Appetizers and Lessons for Mathematics and Reason 
www.whyslopes.com - mathematics as an art and discipline, step-by-step  Parents: Help Your Child/ Teen Learn 
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||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

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1,  Elements of Reason.
1A. Pattern Based Reason 
1B. Math Curriculum Notes
2. Three Skills for Algebra
3. Why Slopes & More Math
 
Avid Readers: Try  Pattern Based Reason 
and calculus previews in Volume 3.
More Site Areas 
1. Solving Linear Equations  
2. Fractions Ratios Rates Proportions, Units
3. Euclidean Geometry
4. Analytic Geometry/Functions 
5. Number Theory
6. Calculus Introduction
7. Complex Numbers 
8. Quebec Maths Education  
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10. Real  Analysis 
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15. Math Education Essays  
Teacher-Tutor Info & How-TOs
1. Arithmetic Reference
2. Algebra Starters 
3. More Algebra 
4. Geometry Starters
5. More Geometry
6. Calculus Modifiers 
7. Multiple Logics in Maths
8. Math Ed. Issues

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YOU are better than YOU think. Show yourself  how:

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 In mathematics, sooner or later you need to learn to read like a lawyer. For that  read logic chapters 1 to 5  in  Three Skills for Algebra. Sooner is better. Good luck.

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On the phone with a classmate or tutor,skrbl now
or twiddla  to write & draw with each other on art, math & science etc. 


 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.

 

Chapter 10
Describing & Changing Calculations

Previous Chapter: 9 First Skill - How to Talk or Describe Numbers and Quantities


Talking about Two More Skills

Besides identifying numbers and quantities or talking about them, we can also describe and change calculations which include them or which say how to compute them. Simple calculations can be described with words alone or with shorthand notation. More complicated computations need the shorthand notation. Manipulating, changing or massaging (term learnt from a fellow instructor in 1984) of calculations, is best done with shorthand notation. Any description of a calculation with or without this shorthand notation gives what is called a formula. There is more to mathematics than just doing arithmetic precisely.


Chapter Sections:  10  Formullas & Shorthand Notation ] 10  Changing Calculations ] 10. Replacement & Substitution ] 10 Find a Number ] 10 Formulas as Potential Calculations ]

Next Section: 10 Shorthand Notation (formulas) for calculations

Next Chapter: 11 Why Shorthand

 


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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a 1983 McGill. Ph. D. in mathematics
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