Two
for One Box Company: Teacher Notes
MA.7.G.4.1
Conceptual Knowledge
Volume
Nets
Ratio
Procedural Knowledge
V = lwh
Problem Solving
Reasoning
Communication
Connections
Representation
Does a box twice as big
hold twice as much? (Twice as big here means doubling each dimension)
Students work individually
or in pairs
 Several sheets of 1 centimeter
square grid paper
 Quantity of 1 centimeter
cubes for each group
 Handouts for each student
 Scissors
 Tape
 Have students draw a net (a twodimensional pattern that can be
formed to make a solid) for making an open top box on the grid paper
for each of the sets of dimensions listed below.
 Cut out the net and fold up each side to form the open box and tape
the sides.
 Find the volume of the box by filing it with 1 centimeter cubes,
and record the results in a table such as the one below.
BOX

DIMENSIONS

VOLUME

A

2
X 2 X 2


B

3
X 3 X 3


C

4
X 4 X 4


D

5
X 5 X 5


E

2
X 4 X 6


F

2
X 3 X 4


 Write a ratio between the first dimension of Box A and Box B.
 Write a ratio between the volumes of Box A and Box B.
 Are they equivalent?
 If not, what can you do to the ratio of dimensions to make it equivalent
to the ratio of volumes?
 How would you change the dimensions of a box to ensure that the
volume is doubled?
As a result of this activity,
students will understand how changing dimensions of a figure affects
its volume.
Have students find volumes
for several different prisms when given the ratio of the dimensions
of the prism and the volume of one prism.
