Transcript Topic 1 - Cambridge Resources for the IB Diploma

Chapter 1
Number
Number systems – introduction of zero
Who invented 0?
Historical timeline of the
development of numbers
Put these events in order –
around what date did each occur?
First reference
to irrational
numbers
Decimal fractions
(tenths,
hundredths, etc.)
Decimal system
using the
decimal point
First use of π
Evidence that
every non-prime
number can be
written as a unique
product of primes
First
recognised
use of
fractions
Symbolic
system of
algebra
Definition of
multiplication
Introduction of
symbols to
represent
unknown numbers
Introduction of
calculus
Formulas for
area and
volume of solids
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First identified
use of decimal
(base 10) system
First
evidence
of zero
Creation of
times tables
Identified
that π was
roughly 3
What if we didn’t have numbers?
TOK
What would happen if we didn’t have numbers?
Prepare a one-minute presentation to the class about why
numbers are necessary.
Structure of numbers
TOK
Is Mathematics like English?
Sentences are made up of different types of words.
Whole numbers are the natural numbers including zero
zero.
Not all whole numbers are natural numbers
numbers,
but all natural numbers are whole numbers.
Adjectives are ‘describing’ words.
They make sense of the nouns and
provide context for them.
Could they be like fractions and
decimals?
Nouns provide the objects of the
sentence, like bullet points.
Without them there is no
structure.
Are they like whole numbers?
Are numbers structured like sentences?
Classification of numbers
Sort these numbers in a sensible way
All of these numbers are Real Numbers
The rest of the numbers are called
Irrational Numbers
Numbers that make fractions are
called Rational Numbers
Sort these numbers in a sensible way
All of these numbers are Real Numbers
If a number is whole then it is an
Integer
The rest of the numbers are called
Irrational Numbers
Numbers that make fractions are
called Rational Numbers
Sort these numbers in a sensible way
All of these numbers are Real Numbers
If a number is whole then it is an
Integer
Natural Numbers
The rest of the numbers are called
Irrational Numbers
Numbers that make fractions are
called Rational Numbers
The effect of error
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Currency rates
1 GDP = 1.1573 EUR
1 USD = 1.4753 EUR
You are buying a house in Italy for €250,000.
You need to convert your currency into euros and see the
exchange rates given above.
Your bank rounds the exchange rates to two decimal places.
Does this matter?
The scale of numbers
TOK
www
How many times bigger is the Eiffel Tower than a grain of sand?