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:   9 Combinatorics Trees Tables and Products/
  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

56 matches:

  1.    wt: 2:   Chapter 30 Truth Tables
  2.    wt: 2:   Chapter 6 Rule Based Reason in Mathematics
  3.    wt: 2:   Chapter 23 Truth Tables
  4.    wt: 1:   teaching tutoring algebraic reason
  5.    wt: 1:   Different Kinds of Reasoning in maths
  6.    wt: 1:   three kinds of reason in mathematics
  7.    wt: 1:   chapitre 04 07 RepetablesEtReproductibles
  8.    wt: 1:   14 Multiplication and Times Tables
  9.    wt: 1:   13 Addition and Addition Tables
  10.    wt: 1:   13 From one to one to many to one
  11.    wt: 1:   12 From Applied To Pure Mathematics
  12.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  13.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  14.    wt: 1:   C Straight Lines Slope from Coordinates
  15.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  16.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  17.    wt: 1:   4 Polar Coordinates to and from
  18.    wt: 1:   11 Volume of Sphere
  19.    wt: 1:   10 Volume of Pyramid
  20.    wt: 1:   9 Volume of Cone
  21.    wt: 1:   5 Box Volume Formula Example
  22.    wt: 1:   13 GCD from given Prime Factorization
  23.    wt: 1:   8 GCD from Euclidean Algorithm
  24.    wt: 1:   7 GCD and LCM from prime factorization
  25.    wt: 1:   6 GCD from Prime
  26.    wt: 1:   5 Counting with Tables Trees Product Rule Take II
  27.    wt: 1:   3 Counting with Tables and Trees II
  28.    wt: 1:   2 Counting with Tables and Trees I
  29.    wt: 1:   3 video Primes and Composites from 9 times table
  30.    wt: 1:   015 School and work day counting tables
  31.    wt: 1:   013 Travel Time Tables
  32.    wt: 1:   Example 2 volume of a cone
  33.    wt: 1:   Example 1 volume of a pyramid
  34.    wt: 1:   Volume of Solid by Cross Sections Lesson
  35.    wt: 1:   A Related Material in Volume 3
  36.    wt: 1:   A Related lessons in Volume 3
  37.    wt: 1:   6 Power rule from product rule
  38.    wt: 1:   B1 Pigeon Hole Principles from combinatorics
  39.    wt: 1:   Chapter 31 Direct and Indirect Reason
  40.    wt: 1:   Chapter 28 Occurrence Tables
  41.    wt: 1:   Chapter 4 Longer Chains of Reason
  42.    wt: 1:   Chapter 3 Chains of Reason
  43.    wt: 1:   Postscript C Consistency as a Tool for Reason
  44.    wt: 1:   Postscript B More on Story Telling and Reason
  45.    wt: 1:   Chapter 24 Direct and Indirect Reason
  46.    wt: 1:   Chapter 21 Occurrence Tables
  47.    wt: 1:   Chapter 16 Origins and Limitations of Rules and Patterns
  48.    wt: 1:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  49.    wt: 1:   Chapter 11 Accidental Patterns
  50.    wt: 1:   Chapter 7 Longer Chains of Reason
  51.    wt: 1:   Chapter 6 Chains of Reason
  52.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  53.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  54.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  55.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  56.    wt: 1:   More Algebra and Slope based Calculus Preview

Extended Search

215 matches:

  1.    wt: 8:   Chapter 23 Truth Tables
  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 21 Occurrence Tables
  6.    wt: 7:   Chapter 16 Origins and Limitations of Rules and Patterns
  7.    wt: 7:   Chapter 13 Geometric Thinking Euclidean Model For Reason
  8.    wt: 7:   Chapter 11 Accidental Patterns
  9.    wt: 7:   Chapter 7 Longer Chains of Reason
  10.    wt: 7:   Chapter 6 Chains of Reason
  11.    wt: 6:   Postscript D Reflections on Law of the Excluded Middle
  12.    wt: 6:   Postscript A Story Telling
  13.    wt: 6:   Chapter 22 Contrapositive and Vacuously True Implications
  14.    wt: 6:   Chapter 20 Shorthand Symbols as Pronouns
  15.    wt: 6:   Chapter 19 What is in chapters 20 to 24
  16.    wt: 6:   Chapter 18 Sense and Knowledge
  17.    wt: 6:   Chapter 17 Objective Ways Trial and Error Discovery
  18.    wt: 6:   Chapter 15 Objective Processes
  19.    wt: 6:   Chapter 14 Deductive and Empirical Views of Mathematics
  20.    wt: 6:   Chapter 12 Islands and Divisions of Knowledge
  21.    wt: 6:   Chapter 10 Responsibility
  22.    wt: 6:   Chapter 9 What is in Chapters 10 to 18
  23.    wt: 6:   Chapter 8 Change of Language
  24.    wt: 6:   Chapter 5 Deception
  25.    wt: 6:   Chapter 4 Implication Rules Forwards and Backwards
  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:   chapitre 04 07 RepetablesEtReproductibles
  32.    wt: 3:   Chapter 30 Truth Tables
  33.    wt: 3:   Chapter 6 Rule Based Reason in Mathematics
  34.    wt: 2:   chapitre 12 00 les iles et division
  35.    wt: 2:   chapitre 07 01 principle D induction mathematique
  36.    wt: 2:   chapitre 07 00 Des chaines plus longues de la raison
  37.    wt: 2:   chapitre 06 00 Chaines de la raison
  38.    wt: 2:   chapitre 05 00 Deception
  39.    wt: 2:   chapitre 04 10 Etapes pour une meilleur raison
  40.    wt: 2:   chapitre 04 09 Regles accidentelles
  41.    wt: 2:   chapitre 04 08 Limitations et benefices
  42.    wt: 2:   chapitre 04 06 engagements
  43.    wt: 2:   chapitre 04 05 Implication versus suggestion
  44.    wt: 2:   chapitre 04 04 Parlons de la logique
  45.    wt: 2:   chapitre 04 03 Unidirectionnel versus bidirectionnel
  46.    wt: 2:   chapitre 04 02 Deuxieme enigme
  47.    wt: 2:   chapitre 04 01 Premiere enigme
  48.    wt: 2:   chapitre 04 00 Les regles d implication
  49.    wt: 2:   chapitre 03 A Propos Des Prochains Chapitre
  50.    wt: 2:   chapitre 02 00 La Communication des idees
  51.    wt: 2:   chapitre 01 00 Introduction
  52.    wt: 2:   5 Counting with Tables Trees Product Rule Take II
  53.    wt: 2:   3 Counting with Tables and Trees II
  54.    wt: 2:   2 Counting with Tables and Trees I
  55.    wt: 2:   Example 2 volume of a cone
  56.    wt: 2:   Example 1 volume of a pyramid
  57.    wt: 2:   Volume of Solid by Cross Sections Lesson
  58.    wt: 2:   Area Between Curves Lesson Take 2
  59.    wt: 2:   A Related Material in Volume 3
  60.    wt: 2:   B1 Pigeon Hole Principles from combinatorics
  61.    wt: 2:   Chapter 31 Direct and Indirect Reason
  62.    wt: 2:   Chapter 28 Occurrence Tables
  63.    wt: 2:   Chapter 4 Longer Chains of Reason
  64.    wt: 2:   Chapter 3 Chains of Reason
  65.    wt: 1:   teaching tutoring algebraic reason
  66.    wt: 1:   Different Kinds of Reasoning in maths
  67.    wt: 1:   three kinds of reason in mathematics
  68.    wt: 1:   14 Multiplication and Times Tables
  69.    wt: 1:   13 Addition and Addition Tables
  70.    wt: 1:   13 From one to one to many to one
  71.    wt: 1:   12 From Applied To Pure Mathematics
  72.    wt: 1:   Proportionality of Line Segments From Parallel Transversals
  73.    wt: 1:   D Straight Lines Slope from Coordinates Examples
  74.    wt: 1:   C Straight Lines Slope from Coordinates
  75.    wt: 1:   13 Straight Lines Finding Equations from 2 points
  76.    wt: 1:   13 Navigation Location from Angles to 2 Landmarks
  77.    wt: 1:   4 Polar Coordinates to and from
  78.    wt: 1:   5 Areas of Rectangles Revisited
  79.    wt: 1:   4 Fraction Operations Axiomatic Development
  80.    wt: 1:   3 Inequalities Algebraically
  81.    wt: 1:   2 Fraction Operations Physical Development
  82.    wt: 1:   1 Decimals Modular and Remainder Arithmetic
  83.    wt: 1:   11 Volume of Sphere
  84.    wt: 1:   10 Volume of Pyramid
  85.    wt: 1:   9 Volume of Cone
  86.    wt: 1:   5 Box Volume Formula Example
  87.    wt: 1:   13 GCD from given Prime Factorization
  88.    wt: 1:   8 GCD from Euclidean Algorithm
  89.    wt: 1:   7 GCD and LCM from prime factorization
  90.    wt: 1:   6 GCD from Prime
  91.    wt: 1:   4 Counting with Trees Product Rule Take I
  92.    wt: 1:   1 Counting and Counting Methods I
  93.    wt: 1:   3 video Primes and Composites from 9 times table
  94.    wt: 1:   015 School and work day counting tables
  95.    wt: 1:   013 Travel Time Tables
  96.    wt: 1:   Example 1. Area Between x and x squared
  97.    wt: 1:   Area Between Crossing Curves Lesson Take 2
  98.    wt: 1:   Area Between Crossing Curves Lesson Take 1
  99.    wt: 1:   Example 4 with x function of y
  100.    wt: 1:   Example 3
  101.    wt: 1:   Example 2
  102.    wt: 1:   Example 1
  103.    wt: 1:   Area Between Curves Lesson Take 1
  104.    wt: 1:   Summary
  105.    wt: 1:   A Related lessons in Volume 3
  106.    wt: 1:   6 Power rule from product rule
  107.    wt: 1:   Postscript One Sided and Intermediate Value Theorems
  108.    wt: 1:   G.2 Lipshitz Conditions Integration Calculus Reform
  109.    wt: 1:   G.1 First Fundamental Theorem of Calculus
  110.    wt: 1:   G.6 Bounded Derivatives implies Lipshitz Continuity
  111.    wt: 1:   G.5 Motions With Bounded Velocities
  112.    wt: 1:   G.4 Lipschitz Continuity implies EquiContinuity
  113.    wt: 1:   G.3 Constant Difference Theorem Proof
  114.    wt: 1:   G.2 Differentiable Functions Mean Value Theorem
  115.    wt: 1:   G.1 Differentiable Functions Rolles Theorem
  116.    wt: 1:   F.5b Extreme Value Theorem
  117.    wt: 1:   F.5a Equicontinuity Theorems
  118.    wt: 1:   F.4 Finite Covering Theorem
  119.    wt: 1:   F.3 Intermediate Value Theorem
  120.    wt: 1:   F.2 Closed Range Theorem
  121.    wt: 1:   F.1 What Functions are Continuous
  122.    wt: 1:   E2 Algebraic Properties of Limits
  123.    wt: 1:   E1 Error Control Inequalities
  124.    wt: 1:   D2 Limits of Monotone Sequences
  125.    wt: 1:   D1 Sets and Sequences GLBs and LGBs
  126.    wt: 1:   C Triangle Inequalities
  127.    wt: 1:   B3 Bolzano Weierstrass Theorem
  128.    wt: 1:   PostScript For and Against Decimal Perspectives
  129.    wt: 1:   A1. Introduction
  130.    wt: 1:   Foreword Calculus Reform and Proofs Decimal Style A Postscript
  131.    wt: 1:   Postscript Pythagorean Theorem yet another proof
  132.    wt: 1:   Chapter 24 Logarithms Powers and Exponentials
  133.    wt: 1:   Chapter 23 Links To Trigonometry
  134.    wt: 1:   Chapter 22 Complex Numbers
  135.    wt: 1:   Chapter 21 Arrow Addition
  136.    wt: 1:   Chapter 20 Vectors and Complex Numbers
  137.    wt: 1:   Chapter 19. Exponentials and Natural Logarithms
  138.    wt: 1:   Chapter 18. Slopes Areas Integration
  139.    wt: 1:   Chapter 17. Area Approximation
  140.    wt: 1:   Chapter 16. Velocity Approximation
  141.    wt: 1:   Chapter 15. Slope Approximation
  142.    wt: 1:   Chapter 15. Algebraic Evaluation of Limits
  143.    wt: 1:   Chapter 14 Limits and Continuity with and sans Decimals
  144.    wt: 1:   Chapter 13. Acceleration
  145.    wt: 1:   Chapter 12. Units and Slopes
  146.    wt: 1:   Chapter 11. Graphing Slope versus Position
  147.    wt: 1:   Chapter 10 Slopes and Units
  148.    wt: 1:   Chapter 9 About First Courses in Calculus
  149.    wt: 1:   Chapter 8. Slope Interpretation
  150.    wt: 1:   Chapter 7 Slopes and Velocity
  151.    wt: 1:   Chapter 6. Slopes and Vertical Shifts
  152.    wt: 1:   Chapter 5. Slope Sign Tests
  153.    wt: 1:   Chapter 4. More Slope Sign Analysis
  154.    wt: 1:   Chapter 3. Slope Sign Analysis
  155.    wt: 1:   Chapter 2. Slopes and Ski Trails
  156.    wt: 1:   Chapter 1.Introduction
  157.    wt: 1:   Fall 1983 Calculus Appetizer
  158.    wt: 1:   Foreword
  159.    wt: 1:   Postscript More on Better Performance
  160.    wt: 1:   Postscript For Better Performance
  161.    wt: 1:   Appendix E. How To Study Mathematics and Why
  162.    wt: 1:   Appendix D. What to do in School and Why
  163.    wt: 1:   Appendix C. How to Read
  164.    wt: 1:   Appendix B. How To Learn
  165.    wt: 1:   Appendix A. Reading Guide For Next Appendices
  166.    wt: 1:   Chapter 29 Contrapositive and Vacuously True Implications
  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 18. Rules for Algebra
  177.    wt: 1:   Chapter 17. Pythagorean Theorem Chinese Square Proof
  178.    wt: 1:   Chapter 16. Painless Theorem Proving
  179.    wt: 1:   Chapter 15. Solving Linear Equations
  180.    wt: 1:   Chapter 14. Forward and Backward Use of a Formula
  181.    wt: 1:   Postscript Unifying Theme A Fourth Skill For Algebra
  182.    wt: 1:   Chapter 13. Second Reading Guide
  183.    wt: 1:   Chapter 12. Shorthand Usage Guide
  184.    wt: 1:   Chapter 11. Why Shorthand
  185.    wt: 1:   Chapter 10 Describing and Changing Calculations
  186.    wt: 1:   Postscript What is a Variable
  187.    wt: 1:   Chapter 9 Talking about Numbers or Quantities
  188.    wt: 1:   Chapter 8 Three Skills For Algebra
  189.    wt: 1:   Solutions For Arithmetic Exercises
  190.    wt: 1:   Chapter 7 Prep for Calculus Arithmetic Exercises
  191.    wt: 1:   Chapter 6 Change of Language
  192.    wt: 1:   Chapter 5 Islands and Divisions of Knowledge
  193.    wt: 1:   Chapter 2 Implication Rules Forwards and Backwards
  194.    wt: 1:   Chapter 1 Introduction to Chapters 2 to 6
  195.    wt: 1:   Foreword
  196.    wt: 1:   Annotated Links to Material Elsehwere
  197.    wt: 1:   Postscript B Mathematics Education References
  198.    wt: 1:   Postscript A Three Remarks
  199.    wt: 1:   Chapter 12 Four Phases
  200.    wt: 1:   Chapter 11 Elementary Instruction
  201.    wt: 1:   Chapter 10 Transition
  202.    wt: 1:   Chapter 9 The Two Ends
  203.    wt: 1:   Chapter 8 Modern Instruction
  204.    wt: 1:   Chapter 7 Two Treatments of Geometry
  205.    wt: 1:   Chapter 5 Four References
  206.    wt: 1:   Chapter 4 Complex Numbers and Why Slopes
  207.    wt: 1:   Chapter 3 Algebra Difficulties
  208.    wt: 1:   Chapter 2 For and Against Mathematics
  209.    wt: 1:   Chapter 1 Introduction
  210.    wt: 1:   Foreword
  211.    wt: 1:   V Reasons and Motivations for Logic and Mathematics
  212.    wt: 1:   Chapter 5 Coordinate Free and Coordinate Based Geometry
  213.    wt: 1:   1 From Number Recognition and Counting to Arithmetic B
  214.    wt: 1:   1 From Number Recognition and Counting to Arithmetic A
  215.    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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