Appetizers and Lessons for Mathematics and Reason - Entrance Level 
||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

Online Volumes
1,  Elements of Reason.
1A. Pattern Based Reason 
1B. Math Curriculum Notes
2. Three Skills for Algebra
3. Why Slopes & More Math
  (Optional Book Orders)

LAMP -Lean Applied Maths Pgm
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1. Help Your Child/ Teen Learn 
2. Solving Linear Equations
3. Fractions Ratios Rates Proportions & Units
4. Euclidean Geometry
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7. More Calculus
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9. Qc Maths  Education  
10. Secondary IV(?) maths
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15. Algebra, Odds & Ends, Etc
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16. Math Education Essays
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20**. Statistics .
** Means Under-construction.

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Maths Jobs/ Courses
for students in or visiting  Montreal

- sponsor required-


YOU are better than YOU think. Show yourself  how:

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Read  logic chapters 1 to 5  in online volume Three Skills for Algebra  
Then seek 4 skills for algebra in it.

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 Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and
writing

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.


After logic  (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;

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Caution: Site advice is approximately correct, for some circumstances, not all. That leaves room for thought

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What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts.


Try the Twiddla Whiteboard. In principle, it  allows to people to draw and chat together online on a copy of this webpage or a clean sheet. The chat may be via text or audio.  Visit www.twiddla.com to set up whiteboards to work with the webpage of your choice.

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

 

Preparation for Calculus 

  • Short Form - mostly links  with very few comments, plus some rough time estimates for each part 

  • Long Form-  links with more comments.

  • Longest Form - links and many more comments.

Calculus gives the best framework for understanding calculations met in business, science and engineering. Describing the same calculation without calculus is long and shallower process.  Good preparation for college mathematics (or calculus)  requires mastery of most, but not all the topics, you meet in high school mathematics: exact arithmetic with whole numbers and fractions, algebra, geometry without and with coordinates, and trig.

Preparation for calculus prepares for most  or all arts, trades and disciplines involving mathematics. That is, preparing for calculus will help you be better than you expect in accounting, art, chemistry, drawing, English, physics, woodwork, metal work, geology, electricity, mechanics, drafting and computing etc.

Many professions apart from mathematics, for instance nursing and policing,  require mastery of mathematics, even arithmetic, as a sign of skill and intelligence in problem solving, or using rules and patterns carefully and precisely  in a repeatable and reproducible manner. Many profession far from mathematics require mathematics mastery because its mastery shows an error in one step makes it and everything after wrong. 

Preparing for calculus will help you be better than you expect in accounting, art, chemistry, drawing, English, physics, woodwork, metal work, geology, electricity, mechanics, drafting and computing etc.

Even for students who do not take calculus, preparation for calculus would or should lead to the ability to apply or use rules and patterns, one at a time and one after another, carefully with the knowledge that an error in one step makes all that follows wrong or give its a lesser value.  Students should not be surprised by the expectation that a multi-step method lead to repeatable and reproducible results when sufficient care is taken. 

Calculus even if unseen by many students,  is unifying subject in mathematics and its applications to other subjects - commerce, business, personal finance, science, technology and engineering.

Reference: The Kyrgyz-Turkish High Schools Mathematics Pages has a lot material in pdf files - look at them

Digression: A Web Guide

  •  Local material  here at www.whyslopes.com is for ages 14 to adult.  Two other sites Maths is Fun  and Math League Help Topics appear to be for ages 9 to 14 say,  site PURPLEmath appear to be for ages ages 10 to 15; and   site SOSmath.com site is for ages 16 to adult.   Two or three views of topic from different authors site put together may be clearer & more informative than one. Explore all to find examples & explanation to help yourself or someone in your care master mathematics, etc.

  •   Kyrgyz-Turkish High Schools Mathematics Pages -Here is a excellent sequence of pdf files for grades 7 to 11 going from arithmetic to calculus. Looks very complete and is well-formatted. Jealously go away.  Here is a great resource for teachers and/or students.  Includes Review ExercisesNew Link, Old Site: Earth Station 9 - a one man reference (link collection) for many, many subjects. 

  •  Free HTML Editors and WYSIWYG Web Editors - A digression

 

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Three Links for Teachers:
(i) First Year High School Math - Lesson Plans with Fraction Focus (ii) Second Year High School Math - Lesson Plans with an algebra focus (iii) Algebra Lesson Plans

 

Help U Learn/ Teach

  1. Algebra
    words before symbols - direct & indirect use of formula, numerical versus algebraic solutions - what is a variable (more words)
  2. Arithmetic
    - exercises
    - with fractions
    - videos on primes, lcm, gcm,lcd, square roots etc
  3. Calculus - geometric preview, algebraic preview,
    3 study guides,
    much more
  4. Complex numbers
    -starter lesson with java applet - easy consequences  for trig & vectors in the plane
  5. Education
    - Empirical Course Design & Delivery
  6. Fractions
    - alone
    - by rote
    - with algebra
    - videos
  7. Functions - introduction
    hindsight - composition aka
    substitution
    -
  8. Geometry, Euclidean - Correspondence of trianglesTriangle construciton,  duplication & Isometry - Failure of ASA & the // line postulate - angle sum in triangles -// grams - Triangle Similarity
  9. Geometry- Analytic - functions, polynomials, complex numbers, unit circle trigonometry
  10. Logic
    - First Steps -
    Symbols in Logic -
     Occurrence & Truth Tables - Indirect Reason -Indirect Reason More
  11. Proportionality
    - Definition - Direct & Indirect Use - Numerical versus Algebraic Solutions
  12. Real Analysis
    - Decimal View of concepts and of proofs
  13. Rules &Patterns in Science, Technology & Society - Pattern Based Reason
  14. Mathematical Reasoning, empirical, inductive or deductive
  15. Units
    - in rates & slopes & (?) derivatives
    - in ratios & proportions - slopes & rates included
  16. Complex Numbers & Vectors & Trig
    trig expression for dot & cross - cosine law

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