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

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

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

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

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

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

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

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  1.    wt: 6:   Volume 1B Mathematics Curriculum Notes/
  2.    wt: 3:   8 Unifying Theme For Algebra/
  3.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  4.    wt: 3:   2 Formula Forward Use Evaluation/
  5.    wt: 3:   Volume 2 Three Skills For Algebra/
  6.    wt: 2:   10 Examples of Algebraic Reasoning/
  7.    wt: 2:   9 Proportionality Backwards and Forwards/
  8.    wt: 1:   LAMP Lean Applied Mathematics Program/
  9.    wt: 1:   Progressive Observable Motivated Mathematics Education/
  10.    wt: 1:   Mathematics Education Essays/
  11.    wt: 1:   Volume 1A Regles et modeles/
  12.    wt: 1:   Mathematics Skills Year by Year/
  13.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  14.    wt: 1:   4 Functions/
  15.    wt: 1:   3 Quadratics Geometrically/
  16.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  17.    wt: 1:   1 Five Polynomial Operations/
  18.    wt: 1:   More Algebra/
  19.    wt: 1:   B Real Numbers Extrinsic Development/
  20.    wt: 1:   A Origins of Counting and Figuring Methods/
  21.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  22.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  23.    wt: 1:   5 Real Numbers/
  24.    wt: 1:   4 Computation Rules and Function Notation/
  25.    wt: 1:   Step 4 Gaussian Elimination/
  26.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  27.    wt: 1:   Step 1 Stick diagram and fractions/
  28.    wt: 1:   3 Solving Linear Equations/
  29.    wt: 1:   1 Working With Sets/
  30.    wt: 1:   Algebra Starter Lessons/
  31.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  32.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  33.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  34.    wt: 1:   Volume 1A Pattern Based Reason/
  35.    wt: 1:   Volume 1 Elements of Reason/
  36.    wt: 1:   Mathematics 506 Lessons/
  37.    wt: 1:   Secondary Mathematics A Practical Approach/
  38.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  39.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

248 matches:

  1.    wt: 3:   need for a mixed mathematics curriculum
  2.    wt: 2:   mathematics curriculum shifts
  3.    wt: 2:   geometric implications for algebra
  4.    wt: 2:   three goals for Mathematics Education
  5.    wt: 2:   04 29 New Mathematics Curriculum
  6.    wt: 2:   three aims for mathematics students
  7.    wt: 2:   formal or informal peer review
  8.    wt: 2:   Leaner mathematics curriculum
  9.    wt: 2:   Prequel In For A Penny In For A Pound
  10.    wt: 2:   words for mathematics instructor
  11.    wt: 2:   12 Goals and Objectives For Mathematics
  12.    wt: 2:   3 Preparing for Science Studies
  13.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  14.    wt: 2:   5 Function notation for geometric transformations
  15.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  16.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  17.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  18.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  19.    wt: 2:   8 Notes for instructors or tutors
  20.    wt: 2:   26 Formulas for products of sines and cosines
  21.    wt: 2:   17E Trig Formulas for dot and cross Products
  22.    wt: 2:   17D cis formulas for sine cosines and tangent
  23.    wt: 2:   13 Trig Formulas for dot and cross Products
  24.    wt: 2:   12 cis formulas for sine cosines and tangent
  25.    wt: 2:   4 Equations for lines three forms
  26.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  27.    wt: 2:   Formula Usage Show Work Format
  28.    wt: 2:   5 Box Volume Formula Example
  29.    wt: 2:   1 Written work formats for developing and showing skill
  30.    wt: 2:   1 Three Skills For Algebra
  31.    wt: 2:   38 Formulas and derivatives for powers and roots
  32.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  33.    wt: 2:   Postscript For Better Performance
  34.    wt: 2:   Chapter 18. Rules for Algebra
  35.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  36.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  37.    wt: 2:   Chapter 8 Three Skills For Algebra
  38.    wt: 2:   Chapter 2 For and Against Mathematics
  39.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  40.    wt: 2:   N Mathematics Prepare for College Studies
  41.    wt: 2:   G. Written work formats for developing and showing skill
  42.    wt: 1:   E LAMP Introduction Modern Mathematics
  43.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  44.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  45.    wt: 1:   Ramblings Introduction Algebra Essay
  46.    wt: 1:   Skills Chapter 3 Algebra
  47.    wt: 1:   11 pure mathematics
  48.    wt: 1:   4 algebra
  49.    wt: 1:   three goals to set for students
  50.    wt: 1:   permissions for teachers
  51.    wt: 1:   activities for students
  52.    wt: 1:   key notes and themes
  53.    wt: 1:   Mathematics Education Professors
  54.    wt: 1:   mathematics in context
  55.    wt: 1:   Education Reform Inconsistencies
  56.    wt: 1:   Secondary Three Mathematics
  57.    wt: 1:   Secondary Two Mathematics
  58.    wt: 1:   Secondary One Mathematics
  59.    wt: 1:   talk the algebra talk
  60.    wt: 1:   teaching tutoring algebraic reason
  61.    wt: 1:   Lessening Algebra Difficulties
  62.    wt: 1:   the trouble with algebra
  63.    wt: 1:   02 21 words for teachers
  64.    wt: 1:   02 20 mathematics education references
  65.    wt: 1:   standards for course material
  66.    wt: 1:   mathematics instruction in general
  67.    wt: 1:   Education in mathematics science and technology
  68.    wt: 1:   three kinds of reason in mathematics
  69.    wt: 1:   Four ways to improve education reform
  70.    wt: 1:   fairness and inductive principles for instruction
  71.    wt: 1:   C Electromotive force conventional current02
  72.    wt: 1:   B Electromotive force conventional current01
  73.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  74.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  75.    wt: 1:   24 Standards For Skill Develoment Take II
  76.    wt: 1:   24 Standards For Skill Develoment
  77.    wt: 1:   22 Student Centered Highschool Mathematics
  78.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  79.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  80.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  81.    wt: 1:   18 Primary School Mathematics
  82.    wt: 1:   17 Math Booklets for children and young teenagers
  83.    wt: 1:   16 Secondary Mathematics Tips
  84.    wt: 1:   15 Counting For Parents
  85.    wt: 1:   10 Ends values for work study instruction
  86.    wt: 1:   5 Patience Please for Yourself and Your Charges
  87.    wt: 1:   4 Learning Takes Time and Effort
  88.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  89.    wt: 1:   6 Set Existence Formation and Notation
  90.    wt: 1:   4 Function notation in and beyond mathematics
  91.    wt: 1:   3 Formula or function graphing exercise
  92.    wt: 1:   2 Algebraic use of function notation
  93.    wt: 1:   8 quadratics backward use of various formulas
  94.    wt: 1:   7 quadratic formulla derivation
  95.    wt: 1:   Rewriting algebraic substitution as function substitutions
  96.    wt: 1:   12 motivation for term arctan
  97.    wt: 1:   9 motivation for name arcsin
  98.    wt: 1:   4 possible motivation for term arccos
  99.    wt: 1:   12 From Applied To Pure Mathematics
  100.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  101.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  102.    wt: 1:   8 Straight Lines Equation for vertical
  103.    wt: 1:   17 tangent function angle sum formulas
  104.    wt: 1:   29 secant cosecant and cotangent for acute angles
  105.    wt: 1:   25 tangent double angle formula Slope connection
  106.    wt: 1:   24 tangent Angle Difference Formula
  107.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  108.    wt: 1:   21 sine and cosine Half Angle Formulas
  109.    wt: 1:   20 sine and cosine Double Angle Formulas
  110.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  111.    wt: 1:   17C sine and cosine double triple angle formulas
  112.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  113.    wt: 1:   12 Graph of tangent function for one period
  114.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  115.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  116.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  117.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  118.    wt: 1:   11 sine and cosine double triple angle formulas
  119.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  120.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  121.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  122.    wt: 1:   8 Mid Point Formula
  123.    wt: 1:   5 Algebraic View of Slopes
  124.    wt: 1:   3 Slope product for perpendicular lines
  125.    wt: 1:   2 point slope equation for a line
  126.    wt: 1:   13 Pythagorean spatial distance formulas
  127.    wt: 1:   10 Pythagorean plane distance formula
  128.    wt: 1:   PS H Distributive Law For Complex Numbers
  129.    wt: 1:   6 Column Methods for Decimal Multiplication
  130.    wt: 1:   5 Distributive Law for Whole Numbers
  131.    wt: 1:   4 Commutative Law Groups Counting Form
  132.    wt: 1:   3 Inequalities Algebraically
  133.    wt: 1:   2 Algebraic View
  134.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  135.    wt: 1:   6 Compound Interest Forward and Backwards
  136.    wt: 1:   5 Triangle Area Formula Backwards
  137.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  138.    wt: 1:   5 Equality in Algebra
  139.    wt: 1:   3 Product Axioms Two Forms
  140.    wt: 1:   2 More and Less Than for Counts and Measures
  141.    wt: 1:   9 Coordinates for Regions in Space
  142.    wt: 1:   8 Coordinates for Maps and Planes
  143.    wt: 1:   3 Geometric Formulas and Function Notation
  144.    wt: 1:   1 Formulas Dependence and Function Notation
  145.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  146.    wt: 1:   6 Algebraic Solution Example
  147.    wt: 1:   5 Algebraic Solutions Introduction
  148.    wt: 1:   Skill Development Notes
  149.    wt: 1:   Using Letters for Physical Quantities
  150.    wt: 1:   13 Naming Identifying Formulas with Words
  151.    wt: 1:   11 Volume of Sphere
  152.    wt: 1:   10 Volume of Pyramid
  153.    wt: 1:   9 Volume of Cone
  154.    wt: 1:   8 Compound Interest Formula Evaluation
  155.    wt: 1:   7 Compound Interest Formula Introduction
  156.    wt: 1:   4 Circle Area Formula Example
  157.    wt: 1:   3 Triangle Area Formula Example
  158.    wt: 1:   2 Another Rectangle Area Formula Example
  159.    wt: 1:   4 A Brief Story of numbers and algebra
  160.    wt: 1:   arithmetic videos Real Player Format
  161.    wt: 1:   1 More and Less Than for Counts and Measures
  162.    wt: 1:   4 signed coordinates for regions in space
  163.    wt: 1:   3 signed coordinates for maps and planes
  164.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  165.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  166.    wt: 1:   21 Reciprocals for Fractions and Wholes
  167.    wt: 1:   13 Fraction Comparison Algebraic View
  168.    wt: 1:   11 Simplification an Algebraic View
  169.    wt: 1:   6 Multiplication Algebraically Take II
  170.    wt: 1:   11 Adding Integers Formulas and Examples
  171.    wt: 1:   10 Integer Multiplication Formulas
  172.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  173.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  174.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  175.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  176.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  177.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  178.    wt: 1:   7 Calculator Usage Notes and Cautions
  179.    wt: 1:   Long Division forwards and backwards Example 3
  180.    wt: 1:   Long Division forwards and backwards Example 2
  181.    wt: 1:   Long Division forwards and backwards Example 1
  182.    wt: 1:   A Elementary Basis for Multiplication Methods
  183.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  184.    wt: 1:   5 A Tip for Efficent Subtraction
  185.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  186.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  187.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  188.    wt: 1:   Quick history of numbers and algebra
  189.    wt: 1:   Formula Evaluation how to show work
  190.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  191.    wt: 1:   Example 2 volume of a cone
  192.    wt: 1:   Example 1 volume of a pyramid
  193.    wt: 1:   Volume of Solid by Cross Sections Lesson
  194.    wt: 1:   A Related Material in Volume 3
  195.    wt: 1:   A Related lessons in Volume 3
  196.    wt: 1:   28 Chain Rule Preparation for a Proof
  197.    wt: 1:   22 Chain Rule for polynomials
  198.    wt: 1:   21 Chain Rule for powers
  199.    wt: 1:   20 Chain Rule for Pulley Systems
  200.    wt: 1:   19 Chain Rule for linear functions
  201.    wt: 1:   10 Power rule for negative integers
  202.    wt: 1:   3 Motivation for Limit Definition Take 2
  203.    wt: 1:   2 Motivation for Limit Definition Take 1
  204.    wt: 1:   3 Decimal insights for limits continuity convergence
  205.    wt: 1:   2 Algebraic codification
  206.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  207.    wt: 1:   E2 Algebraic Properties of Limits
  208.    wt: 1:   PostScript For and Against Decimal Perspectives
  209.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  210.    wt: 1:   Foreword
  211.    wt: 1:   Postscript More on Better Performance
  212.    wt: 1:   Appendix E. How To Study Mathematics and Why
  213.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  214.    wt: 1:   Chapter 23. Notation For Sums
  215.    wt: 1:   Solutions For Arithmetic Exercises
  216.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  217.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  218.    wt: 1:   Foreword
  219.    wt: 1:   Postscript B Mathematics Education References
  220.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  221.    wt: 1:   Chapter 3 Algebra Difficulties
  222.    wt: 1:   Foreword
  223.    wt: 1:   Postscript C Consistency as a Tool for Reason
  224.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  225.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  226.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  227.    wt: 1:   Foreword
  228.    wt: 1:   S Adding words to algebra
  229.    wt: 1:   R Why Learn Mathematics Skills
  230.    wt: 1:   O On Learning Mathematics and Science
  231.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  232.    wt: 1:   Chapter 6 More Algebra and Geometry
  233.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  234.    wt: 1:   Chapter 3 Algebra Starter Lessons
  235.    wt: 1:   7 Games and Activities for Instruction
  236.    wt: 1:   Helping the Blind in Logic and Mathematics
  237.    wt: 1:   Mathematics Education References
  238.    wt: 1:   Mathematics Education References
  239.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  240.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  241.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  242.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  243.    wt: 1:   Implementation Notes
  244.    wt: 1:   More Algebra and Slope based Calculus Preview
  245.    wt: 1:   Systematic Algebra Skill Development Missing Links
  246.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  247.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  248.    wt: 1:   The Math Forum and Site Content

Extended Search

640 matches:

  1.    wt: 8:   Chapter 2 For and Against Mathematics
  2.    wt: 7:   Postscript B Mathematics Education References
  3.    wt: 7:   Chapter 6 Rule Based Reason in Mathematics
  4.    wt: 7:   Chapter 3 Algebra Difficulties
  5.    wt: 7:   Foreword
  6.    wt: 6:   Annotated Links to Material Elsehwere
  7.    wt: 6:   Postscript A Three Remarks
  8.    wt: 6:   Chapter 12 Four Phases
  9.    wt: 6:   Chapter 11 Elementary Instruction
  10.    wt: 6:   Chapter 10 Transition
  11.    wt: 6:   Chapter 9 The Two Ends
  12.    wt: 6:   Chapter 8 Modern Instruction
  13.    wt: 6:   Chapter 7 Two Treatments of Geometry
  14.    wt: 6:   Chapter 5 Four References
  15.    wt: 6:   Chapter 4 Complex Numbers and Why Slopes
  16.    wt: 6:   Chapter 1 Introduction
  17.    wt: 5:   9 Circle Area and Perimeter Formula Backwards Forwards
  18.    wt: 5:   5 Box Volume Formula Example
  19.    wt: 5:   1 Written work formats for developing and showing skill
  20.    wt: 5:   Postscript For Better Performance
  21.    wt: 5:   Chapter 18. Rules for Algebra
  22.    wt: 5:   Chapter 14. Forward and Backward Use of a Formula
  23.    wt: 5:   Postscript Unifying Theme A Fourth Skill For Algebra
  24.    wt: 5:   Chapter 8 Three Skills For Algebra
  25.    wt: 4:   need for a mixed mathematics curriculum
  26.    wt: 4:   8 Pythagorean Relation Forwards Backwards
  27.    wt: 4:   6 Compound Interest Forward and Backwards
  28.    wt: 4:   5 Triangle Area Formula Backwards
  29.    wt: 4:   4 Rectangle Area and Like Formulas Backwards
  30.    wt: 4:   6 Algebraic Solution Example
  31.    wt: 4:   5 Algebraic Solutions Introduction
  32.    wt: 4:   13 Naming Identifying Formulas with Words
  33.    wt: 4:   11 Volume of Sphere
  34.    wt: 4:   10 Volume of Pyramid
  35.    wt: 4:   9 Volume of Cone
  36.    wt: 4:   8 Compound Interest Formula Evaluation
  37.    wt: 4:   7 Compound Interest Formula Introduction
  38.    wt: 4:   4 Circle Area Formula Example
  39.    wt: 4:   3 Triangle Area Formula Example
  40.    wt: 4:   2 Another Rectangle Area Formula Example
  41.    wt: 4:   Postscript More on Better Performance
  42.    wt: 4:   Appendix E. How To Study Mathematics and Why
  43.    wt: 4:   Appendix A. Reading Guide For Next Appendices
  44.    wt: 4:   Chapter 23. Notation For Sums
  45.    wt: 4:   Solutions For Arithmetic Exercises
  46.    wt: 4:   Chapter 7 Prep for Calculus Arithmetic Exercises
  47.    wt: 4:   Chapter 2 Implication Rules Forwards and Backwards
  48.    wt: 4:   Foreword
  49.    wt: 3:   mathematics curriculum shifts
  50.    wt: 3:   geometric implications for algebra
  51.    wt: 3:   three goals for Mathematics Education
  52.    wt: 3:   04 29 New Mathematics Curriculum
  53.    wt: 3:   three aims for mathematics students
  54.    wt: 3:   formal or informal peer review
  55.    wt: 3:   Leaner mathematics curriculum
  56.    wt: 3:   Prequel In For A Penny In For A Pound
  57.    wt: 3:   words for mathematics instructor
  58.    wt: 3:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  59.    wt: 3:   5 Function notation for geometric transformations
  60.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  61.    wt: 3:   8 Formulas for Fractional Exponents with Logarithms
  62.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  63.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  64.    wt: 3:   8 Notes for instructors or tutors
  65.    wt: 3:   3 Inequalities Algebraically
  66.    wt: 3:   2 Algebraic View
  67.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  68.    wt: 3:   3 Linear Equation Literal Solution More
  69.    wt: 3:   2 Linear Equation Literal Solution
  70.    wt: 3:   1 Changing Calculations
  71.    wt: 3:   4 Four Examples Fractional Coefficients
  72.    wt: 3:   3 Four Examples
  73.    wt: 3:   2 Three Examples
  74.    wt: 3:   1 Proper Equal Sign Usage
  75.    wt: 3:   Formula Usage Show Work Format
  76.    wt: 3:   12 Cone Cylinder Sphere Lesson Idea
  77.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  78.    wt: 3:   1 Three Skills For Algebra
  79.    wt: 3:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  80.    wt: 3:   Appendix D. What to do in School and Why
  81.    wt: 3:   Appendix C. How to Read
  82.    wt: 3:   Appendix B. How To Learn
  83.    wt: 3:   Chapter 31 Direct and Indirect Reason
  84.    wt: 3:   Chapter 30 Truth Tables
  85.    wt: 3:   Chapter 29 Contrapositive and Vacuously True Implications
  86.    wt: 3:   Chapter 28 Occurrence Tables
  87.    wt: 3:   Chapter 27 Shorthand Symbols as Pronouns
  88.    wt: 3:   Chapter 26 What is in chapters 27 to 31
  89.    wt: 3:   Chapter 25. Mathematical Induction Examples
  90.    wt: 3:   Chapter 24. Personal Investment and Pension EGS
  91.    wt: 3:   Chapter 22. Geometric Sums and Sequences
  92.    wt: 3:   Chapter 21. Third Reading Guide
  93.    wt: 3:   Chapter 20. Degrees and Radians
  94.    wt: 3:   Chapter 19. Functions and Sets
  95.    wt: 3:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  96.    wt: 3:   Chapter 16. Painless Theorem Proving
  97.    wt: 3:   Chapter 15. Solving Linear Equations
  98.    wt: 3:   Chapter 13. Second Reading Guide
  99.    wt: 3:   Chapter 12. Shorthand Usage Guide
  100.    wt: 3:   Chapter 11. Why Shorthand
  101.    wt: 3:   Chapter 10 Describing and Changing Calculations
  102.    wt: 3:   Postscript What is a Variable
  103.    wt: 3:   Chapter 9 Talking about Numbers or Quantities
  104.    wt: 3:   Chapter 6 Change of Language
  105.    wt: 3:   Chapter 5 Islands and Divisions of Knowledge
  106.    wt: 3:   Chapter 4 Longer Chains of Reason
  107.    wt: 3:   Chapter 3 Chains of Reason
  108.    wt: 3:   Chapter 1 Introduction to Chapters 2 to 6
  109.    wt: 2:   E LAMP Introduction Modern Mathematics
  110.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  111.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  112.    wt: 2:   Ramblings Introduction Algebra Essay
  113.    wt: 2:   Skills Chapter 3 Algebra
  114.    wt: 2:   11 pure mathematics
  115.    wt: 2:   4 algebra
  116.    wt: 2:   three goals to set for students
  117.    wt: 2:   permissions for teachers
  118.    wt: 2:   activities for students
  119.    wt: 2:   key notes and themes
  120.    wt: 2:   Mathematics Education Professors
  121.    wt: 2:   mathematics in context
  122.    wt: 2:   Education Reform Inconsistencies
  123.    wt: 2:   Secondary Three Mathematics
  124.    wt: 2:   Secondary Two Mathematics
  125.    wt: 2:   Secondary One Mathematics
  126.    wt: 2:   talk the algebra talk
  127.    wt: 2:   teaching tutoring algebraic reason
  128.    wt: 2:   Lessening Algebra Difficulties
  129.    wt: 2:   the trouble with algebra
  130.    wt: 2:   02 21 words for teachers
  131.    wt: 2:   02 20 mathematics education references
  132.    wt: 2:   standards for course material
  133.    wt: 2:   mathematics instruction in general
  134.    wt: 2:   Education in mathematics science and technology
  135.    wt: 2:   three kinds of reason in mathematics
  136.    wt: 2:   Four ways to improve education reform
  137.    wt: 2:   fairness and inductive principles for instruction
  138.    wt: 2:   12 Goals and Objectives For Mathematics
  139.    wt: 2:   3 Preparing for Science Studies
  140.    wt: 2:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  141.    wt: 2:   6 Set Existence Formation and Notation
  142.    wt: 2:   4 Function notation in and beyond mathematics
  143.    wt: 2:   3 Formula or function graphing exercise
  144.    wt: 2:   2 Algebraic use of function notation
  145.    wt: 2:   8 quadratics backward use of various formulas
  146.    wt: 2:   7 quadratic formulla derivation
  147.    wt: 2:   Rewriting algebraic substitution as function substitutions
  148.    wt: 2:   26 Formulas for products of sines and cosines
  149.    wt: 2:   17E Trig Formulas for dot and cross Products
  150.    wt: 2:   17D cis formulas for sine cosines and tangent
  151.    wt: 2:   13 Trig Formulas for dot and cross Products
  152.    wt: 2:   12 cis formulas for sine cosines and tangent
  153.    wt: 2:   4 Equations for lines three forms
  154.    wt: 2:   6 Column Methods for Decimal Multiplication
  155.    wt: 2:   5 Distributive Law for Whole Numbers
  156.    wt: 2:   4 Commutative Law Groups Counting Form
  157.    wt: 2:   5 Areas of Rectangles Revisited
  158.    wt: 2:   4 Fraction Operations Axiomatic Development
  159.    wt: 2:   2 Fraction Operations Physical Development
  160.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  161.    wt: 2:   5 Proportionality in Equivalent Fractions
  162.    wt: 2:   4 Rates Ratios and Proporitionality
  163.    wt: 2:   3 Proportionality Examples
  164.    wt: 2:   1 What is Proportionality
  165.    wt: 2:   5 Equality in Algebra
  166.    wt: 2:   3 Product Axioms Two Forms
  167.    wt: 2:   2 More and Less Than for Counts and Measures
  168.    wt: 2:   9 Coordinates for Regions in Space
  169.    wt: 2:   8 Coordinates for Maps and Planes
  170.    wt: 2:   3 Geometric Formulas and Function Notation
  171.    wt: 2:   1 Formulas Dependence and Function Notation
  172.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  173.    wt: 2:   Skill Development Notes
  174.    wt: 2:   Using Letters for Physical Quantities
  175.    wt: 2:   4 A Brief Story of numbers and algebra
  176.    wt: 2:   Example 2 volume of a cone
  177.    wt: 2:   Example 1 volume of a pyramid
  178.    wt: 2:   Volume of Solid by Cross Sections Lesson
  179.    wt: 2:   38 Formulas and derivatives for powers and roots
  180.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  181.    wt: 2:   E2 Algebraic Properties of Limits
  182.    wt: 2:   PostScript For and Against Decimal Perspectives
  183.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  184.    wt: 2:   Foreword
  185.    wt: 2:   Postscript C Consistency as a Tool for Reason
  186.    wt: 2:   Chapter 14 Deductive and Empirical Views of Mathematics
  187.    wt: 2:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  188.    wt: 2:   Chapter 4 Implication Rules Forwards and Backwards
  189.    wt: 2:   Foreword
  190.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  191.    wt: 2:   N Mathematics Prepare for College Studies
  192.    wt: 2:   G. Written work formats for developing and showing skill
  193.    wt: 2:   Appendix A Calculus with Proofs for Keen or Gifted
  194.    wt: 2:   Chapter 6 More Algebra and Geometry
  195.    wt: 2:   Chapter 4 Logic for Reading Writing and Geometry etc
  196.    wt: 2:   Chapter 3 Algebra Starter Lessons
  197.    wt: 2:   7 Games and Activities for Instruction
  198.    wt: 2:   Helping the Blind in Logic and Mathematics
  199.    wt: 2:   Mathematics Education References
  200.    wt: 2:   Mathematics Education References
  201.    wt: 2:   Ends Values Methods For Skill Development Framework Prequel
  202.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  203.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  204.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  205.    wt: 2:   Implementation Notes
  206.    wt: 2:   More Algebra and Slope based Calculus Preview
  207.    wt: 2:   Systematic Algebra Skill Development Missing Links
  208.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  209.    wt: 1:   Appendix 2 primary school Arithmetic 01
  210.    wt: 1:   Appendix 1 primary and preschool mathematic
  211.    wt: 1:   K LAMP Musings Science Education
  212.    wt: 1:   J LAMP Introduction Extrinsic Origins
  213.    wt: 1:   I LAMP Introduction Study Habits
  214.    wt: 1:   H LAMP Introduction Instructional Concepts
  215.    wt: 1:   G LAMP Introduction Problem Solving Skills
  216.    wt: 1:   F LAMP Introduction Prerequisites
  217.    wt: 1:   A Introduction Objectives
  218.    wt: 1:   Skills Chapter 5 Calculus
  219.    wt: 1:   Skills Chapter 4 Logic
  220.    wt: 1:   Ramblings Extrinsic numbers theory
  221.    wt: 1:   Skills Chapter 2 Geometry
  222.    wt: 1:   Skills Chapter 1 Arithmetic
  223.    wt: 1:   Skills Chapter 0 Introduction
  224.    wt: 1:   10 statistics
  225.    wt: 1:   9 combinatorics probability sets
  226.    wt: 1:   8 analytic geometry etc
  227.    wt: 1:   7 logic review and decimals an odd combination
  228.    wt: 1:   6 polynomials etc
  229.    wt: 1:   5 logarithms and exponentials etc
  230.    wt: 1:   3 Euclidean Geometry Leanly
  231.    wt: 1:   2 arithmetic with signed numbers
  232.    wt: 1:   1 arithmetic with unsigned numbers
  233.    wt: 1:   What is POMME
  234.    wt: 1:   why bother
  235.    wt: 1:   which way to go
  236.    wt: 1:   website reviews
  237.    wt: 1:   Teach the teachers plus goals
  238.    wt: 1:   Math Ed if it must be short make it lean effective
  239.    wt: 1:   Applied Maths Program14092009 POMME variant
  240.    wt: 1:   links Education Resources online
  241.    wt: 1:   site origins
  242.    wt: 1:   site eurekas
  243.    wt: 1:   About site lesson plans
  244.    wt: 1:   teacher certification
  245.    wt: 1:   modern education
  246.    wt: 1:   learning takes time
  247.    wt: 1:   grouping students according to ability
  248.    wt: 1:   what should be learnt and When
  249.    wt: 1:   Postscript 2007 01 10
  250.    wt: 1:   five decades make a difference
  251.    wt: 1:   Maps Plans Drawings
  252.    wt: 1:   how letters appear
  253.    wt: 1:   three difficulties
  254.    wt: 1:   teaching tips
  255.    wt: 1:   What to Tell Students
  256.    wt: 1:   05 13 OldSiteEntrancePage
  257.    wt: 1:   04 25 when to stop or suspend mathemat
  258.    wt: 1:   Operational Viewpoint to Value
  259.    wt: 1:   Theory of Knowledge
  260.    wt: 1:   Different Kinds of Reasoning in maths
  261.    wt: 1:   cultivating intelligence
  262.    wt: 1:   How to be a better instructor
  263.    wt: 1:   Motivation and Context Problem
  264.    wt: 1:   education an empirical art
  265.    wt: 1:   chapitre 12 00 les iles et division
  266.    wt: 1:   chapitre 07 01 principle D induction mathematique
  267.    wt: 1:   chapitre 07 00 Des chaines plus longues de la raison
  268.    wt: 1:   chapitre 06 00 Chaines de la raison
  269.    wt: 1:   chapitre 05 00 Deception
  270.    wt: 1:   chapitre 04 10 Etapes pour une meilleur raison
  271.    wt: 1:   chapitre 04 09 Regles accidentelles
  272.    wt: 1:   chapitre 04 08 Limitations et benefices
  273.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  274.    wt: 1:   chapitre 04 06 engagements
  275.    wt: 1:   chapitre 04 05 Implication versus suggestion
  276.    wt: 1:   chapitre 04 04 Parlons de la logique
  277.    wt: 1:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  278.    wt: 1:   chapitre 04 02 Deuxieme enigme
  279.    wt: 1:   chapitre 04 01 Premiere enigme
  280.    wt: 1:   chapitre 04 00 Les regles d implication
  281.    wt: 1:   chapitre 03 A Propos Des Prochains Chapitre
  282.    wt: 1:   chapitre 02 00 La Communication des idees
  283.    wt: 1:   chapitre 01 00 Introduction
  284.    wt: 1:   C Electromotive force conventional current02
  285.    wt: 1:   B Electromotive force conventional current01
  286.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  287.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  288.    wt: 1:   24 Standards For Skill Develoment Take II
  289.    wt: 1:   24 Standards For Skill Develoment
  290.    wt: 1:   22 Student Centered Highschool Mathematics
  291.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  292.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  293.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  294.    wt: 1:   18 Primary School Mathematics
  295.    wt: 1:   17 Math Booklets for children and young teenagers
  296.    wt: 1:   16 Secondary Mathematics Tips
  297.    wt: 1:   15 Counting For Parents
  298.    wt: 1:   10 Ends values for work study instruction
  299.    wt: 1:   5 Patience Please for Yourself and Your Charges
  300.    wt: 1:   4 Learning Takes Time and Effort
  301.    wt: 1:   Ages 12 to 14 Skills with take home value
  302.    wt: 1:   Ages 12 to 14 Geometry
  303.    wt: 1:   Ages 12 to 14 Arithmetic
  304.    wt: 1:   Ages 10 to 12 Geometry
  305.    wt: 1:   Ages 10 to 12 Arithmetic
  306.    wt: 1:   Ages 9 to 10
  307.    wt: 1:   Ages 8 to 9
  308.    wt: 1:   Ages 7 to 8
  309.    wt: 1:   Ages 6 to 7
  310.    wt: 1:   Ages 4 plus to 5 plus
  311.    wt: 1:   Ages 3 plus to 4 plus
  312.    wt: 1:   sign monoticity analysis example 4
  313.    wt: 1:   sign monoticity analysis example 3
  314.    wt: 1:   sign monoticity analysis example 2
  315.    wt: 1:   sign monoticity analysis example 1
  316.    wt: 1:   26 Function definitions done and coming
  317.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  318.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  319.    wt: 1:   23 Inverse Functions
  320.    wt: 1:   22 Square Root function graphically
  321.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  322.    wt: 1:   20 Interchanging coordinates a reflection
  323.    wt: 1:   19 Horizontal line rule and method
  324.    wt: 1:   18 Vertical Line Rule and Method
  325.    wt: 1:   17 Function maxima minima and their location
  326.    wt: 1:   16 Increasing or decreasing on intervals
  327.    wt: 1:   15 Sign analysis of functions
  328.    wt: 1:   14 Surjections Injections Bijections
  329.    wt: 1:   13 From one to one to many to one
  330.    wt: 1:   12 Function Domain Recognition Exercises
  331.    wt: 1:   11 Function Domain Range Source and Targets
  332.    wt: 1:   10 Interval Notation
  333.    wt: 1:   9 Set theory term relation possible origins
  334.    wt: 1:   8 Set view of relations and functions
  335.    wt: 1:   7 Functions with finite domains
  336.    wt: 1:   1 Geometric Introduction of Function Notation
  337.    wt: 1:   Introduction Reading Guide
  338.    wt: 1:   A Quadratics Summary
  339.    wt: 1:   10 quadratic exercises
  340.    wt: 1:   9 quadratics physical and further context
  341.    wt: 1:   6 quadratics numerical approach
  342.    wt: 1:   5 quadratics completing the square
  343.    wt: 1:   4 quadratics difference of two squares
  344.    wt: 1:   3 quadratics factoring by inspection
  345.    wt: 1:   2 quadratics graphing in general
  346.    wt: 1:   1 quadratics graphing exercises
  347.    wt: 1:   Quadratics in 10 steps
  348.    wt: 1:   11 Growth and Decay in Biology
  349.    wt: 1:   10 Exponential Growth and Decay Models
  350.    wt: 1:   5 Natural Logarithm Calculator Exercises
  351.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  352.    wt: 1:   2 Square Root Simplification a prequel
  353.    wt: 1:   1 Calculator Starter Exercises
  354.    wt: 1:   7 Links Lessons Elsewhere
  355.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  356.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  357.    wt: 1:   4 Polynomials Long division linear divisor
  358.    wt: 1:   3 Polynomials Multiplication Addition
  359.    wt: 1:   2 Column Multiplication Method
  360.    wt: 1:   1 Polynomials Distributive Law
  361.    wt: 1:   12 motivation for term arctan
  362.    wt: 1:   9 motivation for name arcsin
  363.    wt: 1:   4 possible motivation for term arccos
  364.    wt: 1:   12 From Applied To Pure Mathematics
  365.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  366.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  367.    wt: 1:   8 Straight Lines Equation for vertical
  368.    wt: 1:   17 tangent function angle sum formulas
  369.    wt: 1:   29 secant cosecant and cotangent for acute angles
  370.    wt: 1:   25 tangent double angle formula Slope connection
  371.    wt: 1:   24 tangent Angle Difference Formula
  372.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  373.    wt: 1:   21 sine and cosine Half Angle Formulas
  374.    wt: 1:   20 sine and cosine Double Angle Formulas
  375.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  376.    wt: 1:   17C sine and cosine double triple angle formulas
  377.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  378.    wt: 1:   12 Graph of tangent function for one period
  379.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  380.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  381.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  382.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  383.    wt: 1:   11 sine and cosine double triple angle formulas
  384.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  385.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  386.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  387.    wt: 1:   8 Mid Point Formula
  388.    wt: 1:   5 Algebraic View of Slopes
  389.    wt: 1:   3 Slope product for perpendicular lines
  390.    wt: 1:   2 point slope equation for a line
  391.    wt: 1:   13 Pythagorean spatial distance formulas
  392.    wt: 1:   10 Pythagorean plane distance formula
  393.    wt: 1:   PS H Distributive Law For Complex Numbers
  394.    wt: 1:   musings do not puiblish real numbers
  395.    wt: 1:   A Modular and Remainder Arithmetic
  396.    wt: 1:   A Signed Number Arithmetic Review
  397.    wt: 1:   26 More Less Greater Than Comparison
  398.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  399.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  400.    wt: 1:   23 Distributive Law Two Derivations
  401.    wt: 1:   22 Multiplication of Signed Numbers
  402.    wt: 1:   21 Addition of Multiples of a Single Vector
  403.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  404.    wt: 1:   19 Signed Multiples of Vectors
  405.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  406.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  407.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  408.    wt: 1:   15 Head to Tails in place Addition Associative
  409.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  410.    wt: 1:   13 Arrows and Vectors in a Plane
  411.    wt: 1:   12 Real Numbers Line Signed Coordinates
  412.    wt: 1:   11 Signed Number Addition and Addition Properties
  413.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  414.    wt: 1:   9 Division with Digits after Decimal Point
  415.    wt: 1:   8 Division and Mulplication of Compound Fractions
  416.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  417.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  418.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  419.    wt: 1:   4 Location of Point in Decimal Addition
  420.    wt: 1:   3 Location of Point in Decimal Multiplication
  421.    wt: 1:   2 Counting Digits in Decimal Multiplication
  422.    wt: 1:   1 Fractions with Finite Decimal Expansions
  423.    wt: 1:   E Long Division Methods more
  424.    wt: 1:   D Long Division Methods
  425.    wt: 1:   C Three Decimal Subtraction Methods
  426.    wt: 1:   B Decimal Comparison and Subtraction
  427.    wt: 1:   A Decimal Addition Columm Methods
  428.    wt: 1:   8 Column Multiplication Methods in General
  429.    wt: 1:   7 Decimals Multiplication Methods Examples
  430.    wt: 1:   3 Multiplicative Counting Skills Principles
  431.    wt: 1:   2 Combing Counts Addition Skills and Principles
  432.    wt: 1:   1 The Counting Origins of Numbers
  433.    wt: 1:   6 Equations and Systems Equivalent or Implied
  434.    wt: 1:   4 Subtraction and Division Axioms
  435.    wt: 1:   2 Addition and Multiplication Axioms
  436.    wt: 1:   1 Equivalent Computation Rules
  437.    wt: 1:   5 Greater More Less Than Signs in General
  438.    wt: 1:   4 Comparison of Negative Numbers
  439.    wt: 1:   3 More and Less Than with Unlike Signs
  440.    wt: 1:   1 Real Numbers Comparison
  441.    wt: 1:   16 Real Numbers Comparison
  442.    wt: 1:   15 Real Number Division
  443.    wt: 1:   14 Real Number Multiplication
  444.    wt: 1:   13 Real Number Subtraction
  445.    wt: 1:   12 Real Number Additive Inverses or Negatives
  446.    wt: 1:   11 Real Number Addition
  447.    wt: 1:   10 Real Number Lengths and Signs
  448.    wt: 1:   7 Real Numbers as Line Cordinates
  449.    wt: 1:   6 Unsigned Real Numbers
  450.    wt: 1:   5 Rational Numbers More
  451.    wt: 1:   4 Rational Numbers
  452.    wt: 1:   3 Fractions
  453.    wt: 1:   2 Integers
  454.    wt: 1:   1 Whole and Natural Numbers
  455.    wt: 1:   5 Independent versus Dependent Variables
  456.    wt: 1:   4 Changing Letters
  457.    wt: 1:   2 Computation Rules Evaluation
  458.    wt: 1:   More Exercises
  459.    wt: 1:   Simple Exercises
  460.    wt: 1:   4 GE III Animated Examples
  461.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  462.    wt: 1:   3 GE III Equation Addition and Multiplication
  463.    wt: 1:   2 GE II Comparison
  464.    wt: 1:   1 GE Substitution four examples
  465.    wt: 1:   4 Solving a triangular system exercise
  466.    wt: 1:   3 Solving triangular system example
  467.    wt: 1:   2 Essentially one exercises three with solution
  468.    wt: 1:   1 Essentially One Unknown
  469.    wt: 1:   10 One Example
  470.    wt: 1:   9 Three Examples
  471.    wt: 1:   8 One Example
  472.    wt: 1:   7 Two Examples
  473.    wt: 1:   6 Three Examples
  474.    wt: 1:   5 Three Examples
  475.    wt: 1:   4 Two Examples
  476.    wt: 1:   3 Two Examples
  477.    wt: 1:   2 Three Examples
  478.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  479.    wt: 1:   9 Sets in Probability and Statistics
  480.    wt: 1:   8 Sets of Numbers
  481.    wt: 1:   7 Cautious or Safe Set Construction
  482.    wt: 1:   6 Power Set Notation
  483.    wt: 1:   5 Product Builder Notation
  484.    wt: 1:   4 Subset Builder Notation
  485.    wt: 1:   3 Counting with Sets etc
  486.    wt: 1:   2 Venn Diagrams
  487.    wt: 1:   1 Finite Sets
  488.    wt: 1:   6 Three Notions of What is a Variable
  489.    wt: 1:   5 Talking about Numbers and Quantities
  490.    wt: 1:   3 Adding Words To Arithmetic
  491.    wt: 1:   2 What is a Variable
  492.    wt: 1:   About Folder Contents
  493.    wt: 1:   arithmetic videos Real Player Format
  494.    wt: 1:   1 More and Less Than for Counts and Measures
  495.    wt: 1:   4 signed coordinates for regions in space
  496.    wt: 1:   3 signed coordinates for maps and planes
  497.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  498.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  499.    wt: 1:   21 Reciprocals for Fractions and Wholes
  500.    wt: 1:   13 Fraction Comparison Algebraic View
  501.    wt: 1:   11 Simplification an Algebraic View
  502.    wt: 1:   6 Multiplication Algebraically Take II
  503.    wt: 1:   11 Adding Integers Formulas and Examples
  504.    wt: 1:   10 Integer Multiplication Formulas
  505.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  506.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  507.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  508.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  509.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  510.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  511.    wt: 1:   7 Calculator Usage Notes and Cautions
  512.    wt: 1:   Long Division forwards and backwards Example 3
  513.    wt: 1:   Long Division forwards and backwards Example 2
  514.    wt: 1:   Long Division forwards and backwards Example 1
  515.    wt: 1:   A Elementary Basis for Multiplication Methods
  516.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  517.    wt: 1:   5 A Tip for Efficent Subtraction
  518.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  519.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  520.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  521.    wt: 1:   Quick history of numbers and algebra
  522.    wt: 1:   Formula Evaluation how to show work
  523.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  524.    wt: 1:   Example 1. Area Between x and x squared
  525.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  526.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  527.    wt: 1:   Example 4 with x function of y
  528.    wt: 1:   Example 3
  529.    wt: 1:   Example 2
  530.    wt: 1:   Example 1
  531.    wt: 1:   Area Between Curves Lesson Take 2
  532.    wt: 1:   Area Between Curves Lesson Take 1
  533.    wt: 1:   Summary
  534.    wt: 1:   A Related Material in Volume 3
  535.    wt: 1:   A Related lessons in Volume 3
  536.    wt: 1:   28 Chain Rule Preparation for a Proof
  537.    wt: 1:   22 Chain Rule for polynomials
  538.    wt: 1:   21 Chain Rule for powers
  539.    wt: 1:   20 Chain Rule for Pulley Systems
  540.    wt: 1:   19 Chain Rule for linear functions
  541.    wt: 1:   10 Power rule for negative integers
  542.    wt: 1:   3 Motivation for Limit Definition Take 2
  543.    wt: 1:   2 Motivation for Limit Definition Take 1
  544.    wt: 1:   3 Decimal insights for limits continuity convergence
  545.    wt: 1:   2 Algebraic codification
  546.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  547.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  548.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  549.    wt: 1:   G.5 Motions With Bounded Velocities
  550.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  551.    wt: 1:   G.3 Constant Difference Theorem Proof
  552.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  553.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  554.    wt: 1:   F.5b Extreme Value Theorem
  555.    wt: 1:   F.5a Equicontinuity Theorems
  556.    wt: 1:   F.4 Finite Covering Theorem
  557.    wt: 1:   F.3 Intermediate Value Theorem
  558.    wt: 1:   F.2 Closed Range Theorem
  559.    wt: 1:   F.1 What Functions are Continuous
  560.    wt: 1:   E1 Error Control Inequalities
  561.    wt: 1:   D2 Limits of Monotone Sequences
  562.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  563.    wt: 1:   C Triangle Inequalities
  564.    wt: 1:   B3 Bolzano Weierstrass Theorem
  565.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  566.    wt: 1:   A1. Introduction
  567.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  568.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  569.    wt: 1:   Chapter 23 Links To Trigonometry
  570.    wt: 1:   Chapter 22 Complex Numbers
  571.    wt: 1:   Chapter 21 Arrow Addition
  572.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  573.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  574.    wt: 1:   Chapter 18. Slopes Areas Integration
  575.    wt: 1:   Chapter 17. Area Approximation
  576.    wt: 1:   Chapter 16. Velocity Approximation
  577.    wt: 1:   Chapter 15. Slope Approximation
  578.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  579.    wt: 1:   Chapter 13. Acceleration
  580.    wt: 1:   Chapter 12. Units and Slopes
  581.    wt: 1:   Chapter 11. Graphing Slope versus Position
  582.    wt: 1:   Chapter 10 Slopes and Units
  583.    wt: 1:   Chapter 9 About First Courses in Calculus
  584.    wt: 1:   Chapter 8. Slope Interpretation
  585.    wt: 1:   Chapter 7 Slopes and Velocity
  586.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  587.    wt: 1:   Chapter 5. Slope Sign Tests
  588.    wt: 1:   Chapter 4. More Slope Sign Analysis
  589.    wt: 1:   Chapter 3. Slope Sign Analysis
  590.    wt: 1:   Chapter 2. Slopes and Ski Trails
  591.    wt: 1:   Chapter 1.Introduction
  592.    wt: 1:   Fall 1983 Calculus Appetizer
  593.    wt: 1:   Postscript D Reflections on Law of the Excluded Middle
  594.    wt: 1:   Postscript B More on Story Telling and Reason
  595.    wt: 1:   Postscript A Story Telling
  596.    wt: 1:   Chapter 24 Direct and Indirect Reason
  597.    wt: 1:   Chapter 23 Truth Tables
  598.    wt: 1:   Chapter 22 Contrapositive and Vacuously True Implications
  599.    wt: 1:   Chapter 21 Occurrence Tables
  600.    wt: 1:   Chapter 20 Shorthand Symbols as Pronouns
  601.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  602.    wt: 1:   Chapter 18 Sense and Knowledge
  603.    wt: 1:   Chapter 17 Objective Ways Trial and Error Discovery
  604.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  605.    wt: 1:   Chapter 15 Objective Processes
  606.    wt: 1:   Chapter 12 Islands and Divisions of Knowledge
  607.    wt: 1:   Chapter 11 Accidental Patterns
  608.    wt: 1:   Chapter 10 Responsibility
  609.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  610.    wt: 1:   Chapter 8 Change of Language
  611.    wt: 1:   Chapter 7 Longer Chains of Reason
  612.    wt: 1:   Chapter 6 Chains of Reason
  613.    wt: 1:   Chapter 5 Deception
  614.    wt: 1:   Chapter 3 What is in chapters 4 to 8
  615.    wt: 1:   Chapter 2 Skill Development
  616.    wt: 1:   Chapter 1 Introduction
  617.    wt: 1:   Three Remarks
  618.    wt: 1:   S Adding words to algebra
  619.    wt: 1:   R Why Learn Mathematics Skills
  620.    wt: 1:   O On Learning Mathematics and Science
  621.    wt: 1:   Chapter 8 Skipped Topics and Why
  622.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  623.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  624.    wt: 1:   Chapter 2 Why Sets
  625.    wt: 1:   Chapter 1 Arithmetic
  626.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  627.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  628.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  629.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  630.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  631.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  632.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  633.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  634.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  635.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  636.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  637.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  638.    wt: 1:   Which Way To Go
  639.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  640.    wt: 1:   The Math Forum and Site Content

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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