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

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

Volumes 1A is for avid readers. Vols 2 & 3 are for adult, senior high school & college students.
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YOU are better than YOU think. Show yourself  how:

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 Read  logic chapters 1 to 5  in  Three Skills for Algebra for that for greater skills & confidence for work  &  study. 

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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.

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

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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;


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.

What is the Main Aim of High School Mathematics?

Most skills and concepts in high school mathematics today are present to prepare  students for college mathematics, that is calculus and beyond.  Calculus mastery is the key to good performance or to advance studies in business, engineering, science, mathematics and medicine. 

In reverse sequence, calculus requires from earlier high school mathematics  mastery of the following: unit circle trig,  analytic geometry, basic Euclidean geometry, exact algebra (solving equations and verifying solutions, operations on roots, polynomials and functions),  exact and efficient, nearly calculator-free, arithmetic with whole numbers and fractions, logic mastery, mathematical induction, arithmetic and geometric sums,  verbal description of numbers and quantities as known or not, constant, variable and so on.  Calculus does not require mastery of probability or combinatorics - labeling and counting items of -interest -  but lessons on probability and combinatorics can serve as a means to develop or reinforce exact operations on fractions - a must for calculus and before that exact reasoning in algebra.  In the foregoing, mastery of complex numbers may help with  roots and factorization of polynomial. Mastering all the foregoing represents a to do list for student aiming for college studies. Mastering all the foregoing represent a two to five year task depending on course design and whether or not students are streamed according their abilities to study and the quality of course design and materials.  

Preparation for calculus and beyond should not be the only end for high school mathematics. But students who are do well in topics needed for calculus are also prepared for less demanding ends.   Both students and teachers need to see how different  parts of the preparation for calculus in high school mathematics could cover most of the trades and quantitative skills students are likely to meet in the workplace and in their personal lives. Describing in detail the mathematical requirements of trades and activities students are likely to meet in the workplace and their personal lives would provide more immediate motivation for mathematics mastery. Writing such a description provides another to do for site expansion. 

 
 

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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

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 twiddla.com to set up whiteboards to work with the webpage of your choice. It works better with some browsers than others.

Precalculus sites mathsisfunwww.purplemath.com  might be appealing than this one.  Do not go. 

 

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