How big is a cubic metre?
Cary Cubemeister presents students with the challenge of estimating how many cubic centimetres are contained in a cubic metre. Students are challenged to provide an estimate and then are shown how their estimate fits within a transparent cubic metre. Feedback is visual and students are offered three opportunities before being given the chance to find out. The feedback animation of their estimate is shown by a series of cubes systematically filling up the cubic metre. An enlargement tool allows students to examine results in detail. A counter records the progress of the animation and the rotation tool enables the cubic metre to be viewed from different aspects.
Students are then asked to estimate the number of cubic centimetres in the length and width of the cubic metre. The concept of volume is further enhanced by students estimating the number of cubic centimetres in each layer of the cubic metre and the idea that the volume of a cuboid can be calculated by multiplying the area of the base by the height.
Inside a cubic metre
The 'Inside a cubic metre' learning object focuses on how many cubic centimetres there are in various fractions of a cubic metre. Students are asked to enter their estimates of the length and width, and then how many cubic centimetres are in parts of a cubic metre. Once they get the estimate correct, assisted by the animation and the counter, the decimal fraction value is displayed. There are several levels of difficulty, each culminating in the presentation of a table on which students are asked to complete blank cells, including the decimal fraction.
This learning object, while focusing on volume, would also be a useful means of discussing large numbers and decimal fractions.
What's in a cube? Levels 1 and 2
In the first level of this learning object, students are presented with a variety of cuboid or cuboid-like objects inside a cubic metre grid and asked to estimate the volume of the objects. The strategy encouraged is to compare the object with the cubic metre - that is, 'I think the DVD player is about one-tenth of the cubic metre' - and to iteratively improve their estimate by watching the animation of their estimate. The rotation tool is available so students can view the object from a number of aspects. An enlargement tool allows close examination of the result of their estimate and of the object.
The iterative approach is enhanced by students being able to override the animation and enter an improved estimation.
The second learning object in this series involves estimating the volumes of objects that are less regular. Students are encouraged to imagine the object broken up into a number of cuboids to estimate the volume of each cuboid piece and then to add their estimates to get their answers. The animation, enlargement and rotation tools are available to help. In addition, if the first estimate is incorrect the object is broken up into the component cuboids, which are arranged to assist in the estimation.
Working it out!
In the 'Working it out!' learning object, students work out the volume of a number of real-life cuboid-shaped objects using the formula: volume = area of base x height. The dimensions are given in centimetres. The student is led step by step through the calculation process, first working out the area of the base of the cuboid, and then the volume. Visual feedback is provided by unit cubes covering the base to show base area, and then filling the cuboid to demonstrate volume. At the end of the learning object the user is asked to complete a table. Included in this table is a column for working out the equivalence in cubic metres.