An Introduction to Volume
Lessons in this chapter
About An Introduction to Volume
An Introduction to Volume does for three dimensions exactly what 3rd grade did for area, and in the same order: count first, then formula.
Explore Volume with Unit Cubes and Find the Volume of Rectangular Prisms by Counting Cubes start by filling a box with unit cubes and counting them. A child who has counted knows what volume means and why its units are cubic, which a child handed the formula does not.
Calculate Volume of Rectangular Prisms Using Formula then shows length times width times height as a shortcut for the same count. The formula should emerge from the counting: one layer is length times width cubes, and there are height layers.
Find Volume of Composite Solids applies the splitting strategy from the area chapter. Break an irregular solid into rectangular prisms, find each volume, and add, which is the same problem-solving move in one more dimension.
Cubic units are the part worth labouring. An answer of 24 means 24 unit cubes fit inside, so it is 24 cubic centimeters, not 24 centimeters and not 24 square centimeters.
All four lessons open as a 5th grade math worksheet in the page. Explore Volume with Unit Cubes, Calculate Volume of Rectangular Prisms Using Formula and Find Volume of Composite Solids each set their own math problems, scored as you answer them. They are free to try, with no login needed for your first 3.
Frequently asked questions
Explore Volume with Unit Cubes and Find the Volume of Rectangular Prisms by Counting Cubes start by filling a box with unit cubes and counting them, which is what makes the cubic units mean something. Calculate Volume of Rectangular Prisms Using Formula then shows length times width times height as a shortcut for the same count, and Find Volume of Composite Solids applies the splitting strategy from the area chapter. The chapter sits in the Common Core domain Measurement and Data (5.MD).
The amount of space a solid takes up, measured by how many unit cubes fit inside it. It is written in cubic units.
Length times width times height. It works because one layer holds length times width cubes, and there are height layers.
Because counting shows what the number means and why the units are cubic. A child who starts with the formula can calculate but cannot explain.
Area is a surface, measured in square units. Volume is space, measured in cubic units. One is two-dimensional, the other three.
Split it into rectangular prisms, find each volume, and add them. It is the same splitting method used for area in 3rd grade.