| Comparing volumes with unit cubes | |
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| Description | |
| Exercise Name: | Comparing volumes with unit cubes |
| Math Missions: | 5th grade (U.S.) Math Mission |
| Types of Problems: | 2 |
The Comparing volumes with unit cubes exercise appears under the 5th grade (U.S.) Math Mission. This exercise practices measuring three-dimensional shapes in terms of volume by using unit cubes.
Types of Problems[]
There are two types of problems in this exercise:
- Tell the volume of the solid figure: This problem provides a diagram that is split into unit cubes. The user is asked to correctly identify the volume of the figure and write it in the space provided.
Tell the volume of the solid figure
- Compare the volumes of the solid figures: This problem provides two solid figures that are split into unit cubes. Users are asked to identify which figure has more volume, or if the volumes are the same.
Compare the volumes of the solid figures
Strategies[]
Counting is the only skill necessary to complete this exercise, although volume formulas can help to find prism volumes more quickly.
- There is no trick holes on these problem, assume a prism is a prism.
- A rectangular prism has volume of length times width times height.
- When comparing, it is sometimes possible to see one shape as an extension of the other. The extension figure would consequently have greater volume.
Real-life applications[]
- The idea of volume is important for packing, shipping and cooking.
- Unit cubes can be used to efficiently store and package items. This is the main reason that boxes are generally rectangular prisms regardless of the items they carry.
- When one fills up their vehicle with gas, the volume of gasoline in their gas tank helps to determine their purchase. Whether they fill up with gallons or liters of gasoline or diesel, the amount is a volume calculation. On a smaller scale, when one fills up a gas can to take to another vehicle or to use the gas to power another device, they again use volume for measuring.
- The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.