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 Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling; and for avid readers not in school

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: 3:   LAMP Lean Applied Mathematics Program/
  2.    wt: 3:   Progressive Observable Motivated Mathematics Education/
  3.    wt: 3:   Mathematics Education Essays/
  4.    wt: 3:   9 Proportionality Backwards and Forwards/
  5.    wt: 3:   8 Unifying Theme For Algebra/
  6.    wt: 3:   Step 2 Algebraic solutions for one unknown/
  7.    wt: 3:   2 Formula Forward Use Evaluation/
  8.    wt: 2:   9 Lines and Slopes Take 2 with tangent function/
  9.    wt: 2:   10 Examples of Algebraic Reasoning/
  10.    wt: 2:   9 Combinatorics Trees Tables and Products/
  11.    wt: 2:   Volume 2 Three Skills For Algebra/
  12.    wt: 2:   Mathematics Skill Development Framework/
  13.    wt: 1:   Archives/
  14.    wt: 1:   Direct Current Electric Circuits/
  15.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  16.    wt: 1:   4 Functions/
  17.    wt: 1:   3 Quadratics Geometrically/
  18.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  19.    wt: 1:   1 Five Polynomial Operations/
  20.    wt: 1:   More Algebra/
  21.    wt: 1:   B Real Numbers Extrinsic Development/
  22.    wt: 1:   A Origins of Counting and Figuring Methods/
  23.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  24.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  25.    wt: 1:   5 Real Numbers/
  26.    wt: 1:   4 Computation Rules and Function Notation/
  27.    wt: 1:   Step 4 Gaussian Elimination/
  28.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  29.    wt: 1:   Step 1 Stick diagram and fractions/
  30.    wt: 1:   3 Solving Linear Equations/
  31.    wt: 1:   1 Working With Sets/
  32.    wt: 1:   Algebra Starter Lessons/
  33.    wt: 1:   Work and Study Tips/

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265 matches:

  1.    wt: 3:   9 Formulas for Real Exponents with Logarithms
  2.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  3.    wt: 3:   19 Remainder Arithmetic Rule of 9 for checking sums III
  4.    wt: 2:   Applied Maths Program14092009 POMME variant
  5.    wt: 2:   geometric implications for algebra
  6.    wt: 2:   formal or informal peer review
  7.    wt: 2:   Prequel In For A Penny In For A Pound
  8.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  9.    wt: 2:   5 Function notation for geometric transformations
  10.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  11.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  12.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  13.    wt: 2:   9 motivation for name arcsin
  14.    wt: 2:   29 secant cosecant and cotangent for acute angles
  15.    wt: 2:   26 Formulas for products of sines and cosines
  16.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  17.    wt: 2:   17E Trig Formulas for dot and cross Products
  18.    wt: 2:   17D cis formulas for sine cosines and tangent
  19.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  20.    wt: 2:   13 Trig Formulas for dot and cross Products
  21.    wt: 2:   12 cis formulas for sine cosines and tangent
  22.    wt: 2:   4 Equations for lines three forms
  23.    wt: 2:   9 Coordinates for Regions in Space
  24.    wt: 2:   Formula Usage Show Work Format
  25.    wt: 2:   1 Written work formats for developing and showing skill
  26.    wt: 2:   1 Three Skills For Algebra
  27.    wt: 2:   25 Divisibility Tests for 2 3 5 9 10 Example
  28.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  29.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  30.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  31.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  32.    wt: 2:   9 video Prime Factorization upto 19 squared
  33.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  34.    wt: 2:   38 Formulas and derivatives for powers and roots
  35.    wt: 2:   19 Chain Rule for linear functions
  36.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  37.    wt: 2:   Postscript For Better Performance
  38.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  39.    wt: 2:   Chapter 18. Rules for Algebra
  40.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  41.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  42.    wt: 2:   Chapter 8 Three Skills For Algebra
  43.    wt: 2:   G. Written work formats for developing and showing skill
  44.    wt: 1:   Ramblings Introduction Algebra Essay
  45.    wt: 1:   Skills Chapter 3 Algebra
  46.    wt: 1:   9 combinatorics probability sets
  47.    wt: 1:   4 algebra
  48.    wt: 1:   three goals to set for students
  49.    wt: 1:   permissions for teachers
  50.    wt: 1:   activities for students
  51.    wt: 1:   Education Reform Inconsistencies
  52.    wt: 1:   talk the algebra talk
  53.    wt: 1:   teaching tutoring algebraic reason
  54.    wt: 1:   Lessening Algebra Difficulties
  55.    wt: 1:   the trouble with algebra
  56.    wt: 1:   three goals for Mathematics Education
  57.    wt: 1:   04 29 New Mathematics Curriculum
  58.    wt: 1:   02 21 words for teachers
  59.    wt: 1:   three aims for mathematics students
  60.    wt: 1:   standards for course material
  61.    wt: 1:   Four ways to improve education reform
  62.    wt: 1:   need for a mixed mathematics curriculum
  63.    wt: 1:   fairness and inductive principles for instruction
  64.    wt: 1:   words for mathematics instructor
  65.    wt: 1:   chapitre 04 09 Regles accidentelles
  66.    wt: 1:   4 Energy Power Heat09
  67.    wt: 1:   C Electromotive force conventional current02
  68.    wt: 1:   B Electromotive force conventional current01
  69.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  70.    wt: 1:   24 Standards For Skill Develoment Take II
  71.    wt: 1:   24 Standards For Skill Develoment
  72.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  73.    wt: 1:   17 Math Booklets for children and young teenagers
  74.    wt: 1:   15 Counting For Parents
  75.    wt: 1:   12 Goals and Objectives For Mathematics
  76.    wt: 1:   10 Ends values for work study instruction
  77.    wt: 1:   9 Streaming by Student Cooperation
  78.    wt: 1:   5 Patience Please for Yourself and Your Charges
  79.    wt: 1:   4 Learning Takes Time and Effort
  80.    wt: 1:   3 Preparing for Science Studies
  81.    wt: 1:   Ages 9 to 10
  82.    wt: 1:   Ages 8 to 9
  83.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  84.    wt: 1:   19 Horizontal line rule and method
  85.    wt: 1:   9 Set theory term relation possible origins
  86.    wt: 1:   6 Set Existence Formation and Notation
  87.    wt: 1:   3 Formula or function graphing exercise
  88.    wt: 1:   2 Algebraic use of function notation
  89.    wt: 1:   Introduction Reading Guide
  90.    wt: 1:   9 quadratics physical and further context
  91.    wt: 1:   8 quadratics backward use of various formulas
  92.    wt: 1:   7 quadratic formulla derivation
  93.    wt: 1:   8 Notes for instructors or tutors
  94.    wt: 1:   Rewriting algebraic substitution as function substitutions
  95.    wt: 1:   12 motivation for term arctan
  96.    wt: 1:   4 possible motivation for term arccos
  97.    wt: 1:   9 Summary Degrees to Radians and back
  98.    wt: 1:   9 Head to Tail Coordinate View
  99.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  100.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  101.    wt: 1:   9 Straight Lines through Origin Equations
  102.    wt: 1:   8 Straight Lines Equation for vertical
  103.    wt: 1:   17 tangent function angle sum formulas
  104.    wt: 1:   25 tangent double angle formula Slope connection
  105.    wt: 1:   24 tangent Angle Difference Formula
  106.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  107.    wt: 1:   21 sine and cosine Half Angle Formulas
  108.    wt: 1:   20 sine and cosine Double Angle Formulas
  109.    wt: 1:   17C sine and cosine double triple angle formulas
  110.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  111.    wt: 1:   12 Graph of tangent function for one period
  112.    wt: 1:   9 Graphs of sine and cosine over one period
  113.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  114.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  115.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  116.    wt: 1:   19 N th Roots of Unity
  117.    wt: 1:   11 sine and cosine double triple angle formulas
  118.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  119.    wt: 1:   9 The complex number valued trig function 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:   9 Similarity of Triangles Usual Criteria
  123.    wt: 1:   9 Midpoint Coordinates Half Endpoint Sum
  124.    wt: 1:   8 Mid Point Formula
  125.    wt: 1:   5 Algebraic View of Slopes
  126.    wt: 1:   3 Slope product for perpendicular lines
  127.    wt: 1:   2 point slope equation for a line
  128.    wt: 1:   13 Pythagorean spatial distance formulas
  129.    wt: 1:   10 Pythagorean plane distance formula
  130.    wt: 1:   9 Pythagorean Theorem Chinese Square Proof
  131.    wt: 1:   PS H Distributive Law For Complex Numbers
  132.    wt: 1:   19 Right Triangle Similarity
  133.    wt: 1:   9 Construction of a right bisector
  134.    wt: 1:   19 Signed Multiples of Vectors
  135.    wt: 1:   9 Division with Digits after Decimal Point
  136.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  137.    wt: 1:   6 Column Methods for Decimal Multiplication
  138.    wt: 1:   5 Distributive Law for Whole Numbers
  139.    wt: 1:   4 Commutative Law Groups Counting Form
  140.    wt: 1:   3 Inequalities Algebraically
  141.    wt: 1:   2 Algebraic View
  142.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  143.    wt: 1:   6 Compound Interest Forward and Backwards
  144.    wt: 1:   5 Triangle Area Formula Backwards
  145.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  146.    wt: 1:   5 Equality in Algebra
  147.    wt: 1:   3 Product Axioms Two Forms
  148.    wt: 1:   2 More and Less Than for Counts and Measures
  149.    wt: 1:   8 Coordinates for Maps and Planes
  150.    wt: 1:   3 Geometric Formulas and Function Notation
  151.    wt: 1:   1 Formulas Dependence and Function Notation
  152.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  153.    wt: 1:   6 Algebraic Solution Example
  154.    wt: 1:   5 Algebraic Solutions Introduction
  155.    wt: 1:   9 Three Examples
  156.    wt: 1:   Using Letters for Physical Quantities
  157.    wt: 1:   13 Naming Identifying Formulas with Words
  158.    wt: 1:   9 Volume of Cone
  159.    wt: 1:   8 Compound Interest Formula Evaluation
  160.    wt: 1:   7 Compound Interest Formula Introduction
  161.    wt: 1:   5 Box Volume Formula Example
  162.    wt: 1:   4 Circle Area Formula Example
  163.    wt: 1:   3 Triangle Area Formula Example
  164.    wt: 1:   2 Another Rectangle Area Formula Example
  165.    wt: 1:   9 Sets in Probability and Statistics
  166.    wt: 1:   4 A Brief Story of numbers and algebra
  167.    wt: 1:   arithmetic videos Real Player Format
  168.    wt: 1:   1 More and Less Than for Counts and Measures
  169.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  170.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  171.    wt: 1:   9 subtracting signed numbers
  172.    wt: 1:   4 signed coordinates for regions in space
  173.    wt: 1:   3 signed coordinates for maps and planes
  174.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  175.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  176.    wt: 1:   21 Reciprocals for Fractions and Wholes
  177.    wt: 1:   19 Dividing Fractions How TO
  178.    wt: 1:   13 Fraction Comparison Algebraic View
  179.    wt: 1:   11 Simplification an Algebraic View
  180.    wt: 1:   9 Improper Fractions and Mixed Numbers
  181.    wt: 1:   6 Multiplication Algebraically Take II
  182.    wt: 1:   11 Adding Integers Formulas and Examples
  183.    wt: 1:   10 Integer Multiplication Formulas
  184.    wt: 1:   9 Multiplying Integers
  185.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  186.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  187.    wt: 1:   15 Remainder Arithmetic Modulo 9 Example
  188.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  189.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  190.    wt: 1:   19 video Prime Factorization Unique
  191.    wt: 1:   16 video Factors of 980 using prime
  192.    wt: 1:   8 video Prime Factorization upto 19
  193.    wt: 1:   3 video Primes and Composites from 9 times table
  194.    wt: 1:   Long Division forwards and backwards Example 3
  195.    wt: 1:   Long Division forwards and backwards Example 2
  196.    wt: 1:   Long Division forwards and backwards Example 1
  197.    wt: 1:   9 Why Long Division Works Take II
  198.    wt: 1:   A Elementary Basis for Multiplication Methods
  199.    wt: 1:   9 22 Minute Subtraction Review Video
  200.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  201.    wt: 1:   5 A Tip for Efficent Subtraction
  202.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  203.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  204.    wt: 1:   Quick history of numbers and algebra
  205.    wt: 1:   Formula Evaluation how to show work
  206.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  207.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  208.    wt: 1:   29 Chain Rule Optional Reading
  209.    wt: 1:   28 Chain Rule Preparation for a Proof
  210.    wt: 1:   22 Chain Rule for polynomials
  211.    wt: 1:   21 Chain Rule for powers
  212.    wt: 1:   20 Chain Rule for Pulley Systems
  213.    wt: 1:   10 Power rule for negative integers
  214.    wt: 1:   9 Reciprocal rule
  215.    wt: 1:   3 Motivation for Limit Definition Take 2
  216.    wt: 1:   2 Motivation for Limit Definition Take 1
  217.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  218.    wt: 1:   9 Limits Continuity and Composition
  219.    wt: 1:   3 Decimal insights for limits continuity convergence
  220.    wt: 1:   2 Algebraic codification
  221.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  222.    wt: 1:   E2 Algebraic Properties of Limits
  223.    wt: 1:   PostScript For and Against Decimal Perspectives
  224.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  225.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  226.    wt: 1:   Chapter 9 About First Courses in Calculus
  227.    wt: 1:   Fall 1983 Calculus Appetizer
  228.    wt: 1:   Foreword
  229.    wt: 1:   Postscript More on Better Performance
  230.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  231.    wt: 1:   Chapter 23. Notation For Sums
  232.    wt: 1:   Chapter 21. Third Reading Guide
  233.    wt: 1:   Chapter 19. Functions and Sets
  234.    wt: 1:   Chapter 13. Second Reading Guide
  235.    wt: 1:   Chapter 12. Shorthand Usage Guide
  236.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  237.    wt: 1:   Solutions For Arithmetic Exercises
  238.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  239.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  240.    wt: 1:   Foreword
  241.    wt: 1:   Chapter 9 The Two Ends
  242.    wt: 1:   Chapter 3 Algebra Difficulties
  243.    wt: 1:   Chapter 2 For and Against Mathematics
  244.    wt: 1:   Foreword
  245.    wt: 1:   Postscript C Consistency as a Tool for Reason
  246.    wt: 1:   Chapter 19 What is in chapters 20 to 24
  247.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  248.    wt: 1:   Chapter 9 What is in Chapters 10 to 18
  249.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  250.    wt: 1:   Foreword
  251.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  252.    wt: 1:   S Adding words to algebra
  253.    wt: 1:   N Mathematics Prepare for College Studies
  254.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  255.    wt: 1:   Chapter 6 More Algebra and Geometry
  256.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  257.    wt: 1:   Chapter 3 Algebra Starter Lessons
  258.    wt: 1:   7 Games and Activities for Instruction
  259.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  260.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  261.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  262.    wt: 1:   More Algebra and Slope based Calculus Preview
  263.    wt: 1:   Systematic Algebra Skill Development Missing Links
  264.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  265.    wt: 1:   The Math Forum and Site Content

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631 matches:

  1.    wt: 6:   9 Circle Area and Perimeter Formula Backwards Forwards
  2.    wt: 6:   Postscript Unifying Theme A Fourth Skill For Algebra
  3.    wt: 5:   9 combinatorics probability sets
  4.    wt: 5:   Applied Maths Program14092009 POMME variant
  5.    wt: 5:   geometric implications for algebra
  6.    wt: 5:   formal or informal peer review
  7.    wt: 5:   Prequel In For A Penny In For A Pound
  8.    wt: 5:   9 Formulas for Real Exponents with Logarithms
  9.    wt: 5:   musings do not puiblish real numbers
  10.    wt: 5:   1 Written work formats for developing and showing skill
  11.    wt: 5:   arithmetic videos Real Player Format
  12.    wt: 5:   1 Links to Online Resources Elsewhere Take 1
  13.    wt: 4:   Appendix 2 primary school Arithmetic 01
  14.    wt: 4:   Appendix 1 primary and preschool mathematic
  15.    wt: 4:   Ramblings Introduction Algebra Essay
  16.    wt: 4:   Skills Chapter 3 Algebra
  17.    wt: 4:   4 algebra
  18.    wt: 4:   three goals to set for students
  19.    wt: 4:   permissions for teachers
  20.    wt: 4:   activities for students
  21.    wt: 4:   mathematics in context
  22.    wt: 4:   Education Reform Inconsistencies
  23.    wt: 4:   Secondary One Mathematics
  24.    wt: 4:   talk the algebra talk
  25.    wt: 4:   teaching tutoring algebraic reason
  26.    wt: 4:   Lessening Algebra Difficulties
  27.    wt: 4:   the trouble with algebra
  28.    wt: 4:   three goals for Mathematics Education
  29.    wt: 4:   04 29 New Mathematics Curriculum
  30.    wt: 4:   02 21 words for teachers
  31.    wt: 4:   three aims for mathematics students
  32.    wt: 4:   standards for course material
  33.    wt: 4:   Four ways to improve education reform
  34.    wt: 4:   How to be a better instructor
  35.    wt: 4:   need for a mixed mathematics curriculum
  36.    wt: 4:   fairness and inductive principles for instruction
  37.    wt: 4:   words for mathematics instructor
  38.    wt: 4:   8 Straight Lines Equation for vertical
  39.    wt: 4:   2 Algebraic View
  40.    wt: 4:   8 Pythagorean Relation Forwards Backwards
  41.    wt: 4:   6 Compound Interest Forward and Backwards
  42.    wt: 4:   5 Triangle Area Formula Backwards
  43.    wt: 4:   4 Rectangle Area and Like Formulas Backwards
  44.    wt: 4:   6 Algebraic Solution Example
  45.    wt: 4:   5 Algebraic Solutions Introduction
  46.    wt: 4:   13 Naming Identifying Formulas with Words
  47.    wt: 4:   9 Volume of Cone
  48.    wt: 4:   8 Compound Interest Formula Evaluation
  49.    wt: 4:   7 Compound Interest Formula Introduction
  50.    wt: 4:   5 Box Volume Formula Example
  51.    wt: 4:   4 Circle Area Formula Example
  52.    wt: 4:   3 Triangle Area Formula Example
  53.    wt: 4:   2 Another Rectangle Area Formula Example
  54.    wt: 4:   A Related lessons in Volume 3
  55.    wt: 4:   Postscript One Sided and Intermediate Value Theorems
  56.    wt: 4:   Postscript For Better Performance
  57.    wt: 4:   Appendix A. Reading Guide For Next Appendices
  58.    wt: 4:   Chapter 29 Contrapositive and Vacuously True Implications
  59.    wt: 4:   Chapter 19. Functions and Sets
  60.    wt: 4:   Chapter 18. Rules for Algebra
  61.    wt: 4:   Chapter 14. Forward and Backward Use of a Formula
  62.    wt: 4:   Chapter 9 Talking about Numbers or Quantities
  63.    wt: 4:   Chapter 8 Three Skills For Algebra
  64.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  65.    wt: 3:   K LAMP Musings Science Education
  66.    wt: 3:   J LAMP Introduction Extrinsic Origins
  67.    wt: 3:   I LAMP Introduction Study Habits
  68.    wt: 3:   H LAMP Introduction Instructional Concepts
  69.    wt: 3:   G LAMP Introduction Problem Solving Skills
  70.    wt: 3:   F LAMP Introduction Prerequisites
  71.    wt: 3:   E LAMP Introduction Modern Mathematics
  72.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  73.    wt: 3:   B LAMP Introduction Curriculum Development Standards
  74.    wt: 3:   A Introduction Objectives
  75.    wt: 3:   Skills Chapter 5 Calculus
  76.    wt: 3:   Skills Chapter 4 Logic
  77.    wt: 3:   Ramblings Extrinsic numbers theory
  78.    wt: 3:   Skills Chapter 2 Geometry
  79.    wt: 3:   Skills Chapter 1 Arithmetic
  80.    wt: 3:   Skills Chapter 0 Introduction
  81.    wt: 3:   11 pure mathematics
  82.    wt: 3:   10 statistics
  83.    wt: 3:   8 analytic geometry etc
  84.    wt: 3:   7 logic review and decimals an odd combination
  85.    wt: 3:   6 polynomials etc
  86.    wt: 3:   5 logarithms and exponentials etc
  87.    wt: 3:   3 Euclidean Geometry Leanly
  88.    wt: 3:   2 arithmetic with signed numbers
  89.    wt: 3:   1 arithmetic with unsigned numbers
  90.    wt: 3:   What is POMME
  91.    wt: 3:   why bother
  92.    wt: 3:   which way to go
  93.    wt: 3:   website reviews
  94.    wt: 3:   Teach the teachers plus goals
  95.    wt: 3:   Math Ed if it must be short make it lean effective
  96.    wt: 3:   links Education Resources online
  97.    wt: 3:   site origins
  98.    wt: 3:   site eurekas
  99.    wt: 3:   About site lesson plans
  100.    wt: 3:   key notes and themes
  101.    wt: 3:   Mathematics Education Professors
  102.    wt: 3:   teacher certification
  103.    wt: 3:   modern education
  104.    wt: 3:   learning takes time
  105.    wt: 3:   grouping students according to ability
  106.    wt: 3:   what should be learnt and When
  107.    wt: 3:   Postscript 2007 01 10
  108.    wt: 3:   five decades make a difference
  109.    wt: 3:   Maps Plans Drawings
  110.    wt: 3:   how letters appear
  111.    wt: 3:   Secondary Three Mathematics
  112.    wt: 3:   Secondary Two Mathematics
  113.    wt: 3:   three difficulties
  114.    wt: 3:   teaching tips
  115.    wt: 3:   What to Tell Students
  116.    wt: 3:   mathematics curriculum shifts
  117.    wt: 3:   05 13 OldSiteEntrancePage
  118.    wt: 3:   04 25 when to stop or suspend mathemat
  119.    wt: 3:   02 20 mathematics education references
  120.    wt: 3:   Operational Viewpoint to Value
  121.    wt: 3:   Theory of Knowledge
  122.    wt: 3:   mathematics instruction in general
  123.    wt: 3:   Education in mathematics science and technology
  124.    wt: 3:   Different Kinds of Reasoning in maths
  125.    wt: 3:   three kinds of reason in mathematics
  126.    wt: 3:   cultivating intelligence
  127.    wt: 3:   Motivation and Context Problem
  128.    wt: 3:   Leaner mathematics curriculum
  129.    wt: 3:   education an empirical art
  130.    wt: 3:   4 Energy Power Heat09
  131.    wt: 3:   19 Horizontal line rule and method
  132.    wt: 3:   9 Set theory term relation possible origins
  133.    wt: 3:   5 Function notation for geometric transformations
  134.    wt: 3:   8 Formulas for Fractional Exponents with Logarithms
  135.    wt: 3:   7 Formulas for Roots with Logarithms Derivation
  136.    wt: 3:   6 Formulas for Even and Odd Roots with Logarithms
  137.    wt: 3:   9 Straight Lines through Origin Equations
  138.    wt: 3:   1 Straight Lines Slope Concept
  139.    wt: 3:   3 Inequalities Algebraically
  140.    wt: 3:   5 Proportionality in Equivalent Fractions
  141.    wt: 3:   4 Rates Ratios and Proporitionality
  142.    wt: 3:   3 Proportionality Examples
  143.    wt: 3:   1 What is Proportionality
  144.    wt: 3:   7 Pythagorean Theorem Chinese Square Proof
  145.    wt: 3:   3 Linear Equation Literal Solution More
  146.    wt: 3:   2 Linear Equation Literal Solution
  147.    wt: 3:   1 Changing Calculations
  148.    wt: 3:   9 Coordinates for Regions in Space
  149.    wt: 3:   Simple Exercises
  150.    wt: 3:   4 Four Examples Fractional Coefficients
  151.    wt: 3:   3 Four Examples
  152.    wt: 3:   2 Three Examples
  153.    wt: 3:   1 Proper Equal Sign Usage
  154.    wt: 3:   9 Three Examples
  155.    wt: 3:   Formula Usage Show Work Format
  156.    wt: 3:   12 Cone Cylinder Sphere Lesson Idea
  157.    wt: 3:   11 Volume of Sphere
  158.    wt: 3:   10 Volume of Pyramid
  159.    wt: 3:   6 Pythagorean Hypotenuse Calculation Example
  160.    wt: 3:   1 Three Skills For Algebra
  161.    wt: 3:   5 Counting with Tables Trees Product Rule Take II
  162.    wt: 3:   25 Divisibility Tests for 2 3 5 9 10 Example
  163.    wt: 3:   19 Remainder Arithmetic Rule of 9 for checking sums III
  164.    wt: 3:   9 video Prime Factorization upto 19 squared
  165.    wt: 3:   38 Formulas and derivatives for powers and roots
  166.    wt: 3:   Postscript More on Better Performance
  167.    wt: 3:   Chapter 23. Notation For Sums
  168.    wt: 3:   Chapter 21. Third Reading Guide
  169.    wt: 3:   Chapter 13. Second Reading Guide
  170.    wt: 3:   Chapter 12. Shorthand Usage Guide
  171.    wt: 3:   Postscript What is a Variable
  172.    wt: 3:   Solutions For Arithmetic Exercises
  173.    wt: 3:   Chapter 7 Prep for Calculus Arithmetic Exercises
  174.    wt: 3:   Chapter 2 Implication Rules Forwards and Backwards
  175.    wt: 3:   Foreword
  176.    wt: 3:   S Adding words to algebra
  177.    wt: 3:   G. Written work formats for developing and showing skill
  178.    wt: 3:   Helping the Blind in Logic and Mathematics
  179.    wt: 3:   Mathematics Education References
  180.    wt: 3:   Mathematics Education References
  181.    wt: 3:   Multiple Ways to Improve Mathematics Skill Development
  182.    wt: 3:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  183.    wt: 3:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  184.    wt: 3:   More Algebra and Slope based Calculus Preview
  185.    wt: 3:   Systematic Algebra Skill Development Missing Links
  186.    wt: 2:   1 Conductance Resistance Duality01
  187.    wt: 2:   H Series Circuit02
  188.    wt: 2:   C Electromotive force conventional current02
  189.    wt: 2:   B Electromotive force conventional current01
  190.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  191.    wt: 2:   9 Streaming by Student Cooperation
  192.    wt: 2:   Ages 9 to 10
  193.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  194.    wt: 2:   sign monoticity analysis example 4
  195.    wt: 2:   sign monoticity analysis example 3
  196.    wt: 2:   sign monoticity analysis example 2
  197.    wt: 2:   sign monoticity analysis example 1
  198.    wt: 2:   6 Set Existence Formation and Notation
  199.    wt: 2:   3 Formula or function graphing exercise
  200.    wt: 2:   2 Algebraic use of function notation
  201.    wt: 2:   Introduction Reading Guide
  202.    wt: 2:   9 quadratics physical and further context
  203.    wt: 2:   8 quadratics backward use of various formulas
  204.    wt: 2:   7 quadratic formulla derivation
  205.    wt: 2:   8 Notes for instructors or tutors
  206.    wt: 2:   Rewriting algebraic substitution as function substitutions
  207.    wt: 2:   9 motivation for name arcsin
  208.    wt: 2:   8 Radian Measures of Common Angles
  209.    wt: 2:   9 Head to Tail Coordinate View
  210.    wt: 2:   D Straight Lines Slope from Coordinates Examples
  211.    wt: 2:   C Straight Lines Slope from Coordinates
  212.    wt: 2:   B Straight Line Slope Scaling Properties More
  213.    wt: 2:   A Straight Line Slope Scaling Properties
  214.    wt: 2:   14 Straight Lines Equations General Case
  215.    wt: 2:   13 Straight Lines Finding Equations from 2 points
  216.    wt: 2:   12 Straight Lines Graphing mx plus b
  217.    wt: 2:   11 Straight Lines Graphing y=mx
  218.    wt: 2:   10 Straight Lines through Origin Equations More
  219.    wt: 2:   7 Tangent Function is odd on this domain
  220.    wt: 2:   6 Tangent Function Inclination Angle Take 2
  221.    wt: 2:   5 Tangent Function Graph
  222.    wt: 2:   4 Tangent Function Properties
  223.    wt: 2:   3 Straight Lines Slope as Tangent of Inclination Angle
  224.    wt: 2:   2 Straight Lines Slopes As Rise Over Run
  225.    wt: 2:   29 secant cosecant and cotangent for acute angles
  226.    wt: 2:   26 Formulas for products of sines and cosines
  227.    wt: 2:   20 sine and cosine Double Angle Formulas
  228.    wt: 2:   19 Pythagorean Identity For sine and cosine functions
  229.    wt: 2:   17E Trig Formulas for dot and cross Products
  230.    wt: 2:   17D cis formulas for sine cosines and tangent
  231.    wt: 2:   12 Graph of tangent function for one period
  232.    wt: 2:   3 sines and cosines for reference angle 90 degrees
  233.    wt: 2:   2 Quadrant I reference Angles
  234.    wt: 2:   1 Unit Points Reflections Rotations
  235.    wt: 2:   19 N th Roots of Unity
  236.    wt: 2:   13 Trig Formulas for dot and cross Products
  237.    wt: 2:   12 cis formulas for sine cosines and tangent
  238.    wt: 2:   9 The complex number valued trig function cis
  239.    wt: 2:   9 Similarity of Triangles Usual Criteria
  240.    wt: 2:   9 Midpoint Coordinates Half Endpoint Sum
  241.    wt: 2:   4 Equations for lines three forms
  242.    wt: 2:   9 Pythagorean Theorem Chinese Square Proof
  243.    wt: 2:   19 Right Triangle Similarity
  244.    wt: 2:   9 Construction of a right bisector
  245.    wt: 2:   A Signed Number Arithmetic Review
  246.    wt: 2:   19 Signed Multiples of Vectors
  247.    wt: 2:   9 Division with Digits after Decimal Point
  248.    wt: 2:   6 Infinite Decimals Ending in 9 repeating
  249.    wt: 2:   E Long Division Methods more
  250.    wt: 2:   D Long Division Methods
  251.    wt: 2:   C Three Decimal Subtraction Methods
  252.    wt: 2:   B Decimal Comparison and Subtraction
  253.    wt: 2:   A Decimal Addition Columm Methods
  254.    wt: 2:   6 Column Methods for Decimal Multiplication
  255.    wt: 2:   5 Distributive Law for Whole Numbers
  256.    wt: 2:   4 Commutative Law Groups Counting Form
  257.    wt: 2:   5 Areas of Rectangles Revisited
  258.    wt: 2:   4 Fraction Operations Axiomatic Development
  259.    wt: 2:   2 Fraction Operations Physical Development
  260.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  261.    wt: 2:   5 Equality in Algebra
  262.    wt: 2:   3 Product Axioms Two Forms
  263.    wt: 2:   2 More and Less Than for Counts and Measures
  264.    wt: 2:   8 Coordinates for Maps and Planes
  265.    wt: 2:   3 Geometric Formulas and Function Notation
  266.    wt: 2:   1 Formulas Dependence and Function Notation
  267.    wt: 2:   5 Gaussian Elimination for 3 unknowns 2nd example
  268.    wt: 2:   Using Letters for Physical Quantities
  269.    wt: 2:   9 Sets in Probability and Statistics
  270.    wt: 2:   4 A Brief Story of numbers and algebra
  271.    wt: 2:   4 Counting with Trees Product Rule Take I
  272.    wt: 2:   3 Counting with Tables and Trees II
  273.    wt: 2:   2 Counting with Tables and Trees I
  274.    wt: 2:   1 Counting and Counting Methods I
  275.    wt: 2:   9 subtracting signed numbers
  276.    wt: 2:   C Equality for Fractions and Two Term Ratios and Fractions
  277.    wt: 2:   9 Multiplying Integers
  278.    wt: 2:   24 Divisibility Tests for 2 3 5 9 10
  279.    wt: 2:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  280.    wt: 2:   18 Remainder Arithmetic Rule of 9 for checking sums II
  281.    wt: 2:   17 Remainder Arithmetic Rule of 9 for checking sums I
  282.    wt: 2:   15 Remainder Arithmetic Modulo 9 Example
  283.    wt: 2:   19 video Prime Factorization Unique
  284.    wt: 2:   Long Division forwards and backwards Example 1
  285.    wt: 2:   9 Why Long Division Works Take II
  286.    wt: 2:   9 22 Minute Subtraction Review Video
  287.    wt: 2:   9 Place Value Review Decimal form of Avogrados number included
  288.    wt: 2:   19 Chain Rule for linear functions
  289.    wt: 2:   2 Motivation for Limit Definition Take 1
  290.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  291.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  292.    wt: 2:   Chapter 9 About First Courses in Calculus
  293.    wt: 2:   Appendix E. How To Study Mathematics and Why
  294.    wt: 2:   Appendix D. What to do in School and Why
  295.    wt: 2:   Appendix C. How to Read
  296.    wt: 2:   Appendix B. How To Learn
  297.    wt: 2:   Chapter 31 Direct and Indirect Reason
  298.    wt: 2:   Chapter 30 Truth Tables
  299.    wt: 2:   Chapter 28 Occurrence Tables
  300.    wt: 2:   Chapter 27 Shorthand Symbols as Pronouns
  301.    wt: 2:   Chapter 26 What is in chapters 27 to 31
  302.    wt: 2:   Chapter 25. Mathematical Induction Examples
  303.    wt: 2:   Chapter 24. Personal Investment and Pension EGS
  304.    wt: 2:   Chapter 22. Geometric Sums and Sequences
  305.    wt: 2:   Chapter 20. Degrees and Radians
  306.    wt: 2:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  307.    wt: 2:   Chapter 16. Painless Theorem Proving
  308.    wt: 2:   Chapter 15. Solving Linear Equations
  309.    wt: 2:   Chapter 11. Why Shorthand
  310.    wt: 2:   Chapter 10 Describing and Changing Calculations
  311.    wt: 2:   Chapter 6 Change of Language
  312.    wt: 2:   Chapter 5 Islands and Divisions of Knowledge
  313.    wt: 2:   Chapter 4 Longer Chains of Reason
  314.    wt: 2:   Chapter 3 Chains of Reason
  315.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  316.    wt: 2:   Chapter 9 The Two Ends
  317.    wt: 2:   Chapter 19 What is in chapters 20 to 24
  318.    wt: 2:   Chapter 9 What is in Chapters 10 to 18
  319.    wt: 2:   V Reasons and Motivations for Logic and Mathematics
  320.    wt: 2:   N Mathematics Prepare for College Studies
  321.    wt: 2:   I. Logic and language skills
  322.    wt: 2:   Implementation Notes
  323.    wt: 2:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  324.    wt: 2:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  325.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  326.    wt: 2:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  327.    wt: 2:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  328.    wt: 2:   Which Way To Go
  329.    wt: 2:   Talking pdf files for online lessons a webvideo alternative
  330.    wt: 1:   chapitre 04 09 Regles accidentelles
  331.    wt: 1:   3 Energy Power Heat08
  332.    wt: 1:   2 Energy Power Heat07
  333.    wt: 1:   1 Energy Power Heat06
  334.    wt: 1:   E Energy Power05
  335.    wt: 1:   D Energy Power04
  336.    wt: 1:   C Energy Power03
  337.    wt: 1:   B Energy Power02
  338.    wt: 1:   A Energy Power01
  339.    wt: 1:   2 Conductance Resistance Duality02
  340.    wt: 1:   F Wire Resistance Calculation04
  341.    wt: 1:   E Wire Resistance Calculation03
  342.    wt: 1:   D Wire Resistance Calculation02
  343.    wt: 1:   C Wire Resistance Calculation01
  344.    wt: 1:   B Wire Resistance Qualitative02
  345.    wt: 1:   A Wire Resistance Qualitative01
  346.    wt: 1:   3 Like resistors in parallel
  347.    wt: 1:   2 Unlike resistors in parallel01
  348.    wt: 1:   1 Like resistors in series
  349.    wt: 1:   G Series Circuit01
  350.    wt: 1:   F Unlike Resistors in Series
  351.    wt: 1:   E Kirchoffs Second Law
  352.    wt: 1:   D Kirchoff First Law
  353.    wt: 1:   A Circuit Elements
  354.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  355.    wt: 1:   24 Standards For Skill Develoment Take II
  356.    wt: 1:   24 Standards For Skill Develoment
  357.    wt: 1:   17 Math Booklets for children and young teenagers
  358.    wt: 1:   15 Counting For Parents
  359.    wt: 1:   12 Goals and Objectives For Mathematics
  360.    wt: 1:   10 Ends values for work study instruction
  361.    wt: 1:   5 Patience Please for Yourself and Your Charges
  362.    wt: 1:   4 Learning Takes Time and Effort
  363.    wt: 1:   3 Preparing for Science Studies
  364.    wt: 1:   Ages 8 to 9
  365.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  366.    wt: 1:   26 Function definitions done and coming
  367.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  368.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  369.    wt: 1:   23 Inverse Functions
  370.    wt: 1:   22 Square Root function graphically
  371.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  372.    wt: 1:   20 Interchanging coordinates a reflection
  373.    wt: 1:   18 Vertical Line Rule and Method
  374.    wt: 1:   17 Function maxima minima and their location
  375.    wt: 1:   16 Increasing or decreasing on intervals
  376.    wt: 1:   15 Sign analysis of functions
  377.    wt: 1:   14 Surjections Injections Bijections
  378.    wt: 1:   13 From one to one to many to one
  379.    wt: 1:   12 Function Domain Recognition Exercises
  380.    wt: 1:   11 Function Domain Range Source and Targets
  381.    wt: 1:   10 Interval Notation
  382.    wt: 1:   8 Set view of relations and functions
  383.    wt: 1:   7 Functions with finite domains
  384.    wt: 1:   4 Function notation in and beyond mathematics
  385.    wt: 1:   1 Geometric Introduction of Function Notation
  386.    wt: 1:   A Quadratics Summary
  387.    wt: 1:   10 quadratic exercises
  388.    wt: 1:   6 quadratics numerical approach
  389.    wt: 1:   5 quadratics completing the square
  390.    wt: 1:   4 quadratics difference of two squares
  391.    wt: 1:   3 quadratics factoring by inspection
  392.    wt: 1:   2 quadratics graphing in general
  393.    wt: 1:   1 quadratics graphing exercises
  394.    wt: 1:   Quadratics in 10 steps
  395.    wt: 1:   11 Growth and Decay in Biology
  396.    wt: 1:   10 Exponential Growth and Decay Models
  397.    wt: 1:   5 Natural Logarithm Calculator Exercises
  398.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  399.    wt: 1:   2 Square Root Simplification a prequel
  400.    wt: 1:   1 Calculator Starter Exercises
  401.    wt: 1:   7 Links Lessons Elsewhere
  402.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  403.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  404.    wt: 1:   4 Polynomials Long division linear divisor
  405.    wt: 1:   3 Polynomials Multiplication Addition
  406.    wt: 1:   2 Column Multiplication Method
  407.    wt: 1:   1 Polynomials Distributive Law
  408.    wt: 1:   12 motivation for term arctan
  409.    wt: 1:   4 possible motivation for term arccos
  410.    wt: 1:   9 Summary Degrees to Radians and back
  411.    wt: 1:   7 Radian Measures in special Triangles
  412.    wt: 1:   6 Radian Measure to Degrees
  413.    wt: 1:   5 Degrees to Radian Measure
  414.    wt: 1:   4 Circle Sector Area proportional to Central Angle
  415.    wt: 1:   3 Circle Arclengh Proportional to Central Angle
  416.    wt: 1:   2 Radian Measure Numerical Value of one degree
  417.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  418.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  419.    wt: 1:   Straight Lines Intersection of
  420.    wt: 1:   17 tangent function angle sum formulas
  421.    wt: 1:   30 unit circle calculation of six trigonometric functions
  422.    wt: 1:   25 tangent double angle formula Slope connection
  423.    wt: 1:   24 tangent Angle Difference Formula
  424.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  425.    wt: 1:   21 sine and cosine Half Angle Formulas
  426.    wt: 1:   17C sine and cosine double triple angle formulas
  427.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  428.    wt: 1:   9 Graphs of sine and cosine over one period
  429.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  430.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  431.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  432.    wt: 1:   11 sine and cosine double triple angle formulas
  433.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  434.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  435.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  436.    wt: 1:   1 Early Concept of Like or Similar Shapes
  437.    wt: 1:   8 Mid Point Formula
  438.    wt: 1:   5 Algebraic View of Slopes
  439.    wt: 1:   3 Slope product for perpendicular lines
  440.    wt: 1:   2 point slope equation for a line
  441.    wt: 1:   13 Pythagorean spatial distance formulas
  442.    wt: 1:   10 Pythagorean plane distance formula
  443.    wt: 1:   PS H Distributive Law For Complex Numbers
  444.    wt: 1:   A Modular and Remainder Arithmetic
  445.    wt: 1:   26 More Less Greater Than Comparison
  446.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  447.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  448.    wt: 1:   23 Distributive Law Two Derivations
  449.    wt: 1:   22 Multiplication of Signed Numbers
  450.    wt: 1:   21 Addition of Multiples of a Single Vector
  451.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  452.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  453.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  454.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  455.    wt: 1:   15 Head to Tails in place Addition Associative
  456.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  457.    wt: 1:   13 Arrows and Vectors in a Plane
  458.    wt: 1:   12 Real Numbers Line Signed Coordinates
  459.    wt: 1:   11 Signed Number Addition and Addition Properties
  460.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  461.    wt: 1:   8 Division and Mulplication of Compound Fractions
  462.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  463.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  464.    wt: 1:   4 Location of Point in Decimal Addition
  465.    wt: 1:   3 Location of Point in Decimal Multiplication
  466.    wt: 1:   2 Counting Digits in Decimal Multiplication
  467.    wt: 1:   1 Fractions with Finite Decimal Expansions
  468.    wt: 1:   8 Column Multiplication Methods in General
  469.    wt: 1:   7 Decimals Multiplication Methods Examples
  470.    wt: 1:   3 Multiplicative Counting Skills Principles
  471.    wt: 1:   2 Combing Counts Addition Skills and Principles
  472.    wt: 1:   1 The Counting Origins of Numbers
  473.    wt: 1:   6 Equations and Systems Equivalent or Implied
  474.    wt: 1:   4 Subtraction and Division Axioms
  475.    wt: 1:   2 Addition and Multiplication Axioms
  476.    wt: 1:   1 Equivalent Computation Rules
  477.    wt: 1:   5 Greater More Less Than Signs in General
  478.    wt: 1:   4 Comparison of Negative Numbers
  479.    wt: 1:   3 More and Less Than with Unlike Signs
  480.    wt: 1:   1 Real Numbers Comparison
  481.    wt: 1:   16 Real Numbers Comparison
  482.    wt: 1:   15 Real Number Division
  483.    wt: 1:   14 Real Number Multiplication
  484.    wt: 1:   13 Real Number Subtraction
  485.    wt: 1:   12 Real Number Additive Inverses or Negatives
  486.    wt: 1:   11 Real Number Addition
  487.    wt: 1:   10 Real Number Lengths and Signs
  488.    wt: 1:   7 Real Numbers as Line Cordinates
  489.    wt: 1:   6 Unsigned Real Numbers
  490.    wt: 1:   5 Rational Numbers More
  491.    wt: 1:   4 Rational Numbers
  492.    wt: 1:   3 Fractions
  493.    wt: 1:   2 Integers
  494.    wt: 1:   1 Whole and Natural Numbers
  495.    wt: 1:   5 Independent versus Dependent Variables
  496.    wt: 1:   4 Changing Letters
  497.    wt: 1:   2 Computation Rules Evaluation
  498.    wt: 1:   More Exercises
  499.    wt: 1:   4 GE III Animated Examples
  500.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  501.    wt: 1:   3 GE III Equation Addition and Multiplication
  502.    wt: 1:   2 GE II Comparison
  503.    wt: 1:   1 GE Substitution four examples
  504.    wt: 1:   4 Solving a triangular system exercise
  505.    wt: 1:   3 Solving triangular system example
  506.    wt: 1:   2 Essentially one exercises three with solution
  507.    wt: 1:   1 Essentially One Unknown
  508.    wt: 1:   Skill Development Notes
  509.    wt: 1:   10 One Example
  510.    wt: 1:   8 One Example
  511.    wt: 1:   7 Two Examples
  512.    wt: 1:   6 Three Examples
  513.    wt: 1:   5 Three Examples
  514.    wt: 1:   4 Two Examples
  515.    wt: 1:   3 Two Examples
  516.    wt: 1:   2 Three Examples
  517.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  518.    wt: 1:   8 Sets of Numbers
  519.    wt: 1:   7 Cautious or Safe Set Construction
  520.    wt: 1:   6 Power Set Notation
  521.    wt: 1:   5 Product Builder Notation
  522.    wt: 1:   4 Subset Builder Notation
  523.    wt: 1:   3 Counting with Sets etc
  524.    wt: 1:   2 Venn Diagrams
  525.    wt: 1:   1 Finite Sets
  526.    wt: 1:   6 Three Notions of What is a Variable
  527.    wt: 1:   5 Talking about Numbers and Quantities
  528.    wt: 1:   3 Adding Words To Arithmetic
  529.    wt: 1:   2 What is a Variable
  530.    wt: 1:   About Folder Contents
  531.    wt: 1:   1 More and Less Than for Counts and Measures
  532.    wt: 1:   10 Euclid Algorithm with 129 125 and with 45 14
  533.    wt: 1:   9 GCD of 360 110 via Primes and Euclid Algorithm
  534.    wt: 1:   4 LCM of 8 and 10 via Prime
  535.    wt: 1:   4 signed coordinates for regions in space
  536.    wt: 1:   3 signed coordinates for maps and planes
  537.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  538.    wt: 1:   D Three Term Ratios
  539.    wt: 1:   B Fractions and Two Term Ratios
  540.    wt: 1:   A Similarities between Fractions and Two Term Ratios
  541.    wt: 1:   21 Reciprocals for Fractions and Wholes
  542.    wt: 1:   19 Dividing Fractions How TO
  543.    wt: 1:   16 Addition Subtraction Comparision Compared
  544.    wt: 1:   15 Adding and Subtracting with Unlike Denominators
  545.    wt: 1:   13 Fraction Comparison Algebraic View
  546.    wt: 1:   11 Simplification an Algebraic View
  547.    wt: 1:   9 Improper Fractions and Mixed Numbers
  548.    wt: 1:   6 Multiplication Algebraically Take II
  549.    wt: 1:   11 Adding Integers Formulas and Examples
  550.    wt: 1:   10 Integer Multiplication Formulas
  551.    wt: 1:   27 Divisibility by 2 3 6 5 9 10 Example
  552.    wt: 1:   16 Remainder Arithmetic Modulo 9 Example 2
  553.    wt: 1:   14 Remainder Arithmetic Modulo 9 Example
  554.    wt: 1:   9 Remainder Arithmetic Divisibility by 5
  555.    wt: 1:   5 Remainder Arithmetic Modulo 5
  556.    wt: 1:   16 video Factors of 980 using prime
  557.    wt: 1:   8 video Prime Factorization upto 19
  558.    wt: 1:   3 video Primes and Composites from 9 times table
  559.    wt: 1:   Long Division Backwards more
  560.    wt: 1:   Long Division Backward
  561.    wt: 1:   Long Division forwards and backwards Example 3
  562.    wt: 1:   Long Division forwards and backwards Example 2
  563.    wt: 1:   C Counting Areas with Powers of Ten
  564.    wt: 1:   A Elementary Basis for Multiplication Methods
  565.    wt: 1:   Appendix 2 Three Decimal Subtraction Methods
  566.    wt: 1:   Appendix 1 Decimals Comparison Method Take II
  567.    wt: 1:   Subtraction with J Conversions Example
  568.    wt: 1:   Subtraction Another Video Lesson
  569.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  570.    wt: 1:   5 A Tip for Efficent Subtraction
  571.    wt: 1:   Appendix 1 Counting Revisited 15 minute video
  572.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  573.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  574.    wt: 1:   Quick history of numbers and algebra
  575.    wt: 1:   Formula Evaluation how to show work
  576.    wt: 1:   The 12 Times Table Visually
  577.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  578.    wt: 1:   9 Comparison and Subtraction of Time Intervals
  579.    wt: 1:   A Chain Rule Real Player video examples
  580.    wt: 1:   36 Cube root derivative animated
  581.    wt: 1:   29 Chain Rule Optional Reading
  582.    wt: 1:   28 Chain Rule Preparation for a Proof
  583.    wt: 1:   22 Chain Rule for polynomials
  584.    wt: 1:   21 Chain Rule for powers
  585.    wt: 1:   20 Chain Rule for Pulley Systems
  586.    wt: 1:   11 Quotient rule
  587.    wt: 1:   10 Power rule for negative integers
  588.    wt: 1:   9 Reciprocal rule
  589.    wt: 1:   3 Motivation for Limit Definition Take 2
  590.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  591.    wt: 1:   9 Limits Continuity and Composition
  592.    wt: 1:   3 Decimal insights for limits continuity convergence
  593.    wt: 1:   2 Algebraic codification
  594.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  595.    wt: 1:   G.5 Motions With Bounded Velocities
  596.    wt: 1:   F.1 What Functions are Continuous
  597.    wt: 1:   E2 Algebraic Properties of Limits
  598.    wt: 1:   PostScript For and Against Decimal Perspectives
  599.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  600.    wt: 1:   Fall 1983 Calculus Appetizer
  601.    wt: 1:   Foreword
  602.    wt: 1:   Chapter 3 Algebra Difficulties
  603.    wt: 1:   Chapter 2 For and Against Mathematics
  604.    wt: 1:   Foreword
  605.    wt: 1:   Postscript C Consistency as a Tool for Reason
  606.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  607.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  608.    wt: 1:   Foreword
  609.    wt: 1:   R Why Learn Mathematics Skills
  610.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  611.    wt: 1:   P Exact Arithmetic With Whole Numbers and Fractions
  612.    wt: 1:   O On Learning Mathematics and Science
  613.    wt: 1:   M Words to extend arithmetic
  614.    wt: 1:   L Skills with take home value
  615.    wt: 1:   N Improving Marks on Tests and Finals
  616.    wt: 1:   J. More on written work and showing skill
  617.    wt: 1:   H more Routine to non routine problem solving
  618.    wt: 1:   H Jigsaw puzzles and problem solving
  619.    wt: 1:   F. The student teacher tutor feedback loop
  620.    wt: 1:   E. When and how to correct errors
  621.    wt: 1:   D. Check work a must with a caution
  622.    wt: 1:   C. Domino effect of being careful
  623.    wt: 1:   B. Domino effect of errors
  624.    wt: 1:   A. Skill has to be seen to believed
  625.    wt: 1:   How to Build Skills and Confidence
  626.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  627.    wt: 1:   Chapter 6 More Algebra and Geometry
  628.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  629.    wt: 1:   Chapter 3 Algebra Starter Lessons
  630.    wt: 1:   7 Games and Activities for Instruction
  631.    wt: 1:   The Math Forum and Site Content
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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