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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See how to compute greatest common divisors with and without the use of prime
factorizations.
- [Play
Video] 7 minutes. Finding All Divisors of a Natural number
from its Prime Factorization/Decomposition
- [Play
Video] 6 minutes. Computing GCD for pairs of Natural
Numbers from their Prime Factorizations /Decompositions)
- [Play
Video] 2½ minutes Computing GCD from Prime
Factorizations /Decompositions, another example.
- [Play
Video] 3 minutes. Computing GCDs using Primes, yet
another example.
- [Play
Video] 6½ minutes. Euclid Algorithm computes GCDs not
using Prime Factorization.
- [Play
Video] 3 minutes. Another Euclid Algorithm GCD
example with result confirmed using Prime Decomposition.
- [Play
Video] 1½ minutes. Two numbers are relatively prime
when and only when they have GCD =1 when and only when the numbers
have no prime divisors in common. Euclid algorithm leads to a
quick identification of relatively prime whole numbers in the
numerators and denominators of fractions by themselves or
products.
.
- [Play
Video] 4 minutes. Two Ways to Find the GCD of a pair of
numbers. Both lead to the same result.
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Euclid's algorithm provides a means to compute the GCD without mentioning
prime factorization. The latter is best for computations with large numbers -
numbers for which the prime factorization is not immediately obvious. Euclid
algorithm can be implemented on calculator.
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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