Examples

This page gives you some practice thinking about what is a good tile and what is a bad tile. Remember the golden rule of ArcShark:

If the black numbers are a good group and the red numbers are a good group then the tile is a good tile.

Example 1

	Can you think of a rule that connects 1, 4 and 5? I can't! Can you think of something that 2, 3 and 6 all have in common? Neither of these groups looks very good. This is a bad tile.
	Both groups of numbers are sequences. 1, 2 and 3 come one after the other and 4, 5 and 6 also come one after the other.
	3, 4 and 5 come one after the other which is good but 1, 2 and 6 don't make a good group. This is a bad tile.

Example 2

	There aren't any simple rules for these groups. This is a bad tile.
	The numbers 2, 3 and 4 come one after the other. The numbers 7, 8 and 9 also come one after the other. Both these groups have rules. This is a good tile!
	There aren't any simple rules for these groups. This is a bad tile.

Example 3

	The black numbers are 5, 6 and 7. This is a good group because these numbers come one after the other. Unfortunately, there is no simple rule for the red numbers 2, 8 and 11 so this is a bad tile.
	What sort of numbers are 5, 7 and 11? What sort of numbers are 2, 6 and 8? The answer is that the first group has odd numbers and the second group has even numbers. The rule for the black numbers is 'they are odd' and the rule for the red numbers is 'they are even'. This is a good tile!
	6 and 8 are both even but 5 is not. 7 and 11 are both odd but 2 is not. Neither of these groups has a simple rule. This is a bad tile.

Example 4

	A good rule for the black numbers is that 'they are all in the two times table' or that 'they are all even numbers'. What about the red numbers? Can you think of a simple rule that connects 3, 8 and 20? No? That's because there isn't one! This is a bad tile!
	Can you think what 3, 6 and 12 have in common? They are all in which times table? The answer is the three times table. What about 8, 16 and 20? They are all in the four times table! The rule for the black numbers is that 'they are all in the three times table' and the rule for the red numbers is that 'they are all in the four times table'. This is a good tile!
	What do 12, 16 and 20 all have in common? That's right, they're all in the four times table. So the rule for the red numbers is 'they are all in the four times table'. What about 3, 6 and 8? Can you think of a rule for them? There isn't a simple rule for these three numbers so this is a bad tile.

Example 5

	The black numbers are all in the two times table but there isn't a simple rule for the red numbers. This is a bad tile.
	A good rule for the black numbers is that 'they are all in the two times table'. What about the red numbers 5, 10 and 20? Can you think of a good rule for them? They are all in the five times table. Both groups have a simple rule so this is a good tile.
	The red numbers -- 8, 10 and 20 -- are all even. What about the black numbers? Is there a simple rule for 2, 4 and 5? I don't think so! This is a bad tile!

Example 6

	Is there a rule for 10, 19 and 22? What about 12, 23 and 28? I don't think there are. This is a bad tile.
	What have 10, 12 and 19 got in common? Can you work it out? That's right, they all start with a '1'. What about 22, 23 and 28? Yes, they all start with a '2'. So the rule for the black numbers is that 'they all start with 1' and the rule for the red numbers is that 'they all start with 2'. This is a good tile.
	Can you think of any rule for 10, 12 and 22? What about 19, 23 and 28? I can't think of any rules for these. This is a bad tile.