Why do this
is one that combines logical thinking about
lengths while using the operations of addition and subtraction in a
practical way. It could be introduced during work on the
measurement of length. It also provides an opportunity for learners
to consider the effectiveness of alternative strategies.
You could start with some simpler examples of this type of
problem with the whole group. Examples which could be used include
having a $3$ unit rod (which cannot be marked) and a $5$ unit pole
and cutting off $1$ unit, and (slightly more difficult) a $2$ unit
rod and a $5$ unit pole and finding out how to cut off firstly $3$
units, then $1$ unit and then $4$ units. Having some
sticks cut in the right proportions with which to demonstrate will
make the problem more accessible.
After this introduction the learners could work in pairs on
the actual problem from a printed sheet so that they are able to
talk through their ideas with a partner. Ideally, each pair, or
even each child, could have sticks to represent the rod and the
pole. It might be helpful to supply some squared paper
for them to work on.
At the end you could bring the whole group together to see how each
pair solved the problem as there is more than one way to do it.
They could consider whether some strategies were more effective
than others. Explaining their thinking to each other can be a real
learning situation. If they have had real sticks, you could even
test out their methods to see whether they work.
If you place the end of the rod next to the end of the pole,
what length is left?
What length is left when you have measured off the rod twice?
Learners could investigate the different methods by which this
problem can be solved. (There are at least five possible ways of
If sticks cannot be made available, cut lengths of card so that the
units can be marked out and the solution found practically.