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YOU are better than YOU think. Show
yourself how:
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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;
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Caution: Site advice is approximately
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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.
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Chapter 9
Talking about Numbers or Quantities
Chapter Sections: [ Up ] [ 9 Numbers & Quantities ] [ 9 Everyday Words ] [ 9 Words Math Usage ] [ 9 Precision or Not ] [ 9 Numbers & Quantities ] [ 9 Changing Units ] [ 9 Further Readings ]
Words have been missing to introduce and describe the
algebraic way of writing and reasoning. The following sections of this
chapter offer words to begin learning or teaching the algebraic way of writing
and reasoning. Enter one section. Then use the next, previous links in these
pages to move between them..
1 Identifying Numbers and Quantities
We first identify some numbers and quantities. After this, perhaps, we can
speak about them, or describe them, all without doing any arithmetic. There is
more to mathematics than just doing arithmetic.
Here are a few not-too-serious examples of numbers and quantities. Height is
a quantity. A building has a height. So has an elephant. The elephant also has a
weight and a width or a girth. A rectangle has a length, a width and an area. A
closed box has a width, a length, a height and a volume. The people in a room or
in a town can be counted. This gives us a number. The difference between a
number and a quantity will be explained later. More examples of numbers and
quantities follow.
- The amount of money in a bank account (measured in dollars, pounds, yen,
etc.)
- the depth of a swimming pool (measured in inches, feet, yards,
centimeters, meters, etc, whereever these units are in used).
- The height of an airplane (measured in feet or meters).
- The radius of a wheel (measured in whatever units you like).
- The number of goats in a field (a count - no units).
- The number of feet in your height.
- The number of meters in your height - not the same as the number of feet!
- The amount of money you have (in your local currency).
- The speed of a car now (measured in miles per hour, feet per second,
meters per second, or kilometers per hour, etc.)
- The radius, area and perimeter (distance around) of a circle (measured in
feet, inches, centimeters, kilometers, etc.)
- The height, width and length and volume of a box (measured in various
units).
- The rate of interest your savings get - compounded or simple, measured in
percent or given by a decimal number, etc.
- The number of days in this month - whatever month it is, a whole number
depending on the month and, in the case of February, depending on the year
as well.
- The distance between you and your home (measured in miles, kilometers,
etc.)
- The time required for a journey (measured in seconds, minutes, hours,
days, weeks, etc.)
This list could continue. We have identified several numbers and quantities.
We can talk and think about these numbers and quantities although we have not
seen and we have not measured them.
Chapter Sections: [ Up ] [ 9 Numbers & Quantities ] [ 9 Everyday Words ] [ 9 Words Math Usage ] [ 9 Precision or Not ] [ 9 Numbers & Quantities ] [ 9 Changing Units ] [ 9 Further Readings ]
Next Section: Using Every Day Words preciesely to
talk about or describe numbers and quantities
Next Topic: What is a Variable:
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www.whyslopes.com
Volume 2, Three Skills for Algebra -
Preview, starter & further lessons for logic and algebra
to (i) improve work & study skills; (ii) to to ease or avoid
algebra (math) fears & difficulties; and (iii) to fill gaps in the
exposition of mathematics.
Foreword, Chapters and Appendices follow.
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
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