### Dining Ducks

Use the information about the ducks on a particular farm to find out which of the statements about them must be true.

### How Big Are Classes 5, 6 and 7?

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

### You Never Get a Six

Charlie thinks that a six comes up less often than the other numbers on the dice. Have a look at the results of the test his class did to see if he was right.

# Graphing Number Patterns

##### Age 7 to 11Challenge Level

Derek, of St John's Primary School, sent us his working on this problem:

The lines will cross when the bottom value and the side value of the two line sare the same, and the next triangle number is bigger than the next number in the six times table. I made a table of the triangle numbers and the six times table until this happened.

 Bottom value Triangle number Six times table 1 1 6 2 3 12 3 6 18 4 10 24 5 15 30 6 21 36 7 28 42 8 36 48 9 45 54 10 55 60 11 66 66 12 78 72
The triangle number and the six times table number are the same at 11. They are both 66. Then the triangle number at 12 is bigger than the six times table number at 12, so the lines have crossed.
I made another table to compare the square numbers with the six times table.
 Bottom value Square number Six times table 1 1 6 2 4 12 3 9 18 4 16 24 5 25 30 6 36 36 7 49 42
The lines cross at 6. I think this is because 6 squared is 6 x 6, which is the sixth number in the six times table.
Thank you, Derek!