Teaching the Common Core Math Standards With Hands-On Activities, Grades 3-5 (85 page)

Measurement and Data: 5.MD.3

“Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”

3. “Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

a.
“A cube with side length 1 unit, called a ‘unit cube,’ is said to have ‘one cubic unit’ of volume, and can be used to measure volume.

b.
“A solid figure which can be packed without gaps or overlaps using
unit cubes is said to have a volume of
cubic units.”

Background

Three-dimensional figures have length, width, and height. The volume, the amount of space inside the figure, is measured in cubic units.

A rectangular prism has three pairs of congruent rectangular faces. The volume of a rectangular prism equals the number of cubes that are required to fill it, without any gaps between the cubes.

Activity: Building a Rectangular Prism

Working in pairs or groups of three, students will create a rectangular prism that has a volume of 16 cubic centimeters.

Materials

16 1-centimeter cubes per pair or group of students.

Procedure

1.
Explain that the volume of a rectangular prism is the amount of space inside the prism. Note that a typical cardboard box is an example of a rectangular prism.

2.
Explain that each 1-centimeter cube is 1 centimeter long, 1 centimeter wide, and 1 centimeter high. The volume of the cube is 1 cubic centimeter. Two cubes have a volume that equals 2 cubic centimeters, 3 cubes have a volume of 3 cubic centimeters, and so on.

3.
Instruct your students to create rectangular prisms using all 16 of their centimeter cubes. They are to record the length, width, and height of each prism they create. Note that 16 centimeter cubes can be used to create 15 rectangular prisms, listed according to length, width, and height. Challenge your students to create all 15.

Closure

Discuss the dimensions of the prisms. Ask your students: How do you know that each prism has the same volume?

Answers

The dimensions of the prisms are provided below.

Measurement and Data: 5.MD.4

“Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”

4. “Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.”

Background

Volume, the amount of space in a container, can be found by counting the number of cubes that fill it. The product of the dimensions of the cube—length times width times height—times the number of cubes is equal to the volume of the container.

For example, if a container can be filled with 12 cubes, each having dimensions of 1 centimeter by 1 centimeter by 1 centimeter, the volume of the container is 12 cubic centimeters. If a container can be filled with 16 dice (an improvised unit), and each die has dimensions of
inch by
inch by
inch, the volume of the container is
cubic inches.

Activity: Finding Volume

Working in pairs or groups of three, students will find the volume of rectangular prisms by counting the number of cubes that form them. They will then determine the actual volume by multiplying the number of cubes by the volume of each cube.

Materials

100 1-centimeter cubes, 100 1-inch cubes, 100
-inch dice (or
-inch dice or similar improvised unit) for a class of 30 students. (Smaller classes will require fewer cubes of each type.)