1. Chapter 1
Number

2. Number systems – introduction of zero

3. Who invented 0?

4. Historical timeline of the development of numbers

5. Put these events in order – around what date did each occur?
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First reference to irrational numbers
Definition of multiplication
First identified use of decimal (base 10) system
Evidence that every non-prime number can be written as a unique product of primes
Introduction of symbols to represent unknown numbers
Decimal fractions (tenths, hundredths, etc.)
First evidence of zero
Introduction of calculus
First recognised use of fractions
Decimal system using the decimal point
Creation of times tables
Formulas for area and volume of solids
Symbolic system of algebra
Identified that π was roughly 3
First use of π

6. What if we didn’t have numbers?

7. What would happen 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

8. Structure of numbers

9. Is Mathematics like English?
TOK
Is Mathematics like English?
Sentences are made up of different types of words
Whole
whole
natural
Whole numbers are the natural numbers including zero.
Not all whole numbers are natural numbers,
but all natural numbers are whole numbers.
numbers
zero
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?

10. Classification of numbers

11. Sort these numbers in a sensible way–3 π –2

12. All of these numbers are Real Numbers
Sort these numbers in a sensible way
Numbers that make fractions are called Rational Numbers
The rest of the numbers are called Irrational Numbers

13. 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
If a number is whole then it is an Integer

14. Natural 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
If a number is whole then it is an Integer
Natural Numbers

15. The effect of error

16. You are buying a house in Italy for €250,000.
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Currency rates
1 GDP = EUR
1 USD = 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?

17. The scale of numbers

18. How many times bigger is the Eiffel Tower than a grain of sand?
TOK
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How many times bigger is the Eiffel Tower than a grain of sand?