Appetizers and Lessons for Mathematics and Reason (www.whyslopes.com)
||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)
More Site Areas 
1. Help Your Child or Teen Learn 
2. Solving Linear Equations
3. Fractions Ratios Rates Proportions & Units
4. Euclidean Geometry
5. Analytic Geometry/Functions 
6. Number Theory
7. More Calculus
More Site Areas 
8. Complex Numbers 
9. Qc Maths  Education  
10. Secondary IV(?) maths
11. Real  Analysis 
12. LaTeX2HotEqn:
13. Electric Circuits Etc  
14.  Français
15. Algebra, Odds & Ends, Etc
More Site Areas 
16. Math Education Essays
17. Telling & Working with Time
18. Maps, Plans & Drawings
19. Quantitative Skills for  home, shopping and work 
20. Statistics Useful, or Not.
Try the
Twiddla Whiteboard
to work online with others.

[Site Entrance & Hub]Back ] Area Entrance ][Site Exit]


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  for greater skills & confidence in  work 
and study

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 Logic chapters 1 to 5  re- appear not in sequence, as is or longer,  in  Volume 1A,  Pattern Based Reason, Bon Appetite.

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

Logic mastery makes the hard, easier. Logic mastery  leads to better, stronger and richer comprehension.  Logic mastery  improves reading and writing.  Logic mastery ease learning difficulties.  Logic mastery gives a headstart.  In sum, 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 liinear 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.

 

Remarks for Teachers

The thought-based development here is semi-formal. Too much formality or rigour would make the inductive-to-deductive development of advance concepts too unwieldy - inaccessible.  The principal objective is to develop the algebraic way of writing and reasoning, and computational skills, needed to further in mathematics and quantitative disciplines in science, technology and business. All that is to be done  without overwhelming students with formalities, that is proofs for all properties and assertion, but with a sufficient amount of mathematical reasoning to lay a found foundation for calculus and beyond that.

As seen here, the role of mathematics courses from arithmetic to advance calculus is to inductively develop skills,  knowledge and computational confidence in logic and applied or mixed mathematics,  so that students see mathematics in context with mixed applications.  The context-free development of mathematics is not for beginners nor for students who have no intention of learning pure mathematics.  While trigonometry and distance concepts in the plane can be developed and formalized without diagrams in advanced mathematics (analysis),  the high school student accessible introduction and use of trig requires  diagrams and geometric drawings inconsistent with the idea that  context-free, exposition of mathematics is possible in the introduction of secondary and junior college mathematics. Since instruction relies on diagrams in the introduction of trig, instruction can also rely on diagrams in others matters and on decimals for arithmetic and beyond that the discussion of limits and continuity from arithmetic to calculus in mathematics course design and delivery.

 

www.whyslopes.com
Lesson & Lesson Plans for
Sec IV (Maths 436)


a reference for learning and teaching functions, polynomials, solving linear systems, 
powers + exponents + bases + radicals (roots) , quadratic formulas, equations of straight lines

1A. Master Logic
1B. Problems Solving Method
2A Solve Linear Equations i
2B.Solve Linear Equation II
2C Use Equal Sign Properly
2D. Perfect Arithmetic Skills
3 Words & Symbols
3 Goals to Set for Students
4 Use Equations Backwardly
5. Master Functions & Relations
6. Exponents & Radicals I
6 Exponents & Radicals II
7. Straight Lines
8. Polynomials (x,/,+/-)
9. Quadratics
10 Prove it
13 Similarity Scale Factors
12 Trig & Triangles
14 Statistics
MEQ Intermediate Objectives
Remarks for Teachers


Sit down and study - no one else can do that for you.

Advice and Directions
What to do in School   & Why
How to Study Maths & Why

Preparing for Science 

Good News: If you can learn to follow a multi-step methods in any subject precisely, you should be able to do so in other subjects, as well. Hint: Start with arithmetic

Words Before Symbols: 
What is a Variable?
Level:  Secondary II to VI, or Grades 7 to 12)
Introduction
Variation between Examples

Variation of Letters

A letter denotes a variable

Cases of Double Variation

Three Notions of a Variable

Constants, Parameters
& Variables

Talking about numbers
Dependent or Independent
Variable, a Matter of Choice

Complex number starter lesson  

Arithmetic Videos
Fractions
Primes
Greatest Common Divisors

Least Common Multiples

Square Root Simplification

Arithmetic Videos

Decimal Addition Methods
Decimal Subtraction Methods
Decimal Multiplication Methods
Decimal Division Methods


Fraction Starter Lesson
(simplify, multiply, divide & 
then add or subtract)


 

 

 



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Favourite SitesBBC News  and  mathematics portion of  English National Curriculum  
Francais: ||Définition d'une variable || Algèbre || Arithmetique || Logique | | 

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The Rest © 1995 onward by site author,   Alan Selby,
a 1983 McGill. Ph. D. in mathematics
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