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: 6:   LAMP Lean Applied Mathematics Program/
  2.    wt: 3:   Mathematics Education Essays/
  3.    wt: 2:   Progressive Observable Motivated Mathematics Education/
  4.    wt: 2:   10 Examples of Algebraic Reasoning/
  5.    wt: 2:   8 Unifying Theme For Algebra/
  6.    wt: 2:   Step 2 Algebraic solutions for one unknown/
  7.    wt: 1:   Archives/
  8.    wt: 1:   Mathematics Skills Year by Year/
  9.    wt: 1:   5 Factored Polynomial Sign Analysis Examples/
  10.    wt: 1:   4 Functions/
  11.    wt: 1:   3 Quadratics Geometrically/
  12.    wt: 1:   2 Natural Logarithms Exponentials Powers Roots/
  13.    wt: 1:   1 Five Polynomial Operations/
  14.    wt: 1:   More Algebra/
  15.    wt: 1:   B Real Numbers Extrinsic Development/
  16.    wt: 1:   A Origins of Counting and Figuring Methods/
  17.    wt: 1:   9 Proportionality Backwards and Forwards/
  18.    wt: 1:   7 Axioms Logic and Equivalent Equations/
  19.    wt: 1:   6 More Less Greater Than Inequalities and Comparison/
  20.    wt: 1:   5 Real Numbers/
  21.    wt: 1:   4 Computation Rules and Function Notation/
  22.    wt: 1:   Step 4 Gaussian Elimination/
  23.    wt: 1:   Step 3 Easy systems in 2 or more unknowns/
  24.    wt: 1:   Step 1 Stick diagram and fractions/
  25.    wt: 1:   3 Solving Linear Equations/
  26.    wt: 1:   2 Formula Forward Use Evaluation/
  27.    wt: 1:   1 Working With Sets/
  28.    wt: 1:   Algebra Starter Lessons/
  29.    wt: 1:   Volume 2 Three Skills For Algebra/
  30.    wt: 1:   Volume 1B Mathematics Curriculum Notes/
  31.    wt: 1:   Mathematics 506 Lessons/
  32.    wt: 1:   Secondary Mathematics A Practical Approach/
  33.    wt: 1:   PreSchool and Primary Mathematics or Quantitative Skills/
  34.    wt: 1:   Mathematics Skill Development Framework/

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105 matches:

  1.    wt: 3:   E LAMP Introduction Modern Mathematics
  2.    wt: 3:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 3:   Ramblings Introduction Algebra Essay
  4.    wt: 2:   J LAMP Introduction Extrinsic Origins
  5.    wt: 2:   I LAMP Introduction Study Habits
  6.    wt: 2:   H LAMP Introduction Instructional Concepts
  7.    wt: 2:   G LAMP Introduction Problem Solving Skills
  8.    wt: 2:   F LAMP Introduction Prerequisites
  9.    wt: 2:   B LAMP Introduction Curriculum Development Standards
  10.    wt: 2:   Applied Maths Program14092009 POMME variant
  11.    wt: 2:   Leaner mathematics curriculum
  12.    wt: 2:   12 From Applied To Pure Mathematics
  13.    wt: 2:   5 Algebraic Solutions Introduction
  14.    wt: 1:   K LAMP Musings Science Education
  15.    wt: 1:   A Introduction Objectives
  16.    wt: 1:   Skills Chapter 3 Algebra
  17.    wt: 1:   Skills Chapter 0 Introduction
  18.    wt: 1:   11 pure mathematics
  19.    wt: 1:   4 algebra
  20.    wt: 1:   3 Euclidean Geometry Leanly
  21.    wt: 1:   Math Ed if it must be short make it lean effective
  22.    wt: 1:   Mathematics Education Professors
  23.    wt: 1:   mathematics in context
  24.    wt: 1:   Secondary Three Mathematics
  25.    wt: 1:   Secondary Two Mathematics
  26.    wt: 1:   Secondary One Mathematics
  27.    wt: 1:   talk the algebra talk
  28.    wt: 1:   mathematics curriculum shifts
  29.    wt: 1:   geometric implications for algebra
  30.    wt: 1:   teaching tutoring algebraic reason
  31.    wt: 1:   Lessening Algebra Difficulties
  32.    wt: 1:   the trouble with algebra
  33.    wt: 1:   three goals for Mathematics Education
  34.    wt: 1:   04 29 New Mathematics Curriculum
  35.    wt: 1:   02 20 mathematics education references
  36.    wt: 1:   three aims for mathematics students
  37.    wt: 1:   mathematics instruction in general
  38.    wt: 1:   Education in mathematics science and technology
  39.    wt: 1:   three kinds of reason in mathematics
  40.    wt: 1:   need for a mixed mathematics curriculum
  41.    wt: 1:   words for mathematics instructor
  42.    wt: 1:   chapitre 01 00 Introduction
  43.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  44.    wt: 1:   22 Student Centered Highschool Mathematics
  45.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  46.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  47.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  48.    wt: 1:   18 Primary School Mathematics
  49.    wt: 1:   16 Secondary Mathematics Tips
  50.    wt: 1:   12 Goals and Objectives For Mathematics
  51.    wt: 1:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  52.    wt: 1:   4 Function notation in and beyond mathematics
  53.    wt: 1:   2 Algebraic use of function notation
  54.    wt: 1:   1 Geometric Introduction of Function Notation
  55.    wt: 1:   Introduction Reading Guide
  56.    wt: 1:   Rewriting algebraic substitution as function substitutions
  57.    wt: 1:   1 Degrees and Radians Introduction
  58.    wt: 1:   5 Algebraic View of Slopes
  59.    wt: 1:   3 Inequalities Algebraically
  60.    wt: 1:   2 Algebraic View
  61.    wt: 1:   5 Equality in Algebra
  62.    wt: 1:   6 Algebraic Solution Example
  63.    wt: 1:   7 Compound Interest Formula Introduction
  64.    wt: 1:   4 A Brief Story of numbers and algebra
  65.    wt: 1:   1 Three Skills For Algebra
  66.    wt: 1:   1 Squares and Square Roots Introduction
  67.    wt: 1:   1 Least Common Multiples LCM Introduction
  68.    wt: 1:   13 Fraction Comparison Algebraic View
  69.    wt: 1:   11 Simplification an Algebraic View
  70.    wt: 1:   6 Multiplication Algebraically Take II
  71.    wt: 1:   4 video Prime Factorization Introduction
  72.    wt: 1:   Quick history of numbers and algebra
  73.    wt: 1:   18 Chain Rule Introduction
  74.    wt: 1:   2 Algebraic codification
  75.    wt: 1:   1 Numerical introduction
  76.    wt: 1:   E2 Algebraic Properties of Limits
  77.    wt: 1:   A1. Introduction
  78.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  79.    wt: 1:   Chapter 1.Introduction
  80.    wt: 1:   Appendix E. How To Study Mathematics and Why
  81.    wt: 1:   Chapter 18. Rules for Algebra
  82.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  83.    wt: 1:   Chapter 8 Three Skills For Algebra
  84.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  85.    wt: 1:   Postscript B Mathematics Education References
  86.    wt: 1:   Chapter 6 Rule Based Reason in Mathematics
  87.    wt: 1:   Chapter 3 Algebra Difficulties
  88.    wt: 1:   Chapter 2 For and Against Mathematics
  89.    wt: 1:   Chapter 1 Introduction
  90.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  91.    wt: 1:   Chapter 1 Introduction
  92.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  93.    wt: 1:   S Adding words to algebra
  94.    wt: 1:   R Why Learn Mathematics Skills
  95.    wt: 1:   O On Learning Mathematics and Science
  96.    wt: 1:   N Mathematics Prepare for College Studies
  97.    wt: 1:   Chapter 6 More Algebra and Geometry
  98.    wt: 1:   Chapter 3 Algebra Starter Lessons
  99.    wt: 1:   Helping the Blind in Logic and Mathematics
  100.    wt: 1:   Mathematics Education References
  101.    wt: 1:   Mathematics Education References
  102.    wt: 1:   Multiple Ways to Improve Mathematics Skill Development
  103.    wt: 1:   More Algebra and Slope based Calculus Preview
  104.    wt: 1:   Systematic Algebra Skill Development Missing Links
  105.    wt: 1:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years

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448 matches:

  1.    wt: 9:   E LAMP Introduction Modern Mathematics
  2.    wt: 9:   C LAMP Introduction Culture in Mathematics Education
  3.    wt: 9:   Ramblings Introduction Algebra Essay
  4.    wt: 8:   J LAMP Introduction Extrinsic Origins
  5.    wt: 8:   I LAMP Introduction Study Habits
  6.    wt: 8:   H LAMP Introduction Instructional Concepts
  7.    wt: 8:   G LAMP Introduction Problem Solving Skills
  8.    wt: 8:   F LAMP Introduction Prerequisites
  9.    wt: 8:   B LAMP Introduction Curriculum Development Standards
  10.    wt: 7:   K LAMP Musings Science Education
  11.    wt: 7:   A Introduction Objectives
  12.    wt: 7:   Skills Chapter 3 Algebra
  13.    wt: 7:   Skills Chapter 0 Introduction
  14.    wt: 6:   Appendix 2 primary school Arithmetic 01
  15.    wt: 6:   Appendix 1 primary and preschool mathematic
  16.    wt: 6:   Skills Chapter 5 Calculus
  17.    wt: 6:   Skills Chapter 4 Logic
  18.    wt: 6:   Ramblings Extrinsic numbers theory
  19.    wt: 6:   Skills Chapter 2 Geometry
  20.    wt: 6:   Skills Chapter 1 Arithmetic
  21.    wt: 5:   Applied Maths Program14092009 POMME variant
  22.    wt: 5:   Leaner mathematics curriculum
  23.    wt: 4:   Math Ed if it must be short make it lean effective
  24.    wt: 4:   Mathematics Education Professors
  25.    wt: 4:   mathematics in context
  26.    wt: 4:   Secondary Three Mathematics
  27.    wt: 4:   Secondary Two Mathematics
  28.    wt: 4:   Secondary One Mathematics
  29.    wt: 4:   talk the algebra talk
  30.    wt: 4:   mathematics curriculum shifts
  31.    wt: 4:   geometric implications for algebra
  32.    wt: 4:   teaching tutoring algebraic reason
  33.    wt: 4:   Lessening Algebra Difficulties
  34.    wt: 4:   the trouble with algebra
  35.    wt: 4:   three goals for Mathematics Education
  36.    wt: 4:   04 29 New Mathematics Curriculum
  37.    wt: 4:   02 20 mathematics education references
  38.    wt: 4:   three aims for mathematics students
  39.    wt: 4:   mathematics instruction in general
  40.    wt: 4:   Education in mathematics science and technology
  41.    wt: 4:   three kinds of reason in mathematics
  42.    wt: 4:   need for a mixed mathematics curriculum
  43.    wt: 4:   words for mathematics instructor
  44.    wt: 4:   5 Algebraic Solutions Introduction
  45.    wt: 3:   11 pure mathematics
  46.    wt: 3:   4 algebra
  47.    wt: 3:   3 Euclidean Geometry Leanly
  48.    wt: 3:   why bother
  49.    wt: 3:   which way to go
  50.    wt: 3:   website reviews
  51.    wt: 3:   three goals to set for students
  52.    wt: 3:   Teach the teachers plus goals
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  55.    wt: 3:   links Education Resources online
  56.    wt: 3:   site origins
  57.    wt: 3:   site eurekas
  58.    wt: 3:   About site lesson plans
  59.    wt: 3:   key notes and themes
  60.    wt: 3:   teacher certification
  61.    wt: 3:   modern education
  62.    wt: 3:   learning takes time
  63.    wt: 3:   grouping students according to ability
  64.    wt: 3:   what should be learnt and When
  65.    wt: 3:   Postscript 2007 01 10
  66.    wt: 3:   Education Reform Inconsistencies
  67.    wt: 3:   five decades make a difference
  68.    wt: 3:   Maps Plans Drawings
  69.    wt: 3:   how letters appear
  70.    wt: 3:   three difficulties
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  72.    wt: 3:   What to Tell Students
  73.    wt: 3:   05 13 OldSiteEntrancePage
  74.    wt: 3:   04 25 when to stop or suspend mathemat
  75.    wt: 3:   02 21 words for teachers
  76.    wt: 3:   standards for course material
  77.    wt: 3:   Operational Viewpoint to Value
  78.    wt: 3:   formal or informal peer review
  79.    wt: 3:   Theory of Knowledge
  80.    wt: 3:   Different Kinds of Reasoning in maths
  81.    wt: 3:   cultivating intelligence
  82.    wt: 3:   Four ways to improve education reform
  83.    wt: 3:   How to be a better instructor
  84.    wt: 3:   Motivation and Context Problem
  85.    wt: 3:   Prequel In For A Penny In For A Pound
  86.    wt: 3:   education an empirical art
  87.    wt: 3:   fairness and inductive principles for instruction
  88.    wt: 3:   3 Inequalities Algebraically
  89.    wt: 3:   6 Algebraic Solution Example
  90.    wt: 2:   10 statistics
  91.    wt: 2:   9 combinatorics probability sets
  92.    wt: 2:   8 analytic geometry etc
  93.    wt: 2:   7 logic review and decimals an odd combination
  94.    wt: 2:   6 polynomials etc
  95.    wt: 2:   5 logarithms and exponentials etc
  96.    wt: 2:   2 arithmetic with signed numbers
  97.    wt: 2:   1 arithmetic with unsigned numbers
  98.    wt: 2:   What is POMME
  99.    wt: 2:   Ages 3 to 14 Terminal Objectives for Algebra Geometry and Probability
  100.    wt: 2:   4 Function notation in and beyond mathematics
  101.    wt: 2:   2 Algebraic use of function notation
  102.    wt: 2:   1 Geometric Introduction of Function Notation
  103.    wt: 2:   Introduction Reading Guide
  104.    wt: 2:   Rewriting algebraic substitution as function substitutions
  105.    wt: 2:   12 From Applied To Pure Mathematics
  106.    wt: 2:   5 Areas of Rectangles Revisited
  107.    wt: 2:   4 Fraction Operations Axiomatic Development
  108.    wt: 2:   2 Fraction Operations Physical Development
  109.    wt: 2:   1 Decimals Modular and Remainder Arithmetic
  110.    wt: 2:   2 Algebraic View
  111.    wt: 2:   9 Circle Area and Perimeter Formula Backwards Forwards
  112.    wt: 2:   8 Pythagorean Relation Forwards Backwards
  113.    wt: 2:   7 Pythagorean Theorem Chinese Square Proof
  114.    wt: 2:   6 Compound Interest Forward and Backwards
  115.    wt: 2:   5 Triangle Area Formula Backwards
  116.    wt: 2:   4 Rectangle Area and Like Formulas Backwards
  117.    wt: 2:   3 Linear Equation Literal Solution More
  118.    wt: 2:   2 Linear Equation Literal Solution
  119.    wt: 2:   1 Changing Calculations
  120.    wt: 2:   5 Equality in Algebra
  121.    wt: 2:   4 Four Examples Fractional Coefficients
  122.    wt: 2:   3 Four Examples
  123.    wt: 2:   2 Three Examples
  124.    wt: 2:   1 Proper Equal Sign Usage
  125.    wt: 2:   7 Compound Interest Formula Introduction
  126.    wt: 2:   4 A Brief Story of numbers and algebra
  127.    wt: 2:   1 Three Skills For Algebra
  128.    wt: 2:   Appendix E. How To Study Mathematics and Why
  129.    wt: 2:   Chapter 18. Rules for Algebra
  130.    wt: 2:   Postscript Unifying Theme A Fourth Skill For Algebra
  131.    wt: 2:   Chapter 8 Three Skills For Algebra
  132.    wt: 2:   Chapter 1 Introduction to Chapters 2 to 6
  133.    wt: 2:   Postscript B Mathematics Education References
  134.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  135.    wt: 2:   Chapter 3 Algebra Difficulties
  136.    wt: 2:   Chapter 2 For and Against Mathematics
  137.    wt: 2:   Chapter 1 Introduction
  138.    wt: 2:   Chapter 6 More Algebra and Geometry
  139.    wt: 2:   Chapter 3 Algebra Starter Lessons
  140.    wt: 2:   Helping the Blind in Logic and Mathematics
  141.    wt: 2:   Mathematics Education References
  142.    wt: 2:   Mathematics Education References
  143.    wt: 2:   Multiple Ways to Improve Mathematics Skill Development
  144.    wt: 2:   More Algebra and Slope based Calculus Preview
  145.    wt: 2:   Systematic Algebra Skill Development Missing Links
  146.    wt: 2:   Phase 3. Logic and Mathematics with possible take home value 1 to 2 years
  147.    wt: 1:   chapitre 01 00 Introduction
  148.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  149.    wt: 1:   22 Student Centered Highschool Mathematics
  150.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  151.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  152.    wt: 1:   19 Extending the Oral Dimension of Mathematics
  153.    wt: 1:   18 Primary School Mathematics
  154.    wt: 1:   16 Secondary Mathematics Tips
  155.    wt: 1:   12 Goals and Objectives For Mathematics
  156.    wt: 1:   Ages 12 to 14 Skills with take home value
  157.    wt: 1:   Ages 12 to 14 Geometry
  158.    wt: 1:   Ages 12 to 14 Arithmetic
  159.    wt: 1:   Ages 10 to 12 Geometry
  160.    wt: 1:   Ages 10 to 12 Arithmetic
  161.    wt: 1:   Ages 9 to 10
  162.    wt: 1:   Ages 8 to 9
  163.    wt: 1:   Ages 7 to 8
  164.    wt: 1:   Ages 6 to 7
  165.    wt: 1:   Ages 4 plus to 5 plus
  166.    wt: 1:   Ages 3 plus to 4 plus
  167.    wt: 1:   Ages 3 to 14 Terminal Objectives for Arithmetic and Statistics
  168.    wt: 1:   sign monoticity analysis example 4
  169.    wt: 1:   sign monoticity analysis example 3
  170.    wt: 1:   sign monoticity analysis example 2
  171.    wt: 1:   sign monoticity analysis example 1
  172.    wt: 1:   26 Function definitions done and coming
  173.    wt: 1:   25 Absolute Value greatest integer and saw tooth functions
  174.    wt: 1:   24 Monotoncity Injectivity and Inverse Functions
  175.    wt: 1:   23 Inverse Functions
  176.    wt: 1:   22 Square Root function graphically
  177.    wt: 1:   21 Graphs of functions given by Horizontal Line Method
  178.    wt: 1:   20 Interchanging coordinates a reflection
  179.    wt: 1:   19 Horizontal line rule and method
  180.    wt: 1:   18 Vertical Line Rule and Method
  181.    wt: 1:   17 Function maxima minima and their location
  182.    wt: 1:   16 Increasing or decreasing on intervals
  183.    wt: 1:   15 Sign analysis of functions
  184.    wt: 1:   14 Surjections Injections Bijections
  185.    wt: 1:   13 From one to one to many to one
  186.    wt: 1:   12 Function Domain Recognition Exercises
  187.    wt: 1:   11 Function Domain Range Source and Targets
  188.    wt: 1:   10 Interval Notation
  189.    wt: 1:   9 Set theory term relation possible origins
  190.    wt: 1:   8 Set view of relations and functions
  191.    wt: 1:   7 Functions with finite domains
  192.    wt: 1:   6 Set Existence Formation and Notation
  193.    wt: 1:   5 Function notation for geometric transformations
  194.    wt: 1:   3 Formula or function graphing exercise
  195.    wt: 1:   A Quadratics Summary
  196.    wt: 1:   10 quadratic exercises
  197.    wt: 1:   9 quadratics physical and further context
  198.    wt: 1:   8 quadratics backward use of various formulas
  199.    wt: 1:   7 quadratic formulla derivation
  200.    wt: 1:   6 quadratics numerical approach
  201.    wt: 1:   5 quadratics completing the square
  202.    wt: 1:   4 quadratics difference of two squares
  203.    wt: 1:   3 quadratics factoring by inspection
  204.    wt: 1:   2 quadratics graphing in general
  205.    wt: 1:   1 quadratics graphing exercises
  206.    wt: 1:   Quadratics in 10 steps
  207.    wt: 1:   11 Growth and Decay in Biology
  208.    wt: 1:   10 Exponential Growth and Decay Models
  209.    wt: 1:   9 Formulas for Real Exponents with Logarithms
  210.    wt: 1:   8 Formulas for Fractional Exponents with Logarithms
  211.    wt: 1:   7 Formulas for Roots with Logarithms Derivation
  212.    wt: 1:   6 Formulas for Even and Odd Roots with Logarithms
  213.    wt: 1:   5 Natural Logarithm Calculator Exercises
  214.    wt: 1:   3 Natural Logarithms and Exponentials Basic Properties
  215.    wt: 1:   2 Square Root Simplification a prequel
  216.    wt: 1:   1 Calculator Starter Exercises
  217.    wt: 1:   8 Notes for instructors or tutors
  218.    wt: 1:   7 Links Lessons Elsewhere
  219.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  220.    wt: 1:   5 Polynomials Long division Nonlinear divisor
  221.    wt: 1:   4 Polynomials Long division linear divisor
  222.    wt: 1:   3 Polynomials Multiplication Addition
  223.    wt: 1:   2 Column Multiplication Method
  224.    wt: 1:   1 Polynomials Distributive Law
  225.    wt: 1:   1 Degrees and Radians Introduction
  226.    wt: 1:   5 Algebraic View of Slopes
  227.    wt: 1:   musings do not puiblish real numbers
  228.    wt: 1:   A Modular and Remainder Arithmetic
  229.    wt: 1:   A Signed Number Arithmetic Review
  230.    wt: 1:   26 More Less Greater Than Comparison
  231.    wt: 1:   25 Mid way Convergence to Axiomatic Approach
  232.    wt: 1:   24 Signed Numbers Arithmmetic Properties
  233.    wt: 1:   23 Distributive Law Two Derivations
  234.    wt: 1:   22 Multiplication of Signed Numbers
  235.    wt: 1:   21 Addition of Multiples of a Single Vector
  236.    wt: 1:   20 Length and Direction of Collinear Vector Sums How to Add Definition
  237.    wt: 1:   19 Signed Multiples of Vectors
  238.    wt: 1:   18 Geometrically Why Vector Addition Commutes
  239.    wt: 1:   17 Arrows Rotate to Reverse with Length Unchanged
  240.    wt: 1:   16 Collinear Horizontal Arrows Vectors
  241.    wt: 1:   15 Head to Tails in place Addition Associative
  242.    wt: 1:   14 Vector Head to Tail Sums and Resultants
  243.    wt: 1:   13 Arrows and Vectors in a Plane
  244.    wt: 1:   12 Real Numbers Line Signed Coordinates
  245.    wt: 1:   11 Signed Number Addition and Addition Properties
  246.    wt: 1:   10 Numbers given by Infinite Aperiodic Decimal Expansions
  247.    wt: 1:   9 Division with Digits after Decimal Point
  248.    wt: 1:   8 Division and Mulplication of Compound Fractions
  249.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  250.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  251.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  252.    wt: 1:   4 Location of Point in Decimal Addition
  253.    wt: 1:   3 Location of Point in Decimal Multiplication
  254.    wt: 1:   2 Counting Digits in Decimal Multiplication
  255.    wt: 1:   1 Fractions with Finite Decimal Expansions
  256.    wt: 1:   E Long Division Methods more
  257.    wt: 1:   D Long Division Methods
  258.    wt: 1:   C Three Decimal Subtraction Methods
  259.    wt: 1:   B Decimal Comparison and Subtraction
  260.    wt: 1:   A Decimal Addition Columm Methods
  261.    wt: 1:   8 Column Multiplication Methods in General
  262.    wt: 1:   7 Decimals Multiplication Methods Examples
  263.    wt: 1:   6 Column Methods for Decimal Multiplication
  264.    wt: 1:   5 Distributive Law for Whole Numbers
  265.    wt: 1:   4 Commutative Law Groups Counting Form
  266.    wt: 1:   3 Multiplicative Counting Skills Principles
  267.    wt: 1:   2 Combing Counts Addition Skills and Principles
  268.    wt: 1:   1 The Counting Origins of Numbers
  269.    wt: 1:   5 Proportionality in Equivalent Fractions
  270.    wt: 1:   4 Rates Ratios and Proporitionality
  271.    wt: 1:   3 Proportionality Examples
  272.    wt: 1:   1 What is Proportionality
  273.    wt: 1:   6 Equations and Systems Equivalent or Implied
  274.    wt: 1:   4 Subtraction and Division Axioms
  275.    wt: 1:   3 Product Axioms Two Forms
  276.    wt: 1:   2 Addition and Multiplication Axioms
  277.    wt: 1:   1 Equivalent Computation Rules
  278.    wt: 1:   5 Greater More Less Than Signs in General
  279.    wt: 1:   4 Comparison of Negative Numbers
  280.    wt: 1:   3 More and Less Than with Unlike Signs
  281.    wt: 1:   2 More and Less Than for Counts and Measures
  282.    wt: 1:   1 Real Numbers Comparison
  283.    wt: 1:   16 Real Numbers Comparison
  284.    wt: 1:   15 Real Number Division
  285.    wt: 1:   14 Real Number Multiplication
  286.    wt: 1:   13 Real Number Subtraction
  287.    wt: 1:   12 Real Number Additive Inverses or Negatives
  288.    wt: 1:   11 Real Number Addition
  289.    wt: 1:   10 Real Number Lengths and Signs
  290.    wt: 1:   9 Coordinates for Regions in Space
  291.    wt: 1:   8 Coordinates for Maps and Planes
  292.    wt: 1:   7 Real Numbers as Line Cordinates
  293.    wt: 1:   6 Unsigned Real Numbers
  294.    wt: 1:   5 Rational Numbers More
  295.    wt: 1:   4 Rational Numbers
  296.    wt: 1:   3 Fractions
  297.    wt: 1:   2 Integers
  298.    wt: 1:   1 Whole and Natural Numbers
  299.    wt: 1:   5 Independent versus Dependent Variables
  300.    wt: 1:   4 Changing Letters
  301.    wt: 1:   3 Geometric Formulas and Function Notation
  302.    wt: 1:   2 Computation Rules Evaluation
  303.    wt: 1:   1 Formulas Dependence and Function Notation
  304.    wt: 1:   More Exercises
  305.    wt: 1:   Simple Exercises
  306.    wt: 1:   5 Gaussian Elimination for 3 unknowns 2nd example
  307.    wt: 1:   4 GE III Animated Examples
  308.    wt: 1:   3 Gaussian Elimination 3 unknowns first example
  309.    wt: 1:   3 GE III Equation Addition and Multiplication
  310.    wt: 1:   2 GE II Comparison
  311.    wt: 1:   1 GE Substitution four examples
  312.    wt: 1:   4 Solving a triangular system exercise
  313.    wt: 1:   3 Solving triangular system example
  314.    wt: 1:   2 Essentially one exercises three with solution
  315.    wt: 1:   1 Essentially One Unknown
  316.    wt: 1:   Skill Development Notes
  317.    wt: 1:   10 One Example
  318.    wt: 1:   9 Three Examples
  319.    wt: 1:   8 One Example
  320.    wt: 1:   7 Two Examples
  321.    wt: 1:   6 Three Examples
  322.    wt: 1:   5 Three Examples
  323.    wt: 1:   4 Two Examples
  324.    wt: 1:   3 Two Examples
  325.    wt: 1:   2 Three Examples
  326.    wt: 1:   Using Letters for Physical Quantities
  327.    wt: 1:   Formula Usage Show Work Format
  328.    wt: 1:   13 Naming Identifying Formulas with Words
  329.    wt: 1:   12 Cone Cylinder Sphere Lesson Idea
  330.    wt: 1:   11 Volume of Sphere
  331.    wt: 1:   10 Volume of Pyramid
  332.    wt: 1:   9 Volume of Cone
  333.    wt: 1:   8 Compound Interest Formula Evaluation
  334.    wt: 1:   6 Pythagorean Hypotenuse Calculation Example
  335.    wt: 1:   5 Box Volume Formula Example
  336.    wt: 1:   4 Circle Area Formula Example
  337.    wt: 1:   3 Triangle Area Formula Example
  338.    wt: 1:   2 Another Rectangle Area Formula Example
  339.    wt: 1:   1 Written work formats for developing and showing skill
  340.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  341.    wt: 1:   9 Sets in Probability and Statistics
  342.    wt: 1:   8 Sets of Numbers
  343.    wt: 1:   7 Cautious or Safe Set Construction
  344.    wt: 1:   6 Power Set Notation
  345.    wt: 1:   5 Product Builder Notation
  346.    wt: 1:   4 Subset Builder Notation
  347.    wt: 1:   3 Counting with Sets etc
  348.    wt: 1:   2 Venn Diagrams
  349.    wt: 1:   1 Finite Sets
  350.    wt: 1:   6 Three Notions of What is a Variable
  351.    wt: 1:   5 Talking about Numbers and Quantities
  352.    wt: 1:   3 Adding Words To Arithmetic
  353.    wt: 1:   2 What is a Variable
  354.    wt: 1:   About Folder Contents
  355.    wt: 1:   1 Squares and Square Roots Introduction
  356.    wt: 1:   1 Least Common Multiples LCM Introduction
  357.    wt: 1:   13 Fraction Comparison Algebraic View
  358.    wt: 1:   11 Simplification an Algebraic View
  359.    wt: 1:   6 Multiplication Algebraically Take II
  360.    wt: 1:   4 video Prime Factorization Introduction
  361.    wt: 1:   Quick history of numbers and algebra
  362.    wt: 1:   18 Chain Rule Introduction
  363.    wt: 1:   2 Algebraic codification
  364.    wt: 1:   1 Numerical introduction
  365.    wt: 1:   E2 Algebraic Properties of Limits
  366.    wt: 1:   A1. Introduction
  367.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  368.    wt: 1:   Chapter 1.Introduction
  369.    wt: 1:   Postscript More on Better Performance
  370.    wt: 1:   Postscript For Better Performance
  371.    wt: 1:   Appendix D. What to do in School and Why
  372.    wt: 1:   Appendix C. How to Read
  373.    wt: 1:   Appendix B. How To Learn
  374.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  375.    wt: 1:   Chapter 31 Direct and Indirect Reason
  376.    wt: 1:   Chapter 30 Truth Tables
  377.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  378.    wt: 1:   Chapter 28 Occurrence Tables
  379.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  380.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  381.    wt: 1:   Chapter 25. Mathematical Induction Examples
  382.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  383.    wt: 1:   Chapter 23. Notation For Sums
  384.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  385.    wt: 1:   Chapter 21. Third Reading Guide
  386.    wt: 1:   Chapter 20. Degrees and Radians
  387.    wt: 1:   Chapter 19. Functions and Sets
  388.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  389.    wt: 1:   Chapter 16. Painless Theorem Proving
  390.    wt: 1:   Chapter 15. Solving Linear Equations
  391.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  392.    wt: 1:   Chapter 13. Second Reading Guide
  393.    wt: 1:   Chapter 12. Shorthand Usage Guide
  394.    wt: 1:   Chapter 11. Why Shorthand
  395.    wt: 1:   Chapter 10 Describing and Changing Calculations
  396.    wt: 1:   Postscript What is a Variable
  397.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  398.    wt: 1:   Solutions For Arithmetic Exercises
  399.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  400.    wt: 1:   Chapter 6 Change of Language
  401.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  402.    wt: 1:   Chapter 4 Longer Chains of Reason
  403.    wt: 1:   Chapter 3 Chains of Reason
  404.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  405.    wt: 1:   Foreword
  406.    wt: 1:   Annotated Links to Material Elsehwere
  407.    wt: 1:   Postscript A Three Remarks
  408.    wt: 1:   Chapter 12 Four Phases
  409.    wt: 1:   Chapter 11 Elementary Instruction
  410.    wt: 1:   Chapter 10 Transition
  411.    wt: 1:   Chapter 9 The Two Ends
  412.    wt: 1:   Chapter 8 Modern Instruction
  413.    wt: 1:   Chapter 7 Two Treatments of Geometry
  414.    wt: 1:   Chapter 5 Four References
  415.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  416.    wt: 1:   Foreword
  417.    wt: 1:   Chapter 14 Deductive and Empirical Views of Mathematics
  418.    wt: 1:   Chapter 1 Introduction
  419.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  420.    wt: 1:   S Adding words to algebra
  421.    wt: 1:   R Why Learn Mathematics Skills
  422.    wt: 1:   O On Learning Mathematics and Science
  423.    wt: 1:   N Mathematics Prepare for College Studies
  424.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  425.    wt: 1:   Chapter 8 Skipped Topics and Why
  426.    wt: 1:   Chapter 7 Calculus Previews and Calculus Lightly
  427.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  428.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  429.    wt: 1:   Chapter 2 Why Sets
  430.    wt: 1:   Chapter 1 Arithmetic
  431.    wt: 1:   Primary and Secondary Skills and Practices with Take Home Value
  432.    wt: 1:   7 Games and Activities for Instruction
  433.    wt: 1:   6 Measuring via counting or arithmetic the role of fractions
  434.    wt: 1:   5 Interpreting and Drawing Maps and Plans.
  435.    wt: 1:   4 Money Matters Saving Earning Buying Selling and Budgets
  436.    wt: 1:   3 Telling Tracking Time Temporal and More Place Sense
  437.    wt: 1:   2 Identifying Size and Position Place and Spatial Sense
  438.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  439.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  440.    wt: 1:   Ends Values Methods For Skill Development Framework Prequel
  441.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  442.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
  443.    wt: 1:   Implementation Notes
  444.    wt: 1:   Euclidean and Analytic Geometry with Complex Numbers and Trigonometry
  445.    wt: 1:   Math Free Euclidean Logic and Non Terminating Decimals 2 Topics
  446.    wt: 1:   Phase 2. More Basic Skills with likely take home value 1 to 2 years
  447.    wt: 1:   Phase 1. Basics Skills with clear take home value 5 to 6 years
  448.    wt: 1:   Which Way To Go
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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