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

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

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits

Ages 12+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5. Fraction Operations by Raising Terms Solving Linear Equations: Take I Take II


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

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

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

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

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  3.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
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  6.    wt: 1:   modern education
  7.    wt: 1:   Education Reform Inconsistencies
  8.    wt: 1:   three goals for Mathematics Education
  9.    wt: 1:   02 20 mathematics education references
  10.    wt: 1:   Education in mathematics science and technology
  11.    wt: 1:   Four ways to improve education reform
  12.    wt: 1:   education an empirical art
  13.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  14.    wt: 1:   11 Help and Defend Your Child or Teens Education
  15.    wt: 1:   3 Multiplicative Counting Skills Principles
  16.    wt: 1:   2 Combing Counts Addition Skills and Principles
  17.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  18.    wt: 1:   Postscript B Mathematics Education References
  19.    wt: 1:   Mathematics Education References
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  4.    wt: 5:   modern education
  5.    wt: 5:   Education Reform Inconsistencies
  6.    wt: 5:   three goals for Mathematics Education
  7.    wt: 5:   02 20 mathematics education references
  8.    wt: 5:   Education in mathematics science and technology
  9.    wt: 5:   Four ways to improve education reform
  10.    wt: 5:   education an empirical art
  11.    wt: 4:   why bother
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  18.    wt: 4:   Applied Maths Program14092009 POMME variant
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  29.    wt: 4:   Postscript 2007 01 10
  30.    wt: 4:   five decades make a difference
  31.    wt: 4:   Maps Plans Drawings
  32.    wt: 4:   how letters appear
  33.    wt: 4:   Secondary Three Mathematics
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  35.    wt: 4:   Secondary One Mathematics
  36.    wt: 4:   talk the algebra talk
  37.    wt: 4:   three difficulties
  38.    wt: 4:   teaching tips
  39.    wt: 4:   What to Tell Students
  40.    wt: 4:   mathematics curriculum shifts
  41.    wt: 4:   geometric implications for algebra
  42.    wt: 4:   teaching tutoring algebraic reason
  43.    wt: 4:   Lessening Algebra Difficulties
  44.    wt: 4:   the trouble with algebra
  45.    wt: 4:   05 13 OldSiteEntrancePage
  46.    wt: 4:   04 29 New Mathematics Curriculum
  47.    wt: 4:   04 25 when to stop or suspend mathemat
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  49.    wt: 4:   three aims for mathematics students
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  53.    wt: 4:   Theory of Knowledge
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  55.    wt: 4:   Different Kinds of Reasoning in maths
  56.    wt: 4:   three kinds of reason in mathematics
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  62.    wt: 4:   Prequel In For A Penny In For A Pound
  63.    wt: 4:   words for mathematics instructor
  64.    wt: 3:   10 statistics
  65.    wt: 2:   K LAMP Musings Science Education
  66.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  67.    wt: 2:   11 pure mathematics
  68.    wt: 2:   9 combinatorics probability sets
  69.    wt: 2:   8 analytic geometry etc
  70.    wt: 2:   7 logic review and decimals an odd combination
  71.    wt: 2:   6 polynomials etc
  72.    wt: 2:   5 logarithms and exponentials etc
  73.    wt: 2:   4 algebra
  74.    wt: 2:   3 Euclidean Geometry Leanly
  75.    wt: 2:   2 arithmetic with signed numbers
  76.    wt: 2:   1 arithmetic with unsigned numbers
  77.    wt: 2:   What is POMME
  78.    wt: 1:   Appendix 2 primary school Arithmetic 01
  79.    wt: 1:   Appendix 1 primary and preschool mathematic
  80.    wt: 1:   J LAMP Introduction Extrinsic Origins
  81.    wt: 1:   I LAMP Introduction Study Habits
  82.    wt: 1:   H LAMP Introduction Instructional Concepts
  83.    wt: 1:   G LAMP Introduction Problem Solving Skills
  84.    wt: 1:   F LAMP Introduction Prerequisites
  85.    wt: 1:   E LAMP Introduction Modern Mathematics
  86.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  87.    wt: 1:   A Introduction Objectives
  88.    wt: 1:   Skills Chapter 5 Calculus
  89.    wt: 1:   Skills Chapter 4 Logic
  90.    wt: 1:   Ramblings Extrinsic numbers theory
  91.    wt: 1:   Ramblings Introduction Algebra Essay
  92.    wt: 1:   Skills Chapter 3 Algebra
  93.    wt: 1:   Skills Chapter 2 Geometry
  94.    wt: 1:   Skills Chapter 1 Arithmetic
  95.    wt: 1:   Skills Chapter 0 Introduction
  96.    wt: 1:   A Circuit Elements
  97.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  98.    wt: 1:   11 Help and Defend Your Child or Teens Education
  99.    wt: 1:   10 Ends values for work study instruction
  100.    wt: 1:   10 Interval Notation
  101.    wt: 1:   1 Geometric Introduction of Function Notation
  102.    wt: 1:   10 Exponential Growth and Decay Models
  103.    wt: 1:   1 Calculator Starter Exercises
  104.    wt: 1:   10 Parallelogram Addition Method
  105.    wt: 1:   Construction Methods and Criteria for Isometric and Similar Triangles
  106.    wt: 1:   SAS Method For Isometric Or Proportional Triangle Construction
  107.    wt: 1:   Analytic View of Triangle Construction or Line Instersection More
  108.    wt: 1:   Straight Lines ASA Intersection Study More
  109.    wt: 1:   Straight Lines ASA Intersection Study
  110.    wt: 1:   Straight Lines Instersection Solving Equations
  111.    wt: 1:   Straight Lines Intersection of
  112.    wt: 1:   10 sine cosine Angle Sum Formulas via cis
  113.    wt: 1:   10 Midpoint of [a b] and [b a]
  114.    wt: 1:   10 Pythagorean plane distance formula
  115.    wt: 1:   10 Dropping a perpendicular to line
  116.    wt: 1:   9 Division with Digits after Decimal Point
  117.    wt: 1:   8 Division and Mulplication of Compound Fractions
  118.    wt: 1:   7 Arithmetic with Infinite Decimal Expansions
  119.    wt: 1:   6 Infinite Decimals Ending in 9 repeating
  120.    wt: 1:   5 Fractions with Infinite Decimal Expansions
  121.    wt: 1:   4 Location of Point in Decimal Addition
  122.    wt: 1:   3 Location of Point in Decimal Multiplication
  123.    wt: 1:   2 Counting Digits in Decimal Multiplication
  124.    wt: 1:   1 Fractions with Finite Decimal Expansions
  125.    wt: 1:   3 Multiplicative Counting Skills Principles
  126.    wt: 1:   2 Combing Counts Addition Skills and Principles
  127.    wt: 1:   9 Coordinates for Regions in Space
  128.    wt: 1:   8 Coordinates for Maps and Planes
  129.    wt: 1:   7 Real Numbers as Line Cordinates
  130.    wt: 1:   6 Unsigned Real Numbers
  131.    wt: 1:   10 One Example
  132.    wt: 1:   10 Set View of Wordy Extensions To Arithmetic
  133.    wt: 1:   10 dividing signed numbers
  134.    wt: 1:   10 Integer Multiplication Formulas
  135.    wt: 1:   10 video Prime Factorization upto 23 squared
  136.    wt: 1:   10 Division by Five Long and Short Ways
  137.    wt: 1:   10 Names for Big Numbers and Powers of Ten Expansion
  138.    wt: 1:   1 Place Value in Three Digit Whole Numbers
  139.    wt: 1:   016 Numbering Occidental Calendar Days
  140.    wt: 1:   015 School and work day counting tables
  141.    wt: 1:   014 Counting Days with Calendars
  142.    wt: 1:   013 Travel Time Tables
  143.    wt: 1:   012 Division of Time Intervals by Time Intervals
  144.    wt: 1:   011 Division of Time Intervals By Numbers
  145.    wt: 1:   010 Repeated Addition of Time Intervals
  146.    wt: 1:   1 Numerical introduction
  147.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  148.    wt: 1:   Foreword
  149.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  150.    wt: 1:   Postscript B Mathematics Education References
  151.    wt: 1:   Mathematics Education References
  152.    wt: 1:   Mathematics Education References
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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