Three Skills
For
Algebra
Volume 2
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Chapters and Appendices
Book Entrance
10 Formullas & Shorthand Notation
10 Changing Calculations
10. Replacement & Substitution
10 Find a Number
10 Formulas as Potential Calculations
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
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Chapter 10
Describing & Changing Calculations
Previous Section:
10- Calculating a Number or Quantity in Different Ways,
Equivalent Calculations, Changing Calculations
2.4 Replacement and Substitution
The replacement idea or principle which appears above,
along with the laws of arithmetic (or algebra), leads to options for changing
how numbers or quantities are computed. Replacement is the key to the chains of
reasoning12
See the chapters Implication Rules
and Chains of Reasoning for the meaning of this
phrase,.
which says how to change the ways in which numbers, amounts and
quantities are computed.
When we have two expressions for a single result or quantity, or two ways of
writing that single result or quantity, we say the two expressions or ways of
writing have equal values. In brief, that they are equal). We further adopt the
rule that equal expressions (or symbols) can replace each other in the
calculation of a number or quantity. All rules for changing formulas use the
replacement rule:
- When two expressions are equal (that is, they give the same value or
result when computed) each expression can replace the other.
- A formula or calculation which gives the same result as another can be
used instead of the other.
- A new formula to compute a quantity or number may be obtained from a
previously found or given formula by replacing an expression in the
previously found or given formula by another expression of equal value.
Again (repetition ad nauseum), the key to massaging calculations is substitution
or replacement. This replacement or substitution principle is the glue that puts
and holds mathematics together.
Chapter Sections: [ 10 Formullas & Shorthand Notation ] [ 10 Changing Calculations ] [ 10. Replacement & Substitution ] [ 10 Find a Number ] [ 10 Formulas as Potential Calculations ]
Next Section: 10. Backward Use of a Formula -
Find a Number.
Next Chapter: 11 Why Shorthand
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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
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