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

What if we didn’t have numbers?

What would happen if we didn’t have numbers? Prepare a one-minute presentation to the class about why numbers are necessary. TOK

Structure of numbers

Is Mathematics like English? Sentences are made up of different types of words. Whole numbers are the natural numbers including zero. Not all whole numbers are natural numbers, but all natural numbers are whole numbers. Whole whole natural Nouns provide the objects of the sentence, like bullet points. Without them there is no structure. Are they like whole numbers? Adjectives are ‘describing’ words. They make sense of the nouns and provide context for them. Could they be like fractions and decimals? Are numbers structured like sentences? numbers numbers. zero TOK

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 The rest of the numbers are called Irrational Numbers Numbers that make fractions are called Rational Numbers If a number is whole then it is an Integer

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

The effect of error

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? www

The scale of numbers

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