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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12 matches:

  1.    wt: 4:   Mathematics Education Essays/
  2.    wt: 2:   Progressive Observable Motivated Mathematics Education/
  3.    wt: 2:   Volume 3 Why Slopes A Calculus Intro Etc/
  4.    wt: 1:   LAMP Lean Applied Mathematics Program/
  5.    wt: 1:   Archives/
  6.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  7.    wt: 1:   5 Lessons on Integration/
  8.    wt: 1:   4 Lessons on Using Derivatives/
  9.    wt: 1:   38 Lessons on Calculating Derivatives/
  10.    wt: 1:   13 Lessons on Limits and Continuity/
  11.    wt: 1:   70 Calculus Starter Lessons/
  12.    wt: 1:   Advanced Calculus Volume 3 Appendices/

Web Page Search

36 matches:

  1.    wt: 3:   Chapter 7 Calculus Previews and Calculus Lightly
  2.    wt: 2:   More Algebra and Slope based Calculus Preview
  3.    wt: 1:   K LAMP Musings Science Education
  4.    wt: 1:   C LAMP Introduction Culture in Mathematics Education
  5.    wt: 1:   Skills Chapter 5 Calculus
  6.    wt: 1:   8 analytic geometry etc
  7.    wt: 1:   6 polynomials etc
  8.    wt: 1:   5 logarithms and exponentials etc
  9.    wt: 1:   links Education Resources online
  10.    wt: 1:   Mathematics Education Professors
  11.    wt: 1:   modern education
  12.    wt: 1:   Education Reform Inconsistencies
  13.    wt: 1:   three goals for Mathematics Education
  14.    wt: 1:   02 20 mathematics education references
  15.    wt: 1:   Education in mathematics science and technology
  16.    wt: 1:   Four ways to improve education reform
  17.    wt: 1:   education an empirical art
  18.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  19.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  20.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  21.    wt: 1:   11 Help and Defend Your Child or Teens Education
  22.    wt: 1:   3 Counting with Sets etc
  23.    wt: 1:   1 Two cubic sketching exercises with 1st derivative
  24.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  25.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  26.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  27.    wt: 1:   Chapter 9 About First Courses in Calculus
  28.    wt: 1:   Fall 1983 Calculus Appetizer
  29.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  30.    wt: 1:   Postscript B Mathematics Education References
  31.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  32.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  33.    wt: 1:   Mathematics Education References
  34.    wt: 1:   Mathematics Education References
  35.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  36.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year

Extended Search

236 matches:

  1.    wt: 5:   links Education Resources online
  2.    wt: 5:   Mathematics Education Professors
  3.    wt: 5:   modern education
  4.    wt: 5:   Education Reform Inconsistencies
  5.    wt: 5:   three goals for Mathematics Education
  6.    wt: 5:   02 20 mathematics education references
  7.    wt: 5:   Education in mathematics science and technology
  8.    wt: 5:   Four ways to improve education reform
  9.    wt: 5:   education an empirical art
  10.    wt: 4:   why bother
  11.    wt: 4:   which way to go
  12.    wt: 4:   website reviews
  13.    wt: 4:   three goals to set for students
  14.    wt: 4:   Teach the teachers plus goals
  15.    wt: 4:   permissions for teachers
  16.    wt: 4:   Math Ed if it must be short make it lean effective
  17.    wt: 4:   Applied Maths Program14092009 POMME variant
  18.    wt: 4:   activities for students
  19.    wt: 4:   site origins
  20.    wt: 4:   site eurekas
  21.    wt: 4:   About site lesson plans
  22.    wt: 4:   key notes and themes
  23.    wt: 4:   teacher certification
  24.    wt: 4:   learning takes time
  25.    wt: 4:   grouping students according to ability
  26.    wt: 4:   what should be learnt and When
  27.    wt: 4:   mathematics in context
  28.    wt: 4:   Postscript 2007 01 10
  29.    wt: 4:   five decades make a difference
  30.    wt: 4:   Maps Plans Drawings
  31.    wt: 4:   how letters appear
  32.    wt: 4:   Secondary Three Mathematics
  33.    wt: 4:   Secondary Two Mathematics
  34.    wt: 4:   Secondary One Mathematics
  35.    wt: 4:   talk the algebra talk
  36.    wt: 4:   three difficulties
  37.    wt: 4:   teaching tips
  38.    wt: 4:   What to Tell Students
  39.    wt: 4:   mathematics curriculum shifts
  40.    wt: 4:   geometric implications for algebra
  41.    wt: 4:   teaching tutoring algebraic reason
  42.    wt: 4:   Lessening Algebra Difficulties
  43.    wt: 4:   the trouble with algebra
  44.    wt: 4:   05 13 OldSiteEntrancePage
  45.    wt: 4:   04 29 New Mathematics Curriculum
  46.    wt: 4:   04 25 when to stop or suspend mathemat
  47.    wt: 4:   02 21 words for teachers
  48.    wt: 4:   three aims for mathematics students
  49.    wt: 4:   standards for course material
  50.    wt: 4:   Operational Viewpoint to Value
  51.    wt: 4:   formal or informal peer review
  52.    wt: 4:   Theory of Knowledge
  53.    wt: 4:   mathematics instruction in general
  54.    wt: 4:   Different Kinds of Reasoning in maths
  55.    wt: 4:   three kinds of reason in mathematics
  56.    wt: 4:   cultivating intelligence
  57.    wt: 4:   How to be a better instructor
  58.    wt: 4:   Motivation and Context Problem
  59.    wt: 4:   need for a mixed mathematics curriculum
  60.    wt: 4:   Leaner mathematics curriculum
  61.    wt: 4:   Prequel In For A Penny In For A Pound
  62.    wt: 4:   fairness and inductive principles for instruction
  63.    wt: 4:   words for mathematics instructor
  64.    wt: 3:   8 analytic geometry etc
  65.    wt: 3:   6 polynomials etc
  66.    wt: 3:   5 logarithms and exponentials etc
  67.    wt: 3:   Chapter 9 About First Courses in Calculus
  68.    wt: 3:   Fall 1983 Calculus Appetizer
  69.    wt: 3:   Chapter 7 Calculus Previews and Calculus Lightly
  70.    wt: 2:   K LAMP Musings Science Education
  71.    wt: 2:   C LAMP Introduction Culture in Mathematics Education
  72.    wt: 2:   Skills Chapter 5 Calculus
  73.    wt: 2:   11 pure mathematics
  74.    wt: 2:   10 statistics
  75.    wt: 2:   9 combinatorics probability sets
  76.    wt: 2:   7 logic review and decimals an odd combination
  77.    wt: 2:   4 algebra
  78.    wt: 2:   3 Euclidean Geometry Leanly
  79.    wt: 2:   2 arithmetic with signed numbers
  80.    wt: 2:   1 arithmetic with unsigned numbers
  81.    wt: 2:   What is POMME
  82.    wt: 2:   1 Two cubic sketching exercises with 1st derivative
  83.    wt: 2:   G.2 Lipshitz Conditions Integration Calculus Reform
  84.    wt: 2:   G.1 First Fundamental Theorem of Calculus
  85.    wt: 2:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  86.    wt: 2:   Postscript Pythagorean Theorem yet another proof
  87.    wt: 2:   Chapter 24 Logarithms Powers and Exponentials
  88.    wt: 2:   Chapter 23 Links To Trigonometry
  89.    wt: 2:   Chapter 22 Complex Numbers
  90.    wt: 2:   Chapter 21 Arrow Addition
  91.    wt: 2:   Chapter 20 Vectors and Complex Numbers
  92.    wt: 2:   Chapter 19. Exponentials and Natural Logarithms
  93.    wt: 2:   Chapter 18. Slopes Areas Integration
  94.    wt: 2:   Chapter 17. Area Approximation
  95.    wt: 2:   Chapter 16. Velocity Approximation
  96.    wt: 2:   Chapter 15. Slope Approximation
  97.    wt: 2:   Chapter 15. Algebraic Evaluation of Limits
  98.    wt: 2:   Chapter 14 Limits and Continuity with and sans Decimals
  99.    wt: 2:   Chapter 13. Acceleration
  100.    wt: 2:   Chapter 12. Units and Slopes
  101.    wt: 2:   Chapter 11. Graphing Slope versus Position
  102.    wt: 2:   Chapter 10 Slopes and Units
  103.    wt: 2:   Chapter 8. Slope Interpretation
  104.    wt: 2:   Chapter 7 Slopes and Velocity
  105.    wt: 2:   Chapter 6. Slopes and Vertical Shifts
  106.    wt: 2:   Chapter 5. Slope Sign Tests
  107.    wt: 2:   Chapter 4. More Slope Sign Analysis
  108.    wt: 2:   Chapter 3. Slope Sign Analysis
  109.    wt: 2:   Chapter 2. Slopes and Ski Trails
  110.    wt: 2:   Chapter 1.Introduction
  111.    wt: 2:   Foreword
  112.    wt: 2:   More Algebra and Slope based Calculus Preview
  113.    wt: 1:   Appendix 2 primary school Arithmetic 01
  114.    wt: 1:   Appendix 1 primary and preschool mathematic
  115.    wt: 1:   J LAMP Introduction Extrinsic Origins
  116.    wt: 1:   I LAMP Introduction Study Habits
  117.    wt: 1:   H LAMP Introduction Instructional Concepts
  118.    wt: 1:   G LAMP Introduction Problem Solving Skills
  119.    wt: 1:   F LAMP Introduction Prerequisites
  120.    wt: 1:   E LAMP Introduction Modern Mathematics
  121.    wt: 1:   B LAMP Introduction Curriculum Development Standards
  122.    wt: 1:   A Introduction Objectives
  123.    wt: 1:   Skills Chapter 4 Logic
  124.    wt: 1:   Ramblings Extrinsic numbers theory
  125.    wt: 1:   Ramblings Introduction Algebra Essay
  126.    wt: 1:   Skills Chapter 3 Algebra
  127.    wt: 1:   Skills Chapter 2 Geometry
  128.    wt: 1:   Skills Chapter 1 Arithmetic
  129.    wt: 1:   Skills Chapter 0 Introduction
  130.    wt: 1:   25 Mathematics Education Leaving A Good Impression
  131.    wt: 1:   21 Calculus Oriented Highschool Mathematics Winners and Orphans Take II
  132.    wt: 1:   20 Calculus Oriented Highschool Mathematics Winners and Orphans Take I
  133.    wt: 1:   11 Help and Defend Your Child or Teens Education
  134.    wt: 1:   3 Counting with Sets etc
  135.    wt: 1:   Example 2 volume of a cone
  136.    wt: 1:   Example 1 volume of a pyramid
  137.    wt: 1:   Volume of Solid by Cross Sections Lesson
  138.    wt: 1:   Example 1. Area Between x and x squared
  139.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  140.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  141.    wt: 1:   Example 4 with x function of y
  142.    wt: 1:   Example 3
  143.    wt: 1:   Example 2
  144.    wt: 1:   Example 1
  145.    wt: 1:   Area Between Curves Lesson Take 2
  146.    wt: 1:   Area Between Curves Lesson Take 1
  147.    wt: 1:   Summary
  148.    wt: 1:   A Related Material in Volume 3
  149.    wt: 1:   5 Area Under Curve Exercise
  150.    wt: 1:   4 Definite Integrals Evaluation Exercises
  151.    wt: 1:   3 Two Chain Rule Method Exercises
  152.    wt: 1:   2 Indefinite Integrals Exercises
  153.    wt: 1:   1 Chain Rule in Reverse Integration Method
  154.    wt: 1:   A Related lessons in Volume 3
  155.    wt: 1:   4 Second derivative test exercise example
  156.    wt: 1:   3 Second derivative test
  157.    wt: 1:   2 Second derivative test prequel
  158.    wt: 1:   A Chain Rule Real Player video examples
  159.    wt: 1:   38 Formulas and derivatives for powers and roots
  160.    wt: 1:   36 Cube root derivative animated
  161.    wt: 1:   34 Derivative of exponential function
  162.    wt: 1:   33 Chain Rule Real Player video examples
  163.    wt: 1:   31 Derivatives of inverse functions
  164.    wt: 1:   30Chain Rule A Proof
  165.    wt: 1:   29 Chain Rule Optional Reading
  166.    wt: 1:   28 Chain Rule Preparation for a Proof
  167.    wt: 1:   27 Chain Rule sinusoidal outer inner functions EGS
  168.    wt: 1:   26 Chain Rule Recognising outer inner functions
  169.    wt: 1:   25 Chain Rule Animated Examples Continued
  170.    wt: 1:   24 Chain Rule Animated Examples
  171.    wt: 1:   23 Chain Rule in general
  172.    wt: 1:   22 Chain Rule for polynomials
  173.    wt: 1:   21 Chain Rule for powers
  174.    wt: 1:   20 Chain Rule for Pulley Systems
  175.    wt: 1:   19 Chain Rule for linear functions
  176.    wt: 1:   18 Chain Rule Introduction
  177.    wt: 1:   17 Derivatives of quotients of sine and cosine
  178.    wt: 1:   16 Derivatives of reciprocals of sine and cosine
  179.    wt: 1:   15 sine and cosine derivatives 3rd step
  180.    wt: 1:   14 sine and cosine derivatives 2nd step
  181.    wt: 1:   13 sine and cosine derivatives 1st step
  182.    wt: 1:   12 Quotient rule examples
  183.    wt: 1:   11 Quotient rule
  184.    wt: 1:   10 Power rule for negative integers
  185.    wt: 1:   9 Reciprocal rule
  186.    wt: 1:   8 Differentiation of polynomials
  187.    wt: 1:   7 Animated Differentiation Examples
  188.    wt: 1:   6 Power rule from product rule
  189.    wt: 1:   5 Product Rule
  190.    wt: 1:   4 Sum Rule
  191.    wt: 1:   3 Motivation for Limit Definition Take 2
  192.    wt: 1:   2 Motivation for Limit Definition Take 1
  193.    wt: 1:   1 Fall 1983 Why Slopes Appetizer
  194.    wt: 1:   13 Limits with Parameters and Derivatives Take II
  195.    wt: 1:   12 Limits with Parameters and Derivatives Take I
  196.    wt: 1:   11 Limits at infinity Three Examples
  197.    wt: 1:   10 Three one sided limits with infinite values
  198.    wt: 1:   9 Limits Continuity and Composition
  199.    wt: 1:   8 Four Animated Examples
  200.    wt: 1:   7 Evaluation by immediate or delayed substitution
  201.    wt: 1:   6 Continuity at a point
  202.    wt: 1:   5 Jumps and absence of unlimited error control
  203.    wt: 1:   4 Numerical properties
  204.    wt: 1:   3 Decimal insights for limits continuity convergence
  205.    wt: 1:   2 Algebraic codification
  206.    wt: 1:   1 Numerical introduction
  207.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  208.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  209.    wt: 1:   G.5 Motions With Bounded Velocities
  210.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  211.    wt: 1:   G.3 Constant Difference Theorem Proof
  212.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  213.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  214.    wt: 1:   F.5b Extreme Value Theorem
  215.    wt: 1:   F.5a Equicontinuity Theorems
  216.    wt: 1:   F.4 Finite Covering Theorem
  217.    wt: 1:   F.3 Intermediate Value Theorem
  218.    wt: 1:   F.2 Closed Range Theorem
  219.    wt: 1:   F.1 What Functions are Continuous
  220.    wt: 1:   E2 Algebraic Properties of Limits
  221.    wt: 1:   E1 Error Control Inequalities
  222.    wt: 1:   D2 Limits of Monotone Sequences
  223.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  224.    wt: 1:   C Triangle Inequalities
  225.    wt: 1:   B3 Bolzano Weierstrass Theorem
  226.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  227.    wt: 1:   PostScript For and Against Decimal Perspectives
  228.    wt: 1:   A1. Introduction
  229.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  230.    wt: 1:   Postscript B Mathematics Education References
  231.    wt: 1:   Appendix A Calculus with Proofs for Keen or Gifted
  232.    wt: 1:   Chapter 4 Logic for Reading Writing and Geometry etc
  233.    wt: 1:   Mathematics Education References
  234.    wt: 1:   Mathematics Education References
  235.    wt: 1:   Phase 5. Calculus Light to Rigourous for 1 to 2 years
  236.    wt: 1:   Phase 4. Preparation for Calculus with Cross Curricula but no take home value 1 year
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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