Language
  271.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  272.    wt: 2:   How to Build Skills and Confidence
  273.    wt: 2:   Chapter 6 More Algebra and Geometry
  274.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  275.    wt: 2:   7 Games and Activities for Instruction
  276.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  277.    wt: 2:   More Algebra and Slope based Calculus Preview
  278.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  279.    wt: 2:   The Math Forum and Site Content
  280.    wt: 1:   Appendix 2 primary school Arithmetic 01
  281.    wt: 1:   Appendix 1 primary and preschool mathematic
  282.    wt: 1:   G LAMP Introduction Problem Solving Skills
  283.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  284.    wt: 1:   Skills Chapter 5 Calculus
  285.    wt: 1:   Skills Chapter 4 Logic
  286.    wt: 1:   Ramblings Introduction Algebra Essay
  287.    wt: 1:   Skills Chapter 1 Arithmetic
  288.    wt: 1:   Skills Chapter 0 Introduction
  289.    wt: 1:   8 analytic geometry etc
  290.    wt: 1:   5 logarithms and exponentials etc
  291.    wt: 1:   4 algebra
  292.    wt: 1:   2 arithmetic with signed numbers
  293.    wt: 1:   permissions for teachers
  294.    wt: 1:   Math Ed if it must be short make it lean effective
  295.    wt: 1:   activities for students
  296.    wt: 1:   About site lesson plans
  297.    wt: 1:   key notes and themes
  298.    wt: 1:   what should be learnt and When
  299.    wt: 1:   Postscript 2007 01 10
  300.    wt: 1:   Education Reform Inconsistencies
  301.    wt: 1:   Maps Plans Drawings
  302.    wt: 1:   Secondary Three Mathematics
  303.    wt: 1:   talk the algebra talk
  304.    wt: 1:   three difficulties
  305.    wt: 1:   teaching tutoring algebraic reason
  306.    wt: 1:   Lessening Algebra Difficulties
  307.    wt: 1:   the trouble with algebra
  308.    wt: 1:   05 13 OldSiteEntrancePage
  309.    wt: 1:   04 29 New Mathematics Curriculum
  310.    wt: 1:   04 25 when to stop or suspend mathemat
  311.    wt: 1:   Education in mathematics science and technology
  312.    wt: 1:   three kinds of reason in mathematics
  313.    wt: 1:   Four ways to improve education reform
  314.    wt: 1:   Motivation and Context Problem
  315.    wt: 1:   need for a mixed mathematics curriculum
  316.    wt: 1:   Leaner mathematics curriculum
  317.    wt: 1:   education an empirical art
  318.    wt: 1:   words for mathematics instructor
  319.    wt: 1:   chapitre 12 00 les iles et division
  320.    wt: 1:   chapitre 04 02 Deuxieme enigme
  321.    wt: 1:   chapitre 02 00 La Communication des idees
  322.    wt: 1:   2 Energy Power Heat07
  323.    wt: 1:   B Energy Power02
  324.    wt: 1:   F Wire Resistance Calculation04
  325.    wt: 1:   E Wire Resistance Calculation03
  326.    wt: 1:   C Wire Resistance Calculation01
  327.    wt: 1:   A Wire Resistance Qualitative01
  328.    wt: 1:   2 Unlike resistors in parallel01
  329.    wt: 1:   H Series Circuit02
  330.    wt: 1:   B Electromotive force conventional current01
  331.    wt: 1:   Home Tutoring and Home Schooling
  332.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  333.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take IV
  334.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take III
  335.    wt: 1:   23 Modularized Skill Development Modularized Rigor Take II
  336.    wt: 1:   23 Modularized Skill Development Modularized Rigor
  337.    wt: 1:   15 Counting For Parents
  338.    wt: 1:   14 Multiplication and Times Tables
  339.    wt: 1:   13 Addition and Addition Tables
  340.    wt: 1:   11 Help and Defend Your Child or Teens Education
  341.    wt: 1:   10 Ends values for work study instruction
  342.    wt: 1:   3 Preparing for Science Studies
  343.    wt: 1:   1 Speaking Skills
  344.    wt: 1:   Ages 12 to 14 Geometry
  345.    wt: 1:   Ages 12 to 14 Arithmetic
  346.    wt: 1:   Ages 10 to 12 Geometry
  347.    wt: 1:   Ages 10 to 12 Arithmetic
  348.    wt: 1:   sign monoticity analysis example 4
  349.    wt: 1:   sign monoticity analysis example 3
  350.    wt: 1:   sign monoticity analysis example 1
  351.    wt: 1:   23 Inverse Functions
  352.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  353.    wt: 1:   19 Horizontal line rule and method
  354.    wt: 1:   18 Vertical Line Rule and Method
  355.    wt: 1:   17 Function maxima minima and their location
  356.    wt: 1:   15 Sign analysis of functions
  357.    wt: 1:   13 From one to one to many to one
  358.    wt: 1:   8 Set view of relations and functions
  359.    wt: 1:   4 Function notation in and beyond mathematics
  360.    wt: 1:   10 quadratic exercises
  361.    wt: 1:   9 quadratics physical and further context
  362.    wt: 1:   8 quadratics backward use of various formulas
  363.    wt: 1:   7 quadratic formulla derivation
  364.    wt: 1:   2 quadratics graphing in general
  365.    wt: 1:   1 quadratics graphing exercises
  366.    wt: 1:   11 Growth and Decay in Biology
  367.    wt: 1:   10 Exponential Growth and Decay Models
  368.    wt: 1:   5 Natural Logarithm Calculator Exercises
  369.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  370.    wt: 1:   2 Square Root Simplification a prequel
  371.    wt: 1:   1 Calculator Starter Exercises
  372.    wt: 1:   8 Notes for instructors or tutors
  373.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  374.    wt: 1:   2 Column Multiplication Method
  375.    wt: 1:   Rewriting algebraic substitution as function substitutions
  376.    wt: 1:   9 motivation for name arcsin
  377.    wt: 1:   4 possible motivation for term arccos
  378.    wt: 1:   2 cosine function more properties
  379.    wt: 1:   6 Radian Measure to Degrees
  380.    wt: 1:   5 Degrees to Radian Measure
  381.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  382.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  383.    wt: 1:   A Global Time and Navigation
  384.    wt: 1:   15 Dot and Cross Product
  385.    wt: 1:   12 From Applied To Pure Mathematics
  386.    wt: 1:   7 Coordinate Addition and Scalar Multiplication
  387.    wt: 1:   4 Resultant of a Sum of Movements
  388.    wt: 1:   2 Signed Coordinates
  389.    wt: 1:   Vector and Complex Number Applet
  390.    wt: 1:   2 Graphing y=Af(x) Vertical Scaling
  391.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  392.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  393.    wt: 1:   12 Straight Lines Graphing mx plus b
  394.    wt: 1:   8 Straight Lines Equation for vertical
  395.    wt: 1:   7 Tangent Function is odd on this domain
  396.    wt: 1:   5 Tangent Function Graph
  397.    wt: 1:   4 Tangent Function Properties
  398.    wt: 1:   2 Straight Lines Slopes As Rise Over Run
  399.    wt: 1:   28 Expressing products of sines cosines as sums
  400.    wt: 1:   17G Pythagorean Theorem Converse
  401.    wt: 1:   15 sine cosine Complementary Angle Relations
  402.    wt: 1:   11 tangent function undefined when terminal side vertical
  403.    wt: 1:   9 Graphs of sine and cosine over one period
  404.    wt: 1:   8 period of tangent function
  405.    wt: 1:   7 period of sine and cosine
  406.    wt: 1:   20 N th Roots of Complex Numbers
  407.    wt: 1:   16 References and Originality Question
  408.    wt: 1:   15 Pythagorean Theorem Converse
  409.    wt: 1:   5 An Easy Proof of the Distributive Law
  410.    wt: 1:   2 Complex Numbers made easier we hope
  411.    wt: 1:   1 Rectangular Polar Coordinates Review
  412.    wt: 1:   8 Triangles Cascade Problem Solving
  413.    wt: 1:   6 Trigonometry Sines of Supplementary Angles
  414.    wt: 1:   3 Trigonometric Ratios sine and cosine
  415.    wt: 1:   1 Angle Measurement with Degrees
  416.    wt: 1:   11 Triangle Similarity Missing Side Problem
  417.    wt: 1:   10 Similarity of Triangles Equivalent of Two Criteria
  418.    wt: 1:   9 Similarity of Triangles Usual Criteria
  419.    wt: 1:   7 Translations Rotations Reflections Dilatations
  420.    wt: 1:   2 Similarity By Design
  421.    wt: 1:   Four Simple Exercises
  422.    wt: 1:   12 Links Lessons elsewhere
  423.    wt: 1:   10 Midpoint of [a b] and [b a]
  424.    wt: 1:   8 Mid Point Formula
  425.    wt: 1:   5 Algebraic View of Slopes
  426.    wt: 1:   3 Slope product for perpendicular lines
  427.    wt: 1:   1 Numerical view of lines and their equations
  428.    wt: 1:   What is and is not here
  429.    wt: 1:   12 Spatial Coordinates
  430.    wt: 1:   11 Triangle Inequality
  431.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  432.    wt: 1:   8 Distance Between Points on a Line
  433.    wt: 1:   6 Polar Multiplication and Rotation
  434.    wt: 1:   4 Polar Coordinates to and from
  435.    wt: 1:   3 Rectangular Coordinates Review
  436.    wt: 1:   Euclidean Geometry Elsewhere LINKS
  437.    wt: 1:   PS H Distributive Law For Complex Numbers
  438.    wt: 1:   PS D Addition with Cartesian Coordinates
  439.    wt: 1:   21 Parallelograms
  440.    wt: 1:   19 Right Triangle Similarity
  441.    wt: 1:   18 Triangle Similarity Take 1
  442.    wt: 1:   17 Right Bisectors of Triangle Sides
  443.    wt: 1:   11 Triangle Construction Fails
  444.    wt: 1:   8 Isoceles Triangles
  445.    wt: 1:   5 Side Angle Side
  446.    wt: 1:   3 Isometry of Triangles Congruence
  447.    wt: 1:   1 Initial Concepts and Terms
  448.    wt: 1:   Short Course on Euclidean Geometry
  449.    wt: 1:   5 Drawing to Scale Avoids Angle Distortions
  450.    wt: 1:   2 Measuring Area Directly
  451.    wt: 1:   A Modular and Remainder Arithmetic
  452.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  453.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  454.    wt: 1:   23 Distributive Law Two Derivations
  455.    wt: 1:   21 Addition of Multiples of a Single Vector
  456.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  457.    wt: 1:   12 Real Numbers Line Signed Coordinates
  458.    wt: 1:   11 Signed Number Addition and Addition Properties
  459.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  460.    wt: 1:   8 Division and Mulplication of Compound Fractions
  461.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  462.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  463.    wt: 1:   2 Counting Digits in Decimal Multiplication
  464.    wt: 1:   1 Fractions with Finite Decimal Expansions
  465.    wt: 1:   C Three Decimal Subtraction Methods
  466.    wt: 1:   B Decimal Comparison and Subtraction
  467.    wt: 1:   6 Column Methods for Decimal Multiplication
  468.    wt: 1:   5 Distributive Law for Whole Numbers
  469.    wt: 1:   4 Commutative Law Groups Counting Form
  470.    wt: 1:   3 Multiplicative Counting Skills Principles
  471.    wt: 1:   5 Areas of Rectangles Revisited
  472.    wt: 1:   3 Inequalities Algebraically
  473.    wt: 1:   2 Fraction Operations Physical Development
  474.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  475.    wt: 1:   4 Rates Ratios and Proporitionality
  476.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  477.    wt: 1:   2 Linear Equation Literal Solution
  478.    wt: 1:   1 Changing Calculations
  479.    wt: 1:   6 Equations and Systems Equivalent or Implied
  480.    wt: 1:   5 Equality in Algebra
  481.    wt: 1:   4 Subtraction and Division Axioms
  482.    wt: 1:   3 Product Axioms Two Forms
  483.    wt: 1:   5 Greater More Less Than Signs in General
  484.    wt: 1:   12 Real Number Additive Inverses or Negatives
  485.    wt: 1:   10 Real Number Lengths and Signs
  486.    wt: 1:   9 Coordinates for Regions in Space
  487.    wt: 1:   2 Integers
  488.    wt: 1:   1 Whole and Natural Numbers
  489.    wt: 1:   4 Changing Letters
  490.    wt: 1:   2 Computation Rules Evaluation
  491.    wt: 1:   More Exercises
  492.    wt: 1:   Simple Exercises
  493.    wt: 1:   4 GE III Animated Examples
  494.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  495.    wt: 1:   3 GE III Equation Addition and Multiplication
  496.    wt: 1:   2 GE II Comparison
  497.    wt: 1:   3 Solving triangular system example
  498.    wt: 1:   6 Algebraic Solution Example
  499.    wt: 1:   5 Algebraic Solutions Introduction
  500.    wt: 1:   9 Three Examples
  501.    wt: 1:   6 Three Examples
  502.    wt: 1:   5 Three Examples
  503.    wt: 1:   13 Naming Identifying Formulas with Words
  504.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  505.    wt: 1:   8 Compound Interest Formula Evaluation
  506.    wt: 1:   7 Compound Interest Formula Introduction
  507.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  508.    wt: 1:   5 Box Volume Formula Example
  509.    wt: 1:   4 Circle Area Formula Example
  510.    wt: 1:   9 Sets in Probability and Statistics
  511.    wt: 1:   2 Venn Diagrams
  512.    wt: 1:   6 Three Notions of What is a Variable
  513.    wt: 1:   2 What is a Variable
  514.    wt: 1:   arithmetic videos Real Player Format
  515.    wt: 1:   4 Greater More Less Than Signs in General
  516.    wt: 1:   2 Square Roots with Prime
  517.    wt: 1:   1 Squares and Square Roots Introduction
  518.    wt: 1:   17 GCD LCM of 85 and 60 via Prime
  519.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  520.    wt: 1:   8 GCD from Euclidean Algorithm
  521.    wt: 1:   7 GCD and LCM from prime factorization
  522.    wt: 1:   4 LCM of 8 and 10 via Prime
  523.    wt: 1:   2 Least Common Multiple LCM intro via list method
  524.    wt: 1:   3 Counting with Tables and Trees II
  525.    wt: 1:   1 Counting and Counting Methods I
  526.    wt: 1:   11 What are real lengths and numbers
  527.    wt: 1:   7 negative and additive inverse
  528.    wt: 1:   5 lengths and signs of numbers
  529.    wt: 1:   4 signed coordinates for regions in space
  530.    wt: 1:   7 Converting or Changing Units
  531.    wt: 1:   3 Multiplying Units and Numbers
  532.    wt: 1:   1 Addition and Subtraction with Units
  533.    wt: 1:   D Three Term Ratios
  534.    wt: 1:   B Fractions and Two Term Ratios
  535.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  536.    wt: 1:   21 Working With Signs
  537.    wt: 1:   20 Dividing Fractions the Why
  538.    wt: 1:   17 Efficient Ways to Add and Subtract
  539.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  540.    wt: 1:   14 Adding and Subtracting with Like Denominators
  541.    wt: 1:   13 Fraction Comparison Algebraic View
  542.    wt: 1:   12 Fraction Comparison
  543.    wt: 1:   10 Simplification of Fractions and Mixed Numerals
  544.    wt: 1:   9 Improper Fractions and Mixed Numbers
  545.    wt: 1:   8 Numerals Fractionals Quantals Take II
  546.    wt: 1:   7 Numerals Fractionals Quantals
  547.    wt: 1:   6 Multiplication Algebraically Take II
  548.    wt: 1:   2 Unit Fraction Multiplication
  549.    wt: 1:   12 Adding Integers More Examples
  550.    wt: 1:   10 Integer Multiplication Formulas
  551.    wt: 1:   5 Zero Movement and Additive Inverses
  552.    wt: 1:   2 Integers Multiplies of a Unit Moverment
  553.    wt: 1:   A Decimals Modular and Remainder Arithmetic
  554.    wt: 1:   21 Remainder Arithmetic Modulo 3
  555.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  556.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  557.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  558.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  559.    wt: 1:   12 Remainder Arithmetic Modulo 10 Example
  560.    wt: 1:   2 Remainder Arithmetic Modulo 10 more
  561.    wt: 1:   20 Uniqueness of Prime Factorization
  562.    wt: 1:   17 Identify and Count Factors using Primes
  563.    wt: 1:   15 video Factors of 20 using Prime Factorization
  564.    wt: 1:   14 video Factors of 24 Take II
  565.    wt: 1:   13 video Factors of 24 using prime
  566.    wt: 1:   10 video Prime Factorization upto 23 squared
  567.    wt: 1:   7 Calculator Usage Notes and Cautions
  568.    wt: 1:   6 Sieve of Eratosthenes and Square Rule
  569.    wt: 1:   5 Prime Factorization and a Square Rule
  570.    wt: 1:   3 video Primes and Composites from 9 times table
  571.    wt: 1:   1 video how Products are bigger than factor
  572.    wt: 1:   Division with Counts and Length
  573.    wt: 1:   12 Why Long Division Works Take III
  574.    wt: 1:   11 Another Single Digit Divisor Example
  575.    wt: 1:   10 Division by Five Long and Short Ways
  576.    wt: 1:   4 Division with 2 Digit Divsors
  577.    wt: 1:   2 Division with Single Digit Divisors
  578.    wt: 1:   A Elementary Basis for Multiplication Methods
  579.    wt: 1:   6 Multiplication Commutes Order Not Important
  580.    wt: 1:   2 One Digit Multipliers
  581.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  582.    wt: 1:   Video Decimal Multiplication Geometric View Example 2
  583.    wt: 1:   Video Power Notation in Decimal Expansion
  584.    wt: 1:   Subtraction Another Video Lesson
  585.    wt: 1:   6 Subtraction with Conversion Example with Exercises
  586.    wt: 1:   5 A Tip for Efficent Subtraction
  587.    wt: 1:   4 Subtraction with Conversions Borrows and Letter J
  588.    wt: 1:   3 Harder Cases Convert to Compare and Subtract
  589.    wt: 1:   2 Subtraction Easy Case Examples
  590.    wt: 1:   1 Comparison and Subtraction Easy Direct Cases
  591.    wt: 1:   3. How to add with decimals A sans conversions
  592.    wt: 1:   2 Decimal Counting Practices
  593.    wt: 1:   11 Place Value SI Standard International way
  594.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  595.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  596.    wt: 1:   Exact Arithmetic Wholes and Fractions
  597.    wt: 1:   Formula Evaluation how to show work
  598.    wt: 1:   The 20 Times Table
  599.    wt: 1:   The 12 Times Table Visually
  600.    wt: 1:   015 School and work day counting tables
  601.    wt: 1:   012 Division of Time Intervals by Time Intervals
  602.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  603.    wt: 1:   3 Units and Lengths of Time
  604.    wt: 1:   1 Intro of Kids To Time Date Skills
  605.    wt: 1:   Example 2 volume of a cone
  606.    wt: 1:   Example 1. Area Between x and x squared
  607.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  608.    wt: 1:   Example 2
  609.    wt: 1:   Area Between Curves Lesson Take 2
  610.    wt: 1:   5 Area Under Curve Exercise
  611.    wt: 1:   4 Definite Integrals Evaluation Exercises
  612.    wt: 1:   3 Two Chain Rule Method Exercises
  613.    wt: 1:   4 Second derivative test exercise example
  614.    wt: 1:   2 Second derivative test prequel
  615.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  616.    wt: 1:   36 Cube root derivative animated
  617.    wt: 1:   29 Chain Rule Optional Reading
  618.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  619.    wt: 1:   26 Chain Rule Recognising outer inner functions
  620.    wt: 1:   23 Chain Rule in general
  621.    wt: 1:   19 Chain Rule for linear functions
  622.    wt: 1:   17 Derivatives of quotients of sine and cosine
  623.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  624.    wt: 1:   15 sine and cosine derivatives 3rd step
  625.    wt: 1:   13 sine and cosine derivatives 1st step
  626.    wt: 1:   12 Quotient rule examples
  627.    wt: 1:   10 Power rule for negative integers
  628.    wt: 1:   7 Animated Differentiation Examples
  629.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  630.    wt: 1:   11 Limits at infinity Three Examples
  631.    wt: 1:   10 Three one sided limits with infinite values
  632.    wt: 1:   9 Limits Continuity and Composition
  633.    wt: 1:   8 Four Animated Examples
  634.    wt: 1:   5 Jumps and absence of unlimited error control
  635.    wt: 1:   3 Decimal insights for limits continuity convergence
  636.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  637.    wt: 1:   G.3 Constant Difference Theorem Proof
  638.    wt: 1:   D2 Limits of Monotone Sequences
  639.    wt: 1:   C Triangle Inequalities
  640.    wt: 1:   B3 Bolzano Weierstrass Theorem
  641.    wt: 1:   Chapter 23 Links To Trigonometry
  642.    wt: 1:   Chapter 21 Arrow Addition
  643.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  644.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  645.    wt: 1:   Chapter 10 Slopes and Units
  646.    wt: 1:   Chapter 7 Slopes and Velocity
  647.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  648.    wt: 1:   Chapter 4. More Slope Sign Analysis
  649.    wt: 1:   Chapter 3. Slope Sign Analysis
  650.    wt: 1:   Foreword
  651.    wt: 1:   Appendix E. How To Study Mathematics and Why
  652.    wt: 1:   Appendix D. What to do in School and Why
  653.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  654.    wt: 1:   Chapter 31 Direct and Indirect Reason
  655.    wt: 1:   Chapter 28 Occurrence Tables
  656.    wt: 1:   Chapter 25. Mathematical Induction Examples
  657.    wt: 1:   Chapter 21. Third Reading Guide
  658.    wt: 1:   Chapter 19. Functions and Sets
  659.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  660.    wt: 1:   Chapter 11. Why Shorthand
  661.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  662.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  663.    wt: 1:   Foreword
  664.    wt: 1:   Annotated Links to Material Elsehwere
  665.    wt: 1:   Postscript A Three Remarks
  666.    wt: 1:   Chapter 12 Four Phases
  667.    wt: 1:   Chapter 10 Transition
  668.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  669.    wt: 1:   Chapter 3 Algebra Difficulties
  670.    wt: 1:   Foreword
  671.    wt: 1:   Postscript C Consistency as a Tool for Reason
  672.    wt: 1:   Postscript B More on Story Telling and Reason
  673.    wt: 1:   Chapter 23 Truth Tables
  674.    wt: 1:   Chapter 21 Occurrence Tables
  675.    wt: 1:   Chapter 18 Sense and Knowledge
  676.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  677.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  678.    wt: 1:   Chapter 2 Skill Development
  679.    wt: 1:   Three Remarks
  680.    wt: 1:   Foreword
  681.    wt: 1:   S Adding words to algebra
  682.    wt: 1:   R Why Learn Mathematics Skills
  683.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  684.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  685.    wt: 1:   O On Learning Mathematics and Science
  686.    wt: 1:   N Mathematics Prepare for College Studies
  687.    wt: 1:   L Skills with take home value
  688.    wt: 1:   N Improving Marks on Tests and Finals
  689.    wt: 1:   J. More on written work and showing skill
  690.    wt: 1:   H Jigsaw puzzles and problem solving
  691.    wt: 1:   E. When and how to correct errors
  692.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  693.    wt: 1:   Chapter 8 Skipped Topics and Why
  694.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  695.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  696.    wt: 1:   Chapter 3 Algebra Starter Lessons
  697.    wt: 1:   Chapter 2 Why Sets
  698.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  699.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  700.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  701.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  702.    wt: 1:   Helping the Blind in Logic and Mathematics
  703.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  704.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  705.    wt: 1:   Systematic Algebra Skill Development Missing Links
  706.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  707.    wt: 1:   Talking pdf files for online lessons a webvideo alternative

Extended Search

1094 matches:

  1.    wt: 9:   29 secant cosecant and cotangent for acute angles
  2.    wt: 9:   2 More and Less Than for Counts and Measures
  3.    wt: 9:   2 Three Examples
  4.    wt: 9:   2 Another Rectangle Area Formula Example
  5.    wt: 9:   2 More and Less Than with Unlike Signs
  6.    wt: 9:   1 More and Less Than for Counts and Measures
  7.    wt: 9:   Postscript For Better Performance
  8.    wt: 9:   Chapter 29 Contrapositive and Vacuously True Implications
  9.    wt: 9:   Chapter 27 Shorthand Symbols as Pronouns
  10.    wt: 9:   Chapter 26 What is in chapters 27 to 31
  11.    wt: 9:   Chapter 24. Personal Investment and Pension EGS
  12.    wt: 9:   Chapter 23. Notation For Sums
  13.    wt: 9:   Chapter 14. Forward and Backward Use of a Formula
  14.    wt: 9:   Chapter 12. Shorthand Usage Guide
  15.    wt: 8:   6 Tangent Function Inclination Angle Take 2
  16.    wt: 8:   22 sine of 22.5 degrees via half angle formulas
  17.    wt: 8:   1 Written work formats for developing and showing skill
  18.    wt: 8:   Long Division forwards and backwards Example 2
  19.    wt: 8:   Appendix 2 Three Decimal Subtraction Methods
  20.    wt: 8:   9 22 Minute Subtraction Review Video
  21.    wt: 8:   7 Subtraction for Decimal Fractions with Exercises
  22.    wt: 8:   2 Subtraction Easy Case Examples
  23.    wt: 8:   Postscript More on Better Performance
  24.    wt: 8:   Chapter 28 Occurrence Tables
  25.    wt: 8:   Chapter 25. Mathematical Induction Examples
  26.    wt: 8:   Chapter 21. Third Reading Guide
  27.    wt: 8:   Chapter 18. Rules for Algebra
  28.    wt: 8:   Postscript Unifying Theme A Fourth Skill For Algebra
  29.    wt: 8:   Chapter 10 Describing and Changing Calculations
  30.    wt: 8:   Solutions For Arithmetic Exercises
  31.    wt: 8:   Chapter 7 Prep for Calculus Arithmetic Exercises
  32.    wt: 8:   Chapter 6 Change of Language
  33.    wt: 8:   Chapter 5 Islands and Divisions of Knowledge
  34.    wt: 7:   9 Summary Degrees to Radians and back
  35.    wt: 7:   Construction Methods and Criteria for Isometric and Similar Triangles
  36.    wt: 7:   3 Straight Lines Slope as Tangent of Inclination Angle
  37.    wt: 7:   23 sine and cosine of 180 plus 22.5 degrees
  38.    wt: 7:   12 cis formulas for sine cosines and tangent
  39.    wt: 7:   10 Pythagorean plane distance formula
  40.    wt: 7:   12 Side Angle Side Failure
  41.    wt: 7:   2 Correspondence between Triangles
  42.    wt: 7:   2 Combing Counts Addition Skills and Principles
  43.    wt: 7:   2 Algebraic View
  44.    wt: 7:   9 Circle Area and Perimeter Formula Backwards Forwards
  45.    wt: 7:   4 Rectangle Area and Like Formulas Backwards
  46.    wt: 7:   2 Essentially one exercises three with solution
  47.    wt: 7:   6 Algebraic Solution Example
  48.    wt: 7:   5 Algebraic Solutions Introduction
  49.    wt: 7:   3 Triangle Area Formula Example
  50.    wt: 7:   16 GCD and LCM of 650 225 via Prime
  51.    wt: 7:   21 Reciprocals for Fractions and Wholes
  52.    wt: 7:   2 Prime and Composites less than 16
  53.    wt: 7:   Long Division forwards and backwards Example 3
  54.    wt: 7:   Video Power Notation in Decimal Expansion
  55.    wt: 7:   Subtraction Another Video Lesson
  56.    wt: 7:   6 Subtraction with Conversion Example with Exercises
  57.    wt: 7:   5 A Tip for Efficent Subtraction
  58.    wt: 7:   4 Subtraction with Conversions Borrows and Letter J
  59.    wt: 7:   3 Harder Cases Convert to Compare and Subtract
  60.    wt: 7:   1 Comparison and Subtraction Easy Direct Cases
  61.    wt: 7:   8 What skills and work habits to require
  62.    wt: 7:   6. Counting and adding units and mixed units
  63.    wt: 7:   2 Decimal Counting Practices
  64.    wt: 7:   Appendix E. How To Study Mathematics and Why
  65.    wt: 7:   Appendix D. What to do in School and Why
  66.    wt: 7:   Appendix B. How To Learn
  67.    wt: 7:   Appendix A. Reading Guide For Next Appendices
  68.    wt: 7:   Chapter 31 Direct and Indirect Reason
  69.    wt: 7:   Chapter 19. Functions and Sets
  70.    wt: 7:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  71.    wt: 7:   Chapter 11. Why Shorthand
  72.    wt: 7:   Chapter 9 Talking about Numbers or Quantities
  73.    wt: 7:   Chapter 1 Introduction to Chapters 2 to 6
  74.    wt: 7:   Foreword
  75.    wt: 7:   2 Identifying Size and Position Place and Spatial Sense
  76.    wt: 6:   6 Formulas for Even and Odd Roots with Logarithms
  77.    wt: 6:   8 Radian Measures of Common Angles
  78.    wt: 6:   7 Radian Measures in special Triangles
  79.    wt: 6:   2 Radian Measure Numerical Value of one degree
  80.    wt: 6:   1 Degrees and Radians Introduction
  81.    wt: 6:   2 Graphing y=Af(x) Vertical Scaling
  82.    wt: 6:   Parallel Lines and Interior Angles
  83.    wt: 6:   8 Straight Lines Equation for vertical
  84.    wt: 6:   7 Tangent Function is odd on this domain
  85.    wt: 6:   5 Tangent Function Graph
  86.    wt: 6:   4 Tangent Function Properties
  87.    wt: 6:   2 Straight Lines Slopes As Rise Over Run
  88.    wt: 6:   26 Formulas for products of sines and cosines
  89.    wt: 6:   25 tangent double angle formula Slope connection
  90.    wt: 6:   24 tangent Angle Difference Formula
  91.    wt: 6:   21 sine and cosine Half Angle Formulas
  92.    wt: 6:   5 Trigonometric Ratios For Tangent and Special Triangles
  93.    wt: 6:   13 Pythagorean spatial distance formulas
  94.    wt: 6:   5 Cartesian Addition and Translation
  95.    wt: 6:   2 Cartesian Coordinates with signs
  96.    wt: 6:   PS H Distributive Law For Complex Numbers
  97.    wt: 6:   PS D Addition with Cartesian Coordinates
  98.    wt: 6:   PS B Parallelogram Construction Methods
  99.    wt: 6:   21 Parallelograms
  100.    wt: 6:   16 Angles Subtended By Chords and Diameters
  101.    wt: 6:   15 Triangle Angle Sum is 180 degrees
  102.    wt: 6:   13 Angle Side Angle Failure
  103.    wt: 6:   7 Angle Side Angle
  104.    wt: 6:   6 Ruler and compass Angle Bisection
  105.    wt: 6:   8 Pythagorean Relation Forwards Backwards
  106.    wt: 6:   6 Compound Interest Forward and Backwards
  107.    wt: 6:   5 Triangle Area Formula Backwards
  108.    wt: 6:   3 More and Less Than with Unlike Signs
  109.    wt: 6:   5 Gaussian Elimination for 3 unknowns 2nd example
  110.    wt: 6:   4 Four Examples Fractional Coefficients
  111.    wt: 6:   3 Four Examples
  112.    wt: 6:   1 Proper Equal Sign Usage
  113.    wt: 6:   2 Three Examples
  114.    wt: 6:   13 Naming Identifying Formulas with Words
  115.    wt: 6:   12 Cone Cylinder Sphere Lesson Idea
  116.    wt: 6:   8 Compound Interest Formula Evaluation
  117.    wt: 6:   7 Compound Interest Formula Introduction
  118.    wt: 6:   6 Pythagorean Hypotenuse Calculation Example
  119.    wt: 6:   5 Box Volume Formula Example
  120.    wt: 6:   4 Circle Area Formula Example
  121.    wt: 6:   1 Three Skills For Algebra
  122.    wt: 6:   4 Greater More Less Than Signs in General
  123.    wt: 6:   10 Euclid Algorithm with 129 125 and with 45 14
  124.    wt: 6:   12 GCD 2700 288 via Prime
  125.    wt: 6:   3 signed coordinates for maps and planes
  126.    wt: 6:   C Equality for Fractions and Two Term Ratios and Fractions
  127.    wt: 6:   22 Complex Compound Fractions
  128.    wt: 6:   27 Divisibility by 2 3 6 5 9 10 Example
  129.    wt: 6:   25 Divisibility Tests for 2 3 5 9 10 Example
  130.    wt: 6:   24 Divisibility Tests for 2 3 5 9 10
  131.    wt: 6:   12 LCD GCD and LCM using Primes
  132.    wt: 6:   Long Division forwards and backwards Example 1
  133.    wt: 6:   12 Why Long Division Works Take III
  134.    wt: 6:   2 Division with Single Digit Divisors
  135.    wt: 6:   4 Two and Three Digit Multipliers
  136.    wt: 6:   2 One Digit Multipliers
  137.    wt: 6:   Video Decimal Multiplication Geometric View Example 2
  138.    wt: 6:   Video Decimal Multiplication Geometric View Example 2
  139.    wt: 6:   Appendix 1 Decimals Comparison Method Take II
  140.    wt: 6:   Subtraction with J Conversions Example
  141.    wt: 6:   8 Subtraction with Units of Measure
  142.    wt: 6:   3. How to add with decimals A sans conversions
  143.    wt: 6:   2 Groups of Three Place Value for Multidigit Decimals
  144.    wt: 6:   Appendix C. How to Read
  145.    wt: 6:   Chapter 30 Truth Tables
  146.    wt: 6:   Chapter 16. Painless Theorem Proving
  147.    wt: 6:   Chapter 15. Solving Linear Equations
  148.    wt: 6:   Chapter 13. Second Reading Guide
  149.    wt: 6:   Postscript What is a Variable
  150.    wt: 6:   Chapter 4 Longer Chains of Reason
  151.    wt: 6:   Chapter 3 Chains of Reason
  152.    wt: 6:   Chapter 22 Contrapositive and Vacuously True Implications
  153.    wt: 6:   V Reasons and Motivations for Logic and Mathematics
  154.    wt: 6:   Primary and Secondary Skills and Practices with Take Home Value
  155.    wt: 6:   5 Interpreting and Drawing Maps and Plans.
  156.    wt: 5:   2 Conductance Resistance Duality02
  157.    wt: 5:   sign monoticity analysis example 2
  158.    wt: 5:   22 Square Root function graphically
  159.    wt: 5:   9 Formulas for Real Exponents with Logarithms
  160.    wt: 5:   8 Formulas for Fractional Exponents with Logarithms
  161.    wt: 5:   7 Formulas for Roots with Logarithms Derivation
  162.    wt: 5:   2 Square Root Simplification a prequel
  163.    wt: 5:   12 motivation for term arctan
  164.    wt: 5:   6 Radian Measure to Degrees
  165.    wt: 5:   5 Degrees to Radian Measure
  166.    wt: 5:   4 Circle Sector Area proportional to Central Angle
  167.    wt: 5:   3 Circle Arclengh Proportional to Central Angle
  168.    wt: 5:   4 graphing y=Asin(x c)
  169.    wt: 5:   3 graphing y=f(x c) plus K
  170.    wt: 5:   1 graphing y=f(x a)
  171.    wt: 5:   Parallel Lines and Parallel Transversals
  172.    wt: 5:   Triangle Angles Sum To 180 Degrees
  173.    wt: 5:   Parallel Lines and Alternating Corresponding Angles
  174.    wt: 5:   SAS Method For Isometric Or Proportional Triangle Construction
  175.    wt: 5:   Analytic View of Triangle Construction or Line Instersection More
  176.    wt: 5:   D Straight Lines Slope from Coordinates Examples
  177.    wt: 5:   C Straight Lines Slope from Coordinates
  178.    wt: 5:   B Straight Line Slope Scaling Properties More
  179.    wt: 5:   A Straight Line Slope Scaling Properties
  180.    wt: 5:   13 Straight Lines Finding Equations from 2 points
  181.    wt: 5:   12 Straight Lines Graphing mx plus b
  182.    wt: 5:   11 Straight Lines Graphing y=mx
  183.    wt: 5:   20 sine and cosine Double Angle Formulas
  184.    wt: 5:   17D cis formulas for sine cosines and tangent
  185.    wt: 5:   5 sines and cosines for reference angle 60 degrees
  186.    wt: 5:   4 Equations for lines three forms
  187.    wt: 5:   2 point slope equation for a line
  188.    wt: 5:   12 Spatial Coordinates
  189.    wt: 5:   1 Cartesian Coordinates sans signs
  190.    wt: 5:   Euclidean Geometry Elsewhere LINKS
  191.    wt: 5:   PS G Rotation Distributes over Addition
  192.    wt: 5:   PS F Scalar Multiplication Distributes over Addition
  193.    wt: 5:   PS E Multiplication with Polar Coordinates
  194.    wt: 5:   PS C Similarity Use Recognize it in Trigonometry
  195.    wt: 5:   PS A Kite Construction Methods
  196.    wt: 5:   19 Right Triangle Similarity
  197.    wt: 5:   18 Triangle Similarity Take 1
  198.    wt: 5:   17 Right Bisectors of Triangle Sides
  199.    wt: 5:   11 Triangle Construction Fails
  200.    wt: 5:   8 Isoceles Triangles
  201.    wt: 5:   5 Side Angle Side
  202.    wt: 5:   3 Isometry of Triangles Congruence
  203.    wt: 5:   1 Initial Concepts and Terms
  204.    wt: 5:   Short Course on Euclidean Geometry
  205.    wt: 5:   3 Lengths and Areas on Maps and Plans
  206.    wt: 5:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  207.    wt: 5:   14 Vector Head to Tail Sums and Resultants
  208.    wt: 5:   13 Arrows and Vectors in a Plane
  209.    wt: 5:   4 Rates Ratios and Proporitionality
  210.    wt: 5:   7 Pythagorean Theorem Chinese Square Proof
  211.    wt: 5:   2 Linear Equation Literal Solution
  212.    wt: 5:   1 Changing Calculations
  213.    wt: 5:   2 Addition and Multiplication Axioms
  214.    wt: 5:   5 Greater More Less Than Signs in General
  215.    wt: 5:   8 Coordinates for Maps and Planes
  216.    wt: 5:   3 Geometric Formulas and Function Notation
  217.    wt: 5:   1 Formulas Dependence and Function Notation
  218.    wt: 5:   2 GE II Comparison
  219.    wt: 5:   4 Solving a triangular system exercise
  220.    wt: 5:   11 Volume of Sphere
  221.    wt: 5:   10 Volume of Pyramid
  222.    wt: 5:   9 Volume of Cone
  223.    wt: 5:   3 Comparison of Negative Numbers
  224.    wt: 5:   15 GCD of 650 225 via Euclid Alg LCM via Product Rule
  225.    wt: 5:   11 GCD 2700 288 via Euclid Algorithm
  226.    wt: 5:   8 GCD from Euclidean Algorithm
  227.    wt: 5:   2 Counting with Tables and Trees I
  228.    wt: 5:   2 signed and unsigned numbers as coordinates
  229.    wt: 5:   5 Reciprocals and Division for Fractions with Units
  230.    wt: 5:   2 Equality and Units
  231.    wt: 5:   21 Working With Signs
  232.    wt: 5:   20 Dividing Fractions the Why
  233.    wt: 5:   11 Simplification an Algebraic View
  234.    wt: 5:   2 Unit Fraction Multiplication
  235.    wt: 5:   26 Divisibility by 2 3 5 Example
  236.    wt: 5:   23 Remainder Arithmetic Modulo 2
  237.    wt: 5:   22 Remainder Arithmetic Modulo 3 more
  238.    wt: 5:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  239.    wt: 5:   18 Remainder Arithmetic Rule of 9 for checking sums II
  240.    wt: 5:   2 Remainder Arithmetic Modulo 10 more
  241.    wt: 5:   20 Uniqueness of Prime Factorization
  242.    wt: 5:   Long Division Backwards more
  243.    wt: 5:   Long Division Backward
  244.    wt: 5:   Division with Counts and Length
  245.    wt: 5:   11 Another Single Digit Divisor Example
  246.    wt: 5:   10 Division by Five Long and Short Ways
  247.    wt: 5:   4 Division with 2 Digit Divsors
  248.    wt: 5:   A Elementary Basis for Multiplication Methods
  249.    wt: 5:   6 Multiplication Commutes Order Not Important
  250.    wt: 5:   Appendix 1 Counting Revisited 15 minute video
  251.    wt: 5:   7 Adding decimal fractions using decimal point
  252.    wt: 5:   5. How to add decimals C. Examples
  253.    wt: 5:   4. How to add with decimals B with conversions
  254.    wt: 5:   1. Explaining Addition Table
  255.    wt: 5:   10 Names for Big Numbers and Powers of Ten Expansion
  256.    wt: 5:   38 Formulas and derivatives for powers and roots
  257.    wt: 5:   G.2 Lipshitz Conditions Integration Calculus Reform
  258.    wt: 5:   Chapter 2 For and Against Mathematics
  259.    wt: 5:   Chapter 12 Islands and Divisions of Knowledge
  260.    wt: 5:   7 Games and Activities for Instruction
  261.    wt: 4:   Skills Chapter 2 Geometry
  262.    wt: 4:   three goals for Mathematics Education
  263.    wt: 4:   02 21 words for teachers
  264.    wt: 4:   27 Graduated Correction and Penalties for Young Offenders
  265.    wt: 4:   24 Standards For Skill Develoment Take II
  266.    wt: 4:   24 Standards For Skill Develoment
  267.    wt: 4:   22 Student Centered Highschool Mathematics
  268.    wt: 4:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  269.    wt: 4:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  270.    wt: 4:   12 Goals and Objectives For Mathematics
  271.    wt: 4:   2 Reading and Writing Skills
  272.    wt: 4:   Ages 12 to 14 Skills with take home value
  273.    wt: 4:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  274.    wt: 4:   26 Function definitions done and coming
  275.    wt: 4:   25 Absolute Value greatest integer and saw tooth functions
  276.    wt: 4:   24 Monotoncity Injectivity and Inverse Functions
  277.    wt: 4:   20 Interchanging coordinates a reflection
  278.    wt: 4:   12 Function Domain Recognition Exercises
  279.    wt: 4:   5 Function notation for geometric transformations
  280.    wt: 4:   2 Algebraic use of function notation
  281.    wt: 4:   11 Growth and Decay in Biology
  282.    wt: 4:   10 Exponential Growth and Decay Models
  283.    wt: 4:   5 Natural Logarithm Calculator Exercises
  284.    wt: 4:   3 Natural Logarithms and Exponentials Basic Properties
  285.    wt: 4:   1 Calculator Starter Exercises
  286.    wt: 4:   16 cotangent function Definition Graph and Inverse
  287.    wt: 4:   15 cosecant function Definition Graph and Inverse
  288.    wt: 4:   14 secant function Definition Graph and Inverse
  289.    wt: 4:   13 cosecant function Definition Graph and Inverse
  290.    wt: 4:   11 arctan left inverse of tangent Graph
  291.    wt: 4:   10 arctan left inverse of tangent Definition
  292.    wt: 4:   Proportionality of Line Segments From Parallel Transversals
  293.    wt: 4:   Straight Lines ASA Intersection Study More
  294.    wt: 4:   14 Straight Lines Equations General Case
  295.    wt: 4:   10 Straight Lines through Origin Equations More
  296.    wt: 4:   9 Straight Lines through Origin Equations
  297.    wt: 4:   1 Straight Lines Slope Concept
  298.    wt: 4:   17 tangent function angle sum formulas
  299.    wt: 4:   33 sines and cosines of 2A 3A 4A 5A
  300.    wt: 4:   31 basic secant cosecant cotangent trig identities
  301.    wt: 4:   27 Logarithmic use of products of sines and cosines
  302.    wt: 4:   19 Pythagorean Identity For sine and cosine functions
  303.    wt: 4:   17E Trig Formulas for dot and cross Products
  304.    wt: 4:   17C sine and cosine double triple angle formulas
  305.    wt: 4:   14 cosine even and sine and tangent are odd
  306.    wt: 4:   12 Graph of tangent function for one period
  307.    wt: 4:   6 sines and cosines for reference angle 30 degrees
  308.    wt: 4:   4 sines and cosines for reference angle 45 degrees
  309.    wt: 4:   3 sines and cosines for reference angle 90 degrees
  310.    wt: 4:   2 Quadrant I reference Angles
  311.    wt: 4:   21 Logarithms Powers and Exponentials
  312.    wt: 4:   13 Trig Formulas for dot and cross Products
  313.    wt: 4:   11 sine and cosine double triple angle formulas
  314.    wt: 4:   4 Trigonometric Ratios For Two Special Triangles
  315.    wt: 4:   2 Similar Triangles Equality of Corresponding Side Ratios
  316.    wt: 4:   13 Navigation Location from Angles to 2 Landmarks
  317.    wt: 4:   12 Triangles Similarity More Problems
  318.    wt: 4:   12 Links Lessons elsewhere
  319.    wt: 4:   7 Exercises to test skill and concept mastery
  320.    wt: 4:   11 Triangle Inequality
  321.    wt: 4:   9 Pythagorean Theorem Chinese Square Proof
  322.    wt: 4:   8 Distance Between Points on a Line
  323.    wt: 4:   6 Polar Multiplication and Rotation
  324.    wt: 4:   4 Polar Coordinates to and from
  325.    wt: 4:   3 Rectangular Coordinates Review
  326.    wt: 4:   14 Parallel Lines Postulate
  327.    wt: 4:   10 Dropping a perpendicular to line
  328.    wt: 4:   9 Construction of a right bisector
  329.    wt: 4:   4 Side Side Side
  330.    wt: 4:   4 Angles on Maps Plans drawn to scale
  331.    wt: 4:   26 More Less Greater Than Comparison
  332.    wt: 4:   22 Multiplication of Signed Numbers
  333.    wt: 4:   21 Addition of Multiples of a Single Vector
  334.    wt: 4:   17 Arrows Rotate to Reverse with Length Unchanged
  335.    wt: 4:   12 Real Numbers Line Signed Coordinates
  336.    wt: 4:   11 Signed Number Addition and Addition Properties
  337.    wt: 4:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  338.    wt: 4:   C Three Decimal Subtraction Methods
  339.    wt: 4:   B Decimal Comparison and Subtraction
  340.    wt: 4:   6 Column Methods for Decimal Multiplication
  341.    wt: 4:   5 Distributive Law for Whole Numbers
  342.    wt: 4:   4 Commutative Law Groups Counting Form
  343.    wt: 4:   3 Multiplicative Counting Skills Principles
  344.    wt: 4:   5 Areas of Rectangles Revisited
  345.    wt: 4:   3 Inequalities Algebraically
  346.    wt: 4:   2 Fraction Operations Physical Development
  347.    wt: 4:   1 Decimals Modular and Remainder Arithmetic
  348.    wt: 4:   5 Proportionality in Equivalent Fractions
  349.    wt: 4:   3 Proportionality Examples
  350.    wt: 4:   1 What is Proportionality
  351.    wt: 4:   3 Linear Equation Literal Solution More
  352.    wt: 4:   6 Equations and Systems Equivalent or Implied
  353.    wt: 4:   5 Equality in Algebra
  354.    wt: 4:   4 Subtraction and Division Axioms
  355.    wt: 4:   3 Product Axioms Two Forms
  356.    wt: 4:   4 Comparison of Negative Numbers
  357.    wt: 4:   1 Real Numbers Comparison
  358.    wt: 4:   12 Real Number Additive Inverses or Negatives
  359.    wt: 4:   10 Real Number Lengths and Signs
  360.    wt: 4:   4 Changing Letters
  361.    wt: 4:   2 Computation Rules Evaluation
  362.    wt: 4:   4 GE III Animated Examples
  363.    wt: 4:   3 Gaussian Elimination 3 unknowns first example
  364.    wt: 4:   3 GE III Equation Addition and Multiplication
  365.    wt: 4:   3 Solving triangular system example
  366.    wt: 4:   9 Three Examples
  367.    wt: 4:   6 Three Examples
  368.    wt: 4:   5 Three Examples
  369.    wt: 4:   Using Letters for Physical Quantities
  370.    wt: 4:   Formula Usage Show Work Format
  371.    wt: 4:   5 Talking about Numbers and Quantities
  372.    wt: 4:   4 A Brief Story of numbers and algebra
  373.    wt: 4:   2 Square Roots with Prime
  374.    wt: 4:   1 Squares and Square Roots Introduction
  375.    wt: 4:   17 GCD LCM of 85 and 60 via Prime
  376.    wt: 4:   9 GCD of 360 110 via Primes and Euclid Algorithm
  377.    wt: 4:   7 GCD and LCM from prime factorization
  378.    wt: 4:   4 LCM of 8 and 10 via Prime
  379.    wt: 4:   2 Least Common Multiple LCM intro via list method
  380.    wt: 4:   3 Counting with Tables and Trees II
  381.    wt: 4:   1 Counting and Counting Methods I
  382.    wt: 4:   7 Converting or Changing Units
  383.    wt: 4:   3 Multiplying Units and Numbers
  384.    wt: 4:   1 Addition and Subtraction with Units
  385.    wt: 4:   D Three Term Ratios
  386.    wt: 4:   B Fractions and Two Term Ratios
  387.    wt: 4:   A Similarities between Fractions and Two Term Ratios
  388.    wt: 4:   19 Dividing Fractions How TO
  389.    wt: 4:   17 Efficient Ways to Add and Subtract
  390.    wt: 4:   15 Adding and Subtracting with Unlike Denominators
  391.    wt: 4:   14 Adding and Subtracting with Like Denominators
  392.    wt: 4:   13 Fraction Comparison Algebraic View
  393.    wt: 4:   12 Fraction Comparison
  394.    wt: 4:   10 Simplification of Fractions and Mixed Numerals
  395.    wt: 4:   9 Improper Fractions and Mixed Numbers
  396.    wt: 4:   8 Numerals Fractionals Quantals Take II
  397.    wt: 4:   7 Numerals Fractionals Quantals
  398.    wt: 4:   6 Multiplication Algebraically Take II
  399.    wt: 4:   12 Adding Integers More Examples
  400.    wt: 4:   11 Adding Integers Formulas and Examples
  401.    wt: 4:   2 Integers Multiplies of a Unit Moverment
  402.    wt: 4:   A Decimals Modular and Remainder Arithmetic
  403.    wt: 4:   21 Remainder Arithmetic Modulo 3
  404.    wt: 4:   19 Remainder Arithmetic Rule of 9 for checking sums III
  405.    wt: 4:   17 Remainder Arithmetic Rule of 9 for checking sums I
  406.    wt: 4:   16 Remainder Arithmetic Modulo 9 Example 2
  407.    wt: 4:   12 Remainder Arithmetic Modulo 10 Example
  408.    wt: 4:   8 Remainder Arithmetic Morulo 5 Examples II
  409.    wt: 4:   5 Remainder Arithmetic Modulo 5
  410.    wt: 4:   4 Remainder Arithmetic Modulo 10 in general
  411.    wt: 4:   3 Remainder Arithmetic Modulos 10 more still
  412.    wt: 4:   1 Remainder Arithmetic Modulo 10
  413.    wt: 4:   17 Identify and Count Factors using Primes
  414.    wt: 4:   15 video Factors of 20 using Prime Factorization
  415.    wt: 4:   14 video Factors of 24 Take II
  416.    wt: 4:   13 video Factors of 24 using prime
  417.    wt: 4:   10 video Prime Factorization upto 23 squared
  418.    wt: 4:   7 Calculator Usage Notes and Cautions
  419.    wt: 4:   6 Sieve of Eratosthenes and Square Rule
  420.    wt: 4:   5 Prime Factorization and a Square Rule
  421.    wt: 4:   3 video Primes and Composites from 9 times table
  422.    wt: 4:   1 video how Products are bigger than factor
  423.    wt: 4:   9 Why Long Division Works Take II
  424.    wt: 4:   8 Correcting the Mistake
  425.    wt: 4:   7 Long Divison Mistake Catching
  426.    wt: 4:   6 Why Decimal Long Division Methods Works Take I
  427.    wt: 4:   5 Long Division Include Zeroes or not
  428.    wt: 4:   3 Division Single Digit Divisor Example
  429.    wt: 4:   1 Divsion Physical Examples
  430.    wt: 4:   D Decimal Multiplication Methods Derived
  431.    wt: 4:   C Counting Areas with Powers of Ten
  432.    wt: 4:   B Powers of Ten
  433.    wt: 4:   5 Decimal Fraction Multiplication
  434.    wt: 4:   3 More One Digit Multipliers
  435.    wt: 4:   1 Why 3 times 5 gives 15
  436.    wt: 4:   8 Review Lesson 1 2 4 and 6 All in One
  437.    wt: 4:   Quick history of numbers and algebra
  438.    wt: 4:   The 20 Times Table
  439.    wt: 4:   Practical Methods Ends and Values for Arithmetic
  440.    wt: 4:   Example 1. Area Between x and x squared
  441.    wt: 4:   22 Chain Rule for polynomials
  442.    wt: 4:   21 Chain Rule for powers
  443.    wt: 4:   2 Algebraic codification
  444.    wt: 4:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  445.    wt: 4:   Chapter 22 Complex Numbers
  446.    wt: 4:   Chapter 24 Direct and Indirect Reason
  447.    wt: 4:   Chapter 20 Shorthand Symbols as Pronouns
  448.    wt: 4:   I. Logic and language skills
  449.    wt: 4:   G. Written work formats for developing and showing skill
  450.    wt: 4:   4 Money Matters Saving Earning Buying Selling and Budgets
  451.    wt: 4:   3 Telling Tracking Time Temporal and More Place Sense
  452.    wt: 4:   1 From Number Recognition and Counting to Arithmetic B
  453.    wt: 4:   1 From Number Recognition and Counting to Arithmetic A
  454.    wt: 4:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  455.    wt: 4:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  456.    wt: 4:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  457.    wt: 3:   Skills Chapter 3 Algebra
  458.    wt: 3:   7 logic review and decimals an odd combination
  459.    wt: 3:   3 Euclidean Geometry Leanly
  460.    wt: 3:   2 arithmetic with signed numbers
  461.    wt: 3:   Applied Maths Program14092009 POMME variant
  462.    wt: 3:   geometric implications for algebra
  463.    wt: 3:   Lessening Algebra Difficulties
  464.    wt: 3:   the trouble with algebra
  465.    wt: 3:   02 20 mathematics education references
  466.    wt: 3:   three aims for mathematics students
  467.    wt: 3:   Prequel In For A Penny In For A Pound
  468.    wt: 3:   fairness and inductive principles for instruction
  469.    wt: 3:   B Energy Power02
  470.    wt: 3:   Ages 12 to 14 Geometry
  471.    wt: 3:   Ages 12 to 14 Arithmetic
  472.    wt: 3:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  473.    wt: 3:   sign monoticity analysis example 4
  474.    wt: 3:   sign monoticity analysis example 3
  475.    wt: 3:   sign monoticity analysis example 1
  476.    wt: 3:   23 Inverse Functions
  477.    wt: 3:   21 Graphs of functions given by Horizontal Line Method
  478.    wt: 3:   11 Function Domain Range Source and Targets
  479.    wt: 3:   6 Set Existence Formation and Notation
  480.    wt: 3:   3 Formula or function graphing exercise
  481.    wt: 3:   12 From Applied To Pure Mathematics
  482.    wt: 3:   2 Signed Coordinates
  483.    wt: 3:   Straight Lines ASA Intersection Study
  484.    wt: 3:   Straight Lines Instersection Solving Equations
  485.    wt: 3:   Straight Lines Intersection of
  486.    wt: 3:   35 sines and cosines of 2A 3A 4A 5A
  487.    wt: 3:   34 sines and cosines of 2A 3A 4A 5A
  488.    wt: 3:   32 seven rows of pascals triangle
  489.    wt: 3:   28 Expressing products of sines cosines as sums
  490.    wt: 3:   17B sine cosine Angle Sum Formulas via cis
  491.    wt: 3:   16 Right Triangle Complementary Angle Relations
  492.    wt: 3:   13 Graph of tangent function many periods
  493.    wt: 3:   10 Graphs of sines and cosines many periods
  494.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  495.    wt: 3:   20 N th Roots of Complex Numbers
  496.    wt: 3:   10 sine cosine Angle Sum Formulas via cis
  497.    wt: 3:   2 Complex Numbers made easier we hope
  498.    wt: 3:   8 Triangles Cascade Problem Solving
  499.    wt: 3:   6 Trigonometry Sines of Supplementary Angles
  500.    wt: 3:   3 Trigonometric Ratios sine and cosine
  501.    wt: 3:   Right Triangle and Unit Circle Trigonometry
  502.    wt: 3:   8 Similarity of Triangles and Polygons
  503.    wt: 3:   5 Similarity of Circles Squares and Rectangles
  504.    wt: 3:   2 Similarity By Design
  505.    wt: 3:   Four Simple Exercises
  506.    wt: 3:   10 Midpoint of [a b] and [b a]
  507.    wt: 3:   8 Mid Point Formula
  508.    wt: 3:   5 Algebraic View of Slopes
  509.    wt: 3:   3 Slope product for perpendicular lines
  510.    wt: 3:   1 Numerical view of lines and their equations
  511.    wt: 3:   What is and is not here
  512.    wt: 3:   7 Complex Numbers Appetizer
  513.    wt: 3:   5 Drawing to Scale Avoids Angle Distortions
  514.    wt: 3:   2 Measuring Area Directly
  515.    wt: 3:   A Modular and Remainder Arithmetic
  516.    wt: 3:   25 Mid way Convergence to Axiomatic Approach
  517.    wt: 3:   24 Signed Numbers Arithmmetic Properties
  518.    wt: 3:   23 Distributive Law Two Derivations
  519.    wt: 3:   19 Signed Multiples of Vectors
  520.    wt: 3:   18 Geometrically Why Vector Addition Commutes
  521.    wt: 3:   16 Collinear Horizontal Arrows Vectors
  522.    wt: 3:   15 Head to Tails in place Addition Associative
  523.    wt: 3:   8 Division and Mulplication of Compound Fractions
  524.    wt: 3:   7 Arithmetic with Infinite Decimal Expansions
  525.    wt: 3:   5 Fractions with Infinite Decimal Expansions
  526.    wt: 3:   2 Counting Digits in Decimal Multiplication
  527.    wt: 3:   1 Fractions with Finite Decimal Expansions
  528.    wt: 3:   E Long Division Methods more
  529.    wt: 3:   D Long Division Methods
  530.    wt: 3:   A Decimal Addition Columm Methods
  531.    wt: 3:   8 Column Multiplication Methods in General
  532.    wt: 3:   7 Decimals Multiplication Methods Examples
  533.    wt: 3:   1 The Counting Origins of Numbers
  534.    wt: 3:   4 Fraction Operations Axiomatic Development
  535.    wt: 3:   1 Equivalent Computation Rules
  536.    wt: 3:   16 Real Numbers Comparison
  537.    wt: 3:   15 Real Number Division
  538.    wt: 3:   14 Real Number Multiplication
  539.    wt: 3:   13 Real Number Subtraction
  540.    wt: 3:   11 Real Number Addition
  541.    wt: 3:   9 Coordinates for Regions in Space
  542.    wt: 3:   2 Integers
  543.    wt: 3:   1 Whole and Natural Numbers
  544.    wt: 3:   5 Independent versus Dependent Variables
  545.    wt: 3:   More Exercises
  546.    wt: 3:   Simple Exercises
  547.    wt: 3:   1 GE Substitution four examples
  548.    wt: 3:   1 Essentially One Unknown
  549.    wt: 3:   Skill Development Notes
  550.    wt: 3:   10 One Example
  551.    wt: 3:   8 One Example
  552.    wt: 3:   7 Two Examples
  553.    wt: 3:   4 Two Examples
  554.    wt: 3:   3 Two Examples
  555.    wt: 3:   9 Sets in Probability and Statistics
  556.    wt: 3:   2 Venn Diagrams
  557.    wt: 3:   6 Three Notions of What is a Variable
  558.    wt: 3:   2 What is a Variable
  559.    wt: 3:   arithmetic videos Real Player Format
  560.    wt: 3:   5 Square Roots with primes more still
  561.    wt: 3:   4 Square Roots with primes more
  562.    wt: 3:   3 Properties of Square Roots with example
  563.    wt: 3:   14 GCD of 650 110 via Primes LCM via Product Rule
  564.    wt: 3:   13 GCD from given Prime Factorization
  565.    wt: 3:   6 GCD from Prime
  566.    wt: 3:   5 Common Divisors 60 45 via Prime
  567.    wt: 3:   LCM 60 45 Avoid List Method Use Prime
  568.    wt: 3:   1 Least Common Multiples LCM Introduction
  569.    wt: 3:   5 Counting with Tables Trees Product Rule Take II
  570.    wt: 3:   4 Counting with Trees Product Rule Take I
  571.    wt: 3:   11 What are real lengths and numbers
  572.    wt: 3:   7 negative and additive inverse
  573.    wt: 3:   5 lengths and signs of numbers
  574.    wt: 3:   4 signed coordinates for regions in space
  575.    wt: 3:   6 Simplification of Fractions with Units
  576.    wt: 3:   4 Fractions with Units
  577.    wt: 3:   18 Efficient Ways to Multiply
  578.    wt: 3:   16 Addition Subtraction Comparision Compared
  579.    wt: 3:   6 Multiplication of Mixed Numbers
  580.    wt: 3:   5 Equivalent Fractions
  581.    wt: 3:   4 Fraction Multiplication
  582.    wt: 3:   3 Unit fraction of a fraction
  583.    wt: 3:   1 What is a fraction Take II
  584.    wt: 3:   1 What is a fraction
  585.    wt: 3:   Fraction Operations by Raising Terms A Simple Innovation
  586.    wt: 3:   13 Subtraction with Additive Inverse
  587.    wt: 3:   10 Integer Multiplication Formulas
  588.    wt: 3:   5 Zero Movement and Additive Inverses
  589.    wt: 3:   15 Remainder Arithmetic Modulo 9 Example
  590.    wt: 3:   14 Remainder Arithmetic Modulo 9 Example
  591.    wt: 3:   13 Remainder Arithmetic Modulo 5 Example
  592.    wt: 3:   11 Remainder Arithmetic Long Division by 5 Quickly more
  593.    wt: 3:   10 Remainder Arithmetic Long Division by 5 Quickly
  594.    wt: 3:   9 Remainder Arithmetic Divisibility by 5
  595.    wt: 3:   7 Remainder Arithmetic Modulo 5 Examples I
  596.    wt: 3:   6 Remainder Arithmetic Modulo 5 Propertie
  597.    wt: 3:   19 video Prime Factorization Unique
  598.    wt: 3:   18 video Count Factors given Prime Factorization
  599.    wt: 3:   16 video Factors of 980 using prime
  600.    wt: 3:   11 Efficient Square Rule Use
  601.    wt: 3:   9 video Prime Factorization upto 19 squared
  602.    wt: 3:   8 video Prime Factorization upto 19
  603.    wt: 3:   4 video Prime Factorization Introduction
  604.    wt: 3:   11 Place Value SI Standard International way
  605.    wt: 3:   9 Place Value Review Decimal form of Avogrados number included
  606.    wt: 3:   1 Place Value in Three Digit Whole Numbers
  607.    wt: 3:   Exact Arithmetic Wholes and Fractions
  608.    wt: 3:   Formula Evaluation how to show work
  609.    wt: 3:   The 12 Times Table Visually
  610.    wt: 3:   4 Mixing and Changing Units of Time
  611.    wt: 3:   2 Time and Date Matters in School
  612.    wt: 3:   Example 2 volume of a cone
  613.    wt: 3:   Area Between Crossing Curves Lesson Take 2
  614.    wt: 3:   Example 3
  615.    wt: 3:   Example 2
  616.    wt: 3:   Area Between Curves Lesson Take 2
  617.    wt: 3:   28 Chain Rule Preparation for a Proof
  618.    wt: 3:   25 Chain Rule Animated Examples Continued
  619.    wt: 3:   24 Chain Rule Animated Examples
  620.    wt: 3:   20 Chain Rule for Pulley Systems
  621.    wt: 3:   16 Derivatives of reciprocals of sine and cosine
  622.    wt: 3:   14 sine and cosine derivatives 2nd step
  623.    wt: 3:   10 Power rule for negative integers
  624.    wt: 3:   7 Animated Differentiation Examples
  625.    wt: 3:   4 Sum Rule
  626.    wt: 3:   3 Motivation for Limit Definition Take 2
  627.    wt: 3:   2 Motivation for Limit Definition Take 1
  628.    wt: 3:   12 Limits with Parameters and Derivatives Take I
  629.    wt: 3:   11 Limits at infinity Three Examples
  630.    wt: 3:   3 Decimal insights for limits continuity convergence
  631.    wt: 3:   G.2 Differentiable Functions Mean Value Theorem
  632.    wt: 3:   F.2 Closed Range Theorem
  633.    wt: 3:   E2 Algebraic Properties of Limits
  634.    wt: 3:   D1 Sets and Sequences GLBs and LGBs
  635.    wt: 3:   PostScript For and Against Decimal Perspectives
  636.    wt: 3:   Chapter 24 Logarithms Powers and Exponentials
  637.    wt: 3:   Chapter 20 Vectors and Complex Numbers
  638.    wt: 3:   Chapter 14 Limits and Continuity with and sans Decimals
  639.    wt: 3:   Chapter 12. Units and Slopes
  640.    wt: 3:   Chapter 2. Slopes and Ski Trails
  641.    wt: 3:   Chapter 12 Four Phases
  642.    wt: 3:   Postscript C Consistency as a Tool for Reason
  643.    wt: 3:   Postscript B More on Story Telling and Reason
  644.    wt: 3:   Chapter 23 Truth Tables
  645.    wt: 3:   Chapter 21 Occurrence Tables
  646.    wt: 3:   Chapter 19 What is in chapters 20 to 24
  647.    wt: 3:   Chapter 16 Origins and Limitations of Rules and Patterns
  648.    wt: 3:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  649.    wt: 3:   Chapter 8 Change of Language
  650.    wt: 3:   Chapter 4 Implication Rules Forwards and Backwards
  651.    wt: 3:   Chapter 2 Skill Development
  652.    wt: 3:   Three Remarks
  653.    wt: 3:   L Skills with take home value
  654.    wt: 3:   How to Build Skills and Confidence
  655.    wt: 3:   6 Measuring via counting or arithmetic the role of fractions
  656.    wt: 2:   Appendix 2 primary school Arithmetic 01
  657.    wt: 2:   Appendix 1 primary and preschool mathematic
  658.    wt: 2:   G LAMP Introduction Problem Solving Skills
  659.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  660.    wt: 2:   Skills Chapter 5 Calculus
  661.    wt: 2:   Skills Chapter 4 Logic
  662.    wt: 2:   Ramblings Introduction Algebra Essay
  663.    wt: 2:   Skills Chapter 1 Arithmetic
  664.    wt: 2:   Skills Chapter 0 Introduction
  665.    wt: 2:   8 analytic geometry etc
  666.    wt: 2:   5 logarithms and exponentials etc
  667.    wt: 2:   4 algebra
  668.    wt: 2:   three goals to set for students
  669.    wt: 2:   About site lesson plans
  670.    wt: 2:   Maps Plans Drawings
  671.    wt: 2:   Secondary Three Mathematics
  672.    wt: 2:   talk the algebra talk
  673.    wt: 2:   three difficulties
  674.    wt: 2:   teaching tutoring algebraic reason
  675.    wt: 2:   05 13 OldSiteEntrancePage
  676.    wt: 2:   04 29 New Mathematics Curriculum
  677.    wt: 2:   04 25 when to stop or suspend mathemat
  678.    wt: 2:   standards for course material
  679.    wt: 2:   formal or informal peer review
  680.    wt: 2:   three kinds of reason in mathematics
  681.    wt: 2:   education an empirical art
  682.    wt: 2:   chapitre 12 00 les iles et division
  683.    wt: 2:   chapitre 04 02 Deuxieme enigme
  684.    wt: 2:   chapitre 02 00 La Communication des idees
  685.    wt: 2:   Quebec cahiers d apprentissage en mathematiques pour 4 16
  686.    wt: 2:   2 Energy Power Heat07
  687.    wt: 2:   1 Conductance Resistance Duality01
  688.    wt: 2:   D Wire Resistance Calculation02
  689.    wt: 2:   B Wire Resistance Qualitative02
  690.    wt: 2:   C Electromotive force conventional current02
  691.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  692.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  693.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  694.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  695.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  696.    wt: 2:   17 Math Booklets for children and young teenagers
  697.    wt: 2:   5 Patience Please for Yourself and Your Charges
  698.    wt: 2:   4 Learning Takes Time and Effort
  699.    wt: 2:   Ages 10 to 12 Geometry
  700.    wt: 2:   Ages 10 to 12 Arithmetic
  701.    wt: 2:   19 Horizontal line rule and method
  702.    wt: 2:   18 Vertical Line Rule and Method
  703.    wt: 2:   17 Function maxima minima and their location
  704.    wt: 2:   15 Sign analysis of functions
  705.    wt: 2:   13 From one to one to many to one
  706.    wt: 2:   8 Set view of relations and functions
  707.    wt: 2:   4 Function notation in and beyond mathematics
  708.    wt: 2:   10 quadratic exercises
  709.    wt: 2:   9 quadratics physical and further context
  710.    wt: 2:   8 quadratics backward use of various formulas
  711.    wt: 2:   7 quadratic formulla derivation
  712.    wt: 2:   2 quadratics graphing in general
  713.    wt: 2:   1 quadratics graphing exercises
  714.    wt: 2:   8 Notes for instructors or tutors
  715.    wt: 2:   6 Polynomial Operations and Equivalent Computation Rules
  716.    wt: 2:   2 Column Multiplication Method
  717.    wt: 2:   Rewriting algebraic substitution as function substitutions
  718.    wt: 2:   9 motivation for name arcsin
  719.    wt: 2:   4 possible motivation for term arccos
  720.    wt: 2:   2 cosine function more properties
  721.    wt: 2:   A Global Time and Navigation
  722.    wt: 2:   15 Dot and Cross Product
  723.    wt: 2:   7 Coordinate Addition and Scalar Multiplication
  724.    wt: 2:   4 Resultant of a Sum of Movements
  725.    wt: 2:   Vector and Complex Number Applet
  726.    wt: 2:   30 unit circle calculation of six trigonometric functions
  727.    wt: 2:   17G Pythagorean Theorem Converse
  728.    wt: 2:   15 sine cosine Complementary Angle Relations
  729.    wt: 2:   11 tangent function undefined when terminal side vertical
  730.    wt: 2:   9 Graphs of sine and cosine over one period
  731.    wt: 2:   8 period of tangent function
  732.    wt: 2:   7 period of sine and cosine
  733.    wt: 2:   16 References and Originality Question
  734.    wt: 2:   15 Pythagorean Theorem Converse
  735.    wt: 2:   5 An Easy Proof of the Distributive Law
  736.    wt: 2:   1 Rectangular Polar Coordinates Review
  737.    wt: 2:   7 Trignometric Ratios Unit Circle
  738.    wt: 2:   1 Angle Measurement with Degrees
  739.    wt: 2:   11 Triangle Similarity Missing Side Problem
  740.    wt: 2:   10 Similarity of Triangles Equivalent of Two Criteria
  741.    wt: 2:   9 Similarity of Triangles Usual Criteria
  742.    wt: 2:   7 Translations Rotations Reflections Dilatations
  743.    wt: 2:   4 Similarity Definition with Coordinate
  744.    wt: 2:   11 A Partial Summary
  745.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  746.    wt: 2:   6 Intersection of lines by solving linear systems
  747.    wt: 2:   A Measurement with Ruler Proper Use
  748.    wt: 2:   8 More Use of Maps Not Drawn to Scale
  749.    wt: 2:   6 Figuring with Maps Not to Scale
  750.    wt: 2:   1 Length Measurement
  751.    wt: 2:   musings do not puiblish real numbers
  752.    wt: 2:   A Signed Number Arithmetic Review
  753.    wt: 2:   9 Division with Digits after Decimal Point
  754.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  755.    wt: 2:   4 Location of Point in Decimal Addition
  756.    wt: 2:   3 Location of Point in Decimal Multiplication
  757.    wt: 2:   7 Real Numbers as Line Cordinates
  758.    wt: 2:   6 Unsigned Real Numbers
  759.    wt: 2:   5 Rational Numbers More
  760.    wt: 2:   4 Rational Numbers
  761.    wt: 2:   3 Fractions
  762.    wt: 2:   10 Set View of Wordy Extensions To Arithmetic
  763.    wt: 2:   8 Sets of Numbers
  764.    wt: 2:   7 Cautious or Safe Set Construction
  765.    wt: 2:   6 Power Set Notation
  766.    wt: 2:   5 Product Builder Notation
  767.    wt: 2:   4 Subset Builder Notation
  768.    wt: 2:   3 Counting with Sets etc
  769.    wt: 2:   1 Finite Sets
  770.    wt: 2:   3 Adding Words To Arithmetic
  771.    wt: 2:   About Folder Contents
  772.    wt: 2:   10 dividing signed numbers
  773.    wt: 2:   9 subtracting signed numbers
  774.    wt: 2:   8 multiplying signed numbers
  775.    wt: 2:   6 adding signed numbers
  776.    wt: 2:   D Remainders Modulo 11 Pair Rule
  777.    wt: 2:   C Divisibility by 11 Integer Recognition Method
  778.    wt: 2:   B Integer Long Division Multiple Choices
  779.    wt: 2:   A Associative Law Theorectical Note
  780.    wt: 2:   9 Multiplying Integers
  781.    wt: 2:   8 Multiplication by Signed Numbers Integers
  782.    wt: 2:   7 Multiplication by Signs
  783.    wt: 2:   6 Multiplication by Natural Numbers
  784.    wt: 2:   4 Adding Movements wiht opposite directions
  785.    wt: 2:   3 Adding Movements with same direction
  786.    wt: 2:   1 Integers as Coordinates
  787.    wt: 2:   7 More on Groups of 3 Place Value in Mixed Decimal Fractions
  788.    wt: 2:   6 Groups of 3 Place Value in Mixed Decimal Fractions
  789.    wt: 2:   5 More on Groups of 3 Place Value in Decimal Fractions
  790.    wt: 2:   4 Groups of 3 Place Value in Decimal Fractions
  791.    wt: 2:   3 More on Groups of 3 Multi Digit Place Value
  792.    wt: 2:   Expression Evaluation how to show work
  793.    wt: 2:   About folder contents
  794.    wt: 2:   015 School and work day counting tables
  795.    wt: 2:   012 Division of Time Intervals by Time Intervals
  796.    wt: 2:   9 Comparison and Subtraction of Time Intervals
  797.    wt: 2:   3 Units and Lengths of Time
  798.    wt: 2:   1 Intro of Kids To Time Date Skills
  799.    wt: 2:   Example 1 volume of a pyramid
  800.    wt: 2:   Volume of Solid by Cross Sections Lesson
  801.    wt: 2:   Area Between Crossing Curves Lesson Take 1
  802.    wt: 2:   Example 4 with x function of y
  803.    wt: 2:   Example 1
  804.    wt: 2:   Area Between Curves Lesson Take 1
  805.    wt: 2:   Summary
  806.    wt: 2:   2 Indefinite Integrals Exercises
  807.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  808.    wt: 2:   A Chain Rule Real Player video examples
  809.    wt: 2:   36 Cube root derivative animated
  810.    wt: 2:   30Chain Rule A Proof
  811.    wt: 2:   29 Chain Rule Optional Reading
  812.    wt: 2:   27 Chain Rule sinusoidal outer inner functions EGS
  813.    wt: 2:   26 Chain Rule Recognising outer inner functions
  814.    wt: 2:   23 Chain Rule in general
  815.    wt: 2:   19 Chain Rule for linear functions
  816.    wt: 2:   17 Derivatives of quotients of sine and cosine
  817.    wt: 2:   15 sine and cosine derivatives 3rd step
  818.    wt: 2:   13 sine and cosine derivatives 1st step
  819.    wt: 2:   12 Quotient rule examples
  820.    wt: 2:   11 Quotient rule
  821.    wt: 2:   9 Reciprocal rule
  822.    wt: 2:   8 Differentiation of polynomials
  823.    wt: 2:   6 Power rule from product rule
  824.    wt: 2:   5 Product Rule
  825.    wt: 2:   13 Limits with Parameters and Derivatives Take II
  826.    wt: 2:   10 Three one sided limits with infinite values
  827.    wt: 2:   9 Limits Continuity and Composition
  828.    wt: 2:   8 Four Animated Examples
  829.    wt: 2:   5 Jumps and absence of unlimited error control
  830.    wt: 2:   Postscript One Sided and Intermediate Value Theorems
  831.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  832.    wt: 2:   G.6 Bounded Derivatives implies Lipshitz Continuity
  833.    wt: 2:   G.3 Constant Difference Theorem Proof
  834.    wt: 2:   F.4 Finite Covering Theorem
  835.    wt: 2:   D2 Limits of Monotone Sequences
  836.    wt: 2:   C Triangle Inequalities
  837.    wt: 2:   B3 Bolzano Weierstrass Theorem
  838.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  839.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  840.    wt: 2:   Chapter 23 Links To Trigonometry
  841.    wt: 2:   Chapter 21 Arrow Addition
  842.    wt: 2:   Annotated Links to Material Elsehwere
  843.    wt: 2:   Postscript A Three Remarks
  844.    wt: 2:   Chapter 10 Transition
  845.    wt: 2:   Chapter 4 Complex Numbers and Why Slopes
  846.    wt: 2:   Chapter 3 Algebra Difficulties
  847.    wt: 2:   Foreword
  848.    wt: 2:   Postscript D Reflections on Law of the Excluded Middle
  849.    wt: 2:   Postscript A Story Telling
  850.    wt: 2:   Chapter 18 Sense and Knowledge
  851.    wt: 2:   Chapter 17 Objective Ways Trial and Error Discovery
  852.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  853.    wt: 2:   Foreword
  854.    wt: 2:   S Adding words to algebra
  855.    wt: 2:   R Why Learn Mathematics Skills
  856.    wt: 2:   Q How Logic and Proofs extend Show Work Practices
  857.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  858.    wt: 2:   O On Learning Mathematics and Science
  859.    wt: 2:   N Mathematics Prepare for College Studies
  860.    wt: 2:   N Improving Marks on Tests and Finals
  861.    wt: 2:   J. More on written work and showing skill
  862.    wt: 2:   H Jigsaw puzzles and problem solving
  863.    wt: 2:   E. When and how to correct errors
  864.    wt: 2:   B. Domino effect of errors
  865.    wt: 2:   Chapter 6 More Algebra and Geometry
  866.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  867.    wt: 2:   Chapter 2 Why Sets
  868.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  869.    wt: 2:   More Algebra and Slope based Calculus Preview
  870.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  871.    wt: 2:   The Math Forum and Site Content
  872.    wt: 1:   K LAMP Musings Science Education
  873.    wt: 1:   J LAMP Introduction Extrinsic Origins
  874.    wt: 1:   I LAMP Introduction Study Habits
  875.    wt: 1:   H LAMP Introduction Instructional Concepts
  876.    wt: 1:   F LAMP Introduction Prerequisites
  877.    wt: 1:   E LAMP Introduction Modern Mathematics
  878.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  879.    wt: 1:   A Introduction Objectives
  880.    wt: 1:   Ramblings Extrinsic numbers theory
  881.    wt: 1:   11 pure mathematics
  882.    wt: 1:   10 statistics
  883.    wt: 1:   9 combinatorics probability sets
  884.    wt: 1:   6 polynomials etc
  885.    wt: 1:   1 arithmetic with unsigned numbers
  886.    wt: 1:   What is POMME
  887.    wt: 1:   why bother
  888.    wt: 1:   permissions for teachers
  889.    wt: 1:   Math Ed if it must be short make it lean effective
  890.    wt: 1:   activities for students
  891.    wt: 1:   key notes and themes
  892.    wt: 1:   learning takes time
  893.    wt: 1:   what should be learnt and When
  894.    wt: 1:   Postscript 2007 01 10
  895.    wt: 1:   Education Reform Inconsistencies
  896.    wt: 1:   how letters appear
  897.    wt: 1:   Secondary Two Mathematics
  898.    wt: 1:   Secondary One Mathematics
  899.    wt: 1:   teaching tips
  900.    wt: 1:   What to Tell Students
  901.    wt: 1:   mathematics curriculum shifts
  902.    wt: 1:   Education in mathematics science and technology
  903.    wt: 1:   Four ways to improve education reform
  904.    wt: 1:   Motivation and Context Problem
  905.    wt: 1:   need for a mixed mathematics curriculum
  906.    wt: 1:   Leaner mathematics curriculum
  907.    wt: 1:   words for mathematics instructor
  908.    wt: 1:   chapitre 07 01 principle D induction mathematique
  909.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  910.    wt: 1:   chapitre 06 00 Chaines de la raison
  911.    wt: 1:   chapitre 05 00 Deception
  912.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  913.    wt: 1:   chapitre 04 09 Regles accidentelles
  914.    wt: 1:   chapitre 04 08 Limitations et benefices
  915.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  916.    wt: 1:   chapitre 04 06 engagements
  917.    wt: 1:   chapitre 04 05 Implication versus suggestion
  918.    wt: 1:   chapitre 04 04 Parlons de la logique
  919.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  920.    wt: 1:   chapitre 04 01 Premiere enigme
  921.    wt: 1:   chapitre 04 00 Les regles d implication
  922.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  923.    wt: 1:   chapitre 01 00 Introduction
  924.    wt: 1:   liens
  925.    wt: 1:   problemes responses
  926.    wt: 1:   problemes algebre et arithmetique
  927.    wt: 1:   Trois Notions qui menent a algebre
  928.    wt: 1:   deux definitions pour variable
  929.    wt: 1:   logique deux enigme
  930.    wt: 1:   4 Energy Power Heat09
  931.    wt: 1:   3 Energy Power Heat08
  932.    wt: 1:   1 Energy Power Heat06
  933.    wt: 1:   E Energy Power05
  934.    wt: 1:   D Energy Power04
  935.    wt: 1:   C Energy Power03
  936.    wt: 1:   A Energy Power01
  937.    wt: 1:   F Wire Resistance Calculation04
  938.    wt: 1:   E Wire Resistance Calculation03
  939.    wt: 1:   C Wire Resistance Calculation01
  940.    wt: 1:   A Wire Resistance Qualitative01
  941.    wt: 1:   3 Like resistors in parallel
  942.    wt: 1:   2 Unlike resistors in parallel01
  943.    wt: 1:   H Series Circuit02
  944.    wt: 1:   B Electromotive force conventional current01
  945.    wt: 1:   Home Tutoring and Home Schooling
  946.    wt: 1:   15 Counting For Parents
  947.    wt: 1:   14 Multiplication and Times Tables
  948.    wt: 1:   13 Addition and Addition Tables
  949.    wt: 1:   11 Help and Defend Your Child or Teens Education
  950.    wt: 1:   10 Ends values for work study instruction
  951.    wt: 1:   3 Preparing for Science Studies
  952.    wt: 1:   1 Speaking Skills
  953.    wt: 1:   Ages 9 to 10
  954.    wt: 1:   Ages 8 to 9
  955.    wt: 1:   Ages 7 to 8
  956.    wt: 1:   Ages 6 to 7
  957.    wt: 1:   Ages 4 plus to 5 plus
  958.    wt: 1:   Ages 3 plus to 4 plus
  959.    wt: 1:   16 Increasing or decreasing on intervals
  960.    wt: 1:   14 Surjections Injections Bijections
  961.    wt: 1:   10 Interval Notation
  962.    wt: 1:   9 Set theory term relation possible origins
  963.    wt: 1:   7 Functions with finite domains
  964.    wt: 1:   1 Geometric Introduction of Function Notation
  965.    wt: 1:   Introduction Reading Guide
  966.    wt: 1:   A Quadratics Summary
  967.    wt: 1:   6 quadratics numerical approach
  968.    wt: 1:   5 quadratics completing the square
  969.    wt: 1:   4 quadratics difference of two squares
  970.    wt: 1:   3 quadratics factoring by inspection
  971.    wt: 1:   Quadratics in 10 steps
  972.    wt: 1:   7 Links Lessons Elsewhere
  973.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  974.    wt: 1:   4 Polynomials Long division linear divisor
  975.    wt: 1:   3 Polynomials Multiplication Addition
  976.    wt: 1:   1 Polynomials Distributive Law
  977.    wt: 1:   8 arcsin left inverse of sine Graph
  978.    wt: 1:   7 arcsin left inverse of sine Definition
  979.    wt: 1:   6 Graph of arccos function
  980.    wt: 1:   5 Swapping Coordinates is a reflection
  981.    wt: 1:   3 Left Inverse of cosine arccos definition
  982.    wt: 1:   1 cosine function properties
  983.    wt: 1:   14 Why Scalar Multiplication Distributes Physical Argument
  984.    wt: 1:   13 Velocity Vectors in Physics
  985.    wt: 1:   11 Component Method
  986.    wt: 1:   10 Parallelogram Addition Method
  987.    wt: 1:   9 Head to Tail Coordinate View
  988.    wt: 1:   8 Parallel Vectors
  989.    wt: 1:   6 Vectors with Coordinates
  990.    wt: 1:   5 Head To Tail Arrow Addition
  991.    wt: 1:   3 Navigation with Arrows or Vectors
  992.    wt: 1:   1 Unsigned Coordinates
  993.    wt: 1:   18 sum of sinusoidal waves as a single wave
  994.    wt: 1:   17F Law of cosines
  995.    wt: 1:   17A The complex number valued trig function cis
  996.    wt: 1:   1 Unit Points Reflections Rotations
  997.    wt: 1:   Unit Circle Development of Trigonometry
  998.    wt: 1:   19 N th Roots of Unity
  999.    wt: 1:   18 Sixth Roots of Unity
  1000.    wt: 1:   17 Cube Roots of unity
  1001.    wt: 1:   14 Law of cosines
  1002.    wt: 1:   9 The complex number valued trig function cis
  1003.    wt: 1:   8 Unit Circle Development of Trigonometry
  1004.    wt: 1:   7 Second Way to Calculate Products
  1005.    wt: 1:   6 Field Properties of Complex Number
  1006.    wt: 1:   4 Multiplication Properties
  1007.    wt: 1:   3 Addition Properties
  1008.    wt: 1:   Appetizer A Complex Number Applet
  1009.    wt: 1:   Why Trigonometry the whyslopes view
  1010.    wt: 1:   6 Geometric Diagrams in Class
  1011.    wt: 1:   3 Similarity by Design with coordinates
  1012.    wt: 1:   1 Early Concept of Like or Similar Shapes
  1013.    wt: 1:   About Folder Contents
  1014.    wt: 1:   016 Numbering Occidental Calendar Days
  1015.    wt: 1:   014 Counting Days with Calendars
  1016.    wt: 1:   013 Travel Time Tables
  1017.    wt: 1:   011 Division of Time Intervals By Numbers
  1018.    wt: 1:   010 Repeated Addition of Time Intervals
  1019.    wt: 1:   8 Addition of Time Intervals via subtotaling
  1020.    wt: 1:   7 Addition of Time Intervals
  1021.    wt: 1:   6 How long is a million seconds
  1022.    wt: 1:   5 Conversion Arithmetic
  1023.    wt: 1:   5 Area Under Curve Exercise
  1024.    wt: 1:   4 Definite Integrals Evaluation Exercises
  1025.    wt: 1:   3 Two Chain Rule Method Exercises
  1026.    wt: 1:   1 Chain Rule in Reverse Integration Method
  1027.    wt: 1:   4 Second derivative test exercise example
  1028.    wt: 1:   2 Second derivative test prequel
  1029.    wt: 1:   34 Derivative of exponential function
  1030.    wt: 1:   33 Chain Rule Real Player video examples
  1031.    wt: 1:   31 Derivatives of inverse functions
  1032.    wt: 1:   18 Chain Rule Introduction
  1033.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  1034.    wt: 1:   7 Evaluation by immediate or delayed substitution
  1035.    wt: 1:   6 Continuity at a point
  1036.    wt: 1:   4 Numerical properties
  1037.    wt: 1:   1 Numerical introduction
  1038.    wt: 1:   G.5 Motions With Bounded Velocities
  1039.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  1040.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  1041.    wt: 1:   F.5b Extreme Value Theorem
  1042.    wt: 1:   F.5a Equicontinuity Theorems
  1043.    wt: 1:   F.3 Intermediate Value Theorem
  1044.    wt: 1:   F.1 What Functions are Continuous
  1045.    wt: 1:   E1 Error Control Inequalities
  1046.    wt: 1:   A1. Introduction
  1047.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  1048.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  1049.    wt: 1:   Chapter 10 Slopes and Units
  1050.    wt: 1:   Chapter 7 Slopes and Velocity
  1051.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  1052.    wt: 1:   Chapter 4. More Slope Sign Analysis
  1053.    wt: 1:   Chapter 3. Slope Sign Analysis
  1054.    wt: 1:   Fall 1983 Calculus Appetizer
  1055.    wt: 1:   Foreword
  1056.    wt: 1:   Postscript B Mathematics Education References
  1057.    wt: 1:   Chapter 11 Elementary Instruction
  1058.    wt: 1:   Chapter 9 The Two Ends
  1059.    wt: 1:   Chapter 8 Modern Instruction
  1060.    wt: 1:   Chapter 7 Two Treatments of Geometry
  1061.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  1062.    wt: 1:   Chapter 5 Four References
  1063.    wt: 1:   Chapter 1 Introduction
  1064.    wt: 1:   Chapter 15 Objective Processes
  1065.    wt: 1:   Chapter 11 Accidental Patterns
  1066.    wt: 1:   Chapter 10 Responsibility
  1067.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  1068.    wt: 1:   Chapter 7 Longer Chains of Reason
  1069.    wt: 1:   Chapter 6 Chains of Reason
  1070.    wt: 1:   Chapter 5 Deception
  1071.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  1072.    wt: 1:   Chapter 1 Introduction
  1073.    wt: 1:   1 Links to Online Resources Elsewhere Take 1
  1074.    wt: 1:   M Words to extend arithmetic
  1075.    wt: 1:   H more Routine to non routine problem solving
  1076.    wt: 1:   F. The student teacher tutor feedback loop
  1077.    wt: 1:   D. Check work a must with a caution
  1078.    wt: 1:   C. Domino effect of being careful
  1079.    wt: 1:   A. Skill has to be seen to believed
  1080.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  1081.    wt: 1:   Chapter 8 Skipped Topics and Why
  1082.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  1083.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  1084.    wt: 1:   Chapter 3 Algebra Starter Lessons
  1085.    wt: 1:   Helping the Blind in Logic and Mathematics
  1086.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  1087.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  1088.    wt: 1:   Systematic Algebra Skill Development Missing Links
  1089.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  1090.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  1091.    wt: 11:   Chapter 22. Geometric Sums and Sequences
  1092.    wt: 10:   Chapter 20. Degrees and Radians
  1093.    wt: 10:   Chapter 8 Three Skills For Algebra
  1094.    wt: 10:   Chapter 2 Implication Rules Forwards and Backwards

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

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

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

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

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

The 8 Most Popular Site Inlinks

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

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

Parent Center: Help your child or teen learn:

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

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

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

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

Arithmetic and Number Theory Skills

Algebra Starter Lessons

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


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

Geometry - maps plans trigonometry vectors

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

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

More Algebra

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

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

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

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

  2. Flash Video for Calculus Phobics

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

Unsolicited Advice

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

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

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

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

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