Three Skills
For
Algebra
Volume 2
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Chapters and Appendices
Book Entrance
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
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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- [Play
Video] 4 minutes. Filling in the times table is a good way
to review basic addition, and a good way to set the stage for
decimal multiplication methods for whole numbers.
- [Play
Video] 2 minutes, Power (shorthand) Notation for Powers of
Ten. The power or exponent gives the number of times
that 10 appears as a factor in a product.
- [Play
Video] 5 minutes. Calculation of Rectangle Areas by
Subvision into Subrectangles, and two ways to sum. Here
is a geometric view of the distributive law (what ever that
is),based on the principle that the numbers in a large rectangle
will not change if the rectangle is viewed as a union of
subrectangles. So there are two ways to count or sum the number of
unit squares covering a large rectangle.
- [Play
Video] 5¾ minutes. Geometric View or Explanation of
Distributive Law for the multiplication of lengths or whole
numbers in two examples with letters for lengths instead of
numbers. Here is a geometric hint of algebra, and a foretaste of
the algebraic description of the distributive law.
- [Play
Video] 5 minutes. Geometric Justification for
Column Methods. How Calculation of the area of large rectangle
by subdividing it into subrectangles (not drawn to scale) leads to
decimal column methods for multiplication of whole numbers.
- [Play
Video] 7½ minutes. More on the Geometric
Viewpoint of Decimal Methods for Multiplication of whole numbers
with Hints of a table.
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More Videos: [ Up ] [ 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 ]
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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
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