The best that can be done with 40 is to isolate the pair of 2s: 40 = (2 x 2) x (2 x 5).

40 is not a perfect square because it does not have this symmetry. The square root of 36 is just one of the pairs, thus: √36 = 2 x 3. Perfect squares have symmetry in this respect (eg, 36 has a pair of 2s and a pair of 3s, ie, 36 = (2 x 3) x (2 x 3). Now verify that all these are really the same factorisation in other words check out for a single case that the prime factorisation is unique. Get the whole class to find the prime factorisation for 716625. Choose some numbers of your own (even large ones) and write them as the product of primes. The order can change but these will always be the prime factors. All numbers can be uniquely factorised into primes.What is left is the primes less than 200. Students cross out 1, all the even numbers except the first, all the multiples of 3 except the first, all the multiples of 5 except the first (why don’t they need to cross out the multiples of 4?), all the multiples of 7 except the first, all the multiples of 11 except the first, and all the multiples of 13 except the first (why need they not go further?). That is, give each group a 10 by 20 grid with the numbers 1 to 200 listed in order in the grid squares. Use the ‘Sieve of Eratosthenes’ to find all the primes between 1 and 200. Why are they similar to the primary colours in painting? Which numbers between have square roots that are whole numbers? What is a prime number? Before we go on to discuss the reason why these symbols are displayed like this it is necessary to revise the meaning of ‘square root’ and ‘prime number’.Sachs (1945) Mathematical Cuneiform Texts, published jointly by the American Oriental Society and the American Schools of Oriental Research, New Haven, Connecticut, page 43. The answer is on the diagram: Interpretation of the Symbols (see Copymaster 3 and below). What do the symbols mean? Consult the diagram: Meaning of Babylonian Symbols ( Copymaster 2 and below) and see if you can decode the numbers (taken from the internet). They were used by students of mathematics 4000 years ago. They are equivalent to what we would call mathematics exercise books today. The Babylonians stamped special shapes onto the wet clay before it set hard. This was before paper and pens were around. This mathematics was done 4000 years ago.Sachs (1945) Mathematical Cuneiform Texts, published jointly by the American Oriental Society and the American Schools of Oriental Research, New Haven, Connecticut, page 42. See also the diagrammatic version ( Copymaster 1 and below). Neugebauer (1957) The Exact Sciences in Antiquity, published by Brown University Press, Providence, Rhode Island. Show the students the photograph of a Babylonian clay tablet containing some mathematics (see Copymaster 1 and below).What major inventions occurred around this time?Īs groups report their thumbnail sketches create a timeline documenting the key achievements and historical benchmarks. What sort of transportation was typically used? Which famous people were alive around then? Activity: In groups, undertake some reserach to create a thumbnail sketch of life and times at each of the following periods of history: 100 years ago 500 years ago 1000 years ago 2000 years ago 3000 years ago and 4000 years ago:.We are talking about the mathematics done by people 4000 years ago! What was life like back then? In order for students to appreciate the significance of the clay tablet we will shortly discuss, they need to have some sense of what 2000BC means in concrete terms. We then consider prime numbers, surds, prime factorisation, and the squares of odd and even numbers. Before this session starts we expect that students will have explored a period of history and that they will report this back to the rest of the class.

Babylonian numerals 1000