Volumes worksheet, page 1 (one per person)
Geometric solids (one set per group)
Self-sticking sand to fill models (one per group)
Bin to contain sand (one per group)
This page is still under construction - Images will be included soon!
The first part of this activity will give students a chance to "play" and familiarize themselves with the models of the solids, how they are assembled, and how to work with the self-sticking sand. Students should pick at least two shapes for closer inspection such as the three rectangular prisms with the same heights.
Firstly, the shapes are all the same - they are rectangular prisms because they each have two rectangular bases that are parallel to each other. They should be able to observe that all the heights are the same. The second largest prism has one side length on the base that is equal to each of the others.
There are also dimensions that are similar. The second largest prism has one side on the base that is half the length of the corresponding side largest prism and one that is twice the length of the corresponding side on the smallest prism. The lengths of the base on the smallest prism are both half the lengths of the corresponding sides on the largest prism.
Because the shapes are all the same, there isn't anything that is entirely different about them like comparing a pyramid with a prism or a rectangular prism to a pentagonal prism.
Using the sand or even directly looking at these particular prisms should be straightforward to compare the volumes. Using A to represent the largest prism, B to represent the second largest, and C to represent the smallest prism, a student migtht conjecture: