YOU are better than YOU think. Show
yourself how:
|
// _ _ \\
/\ /\
<| (o) (o) |>
\ | | /
|
Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study.
Learn to read notes and textbooks like a lawyer, so that no nuance, no
subtlety and no clause escapes your attention. |
-/[]\-
||
/ \_
||||||||||||||||||||||||||||
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;
|
// _ _ \\
/\ /\
<| (o) (o) |>
| |
| |
\
/
\ = /
|
Caution: Site advice is approximately
correct, for some circumstances, not all. That leaves room for thought |
-/[]\-
||
_ / \
||||||||||||||||||||||||||||
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.
| |
- [Play
Video] 2 minutes. Explaining and Justifying Decimal Column
Method for Subtraction, when digits subtracted are
smaller than those above them.
- [Play
Video] 3 ¼ minutes. Subtraction with all digits
being beneath zeros. Here is the Shop Keeper's
Method for giving change when paid with bills.
- [Play
Video] 3 minutes. A new Subtraction
Method with two steps, where the second step
involves a second subtraction with all digits being
beneath zeros, and the digits subtracted are not always
smaller than those above them.
- [Play
Video] 5¼ Two Examples of the new Subtraction Method,
one short, one long.
- [Play
Video] 2½ minutes. Example of the new Subtraction with
mixed units of time, seconds, minutes, hours and days.
- [Play
Video] 5. Minutes, The Old Borrowing Method. A
cleaner way to record borrows, a way that avoids
crossing-outs.
- [Play
Video] 4½ minutes. A variation of Old Borrowing
Method for Subtraction - for better or worse.. Explanation of
how conversion of tens into ones justifies borrows. Two Examples
are given.
- [Play
Video] 2¾ minutes - A variation of Old Borrowing
Method for Subtraction - two more examples.
- [Play
Video] 1½ minutes. Example of Borrows with units of
time to explain further the borrow or unit conversion process.
|
More Videos: [ Up ] [ Arithmetic Videos Summary ] [ 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 ]
| |
www.whyslopes.com
2. Three Skills for Algebra
Foreword, Chapters
& Appendices
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
|