Aims and objectives
This is a set of problem solving activities to develop and test
mathematical reasoning and logic. Students will be presented with
two containers of differing capacities and a target volume that
they have to reach. The containers can be filled, emptied or their
contents transferred from one to the other. There are a number of
different ways to meet the target but there is also a minimum number
of possible moves. This is a familiar problem but presented in an
engaging way.
Previous knowledge
No previous knowledge is required for this activity as it is reliant
on students’ problem solving skills. It would be useful as
an introduction, however, if the principles of the model could be
demonstrated by the teacher using real containers and water before
the students get involved with the ‘virtual’ activities.
In the classroom
The student is faced with two different sized containers and a target
volume to achieve. The aim of the activity is for one of the containers
to be left with the target amount. This is achieved by filling the
containers with a liquid, transferring the contents from one container
to the other and then emptying the containers until the target is
achieved.
There are five different combinations from which to choose. Each
activity has a minimum number of 'moves' to achieve the target.
If a pupil manages the task successfully, feedback will let them
know if they have achieved the result with the minimum number of
actions.
The activities promote problem solving in a familiar context and
incorporate elements of mental maths, prediction and lateral thinking.
They also work well if used in small groups as this encourages dialogue
between pupils and allows assessment of problem solving strategies.
This can prove to be a really successful exercise if used with
an interactive whiteboard with large groups or even the whole class.
Not only can the students become involved in dialogue and talking
about the problem solving approaches, but also the underlying mathematics
can be drawn out.
Curriculum references
Mathematics – KS3:
Ma2 1a, c, d; 4b
