1. Mathematics Pascals Triangle Date 22.10.13 James McKee

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

3. 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

4. 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

5. 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

6. 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

7. 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

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

9. 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

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

11. Curriculum links Statistics 11 Design experiments Appreciate the concept of bias

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

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

14. Questions?