2. Finding position-to-term rules

10. Find position-to-term rules for these sequences:

11. Squares investigation

12. Imagine a 3 x 3 square:

13. Squares investigation Imagine a 3 x 3 square: Colour the outside red:

14. Squares investigation Imagine a 3 x 3 square: Colour the outside red:

15. Squares investigation How many of the small squares have  0 red sides?  1 red side?  2 red sides?  3 red sides?  4 red sides?

16. Squares investigation Now change the size of the starting square to 2 x 2 ? 4 x 4 ? etc…

17. Squares investigation How many of the small squares now have  0 red sides?  1 red side?  2 red sides?  3 red sides?  4 red sides? INVESTIGATE!

18. Generalising from Diagrams 8 by 8

19. Generalising from Diagrams 20 by 20 50 by 50 100 by 100 n by n 2 red sides = ? 1 red side = ? 0 red sides = ?

20. Generalising from Diagram 20 by 30 50 by 40 90 by 50 a by b 2 red sides = ? 1 red side = ? 0 red sides = ?

21. Squares investigation Put your results into a table! (If you need to) Work methodically! Spot patterns! Try to find some general rules!