This unit builds on work done in third grade with area and fourth grade with liquid volume to build an understanding of volume as a measurement of three-dimensional space.
Students use unit cubes to understand that solid volume means “packing” a three-dimensional space with no gaps. This is different than liquid volume where students “fill” a container. Much of the early work in the unit relies on students creating three dimensional rectangular prisms and packing them with centimeter cubes, then counting the cubes. Next, students start to think of the cubes in layers, building the foundation for the formula V=bxh. Finally students look at the dimensions of the rectangular prisms in relation to the total volume to understand the formula V=lxwxh.
Complexity is built when students consider what happens to the total volume when one dimension is doubled or halved. Students also build visual spatial reasoning and continue to develop their understanding of volume as an additive quantity when working to find the area of composite rectangular prisms. Videos to help support these concepts are linked below.
This unit will address the Common Core State Standards (CCSS) 5.MD.3, 5.MD.4, 5.MD.5 and 5.NBT.2.
Students will be able to:
- find the volume of rectangular prisms using cubes and nets
- find the volume of composite figures
- understand why three-dimensional figures are measured in cubic units
Volume of Rectangular Prisms
Base x Height
Length x Width x Height
Volume of Composite Rectangular Prisms
Decomposing using Unit Cubes
Decomposing without Unit Cubes