This Filling Objects interactivity has been designed to give students an opportunity to use and develop their mathematical problem solving skills in a simulation of a practical context. The interactivity allows students to manipulate a variety of 3D geometric objects as they fill with water in real time. Students will need to collect data, carry out calculations and use problem-solving techniques to gain a greater insight into each situation and determine the rate at which the height of liquid in the object is changing with respect to time dy/dt.
Students can select the geometric object, its dimensions and orientation.
This interactivity can be used as a context for students to apply their knowledge of calculus to a situation in which there are connected rates of change. Alternatively it could be used as an introduction to working on problems of this type.
Students will benefit most from the interactivity if they are given very little guidance towards solving the problems and they work their way towards a solution using their prior knowledge and problem-solving experience. As a tutor you might want to suggest a geometric shape for students to start with (e.g. the cube).
This interactivity illustrates how mathematics can be used to gain further insight into real-world problems. Can they think of other situations where this is the case?
Students could choose their own objects to study. They could be asked to think of a simple example and a challenging (but possible!) example for another student to tackle. Posing problems in this way will help them to consider what makes some objects easier to study than others, and will challenge them to be creative in their choice of vessel to fill.
The interactivity illustrates how mathematics can be used to gain further insight into real-world problems. Can they think of other applications of the techniques used in this problem?
Students may need to be encouraged to identify the important quantities, and to write down the relationships between them. They may need to remind themselves of the relevant tools from calculus, including the chain rule.
Students could be encouraged to start with a simple example to start with, such as the cube.