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: 4:   Mathematics Education Essays/
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  5.    wt: 1:   Archives/
  6.    wt: 1:   9 Proportionality Backwards and Forwards/
  7.    wt: 1:   8 Unifying Theme For Algebra/
  8.    wt: 1:   Step 2 Algebraic solutions for one unknown/
  9.    wt: 1:   Volume 2 Three Skills For Algebra/

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188 matches:

  1.    wt: 3:   02 21 words for teachers
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  3.    wt: 2:   Education Reform Inconsistencies
  4.    wt: 2:   three goals for Mathematics Education
  5.    wt: 2:   formal or informal peer review
  6.    wt: 2:   Four ways to improve education reform
  7.    wt: 2:   Prequel In For A Penny In For A Pound
  8.    wt: 2:   words for mathematics instructor
  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 Usage Show Work Format
  22.    wt: 2:   13 Naming Identifying Formulas with Words
  23.    wt: 2:   1 Written work formats for developing and showing skill
  24.    wt: 2:   38 Formulas and derivatives for powers and roots
  25.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  26.    wt: 2:   Postscript For Better Performance
  27.    wt: 2:   Chapter 14. Forward and Backward Use of a Formula
  28.    wt: 2:   G. Written work formats for developing and showing skill
  29.    wt: 1:   K LAMP Musings Science Education
  30.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  31.    wt: 1:   three goals to set for students
  32.    wt: 1:   Teach the teachers plus goals
  33.    wt: 1:   activities for students
  34.    wt: 1:   links Education Resources online
  35.    wt: 1:   Mathematics Education Professors
  36.    wt: 1:   modern education
  37.    wt: 1:   geometric implications for algebra
  38.    wt: 1:   02 20 mathematics education references
  39.    wt: 1:   three aims for mathematics students
  40.    wt: 1:   standards for course material
  41.    wt: 1:   Education in mathematics science and technology
  42.    wt: 1:   need for a mixed mathematics curriculum
  43.    wt: 1:   education an empirical art
  44.    wt: 1:   fairness and inductive principles for instruction
  45.    wt: 1:   C Electromotive force conventional current02
  46.    wt: 1:   B Electromotive force conventional current01
  47.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  48.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  49.    wt: 1:   24 Standards For Skill Develoment Take II
  50.    wt: 1:   24 Standards For Skill Develoment
  51.    wt: 1:   17 Math Booklets for children and young teenagers
  52.    wt: 1:   15 Counting For Parents
  53.    wt: 1:   12 Goals and Objectives For Mathematics
  54.    wt: 1:   11 Help and Defend Your Child or Teens Education
  55.    wt: 1:   10 Ends values for work study instruction
  56.    wt: 1:   5 Patience Please for Yourself and Your Charges
  57.    wt: 1:   4 Learning Takes Time and Effort
  58.    wt: 1:   3 Preparing for Science Studies
  59.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  60.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  61.    wt: 1:   6 Set Existence Formation and Notation
  62.    wt: 1:   3 Formula or function graphing exercise
  63.    wt: 1:   8 quadratics backward use of various formulas
  64.    wt: 1:   7 quadratic formulla derivation
  65.    wt: 1:   8 Notes for instructors or tutors
  66.    wt: 1:   12 motivation for term arctan
  67.    wt: 1:   9 motivation for name arcsin
  68.    wt: 1:   4 possible motivation for term arccos
  69.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  70.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  71.    wt: 1:   8 Straight Lines Equation for vertical
  72.    wt: 1:   17 tangent function angle sum formulas
  73.    wt: 1:   29 secant cosecant and cotangent for acute angles
  74.    wt: 1:   25 tangent double angle formula Slope connection
  75.    wt: 1:   24 tangent Angle Difference Formula
  76.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  77.    wt: 1:   21 sine and cosine Half Angle Formulas
  78.    wt: 1:   20 sine and cosine Double Angle Formulas
  79.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  80.    wt: 1:   17C sine and cosine double triple angle formulas
  81.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  82.    wt: 1:   12 Graph of tangent function for one period
  83.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  84.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  85.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  86.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  87.    wt: 1:   11 sine and cosine double triple angle formulas
  88.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  89.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  90.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  91.    wt: 1:   8 Mid Point Formula
  92.    wt: 1:   3 Slope product for perpendicular lines
  93.    wt: 1:   2 point slope equation for a line
  94.    wt: 1:   13 Pythagorean spatial distance formulas
  95.    wt: 1:   10 Pythagorean plane distance formula
  96.    wt: 1:   PS H Distributive Law For Complex Numbers
  97.    wt: 1:   6 Column Methods for Decimal Multiplication
  98.    wt: 1:   5 Distributive Law for Whole Numbers
  99.    wt: 1:   4 Commutative Law Groups Counting Form
  100.    wt: 1:   8 Pythagorean Relation Forwards Backwards
  101.    wt: 1:   6 Compound Interest Forward and Backwards
  102.    wt: 1:   5 Triangle Area Formula Backwards
  103.    wt: 1:   4 Rectangle Area and Like Formulas Backwards
  104.    wt: 1:   3 Product Axioms Two Forms
  105.    wt: 1:   2 More and Less Than for Counts and Measures
  106.    wt: 1:   9 Coordinates for Regions in Space
  107.    wt: 1:   8 Coordinates for Maps and Planes
  108.    wt: 1:   3 Geometric Formulas and Function Notation
  109.    wt: 1:   1 Formulas Dependence and Function Notation
  110.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  111.    wt: 1:   Using Letters for Physical Quantities
  112.    wt: 1:   8 Compound Interest Formula Evaluation
  113.    wt: 1:   7 Compound Interest Formula Introduction
  114.    wt: 1:   5 Box Volume Formula Example
  115.    wt: 1:   4 Circle Area Formula Example
  116.    wt: 1:   3 Triangle Area Formula Example
  117.    wt: 1:   2 Another Rectangle Area Formula Example
  118.    wt: 1:   3 Adding Words To Arithmetic
  119.    wt: 1:   1 Three Skills For Algebra
  120.    wt: 1:   arithmetic videos Real Player Format
  121.    wt: 1:   1 More and Less Than for Counts and Measures
  122.    wt: 1:   4 signed coordinates for regions in space
  123.    wt: 1:   3 signed coordinates for maps and planes
  124.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  125.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  126.    wt: 1:   21 Reciprocals for Fractions and Wholes
  127.    wt: 1:   11 Adding Integers Formulas and Examples
  128.    wt: 1:   10 Integer Multiplication Formulas
  129.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  130.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  131.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  132.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  133.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  134.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  135.    wt: 1:   Long Division forwards and backwards Example 3
  136.    wt: 1:   Long Division forwards and backwards Example 2
  137.    wt: 1:   Long Division forwards and backwards Example 1
  138.    wt: 1:   A Elementary Basis for Multiplication Methods
  139.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  140.    wt: 1:   5 A Tip for Efficent Subtraction
  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:   Formula Evaluation how to show work
  145.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  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:   3 Decimal insights for limits continuity convergence
  155.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  156.    wt: 1:   PostScript For and Against Decimal Perspectives
  157.    wt: 1:   Foreword
  158.    wt: 1:   Postscript More on Better Performance
  159.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  160.    wt: 1:   Chapter 23. Notation For Sums
  161.    wt: 1:   Chapter 18. Rules for Algebra
  162.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  163.    wt: 1:   Chapter 8 Three Skills For Algebra
  164.    wt: 1:   Solutions For Arithmetic Exercises
  165.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  166.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  167.    wt: 1:   Foreword
  168.    wt: 1:   Postscript B Mathematics Education References
  169.    wt: 1:   Chapter 2 For and Against Mathematics
  170.    wt: 1:   Foreword
  171.    wt: 1:   Postscript C Consistency as a Tool for Reason
  172.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  173.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  174.    wt: 1:   Foreword
  175.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  176.    wt: 1:   S Adding words to algebra
  177.    wt: 1:   N Mathematics Prepare for College Studies
  178.    wt: 1:   M Words to extend arithmetic
  179.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  180.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  181.    wt: 1:   7 Games and Activities for Instruction
  182.    wt: 1:   Mathematics Education References
  183.    wt: 1:   Mathematics Education References
  184.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  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

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309 matches:

  1.    wt: 7:   02 21 words for teachers
  2.    wt: 6:   permissions for teachers
  3.    wt: 6:   Education Reform Inconsistencies
  4.    wt: 6:   three goals for Mathematics Education
  5.    wt: 6:   formal or informal peer review
  6.    wt: 6:   Four ways to improve education reform
  7.    wt: 6:   Prequel In For A Penny In For A Pound
  8.    wt: 6:   words for mathematics instructor
  9.    wt: 5:   three goals to set for students
  10.    wt: 5:   Teach the teachers plus goals
  11.    wt: 5:   activities for students
  12.    wt: 5:   links Education Resources online
  13.    wt: 5:   Mathematics Education Professors
  14.    wt: 5:   modern education
  15.    wt: 5:   geometric implications for algebra
  16.    wt: 5:   02 20 mathematics education references
  17.    wt: 5:   three aims for mathematics students
  18.    wt: 5:   standards for course material
  19.    wt: 5:   Education in mathematics science and technology
  20.    wt: 5:   need for a mixed mathematics curriculum
  21.    wt: 5:   education an empirical art
  22.    wt: 5:   fairness and inductive principles for instruction
  23.    wt: 4:   why bother
  24.    wt: 4:   which way to go
  25.    wt: 4:   website reviews
  26.    wt: 4:   Math Ed if it must be short make it lean effective
  27.    wt: 4:   Applied Maths Program14092009 POMME variant
  28.    wt: 4:   site origins
  29.    wt: 4:   site eurekas
  30.    wt: 4:   About site lesson plans
  31.    wt: 4:   key notes and themes
  32.    wt: 4:   teacher certification
  33.    wt: 4:   learning takes time
  34.    wt: 4:   grouping students according to ability
  35.    wt: 4:   what should be learnt and When
  36.    wt: 4:   mathematics in context
  37.    wt: 4:   Postscript 2007 01 10
  38.    wt: 4:   five decades make a difference
  39.    wt: 4:   Maps Plans Drawings
  40.    wt: 4:   how letters appear
  41.    wt: 4:   Secondary Three Mathematics
  42.    wt: 4:   Secondary Two Mathematics
  43.    wt: 4:   Secondary One Mathematics
  44.    wt: 4:   talk the algebra talk
  45.    wt: 4:   three difficulties
  46.    wt: 4:   teaching tips
  47.    wt: 4:   What to Tell Students
  48.    wt: 4:   mathematics curriculum shifts
  49.    wt: 4:   teaching tutoring algebraic reason
  50.    wt: 4:   Lessening Algebra Difficulties
  51.    wt: 4:   the trouble with algebra
  52.    wt: 4:   05 13 OldSiteEntrancePage
  53.    wt: 4:   04 29 New Mathematics Curriculum
  54.    wt: 4:   04 25 when to stop or suspend mathemat
  55.    wt: 4:   Operational Viewpoint to Value
  56.    wt: 4:   Theory of Knowledge
  57.    wt: 4:   mathematics instruction in general
  58.    wt: 4:   Different Kinds of Reasoning in maths
  59.    wt: 4:   three kinds of reason in mathematics
  60.    wt: 4:   cultivating intelligence
  61.    wt: 4:   How to be a better instructor
  62.    wt: 4:   Motivation and Context Problem
  63.    wt: 4:   Leaner mathematics curriculum
  64.    wt: 4:   13 Naming Identifying Formulas with Words
  65.    wt: 4:   1 Written work formats for developing and showing skill
  66.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  67.    wt: 3:   8 Compound Interest Formula Evaluation
  68.    wt: 3:   7 Compound Interest Formula Introduction
  69.    wt: 3:   5 Box Volume Formula Example
  70.    wt: 3:   4 Circle Area Formula Example
  71.    wt: 3:   3 Triangle Area Formula Example
  72.    wt: 3:   2 Another Rectangle Area Formula Example
  73.    wt: 3:   Postscript For Better Performance
  74.    wt: 3:   Chapter 14. Forward and Backward Use of a Formula
  75.    wt: 2:   K LAMP Musings Science Education
  76.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  77.    wt: 2:   11 pure mathematics
  78.    wt: 2:   10 statistics
  79.    wt: 2:   9 combinatorics probability sets
  80.    wt: 2:   8 analytic geometry etc
  81.    wt: 2:   7 logic review and decimals an odd combination
  82.    wt: 2:   6 polynomials etc
  83.    wt: 2:   5 logarithms and exponentials etc
  84.    wt: 2:   4 algebra
  85.    wt: 2:   3 Euclidean Geometry Leanly
  86.    wt: 2:   2 arithmetic with signed numbers
  87.    wt: 2:   1 arithmetic with unsigned numbers
  88.    wt: 2:   What is POMME
  89.    wt: 2:   5 Function notation for geometric transformations
  90.    wt: 2:   9 Formulas for Real Exponents with Logarithms
  91.    wt: 2:   8 Formulas for Fractional Exponents with Logarithms
  92.    wt: 2:   7 Formulas for Roots with Logarithms Derivation
  93.    wt: 2:   6 Formulas for Even and Odd Roots with Logarithms
  94.    wt: 2:   26 Formulas for products of sines and cosines
  95.    wt: 2:   17E Trig Formulas for dot and cross Products
  96.    wt: 2:   17D cis formulas for sine cosines and tangent
  97.    wt: 2:   13 Trig Formulas for dot and cross Products
  98.    wt: 2:   12 cis formulas for sine cosines and tangent
  99.    wt: 2:   4 Equations for lines three forms
  100.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  101.    wt: 2:   6 Compound Interest Forward and Backwards
  102.    wt: 2:   5 Triangle Area Formula Backwards
  103.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  104.    wt: 2:   Formula Usage Show Work Format
  105.    wt: 2:   12 Cone Cylinder Sphere Lesson Idea
  106.    wt: 2:   11 Volume of Sphere
  107.    wt: 2:   10 Volume of Pyramid
  108.    wt: 2:   9 Volume of Cone
  109.    wt: 2:   6 Pythagorean Hypotenuse Calculation Example
  110.    wt: 2:   38 Formulas and derivatives for powers and roots
  111.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  112.    wt: 2:   Postscript More on Better Performance
  113.    wt: 2:   Appendix A. Reading Guide For Next Appendices
  114.    wt: 2:   Chapter 23. Notation For Sums
  115.    wt: 2:   Chapter 18. Rules for Algebra
  116.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  117.    wt: 2:   Chapter 8 Three Skills For Algebra
  118.    wt: 2:   Solutions For Arithmetic Exercises
  119.    wt: 2:   Chapter 7 Prep for Calculus Arithmetic Exercises
  120.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  121.    wt: 2:   Foreword
  122.    wt: 2:   G. Written work formats for developing and showing skill
  123.    wt: 1:   Appendix 2 primary school Arithmetic 01
  124.    wt: 1:   Appendix 1 primary and preschool mathematic
  125.    wt: 1:   J LAMP Introduction Extrinsic Origins
  126.    wt: 1:   I LAMP Introduction Study Habits
  127.    wt: 1:   H LAMP Introduction Instructional Concepts
  128.    wt: 1:   G LAMP Introduction Problem Solving Skills
  129.    wt: 1:   F LAMP Introduction Prerequisites
  130.    wt: 1:   E LAMP Introduction Modern Mathematics
  131.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  132.    wt: 1:   A Introduction Objectives
  133.    wt: 1:   Skills Chapter 5 Calculus
  134.    wt: 1:   Skills Chapter 4 Logic
  135.    wt: 1:   Ramblings Extrinsic numbers theory
  136.    wt: 1:   Ramblings Introduction Algebra Essay
  137.    wt: 1:   Skills Chapter 3 Algebra
  138.    wt: 1:   Skills Chapter 2 Geometry
  139.    wt: 1:   Skills Chapter 1 Arithmetic
  140.    wt: 1:   Skills Chapter 0 Introduction
  141.    wt: 1:   C Electromotive force conventional current02
  142.    wt: 1:   B Electromotive force conventional current01
  143.    wt: 1:   27 Graduated Correction and Penalties for Young Offenders
  144.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  145.    wt: 1:   24 Standards For Skill Develoment Take II
  146.    wt: 1:   24 Standards For Skill Develoment
  147.    wt: 1:   17 Math Booklets for children and young teenagers
  148.    wt: 1:   15 Counting For Parents
  149.    wt: 1:   12 Goals and Objectives For Mathematics
  150.    wt: 1:   11 Help and Defend Your Child or Teens Education
  151.    wt: 1:   10 Ends values for work study instruction
  152.    wt: 1:   5 Patience Please for Yourself and Your Charges
  153.    wt: 1:   4 Learning Takes Time and Effort
  154.    wt: 1:   3 Preparing for Science Studies
  155.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  156.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  157.    wt: 1:   6 Set Existence Formation and Notation
  158.    wt: 1:   3 Formula or function graphing exercise
  159.    wt: 1:   8 quadratics backward use of various formulas
  160.    wt: 1:   7 quadratic formulla derivation
  161.    wt: 1:   8 Notes for instructors or tutors
  162.    wt: 1:   12 motivation for term arctan
  163.    wt: 1:   9 motivation for name arcsin
  164.    wt: 1:   4 possible motivation for term arccos
  165.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  166.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  167.    wt: 1:   8 Straight Lines Equation for vertical
  168.    wt: 1:   17 tangent function angle sum formulas
  169.    wt: 1:   29 secant cosecant and cotangent for acute angles
  170.    wt: 1:   25 tangent double angle formula Slope connection
  171.    wt: 1:   24 tangent Angle Difference Formula
  172.    wt: 1:   22 sine of 22.5 degrees via half angle formulas
  173.    wt: 1:   21 sine and cosine Half Angle Formulas
  174.    wt: 1:   20 sine and cosine Double Angle Formulas
  175.    wt: 1:   19 Pythagorean Identity For sine and cosine functions
  176.    wt: 1:   17C sine and cosine double triple angle formulas
  177.    wt: 1:   17B sine cosine Angle Sum Formulas via cis
  178.    wt: 1:   12 Graph of tangent function for one period
  179.    wt: 1:   6 sines and cosines for reference angle 30 degrees
  180.    wt: 1:   5 sines and cosines for reference angle 60 degrees
  181.    wt: 1:   4 sines and cosines for reference angle 45 degrees
  182.    wt: 1:   3 sines and cosines for reference angle 90 degrees
  183.    wt: 1:   11 sine and cosine double triple angle formulas
  184.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  185.    wt: 1:   5 Trigonometric Ratios For Tangent and Special Triangles
  186.    wt: 1:   4 Trigonometric Ratios For Two Special Triangles
  187.    wt: 1:   8 Mid Point Formula
  188.    wt: 1:   3 Slope product for perpendicular lines
  189.    wt: 1:   2 point slope equation for a line
  190.    wt: 1:   13 Pythagorean spatial distance formulas
  191.    wt: 1:   10 Pythagorean plane distance formula
  192.    wt: 1:   PS H Distributive Law For Complex Numbers
  193.    wt: 1:   6 Column Methods for Decimal Multiplication
  194.    wt: 1:   5 Distributive Law for Whole Numbers
  195.    wt: 1:   4 Commutative Law Groups Counting Form
  196.    wt: 1:   5 Proportionality in Equivalent Fractions
  197.    wt: 1:   4 Rates Ratios and Proporitionality
  198.    wt: 1:   3 Proportionality Examples
  199.    wt: 1:   2 Algebraic View
  200.    wt: 1:   1 What is Proportionality
  201.    wt: 1:   7 Pythagorean Theorem Chinese Square Proof
  202.    wt: 1:   3 Linear Equation Literal Solution More
  203.    wt: 1:   2 Linear Equation Literal Solution
  204.    wt: 1:   1 Changing Calculations
  205.    wt: 1:   3 Product Axioms Two Forms
  206.    wt: 1:   2 More and Less Than for Counts and Measures
  207.    wt: 1:   9 Coordinates for Regions in Space
  208.    wt: 1:   8 Coordinates for Maps and Planes
  209.    wt: 1:   3 Geometric Formulas and Function Notation
  210.    wt: 1:   1 Formulas Dependence and Function Notation
  211.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  212.    wt: 1:   6 Algebraic Solution Example
  213.    wt: 1:   5 Algebraic Solutions Introduction
  214.    wt: 1:   4 Four Examples Fractional Coefficients
  215.    wt: 1:   3 Four Examples
  216.    wt: 1:   2 Three Examples
  217.    wt: 1:   1 Proper Equal Sign Usage
  218.    wt: 1:   Using Letters for Physical Quantities
  219.    wt: 1:   3 Adding Words To Arithmetic
  220.    wt: 1:   1 Three Skills For Algebra
  221.    wt: 1:   arithmetic videos Real Player Format
  222.    wt: 1:   1 More and Less Than for Counts and Measures
  223.    wt: 1:   4 signed coordinates for regions in space
  224.    wt: 1:   3 signed coordinates for maps and planes
  225.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  226.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  227.    wt: 1:   21 Reciprocals for Fractions and Wholes
  228.    wt: 1:   11 Adding Integers Formulas and Examples
  229.    wt: 1:   10 Integer Multiplication Formulas
  230.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  231.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  232.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  233.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  234.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  235.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  236.    wt: 1:   Long Division forwards and backwards Example 3
  237.    wt: 1:   Long Division forwards and backwards Example 2
  238.    wt: 1:   Long Division forwards and backwards Example 1
  239.    wt: 1:   A Elementary Basis for Multiplication Methods
  240.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  241.    wt: 1:   5 A Tip for Efficent Subtraction
  242.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  243.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  244.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  245.    wt: 1:   Formula Evaluation how to show work
  246.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  247.    wt: 1:   28 Chain Rule Preparation for a Proof
  248.    wt: 1:   22 Chain Rule for polynomials
  249.    wt: 1:   21 Chain Rule for powers
  250.    wt: 1:   20 Chain Rule for Pulley Systems
  251.    wt: 1:   19 Chain Rule for linear functions
  252.    wt: 1:   10 Power rule for negative integers
  253.    wt: 1:   3 Motivation for Limit Definition Take 2
  254.    wt: 1:   2 Motivation for Limit Definition Take 1
  255.    wt: 1:   3 Decimal insights for limits continuity convergence
  256.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  257.    wt: 1:   PostScript For and Against Decimal Perspectives
  258.    wt: 1:   Foreword
  259.    wt: 1:   Appendix E. How To Study Mathematics and Why
  260.    wt: 1:   Appendix D. What to do in School and Why
  261.    wt: 1:   Appendix C. How to Read
  262.    wt: 1:   Appendix B. How To Learn
  263.    wt: 1:   Chapter 31 Direct and Indirect Reason
  264.    wt: 1:   Chapter 30 Truth Tables
  265.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  266.    wt: 1:   Chapter 28 Occurrence Tables
  267.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  268.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  269.    wt: 1:   Chapter 25. Mathematical Induction Examples
  270.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  271.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  272.    wt: 1:   Chapter 21. Third Reading Guide
  273.    wt: 1:   Chapter 20. Degrees and Radians
  274.    wt: 1:   Chapter 19. Functions and Sets
  275.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  276.    wt: 1:   Chapter 16. Painless Theorem Proving
  277.    wt: 1:   Chapter 15. Solving Linear Equations
  278.    wt: 1:   Chapter 13. Second Reading Guide
  279.    wt: 1:   Chapter 12. Shorthand Usage Guide
  280.    wt: 1:   Chapter 11. Why Shorthand
  281.    wt: 1:   Chapter 10 Describing and Changing Calculations
  282.    wt: 1:   Postscript What is a Variable
  283.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  284.    wt: 1:   Chapter 6 Change of Language
  285.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  286.    wt: 1:   Chapter 4 Longer Chains of Reason
  287.    wt: 1:   Chapter 3 Chains of Reason
  288.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  289.    wt: 1:   Postscript B Mathematics Education References
  290.    wt: 1:   Chapter 2 For and Against Mathematics
  291.    wt: 1:   Foreword
  292.    wt: 1:   Postscript C Consistency as a Tool for Reason
  293.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  294.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  295.    wt: 1:   Foreword
  296.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  297.    wt: 1:   S Adding words to algebra
  298.    wt: 1:   N Mathematics Prepare for College Studies
  299.    wt: 1:   M Words to extend arithmetic
  300.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  301.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  302.    wt: 1:   7 Games and Activities for Instruction
  303.    wt: 1:   Mathematics Education References
  304.    wt: 1:   Mathematics Education References
  305.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  306.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  307.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  308.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  309.    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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