In these video clips we see the students applying the information and experiences from previous mathematical activities to a new situation. They are trying to make sense of the relationships among centimeter cubes as a measure of volume and the proportional relationship among cubes of differing sizes.

An investigation of volume concepts like this one would take place over several class periods. Prior to activities like this students should have opportunities to develop a general understanding of the process of measurement and to measure different attributes (See Related 6-8 Measurement Standard). These understandings include identifying an attribute to be measured, choosing an appropriate unit, and iterating that unit in order to assign a number to a particular attribute of an object. As part of this investigation, the students have constructed cubes of varying sizes by using centimeter cubes and grid paper to create models. Then, they filled the models with centimeter cubes. This experience enabled students to see the relationship among the individual units and the whole. The students then made predictions as to how many centimeter cubes are required to fill the model. Next they tested their estimations. This assisted students in developing a visual sense of how and how many unit cubes are arranged to create a larger cube.

Formulas for measuring attributes such as volume should later emerge as students have opportunities to measure, record information, and look at patterns. One goal for students in the middle grades is to become proficient at determining the perimeter, area, and volume of many figures and to use this proficiency in problem situations (See Related 6-8 Measurement Standard).

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