Chapters and Appendices

Book Entrance

9 Numbers & Quantities
9 Everyday Words
9 Words Math Usage
9 Precision or Not
9 Numbers & Quantities
9 Changing Units
9 Further Readings

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

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.

1. The amount of money in a bank account (measured in dollars, pounds, yen, etc.)
2. the depth of a swimming pool (measured in inches, feet, yards, centimeters, meters, etc, whereever these units are in used).
3. The height of an airplane (measured in feet or meters).
4. The radius of a wheel (measured in whatever units you like).
5. The number of goats in a field (a count - no units).
6. The number of feet in your height.
7. The number of meters in your height - not the same as the number of feet!
8. The amount of money you have (in your local currency).
9. The speed of a car now (measured in miles per hour, feet per second, meters per second, or kilometers per hour, etc.)
10. The radius, area and perimeter (distance around) of a circle (measured in feet, inches, centimeters, kilometers, etc.)
11. The height, width and length and volume of a box (measured in various units).
12. The rate of interest your savings get - compounded or simple, measured in percent or given by a decimal number, etc.
13. 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.
14. The distance between you and your home (measured in miles, kilometers, etc.)
15. 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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