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:

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

Real Player Videos Perfect arithmetic skills with whole numbers & fractions after or besides chapters 1 to 14. 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

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

[ Area Intro ] [ Up ] [ Next ] [Top of this Page]  
Road Safety Message  Do not walk on a road with your back to the traffic. 
  Favourite Sites:  BBC News  and mathematics portion of  English National Curriculum  
[Site Author Contact Form]  If you find an error, please cut and paste its 
web page location (URL) into its report.

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby (email) All Rights Reserved. 

www.whyslopes.com