Original Site Title: Appetizers and Lessons for Mathematics and Reason, June 1995 to April 2012. New site title:
Logic and Mathematics Skill & Concept Development with How-TOs Français: 26 pages
for college students, gifted teens, home-tutoring and K1-12 schooling. Avid readers in school and out may like Site Volumes.

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

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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  3.    wt: 2:   2 Formula Forward Use Evaluation/
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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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185 matches:

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

Extended Search

306 matches:

  1.    wt: 7:   permissions for teachers
  2.    wt: 6:   Education Reform Inconsistencies
  3.    wt: 6:   three goals for Mathematics Education
  4.    wt: 6:   02 21 words for teachers
  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: 5:   three goals to set for students
  9.    wt: 5:   Teach the teachers plus goals
  10.    wt: 5:   activities for students
  11.    wt: 5:   links Education Resources online
  12.    wt: 5:   Mathematics Education Professors
  13.    wt: 5:   modern education
  14.    wt: 5:   geometric implications for algebra
  15.    wt: 5:   02 20 mathematics education references
  16.    wt: 5:   three aims for mathematics students
  17.    wt: 5:   standards for course material
  18.    wt: 5:   Education in mathematics science and technology
  19.    wt: 5:   need for a mixed mathematics curriculum
  20.    wt: 5:   education an empirical art
  21.    wt: 5:   fairness and inductive principles for instruction
  22.    wt: 5:   words for mathematics instructor
  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:   1 Written work formats for developing and showing skill
  65.    wt: 3:   9 Circle Area and Perimeter Formula Backwards Forwards
  66.    wt: 3:   13 Naming Identifying Formulas with Words
  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:   1 Three Skills For Algebra
  220.    wt: 1:   arithmetic videos Real Player Format
  221.    wt: 1:   1 More and Less Than for Counts and Measures
  222.    wt: 1:   4 signed coordinates for regions in space
  223.    wt: 1:   3 signed coordinates for maps and planes
  224.    wt: 1:   5 Reciprocals and Division for Fractions with Units
  225.    wt: 1:   C Equality for Fractions and Two Term Ratios and Fractions
  226.    wt: 1:   21 Reciprocals for Fractions and Wholes
  227.    wt: 1:   11 Adding Integers Formulas and Examples
  228.    wt: 1:   10 Integer Multiplication Formulas
  229.    wt: 1:   25 Divisibility Tests for 2 3 5 9 10 Example
  230.    wt: 1:   24 Divisibility Tests for 2 3 5 9 10
  231.    wt: 1:   20 Remainder Arithmetic Rule of 9 for checking sums IV
  232.    wt: 1:   19 Remainder Arithmetic Rule of 9 for checking sums III
  233.    wt: 1:   18 Remainder Arithmetic Rule of 9 for checking sums II
  234.    wt: 1:   17 Remainder Arithmetic Rule of 9 for checking sums I
  235.    wt: 1:   Long Division forwards and backwards Example 3
  236.    wt: 1:   Long Division forwards and backwards Example 2
  237.    wt: 1:   Long Division forwards and backwards Example 1
  238.    wt: 1:   A Elementary Basis for Multiplication Methods
  239.    wt: 1:   7 Subtraction for Decimal Fractions with Exercises
  240.    wt: 1:   5 A Tip for Efficent Subtraction
  241.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  242.    wt: 1:   9 Place Value Review Decimal form of Avogrados number included
  243.    wt: 1:   2 Groups of Three Place Value for Multidigit Decimals
  244.    wt: 1:   Formula Evaluation how to show work
  245.    wt: 1:   Practical Methods Ends and Values for Arithmetic
  246.    wt: 1:   28 Chain Rule Preparation for a Proof
  247.    wt: 1:   22 Chain Rule for polynomials
  248.    wt: 1:   21 Chain Rule for powers
  249.    wt: 1:   20 Chain Rule for Pulley Systems
  250.    wt: 1:   19 Chain Rule for linear functions
  251.    wt: 1:   10 Power rule for negative integers
  252.    wt: 1:   3 Motivation for Limit Definition Take 2
  253.    wt: 1:   2 Motivation for Limit Definition Take 1
  254.    wt: 1:   3 Decimal insights for limits continuity convergence
  255.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  256.    wt: 1:   PostScript For and Against Decimal Perspectives
  257.    wt: 1:   Foreword
  258.    wt: 1:   Appendix E. How To Study Mathematics and Why
  259.    wt: 1:   Appendix D. What to do in School and Why
  260.    wt: 1:   Appendix C. How to Read
  261.    wt: 1:   Appendix B. How To Learn
  262.    wt: 1:   Chapter 31 Direct and Indirect Reason
  263.    wt: 1:   Chapter 30 Truth Tables
  264.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  265.    wt: 1:   Chapter 28 Occurrence Tables
  266.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  267.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  268.    wt: 1:   Chapter 25. Mathematical Induction Examples
  269.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  270.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  271.    wt: 1:   Chapter 21. Third Reading Guide
  272.    wt: 1:   Chapter 20. Degrees and Radians
  273.    wt: 1:   Chapter 19. Functions and Sets
  274.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  275.    wt: 1:   Chapter 16. Painless Theorem Proving
  276.    wt: 1:   Chapter 15. Solving Linear Equations
  277.    wt: 1:   Chapter 13. Second Reading Guide
  278.    wt: 1:   Chapter 12. Shorthand Usage Guide
  279.    wt: 1:   Chapter 11. Why Shorthand
  280.    wt: 1:   Chapter 10 Describing and Changing Calculations
  281.    wt: 1:   Postscript What is a Variable
  282.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  283.    wt: 1:   Chapter 6 Change of Language
  284.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  285.    wt: 1:   Chapter 4 Longer Chains of Reason
  286.    wt: 1:   Chapter 3 Chains of Reason
  287.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  288.    wt: 1:   Postscript B Mathematics Education References
  289.    wt: 1:   Chapter 2 For and Against Mathematics
  290.    wt: 1:   Foreword
  291.    wt: 1:   Postscript C Consistency as a Tool for Reason
  292.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  293.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  294.    wt: 1:   Foreword
  295.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  296.    wt: 1:   N Mathematics Prepare for College Studies
  297.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  298.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  299.    wt: 1:   7 Games and Activities for Instruction
  300.    wt: 1:   Mathematics Education References
  301.    wt: 1:   Mathematics Education References
  302.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  303.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  304.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  305.    wt: 1:   Talking pdf files for online lessons a webvideo alternative
  306.    wt: 1:   The Math Forum and Site Content

Teachers & Tutors: Site pages offer better or best practices for providing skills - simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do. Others are welcome to refine or exceed it. Please do.

Secondary Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges with local curriculum control. Study how to include site content - its skill development how-TOs and innovations into present or future lesson plans - some reading required.

Road Safety Messages and Questions: When and why should you face traffic when walking along a road or cycle path? Is it a good idea to hang limbs outside of cars etc? What gives more protection in a crash: a car, motorbike or bicycle? See too, the BBC-Belgium story Texting and Driving - texting & the impossible test - the article links to a gruesome utube video on the subject

The Logic of Injustice: How Texas sent an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate is not compensation for years or decade of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern Based Reason may slowly lead to greater precision in reading, applying and writing laws.

May 2012, Composition Starting: Pre-School and Primary Mathematics - Quantitative Skills, An Intellectual View, Feedback Welcome:

The 8 Most Popular Site Inlinks

20 Times Table - the most popular site page - popular pages - unexpected.
Fractions & Ratios - with lesson on raising terms to introduce & justify times, division & comparison as well addition & subtraction
Parent Center - See below
Volume 1, Elements of Reason - Intro to all site books.
What is a Variable - best for ages 13+
Written work formats for Arithmetic and Algebra - a skill method and standard!
Complex Numbers Visually - best for ages 13+
Natural Logs, Exponentials, Powers, Roots

Division of Labour: This site offers advice and directions with pointers to resources elsewhere, if known, when they help or lessen the need to write more.

Parent Center: Help your child or teen learn:

Parent-friendly Work Booklets for ages 3+ to 13 Use these or others to check or build skills. Other booklets are available but these booklets allow parents unsure of themselves in mathematics to help their children. The selection acquired in Canada is published in the USA. So it has a US orientation. In retrospect, the selection shows parents what to check with the booklets or by other ways, the choice is theirs. But in retrospect, the selection does not cover integral and fractions liquid weights and measures - ask the publishers to correct that! For ages 9 to 12 say, parents may compensate by showing boys and girls how to use weights or mass, and further measures in food preparation. Beyond that children may be shown how to measure and calculate angles, lengths and areas [proportional amounts too] directly or by using maps and plans drawns to scale. Learning how to gather and measure all the ingredients, pots and pans for a dish or a meal, along with cleaning up sets the stage for like activities or experiments in science courses, and in developing organizational skills, gives boys and girls a head start. Good luck. At the other extreme, more comprehensive than light, if your motto is McCainian: drill, drill, drill then Toronto mathematician and actor John Mighton's jump math organization has jump math workbooks for at least grades 3 to 8 for at-home and in-school use - training sessions for teachers available. Jump math has been expanding to cover older students. Jump Math Samples: plus Fractions for Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8 [unread - likely to be good]. and

Mathematics Skills For Ages 3 to 14 - technical!

Skills with take home value - A few ideas

Basic skills include time-date-calendar Matters; money matters; map, plan and scale diagram matters;counting, measuring and figuring; decision making with logic and likelyhood; being careful and being aware of the domino effect of mistakes; reading and writing with precision.

Is your child able to add, subtract and multiply amounts of money, work with fractions, work with clocks and calendars, work with maps and plans, and measure length, weight-mass and volume? Schools may promote your son or daughter without providing basic skills in reading, writing and arithmetic.

Arithmetic and Number Theory Skills

Algebra Starter Lessons

1 Working With Sets
2 Formula Forward Use - Evaluation
3 Solving Linear Equations - Skip first step with students able to solve 1 eqn in 1 unknown.
4 Computation Rules and Function Notation
5 Real Numbers
6 More Less Greater Than Inequalities and Comparison
7 Axioms Logic and Equivalent Equations
8 Unifying Theme For Algebra
9 Proportionality Backwards and Forwards
10 Examples of Algebraic Reasoning
A Origins of Counting and Figuring Methods
B Real Numbers Extrinsic Development


Site coverage of formuala evaluation format, of computation rules and axioms, and of the forward and backward use of formulas and proportionality relations lessens the amount of natural talent needed to understand and explain algebra.

Geometry - maps plans trigonometry vectors

1 Maps Plans Measurement
2 Euclidean Geometry - Constructions + extras
3 Cartesian and Polar Coordinates
4 Lines and Slopes Take 1
5 What is Similarity
6 Trigonometry first steps
7 Complex Numbers
8 Unit-Circle Trigonometry
9 Lines and Slopes Take 2 with tangent function
10 Intersecting Straight Lines and Transversals
11 Parallel Straight Lines and Transversals
12 Function Translating and Rescaling
13 Vectors
14 Degrees to Radians and Radians to Degrees
15 Arc or Inverse Trigonometric Function

Pre-Teen and young teen mastery of skills and practices which should be common with map-plans-diagrams drawn to scale, contour interpretation included, has actual or potential take-home value for daily- and adult-life in solving routine problems. Elevating some practices to principles, axioms or postualates, provides a base for analytic and Euclidean geometry, an analytic view of similarity, and an efficient mastery of trigonometry and complex numbers. Right triangle trigonometry provide an analytic alternative to solving geometric problems by drawing diagrams to scale.

More Algebra

Natural-Logarithms Exponentials Powers Roots
Five Polynomial Operations
Quadratics Geometrically
Functions
5 Factored Polynomial Sign Analysis Examples
Rewriting algebraic substitution as function substitutions

The first topic leads to a full high school level theory for the forward and backward mastery of growth and decay models and for definition, range and domains of radicals, roots and powers. The next two topics make quadratics and polynomials easier to learn and teach. Site coverage of functions turns vertical and horizontal line rules into computation methods for evaluating functions.

70 Calculus Starter Lessons

Calculus Lessons Elsewhere:

  1. How to Ace Calculus: Street Wise Guide - Mostly Text.

  2. Flash Video for Calculus Phobics

They cover basic topics in ways likely to complement your notes, your textbooks and site material. When Goldilocks trespassed in the house of the three bears, she found three bowls of porridge, two not to her liking, and one just right. Different bears have different tastes. As invited guest here and elsewhere, if one or more explanations is not to liking, try another. It may be better or just right.

Unsolicited Advice

Learning to do and high marks if it comes to easy is often deceptive - light rather than deep. For that reason, students with learning difficulties determined not to let it get in their way may go deeper and farther than those with none. High marks, if the come easy, may be deceptive - provide a too light and not a deep mastery. That could have been your problem in secondary school, one that leads to comprehension shock or difficulties in calculus and more generally in the first year of college. Bon Appetite.

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Logic-Reason for all
Careful Thinking
Chains of Reason
Mathematical Induction
Responsibility
Bodies-of-Knowledge

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science

Geometry
1 Maps + Plans Use
2 Euclidean Geometry
3 Rct +Polr Coordinates
4 Lines-Slopes [I]
5. What is Similarity 		Algebra Starters - the base
1. Better Work Format
2. Solve Linear Eqns
3. Computation Rules
4. Axioms, Item 3 Viewpnt
5. Formulas Backwards 		More Algebra
Logarithms-ax & m/nth roots
Five Polynomial Operations
Quadratics Geometrically
Functions || Vectors too
Arith. Skill Check+Answers 		Calculus Prep/Preview
What is a Variable
Why study slopes
Why factor polynomials
Complex Numbers
Limits + Continuity

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