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YOU are better than YOU think. Show
yourself how:
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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.
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Appendix A
Pathways for Better Learning
A About the Next appendices B to E
The next appendices and two PS postscripts offer advice and directions
(suggestions) for better learning.
They suggest why and how to study every subject including mathematics.
These appendices form a study guide for senior high school and beginning college
students. The advice and goals offered in these appendices apply to some but
not all circumstances. You and your neighbor may like different parts of
this advice or none - there is no pleasing everyone. Some of the advice or
suggestive is repetitive. The site author does not know when to stop writing.
Next Appendix: B How to Learn
Eight Study Tips
-
Identify what you do not understand among the skills and
concepts you need to know to give yourself a plan for further studies by
yourself or with help.
-
A subject is only understood when you know how to explain it
to another.
-
If you cannot read precisely, how will you understand and
how will you catch errors in writings, yours and others? If you cannot write
precisely, who will you understand? Arithmetic and logic both require
exactness in following steps or patterns, one at a time and one after
another. Precision in your daily life may follow if you master Arithmetic
and Logic. When you use arithmetic or logic do
you get the same results as others. If not, someone has made a mistake.
-
In mathematics, notes and work for doing problems must be
written on paper and must be written precisely. To completely master a
mathematical concept, one must be able to write calculations precisely and
exactly on paper. Errors of notation create misinterpretations which when
read later on lead to more misunderstanding or errors in further
reasoning. Ideas incorrectly understood or described will be a source
of error later at the time of reading or further reasoning.
-
You can be better than you think in most arts and
disciplined if you to learn that an error in one step of a
method lessens or destroys the value of whatever follows.
-
When you plan for the future career or studies in any
subject, see what mathematics courses are required. Then take them in
advance if possible.
-
Use of the electronic calculator for decimal computations
does not provide the exact answers that are needed for derivations of
formulas in algebra and beyond. For true understanding of concepts beyond
arithmetic, you need to understand and efficiently do arithmetic operations
with fractions
-
Learning takes time and effort, yours. In my
classes if not yours, students answering homework may look at the work
of others to to see how to solve a problem but must write their solutions
without copying. Students who have to copy will suffer on quizzes,
tests and examinations.
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www.whyslopes.com
Volume 2, Three Skills for Algebra -
Preview, starter & further lessons for logic and algebra
to (i) improve work & study skills; (ii) to to ease or avoid
algebra (math) fears & difficulties; and (iii) to fill gaps in the
exposition of mathematics.
Foreword, Chapters and Appendices follow.
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
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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