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A Rod and a Pole

Age 7 to 11 Challenge Level:

Why do this problem?

This problem 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.

Possible approach

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.

Key questions

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?

Possible extension

Learners could investigate the different methods by which this problem can be solved. (There are at least five possible ways of doing it!)

Possible support

If sticks cannot be made available, cut lengths of card so that the units can be marked out and the solution found practically.