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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10 matches:

  1.    wt: 6:   Volume 1A Pattern Based Reason/
  2.    wt: 2:   Volume 1A Regles et modeles/
  3.    wt: 2:   Volume 1 Elements of Reason/
  4.    wt: 1:   10 Examples of Algebraic Reasoning/
  5.    wt: 1:   4 Computation Rules and Function Notation/
  6.    wt: 1:   12 Webvideo Lessons on Area and Volume Calculation/
  7.    wt: 1:   Advanced Calculus Volume 3 Appendices/
  8.    wt: 1:   Volume 3 Why Slopes A Calculus Intro Etc/
  9.    wt: 1:   Volume 2 Three Skills For Algebra/
  10.    wt: 1:   Volume 1B Mathematics Curriculum Notes/

Web Page Search

50 matches:

  1.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  2.    wt: 2:   Chapter 16 Origins and Limitations of Rules and Patterns
  3.    wt: 1:   teaching tutoring algebraic reason
  4.    wt: 1:   Different Kinds of Reasoning in maths
  5.    wt: 1:   three kinds of reason in mathematics
  6.    wt: 1:   13 From one to one to many to one
  7.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  8.    wt: 1:   12 From Applied To Pure Mathematics
  9.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  10.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  11.    wt: 1:   C Straight Lines Slope from Coordinates
  12.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  13.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  14.    wt: 1:   4 Polar Coordinates to and from
  15.    wt: 1:   1 Equivalent Computation Rules
  16.    wt: 1:   2 Computation Rules Evaluation
  17.    wt: 1:   11 Volume of Sphere
  18.    wt: 1:   10 Volume of Pyramid
  19.    wt: 1:   9 Volume of Cone
  20.    wt: 1:   5 Box Volume Formula Example
  21.    wt: 1:   13 GCD from given Prime Factorization
  22.    wt: 1:   8 GCD from Euclidean Algorithm
  23.    wt: 1:   7 GCD and LCM from prime factorization
  24.    wt: 1:   6 GCD from Prime
  25.    wt: 1:   3 video Primes and Composites from 9 times table
  26.    wt: 1:   Example 2 volume of a cone
  27.    wt: 1:   Example 1 volume of a pyramid
  28.    wt: 1:   Volume of Solid by Cross Sections Lesson
  29.    wt: 1:   A Related Material in Volume 3
  30.    wt: 1:   A Related lessons in Volume 3
  31.    wt: 1:   6 Power rule from product rule
  32.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  33.    wt: 1:   Chapter 31 Direct and Indirect Reason
  34.    wt: 1:   Chapter 18. Rules for Algebra
  35.    wt: 1:   Chapter 4 Longer Chains of Reason
  36.    wt: 1:   Chapter 3 Chains of Reason
  37.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  38.    wt: 1:   Postscript C Consistency as a Tool for Reason
  39.    wt: 1:   Postscript B More on Story Telling and Reason
  40.    wt: 1:   Chapter 24 Direct and Indirect Reason
  41.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  42.    wt: 1:   Chapter 11 Accidental Patterns
  43.    wt: 1:   Chapter 7 Longer Chains of Reason
  44.    wt: 1:   Chapter 6 Chains of Reason
  45.    wt: 1:   Chapter 4 Implication Rules Forwards and Backwards
  46.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  47.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  48.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  49.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  50.    wt: 1:   More Algebra and Slope based Calculus Preview

Extended Search

213 matches:

  1.    wt: 8:   Chapter 16 Origins and Limitations of Rules and Patterns
  2.    wt: 7:   Postscript C Consistency as a Tool for Reason
  3.    wt: 7:   Postscript B More on Story Telling and Reason
  4.    wt: 7:   Chapter 24 Direct and Indirect Reason
  5.    wt: 7:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  6.    wt: 7:   Chapter 11 Accidental Patterns
  7.    wt: 7:   Chapter 7 Longer Chains of Reason
  8.    wt: 7:   Chapter 6 Chains of Reason
  9.    wt: 7:   Chapter 4 Implication Rules Forwards and Backwards
  10.    wt: 6:   Postscript D Reflections on Law of the Excluded Middle
  11.    wt: 6:   Postscript A Story Telling
  12.    wt: 6:   Chapter 23 Truth Tables
  13.    wt: 6:   Chapter 22 Contrapositive and Vacuously True Implications
  14.    wt: 6:   Chapter 21 Occurrence Tables
  15.    wt: 6:   Chapter 20 Shorthand Symbols as Pronouns
  16.    wt: 6:   Chapter 19 What is in chapters 20 to 24
  17.    wt: 6:   Chapter 18 Sense and Knowledge
  18.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  19.    wt: 6:   Chapter 15 Objective Processes
  20.    wt: 6:   Chapter 14 Deductive and Empirical Views of Mathematics
  21.    wt: 6:   Chapter 12 Islands and Divisions of Knowledge
  22.    wt: 6:   Chapter 10 Responsibility
  23.    wt: 6:   Chapter 9 What is in Chapters 10 to 18
  24.    wt: 6:   Chapter 8 Change of Language
  25.    wt: 6:   Chapter 5 Deception
  26.    wt: 6:   Chapter 3 What is in chapters 4 to 8
  27.    wt: 6:   Chapter 2 Skill Development
  28.    wt: 6:   Chapter 1 Introduction
  29.    wt: 6:   Three Remarks
  30.    wt: 6:   Foreword
  31.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  32.    wt: 2:   chapitre 12 00 les iles et division
  33.    wt: 2:   chapitre 07 01 principle D induction mathematique
  34.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  35.    wt: 2:   chapitre 06 00 Chaines de la raison
  36.    wt: 2:   chapitre 05 00 Deception
  37.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  38.    wt: 2:   chapitre 04 09 Regles accidentelles
  39.    wt: 2:   chapitre 04 08 Limitations et benefices
  40.    wt: 2:   chapitre 04 07 RepetablesEtReproductibles
  41.    wt: 2:   chapitre 04 06 engagements
  42.    wt: 2:   chapitre 04 05 Implication versus suggestion
  43.    wt: 2:   chapitre 04 04 Parlons de la logique
  44.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  45.    wt: 2:   chapitre 04 02 Deuxieme enigme
  46.    wt: 2:   chapitre 04 01 Premiere enigme
  47.    wt: 2:   chapitre 04 00 Les regles d implication
  48.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  49.    wt: 2:   chapitre 02 00 La Communication des idees
  50.    wt: 2:   chapitre 01 00 Introduction
  51.    wt: 2:   2 Computation Rules Evaluation
  52.    wt: 2:   Example 2 volume of a cone
  53.    wt: 2:   Example 1 volume of a pyramid
  54.    wt: 2:   Volume of Solid by Cross Sections Lesson
  55.    wt: 2:   Area Between Curves Lesson Take 2
  56.    wt: 2:   A Related Material in Volume 3
  57.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  58.    wt: 2:   Chapter 31 Direct and Indirect Reason
  59.    wt: 2:   Chapter 18. Rules for Algebra
  60.    wt: 2:   Chapter 4 Longer Chains of Reason
  61.    wt: 2:   Chapter 3 Chains of Reason
  62.    wt: 2:   Chapter 2 Implication Rules Forwards and Backwards
  63.    wt: 1:   teaching tutoring algebraic reason
  64.    wt: 1:   Different Kinds of Reasoning in maths
  65.    wt: 1:   three kinds of reason in mathematics
  66.    wt: 1:   13 From one to one to many to one
  67.    wt: 1:   6 Polynomial Operations and Equivalent Computation Rules
  68.    wt: 1:   12 From Applied To Pure Mathematics
  69.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  70.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  71.    wt: 1:   C Straight Lines Slope from Coordinates
  72.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  73.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  74.    wt: 1:   4 Polar Coordinates to and from
  75.    wt: 1:   5 Areas of Rectangles Revisited
  76.    wt: 1:   4 Fraction Operations Axiomatic Development
  77.    wt: 1:   3 Inequalities Algebraically
  78.    wt: 1:   2 Fraction Operations Physical Development
  79.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  80.    wt: 1:   1 Equivalent Computation Rules
  81.    wt: 1:   5 Independent versus Dependent Variables
  82.    wt: 1:   4 Changing Letters
  83.    wt: 1:   3 Geometric Formulas and Function Notation
  84.    wt: 1:   1 Formulas Dependence and Function Notation
  85.    wt: 1:   11 Volume of Sphere
  86.    wt: 1:   10 Volume of Pyramid
  87.    wt: 1:   9 Volume of Cone
  88.    wt: 1:   5 Box Volume Formula Example
  89.    wt: 1:   13 GCD from given Prime Factorization
  90.    wt: 1:   8 GCD from Euclidean Algorithm
  91.    wt: 1:   7 GCD and LCM from prime factorization
  92.    wt: 1:   6 GCD from Prime
  93.    wt: 1:   3 video Primes and Composites from 9 times table
  94.    wt: 1:   Example 1. Area Between x and x squared
  95.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  96.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  97.    wt: 1:   Example 4 with x function of y
  98.    wt: 1:   Example 3
  99.    wt: 1:   Example 2
  100.    wt: 1:   Example 1
  101.    wt: 1:   Area Between Curves Lesson Take 1
  102.    wt: 1:   Summary
  103.    wt: 1:   A Related lessons in Volume 3
  104.    wt: 1:   6 Power rule from product rule
  105.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  106.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  107.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  108.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  109.    wt: 1:   G.5 Motions With Bounded Velocities
  110.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  111.    wt: 1:   G.3 Constant Difference Theorem Proof
  112.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  113.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  114.    wt: 1:   F.5b Extreme Value Theorem
  115.    wt: 1:   F.5a Equicontinuity Theorems
  116.    wt: 1:   F.4 Finite Covering Theorem
  117.    wt: 1:   F.3 Intermediate Value Theorem
  118.    wt: 1:   F.2 Closed Range Theorem
  119.    wt: 1:   F.1 What Functions are Continuous
  120.    wt: 1:   E2 Algebraic Properties of Limits
  121.    wt: 1:   E1 Error Control Inequalities
  122.    wt: 1:   D2 Limits of Monotone Sequences
  123.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  124.    wt: 1:   C Triangle Inequalities
  125.    wt: 1:   B3 Bolzano Weierstrass Theorem
  126.    wt: 1:   PostScript For and Against Decimal Perspectives
  127.    wt: 1:   A1. Introduction
  128.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  129.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  130.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  131.    wt: 1:   Chapter 23 Links To Trigonometry
  132.    wt: 1:   Chapter 22 Complex Numbers
  133.    wt: 1:   Chapter 21 Arrow Addition
  134.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  135.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  136.    wt: 1:   Chapter 18. Slopes Areas Integration
  137.    wt: 1:   Chapter 17. Area Approximation
  138.    wt: 1:   Chapter 16. Velocity Approximation
  139.    wt: 1:   Chapter 15. Slope Approximation
  140.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  141.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  142.    wt: 1:   Chapter 13. Acceleration
  143.    wt: 1:   Chapter 12. Units and Slopes
  144.    wt: 1:   Chapter 11. Graphing Slope versus Position
  145.    wt: 1:   Chapter 10 Slopes and Units
  146.    wt: 1:   Chapter 9 About First Courses in Calculus
  147.    wt: 1:   Chapter 8. Slope Interpretation
  148.    wt: 1:   Chapter 7 Slopes and Velocity
  149.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  150.    wt: 1:   Chapter 5. Slope Sign Tests
  151.    wt: 1:   Chapter 4. More Slope Sign Analysis
  152.    wt: 1:   Chapter 3. Slope Sign Analysis
  153.    wt: 1:   Chapter 2. Slopes and Ski Trails
  154.    wt: 1:   Chapter 1.Introduction
  155.    wt: 1:   Fall 1983 Calculus Appetizer
  156.    wt: 1:   Foreword
  157.    wt: 1:   Postscript More on Better Performance
  158.    wt: 1:   Postscript For Better Performance
  159.    wt: 1:   Appendix E. How To Study Mathematics and Why
  160.    wt: 1:   Appendix D. What to do in School and Why
  161.    wt: 1:   Appendix C. How to Read
  162.    wt: 1:   Appendix B. How To Learn
  163.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  164.    wt: 1:   Chapter 30 Truth Tables
  165.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  166.    wt: 1:   Chapter 28 Occurrence Tables
  167.    wt: 1:   Chapter 27 Shorthand Symbols as Pronouns
  168.    wt: 1:   Chapter 26 What is in chapters 27 to 31
  169.    wt: 1:   Chapter 25. Mathematical Induction Examples
  170.    wt: 1:   Chapter 24. Personal Investment and Pension EGS
  171.    wt: 1:   Chapter 23. Notation For Sums
  172.    wt: 1:   Chapter 22. Geometric Sums and Sequences
  173.    wt: 1:   Chapter 21. Third Reading Guide
  174.    wt: 1:   Chapter 20. Degrees and Radians
  175.    wt: 1:   Chapter 19. Functions and Sets
  176.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  177.    wt: 1:   Chapter 16. Painless Theorem Proving
  178.    wt: 1:   Chapter 15. Solving Linear Equations
  179.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  180.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  181.    wt: 1:   Chapter 13. Second Reading Guide
  182.    wt: 1:   Chapter 12. Shorthand Usage Guide
  183.    wt: 1:   Chapter 11. Why Shorthand
  184.    wt: 1:   Chapter 10 Describing and Changing Calculations
  185.    wt: 1:   Postscript What is a Variable
  186.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  187.    wt: 1:   Chapter 8 Three Skills For Algebra
  188.    wt: 1:   Solutions For Arithmetic Exercises
  189.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  190.    wt: 1:   Chapter 6 Change of Language
  191.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  192.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  193.    wt: 1:   Foreword
  194.    wt: 1:   Annotated Links to Material Elsehwere
  195.    wt: 1:   Postscript B Mathematics Education References
  196.    wt: 1:   Postscript A Three Remarks
  197.    wt: 1:   Chapter 12 Four Phases
  198.    wt: 1:   Chapter 11 Elementary Instruction
  199.    wt: 1:   Chapter 10 Transition
  200.    wt: 1:   Chapter 9 The Two Ends
  201.    wt: 1:   Chapter 8 Modern Instruction
  202.    wt: 1:   Chapter 7 Two Treatments of Geometry
  203.    wt: 1:   Chapter 5 Four References
  204.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  205.    wt: 1:   Chapter 3 Algebra Difficulties
  206.    wt: 1:   Chapter 2 For and Against Mathematics
  207.    wt: 1:   Chapter 1 Introduction
  208.    wt: 1:   Foreword
  209.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  210.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  211.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  212.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  213.    wt: 1:   More Algebra and Slope based Calculus Preview

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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