Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Building Site Map || Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling, with chapters on Logic and Pattern Based Reason to inform and amuse.

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 material may develop critical thinking, improve reading and writing, and build mathematics and pattern based reasoning skills. Online Volumes 1, 1A and 2 give avid readers in school and out the best places to begin.

Teachers & Tutors: This December 2011, 5-phase framework offers a context for mathematics & logic education. Phases 1 to 3 focus on skills with actual or potential local 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.

Home << Search

[1] [2] [3] [4]

Key Word Search

Folder Search

9 matches:

  1.    wt: 2:   Parent Center/
  2.    wt: 2:   2 Formula Forward Use Evaluation/
  3.    wt: 2:   Work and Study Tips/
  4.    wt: 1:   9 Proportionality Backwards and Forwards/
  5.    wt: 1:   8 Unifying Theme For Algebra/
  6.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  7.    wt: 1:   1 Working With Sets/
  8.    wt: 1:   Volume 2 Three Skills For Algebra/
  9.    wt: 1:   Mathematics Skill Development Framework/

Web Page Search

192 matches:

  1.    wt: 6:   10 Ends values for work study instruction
  2.    wt: 4:   Ends Values Methods For Skill Development Framework Prequel
  3.    wt: 3:   Formula Usage Show Work Format
  4.    wt: 3:   1 Written work formats for developing and showing skill
  5.    wt: 3:   Practical Methods Ends and Values for Arithmetic
  6.    wt: 3:   G. Written work formats for developing and showing skill
  7.    wt: 2:   formal or informal peer review
  8.    wt: 2:   Prequel In For A Penny In For A Pound
  9.    wt: 2:   fairness and inductive principles for instruction
  10.    wt: 2:   5 Function notation for geometric transformations
  11.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  12.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  13.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  14.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  15.    wt: 2:   26 Formulas for products of sines and cosines
  16.    wt: 2:   17E Trig Formulas for dot and cross Products
  17.    wt: 2:   17D cis formulas for sine cosines and tangent
  18.    wt: 2:   13 Trig Formulas for dot and cross Products
  19.    wt: 2:   12 cis formulas for sine cosines and tangent
  20.    wt: 2:   4 Equations for lines three forms
  21.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  22.    wt: 2:   Formula Evaluation how to show work
  23.    wt: 2:   38 Formulas and derivatives for powers and roots
  24.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  25.    wt: 2:   Postscript For Better Performance
  26.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  27.    wt: 2:   7 Games and Activities for Instruction
  28.    wt: 1:   I LAMP Introduction Study Habits
  29.    wt: 1:   H LAMP Introduction Instructional Concepts
  30.    wt: 1:   three goals to set for students
  31.    wt: 1:   permissions for teachers
  32.    wt: 1:   activities for students
  33.    wt: 1:   Education Reform Inconsistencies
  34.    wt: 1:   geometric implications for algebra
  35.    wt: 1:   three goals for Mathematics Education
  36.    wt: 1:   02 21 words for teachers
  37.    wt: 1:   three aims for mathematics students
  38.    wt: 1:   standards for course material
  39.    wt: 1:   mathematics instruction in general
  40.    wt: 1:   Four ways to improve education reform
  41.    wt: 1:   need for a mixed mathematics curriculum
  42.    wt: 1:   words for mathematics instructor
  43.    wt: 1:   C Electromotive force conventional current02
  44.    wt: 1:   B Electromotive force conventional current01
  45.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  46.    wt: 1:   24 Standards For Skill Develoment Take II
  47.    wt: 1:   24 Standards For Skill Develoment
  48.    wt: 1:   22 Student Centered Highschool Mathematics
  49.    wt: 1:   17 Math Booklets for children and young teenagers
  50.    wt: 1:   15 Counting For Parents
  51.    wt: 1:   12 Goals and Objectives For Mathematics
  52.    wt: 1:   5 Patience Please for Yourself and Your Charges
  53.    wt: 1:   4 Learning Takes Time and Effort
  54.    wt: 1:   3 Preparing for Science Studies
  55.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  56.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  57.    wt: 1:   6 Set Existence Formation and Notation
  58.    wt: 1:   3 Formula or function graphing exercise
  59.    wt: 1:   8 quadratics backward use of various formulas
  60.    wt: 1:   7 quadratic formulla derivation
  61.    wt: 1:   8 Notes for instructors or tutors
  62.    wt: 1:   12 motivation for term arctan
  63.    wt: 1:   9 motivation for name arcsin
  64.    wt: 1:   4 possible motivation for term arccos
  65.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  66.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  67.    wt: 1:   Straight Lines ASA Intersection Study More
  68.    wt: 1:   Straight Lines ASA Intersection Study
  69.    wt: 1:   8 Straight Lines Equation for vertical
  70.    wt: 1:   17 tangent function angle sum formulas
  71.    wt: 1:   29 secant cosecant and cotangent for acute angles
  72.    wt: 1:   25 tangent double angle formula Slope connection
  73.    wt: 1:   24 tangent Angle Difference Formula
  74.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  75.    wt: 1:   21 sine and cosine Half Angle Formulas
  76.    wt: 1:   20 sine and cosine Double Angle Formulas
  77.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  78.    wt: 1:   17C sine and cosine double triple angle formulas
  79.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  80.    wt: 1:   12 Graph of tangent function for one period
  81.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  82.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  83.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  84.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  85.    wt: 1:   11 sine and cosine double triple angle formulas
  86.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  87.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  88.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  89.    wt: 1:   8 Mid Point Formula
  90.    wt: 1:   3 Slope product for perpendicular lines
  91.    wt: 1:   2 point slope equation for a line
  92.    wt: 1:   13 Pythagorean spatial distance formulas
  93.    wt: 1:   10 Pythagorean plane distance formula
  94.    wt: 1:   PS H Distributive Law For Complex Numbers
  95.    wt: 1:   6 Column Methods for Decimal Multiplication
  96.    wt: 1:   5 Distributive Law for Whole Numbers
  97.    wt: 1:   4 Commutative Law Groups Counting Form
  98.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  99.    wt: 1:   6 Compound Interest Forward and Backwards
  100.    wt: 1:   5 Triangle Area Formula Backwards
  101.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  102.    wt: 1:   3 Product Axioms Two Forms
  103.    wt: 1:   2 More and Less Than for Counts and Measures
  104.    wt: 1:   9 Coordinates for Regions in Space
  105.    wt: 1:   8 Coordinates for Maps and Planes
  106.    wt: 1:   3 Geometric Formulas and Function Notation
  107.    wt: 1:   1 Formulas Dependence and Function Notation
  108.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  109.    wt: 1:   Using Letters for Physical Quantities
  110.    wt: 1:   13 Naming Identifying Formulas with Words
  111.    wt: 1:   8 Compound Interest Formula Evaluation
  112.    wt: 1:   7 Compound Interest Formula Introduction
  113.    wt: 1:   5 Box Volume Formula Example
  114.    wt: 1:   4 Circle Area Formula Example
  115.    wt: 1:   3 Triangle Area Formula Example
  116.    wt: 1:   2 Another Rectangle Area Formula Example
  117.    wt: 1:   1 Three Skills For Algebra
  118.    wt: 1:   arithmetic videos Real Player Format
  119.    wt: 1:   1 More and Less Than for Counts and Measures
  120.    wt: 1:   4 signed coordinates for regions in space
  121.    wt: 1:   3 signed coordinates for maps and planes
  122.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  123.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  124.    wt: 1:   21 Working With Signs
  125.    wt: 1:   21 Reciprocals for Fractions and Wholes
  126.    wt: 1:   11 Adding Integers Formulas and Examples
  127.    wt: 1:   10 Integer Multiplication Formulas
  128.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  129.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  130.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  131.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  132.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  133.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  134.    wt: 1:   Long Division forwards and backwards Example 3
  135.    wt: 1:   Long Division forwards and backwards Example 2
  136.    wt: 1:   Long Division forwards and backwards Example 1
  137.    wt: 1:   12 Why Long Division Works Take III
  138.    wt: 1:   9 Why Long Division Works Take II
  139.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  140.    wt: 1:   A Elementary Basis for Multiplication Methods
  141.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  142.    wt: 1:   5 A Tip for Efficent Subtraction
  143.    wt: 1:   8 What skills and work habits to require
  144.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  145.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  146.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  147.    wt: 1:   Expression Evaluation how to show work
  148.    wt: 1:   015 School and work day counting tables
  149.    wt: 1:   28 Chain Rule Preparation for a Proof
  150.    wt: 1:   22 Chain Rule for polynomials
  151.    wt: 1:   21 Chain Rule for powers
  152.    wt: 1:   20 Chain Rule for Pulley Systems
  153.    wt: 1:   19 Chain Rule for linear functions
  154.    wt: 1:   10 Power rule for negative integers
  155.    wt: 1:   3 Motivation for Limit Definition Take 2
  156.    wt: 1:   2 Motivation for Limit Definition Take 1
  157.    wt: 1:   10 Three one sided limits with infinite values
  158.    wt: 1:   3 Decimal insights for limits continuity convergence
  159.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  160.    wt: 1:   PostScript For and Against Decimal Perspectives
  161.    wt: 1:   Foreword
  162.    wt: 1:   Postscript More on Better Performance
  163.    wt: 1:   Appendix E. How To Study Mathematics and Why
  164.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  165.    wt: 1:   Chapter 23. Notation For Sums
  166.    wt: 1:   Chapter 18. Rules for Algebra
  167.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  168.    wt: 1:   Chapter 8 Three Skills For Algebra
  169.    wt: 1:   Solutions For Arithmetic Exercises
  170.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  171.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  172.    wt: 1:   Foreword
  173.    wt: 1:   Chapter 11 Elementary Instruction
  174.    wt: 1:   Chapter 9 The Two Ends
  175.    wt: 1:   Chapter 8 Modern Instruction
  176.    wt: 1:   Chapter 2 For and Against Mathematics
  177.    wt: 1:   Foreword
  178.    wt: 1:   Postscript C Consistency as a Tool for Reason
  179.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  180.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  181.    wt: 1:   Foreword
  182.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  183.    wt: 1:   Q How Logic and Proofs extend Show Work Practices
  184.    wt: 1:   N Mathematics Prepare for College Studies
  185.    wt: 1:   J. More on written work and showing skill
  186.    wt: 1:   D. Check work a must with a caution
  187.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  188.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  189.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  190.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  191.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  192.    wt: 1:   The Math Forum and Site Content

Extended Search

301 matches:

  1.    wt: 8:   10 Ends values for work study instruction
  2.    wt: 5:   1 Written work formats for developing and showing skill
  3.    wt: 5:   G. Written work formats for developing and showing skill
  4.    wt: 5:   Ends Values Methods For Skill Development Framework Prequel
  5.    wt: 3:   27 Graduated Correction and Penalties for Young Offenders
  6.    wt: 3:   24 Standards For Skill Develoment Take II
  7.    wt: 3:   24 Standards For Skill Develoment
  8.    wt: 3:   22 Student Centered Highschool Mathematics
  9.    wt: 3:   17 Math Booklets for children and young teenagers
  10.    wt: 3:   15 Counting For Parents
  11.    wt: 3:   12 Goals and Objectives For Mathematics
  12.    wt: 3:   5 Patience Please for Yourself and Your Charges
  13.    wt: 3:   4 Learning Takes Time and Effort
  14.    wt: 3:   3 Preparing for Science Studies
  15.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  16.    wt: 3:   Formula Usage Show Work Format
  17.    wt: 3:   13 Naming Identifying Formulas with Words
  18.    wt: 3:   8 Compound Interest Formula Evaluation
  19.    wt: 3:   7 Compound Interest Formula Introduction
  20.    wt: 3:   5 Box Volume Formula Example
  21.    wt: 3:   4 Circle Area Formula Example
  22.    wt: 3:   3 Triangle Area Formula Example
  23.    wt: 3:   2 Another Rectangle Area Formula Example
  24.    wt: 3:   Practical Methods Ends and Values for Arithmetic
  25.    wt: 3:   Postscript For Better Performance
  26.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  27.    wt: 3:   V Reasons and Motivations for Logic and Mathematics
  28.    wt: 3:   Q How Logic and Proofs extend Show Work Practices
  29.    wt: 3:   N Mathematics Prepare for College Studies
  30.    wt: 3:   J. More on written work and showing skill
  31.    wt: 3:   D. Check work a must with a caution
  32.    wt: 2:   formal or informal peer review
  33.    wt: 2:   Prequel In For A Penny In For A Pound
  34.    wt: 2:   fairness and inductive principles for instruction
  35.    wt: 2:   Home Tutoring and Home Schooling
  36.    wt: 2:   25 Mathematics Education Leaving A Good Impression
  37.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take IV
  38.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take III
  39.    wt: 2:   23 Modularized Skill Development Modularized Rigor Take II
  40.    wt: 2:   23 Modularized Skill Development Modularized Rigor
  41.    wt: 2:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  42.    wt: 2:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  43.    wt: 2:   19 Extending the Oral Dimension of Mathematics
  44.    wt: 2:   18 Primary School Mathematics
  45.    wt: 2:   16 Secondary Mathematics Tips
  46.    wt: 2:   14 Multiplication and Times Tables
  47.    wt: 2:   13 Addition and Addition Tables
  48.    wt: 2:   11 Help and Defend Your Child or Teens Education
  49.    wt: 2:   9 Streaming by Student Cooperation
  50.    wt: 2:   8 The Effect of Negative Remarks
  51.    wt: 2:   7 Student Motivation
  52.    wt: 2:   6 Discipline Who is in Charge Conserving Authority
  53.    wt: 2:   2 Reading and Writing Skills
  54.    wt: 2:   1 Speaking Skills
  55.    wt: 2:   5 Function notation for geometric transformations
  56.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  57.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  58.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  59.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  60.    wt: 2:   26 Formulas for products of sines and cosines
  61.    wt: 2:   17E Trig Formulas for dot and cross Products
  62.    wt: 2:   17D cis formulas for sine cosines and tangent
  63.    wt: 2:   13 Trig Formulas for dot and cross Products
  64.    wt: 2:   12 cis formulas for sine cosines and tangent
  65.    wt: 2:   4 Equations for lines three forms
  66.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  67.    wt: 2:   6 Compound Interest Forward and Backwards
  68.    wt: 2:   5 Triangle Area Formula Backwards
  69.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  70.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  71.    wt: 2:   11 Volume of Sphere
  72.    wt: 2:   10 Volume of Pyramid
  73.    wt: 2:   9 Volume of Cone
  74.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  75.    wt: 2:   Formula Evaluation how to show work
  76.    wt: 2:   38 Formulas and derivatives for powers and roots
  77.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  78.    wt: 2:   Postscript More on Better Performance
  79.    wt: 2:   Appendix E. How To Study Mathematics and Why
  80.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  81.    wt: 2:   Chapter 23. Notation For Sums
  82.    wt: 2:   Chapter 18. Rules for Algebra
  83.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  84.    wt: 2:   Chapter 8 Three Skills For Algebra
  85.    wt: 2:   Solutions For Arithmetic Exercises
  86.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  87.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  88.    wt: 2:   Foreword
  89.    wt: 2:   1 Links to Online Resources Elsewhere Take 1
  90.    wt: 2:   S Adding words to algebra
  91.    wt: 2:   R Why Learn Mathematics Skills
  92.    wt: 2:   P Exact Arithmetic With Whole Numbers and Fractions
  93.    wt: 2:   O On Learning Mathematics and Science
  94.    wt: 2:   M Words to extend arithmetic
  95.    wt: 2:   L Skills with take home value
  96.    wt: 2:   N Improving Marks on Tests and Finals
  97.    wt: 2:   I. Logic and language skills
  98.    wt: 2:   H more Routine to non routine problem solving
  99.    wt: 2:   H Jigsaw puzzles and problem solving
  100.    wt: 2:   F. The student teacher tutor feedback loop
  101.    wt: 2:   E. When and how to correct errors
  102.    wt: 2:   C. Domino effect of being careful
  103.    wt: 2:   B. Domino effect of errors
  104.    wt: 2:   A. Skill has to be seen to believed
  105.    wt: 2:   How to Build Skills and Confidence
  106.    wt: 2:   7 Games and Activities for Instruction
  107.    wt: 2:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  108.    wt: 2:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  109.    wt: 1:   I LAMP Introduction Study Habits
  110.    wt: 1:   H LAMP Introduction Instructional Concepts
  111.    wt: 1:   three goals to set for students
  112.    wt: 1:   permissions for teachers
  113.    wt: 1:   activities for students
  114.    wt: 1:   Education Reform Inconsistencies
  115.    wt: 1:   geometric implications for algebra
  116.    wt: 1:   three goals for Mathematics Education
  117.    wt: 1:   02 21 words for teachers
  118.    wt: 1:   three aims for mathematics students
  119.    wt: 1:   standards for course material
  120.    wt: 1:   mathematics instruction in general
  121.    wt: 1:   Four ways to improve education reform
  122.    wt: 1:   need for a mixed mathematics curriculum
  123.    wt: 1:   words for mathematics instructor
  124.    wt: 1:   C Electromotive force conventional current02
  125.    wt: 1:   B Electromotive force conventional current01
  126.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  127.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  128.    wt: 1:   6 Set Existence Formation and Notation
  129.    wt: 1:   3 Formula or function graphing exercise
  130.    wt: 1:   8 quadratics backward use of various formulas
  131.    wt: 1:   7 quadratic formulla derivation
  132.    wt: 1:   8 Notes for instructors or tutors
  133.    wt: 1:   12 motivation for term arctan
  134.    wt: 1:   9 motivation for name arcsin
  135.    wt: 1:   4 possible motivation for term arccos
  136.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  137.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  138.    wt: 1:   Straight Lines ASA Intersection Study More
  139.    wt: 1:   Straight Lines ASA Intersection Study
  140.    wt: 1:   8 Straight Lines Equation for vertical
  141.    wt: 1:   17 tangent function angle sum formulas
  142.    wt: 1:   29 secant cosecant and cotangent for acute angles
  143.    wt: 1:   25 tangent double angle formula Slope connection
  144.    wt: 1:   24 tangent Angle Difference Formula
  145.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  146.    wt: 1:   21 sine and cosine Half Angle Formulas
  147.    wt: 1:   20 sine and cosine Double Angle Formulas
  148.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  149.    wt: 1:   17C sine and cosine double triple angle formulas
  150.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  151.    wt: 1:   12 Graph of tangent function for one period
  152.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  153.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  154.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  155.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  156.    wt: 1:   11 sine and cosine double triple angle formulas
  157.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  158.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  159.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  160.    wt: 1:   8 Mid Point Formula
  161.    wt: 1:   3 Slope product for perpendicular lines
  162.    wt: 1:   2 point slope equation for a line
  163.    wt: 1:   13 Pythagorean spatial distance formulas
  164.    wt: 1:   10 Pythagorean plane distance formula
  165.    wt: 1:   PS H Distributive Law For Complex Numbers
  166.    wt: 1:   6 Column Methods for Decimal Multiplication
  167.    wt: 1:   5 Distributive Law for Whole Numbers
  168.    wt: 1:   4 Commutative Law Groups Counting Form
  169.    wt: 1:   5 Proportionality in Equivalent Fractions
  170.    wt: 1:   4 Rates Ratios and Proporitionality
  171.    wt: 1:   3 Proportionality Examples
  172.    wt: 1:   2 Algebraic View
  173.    wt: 1:   1 What is Proportionality
  174.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  175.    wt: 1:   3 Linear Equation Literal Solution More
  176.    wt: 1:   2 Linear Equation Literal Solution
  177.    wt: 1:   1 Changing Calculations
  178.    wt: 1:   3 Product Axioms Two Forms
  179.    wt: 1:   2 More and Less Than for Counts and Measures
  180.    wt: 1:   9 Coordinates for Regions in Space
  181.    wt: 1:   8 Coordinates for Maps and Planes
  182.    wt: 1:   3 Geometric Formulas and Function Notation
  183.    wt: 1:   1 Formulas Dependence and Function Notation
  184.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  185.    wt: 1:   6 Algebraic Solution Example
  186.    wt: 1:   5 Algebraic Solutions Introduction
  187.    wt: 1:   4 Four Examples Fractional Coefficients
  188.    wt: 1:   3 Four Examples
  189.    wt: 1:   2 Three Examples
  190.    wt: 1:   1 Proper Equal Sign Usage
  191.    wt: 1:   Using Letters for Physical Quantities
  192.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  193.    wt: 1:   9 Sets in Probability and Statistics
  194.    wt: 1:   8 Sets of Numbers
  195.    wt: 1:   7 Cautious or Safe Set Construction
  196.    wt: 1:   6 Power Set Notation
  197.    wt: 1:   5 Product Builder Notation
  198.    wt: 1:   4 Subset Builder Notation
  199.    wt: 1:   3 Counting with Sets etc
  200.    wt: 1:   2 Venn Diagrams
  201.    wt: 1:   1 Finite Sets
  202.    wt: 1:   1 Three Skills For Algebra
  203.    wt: 1:   arithmetic videos Real Player Format
  204.    wt: 1:   1 More and Less Than for Counts and Measures
  205.    wt: 1:   4 signed coordinates for regions in space
  206.    wt: 1:   3 signed coordinates for maps and planes
  207.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  208.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  209.    wt: 1:   21 Working With Signs
  210.    wt: 1:   21 Reciprocals for Fractions and Wholes
  211.    wt: 1:   11 Adding Integers Formulas and Examples
  212.    wt: 1:   10 Integer Multiplication Formulas
  213.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  214.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  215.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  216.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  217.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  218.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  219.    wt: 1:   Long Division forwards and backwards Example 3
  220.    wt: 1:   Long Division forwards and backwards Example 2
  221.    wt: 1:   Long Division forwards and backwards Example 1
  222.    wt: 1:   12 Why Long Division Works Take III
  223.    wt: 1:   9 Why Long Division Works Take II
  224.    wt: 1:   6 Why Decimal Long Division Methods Works Take I
  225.    wt: 1:   A Elementary Basis for Multiplication Methods
  226.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  227.    wt: 1:   5 A Tip for Efficent Subtraction
  228.    wt: 1:   8 What skills and work habits to require
  229.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  230.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  231.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  232.    wt: 1:   Expression Evaluation how to show work
  233.    wt: 1:   015 School and work day counting tables
  234.    wt: 1:   28 Chain Rule Preparation for a Proof
  235.    wt: 1:   22 Chain Rule for polynomials
  236.    wt: 1:   21 Chain Rule for powers
  237.    wt: 1:   20 Chain Rule for Pulley Systems
  238.    wt: 1:   19 Chain Rule for linear functions
  239.    wt: 1:   10 Power rule for negative integers
  240.    wt: 1:   3 Motivation for Limit Definition Take 2
  241.    wt: 1:   2 Motivation for Limit Definition Take 1
  242.    wt: 1:   10 Three one sided limits with infinite values
  243.    wt: 1:   3 Decimal insights for limits continuity convergence
  244.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  245.    wt: 1:   PostScript For and Against Decimal Perspectives
  246.    wt: 1:   Foreword
  247.    wt: 1:   Appendix D. What to do in School and Why
  248.    wt: 1:   Appendix C. How to Read
  249.    wt: 1:   Appendix B. How To Learn
  250.    wt: 1:   Chapter 31 Direct and Indirect Reason
  251.    wt: 1:   Chapter 30 Truth Tables
  252.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  253.    wt: 1:   Chapter 28 Occurrence Tables
  254.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  255.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  256.    wt: 1:   Chapter 25. Mathematical Induction Examples
  257.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  258.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  259.    wt: 1:   Chapter 21. Third Reading Guide
  260.    wt: 1:   Chapter 20. Degrees and Radians
  261.    wt: 1:   Chapter 19. Functions and Sets
  262.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  263.    wt: 1:   Chapter 16. Painless Theorem Proving
  264.    wt: 1:   Chapter 15. Solving Linear Equations
  265.    wt: 1:   Chapter 13. Second Reading Guide
  266.    wt: 1:   Chapter 12. Shorthand Usage Guide
  267.    wt: 1:   Chapter 11. Why Shorthand
  268.    wt: 1:   Chapter 10 Describing and Changing Calculations
  269.    wt: 1:   Postscript What is a Variable
  270.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  271.    wt: 1:   Chapter 6 Change of Language
  272.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  273.    wt: 1:   Chapter 4 Longer Chains of Reason
  274.    wt: 1:   Chapter 3 Chains of Reason
  275.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  276.    wt: 1:   Chapter 11 Elementary Instruction
  277.    wt: 1:   Chapter 9 The Two Ends
  278.    wt: 1:   Chapter 8 Modern Instruction
  279.    wt: 1:   Chapter 2 For and Against Mathematics
  280.    wt: 1:   Foreword
  281.    wt: 1:   Postscript C Consistency as a Tool for Reason
  282.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  283.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  284.    wt: 1:   Foreword
  285.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  286.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  287.    wt: 1:   Helping the Blind in Logic and Mathematics
  288.    wt: 1:   Mathematics Education References
  289.    wt: 1:   Mathematics Education References
  290.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  291.    wt: 1:   Implementation Notes
  292.    wt: 1:   More Algebra and Slope based Calculus Preview
  293.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  294.    wt: 1:   Systematic Algebra Skill Development Missing Links
  295.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  296.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  297.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  298.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  299.    wt: 1:   Which Way To Go
  300.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  301.    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.

Return to Page Top

Home << Search

[1] [2] [3] [4]

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

All trademarks and copyrights in this are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster.
The Rest © 1995-2011, by site author, Alan Selby, Ph. D., Montreal,
All Rights Reserved --- Skype or Email to contact.