www.whyslopes.com:  Parents:  Help Your Child/ Teen Learn
Appetizers and Lessons for Mathematics and Reason  (Français)
Online tutor-teacher  seminars available

Online Volumes (Book Orders)
1,  Elements of Reason. (1996)
1A. Pattern Based Reason  (1995)
1B. Math Curriculum Notes (1996)
2. Three Skills for Algebra  (1995)
3.-Why Slopes & More Math  - (1995)

Read chapters 1-5, 8-12, 14, 16 & 17 
in  Three Skills for Algebra 

 More Site Areas 
1.  Solving Linear Equations  (04-2005)
2.  Fractns, Rates Proportns, Units  (2006)
3.  Algebra, Odds & Ends, HS level-(2001)
4.  Euclidean Geometry  & Cmplx NOs-new 
5.  Analytic Geometry/Functions (2006)
6.  Number Theory. (2006-7)
7.  Complex Numbers (2001)
8.  Calculus Introduction (2005)		 More Site Areas 
99   Real  Analysis (1995)
10. Secondary IV(?) maths (2006-7)
11. Math Education Essays  (2006-7)
12. LaTeX2HotEqn: (2004)
13. Electric Circuits Etc  (2007)
14. Quebec Math Ed (2004 -8))
15  Prequel to the How-TOs (06-2008)
16-Virtual-Classroom (Take a peek)		 Tutor -Teacher-How TOs-(08- 2008)
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths
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YOU are better than YOU think. Show yourself  how:

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 For better work & study skills, read logic chapters 1 to 5  in  Three Skills for Algebra. Sooner is better. Good luck.

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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. Site How-TOs are logically developed, but not tried and tested. That leaves room for thought and refinement..

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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.

Explore collaborative whiteboards from groupboard,  twiddla  or scriblink.

Chapter 12
Shorthand Usage Guide

Previous Section: Offspring Naming Conventions

9  A Review

A symbol or letter can serve as a shorthand label, a name, a place-holder or a pronoun for some number or quantity. A symbol, letter, label etc., can be written whenever the number or quantity is to be used or called upon. For clarity, within the same context or problem, different letters and symbols are to be used for different quantities, people and objects.

We have much choice in selecting a shorthand notation. But the same letters can be used in different problems. Once we realize or allow this, all we have to do is to find a statement, picture or some other indication of the shorthand roles of each symbol and letter in each formula, problem or context.

Answers to Exercise

 
Number or Quantity Example Shorthand Notation
Quantity the weight of the second car in a line.  
Quantity the height of a building.  
Quantity the area of a rectangular carpet or room.  
Quantity the volume of a box.  
Quantity the speed of a car.  
Quantity the total amount of interest earned by your bank account.  
Quantity the age of a child.  
Number the number of square inches in the area of a rectangle.  
Number the number of square centimeters in the area of the same rectangle.  
Number the number of square meters in the area of a circle.  
Quantity. the population of a city. Unit is say persons.  
Quantity the number of people in your school.  
Quantity the radius of a small circle.  
Quantity the radius of a bigger circle.  
Quantity the age of the first man in a line.  


No answers are given for the shorthand notation column since many different responses are possible and valid.   

Chapter Sections:  [ 12 Symbols & Pronouns ] [ 12 Pronouns ] [ 12 Shorthand Usage Guide ] [ 12 Pronouns in Mathematics ] [ 12  Big and Small Letters ] [ 12  Subscripts Etc ] [ 12 An Exercise ] [ 12 Symbols & Numbers ] [ 12  Offspring Naming Conventions ] [ 12  A Review & Answers to Exercise ]

Next Chapter: 13 What's Next

 

www.whyslopes.com
2. Three Skills for Algebra 

Foreword, Chapters 
& Appendices 

Foreword
1. Introduction
2. Implication Rules
3. Chains of Reason
4. Romeo and Juliet
4. Induction Mathematical
5 Knowledge Islands
6  Old Language
7  Arith Skill Check
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable
9. Algebra Talk
10 Two More Skills
11 Why Shorthand
12 Shorthand Usage
13 What's Next
14 Compound Interest
15 Linear Equations
PS I.  Distributive Law
PS II. Polynomials
16 Painless Proofs
17 Pythagoras
18 Rules of Algebra
19  Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums
23 Summation Notation
24 Your Money
25 Induction & Recursion
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
A. Advice For Learning

Real Player Videos

Perfect arithmetic skills with whole numbers & fractions after or besides chapters 1 to 14.

Arithmetic Videos Summary
Addition with Decimals
Subtraction with Decimals
Multiplication with Decimals
Fraction Arithmetic
Recognizing Primes
Long Division for Decimals
Square Root Simplification
Greatest Common Divisors
Least Common Multiples

Words Before Symbols: 
What is a Variable?
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  

Solving Linear Equations:

A. Letters and Lengths
B. & C. Solving Linear Eq'ns
with stick diagrams.

(i) x + 20 = 29
(ii) 2x + 5 = 20
(iii) 3x + 10 = 32
(iv) 5a + 16 = 3a+ 24
(v)  (½)x + 8 = 24½
(vI)  (¾)a + 16 = (¼)a+ 24
(vii) (¾)q + 17 = 32
(viii) 13 =[2/3]x +7 twice
(x) Animated Examples
(i) Integral Coefficients (A)
(ii) Integral Coefficients (B)
(iii) Fractional Coefficients
(iv) With Parameters

Problem Solving with Linear
Equations in one or many
unknowns, and in essentially 
one unknown - Symbols before
words. 

C. Solving Linear Eq'ns 
without
Stick Diagrams
D. Problems in 
essentially one unknown
E: 2D Systems - Sub Methods.
F. Larger Systems

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