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
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to work online with others.

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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.

Incomplete

5. Polynomials and Operations on them

Site Objective: Explain and introduce efficiently polynomials and operation on them: Addition, subtraction, multiplication, division by a linear factor, simplification of quotients.

Four Operations on Polynomials

For polynomials, site lessons present the following

  1. Area Viewpoint of Multiplication
  2. Multiplication Addition and Subtraction
  3. Long Division  with linear divisors
  4. Column Methods for Mulitplication

Together they point to a different approach for understanding and explaining four arithmetic operations on polynomials. 

Mastery of long division and methods to check its results implies mastery of the other three operations (addition, subtraction, and multiplication).

Let mastery of long division with linear or nonlinear factors be your aim. Explore the above lessons alone or with help. And for long division, do the checks. Division with nonlinear factors is optional - not part of the 436 program.

Links

Visit  www.purplemath.com  lessons

  1. Polynomials  (definitions & "like terms")
  2. Polynomials: Adding &  Subtracting
  3. Polynomials: Multiplying
  4. Polynomials: Dividing
  5. Polynomials, simple factoring (2 lessons)

to met and master the definition, addition, subtraction, multiplication and division of polynomials in a more traditional approach.

 Two online perspectives are better than one.



Teachers 1. The area view of products - how multiplication distributes over  addition takes 20 minutes.  Then you can introduce multiplication of polynomials via the area approach. Then introduce and shift to the column method for multiplication of polynomials in general.  That being said, the column method for addition is implicit or very close to the surface in the column method for multiplication. So column addition methods for adding polynomials comes next. Finally, the latter is modified to imply a column method for subtraction.  There-in goes two lesson to cover addition, subtraction and multiplication.  Long division (with checks included) may take a few more lessons. The approach here might be use in all or part in secondary III (314), secondary IV (416-426-436) and secondary V (536) mathematics.

Teachers 2.  Chapter 3, Slope Sign Analysis, in Volume 3, Why Slopes and More Math , shows how to do sign and zero analysis for factored polynomials, alone or in rational functions. Those examples as is or adapted would improve the algebraic thinking skills of your students - focus of the sign analysis of the expressions in question and not on their role as slopes or derivatives to functions.

 

 

Site lessons here

offer a different approach for understanding and explaining operations on polynomials. which is still under-construction - present form is sufficient for teachers, but not for students.

Teachers: Chapter 3, Slope Sign Analysis, in Volume 3, Why Slopes and More Math , shows how to do sign and zero analysis for factored polynomials, alone or in rational functions. Those examples as is or adapted would improve the algebraic thinking skills of your students - focus of the sign analysis of the expressions in question and not on their role as slopes or derivatives to functions.

 


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