Mathematics/Physics
Liquid
Volume
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Robert Foote |
Disney Magnet
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4140 N.
Marine Drive |
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CHICAGO IL 60613 |
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(773) 534-5844 |
Objective(s):
Students
will learn and use formulas for the volume of a rectangular prism and
volume of
a cylinder.
Students
will see the relationship between cubic centimeters and milliliters.
Students
will compute formulas with and without calculators.
This
lesson is designed for a junior high classroom.
Materials:
Depending
on how many students you will use for this project, the amount of
materials
vary. If you break students up into
small groups, you should use one of each of these materials in each
group.
1.
Plastic graduated cylinder measuring milliliters
2. Different size
cylindrical containers such as coffee cans, Pringles potato chip cans,
cookie
tins, and the like. (Make sure these are made of a durable material
that can
hold water without falling apart. Cardboard is not good.)
3. Different size
rectangular prism containers such as plastic storage containers, tins,
and the
like. Make sure the base is either square or rectangular.
4.
Water
5.
Food dye (Optional)
6.
Rulers or tape measures
7.
Calculators (optional)
Strategy:
At
the beginning of the class, go over the formulas for finding the volume
of a
rectangular prism; that is base times height or length times width
times
height. Explain that the basic formula (base times height) also applies
to the
volume of a cylinder, except that the base is now a circle so the
formula for
the base is Pi multiplied by radius squared. Then multiply the base
times the
height. Once students are comfortable using these formulas, take one of
the
smaller rectangular containers and have students measure the length,
width and
height in centimeters of the container using tape measures. (DO NOT TELL THEM HOW TO MEASURE. This will lead to interesting
discussion.)
Once they have measured the sides, compute the volume. Your answer will
be in
cubic centimeters. This is the same as milliliters since there are 1000
cubic
centimeters in a liter and 1000 milliliters in a liter. Once the volume
is
computed, measure the water in milliliters to see how it compares to
the
computed volume. If all is done correctly, you should have a close
match. If
the water overflows or the container is not completely full, a mistake
was
made. Elicit a discussion with your students to see why this happened.
After
showing how to do one to the class as a whole, then break up the class
into
groups and have them do two containers per group (One cylinder and one
rectangular prism). After they have measured and calculated as a group
the
volume of their containers, let them check the volume with water.
Observe as
they measure and pour to determine accuracy of calculations and
measurement. First calculate using the
formula, then
check using water. At the end of the class, discuss each of your
findings and
any problems you may have had. To more clearly see and measure the
water used
in this lesson, you may elect to use drops of food dye in the water.
Performance
Assessment:
As
a performance assessment for this lesson, give a child a container of
each type
to calculate the volume. Then have the child measure and pour the water
into
the containers to check his or her work. This lesson in itself is a
performance
assessment.
Conclusions:
Students
should conclude in the end of this lesson that the formula for volume
in cubic
centimeters comes very close to the actual volume of the container in
milliliters. They should also be able to detect what went wrong if a
mistake
occurs.
References:
The
Only Math Book You’ll Ever Need by Stanley
Kogelman, Ph. D. and Barbara R. Heller, M. A., 1993, revised edition,
page 143.