Why do this problem?
involves complicated reasoning about fractions that challenges children's understandings of the concepts involved. It is a good example of how fractions relate to multiplication and division.
You could start a lesson with some oral challenges, such as:
"I bought some apples at the market. After I had given half of them to my sister I had $7$ left. How many did I buy?"
"Tom gave a quarter of his bag of sweets to Ben and ate half of them himself. He had $6$ left. How many sweets were there in the bag to begin with?"
Encourage learners to talk to each other about how they solved each of the above - they may not have used exactly the same method.
You could introduce the problem verbally, as a printed sheet
or on an interactive whiteboard. Ask learners to spend a bit of time working on it in pairs and then share ideas on how to get started amongst the whole group. It would be good to encourage children to jot down whatever they find helpful as they tackle the
problem. Make it clear that these jottings are purely for pairs themselves and that you do not need to be able to understand them!
Where shall we start?
How many marbles did Andy and Sam rescue?
How might this help you to work out the number of marbles Andy had before the bag split?
Children could be encouraged to make up their own version of a similar problem for a friend to solve.
It might help some learners to start slowly from the end asking questions such as:
"How many marbles did Andy have at the end?"
"How many did he give to Sam? And how many did he keep for himself?"
"Can you work out from that how many Andy and Sam picked up altogether?"