Volume formula intuition

The  exercise appears under the 5th grade (U.S.) Math Mission. This exercise develops the volume formula and increases understanding of volume as three dimensional multiplication.

Types of Problems
There is one type of problem in this exercise:


 * 1) Use slices to find volume: This problem has a rectangular prism that is cut into some colored slices. The student is asked to find the number of blocks in a slice, the number of slices, and use these to determine the volume. The answers are typed into the spaces provided.Volforint1.png

Strategies
Knowledge of the volume formula is encouraged to ensure success on this exercise, but area is and counting are all that are required.
 * 1) The first number will be the number of blocks of a single color.
 * 2) The second is the number of colors.
 * 3) The third is always the product of the first two, which is the volume of the entire object.

Real-life Applications

 * 1) Slicing a figure to find it's volume motivates the volume formula that arises in Geometry.
 * 2) A visual understanding of slices to find volume is applied in later calculus as an application of integration (finding volume of shapes rotated around the axes).