Think of a Number and Flow Diagram

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Presentation transcript:

Think of a Number and Flow Diagram Problems

Take the number of times that you would like to eat KFC per week. Multiply your number by 2. Add 5. Multiply your number by 50. If you have already had your birthday this year add 1766; otherwise add 1765. Subtract the year of your birth.

The 3-digit number that you have should be your KFC number next to your age.

What has to be changed to make it work next year? Why does this work? What has to be changed to make it work next year? How would it have to change to work in 1998?

I think of a number. When I add 7 and double the result, I get 24. What was my number? Draw a flow diagram of the problem. n + 7 × 2 24 n – 7 ÷ 2 24

– 7 × 15 × 4 20 × 2 – 16 ÷12 + 11 + 26 – 4 × 2 ? – 44 ÷ 20

– 7 × 15 × 4 ? × 2 – 16 ÷12 + 11 + 26 – 4 × 2 17 – 44 ÷ 20

– 7 × 15 × 4 26 × 2 – 16 ÷12 + 11 + 26 – 4 × 2 ? – 44 ÷ 20

– 7 × 15 × 4 ? × 2 – 16 ÷12 + 11 + 26 – 4 × 2 41 – 44 ÷ 20

– 7 × 15 × 4 12 × 2 – 16 ÷12 + 11 + 26 – 4 × 2 ? – 44 ÷ 20

– 7 × 15 × 4 84 × 2 – 16 ÷12 + 11 + 26 – 4 × 2 ? – 44 ÷ 20

– 7 × 15 × 4 ? × 2 – 16 ÷12 + 11 + 26 – 4 × 2 12½ – 44 ÷ 20

How can you show that it will always work? What do you notice?

+ 3 + 9 × 2 1 ÷ 6 – 1 × 3 – 18 – 7 + 8 × 4 ? ÷ 2 + 20

Replace all of that: 5 →? 9 →? 2 →? . . . with this: ? ?

+ 8 × 3 ? × 3 + 8

G.H. Hardy The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.

Jack Littlewood He lived in Wynberg, Cape Town from 1892 to 1900 where his father was a headmaster.

Jack Littlewood Nowadays, there are only three really great English mathematicians: Hardy, Littlewood and Hardy-Littlewood. - Harald Bohr in 1947

Jack Littlewood Does the attitude to one’s schoolmaster persist? On the question who were the greatest intellects: “Well of course there’s Newton and Archimedes . . . As a matter of fact the really greatest man – you wouldn’t know him – he was the man who taught me algebra.”