Well, this next challenge is about chocolate. You have to imagine - if that's necessary - that everyone involved in this challenge enjoys chocolate and wants to have as much as possible.

There's a room in your school that has three tables in it with plenty of space for chairs to go around. 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. 30 of them all lined up ready to go in and eat the chocolate. These children are allowed to come in one at a time, when the person in front of them has sat down. When a child enters the room they ask themselves this question:- [We do imagine that the sharing happens equally around each individual table.] "IF THE SHARING OUT WERE TO HAPPEN WHEN I SAT DOWN WHICH WOULD BE THE BEST TABLE TO SIT DOWN AT?"

Table 1 Table 2 Table 3

However, that sharing DOES NOT take place [perhaps at the very end it could!!] and so it is important to remember that while each person thinks about that question:- "IF THE SHARING OUT WERE TO HAPPEN WHEN I SAT DOWN WHICH WOULD BE THE BEST TABLE TO SIT DOWN AT?" the sharing does not take place when they sit down.

It is fairly easy for the first few children to decide where to sit, but the question gets harder to answer, so, for example:- it MAY be that when person 9 comes into the room they see at Table 1 >>> 2 people at Table 2 >>> 3 people and at Table 3 >>> 3 people . . . . so the thinking that goes on to answer the question MAY go along these lines;
"If I go to table 1 there will be 3 people altogether then so the one block of chocolate will have to be shared among three and I'll get one third; BUT if I go to table 2 there will be 4 people altogether then so the two blocks of chocolate will have to be shared among four and I'll get one quarter; BUT if I go to table 3 there will be 4 people altogether then so the three blocks of chocolate will have to be shared among four and I'll get one three quarters. Three quarters I know is bigger than a half or a third so I'll go along to table 3."

Person number 10 would now see as they enter the room at Table 1 >>> 2 people at Table 2 >>> 3 people and at Table 3 >>> 4 people .... and they would have to go through similar thoughts to decide where to sit.


It might be good to read all of this, so far again!


I suggest that you get lots of paper the same size to stand for the chocolate. Then you could set out the pretend three tables with the correct number on each. You may well need lots of spare , same sized papers as you might find it necessary to do lots of folding or cutting in order to see which fractions are biggest!


You may find it useful, but it is only a suggestion to make a chart with headings like:

Person  |  Goes to  |  Number at  |  Number at  |  Number at  |  Amount they
 
Number  |  Table    |  Table 1    |  Table 2    |  Table 3    |  would get 
 
        |           |             |             |             |
 
        |           |             |             |             |
 
        |           |             |             |             |
 
        |           |             |             |             |

You might then start of with something like this:-

Person  |  Goes to  |  Number at  |  Number at  |  Number at  |  Amount they
 
Number  |  Table    |  Table 1    |  Table 2    |  Table 3    |  would get 
 
  1     |    3      |     0       |     0       |     1       |      3
 
  2     |    2      |     0       |     1       |     1       |      2
 
  3     |    .      |     .       |     .       |     .       |      ...
 
        |           |             |             |             |

Go ahead and find out how much each child receives as they go to the "best table for them".


Well if you've completed that, WELL DONE! You can then , as usual ask the question 'I wonder what would happen if...?" and this time it could be ".....if there were 4 tables or even five?" ; OR maybe"....if there were many more children involved.