Why do this problem?
is an excellent problem for helping youngsters to develop their concepts of fractions. It's not so much to do with arithmetical manipulation of fractions, but more with youngsters exploring and developing their ideas. By encouraging learners to share their methods, there is an opportunity to discuss
which might be the 'best' (this might depend on the individual's preference too).
Children will need plenty of (the same sized) paper available for folding and tearing in order to explore sizes of fraction.
To begin the activity, you could act out the problem using large sheets of paper to stand for the chocolate bars (or real bars!), placed on tables. The acting could go through the situation with the first six children coming up one by one to the tables. Encourage them to justify their decisions and make sure the whole group agrees with their choice.
Then learners could work in pairs on what happens when further children come to the tables. By listening to their conversations you can get a good insight into the ways that those youngsters think about and visualise fractions. Some surprises are very likely!
After some time, bring everyone together again to talk about their ways of working. Invite comments about each method and then once all the different ways have been explained, ask pairs to discuss which method they would use now they have seen so many. You can then suggest they continue working on the problem, choosing any approach (or see the extension below). It would be
interesting to talk to those pairs who have changed the way they tackle the task to find out what it is about their new method that they preferred to the original one. Some of their reflections could be recorded for display.
Tell me about this. (Probably in reference to a torn-up piece of paper.)
What size do you think this is ...?
Why? (In response to the answer to the above.)
Challenge children to come up with a system or pattern that would help them to solve similar challenges.
For more extension work
These pupils can then move onto the situation of four tables set out with $1, 2, 3, 4$ chocolate bars on them. The two different activities can then be compared, looking at similarities and differences, and giving proofs where appropriate.
You could start off with just two tables and a total of three bars of chocolate.