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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 two-dimensional 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.
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BOX
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DIMENSIONS
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VOLUME
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A
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2
X 2 X 2
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B
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3
X 3 X 3
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C
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4
X 4 X 4
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D
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5
X 5 X 5
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E
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2
X 4 X 6
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F
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2
X 3 X 4
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- 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.
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