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There's a room in your school that has three tables in it with plenty of space for chairs to go round. Table $1$ has one block of chocolate on it, table $2$ has two blocks of chocolate on it and, guess what, table $3$ has three blocks of chocolate on it.
Now ... outside the room is a class of children. Thirty of them all lined up ready to go in and eat the chocolate. These children are allowed to come in one at a time and can enter when the person in front of them has sat down. When a child enters the room they ask themself this question:
"If the chocolate on the table I sit at is to be shared out equally when I sit down, which would be the best table to sit at?"
It is fairly easy for the first few children to decide where to sit, but the question gets harder to answer, e.g.
It maybe that when child $9$ comes into the room they see:
Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?
The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.