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Mathematics Pascals Triangle Date 22.10.13 James McKee

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Challenge overview What is Pascals triangle? 2 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

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Challenge overview What is Pascals triangle? What patterns can you spot? 3 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

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Challenge overview What is Pascals triangle? What patterns can you spot? Which rows have only odd numbers? 4 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

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Challenge overview What is Pascals triangle? What patterns can you spot? Which rows have only odd numbers? Odd/even pattern: fractals. 5 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

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Challenge overview What is Pascals triangle? What patterns can you spot? Which rows have only odd numbers? Odd/even pattern: fractals. Joke: Q. What does the B in Benoît B Mandlebrot stand for? 6 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

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Challenge overview What is Pascals triangle? What patterns can you spot? Which rows have only odd numbers? Odd/even pattern: fractals. Joke: Q.What does the B in Benoît B Mandlebrot stand for? A. Benoît B Mandelbrot 7 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

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Challenge overview Class experiment: coin tossing. Come to the Science Festival to see a Galton board. Challenge: understand the connection with Pascals triangle. 8

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Challenge overview Class experiment: biased coin tossing. Is the first digit after the decimal point of sin(n) even or odd? Challenge: understand the connection with Pascals triangle. 9

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Curriculum links Number 10 Spot patterns Use decimal numbers Divisibility: odd or even

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Curriculum links Statistics 11 Design experiments Appreciate the concept of bias

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Added value Support and feedback from enthusiastic Royal Holloway staff. 12

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Added value Support and feedback from enthusiastic Royal Holloway staff. Come to Super Science Saturday and play with a Galton Board. 13

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