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

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

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

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

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

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

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

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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

188 matches:

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

Extended Search

297 matches:

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

Teachers, Tutors, Parents: Site material offers better or best practices for mathematics skill building - simpler than expected and comprehensive. Your duty is to study them alone or with help. Start now.

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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