Three Skills
For
Algebra
Volume 2
|
Chapters and Appendices
Book Entrance
Conclusions From a Single Rule
Linking and Chaining
Empirical & Deductive REASon
Foreword
1. Introduction
2. Implication Rules [4]
3. Chains of Reason [3]
4. Induction Mathematical
4. Romeo and Juliet
6 Old Language
5 Knowledge Islands [2]
7 Arith Skill Check [4 X 2]
Arith Webvideos
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable [8]
9. Algebra Talk [7]
10 Two More Skills[5]
11 Why Shorthand
12 Shorthand Usage [10]
13 What's Next
PS: The 4-th Skill For Algebra
14 Compound Interest [6]
15 Linear Equations [5]
16 Painless Proofs
17 Pythagoras
PS I. Distributive Law
PS II. Polynomials
18 Rules of Algebra [20]
19 Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums [2]
23 Summation Notation
24 Your Money [3]
25 Induction & Recursion [4]
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
Pathways for Learning
Would you like to show yourself or others how to be algebra
power users?
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
| |
Previous: Chapter Instroduction
Conclusions From a Single Rule
Pretend the following implication rule is never disobeyed.
Each time Suzy the cat is on the ground and Suzy sees a dog, Suzy climbs a
tree and stays in it for at least five minutes.
Direct Usage
What can we say for sure when Suzy the cat sees a dog? One possible answer is
that Suzy the cat stays in a tree for at least five minutes. Another possible
answer is that Suzy the cat climbs a tree. A more complete answer is that Suzy
the cat climbs a tree and stays there for at least five minutes. Each of these
answers or conclusions is correct. The last conclusion or result is fuller and
more complete than the others. It gives more information. Which answer or
conclusion is wanted here depends on who is interested in what. When many
conclusions are possible, we state only those conclusions of interest to us. We
do not have to state the most complete conclusion. The choice is ours.
Indirect Usage
What can you say for sure if Suzy the cat has not climbed nor stayed in any
tree for at least five minutes? To check your answer, you might have to remember
or revisit the questions in the chapter Implication Rules. But you should
do this after you have read the following words.
Chapter Sections: [Conclusions
From a Single Implication] [Linking
and Chaining Implication Rules] [ Deductive
Reason]
Next Section: Linking and
Chaining
Next Chapter: Longer Chains of Reason
| |
|
|
|
www.whyslopes.com
site
search
Parents: Help
your Child/Teen Learn covers Speaking
Skills, Reading
& Writing,
Preparing for Science &
Having Patience, etc
Math How-TOs
1. Arithmetic
2. Algebra
3. More
Algebra 4. Geometry
5 More
Geometry 6. Calculus
>> densely written
>> use as skill checklists
Online Volumes (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
Skill &
Concept
Review or Development
1. Decimal
Arith - Video Based ]
2 Fractions
3. Fractions
with Units
3. Solving
Linear Equations -
making alg easier
4. Formulas
forwards & Backwards - unifying theme for Algebra
5. Proportionality,
Back- & For-wards - theme at work.
6. Logic
- Math Free, good for precision in work & studies
7. Euclidean-Geometry
(leanly)
8. Slopes
and Lines
9. Why
Study Slopes - a context
10. Quadratics
11 Polynomials
12 Factored
Polys - a context
13 Functions
- For-& Back -wards
14 Number Theory,
Richly
15. Exponents, Radicals
& logs.
16 Calculus
- Examples & Advice
17. Real
Analysis
18 Electric
Circuits Etc (So So)
19 Maps,
Similarity & Trig, (alt view)
20 Complex
numbers
21
Logic with Symbols+truth tables
22 Consistent
Story Telling
23. Even
More Logic
|
|