Volumes and Capacities
 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