Partnerships Implementing Engineering Education
Worcester Polytechnic Institute – Worcester Public Schools
Supported by: National Science Foundation
Measurements 6.F.4
Mass/Volume=Density
Grade Level
Sessions
Seasonality
Instructional Mode(s)
Team Size
WPS Benchmarks
MA Frameworks
Key Words
6
1 – approximately 90 minutes (could be split up)
N/A
Groups
4-5 students
06.SC.PS.02
06.SC.PS.06
6-8.PS.3.2
6-8.PS.3.3
Mass, Volume, Matter, Meniscus, International System of Units
Summary
Students will learn what mass is, and how to find it for a solid object. They will also
learn the technique of finding volume by the method of water displacement. They will
use these two values to calculate the density of a given solid object.
Learning Objectives
2002 Worcester Public Schools (WPS) Benchmarks for Grade 6
06.SC.PS.02 – Explain how to determine the weight of a dense object in air and in
water.
06.SC.PS.06 – Calculate the volumes of regular objects from linear measurements.
Measure the volumes of the same objects by displacement of water. Use the metric
system. Discuss the accuracy limits of the procedures and how they explain any
differences between the calculated volumes and the measured volumes.
Additional Learning Objectives
6-8.PS.3.2 Differentiate between volume and mass. Define density.
6-8.PS.3.3 Recognize that the measurement of volume and mass requires
understanding of sensitivity of measurement tools (e.g., rulers, graduated cylinders,
balances) and knowledge and appropriate use of significant digits.
1
Partnerships Implementing Engineering Education
Worcester Polytechnic Institute – Worcester Public Schools
Supported by: National Science Foundation
1. Understand why properties of materials are important, and how they are used to
decide what material should be used to create something.
Required Background Knowledge
See What you need to know about Density worksheet.
Essential Questions
1. What is volume?
2. What does density tell us about an object?
3. Why would you need to know the density of an object?
Introduction / Motivation
Begin by introducing the concepts of mass and volume. Follow the overhead What you
need to know about Density with the students to review the main ideas of what
density is. Make sure they understand that density is a property of a material.
Procedure
1. Have the students get into groups of 3-4.
2. The irregular objects used in this lesson could be different types of rocks,
whether found outside, collected from a beach trip, or purchased rocks such as
hematite, tiger eye, etc. Geometric, regular shaped objects could be used, and
calculations for volume according to shape could be used and compared to those
calculations made by water displacement. Students would need a ruler in order
to record dimensions of regular shaped objects and calculate by using a given
equation.
3. Explain to them that they will be finding the mass and volume of an object today
in order to calculate its density. Follow the What you need to know about
DENSITY worksheet on what mass and density are to make sure they
understand what the lesson will be focusing on.
2
Partnerships Implementing Engineering Education
Worcester Polytechnic Institute – Worcester Public Schools
Supported by: National Science Foundation
4. The students will be finding the mass of their object first using whatever scale, or
balance is available. Have them record this measurement on the Understanding
Density worksheet.
5. Explain to the students they should always mass the object(s) before determining
volume with the water displacement method. By massing the object(s) after
placing them in water, you allow the chance for water to remain on the object(s)
after being removed from the graduated cylinder. This could result in the water
being massed and, in turn, lead to a source of error.
6. Have the students then find the volume of their object following the procedure on
the Finding Volume by Water Displacement worksheet.
7. Have the students calculate the density of the object on the Understanding
Density worksheet.
Materials List
Materials per class
Amount
Location
Copies of each of the (3) worksheets
1 per student
School
Objects as samples to test
1 per group
Classroom
Pencil and paper
1/student
Classroom
Vocabulary with Definitions (in alphabetical order)
1.
International System of Units (SI) – the new metric system that we use today
Density in terms of the SI base units is expressed in terms of kilograms per
cubic meter (kg/m³).
2.
Mass- the property of a body that causes it to have weight in a gravitational
field
3.
Matter- that which has mass and occupies space; "an atom is the smallest
indivisible unit of matter"
4.
Volume- the amount of 3-dimensional space occupied by an object; "the gas
expanded to twice its original volume"
3
Partnerships Implementing Engineering Education
Worcester Polytechnic Institute – Worcester Public Schools
Supported by: National Science Foundation
Assessment / Evaluation of Students
For homework or as a second session have the students complete the “Understanding
Density” worksheet.
Lesson Extensions
None
Attachments
_____
1. What you need to know about DENSITY
2. Understanding Density
3. Finding Volume by Water Displacement
Troubleshooting Tips
None
Safety Issues
None
Additional Resources
None
Key Words
Mass, Volume, Matter, Meniscus, International System of Units
4
What you need to know about DENSITY
The box that has more balls has more mass per unit of volume. This property of matter is called
density. The higher an object's density, the higher its mass per volume. The density of a material
helps to distinguish it from other materials. Since mass is usually expressed in grams and volume
in cubic centimeters, density is expressed in grams/cubic centimeter.
Density is affected by the melting and cooling processes:
Loose granular sugar, like sand, contains a lot of air and is not tightly packed, but when it has
melted and starts to boil, the sugar loses its granularity and entrained air and becomes a fluid.
When you mold it to make a smaller, compacted shape, the syrup tightens up and loses more air.
As it cools, it contracts and gains moisture, making the already heavy candy even more dense
ρ is the object's density (measured in kilograms per cubic meters)
m is the object's total mass (measured in kilograms)
V is the object's total volume (measured in cubic meters)
International System of Units (SI) – the new metric system that we use today
Density in terms of the SI base units is expressed in terms of kilograms per cubic meter
(kg/m³).
Mass- the property of a body that causes it to have weight in a gravitational field
Matter- that which has mass and occupies space; "an atom is the smallest indivisible unit of
matter"
Volume- the amount of 3-dimensional space occupied by an object; "the gas expanded to twice
its original volume"— The volume of irregular objects (those that are not a geometrical shape
such as a sphere or cube) is found by water displacement.
Information courtesy of:
http://en.wikipedia.org/wiki/Density
http://www.nyu.edu/pages/mathmol/textbook/density.html
http://www.wordreference.com/definition/matter
Understanding Density
Name _______________________________ Date____________________
(a) Mass of object: __________________ (units!)
(b) Volume of object: ________________ (units!)
Mass/Volume= Density
(a)/(b) = Density of your object: ______________________ (units, think!)
What does density tell you about an object?
Does your object have a greater or lesser density than water?
Brainstorm: Think of three reasons you would need to know the density of an object. (Ex. You
need to know the density of the material to make an airplane to make sure the engines are
powerful enough to make it fly.)
1)
2)
3)
Finding the Volume by Water Displacement
Name _________________________________ Date____________________________
The curved surface of the liquid is called a meniscus. As a standard procedure, always read the
level of the liquid at the bottom of the curve. Therefore the reading above shows approximately
6.7mL of water.
1) Find a graduated cylinder that will be large enough to fit the object(s) being measured.
2) Fill this graduated cylinder enough so that when placed in the graduated cylinder, the object(s)
in question will be fully submerged in the water. Also be careful not to put in so much water that
the water level will rise past the graduated cylinder’s markings when the object(s) are placed in
the graduated cylinder. You must use your own judgment to determine what amount of water
meets these requirements. * Note that if the object(s) are not fully submerged in the water, the
recorded volume of the object(s) is invalid.*
3) After filling the graduated cylinder to a satisfactory level, record the volume of the water as
(a) in your data. Make sure to read the meniscus when determining volume. *Also, if placing the
object(s) in the graduated cylinder causes the water level rises past the graduated cylinder’s
markings, an accurate reading cannot be made.*
(a) Volume before object: ______________________ (be sure to include units)
4) After the water’s volume has been recorded, carefully place the object(s) in the graduated
cylinder and record this volume as (b) in your data (use meniscus). * The object(s) being
measured should not be dropped into the graduated cylinder. This could result in water splashing
onto the sides if the graduated cylinder. This water’s volume would go unrecorded and alter the
recorded volume of the object(s) in question resulting in a source of error.*
(b) Volume after object: _______________________ (units!)
5) In order to calculate the volume of the irregularly shaped object(s), subtract the volume of the
water alone from the volume of the water and object(s) [(b) – (a)].
Volume of object (b)-(a): ________________________ (units!)
Sources: http://www.newton.dep.anl.gov/askasci/eng99/eng99421.htm
http://www.aestheticrealism.net/Education-Solution-HS-B.htm
http://www.fordhamprep.org/gcurran/sho/sho/skills/h2odisskill.htm
http://www.lincoln.smmusd.org/staff/burdettet_web/meniscus.html